%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRA168-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 06:34:21 PM UTC 2026
% Result : Unsatisfiable 2.74s 2.93s
% Output : Proof 5.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : GRA168-1 : TPTP v9.3.0. Released v9.3.0.
% 0.13/0.13 % Command : run_E %s %d THM
% 0.18/0.34 % Computer : n001.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue May 5 00:49:50 EDT 2026
% 0.18/0.34 % CPUTime :
% 2.74/2.93 % SZS status Unsatisfiable
% 2.74/2.93 % SZS output start Proof
% 2.74/2.93 tff(b_type, type, (
% 2.74/2.93 b: ( $i * $i ) > $o)).
% 2.74/2.93 tff(s_type, type, (
% 2.74/2.93 s: $i > $i)).
% 2.74/2.93 tff(z_type, type, (
% 2.74/2.93 z: $i)).
% 2.74/2.93 tff(elem_1_type, type, (
% 2.74/2.93 elem_1: $i)).
% 2.74/2.93 tff(inj_0_type, type, (
% 2.74/2.93 inj_0: $i > $i)).
% 2.74/2.93 tff(r_type, type, (
% 2.74/2.93 r: ( $i * $i ) > $o)).
% 2.74/2.93 tff(1,assumption,(~b(z, s(s(s(s(z)))))), introduced(assumption)).
% 2.74/2.93 tff(2,plain,
% 2.74/2.93 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(3,plain,
% 2.74/2.93 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(4,plain,
% 2.74/2.93 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(5,axiom,(![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sinj')).
% 2.74/2.93 tff(6,plain,
% 2.74/2.93 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[5, 4])).
% 2.74/2.93 tff(7,plain,(
% 2.74/2.93 ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 2.74/2.93 inference(skolemize,[status(sab)],[6])).
% 2.74/2.93 tff(8,plain,
% 2.74/2.93 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[7, 3])).
% 2.74/2.93 tff(9,plain,
% 2.74/2.93 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[8, 2])).
% 2.74/2.93 tff(10,plain,
% 2.74/2.93 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(z))))) = s(s(s(z))))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(11,plain,
% 2.74/2.93 (inj_0(s(s(s(s(z))))) = s(s(s(z)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[10, 9])).
% 2.74/2.93 tff(12,assumption,(~(s(s(z)) = elem!1)), introduced(assumption)).
% 2.74/2.93 tff(13,assumption,(z = elem!1), introduced(assumption)).
% 2.74/2.93 tff(14,plain,
% 2.74/2.93 (s(z) = s(elem!1)),
% 2.74/2.93 inference(monotonicity,[status(thm)],[13])).
% 2.74/2.93 tff(15,plain,
% 2.74/2.93 (s(s(z)) = s(s(elem!1))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[14])).
% 2.74/2.93 tff(16,plain,
% 2.74/2.93 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[15])).
% 2.74/2.93 tff(17,plain,
% 2.74/2.93 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16])).
% 2.74/2.93 tff(18,plain,
% 2.74/2.93 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[17, 15])).
% 2.74/2.93 tff(19,plain,
% 2.74/2.93 ((z = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = z)),
% 2.74/2.93 inference(commutativity,[status(thm)],[])).
% 2.74/2.93 tff(20,plain,
% 2.74/2.93 ((s(s(s(s(z)))) = z) <=> (z = s(s(s(s(z)))))),
% 2.74/2.93 inference(symmetry,[status(thm)],[19])).
% 2.74/2.93 tff(21,plain,
% 2.74/2.93 ((~(s(s(s(s(z)))) = z)) <=> (~(z = s(s(s(s(z))))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[20])).
% 2.74/2.93 tff(22,plain,
% 2.74/2.93 (^[X: $i] : refl((~(s(X) = z)) <=> (~(s(X) = z)))),
% 2.74/2.93 inference(bind,[status(th)],[])).
% 2.74/2.93 tff(23,plain,
% 2.74/2.93 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 2.74/2.93 inference(quant_intro,[status(thm)],[22])).
% 2.74/2.93 tff(24,plain,
% 2.74/2.93 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(25,axiom,(![X: $i] : (~(s(X) = z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','snz')).
% 2.74/2.93 tff(26,plain,
% 2.74/2.93 (![X: $i] : (~(s(X) = z))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[25, 24])).
% 2.74/2.93 tff(27,plain,(
% 2.74/2.93 ![X: $i] : (~(s(X) = z))),
% 2.74/2.93 inference(skolemize,[status(sab)],[26])).
% 2.74/2.93 tff(28,plain,
% 2.74/2.93 (![X: $i] : (~(s(X) = z))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[27, 23])).
% 2.74/2.93 tff(29,plain,
% 2.74/2.93 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(z)))) = z))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(30,plain,
% 2.74/2.93 (~(s(s(s(s(z)))) = z)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[29, 28])).
% 2.74/2.93 tff(31,plain,
% 2.74/2.93 (~(z = s(s(s(s(z)))))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[30, 21])).
% 2.74/2.93 tff(32,plain,
% 2.74/2.93 (^[Y: $i, X: $i] : refl(((X = Y) | b(X, Y) | r(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 2.74/2.93 inference(bind,[status(th)],[])).
% 2.74/2.93 tff(33,plain,
% 2.74/2.93 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 2.74/2.93 inference(quant_intro,[status(thm)],[32])).
% 2.74/2.93 tff(34,plain,
% 2.74/2.93 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(35,plain,
% 2.74/2.93 (^[Y: $i, X: $i] : rewrite((((X = Y) | r(X, Y)) | b(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 2.74/2.93 inference(bind,[status(th)],[])).
% 2.74/2.93 tff(36,plain,
% 2.74/2.93 (![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 2.74/2.93 inference(quant_intro,[status(thm)],[35])).
% 2.74/2.93 tff(37,axiom,(![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rb')).
% 2.74/2.93 tff(38,plain,
% 2.74/2.93 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[37, 36])).
% 2.74/2.93 tff(39,plain,
% 2.74/2.93 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[38, 34])).
% 2.74/2.93 tff(40,plain,(
% 2.74/2.93 ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 2.74/2.93 inference(skolemize,[status(sab)],[39])).
% 2.74/2.93 tff(41,plain,
% 2.74/2.93 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[40, 33])).
% 2.74/2.93 tff(42,plain,
% 2.74/2.93 (((~![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))))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(43,plain,
% 2.74/2.93 ((~![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))))))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(44,plain,
% 2.74/2.93 ((~![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)))))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[43, 42])).
% 2.74/2.93 tff(45,plain,
% 2.74/2.93 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[44, 41])).
% 2.74/2.93 tff(46,plain,
% 2.74/2.93 (b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[45, 31])).
% 2.74/2.93 tff(47,plain,
% 2.74/2.93 (r(z, s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[46, 1])).
% 2.74/2.93 tff(48,assumption,(~r(z, s(s(z)))), introduced(assumption)).
% 2.74/2.93 tff(49,assumption,(~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))), introduced(assumption)).
% 2.74/2.93 tff(50,plain,
% 2.74/2.93 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(z)) = z)),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(51,plain,
% 2.74/2.93 (inj_0(s(z)) = z),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[50, 9])).
% 2.74/2.93 tff(52,plain,
% 2.74/2.93 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(53,plain,
% 2.74/2.93 (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[52, 9])).
% 2.74/2.93 tff(54,plain,
% 2.74/2.93 ((~![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))))))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(55,plain,
% 2.74/2.93 (inj_0(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[54, 9])).
% 2.74/2.93 tff(56,plain,
% 2.74/2.93 ((~![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)))))))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(57,plain,
% 2.74/2.93 (inj_0(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(s(z))))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[56, 9])).
% 2.74/2.93 tff(58,assumption,(s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))), introduced(assumption)).
% 2.74/2.93 tff(59,plain,
% 2.74/2.93 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(s(s(z)))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[58])).
% 2.74/2.93 tff(60,plain,
% 2.74/2.93 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 2.74/2.93 inference(symmetry,[status(thm)],[59])).
% 2.74/2.93 tff(61,plain,
% 2.74/2.93 (s(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 2.74/2.93 inference(symmetry,[status(thm)],[11])).
% 2.74/2.93 tff(62,plain,
% 2.74/2.93 (s(s(s(z))) = s(s(s(s(s(s(z))))))),
% 2.74/2.93 inference(transitivity,[status(thm)],[61, 60, 57])).
% 2.74/2.93 tff(63,plain,
% 2.74/2.93 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(s(z)))))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[62])).
% 2.74/2.93 tff(64,plain,
% 2.74/2.93 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(z)))) = s(s(z)))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(65,plain,
% 2.74/2.93 (inj_0(s(s(s(z)))) = s(s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[64, 9])).
% 2.74/2.93 tff(66,plain,
% 2.74/2.93 (s(s(z)) = inj_0(s(s(s(z))))),
% 2.74/2.93 inference(symmetry,[status(thm)],[65])).
% 2.74/2.93 tff(67,plain,
% 2.74/2.93 (s(s(z)) = s(s(s(s(s(z)))))),
% 2.74/2.93 inference(transitivity,[status(thm)],[66, 63, 55])).
% 2.74/2.93 tff(68,plain,
% 2.74/2.93 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(z))))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[67])).
% 2.74/2.93 tff(69,plain,
% 2.74/2.93 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(z))) = s(z))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(70,plain,
% 2.74/2.93 (inj_0(s(s(z))) = s(z)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[69, 9])).
% 2.74/2.93 tff(71,plain,
% 2.74/2.93 (s(z) = inj_0(s(s(z)))),
% 2.74/2.93 inference(symmetry,[status(thm)],[70])).
% 2.74/2.93 tff(72,plain,
% 2.74/2.93 (s(z) = s(s(s(s(z))))),
% 2.74/2.93 inference(transitivity,[status(thm)],[71, 68, 53])).
% 2.74/2.93 tff(73,plain,
% 2.74/2.93 (inj_0(s(z)) = inj_0(s(s(s(s(z)))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[72])).
% 2.74/2.93 tff(74,plain,
% 2.74/2.93 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 2.74/2.93 inference(symmetry,[status(thm)],[73])).
% 2.74/2.93 tff(75,plain,
% 2.74/2.93 (s(s(s(z))) = z),
% 2.74/2.93 inference(transitivity,[status(thm)],[61, 74, 51])).
% 2.74/2.93 tff(76,plain,
% 2.74/2.93 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(z))) = z))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(77,plain,
% 2.74/2.93 (~(s(s(s(z))) = z)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[76, 28])).
% 2.74/2.93 tff(78,plain,
% 2.74/2.93 ($false),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[77, 75])).
% 2.74/2.93 tff(79,plain,(~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.93 tff(80,plain,
% 2.74/2.93 (((~![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))))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(81,plain,
% 2.74/2.93 ((~![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))))))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(82,plain,
% 2.74/2.93 ((~![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)))))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[81, 80])).
% 2.74/2.93 tff(83,plain,
% 2.74/2.93 ((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)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[82, 41])).
% 2.74/2.93 tff(84,plain,
% 2.74/2.93 (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)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[83, 79])).
% 2.74/2.93 tff(85,plain,
% 2.74/2.93 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[84, 49])).
% 2.74/2.93 tff(86,assumption,(~b(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 2.74/2.93 tff(87,assumption,(s(s(s(s(z)))) = s(s(z))), introduced(assumption)).
% 2.74/2.93 tff(88,plain,
% 2.74/2.93 (inj_0(s(s(s(s(z))))) = inj_0(s(s(z)))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[87])).
% 2.74/2.93 tff(89,plain,
% 2.74/2.93 (inj_0(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 2.74/2.93 inference(symmetry,[status(thm)],[88])).
% 2.74/2.93 tff(90,plain,
% 2.74/2.93 (s(z) = s(s(s(z)))),
% 2.74/2.93 inference(transitivity,[status(thm)],[71, 89, 11])).
% 2.74/2.93 tff(91,plain,
% 2.74/2.93 (inj_0(s(z)) = inj_0(s(s(s(z))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[90])).
% 2.74/2.93 tff(92,plain,
% 2.74/2.93 (inj_0(s(s(s(z)))) = inj_0(s(z))),
% 2.74/2.93 inference(symmetry,[status(thm)],[91])).
% 2.74/2.93 tff(93,plain,
% 2.74/2.93 (s(s(z)) = z),
% 2.74/2.93 inference(transitivity,[status(thm)],[66, 92, 51])).
% 2.74/2.93 tff(94,plain,
% 2.74/2.93 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(z)) = z))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(95,plain,
% 2.74/2.93 (~(s(s(z)) = z)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[94, 28])).
% 2.74/2.93 tff(96,plain,
% 2.74/2.93 ($false),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[95, 93])).
% 2.74/2.93 tff(97,plain,(~(s(s(s(s(z)))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.93 tff(98,plain,
% 2.74/2.93 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(99,plain,
% 2.74/2.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(100,plain,
% 2.74/2.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z)))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[99, 98])).
% 2.74/2.93 tff(101,plain,
% 2.74/2.93 ((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)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[100, 41])).
% 2.74/2.93 tff(102,plain,
% 2.74/2.93 (b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[101, 97])).
% 2.74/2.93 tff(103,plain,
% 2.74/2.93 (r(s(s(s(s(z)))), s(s(z)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[102, 86])).
% 2.74/2.93 tff(104,assumption,(b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))), introduced(assumption)).
% 2.74/2.93 tff(105,assumption,(~b(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 2.74/2.93 tff(106,assumption,(r(s(s(z)), z)), introduced(assumption)).
% 2.74/2.93 tff(107,assumption,(r(s(s(s(s(s(s(s(z))))))), s(s(z)))), introduced(assumption)).
% 2.74/2.93 tff(108,assumption,(r(s(s(s(s(s(s(s(z))))))), z)), introduced(assumption)).
% 2.74/2.93 tff(109,plain,
% 2.74/2.93 (^[X0: $i, X2: $i, X1: $i] : refl(((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))))),
% 2.74/2.93 inference(bind,[status(th)],[])).
% 2.74/2.93 tff(110,plain,
% 2.74/2.93 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 2.74/2.93 inference(quant_intro,[status(thm)],[109])).
% 2.74/2.93 tff(111,plain,
% 2.74/2.93 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(112,plain,
% 2.74/2.93 (^[X0: $i, X2: $i, X1: $i] : rewrite((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) <=> ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))))),
% 2.74/2.93 inference(bind,[status(th)],[])).
% 2.74/2.93 tff(113,plain,
% 2.74/2.93 (![X0: $i, X2: $i, X1: $i] : (((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) <=> ![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 2.74/2.93 inference(quant_intro,[status(thm)],[112])).
% 2.74/2.93 tff(114,axiom,(![X0: $i, X2: $i, X1: $i] : (((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axr')).
% 2.74/2.93 tff(115,plain,
% 2.74/2.93 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[114, 113])).
% 2.74/2.93 tff(116,plain,
% 2.74/2.93 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[115, 111])).
% 2.74/2.93 tff(117,plain,(
% 2.74/2.93 ![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 2.74/2.93 inference(skolemize,[status(sab)],[116])).
% 2.74/2.93 tff(118,plain,
% 2.74/2.93 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[117, 110])).
% 2.74/2.93 tff(119,plain,
% 2.74/2.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(120,plain,
% 2.74/2.93 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(121,plain,
% 2.74/2.93 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[120, 119])).
% 2.74/2.93 tff(122,plain,
% 2.74/2.93 ($false),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[121, 118, 106, 108, 107])).
% 2.74/2.93 tff(123,plain,((~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))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.93 tff(124,plain,
% 2.74/2.93 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[123, 107, 106])).
% 2.74/2.93 tff(125,assumption,(~b(s(s(s(s(s(s(s(z))))))), z)), introduced(assumption)).
% 2.74/2.93 tff(126,assumption,(~r(s(s(s(s(s(s(s(z))))))), z)), introduced(assumption)).
% 2.74/2.93 tff(127,plain,
% 2.74/2.93 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(s(z))))))) = z))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(128,plain,
% 2.74/2.93 (~(s(s(s(s(s(s(s(z))))))) = z)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[127, 28])).
% 2.74/2.93 tff(129,plain,
% 2.74/2.93 (((~![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))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(130,plain,
% 2.74/2.93 ((~![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))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(131,plain,
% 2.74/2.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = z) | b(s(s(s(s(s(s(s(z))))))), z) | r(s(s(s(s(s(s(s(z))))))), z)),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[130, 129])).
% 2.74/2.93 tff(132,plain,
% 2.74/2.93 ($false),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[131, 41, 128, 126, 125])).
% 2.74/2.93 tff(133,plain,(b(s(s(s(s(s(s(s(z))))))), z) | r(s(s(s(s(s(s(s(z))))))), z)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.93 tff(134,plain,
% 2.74/2.93 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[133, 124])).
% 2.74/2.93 tff(135,plain,
% 2.74/2.93 ((z = s(s(z))) <=> (s(s(z)) = z)),
% 2.74/2.93 inference(commutativity,[status(thm)],[])).
% 2.74/2.93 tff(136,plain,
% 2.74/2.93 ((s(s(z)) = z) <=> (z = s(s(z)))),
% 2.74/2.93 inference(symmetry,[status(thm)],[135])).
% 2.74/2.93 tff(137,plain,
% 2.74/2.93 ((~(s(s(z)) = z)) <=> (~(z = s(s(z))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[136])).
% 2.74/2.93 tff(138,plain,
% 2.74/2.93 (~(z = s(s(z)))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[95, 137])).
% 2.74/2.93 tff(139,plain,
% 2.74/2.93 (((~![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))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(140,plain,
% 2.74/2.93 ((~![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))))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(141,plain,
% 2.74/2.93 ((~![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)))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[140, 139])).
% 2.74/2.93 tff(142,plain,
% 2.74/2.93 ((z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[141, 41])).
% 2.74/2.93 tff(143,plain,
% 2.74/2.93 (b(z, s(s(z))) | r(z, s(s(z)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[142, 138])).
% 2.74/2.93 tff(144,plain,
% 2.74/2.93 (b(z, s(s(z)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[143, 48])).
% 2.74/2.93 tff(145,assumption,(r(z, s(s(s(s(z)))))), introduced(assumption)).
% 2.74/2.93 tff(146,assumption,(b(s(s(s(s(s(s(s(z))))))), z)), introduced(assumption)).
% 2.74/2.93 tff(147,assumption,(r(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 2.74/2.93 tff(148,plain,
% 2.74/2.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(149,plain,
% 2.74/2.93 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(150,plain,
% 2.74/2.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[149])).
% 2.74/2.93 tff(151,plain,
% 2.74/2.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.74/2.93 inference(transitivity,[status(thm)],[150, 148])).
% 2.74/2.93 tff(152,plain,
% 2.74/2.93 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(153,plain,
% 2.74/2.93 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[152, 151])).
% 2.74/2.93 tff(154,plain,
% 2.74/2.93 ($false),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[153, 118, 106, 145, 147])).
% 2.74/2.93 tff(155,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.93 tff(156,plain,
% 2.74/2.93 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[155, 106, 145])).
% 2.74/2.93 tff(157,plain,
% 2.74/2.93 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 2.74/2.93 inference(commutativity,[status(thm)],[])).
% 2.74/2.93 tff(158,plain,
% 2.74/2.93 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(z))))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[157])).
% 2.74/2.93 tff(159,plain,
% 2.74/2.93 (~(s(s(z)) = s(s(s(s(z)))))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[97, 158])).
% 2.74/2.93 tff(160,plain,
% 2.74/2.93 (((~![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))))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(161,plain,
% 2.74/2.93 ((~![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))))))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(162,plain,
% 2.74/2.93 ((~![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)))))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[161, 160])).
% 2.74/2.93 tff(163,plain,
% 2.74/2.93 ((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)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[162, 41])).
% 2.74/2.93 tff(164,plain,
% 2.74/2.93 (b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[163, 159])).
% 2.74/2.93 tff(165,plain,
% 2.74/2.93 (b(s(s(z)), s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[164, 156])).
% 2.74/2.93 tff(166,assumption,(b(s(s(z)), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.74/2.93 tff(167,assumption,(b(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 2.74/2.93 tff(168,assumption,(b(s(s(s(s(z)))), z)), introduced(assumption)).
% 2.74/2.93 tff(169,plain,
% 2.74/2.93 (^[X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) <=> ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))))),
% 2.74/2.93 inference(bind,[status(th)],[])).
% 2.74/2.93 tff(170,plain,
% 2.74/2.93 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 2.74/2.93 inference(quant_intro,[status(thm)],[169])).
% 2.74/2.93 tff(171,plain,
% 2.74/2.93 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(172,plain,
% 2.74/2.93 (^[X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~b(X0, X1)) | (~b(X1, X2))) <=> ((~b(X1, X2)) | (~b(X0, X1)))), ((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) <=> (((~b(X1, X2)) | (~b(X0, X1))) | (~b(X0, X3))))), rewrite((((~b(X1, X2)) | (~b(X0, X1))) | (~b(X0, X3))) <=> ((~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))), ((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) <=> ((~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))))), (((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) <=> (((~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X1, X3))))), rewrite((((~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X1, X3))) <=> ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))), (((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) <=> ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))))), ((((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) | (~b(X1, X4))) <=> (((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X1, X4))))), rewrite((((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X1, X4))) <=> ((~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))), ((((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) | (~b(X1, X4))) <=> ((~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))))), (((((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) | (~b(X1, X4))) | (~b(X2, X4))) <=> (((~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X2, X4))))), rewrite((((~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X2, X4))) <=> ((~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))), (((((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) | (~b(X1, X4))) | (~b(X2, X4))) <=> ((~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))))), ((((((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) | (~b(X1, X4))) | (~b(X2, X4))) | (~b(X3, X4))) <=> (((~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X3, X4))))), rewrite((((~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X3, X4))) <=> ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))), ((((((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) | (~b(X1, X4))) | (~b(X2, X4))) | (~b(X3, X4))) <=> ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))))),
% 2.74/2.93 inference(bind,[status(th)],[])).
% 2.74/2.93 tff(173,plain,
% 2.74/2.93 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : (((((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) | (~b(X1, X4))) | (~b(X2, X4))) | (~b(X3, X4))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 2.74/2.93 inference(quant_intro,[status(thm)],[172])).
% 2.74/2.93 tff(174,axiom,(![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : (((((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) | (~b(X1, X4))) | (~b(X2, X4))) | (~b(X3, X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axb')).
% 2.74/2.93 tff(175,plain,
% 2.74/2.93 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[174, 173])).
% 2.74/2.93 tff(176,plain,
% 2.74/2.93 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[175, 171])).
% 2.74/2.93 tff(177,plain,(
% 2.74/2.94 ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 2.74/2.94 inference(skolemize,[status(sab)],[176])).
% 2.74/2.94 tff(178,plain,
% 2.74/2.94 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[177, 170])).
% 2.74/2.94 tff(179,plain,
% 2.74/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(180,plain,
% 2.74/2.94 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(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(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(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(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(181,plain,
% 2.74/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(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(s(z))))))), s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[180])).
% 2.74/2.94 tff(182,plain,
% 2.74/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(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(s(z))))))), s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.74/2.94 inference(transitivity,[status(thm)],[181, 179])).
% 2.74/2.94 tff(183,plain,
% 2.74/2.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(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(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.74/2.94 inference(quant_inst,[status(thm)],[])).
% 2.74/2.94 tff(184,plain,
% 2.74/2.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[183, 182])).
% 2.74/2.94 tff(185,plain,
% 2.74/2.94 ($false),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[184, 178, 104, 166, 168, 167, 146])).
% 2.74/2.94 tff(186,plain,((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.94 tff(187,plain,
% 2.74/2.94 (~b(s(s(s(s(z)))), z)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[186, 166, 104, 165, 146])).
% 2.74/2.94 tff(188,plain,
% 2.74/2.94 (((~![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))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(189,plain,
% 2.74/2.94 ((~![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))),
% 2.74/2.94 inference(quant_inst,[status(thm)],[])).
% 2.74/2.94 tff(190,plain,
% 2.74/2.94 ((~![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)),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[189, 188])).
% 2.74/2.94 tff(191,plain,
% 2.74/2.94 (b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[190, 41, 30])).
% 2.74/2.94 tff(192,plain,
% 2.74/2.94 (r(s(s(s(s(z)))), z)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[191, 187])).
% 2.74/2.94 tff(193,assumption,(r(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 2.74/2.94 tff(194,assumption,(r(s(s(s(s(z)))), z)), introduced(assumption)).
% 2.74/2.94 tff(195,plain,
% 2.74/2.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(196,plain,
% 2.74/2.94 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.74/2.94 inference(quant_inst,[status(thm)],[])).
% 2.74/2.94 tff(197,plain,
% 2.74/2.94 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[196, 195])).
% 2.74/2.94 tff(198,plain,
% 2.74/2.94 ($false),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[197, 118, 106, 194, 193])).
% 2.74/2.94 tff(199,plain,((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.94 tff(200,plain,
% 2.74/2.94 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[199, 192, 106])).
% 2.74/2.94 tff(201,plain,
% 2.74/2.94 (b(s(s(s(s(z)))), s(s(z)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[102, 200])).
% 2.74/2.94 tff(202,assumption,(b(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 2.74/2.94 tff(203,assumption,(r(z, s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.74/2.94 tff(204,assumption,(r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.74/2.94 tff(205,plain,
% 2.74/2.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(206,plain,
% 2.74/2.94 (((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(207,plain,
% 2.74/2.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[206])).
% 2.74/2.94 tff(208,plain,
% 2.74/2.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.74/2.94 inference(transitivity,[status(thm)],[207, 205])).
% 2.74/2.94 tff(209,plain,
% 2.74/2.94 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(z)))))))),
% 2.74/2.94 inference(quant_inst,[status(thm)],[])).
% 2.74/2.94 tff(210,plain,
% 2.74/2.94 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[209, 208])).
% 2.74/2.94 tff(211,plain,
% 2.74/2.94 ($false),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[210, 118, 145, 204, 203])).
% 2.74/2.94 tff(212,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.94 tff(213,plain,
% 2.74/2.94 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[212, 203, 145])).
% 2.74/2.94 tff(214,plain,
% 2.74/2.94 ((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)))))),
% 2.74/2.94 inference(commutativity,[status(thm)],[])).
% 2.74/2.94 tff(215,plain,
% 2.74/2.94 ((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))))))))),
% 2.74/2.94 inference(symmetry,[status(thm)],[214])).
% 2.74/2.94 tff(216,plain,
% 2.74/2.94 ((~(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)))))))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[215])).
% 2.74/2.94 tff(217,plain,
% 2.74/2.94 (~(s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[79, 216])).
% 2.74/2.94 tff(218,plain,
% 2.74/2.94 (((~![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)))))))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(219,plain,
% 2.74/2.94 ((~![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)))))))))),
% 2.74/2.94 inference(quant_inst,[status(thm)],[])).
% 2.74/2.94 tff(220,plain,
% 2.74/2.94 ((~![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))))))))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[219, 218])).
% 2.74/2.94 tff(221,plain,
% 2.74/2.94 ((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))))))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[220, 41])).
% 2.74/2.94 tff(222,plain,
% 2.74/2.94 (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))))))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[221, 217])).
% 2.74/2.94 tff(223,plain,
% 2.74/2.94 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[222, 213])).
% 2.74/2.94 tff(224,assumption,(r(s(s(z)), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.74/2.94 tff(225,plain,
% 2.74/2.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(226,plain,
% 2.74/2.94 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(227,plain,
% 2.74/2.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[226])).
% 2.74/2.94 tff(228,plain,
% 2.74/2.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.74/2.94 inference(transitivity,[status(thm)],[227, 225])).
% 2.74/2.94 tff(229,plain,
% 2.74/2.94 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))),
% 2.74/2.94 inference(quant_inst,[status(thm)],[])).
% 2.74/2.94 tff(230,plain,
% 2.74/2.94 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[229, 228])).
% 2.74/2.94 tff(231,plain,
% 2.74/2.94 ($false),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[230, 118, 106, 224, 203])).
% 2.74/2.94 tff(232,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.94 tff(233,plain,
% 2.74/2.94 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[232, 203, 106])).
% 2.74/2.94 tff(234,assumption,(s(s(z)) = s(s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 2.74/2.94 tff(235,plain,
% 2.74/2.94 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[234])).
% 2.74/2.94 tff(236,plain,
% 2.74/2.94 (s(z) = s(s(s(s(s(s(z))))))),
% 2.74/2.94 inference(transitivity,[status(thm)],[71, 235, 57])).
% 2.74/2.94 tff(237,plain,
% 2.74/2.94 (inj_0(s(z)) = inj_0(s(s(s(s(s(s(z)))))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[236])).
% 2.74/2.94 tff(238,plain,
% 2.74/2.94 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(z))),
% 2.74/2.94 inference(symmetry,[status(thm)],[237])).
% 2.74/2.94 tff(239,plain,
% 2.74/2.94 (s(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 2.74/2.94 inference(symmetry,[status(thm)],[55])).
% 2.74/2.94 tff(240,plain,
% 2.74/2.94 (s(s(s(s(s(z))))) = z),
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% 2.74/2.94 tff(241,plain,
% 2.74/2.94 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(z))))) = z))),
% 2.74/2.94 inference(quant_inst,[status(thm)],[])).
% 2.74/2.94 tff(242,plain,
% 2.74/2.94 (~(s(s(s(s(s(z))))) = z)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[241, 28])).
% 2.74/2.94 tff(243,plain,
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% 2.74/2.94 inference(unit_resolution,[status(thm)],[242, 240])).
% 2.74/2.94 tff(244,plain,(~(s(s(z)) = s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.94 tff(245,plain,
% 2.74/2.94 (((~![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)))))))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(246,plain,
% 2.74/2.94 ((~![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)))))))))),
% 2.74/2.94 inference(quant_inst,[status(thm)],[])).
% 2.74/2.94 tff(247,plain,
% 2.74/2.94 ((~![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))))))))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[246, 245])).
% 2.74/2.94 tff(248,plain,
% 2.74/2.94 ((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))))))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[247, 41])).
% 2.74/2.94 tff(249,plain,
% 2.74/2.94 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[248, 244])).
% 2.74/2.94 tff(250,plain,
% 2.74/2.94 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[249, 233])).
% 2.74/2.94 tff(251,assumption,(b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.74/2.94 tff(252,plain,
% 2.74/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(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))))))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(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))))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(253,plain,
% 2.74/2.94 (((~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(z)), s(s(s(s(z)))))) | (~b(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))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(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))))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(254,plain,
% 2.74/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(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(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(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))))))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[253])).
% 2.74/2.94 tff(255,plain,
% 2.74/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(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(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(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))))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.74/2.94 inference(transitivity,[status(thm)],[254, 252])).
% 2.74/2.94 tff(256,plain,
% 2.74/2.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(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(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.74/2.94 inference(quant_inst,[status(thm)],[])).
% 2.74/2.94 tff(257,plain,
% 2.74/2.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[256, 255])).
% 2.74/2.94 tff(258,plain,
% 2.74/2.94 ($false),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[257, 178, 104, 166, 167, 251, 202])).
% 2.74/2.94 tff(259,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(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(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.94 tff(260,plain,
% 2.74/2.94 ($false),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[259, 250, 223, 104, 202, 165])).
% 2.74/2.94 tff(261,plain,((~r(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(s(s(z)))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.94 tff(262,plain,
% 2.74/2.94 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[261, 201, 106, 104, 145])).
% 2.74/2.94 tff(263,plain,
% 2.74/2.94 ((z = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = z)),
% 2.74/2.94 inference(commutativity,[status(thm)],[])).
% 2.74/2.94 tff(264,plain,
% 2.74/2.94 ((s(s(s(s(s(s(s(z))))))) = z) <=> (z = s(s(s(s(s(s(s(z))))))))),
% 2.74/2.94 inference(symmetry,[status(thm)],[263])).
% 2.74/2.94 tff(265,plain,
% 2.74/2.94 ((~(s(s(s(s(s(s(s(z))))))) = z)) <=> (~(z = s(s(s(s(s(s(s(z)))))))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[264])).
% 2.74/2.94 tff(266,plain,
% 2.74/2.94 (~(z = s(s(s(s(s(s(s(z))))))))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[128, 265])).
% 2.74/2.94 tff(267,plain,
% 2.74/2.94 (((~![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)))))))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(268,plain,
% 2.74/2.94 ((~![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)))))))))),
% 2.74/2.94 inference(quant_inst,[status(thm)],[])).
% 2.74/2.94 tff(269,plain,
% 2.74/2.94 ((~![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))))))))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[268, 267])).
% 2.74/2.94 tff(270,plain,
% 2.74/2.94 ((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))))))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[269, 41])).
% 2.74/2.94 tff(271,plain,
% 2.74/2.94 (b(z, s(s(s(s(s(s(s(z)))))))) | r(z, s(s(s(s(s(s(s(z))))))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[270, 266])).
% 2.74/2.94 tff(272,plain,
% 2.74/2.94 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[271, 262])).
% 2.74/2.94 tff(273,assumption,(b(z, s(s(z)))), introduced(assumption)).
% 2.74/2.94 tff(274,plain,
% 2.74/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(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(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(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(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(275,plain,
% 2.74/2.94 (((~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(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(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(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(276,plain,
% 2.74/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(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(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(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(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[275])).
% 2.74/2.95 tff(277,plain,
% 2.74/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(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(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(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(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.74/2.95 inference(transitivity,[status(thm)],[276, 274])).
% 2.74/2.95 tff(278,plain,
% 2.74/2.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(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(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))))),
% 2.74/2.95 inference(quant_inst,[status(thm)],[])).
% 2.74/2.95 tff(279,plain,
% 2.74/2.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[278, 277])).
% 2.74/2.95 tff(280,plain,
% 2.74/2.95 ($false),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[279, 178, 273, 104, 166, 165, 272])).
% 2.74/2.95 tff(281,plain,((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.95 tff(282,plain,
% 2.74/2.95 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[281, 134, 104, 106, 47, 144])).
% 2.74/2.95 tff(283,plain,
% 2.74/2.95 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[249, 282])).
% 2.74/2.95 tff(284,plain,
% 2.74/2.95 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[232, 283, 106])).
% 2.74/2.95 tff(285,plain,
% 2.74/2.95 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[271, 284])).
% 2.74/2.95 tff(286,assumption,(~b(s(s(z)), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.74/2.95 tff(287,plain,
% 2.74/2.95 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[249, 286])).
% 2.74/2.95 tff(288,plain,
% 2.74/2.95 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[232, 287, 106])).
% 2.74/2.95 tff(289,plain,
% 2.74/2.95 (b(z, s(s(s(s(s(s(s(z))))))))),
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% 2.74/2.95 tff(290,assumption,(~(elem!1 = z)), introduced(assumption)).
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% 2.74/2.95 tff(299,plain,
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% 2.74/2.95 tff(318,plain,
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% 2.74/2.95 inference(unit_resolution,[status(thm)],[317, 290])).
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% 2.74/2.95 tff(326,plain,
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% 2.74/2.96 inference(unit_resolution,[status(thm)],[410, 41, 242, 407])).
% 2.74/2.96 tff(412,plain,
% 2.74/2.96 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(413,plain,
% 2.74/2.96 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.74/2.96 inference(quant_inst,[status(thm)],[])).
% 2.74/2.96 tff(414,plain,
% 2.74/2.96 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[413, 412])).
% 2.74/2.96 tff(415,plain,
% 2.74/2.96 ($false),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[414, 118, 106, 364, 411])).
% 2.74/2.96 tff(416,plain,((~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), z)) | (~(elem!1 = s(s(s(s(z)))))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.96 tff(417,plain,
% 2.74/2.96 (~r(s(elem!1), s(s(z)))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[416, 319, 106, 349, 107, 224])).
% 2.74/2.96 tff(418,plain,
% 2.74/2.96 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(419,plain,
% 2.74/2.96 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z))))),
% 2.74/2.96 inference(quant_inst,[status(thm)],[])).
% 2.74/2.96 tff(420,plain,
% 2.74/2.96 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z)))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[419, 418])).
% 2.74/2.96 tff(421,plain,
% 2.74/2.96 ((s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z)))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[420, 41])).
% 2.74/2.96 tff(422,plain,
% 2.74/2.96 (s(elem!1) = s(s(z))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[421, 417, 305])).
% 2.74/2.96 tff(423,plain,
% 2.74/2.96 (s(s(z)) = s(elem!1)),
% 2.74/2.96 inference(symmetry,[status(thm)],[422])).
% 2.74/2.96 tff(424,plain,
% 2.74/2.96 (s(s(z)) = s(s(s(s(s(z)))))),
% 2.74/2.96 inference(transitivity,[status(thm)],[423, 320])).
% 2.74/2.96 tff(425,plain,
% 2.74/2.96 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(z))))))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[424])).
% 2.74/2.96 tff(426,plain,
% 2.74/2.96 (s(z) = s(s(s(s(z))))),
% 2.74/2.96 inference(transitivity,[status(thm)],[71, 425, 53])).
% 2.74/2.96 tff(427,plain,
% 2.74/2.96 (inj_0(s(z)) = inj_0(s(s(s(s(z)))))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[426])).
% 2.74/2.96 tff(428,plain,
% 2.74/2.96 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 2.74/2.96 inference(symmetry,[status(thm)],[427])).
% 2.74/2.96 tff(429,plain,
% 2.74/2.96 (s(s(s(z))) = s(s(s(s(s(s(z))))))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[424])).
% 2.74/2.96 tff(430,plain,
% 2.74/2.96 (s(s(s(s(s(s(z)))))) = s(s(s(z)))),
% 2.74/2.96 inference(symmetry,[status(thm)],[429])).
% 2.74/2.96 tff(431,plain,
% 2.74/2.96 (s(s(s(s(s(s(z)))))) = z),
% 2.74/2.96 inference(transitivity,[status(thm)],[430, 61, 428, 51])).
% 2.74/2.96 tff(432,plain,
% 2.74/2.96 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(z)))))) = z))),
% 2.74/2.96 inference(quant_inst,[status(thm)],[])).
% 2.74/2.96 tff(433,plain,
% 2.74/2.96 (~(s(s(s(s(s(s(z)))))) = z)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[432, 28])).
% 2.74/2.96 tff(434,plain,
% 2.74/2.96 ($false),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[433, 431])).
% 2.74/2.96 tff(435,plain,((~(elem!1 = s(s(s(s(z)))))) | b(s(elem!1), s(s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.96 tff(436,plain,
% 2.74/2.96 (~(elem!1 = s(s(s(s(z)))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[435, 287, 106, 107, 305, 12])).
% 2.74/2.96 tff(437,assumption,(r(elem!1, z)), introduced(assumption)).
% 2.74/2.96 tff(438,assumption,(r(s(s(z)), elem!1)), introduced(assumption)).
% 2.74/2.96 tff(439,plain,
% 2.74/2.96 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(440,plain,
% 2.74/2.96 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))),
% 2.74/2.96 inference(quant_inst,[status(thm)],[])).
% 2.74/2.96 tff(441,plain,
% 2.74/2.96 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[440, 439])).
% 2.74/2.96 tff(442,plain,
% 2.74/2.96 ($false),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[441, 118, 437, 438, 106])).
% 2.74/2.96 tff(443,plain,((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.96 tff(444,plain,
% 2.74/2.96 (~r(s(s(z)), elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[443, 437, 106])).
% 2.74/2.96 tff(445,plain,
% 2.74/2.96 (((~![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))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(446,plain,
% 2.74/2.96 ((~![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))),
% 2.74/2.96 inference(quant_inst,[status(thm)],[])).
% 2.74/2.96 tff(447,plain,
% 2.74/2.96 ((~![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)),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[446, 445])).
% 2.74/2.96 tff(448,plain,
% 2.74/2.96 ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[447, 41])).
% 2.74/2.96 tff(449,plain,
% 2.74/2.96 (b(s(s(z)), elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[448, 444, 12])).
% 2.74/2.96 tff(450,assumption,(r(elem!1, s(s(z)))), introduced(assumption)).
% 2.74/2.96 tff(451,plain,
% 2.74/2.96 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), z)))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(452,plain,
% 2.74/2.96 (((~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(z))))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), z)))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(453,plain,
% 2.74/2.96 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), z))))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[452])).
% 2.74/2.96 tff(454,plain,
% 2.74/2.96 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), z)))),
% 2.74/2.96 inference(transitivity,[status(thm)],[453, 451])).
% 2.74/2.96 tff(455,plain,
% 2.74/2.96 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))))),
% 2.74/2.96 inference(quant_inst,[status(thm)],[])).
% 2.74/2.96 tff(456,plain,
% 2.74/2.96 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), z))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[455, 454])).
% 2.74/2.96 tff(457,plain,
% 2.74/2.96 ($false),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[456, 118, 437, 106, 450])).
% 2.74/2.96 tff(458,plain,((~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.96 tff(459,plain,
% 2.74/2.96 (~r(elem!1, s(s(z)))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[458, 437, 106])).
% 2.74/2.96 tff(460,assumption,(~r(elem!1, s(s(z)))), introduced(assumption)).
% 2.74/2.96 tff(461,assumption,(~b(elem!1, s(s(z)))), introduced(assumption)).
% 2.74/2.96 tff(462,assumption,(~(elem!1 = s(s(z)))), introduced(assumption)).
% 2.74/2.96 tff(463,plain,
% 2.74/2.96 (((~![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))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(464,plain,
% 2.74/2.96 ((~![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))))),
% 2.74/2.96 inference(quant_inst,[status(thm)],[])).
% 2.74/2.96 tff(465,plain,
% 2.74/2.96 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z)))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[464, 463])).
% 2.74/2.96 tff(466,plain,
% 2.74/2.96 ($false),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[465, 41, 462, 461, 460])).
% 2.74/2.96 tff(467,plain,(b(elem!1, s(s(z))) | (elem!1 = s(s(z))) | r(elem!1, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.96 tff(468,plain,
% 2.74/2.96 (b(elem!1, s(s(z)))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[467, 459, 312])).
% 2.74/2.96 tff(469,assumption,(~(elem!1 = s(s(s(s(z)))))), introduced(assumption)).
% 2.74/2.96 tff(470,assumption,(r(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 2.74/2.96 tff(471,plain,
% 2.74/2.96 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(472,plain,
% 2.74/2.96 (((~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(473,plain,
% 2.74/2.96 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[472])).
% 2.74/2.96 tff(474,plain,
% 2.74/2.96 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.74/2.96 inference(transitivity,[status(thm)],[473, 471])).
% 2.74/2.96 tff(475,plain,
% 2.74/2.96 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, z)))),
% 2.74/2.96 inference(quant_inst,[status(thm)],[])).
% 2.74/2.96 tff(476,plain,
% 2.74/2.96 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[475, 474])).
% 2.74/2.96 tff(477,plain,
% 2.74/2.96 ($false),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[476, 118, 437, 145, 470])).
% 2.74/2.96 tff(478,plain,((~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.96 tff(479,plain,
% 2.74/2.96 (~r(elem!1, s(s(s(s(z)))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[478, 437, 145])).
% 2.74/2.96 tff(480,plain,
% 2.74/2.96 (((~![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))))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(481,plain,
% 2.74/2.96 ((~![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))))))),
% 2.74/2.96 inference(quant_inst,[status(thm)],[])).
% 2.74/2.96 tff(482,plain,
% 2.74/2.96 ((~![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)))))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[481, 480])).
% 2.74/2.96 tff(483,plain,
% 2.74/2.96 ((elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z)))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[482, 41])).
% 2.74/2.96 tff(484,plain,
% 2.74/2.96 (b(elem!1, s(s(s(s(z)))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[483, 479, 469])).
% 2.74/2.96 tff(485,plain,
% 2.74/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, 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)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, 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)))), s(s(z)))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(486,plain,
% 2.74/2.96 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(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)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(487,plain,
% 2.74/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, 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)))), s(s(z))))))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[486])).
% 2.74/2.96 tff(488,plain,
% 2.74/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, 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)))), s(s(z)))))),
% 2.74/2.96 inference(transitivity,[status(thm)],[487, 485])).
% 2.74/2.96 tff(489,plain,
% 2.74/2.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 2.74/2.96 inference(quant_inst,[status(thm)],[])).
% 2.74/2.96 tff(490,plain,
% 2.74/2.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[489, 488])).
% 2.74/2.96 tff(491,plain,
% 2.74/2.96 ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[490, 178])).
% 2.74/2.96 tff(492,plain,
% 2.74/2.96 ($false),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[491, 484, 468, 167, 449, 202])).
% 2.74/2.96 tff(493,plain,((~r(elem!1, z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (elem!1 = s(s(s(s(z))))) | (s(s(z)) = elem!1) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.96 tff(494,plain,
% 2.74/2.96 (~r(elem!1, z)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[493, 436, 307, 167, 12, 145, 106])).
% 2.74/2.96 tff(495,plain,
% 2.74/2.96 (((~![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))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(496,plain,
% 2.74/2.96 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = z) | b(elem!1, z) | r(elem!1, z))),
% 2.74/2.96 inference(quant_inst,[status(thm)],[])).
% 2.74/2.96 tff(497,plain,
% 2.74/2.96 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[496, 495])).
% 2.74/2.96 tff(498,plain,
% 2.74/2.96 ((elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[497, 41])).
% 2.74/2.96 tff(499,plain,
% 2.74/2.96 (b(elem!1, z)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[498, 494, 290])).
% 2.74/2.96 tff(500,plain,
% 2.74/2.96 (~(elem!1 = s(s(s(s(z)))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[435, 224, 106, 107, 305, 12])).
% 2.74/2.96 tff(501,plain,
% 2.74/2.96 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(s(s(s(z)))))),
% 2.74/2.96 inference(symmetry,[status(thm)],[321])).
% 2.74/2.96 tff(502,plain,
% 2.74/2.96 (elem!1 = s(s(s(s(z))))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[331, 501])).
% 2.74/2.96 tff(503,plain,
% 2.74/2.96 ($false),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[469, 502])).
% 2.74/2.96 tff(504,plain,((~(s(s(s(s(z)))) = elem!1)) | (elem!1 = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.96 tff(505,plain,
% 2.74/2.96 (~(s(s(s(s(z)))) = elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[504, 500])).
% 2.74/2.96 tff(506,assumption,(b(elem!1, z)), introduced(assumption)).
% 2.74/2.96 tff(507,assumption,(~(z = elem!1)), introduced(assumption)).
% 2.74/2.96 tff(508,plain,
% 2.74/2.96 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(509,plain,
% 2.74/2.96 (((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(510,plain,
% 2.74/2.96 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[509])).
% 2.74/2.96 tff(511,plain,
% 2.74/2.96 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.74/2.96 inference(transitivity,[status(thm)],[510, 508])).
% 2.74/2.96 tff(512,plain,
% 2.74/2.96 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.74/2.96 inference(quant_inst,[status(thm)],[])).
% 2.74/2.96 tff(513,plain,
% 2.74/2.96 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[512, 511])).
% 2.74/2.96 tff(514,plain,
% 2.74/2.96 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[513, 118, 450, 107])).
% 2.74/2.96 tff(515,assumption,(s(elem!1) = s(s(z))), introduced(assumption)).
% 2.74/2.96 tff(516,plain,
% 2.74/2.96 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[515])).
% 2.74/2.96 tff(517,plain,
% 2.74/2.96 (elem!1 = inj_0(s(elem!1))),
% 2.74/2.96 inference(symmetry,[status(thm)],[304])).
% 2.74/2.96 tff(518,plain,
% 2.74/2.96 (elem!1 = s(z)),
% 2.74/2.96 inference(transitivity,[status(thm)],[517, 516, 70])).
% 2.74/2.96 tff(519,plain,
% 2.74/2.96 (b(z, elem!1) <=> b(z, s(z))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[518])).
% 2.74/2.96 tff(520,plain,
% 2.74/2.96 (b(elem!1, s(s(s(s(z))))) <=> b(s(z), s(s(s(s(z)))))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[518])).
% 2.74/2.96 tff(521,assumption,(r(z, elem!1)), introduced(assumption)).
% 2.74/2.96 tff(522,plain,
% 2.74/2.96 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(523,plain,
% 2.74/2.96 (((~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(524,plain,
% 2.74/2.96 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[523])).
% 2.74/2.96 tff(525,plain,
% 2.74/2.96 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.74/2.97 inference(transitivity,[status(thm)],[524, 522])).
% 2.74/2.97 tff(526,plain,
% 2.74/2.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, elem!1)))),
% 2.74/2.97 inference(quant_inst,[status(thm)],[])).
% 2.74/2.97 tff(527,plain,
% 2.74/2.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[526, 525])).
% 2.74/2.97 tff(528,plain,
% 2.74/2.97 ($false),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[527, 118, 521, 145, 470])).
% 2.74/2.97 tff(529,plain,((~r(z, s(s(s(s(z)))))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.97 tff(530,plain,
% 2.74/2.97 (~r(elem!1, s(s(s(s(z)))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[529, 521, 145])).
% 2.74/2.97 tff(531,plain,
% 2.74/2.97 (b(elem!1, s(s(s(s(z)))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[483, 530, 469])).
% 2.74/2.97 tff(532,plain,
% 2.74/2.97 (b(s(z), s(s(s(s(z)))))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[531, 520])).
% 2.74/2.97 tff(533,plain,
% 2.74/2.97 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 2.74/2.97 inference(symmetry,[status(thm)],[516])).
% 2.74/2.97 tff(534,plain,
% 2.74/2.97 (s(z) = elem!1),
% 2.74/2.97 inference(transitivity,[status(thm)],[71, 533, 304])).
% 2.74/2.97 tff(535,plain,
% 2.74/2.97 (b(s(s(z)), s(z)) <=> b(s(s(z)), elem!1)),
% 2.74/2.97 inference(monotonicity,[status(thm)],[534])).
% 2.74/2.97 tff(536,plain,
% 2.74/2.97 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(z))),
% 2.74/2.97 inference(symmetry,[status(thm)],[535])).
% 2.74/2.97 tff(537,plain,
% 2.74/2.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(538,plain,
% 2.74/2.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))),
% 2.74/2.97 inference(quant_inst,[status(thm)],[])).
% 2.74/2.97 tff(539,plain,
% 2.74/2.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[538, 537])).
% 2.74/2.97 tff(540,plain,
% 2.74/2.97 ($false),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[539, 118, 521, 438, 106])).
% 2.74/2.97 tff(541,plain,((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.97 tff(542,plain,
% 2.74/2.97 (~r(s(s(z)), elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[541, 521, 106])).
% 2.74/2.97 tff(543,plain,
% 2.74/2.97 (b(s(s(z)), elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[448, 542, 12])).
% 2.74/2.97 tff(544,plain,
% 2.74/2.97 (b(s(s(z)), s(z))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[543, 536])).
% 2.74/2.97 tff(545,plain,
% 2.74/2.97 (s(s(elem!1)) = s(s(s(z)))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[515])).
% 2.74/2.97 tff(546,plain,
% 2.74/2.97 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[545])).
% 2.74/2.97 tff(547,plain,
% 2.74/2.97 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[546, 518])).
% 2.74/2.97 tff(548,plain,
% 2.74/2.97 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(s(z)))) = elem!1)),
% 2.74/2.97 inference(monotonicity,[status(thm)],[546])).
% 2.74/2.97 tff(549,plain,
% 2.74/2.97 ((s(s(s(s(z)))) = elem!1) <=> (s(s(s(elem!1))) = elem!1)),
% 2.74/2.97 inference(symmetry,[status(thm)],[548])).
% 2.74/2.97 tff(550,plain,
% 2.74/2.97 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[549])).
% 2.74/2.97 tff(551,plain,
% 2.74/2.97 (~(s(s(s(s(z)))) = elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[504, 469])).
% 2.74/2.97 tff(552,plain,
% 2.74/2.97 (~(s(s(s(elem!1))) = elem!1)),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[551, 550])).
% 2.74/2.97 tff(553,plain,
% 2.74/2.97 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(z)))))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[546])).
% 2.74/2.97 tff(554,plain,
% 2.74/2.97 (r(z, s(s(s(s(z))))) <=> r(z, s(s(s(elem!1))))),
% 2.74/2.97 inference(symmetry,[status(thm)],[553])).
% 2.74/2.97 tff(555,plain,
% 2.74/2.97 (r(z, s(s(s(elem!1))))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[145, 554])).
% 2.74/2.97 tff(556,assumption,(r(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 2.74/2.97 tff(557,assumption,(r(z, s(s(s(elem!1))))), introduced(assumption)).
% 2.74/2.97 tff(558,plain,
% 2.74/2.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(559,plain,
% 2.74/2.97 (((~r(s(s(s(elem!1))), elem!1)) | (~r(z, 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))))))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(560,plain,
% 2.74/2.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1)))))))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[559])).
% 2.74/2.97 tff(561,plain,
% 2.74/2.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))))),
% 2.74/2.97 inference(transitivity,[status(thm)],[560, 558])).
% 2.74/2.97 tff(562,plain,
% 2.74/2.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))),
% 2.74/2.97 inference(quant_inst,[status(thm)],[])).
% 2.74/2.97 tff(563,plain,
% 2.74/2.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1)))))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[562, 561])).
% 2.74/2.97 tff(564,plain,
% 2.74/2.97 ($false),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[563, 118, 521, 557, 556])).
% 2.74/2.97 tff(565,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.97 tff(566,plain,
% 2.74/2.97 (~r(s(s(s(elem!1))), elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[565, 521, 555])).
% 2.74/2.97 tff(567,plain,
% 2.74/2.97 (((~![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))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(568,plain,
% 2.74/2.97 ((~![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))),
% 2.74/2.97 inference(quant_inst,[status(thm)],[])).
% 2.74/2.97 tff(569,plain,
% 2.74/2.97 ((~![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)),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[568, 567])).
% 2.74/2.97 tff(570,plain,
% 2.74/2.97 ((s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[569, 41])).
% 2.74/2.97 tff(571,plain,
% 2.74/2.97 (b(s(s(s(elem!1))), elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[570, 566, 552])).
% 2.74/2.97 tff(572,plain,
% 2.74/2.97 (b(s(s(s(s(z)))), s(z))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[571, 547])).
% 2.74/2.97 tff(573,plain,
% 2.74/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(574,plain,
% 2.74/2.97 (((~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(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(575,plain,
% 2.74/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(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(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[574])).
% 2.74/2.97 tff(576,plain,
% 2.74/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(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(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.74/2.97 inference(transitivity,[status(thm)],[575, 573])).
% 2.74/2.97 tff(577,plain,
% 2.74/2.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(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(s(s(z)))), s(s(z)))))),
% 2.74/2.97 inference(quant_inst,[status(thm)],[])).
% 2.74/2.97 tff(578,plain,
% 2.74/2.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[577, 576])).
% 2.74/2.97 tff(579,plain,
% 2.74/2.97 ($false),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[578, 178, 165, 202, 572, 544, 532])).
% 2.74/2.97 tff(580,plain,((~r(z, elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~(s(elem!1) = s(s(z)))) | (elem!1 = s(s(s(s(z))))) | (s(s(z)) = elem!1) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.97 tff(581,plain,
% 2.74/2.97 (~r(z, elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[580, 515, 202, 469, 12, 145, 106])).
% 2.74/2.97 tff(582,plain,
% 2.74/2.97 (((~![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))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(583,plain,
% 2.74/2.97 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = elem!1) | b(z, elem!1) | r(z, elem!1))),
% 2.74/2.97 inference(quant_inst,[status(thm)],[])).
% 2.74/2.97 tff(584,plain,
% 2.74/2.97 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[583, 582])).
% 2.74/2.97 tff(585,plain,
% 2.74/2.97 ((z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[584, 41])).
% 2.74/2.97 tff(586,plain,
% 2.74/2.97 (b(z, elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[585, 581, 507])).
% 2.74/2.97 tff(587,plain,
% 2.74/2.97 (b(z, s(z))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[586, 519])).
% 2.74/2.97 tff(588,plain,
% 2.74/2.97 (b(s(z), z) <=> b(elem!1, z)),
% 2.74/2.97 inference(monotonicity,[status(thm)],[534])).
% 2.74/2.97 tff(589,plain,
% 2.74/2.97 (b(elem!1, z) <=> b(s(z), z)),
% 2.74/2.97 inference(symmetry,[status(thm)],[588])).
% 2.74/2.97 tff(590,plain,
% 2.74/2.97 (b(s(z), z)),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[506, 589])).
% 2.74/2.97 tff(591,assumption,(~b(s(z), z)), introduced(assumption)).
% 2.74/2.97 tff(592,plain,
% 2.74/2.97 ($false),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[591, 590])).
% 2.74/2.97 tff(593,plain,(b(s(z), z) | (~b(elem!1, z)) | (~(s(elem!1) = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.97 tff(594,plain,
% 2.74/2.97 (b(s(z), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[593, 515, 506])).
% 2.74/2.97 tff(595,assumption,(b(z, s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.74/2.97 tff(596,plain,
% 2.74/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(z, s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(597,plain,
% 2.74/2.97 (((~b(s(z), 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(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(598,plain,
% 2.74/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[597])).
% 2.74/2.97 tff(599,plain,
% 2.74/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.74/2.97 inference(transitivity,[status(thm)],[598, 596])).
% 2.74/2.97 tff(600,plain,
% 2.74/2.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.74/2.97 inference(quant_inst,[status(thm)],[])).
% 2.74/2.97 tff(601,plain,
% 2.74/2.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[600, 599])).
% 2.74/2.97 tff(602,plain,
% 2.74/2.97 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[601, 178, 595, 594, 587, 146])).
% 2.74/2.97 tff(603,plain,
% 2.74/2.97 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[518])).
% 2.74/2.97 tff(604,plain,
% 2.74/2.97 ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) <=> (~r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[603])).
% 2.74/2.97 tff(605,assumption,(~r(s(s(s(s(s(s(s(z))))))), elem!1)), introduced(assumption)).
% 2.74/2.97 tff(606,plain,
% 2.74/2.97 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[605, 604])).
% 2.74/2.97 tff(607,assumption,(s(s(s(s(s(s(s(z))))))) = s(z)), introduced(assumption)).
% 2.74/2.97 tff(608,plain,
% 2.74/2.97 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(z))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[607])).
% 2.74/2.97 tff(609,plain,
% 2.74/2.97 (s(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 2.74/2.97 inference(symmetry,[status(thm)],[57])).
% 2.74/2.97 tff(610,plain,
% 2.74/2.97 (s(s(s(s(s(s(z)))))) = z),
% 2.74/2.97 inference(transitivity,[status(thm)],[609, 608, 51])).
% 2.74/2.97 tff(611,plain,
% 2.74/2.97 ($false),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[433, 610])).
% 2.74/2.97 tff(612,plain,(~(s(s(s(s(s(s(s(z))))))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.97 tff(613,plain,
% 2.74/2.97 (((~![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)))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(614,plain,
% 2.74/2.97 ((~![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)))),
% 2.74/2.97 inference(quant_inst,[status(thm)],[])).
% 2.74/2.97 tff(615,plain,
% 2.74/2.97 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(z)) | b(s(s(s(s(s(s(s(z))))))), s(z)) | r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[614, 613])).
% 2.74/2.97 tff(616,plain,
% 2.74/2.97 ($false),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[615, 41, 612, 606, 602])).
% 2.74/2.97 tff(617,plain,((~(s(elem!1) = s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (z = elem!1) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (elem!1 = s(s(s(s(z))))) | (s(s(z)) = elem!1) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.97 tff(618,plain,
% 2.74/2.97 (~(s(elem!1) = s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[617, 514, 134, 399, 507, 506, 202, 500, 12, 145, 106])).
% 2.74/2.97 tff(619,plain,
% 2.74/2.97 (r(s(elem!1), s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[421, 618, 305])).
% 2.74/2.97 tff(620,plain,
% 2.74/2.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(z)))))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(621,plain,
% 2.74/2.97 (((~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(z)))))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(622,plain,
% 2.74/2.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(z))))))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[621])).
% 2.74/2.97 tff(623,plain,
% 2.74/2.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(z)))))),
% 2.74/2.97 inference(transitivity,[status(thm)],[622, 620])).
% 2.74/2.97 tff(624,plain,
% 2.74/2.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), elem!1)))),
% 2.74/2.97 inference(quant_inst,[status(thm)],[])).
% 2.74/2.97 tff(625,plain,
% 2.74/2.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(z))))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[624, 623])).
% 2.74/2.97 tff(626,plain,
% 2.74/2.97 (~r(s(elem!1), elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[625, 118, 450, 619])).
% 2.74/2.97 tff(627,plain,
% 2.74/2.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(z)))))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(628,plain,
% 2.74/2.97 (((~r(s(elem!1), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(z)))))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(629,plain,
% 2.74/2.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(z))))))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[628])).
% 2.74/2.97 tff(630,plain,
% 2.74/2.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(z)))))),
% 2.74/2.97 inference(transitivity,[status(thm)],[629, 627])).
% 2.74/2.97 tff(631,plain,
% 2.74/2.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(elem!1))))),
% 2.74/2.97 inference(quant_inst,[status(thm)],[])).
% 2.74/2.97 tff(632,plain,
% 2.74/2.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(z))))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[631, 630])).
% 2.74/2.97 tff(633,plain,
% 2.74/2.97 (~r(elem!1, s(elem!1))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[632, 118, 450, 619])).
% 2.74/2.97 tff(634,plain,
% 2.74/2.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(635,plain,
% 2.74/2.97 (((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(636,plain,
% 2.74/2.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[635])).
% 2.74/2.97 tff(637,plain,
% 2.74/2.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.74/2.97 inference(transitivity,[status(thm)],[636, 634])).
% 2.74/2.97 tff(638,plain,
% 2.74/2.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.74/2.98 inference(quant_inst,[status(thm)],[])).
% 2.74/2.98 tff(639,plain,
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% 2.74/2.98 inference(modus_ponens,[status(thm)],[638, 637])).
% 2.74/2.98 tff(640,plain,
% 2.74/2.98 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[639, 118, 450, 107])).
% 2.74/2.98 tff(641,plain,
% 2.74/2.98 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[390, 619, 224])).
% 2.74/2.98 tff(642,assumption,(~r(s(elem!1), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.74/2.98 tff(643,assumption,(~b(s(elem!1), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.74/2.98 tff(644,assumption,(~r(elem!1, s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.74/2.98 tff(645,assumption,(s(elem!1) = s(s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 2.74/2.98 tff(646,plain,
% 2.74/2.98 (inj_0(s(elem!1)) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 2.74/2.98 inference(monotonicity,[status(thm)],[645])).
% 2.74/2.98 tff(647,plain,
% 2.74/2.98 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(elem!1))),
% 2.74/2.98 inference(symmetry,[status(thm)],[646])).
% 2.74/2.98 tff(648,plain,
% 2.74/2.98 (s(s(s(s(s(s(z)))))) = elem!1),
% 2.74/2.98 inference(transitivity,[status(thm)],[609, 647, 304])).
% 2.74/2.98 tff(649,plain,
% 2.74/2.98 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.74/2.98 inference(monotonicity,[status(thm)],[648])).
% 2.74/2.98 tff(650,plain,
% 2.74/2.98 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 2.74/2.98 inference(symmetry,[status(thm)],[649])).
% 2.74/2.98 tff(651,plain,
% 2.74/2.98 (r(s(elem!1), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.74/2.98 inference(monotonicity,[status(thm)],[645])).
% 2.74/2.98 tff(652,plain,
% 2.74/2.98 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(elem!1), elem!1)),
% 2.74/2.98 inference(symmetry,[status(thm)],[651])).
% 2.74/2.98 tff(653,plain,
% 2.74/2.98 ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) <=> (~r(s(elem!1), elem!1))),
% 2.74/2.98 inference(monotonicity,[status(thm)],[652])).
% 2.74/2.98 tff(654,plain,
% 2.74/2.98 (~r(s(elem!1), elem!1)),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[605, 653])).
% 2.74/2.98 tff(655,plain,
% 2.74/2.98 ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.74/2.98 inference(symmetry,[status(thm)],[377])).
% 2.74/2.98 tff(656,plain,
% 2.74/2.98 (s(s(s(s(s(s(s(z))))))) = s(elem!1)),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[645, 655])).
% 2.74/2.98 tff(657,assumption,(s(s(s(s(s(s(s(z))))))) = s(elem!1)), introduced(assumption)).
% 2.74/2.98 tff(658,plain,
% 2.74/2.98 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(elem!1))),
% 2.74/2.98 inference(monotonicity,[status(thm)],[657])).
% 2.74/2.98 tff(659,plain,
% 2.74/2.98 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 2.74/2.98 inference(transitivity,[status(thm)],[609, 658, 304, 330])).
% 2.74/2.98 tff(660,plain,
% 2.74/2.98 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(elem!1)))),
% 2.74/2.98 inference(monotonicity,[status(thm)],[659])).
% 2.74/2.98 tff(661,plain,
% 2.74/2.98 (s(s(s(s(s(z))))) = s(elem!1)),
% 2.74/2.98 inference(transitivity,[status(thm)],[239, 660, 328])).
% 2.74/2.98 tff(662,plain,
% 2.74/2.98 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(elem!1))),
% 2.74/2.98 inference(monotonicity,[status(thm)],[661])).
% 2.74/2.98 tff(663,plain,
% 2.74/2.98 (s(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 2.74/2.98 inference(symmetry,[status(thm)],[53])).
% 2.74/2.98 tff(664,plain,
% 2.74/2.98 (s(s(s(s(z)))) = elem!1),
% 2.74/2.98 inference(transitivity,[status(thm)],[663, 662, 304])).
% 2.74/2.98 tff(665,plain,
% 2.74/2.98 ($false),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[323, 664])).
% 2.74/2.98 tff(666,plain,((~(s(s(s(s(s(s(s(z))))))) = s(elem!1))) | (s(s(s(s(z)))) = elem!1) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.98 tff(667,plain,
% 2.74/2.98 (~(s(s(elem!1)) = elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[666, 656, 323])).
% 2.74/2.98 tff(668,assumption,(s(elem!1) = elem!1), introduced(assumption)).
% 2.74/2.98 tff(669,plain,
% 2.74/2.98 (s(s(elem!1)) = s(elem!1)),
% 2.74/2.98 inference(monotonicity,[status(thm)],[668])).
% 2.74/2.98 tff(670,plain,
% 2.74/2.98 (s(s(elem!1)) = elem!1),
% 2.74/2.98 inference(transitivity,[status(thm)],[669, 668])).
% 2.74/2.98 tff(671,plain,
% 2.74/2.98 ($false),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[346, 670])).
% 2.74/2.98 tff(672,plain,((~(s(elem!1) = elem!1)) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.98 tff(673,plain,
% 2.74/2.98 (~(s(elem!1) = elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[672, 667])).
% 2.74/2.98 tff(674,plain,
% 2.74/2.98 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(675,plain,
% 2.74/2.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1))),
% 2.74/2.98 inference(quant_inst,[status(thm)],[])).
% 2.74/2.98 tff(676,plain,
% 2.74/2.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1)),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[675, 674])).
% 2.74/2.98 tff(677,plain,
% 2.74/2.98 ((s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[676, 41])).
% 2.74/2.98 tff(678,plain,
% 2.74/2.98 (b(s(elem!1), elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[677, 673, 654])).
% 2.74/2.98 tff(679,assumption,(elem!1 = s(s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 2.74/2.98 tff(680,plain,
% 2.74/2.98 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 2.74/2.98 inference(symmetry,[status(thm)],[679])).
% 2.74/2.98 tff(681,plain,
% 2.74/2.98 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), elem!1)),
% 2.74/2.98 inference(monotonicity,[status(thm)],[680])).
% 2.74/2.98 tff(682,plain,
% 2.74/2.98 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.74/2.98 inference(symmetry,[status(thm)],[681])).
% 2.74/2.98 tff(683,assumption,(b(s(elem!1), elem!1)), introduced(assumption)).
% 2.74/2.98 tff(684,plain,
% 2.74/2.98 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[683, 682])).
% 2.74/2.98 tff(685,plain,
% 2.74/2.98 ($false),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[643, 684])).
% 2.74/2.98 tff(686,plain,((~(elem!1 = s(s(s(s(s(s(s(z))))))))) | b(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.98 tff(687,plain,
% 2.74/2.98 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[686, 678, 643])).
% 2.74/2.98 tff(688,plain,
% 2.74/2.98 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(s(s(z)))))))) | b(elem!1, s(s(s(s(s(s(s(z)))))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | b(elem!1, s(s(s(s(s(s(s(z)))))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(689,plain,
% 2.74/2.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(s(s(z)))))))) | b(elem!1, s(s(s(s(s(s(s(z)))))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 2.74/2.98 inference(quant_inst,[status(thm)],[])).
% 2.74/2.98 tff(690,plain,
% 2.74/2.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | b(elem!1, s(s(s(s(s(s(s(z)))))))) | r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[689, 688])).
% 2.74/2.98 tff(691,plain,
% 2.74/2.98 ((elem!1 = s(s(s(s(s(s(s(z)))))))) | b(elem!1, s(s(s(s(s(s(s(z)))))))) | r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[690, 41])).
% 2.74/2.98 tff(692,plain,
% 2.74/2.98 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[691, 687, 644])).
% 2.74/2.98 tff(693,plain,
% 2.74/2.98 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[692, 650])).
% 2.74/2.98 tff(694,plain,
% 2.74/2.98 (elem!1 = s(s(s(s(s(s(z))))))),
% 2.74/2.98 inference(transitivity,[status(thm)],[517, 646, 57])).
% 2.74/2.98 tff(695,plain,
% 2.74/2.98 (b(elem!1, z) <=> b(s(s(s(s(s(s(z)))))), z)),
% 2.74/2.98 inference(monotonicity,[status(thm)],[694])).
% 2.74/2.98 tff(696,plain,
% 2.74/2.98 (b(s(s(s(s(s(s(z)))))), z)),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[506, 695])).
% 2.74/2.98 tff(697,plain,
% 2.74/2.98 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.74/2.98 inference(monotonicity,[status(thm)],[648])).
% 2.74/2.98 tff(698,plain,
% 2.74/2.98 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 2.74/2.98 inference(symmetry,[status(thm)],[697])).
% 2.74/2.98 tff(699,assumption,(s(s(s(s(s(s(s(z))))))) = elem!1), introduced(assumption)).
% 2.74/2.98 tff(700,plain,
% 2.74/2.98 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 2.74/2.98 inference(symmetry,[status(thm)],[699])).
% 2.74/2.98 tff(701,assumption,(~(elem!1 = s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.74/2.98 tff(702,plain,
% 2.74/2.98 ($false),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[701, 700])).
% 2.74/2.98 tff(703,plain,((~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (elem!1 = s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.98 tff(704,plain,
% 2.74/2.98 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[703, 687])).
% 2.74/2.98 tff(705,plain,
% 2.74/2.98 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(706,plain,
% 2.74/2.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.74/2.98 inference(quant_inst,[status(thm)],[])).
% 2.74/2.98 tff(707,plain,
% 2.74/2.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[706, 705])).
% 2.74/2.98 tff(708,plain,
% 2.74/2.98 ((s(s(s(s(s(s(s(z))))))) = elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[707, 41, 605])).
% 2.74/2.98 tff(709,plain,
% 2.74/2.98 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[708, 704])).
% 2.74/2.98 tff(710,plain,
% 2.74/2.98 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[709, 698])).
% 2.74/2.98 tff(711,plain,
% 2.74/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(712,plain,
% 2.74/2.98 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))))) <=> ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(713,plain,
% 2.74/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))))),
% 2.74/2.98 inference(monotonicity,[status(thm)],[712])).
% 2.74/2.98 tff(714,plain,
% 2.74/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.74/2.98 inference(transitivity,[status(thm)],[713, 711])).
% 2.74/2.98 tff(715,plain,
% 2.74/2.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))),
% 2.74/2.98 inference(quant_inst,[status(thm)],[])).
% 2.74/2.98 tff(716,plain,
% 2.74/2.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[715, 714])).
% 2.74/2.98 tff(717,plain,
% 2.74/2.98 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[716, 178, 595, 710, 146, 696])).
% 2.74/2.98 tff(718,plain,
% 2.74/2.98 ($false),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[717, 693])).
% 2.74/2.98 tff(719,plain,((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | b(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (s(s(s(s(z)))) = elem!1) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.98 tff(720,plain,
% 2.74/2.98 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[719, 643, 146, 605, 644, 595, 323, 506])).
% 2.74/2.98 tff(721,plain,
% 2.74/2.98 ($false),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[395, 720, 643, 642])).
% 2.74/2.98 tff(722,plain,(b(s(elem!1), s(s(s(s(s(s(s(z)))))))) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(z)))) = elem!1) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.98 tff(723,plain,
% 2.74/2.98 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[722, 641, 134, 514, 640, 399, 505, 506])).
% 2.74/2.98 tff(724,assumption,(~r(s(elem!1), elem!1)), introduced(assumption)).
% 2.74/2.98 tff(725,assumption,(~(s(elem!1) = elem!1)), introduced(assumption)).
% 2.74/2.98 tff(726,plain,
% 2.74/2.98 (b(s(elem!1), elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[677, 725, 724])).
% 2.74/2.98 tff(727,assumption,(b(s(elem!1), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.74/2.98 tff(728,plain,
% 2.74/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(729,plain,
% 2.74/2.98 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(730,plain,
% 2.74/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 2.74/2.98 inference(monotonicity,[status(thm)],[729])).
% 2.74/2.98 tff(731,plain,
% 2.74/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.74/2.98 inference(transitivity,[status(thm)],[730, 728])).
% 2.74/2.98 tff(732,plain,
% 2.74/2.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)))),
% 2.74/2.98 inference(quant_inst,[status(thm)],[])).
% 2.74/2.98 tff(733,plain,
% 2.74/2.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[732, 731])).
% 2.74/2.98 tff(734,plain,
% 2.74/2.98 ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[733, 178, 506, 727, 146])).
% 2.74/2.98 tff(735,plain,
% 2.74/2.98 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[734, 726])).
% 2.74/2.98 tff(736,plain,
% 2.74/2.98 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[691, 735, 644])).
% 2.74/2.98 tff(737,plain,
% 2.74/2.98 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 2.74/2.98 inference(monotonicity,[status(thm)],[736])).
% 2.74/2.98 tff(738,plain,
% 2.74/2.98 (s(s(s(s(s(s(s(s(z)))))))) = s(elem!1)),
% 2.74/2.98 inference(symmetry,[status(thm)],[737])).
% 2.74/2.98 tff(739,plain,
% 2.74/2.98 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 2.74/2.98 inference(monotonicity,[status(thm)],[738])).
% 2.74/2.98 tff(740,plain,
% 2.74/2.98 (r(s(elem!1), s(s(z))) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 2.74/2.98 inference(symmetry,[status(thm)],[739])).
% 2.74/2.98 tff(741,plain,
% 2.74/2.98 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[363, 740])).
% 2.74/2.98 tff(742,plain,
% 2.74/2.98 (r(s(s(s(s(s(s(s(s(z)))))))), z) <=> r(s(elem!1), z)),
% 2.74/2.98 inference(monotonicity,[status(thm)],[738])).
% 2.74/2.98 tff(743,plain,
% 2.74/2.98 (r(s(elem!1), z) <=> r(s(s(s(s(s(s(s(s(z)))))))), z)),
% 2.74/2.98 inference(symmetry,[status(thm)],[742])).
% 2.74/2.98 tff(744,assumption,(~r(elem!1, s(elem!1))), introduced(assumption)).
% 2.74/2.98 tff(745,assumption,(elem!1 = s(elem!1)), introduced(assumption)).
% 2.74/2.98 tff(746,plain,
% 2.74/2.98 (s(elem!1) = elem!1),
% 2.74/2.98 inference(symmetry,[status(thm)],[745])).
% 2.74/2.98 tff(747,plain,
% 2.74/2.98 ($false),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[725, 746])).
% 2.74/2.98 tff(748,plain,((~(elem!1 = s(elem!1))) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.98 tff(749,plain,
% 2.74/2.98 (~(elem!1 = s(elem!1))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[748, 725])).
% 2.74/2.98 tff(750,assumption,(~(elem!1 = s(elem!1))), introduced(assumption)).
% 2.74/2.98 tff(751,assumption,(~b(elem!1, s(elem!1))), introduced(assumption)).
% 2.74/2.98 tff(752,plain,
% 2.74/2.98 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1)))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(753,plain,
% 2.74/2.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1)))),
% 2.74/2.98 inference(quant_inst,[status(thm)],[])).
% 2.74/2.98 tff(754,plain,
% 2.74/2.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1))),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[753, 752])).
% 2.74/2.98 tff(755,plain,
% 2.74/2.98 ($false),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[754, 41, 744, 751, 750])).
% 2.74/2.98 tff(756,plain,(r(elem!1, s(elem!1)) | b(elem!1, s(elem!1)) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.98 tff(757,plain,
% 2.74/2.98 (b(elem!1, s(elem!1))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[756, 749, 744])).
% 2.74/2.98 tff(758,plain,
% 2.74/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(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))))))))))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(759,plain,
% 2.74/2.98 (((~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(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(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))))))))))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(760,plain,
% 2.74/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(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)))))))))))),
% 2.74/2.98 inference(monotonicity,[status(thm)],[759])).
% 2.74/2.98 tff(761,plain,
% 2.74/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(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))))))))))),
% 2.74/2.98 inference(transitivity,[status(thm)],[760, 758])).
% 2.74/2.98 tff(762,plain,
% 2.74/2.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))),
% 2.74/2.99 inference(quant_inst,[status(thm)],[])).
% 2.74/2.99 tff(763,plain,
% 2.74/2.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(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)))))))))),
% 2.74/2.99 inference(modus_ponens,[status(thm)],[762, 761])).
% 2.74/2.99 tff(764,plain,
% 2.74/2.99 ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), z))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[763, 178, 506, 727, 595])).
% 2.74/2.99 tff(765,plain,
% 2.74/2.99 (~b(s(elem!1), z)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[764, 757])).
% 2.74/2.99 tff(766,assumption,(~b(s(elem!1), z)), introduced(assumption)).
% 2.74/2.99 tff(767,assumption,(~r(s(elem!1), z)), introduced(assumption)).
% 2.74/2.99 tff(768,plain,
% 2.74/2.99 ((~![X: $i] : (~(s(X) = z))) | (~(s(elem!1) = z))),
% 2.74/2.99 inference(quant_inst,[status(thm)],[])).
% 2.74/2.99 tff(769,plain,
% 2.74/2.99 (~(s(elem!1) = z)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[768, 28])).
% 2.74/2.99 tff(770,plain,
% 2.74/2.99 (((~![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))),
% 2.74/2.99 inference(rewrite,[status(thm)],[])).
% 2.74/2.99 tff(771,plain,
% 2.74/2.99 ((~![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))),
% 2.74/2.99 inference(quant_inst,[status(thm)],[])).
% 2.74/2.99 tff(772,plain,
% 2.74/2.99 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z)),
% 2.74/2.99 inference(modus_ponens,[status(thm)],[771, 770])).
% 2.74/2.99 tff(773,plain,
% 2.74/2.99 ($false),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[772, 41, 769, 767, 766])).
% 2.74/2.99 tff(774,plain,(r(s(elem!1), z) | b(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.99 tff(775,plain,
% 2.74/2.99 (r(s(elem!1), z)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[774, 765])).
% 2.74/2.99 tff(776,plain,
% 2.74/2.99 (r(s(s(s(s(s(s(s(s(z)))))))), z)),
% 2.74/2.99 inference(modus_ponens,[status(thm)],[775, 743])).
% 2.74/2.99 tff(777,plain,
% 2.74/2.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))))),
% 2.74/2.99 inference(rewrite,[status(thm)],[])).
% 2.74/2.99 tff(778,plain,
% 2.74/2.99 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))))),
% 2.74/2.99 inference(quant_inst,[status(thm)],[])).
% 2.74/2.99 tff(779,plain,
% 2.74/2.99 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(z))))),
% 2.74/2.99 inference(modus_ponens,[status(thm)],[778, 777])).
% 2.74/2.99 tff(780,plain,
% 2.74/2.99 (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[779, 118, 106, 776])).
% 2.74/2.99 tff(781,plain,
% 2.74/2.99 ($false),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[780, 741])).
% 2.74/2.99 tff(782,plain,((s(elem!1) = elem!1) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), z)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | r(elem!1, s(elem!1)) | r(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.99 tff(783,plain,
% 2.74/2.99 (s(elem!1) = elem!1),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[782, 619, 106, 640, 506, 723, 399, 134, 633, 626])).
% 2.74/2.99 tff(784,plain,
% 2.74/2.99 (s(s(elem!1)) = elem!1),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[672, 783])).
% 2.74/2.99 tff(785,plain,
% 2.74/2.99 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[666, 784, 505])).
% 2.74/2.99 tff(786,plain,
% 2.74/2.99 (b(s(elem!1), z) <=> b(elem!1, z)),
% 2.74/2.99 inference(monotonicity,[status(thm)],[668])).
% 2.74/2.99 tff(787,plain,
% 2.74/2.99 (b(elem!1, z) <=> b(s(elem!1), z)),
% 2.74/2.99 inference(symmetry,[status(thm)],[786])).
% 2.74/2.99 tff(788,plain,
% 2.74/2.99 (b(s(elem!1), z)),
% 2.74/2.99 inference(modus_ponens,[status(thm)],[506, 787])).
% 2.74/2.99 tff(789,plain,
% 2.74/2.99 ($false),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[766, 788])).
% 2.74/2.99 tff(790,plain,((~(s(elem!1) = elem!1)) | b(s(elem!1), z) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.99 tff(791,plain,
% 2.74/2.99 (b(s(elem!1), z)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[790, 783, 506])).
% 2.74/2.99 tff(792,plain,
% 2.74/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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))))))))) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.74/2.99 inference(rewrite,[status(thm)],[])).
% 2.74/2.99 tff(793,plain,
% 2.74/2.99 (((~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(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~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))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.74/2.99 inference(rewrite,[status(thm)],[])).
% 2.74/2.99 tff(794,plain,
% 2.74/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(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(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 2.74/2.99 inference(monotonicity,[status(thm)],[793])).
% 2.74/2.99 tff(795,plain,
% 2.74/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(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(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.74/2.99 inference(transitivity,[status(thm)],[794, 792])).
% 2.74/2.99 tff(796,plain,
% 2.74/2.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(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(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.74/2.99 inference(quant_inst,[status(thm)],[])).
% 2.74/2.99 tff(797,plain,
% 2.74/2.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 2.74/2.99 inference(modus_ponens,[status(thm)],[796, 795])).
% 2.74/2.99 tff(798,plain,
% 2.74/2.99 ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[797, 178, 723, 399, 134])).
% 2.74/2.99 tff(799,plain,
% 2.74/2.99 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[798, 791])).
% 2.74/2.99 tff(800,plain,
% 2.74/2.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), 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(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), 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(elem!1))))),
% 2.74/2.99 inference(rewrite,[status(thm)],[])).
% 2.74/2.99 tff(801,plain,
% 2.74/2.99 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), 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(elem!1))))),
% 2.74/2.99 inference(quant_inst,[status(thm)],[])).
% 2.74/2.99 tff(802,plain,
% 2.74/2.99 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), 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(elem!1)))),
% 2.74/2.99 inference(modus_ponens,[status(thm)],[801, 800])).
% 2.74/2.99 tff(803,plain,
% 2.74/2.99 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[802, 118, 619, 107])).
% 2.74/2.99 tff(804,plain,
% 2.74/2.99 (((~![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)))),
% 2.74/2.99 inference(rewrite,[status(thm)],[])).
% 2.74/2.99 tff(805,plain,
% 2.74/2.99 ((~![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)))),
% 2.74/2.99 inference(quant_inst,[status(thm)],[])).
% 2.74/2.99 tff(806,plain,
% 2.74/2.99 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | b(s(s(s(s(s(s(s(z))))))), s(elem!1)) | r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.74/2.99 inference(modus_ponens,[status(thm)],[805, 804])).
% 2.74/2.99 tff(807,plain,
% 2.74/2.99 ((s(s(s(s(s(s(s(z))))))) = s(elem!1)) | b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[806, 41, 803])).
% 2.74/2.99 tff(808,plain,
% 2.74/2.99 ($false),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[807, 799, 785])).
% 2.74/2.99 tff(809,plain,((~r(elem!1, s(s(z)))) | (~b(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | b(s(elem!1), s(s(z))) | (z = elem!1) | (~b(s(s(s(s(z)))), s(s(z)))) | (s(s(z)) = elem!1) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.99 tff(810,plain,
% 2.74/2.99 (~r(elem!1, s(s(z)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[809, 499, 106, 107, 287, 305, 318, 307, 12, 145])).
% 2.74/2.99 tff(811,plain,
% 2.74/2.99 (b(elem!1, s(s(z)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[467, 810, 312])).
% 2.74/2.99 tff(812,assumption,(b(elem!1, s(s(z)))), introduced(assumption)).
% 2.74/2.99 tff(813,plain,
% 2.74/2.99 ($false),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[491, 531, 543, 167, 812, 202])).
% 2.74/2.99 tff(814,plain,((~r(z, elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (elem!1 = s(s(s(s(z))))) | (s(s(z)) = elem!1) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.99 tff(815,plain,
% 2.74/2.99 (~r(z, elem!1)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[814, 811, 167, 307, 436, 12, 145, 106])).
% 2.74/2.99 tff(816,plain,
% 2.74/2.99 (b(z, elem!1)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[585, 815, 318])).
% 2.74/2.99 tff(817,assumption,(b(s(s(z)), elem!1)), introduced(assumption)).
% 2.74/2.99 tff(818,assumption,(b(z, elem!1)), introduced(assumption)).
% 2.74/2.99 tff(819,plain,
% 2.74/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))))),
% 2.74/2.99 inference(rewrite,[status(thm)],[])).
% 2.74/2.99 tff(820,plain,
% 2.74/2.99 (((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, z))) <=> ((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))))),
% 2.74/2.99 inference(rewrite,[status(thm)],[])).
% 2.74/2.99 tff(821,plain,
% 2.74/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z))))))),
% 2.74/2.99 inference(monotonicity,[status(thm)],[820])).
% 2.74/2.99 tff(822,plain,
% 2.74/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))))),
% 2.74/2.99 inference(transitivity,[status(thm)],[821, 819])).
% 2.74/2.99 tff(823,plain,
% 2.74/2.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, z)))),
% 2.74/2.99 inference(quant_inst,[status(thm)],[])).
% 2.74/2.99 tff(824,plain,
% 2.74/2.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z))))),
% 2.74/2.99 inference(modus_ponens,[status(thm)],[823, 822])).
% 2.74/2.99 tff(825,plain,
% 2.74/2.99 ($false),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[824, 178, 818, 506, 817, 273, 812])).
% 2.74/2.99 tff(826,plain,((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.99 tff(827,plain,
% 2.74/2.99 (~b(s(s(z)), elem!1)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[826, 816, 499, 273, 811])).
% 2.74/2.99 tff(828,plain,
% 2.74/2.99 (r(s(s(z)), elem!1)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[448, 827, 12])).
% 2.74/2.99 tff(829,plain,
% 2.74/2.99 (b(elem!1, s(s(z)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[467, 460, 312])).
% 2.74/2.99 tff(830,plain,
% 2.74/2.99 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.74/2.99 inference(monotonicity,[status(thm)],[694])).
% 2.74/2.99 tff(831,plain,
% 2.74/2.99 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.74/2.99 inference(monotonicity,[status(thm)],[694])).
% 2.74/2.99 tff(832,plain,
% 2.74/2.99 (r(s(s(z)), s(s(s(s(s(s(z))))))) <=> r(s(s(z)), elem!1)),
% 2.74/2.99 inference(symmetry,[status(thm)],[831])).
% 2.74/2.99 tff(833,plain,
% 2.74/2.99 ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) <=> (~r(s(s(z)), elem!1))),
% 2.74/2.99 inference(monotonicity,[status(thm)],[832])).
% 2.74/2.99 tff(834,plain,
% 2.74/2.99 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.74/2.99 inference(monotonicity,[status(thm)],[648])).
% 2.74/2.99 tff(835,plain,
% 2.74/2.99 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 2.74/2.99 inference(symmetry,[status(thm)],[834])).
% 2.74/2.99 tff(836,plain,
% 2.74/2.99 ((s(s(s(s(s(s(s(z))))))) = elem!1) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.74/2.99 inference(commutativity,[status(thm)],[])).
% 2.74/2.99 tff(837,plain,
% 2.74/2.99 ((s(elem!1) = elem!1) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.74/2.99 inference(monotonicity,[status(thm)],[645])).
% 2.74/2.99 tff(838,plain,
% 2.74/2.99 ((s(elem!1) = elem!1) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.74/2.99 inference(transitivity,[status(thm)],[837, 836])).
% 2.74/2.99 tff(839,plain,
% 2.74/2.99 ((~(s(elem!1) = elem!1)) <=> (~(elem!1 = s(s(s(s(s(s(s(z)))))))))),
% 2.74/2.99 inference(monotonicity,[status(thm)],[838])).
% 2.74/2.99 tff(840,plain,
% 2.74/2.99 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.74/2.99 inference(modus_ponens,[status(thm)],[725, 839])).
% 2.74/2.99 tff(841,plain,
% 2.74/2.99 (s(s(s(s(s(s(s(z))))))) = s(elem!1)),
% 2.74/2.99 inference(symmetry,[status(thm)],[645])).
% 2.74/2.99 tff(842,plain,
% 2.74/2.99 (r(s(s(s(s(s(s(s(z))))))), z) <=> r(s(elem!1), z)),
% 2.74/2.99 inference(monotonicity,[status(thm)],[841])).
% 2.74/2.99 tff(843,plain,
% 2.74/2.99 (r(s(elem!1), z) <=> r(s(s(s(s(s(s(s(z))))))), z)),
% 2.74/2.99 inference(symmetry,[status(thm)],[842])).
% 2.74/2.99 tff(844,assumption,(r(s(elem!1), z)), introduced(assumption)).
% 2.74/2.99 tff(845,plain,
% 2.74/2.99 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.74/2.99 inference(modus_ponens,[status(thm)],[844, 843])).
% 2.74/2.99 tff(846,plain,
% 2.74/2.99 ($false),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[126, 845])).
% 2.74/2.99 tff(847,plain,((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), z) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.99 tff(848,plain,
% 2.74/2.99 (~r(s(elem!1), z)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[847, 645, 126])).
% 2.74/2.99 tff(849,plain,
% 2.74/2.99 (b(s(elem!1), z)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[774, 848])).
% 2.74/2.99 tff(850,plain,
% 2.74/2.99 (b(z, s(elem!1)) <=> b(z, s(s(s(s(s(s(s(z))))))))),
% 2.74/2.99 inference(monotonicity,[status(thm)],[645])).
% 2.74/2.99 tff(851,plain,
% 2.74/2.99 (b(z, s(s(s(s(s(s(s(z)))))))) <=> b(z, s(elem!1))),
% 2.74/2.99 inference(symmetry,[status(thm)],[850])).
% 2.74/2.99 tff(852,plain,
% 2.74/2.99 (b(z, s(elem!1))),
% 2.74/2.99 inference(modus_ponens,[status(thm)],[595, 851])).
% 2.74/2.99 tff(853,assumption,(b(s(elem!1), z)), introduced(assumption)).
% 2.74/2.99 tff(854,assumption,(b(elem!1, s(elem!1))), introduced(assumption)).
% 2.74/2.99 tff(855,assumption,(b(z, s(elem!1))), introduced(assumption)).
% 2.74/2.99 tff(856,plain,
% 2.74/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)))),
% 2.74/2.99 inference(rewrite,[status(thm)],[])).
% 2.74/2.99 tff(857,plain,
% 2.74/2.99 (((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)))),
% 2.74/2.99 inference(rewrite,[status(thm)],[])).
% 2.74/2.99 tff(858,plain,
% 2.74/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z))))),
% 2.74/2.99 inference(monotonicity,[status(thm)],[857])).
% 2.74/2.99 tff(859,plain,
% 2.74/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)))),
% 2.74/2.99 inference(transitivity,[status(thm)],[858, 856])).
% 2.74/2.99 tff(860,plain,
% 2.74/2.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)))),
% 2.74/2.99 inference(quant_inst,[status(thm)],[])).
% 2.74/2.99 tff(861,plain,
% 2.74/2.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z))),
% 2.74/2.99 inference(modus_ponens,[status(thm)],[860, 859])).
% 2.74/2.99 tff(862,plain,
% 2.74/2.99 ($false),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[861, 178, 818, 506, 855, 854, 853])).
% 2.74/2.99 tff(863,plain,((~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.99 tff(864,plain,
% 2.74/2.99 (~b(elem!1, s(elem!1))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[863, 852, 818, 849, 506])).
% 2.74/2.99 tff(865,plain,
% 2.74/2.99 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(elem!1))),
% 2.74/2.99 inference(monotonicity,[status(thm)],[841])).
% 2.74/2.99 tff(866,plain,
% 2.74/2.99 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.74/2.99 inference(symmetry,[status(thm)],[865])).
% 2.74/2.99 tff(867,plain,
% 2.74/2.99 ((~b(elem!1, s(elem!1))) <=> (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 2.74/2.99 inference(monotonicity,[status(thm)],[866])).
% 2.74/2.99 tff(868,plain,
% 2.74/2.99 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.74/2.99 inference(modus_ponens,[status(thm)],[751, 867])).
% 2.74/2.99 tff(869,assumption,(b(elem!1, s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.74/2.99 tff(870,plain,
% 2.74/2.99 ($false),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[869, 868])).
% 2.74/2.99 tff(871,plain,((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | b(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.99 tff(872,plain,
% 2.74/2.99 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[871, 864, 645])).
% 2.74/2.99 tff(873,plain,
% 2.74/2.99 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[691, 872, 840])).
% 2.74/2.99 tff(874,plain,
% 2.74/2.99 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 2.74/2.99 inference(modus_ponens,[status(thm)],[873, 835])).
% 2.74/2.99 tff(875,plain,
% 2.74/2.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.74/2.99 inference(rewrite,[status(thm)],[])).
% 2.74/2.99 tff(876,plain,
% 2.74/2.99 (((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.74/2.99 inference(rewrite,[status(thm)],[])).
% 2.74/2.99 tff(877,plain,
% 2.74/2.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))))),
% 2.74/2.99 inference(monotonicity,[status(thm)],[876])).
% 2.74/2.99 tff(878,plain,
% 2.74/2.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.74/3.00 inference(transitivity,[status(thm)],[877, 875])).
% 2.74/3.00 tff(879,plain,
% 2.74/3.00 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.74/3.00 inference(quant_inst,[status(thm)],[])).
% 2.74/3.00 tff(880,plain,
% 2.74/3.00 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[879, 878])).
% 2.74/3.00 tff(881,plain,
% 2.74/3.00 ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[880, 118, 224])).
% 2.74/3.00 tff(882,plain,
% 2.74/3.00 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[881, 874])).
% 2.74/3.00 tff(883,plain,
% 2.74/3.00 (~r(s(s(z)), elem!1)),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[882, 833])).
% 2.74/3.00 tff(884,plain,
% 2.74/3.00 (b(s(s(z)), elem!1)),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[448, 883, 12])).
% 2.74/3.00 tff(885,plain,
% 2.74/3.00 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[884, 830])).
% 2.74/3.00 tff(886,plain,
% 2.74/3.00 (b(elem!1, s(s(z))) <=> b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[694])).
% 2.74/3.00 tff(887,plain,
% 2.74/3.00 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[812, 886])).
% 2.74/3.00 tff(888,plain,
% 2.74/3.00 (b(z, elem!1) <=> b(z, s(s(s(s(s(s(z)))))))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[694])).
% 2.74/3.00 tff(889,plain,
% 2.74/3.00 (b(z, s(s(s(s(s(s(z)))))))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[818, 888])).
% 2.74/3.00 tff(890,plain,
% 2.74/3.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(891,plain,
% 2.74/3.00 (((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(892,plain,
% 2.74/3.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[891])).
% 2.74/3.00 tff(893,plain,
% 2.74/3.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 2.74/3.00 inference(transitivity,[status(thm)],[892, 890])).
% 2.74/3.00 tff(894,plain,
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% 2.74/3.00 inference(quant_inst,[status(thm)],[])).
% 2.74/3.00 tff(895,plain,
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% 2.74/3.00 inference(modus_ponens,[status(thm)],[894, 893])).
% 2.74/3.00 tff(896,plain,
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% 2.74/3.00 inference(unit_resolution,[status(thm)],[895, 178, 273, 889, 887, 885, 696])).
% 2.74/3.00 tff(897,plain,((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (s(s(z)) = elem!1) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (s(elem!1) = elem!1) | (~b(z, s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), z)), inference(lemma,lemma(discharge,[]))).
% 2.74/3.00 tff(898,plain,
% 2.74/3.00 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[897, 725, 12, 224, 818, 506, 829, 273, 399, 126])).
% 2.74/3.00 tff(899,plain,
% 2.74/3.00 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[395, 898, 643])).
% 2.74/3.00 tff(900,plain,
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% 2.74/3.00 inference(unit_resolution,[status(thm)],[390, 899, 224])).
% 2.74/3.00 tff(901,plain,
% 2.74/3.00 (s(elem!1) = s(s(z))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[421, 900, 305])).
% 2.74/3.00 tff(902,plain,
% 2.74/3.00 (r(s(elem!1), z) <=> r(s(s(z)), z)),
% 2.74/3.00 inference(monotonicity,[status(thm)],[515])).
% 2.74/3.00 tff(903,plain,
% 2.74/3.00 (r(s(s(z)), z) <=> r(s(elem!1), z)),
% 2.74/3.00 inference(symmetry,[status(thm)],[902])).
% 2.74/3.00 tff(904,plain,
% 2.74/3.00 (r(s(elem!1), z)),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[106, 903])).
% 2.74/3.00 tff(905,plain,
% 2.74/3.00 ($false),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[767, 904])).
% 2.74/3.00 tff(906,plain,((~(s(elem!1) = s(s(z)))) | r(s(elem!1), z) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.00 tff(907,plain,
% 2.74/3.00 (r(s(elem!1), z)),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[906, 901, 106])).
% 2.74/3.00 tff(908,assumption,(r(s(elem!1), s(s(s(s(z)))))), introduced(assumption)).
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% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(910,plain,
% 2.74/3.00 (((~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(z))))))) <=> ((~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(911,plain,
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% 2.74/3.00 inference(monotonicity,[status(thm)],[910])).
% 2.74/3.00 tff(912,plain,
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% 2.74/3.00 inference(transitivity,[status(thm)],[911, 909])).
% 2.74/3.00 tff(913,plain,
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% 2.74/3.00 inference(quant_inst,[status(thm)],[])).
% 2.74/3.00 tff(914,plain,
% 2.74/3.00 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z))))))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[913, 912])).
% 2.74/3.00 tff(915,plain,
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% 2.74/3.00 inference(unit_resolution,[status(thm)],[914, 118, 844, 194, 908])).
% 2.74/3.00 tff(916,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.00 tff(917,plain,
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% 2.74/3.00 inference(unit_resolution,[status(thm)],[916, 907, 194])).
% 2.74/3.00 tff(918,plain,
% 2.74/3.00 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(z)))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[901])).
% 2.74/3.00 tff(919,plain,
% 2.74/3.00 (r(elem!1, s(s(z))) <=> r(elem!1, s(elem!1))),
% 2.74/3.00 inference(symmetry,[status(thm)],[918])).
% 2.74/3.00 tff(920,plain,
% 2.74/3.00 ((~r(elem!1, s(s(z)))) <=> (~r(elem!1, s(elem!1)))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[919])).
% 2.74/3.00 tff(921,plain,
% 2.74/3.00 (~r(elem!1, s(elem!1))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[460, 920])).
% 2.74/3.00 tff(922,plain,
% 2.74/3.00 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(z)))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[901])).
% 2.74/3.00 tff(923,plain,
% 2.74/3.00 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 2.74/3.00 inference(symmetry,[status(thm)],[922])).
% 2.74/3.00 tff(924,plain,
% 2.74/3.00 ((~r(s(s(s(s(z)))), s(s(z)))) <=> (~r(s(s(s(s(z)))), s(elem!1)))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[923])).
% 2.74/3.00 tff(925,plain,
% 2.74/3.00 (~r(s(s(s(s(z)))), s(elem!1))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[306, 924])).
% 2.74/3.00 tff(926,assumption,(~r(s(elem!1), s(s(s(s(z)))))), introduced(assumption)).
% 2.74/3.00 tff(927,assumption,(~r(s(elem!1), s(s(z)))), introduced(assumption)).
% 2.74/3.00 tff(928,assumption,(elem!1 = z), introduced(assumption)).
% 2.74/3.00 tff(929,plain,
% 2.74/3.00 (s(elem!1) = s(z)),
% 2.74/3.00 inference(monotonicity,[status(thm)],[928])).
% 2.74/3.00 tff(930,plain,
% 2.74/3.00 (s(s(elem!1)) = s(s(z))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[929])).
% 2.74/3.00 tff(931,plain,
% 2.74/3.00 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[930])).
% 2.74/3.00 tff(932,plain,
% 2.74/3.00 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[931])).
% 2.74/3.00 tff(933,plain,
% 2.74/3.00 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(z)))))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[932])).
% 2.74/3.00 tff(934,plain,
% 2.74/3.00 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[929])).
% 2.74/3.00 tff(935,plain,
% 2.74/3.00 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(z)))))),
% 2.74/3.00 inference(transitivity,[status(thm)],[934, 933])).
% 2.74/3.00 tff(936,plain,
% 2.74/3.00 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = z)),
% 2.74/3.00 inference(monotonicity,[status(thm)],[928])).
% 2.74/3.00 tff(937,plain,
% 2.74/3.00 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 2.74/3.00 inference(symmetry,[status(thm)],[936])).
% 2.74/3.00 tff(938,plain,
% 2.74/3.00 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[937])).
% 2.74/3.00 tff(939,plain,
% 2.74/3.00 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(elem!1))) = z))),
% 2.74/3.00 inference(quant_inst,[status(thm)],[])).
% 2.74/3.00 tff(940,plain,
% 2.74/3.00 (~(s(s(s(elem!1))) = z)),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[939, 28])).
% 2.74/3.00 tff(941,plain,
% 2.74/3.00 (~(s(s(s(elem!1))) = elem!1)),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[940, 938])).
% 2.74/3.00 tff(942,assumption,(s(elem!1) = s(s(s(s(elem!1))))), introduced(assumption)).
% 2.74/3.00 tff(943,plain,
% 2.74/3.00 (s(s(s(s(elem!1)))) = s(elem!1)),
% 2.74/3.00 inference(symmetry,[status(thm)],[942])).
% 2.74/3.00 tff(944,plain,
% 2.74/3.00 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[943])).
% 2.74/3.00 tff(945,plain,
% 2.74/3.00 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 2.74/3.00 inference(quant_inst,[status(thm)],[])).
% 2.74/3.00 tff(946,plain,
% 2.74/3.00 (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[945, 9])).
% 2.74/3.00 tff(947,plain,
% 2.74/3.00 (s(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 2.74/3.00 inference(symmetry,[status(thm)],[946])).
% 2.74/3.00 tff(948,plain,
% 2.74/3.00 (s(s(s(elem!1))) = elem!1),
% 2.74/3.00 inference(transitivity,[status(thm)],[947, 944, 304])).
% 2.74/3.00 tff(949,assumption,(~(s(s(s(elem!1))) = elem!1)), introduced(assumption)).
% 2.74/3.00 tff(950,plain,
% 2.74/3.00 ($false),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[949, 948])).
% 2.74/3.00 tff(951,plain,((~(s(elem!1) = s(s(s(s(elem!1)))))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/3.00 tff(952,plain,
% 2.74/3.00 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[951, 941])).
% 2.74/3.00 tff(953,plain,
% 2.74/3.00 (r(s(elem!1), s(s(s(s(elem!1))))) <=> r(s(z), s(s(s(s(z)))))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[929, 932])).
% 2.74/3.00 tff(954,plain,
% 2.74/3.00 (r(s(z), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.74/3.00 inference(symmetry,[status(thm)],[953])).
% 2.74/3.00 tff(955,plain,
% 2.74/3.00 ((~r(s(z), s(s(s(s(z)))))) <=> (~r(s(elem!1), s(s(s(s(elem!1))))))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[954])).
% 2.74/3.00 tff(956,plain,
% 2.74/3.00 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(z), s(s(s(s(z)))))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[929])).
% 2.74/3.00 tff(957,plain,
% 2.74/3.00 ((~r(s(elem!1), s(s(s(s(z)))))) <=> (~r(s(z), s(s(s(s(z))))))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[956])).
% 2.74/3.00 tff(958,plain,
% 2.74/3.00 (~r(s(z), s(s(s(s(z)))))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[926, 957])).
% 2.74/3.00 tff(959,plain,
% 2.74/3.00 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[958, 955])).
% 2.74/3.00 tff(960,plain,
% 2.74/3.00 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), s(s(s(s(elem!1))))) | r(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), s(s(s(s(elem!1))))) | r(s(elem!1), s(s(s(s(elem!1))))))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(961,plain,
% 2.74/3.00 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), s(s(s(s(elem!1))))) | r(s(elem!1), s(s(s(s(elem!1))))))),
% 2.74/3.00 inference(quant_inst,[status(thm)],[])).
% 2.74/3.00 tff(962,plain,
% 2.74/3.00 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), s(s(s(s(elem!1))))) | r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[961, 960])).
% 2.74/3.00 tff(963,plain,
% 2.74/3.00 ((s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), s(s(s(s(elem!1))))) | r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[962, 41])).
% 2.74/3.00 tff(964,plain,
% 2.74/3.00 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[963, 959, 952])).
% 2.74/3.00 tff(965,plain,
% 2.74/3.00 (b(s(z), s(s(s(s(z)))))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[964, 935])).
% 2.74/3.00 tff(966,plain,
% 2.74/3.00 ((s(s(elem!1)) = elem!1) <=> (s(s(elem!1)) = z)),
% 2.74/3.00 inference(monotonicity,[status(thm)],[928])).
% 2.74/3.00 tff(967,plain,
% 2.74/3.00 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 2.74/3.00 inference(symmetry,[status(thm)],[966])).
% 2.74/3.00 tff(968,plain,
% 2.74/3.00 ((~(s(s(elem!1)) = z)) <=> (~(s(s(elem!1)) = elem!1))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[967])).
% 2.74/3.00 tff(969,plain,
% 2.74/3.00 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(elem!1)) = z))),
% 2.74/3.00 inference(quant_inst,[status(thm)],[])).
% 2.74/3.00 tff(970,plain,
% 2.74/3.00 (~(s(s(elem!1)) = z)),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[969, 28])).
% 2.74/3.00 tff(971,plain,
% 2.74/3.00 (~(s(s(elem!1)) = elem!1)),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[970, 968])).
% 2.74/3.00 tff(972,assumption,(s(elem!1) = s(s(elem!1))), introduced(assumption)).
% 2.74/3.00 tff(973,plain,
% 2.74/3.00 (inj_0(s(elem!1)) = inj_0(s(s(elem!1)))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[972])).
% 2.74/3.00 tff(974,plain,
% 2.74/3.00 (inj_0(s(s(elem!1))) = inj_0(s(elem!1))),
% 2.74/3.00 inference(symmetry,[status(thm)],[973])).
% 2.74/3.00 tff(975,plain,
% 2.74/3.00 (s(elem!1) = inj_0(s(s(elem!1)))),
% 2.74/3.00 inference(symmetry,[status(thm)],[328])).
% 2.74/3.00 tff(976,plain,
% 2.74/3.00 (s(s(elem!1)) = s(elem!1)),
% 2.74/3.00 inference(symmetry,[status(thm)],[972])).
% 2.74/3.00 tff(977,plain,
% 2.74/3.00 (s(s(elem!1)) = elem!1),
% 2.74/3.00 inference(transitivity,[status(thm)],[976, 975, 974, 304])).
% 2.74/3.00 tff(978,plain,
% 2.74/3.00 ($false),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[346, 977])).
% 2.74/3.00 tff(979,plain,((~(s(elem!1) = s(s(elem!1)))) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/3.00 tff(980,plain,
% 2.74/3.00 (~(s(elem!1) = s(s(elem!1)))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[979, 971])).
% 2.74/3.00 tff(981,plain,
% 2.74/3.00 ((s(s(elem!1)) = s(elem!1)) <=> (s(elem!1) = s(s(elem!1)))),
% 2.74/3.00 inference(commutativity,[status(thm)],[])).
% 2.74/3.00 tff(982,assumption,(s(s(elem!1)) = s(elem!1)), introduced(assumption)).
% 2.74/3.00 tff(983,plain,
% 2.74/3.00 (s(elem!1) = s(s(elem!1))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[982, 981])).
% 2.74/3.00 tff(984,assumption,(~(s(elem!1) = s(s(elem!1)))), introduced(assumption)).
% 2.74/3.00 tff(985,plain,
% 2.74/3.00 ($false),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[984, 983])).
% 2.74/3.00 tff(986,plain,((~(s(s(elem!1)) = s(elem!1))) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.00 tff(987,plain,
% 2.74/3.00 (~(s(s(elem!1)) = s(elem!1))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[986, 980])).
% 2.74/3.00 tff(988,plain,
% 2.74/3.00 (r(s(s(elem!1)), z) <=> r(s(s(z)), z)),
% 2.74/3.00 inference(monotonicity,[status(thm)],[930])).
% 2.74/3.00 tff(989,plain,
% 2.74/3.00 (r(s(s(z)), z) <=> r(s(s(elem!1)), z)),
% 2.74/3.00 inference(symmetry,[status(thm)],[988])).
% 2.74/3.00 tff(990,plain,
% 2.74/3.00 (r(s(s(elem!1)), z)),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[106, 989])).
% 2.74/3.00 tff(991,assumption,(r(s(s(elem!1)), z)), introduced(assumption)).
% 2.74/3.00 tff(992,assumption,(r(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 2.74/3.00 tff(993,plain,
% 2.74/3.00 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(994,plain,
% 2.74/3.00 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.74/3.00 inference(quant_inst,[status(thm)],[])).
% 2.74/3.00 tff(995,plain,
% 2.74/3.00 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1)))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[994, 993])).
% 2.74/3.00 tff(996,plain,
% 2.74/3.00 ($false),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[995, 118, 844, 992, 991])).
% 2.74/3.00 tff(997,plain,((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.00 tff(998,plain,
% 2.74/3.00 (~r(s(s(elem!1)), s(elem!1))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[997, 990, 844])).
% 2.74/3.00 tff(999,assumption,(~r(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 2.74/3.00 tff(1000,assumption,(~(s(s(elem!1)) = s(elem!1))), introduced(assumption)).
% 2.74/3.00 tff(1001,assumption,(~b(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 2.74/3.00 tff(1002,plain,
% 2.74/3.00 (((~![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)))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(1003,plain,
% 2.74/3.00 ((~![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)))),
% 2.74/3.00 inference(quant_inst,[status(thm)],[])).
% 2.74/3.00 tff(1004,plain,
% 2.74/3.00 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[1003, 1002])).
% 2.74/3.00 tff(1005,plain,
% 2.74/3.00 ($false),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[1004, 41, 1001, 1000, 999])).
% 2.74/3.00 tff(1006,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,[]))).
% 2.74/3.00 tff(1007,plain,
% 2.74/3.00 (b(s(s(elem!1)), s(elem!1))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[1006, 998, 987])).
% 2.74/3.00 tff(1008,plain,
% 2.74/3.00 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(z)), s(z))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[930, 929])).
% 2.74/3.00 tff(1009,plain,
% 2.74/3.00 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 2.74/3.00 inference(symmetry,[status(thm)],[1008])).
% 2.74/3.00 tff(1010,plain,
% 2.74/3.00 ((~b(s(s(z)), s(z))) <=> (~b(s(s(elem!1)), s(elem!1)))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[1009])).
% 2.74/3.00 tff(1011,assumption,(~b(s(s(z)), s(z))), introduced(assumption)).
% 2.74/3.00 tff(1012,plain,
% 2.74/3.00 (~b(s(s(elem!1)), s(elem!1))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[1011, 1010])).
% 2.74/3.00 tff(1013,assumption,(b(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 2.74/3.00 tff(1014,plain,
% 2.74/3.00 ($false),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[1013, 1012])).
% 2.74/3.00 tff(1015,plain,(b(s(s(z)), s(z)) | (~b(s(s(elem!1)), s(elem!1))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.00 tff(1016,plain,
% 2.74/3.00 (b(s(s(z)), s(z))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[1015, 1007, 928])).
% 2.74/3.00 tff(1017,plain,
% 2.74/3.00 (b(s(elem!1), s(s(elem!1))) <=> b(s(z), s(s(z)))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[929, 930])).
% 2.74/3.00 tff(1018,plain,
% 2.74/3.00 (r(s(elem!1), s(s(elem!1))) <=> r(s(z), s(s(z)))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[929, 930])).
% 2.74/3.00 tff(1019,plain,
% 2.74/3.00 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.74/3.00 inference(symmetry,[status(thm)],[1018])).
% 2.74/3.00 tff(1020,plain,
% 2.74/3.00 ((~r(s(z), s(s(z)))) <=> (~r(s(elem!1), s(s(elem!1))))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[1019])).
% 2.74/3.00 tff(1021,plain,
% 2.74/3.00 (r(s(elem!1), s(s(z))) <=> r(s(z), s(s(z)))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[929])).
% 2.74/3.00 tff(1022,plain,
% 2.74/3.00 ((~r(s(elem!1), s(s(z)))) <=> (~r(s(z), s(s(z))))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[1021])).
% 2.74/3.00 tff(1023,plain,
% 2.74/3.00 (~r(s(z), s(s(z)))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[927, 1022])).
% 2.74/3.00 tff(1024,plain,
% 2.74/3.00 (~r(s(elem!1), s(s(elem!1)))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[1023, 1020])).
% 2.74/3.00 tff(1025,plain,
% 2.74/3.00 (((~![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))))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(1026,plain,
% 2.74/3.00 ((~![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))))),
% 2.74/3.00 inference(quant_inst,[status(thm)],[])).
% 2.74/3.00 tff(1027,plain,
% 2.74/3.00 ((~![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)))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[1026, 1025])).
% 2.74/3.00 tff(1028,plain,
% 2.74/3.00 ((s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[1027, 41])).
% 2.74/3.00 tff(1029,plain,
% 2.74/3.00 (b(s(elem!1), s(s(elem!1)))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[1028, 1024, 980])).
% 2.74/3.00 tff(1030,plain,
% 2.74/3.00 (b(s(z), s(s(z)))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[1029, 1017])).
% 2.74/3.00 tff(1031,plain,
% 2.74/3.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(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)))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(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)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(1032,plain,
% 2.74/3.00 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), s(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)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(1033,plain,
% 2.74/3.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(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)))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[1032])).
% 2.74/3.00 tff(1034,plain,
% 2.74/3.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(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)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.74/3.00 inference(transitivity,[status(thm)],[1033, 1031])).
% 2.74/3.00 tff(1035,plain,
% 2.74/3.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 2.74/3.00 inference(quant_inst,[status(thm)],[])).
% 2.74/3.00 tff(1036,plain,
% 2.74/3.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[1035, 1034])).
% 2.74/3.00 tff(1037,plain,
% 2.74/3.00 ($false),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[1036, 178, 1030, 167, 202, 1016, 965])).
% 2.74/3.00 tff(1038,plain,((~(elem!1 = z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(elem!1), z)) | (~r(s(s(z)), z)) | r(s(elem!1), s(s(s(s(z))))) | r(s(elem!1), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.00 tff(1039,plain,
% 2.74/3.00 (~(elem!1 = z)),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[1038, 927, 202, 844, 106, 926, 165])).
% 2.74/3.00 tff(1040,plain,
% 2.74/3.00 (~(z = elem!1)),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[317, 1039])).
% 2.74/3.00 tff(1041,assumption,(~r(s(s(s(s(z)))), s(elem!1))), introduced(assumption)).
% 2.74/3.00 tff(1042,plain,
% 2.74/3.00 (r(elem!1, s(s(z)))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[467, 312, 461])).
% 2.74/3.00 tff(1043,plain,
% 2.74/3.00 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(z)))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[515])).
% 2.74/3.00 tff(1044,plain,
% 2.74/3.00 (r(elem!1, s(s(z))) <=> r(elem!1, s(elem!1))),
% 2.74/3.00 inference(symmetry,[status(thm)],[1043])).
% 2.74/3.00 tff(1045,plain,
% 2.74/3.00 (r(elem!1, s(elem!1))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[450, 1044])).
% 2.74/3.00 tff(1046,plain,
% 2.74/3.00 ($false),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[744, 1045])).
% 2.74/3.00 tff(1047,plain,((~(s(elem!1) = s(s(z)))) | r(elem!1, s(elem!1)) | (~r(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.00 tff(1048,plain,
% 2.74/3.00 (~(s(elem!1) = s(s(z)))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[1047, 1042, 744])).
% 2.74/3.00 tff(1049,plain,
% 2.74/3.00 (b(s(elem!1), s(s(z)))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[421, 1048, 927])).
% 2.74/3.00 tff(1050,plain,
% 2.74/3.00 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1))))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(1051,plain,
% 2.74/3.00 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1))))),
% 2.74/3.00 inference(quant_inst,[status(thm)],[])).
% 2.74/3.00 tff(1052,plain,
% 2.74/3.01 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1)))),
% 2.74/3.01 inference(modus_ponens,[status(thm)],[1051, 1050])).
% 2.74/3.01 tff(1053,plain,
% 2.74/3.01 (~r(s(s(z)), s(elem!1))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[1052, 118, 844, 106])).
% 2.74/3.01 tff(1054,assumption,(s(s(z)) = s(elem!1)), introduced(assumption)).
% 2.74/3.01 tff(1055,plain,
% 2.74/3.01 (s(elem!1) = s(s(z))),
% 2.74/3.01 inference(symmetry,[status(thm)],[1054])).
% 2.74/3.01 tff(1056,assumption,(~(s(elem!1) = s(s(z)))), introduced(assumption)).
% 2.74/3.01 tff(1057,plain,
% 2.74/3.01 ($false),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[1056, 1055])).
% 2.74/3.01 tff(1058,plain,((~(s(s(z)) = s(elem!1))) | (s(elem!1) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.01 tff(1059,plain,
% 2.74/3.01 (~(s(s(z)) = s(elem!1))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[1058, 1048])).
% 2.74/3.01 tff(1060,assumption,(~(s(s(z)) = s(elem!1))), introduced(assumption)).
% 2.74/3.01 tff(1061,assumption,(~b(s(s(z)), s(elem!1))), introduced(assumption)).
% 2.74/3.01 tff(1062,assumption,(~r(s(s(z)), s(elem!1))), introduced(assumption)).
% 2.74/3.01 tff(1063,plain,
% 2.74/3.01 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1)))),
% 2.74/3.01 inference(rewrite,[status(thm)],[])).
% 2.74/3.01 tff(1064,plain,
% 2.74/3.01 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1)))),
% 2.74/3.01 inference(quant_inst,[status(thm)],[])).
% 2.74/3.01 tff(1065,plain,
% 2.74/3.01 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1))),
% 2.74/3.01 inference(modus_ponens,[status(thm)],[1064, 1063])).
% 2.74/3.01 tff(1066,plain,
% 2.74/3.01 ($false),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[1065, 41, 1062, 1061, 1060])).
% 2.74/3.01 tff(1067,plain,((s(s(z)) = s(elem!1)) | r(s(s(z)), s(elem!1)) | b(s(s(z)), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.01 tff(1068,plain,
% 2.74/3.01 (b(s(s(z)), s(elem!1))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[1067, 1059, 1053])).
% 2.74/3.01 tff(1069,assumption,(b(s(elem!1), s(s(s(s(z)))))), introduced(assumption)).
% 2.74/3.01 tff(1070,assumption,(b(s(elem!1), s(s(z)))), introduced(assumption)).
% 2.74/3.01 tff(1071,assumption,(b(s(s(z)), s(elem!1))), introduced(assumption)).
% 2.74/3.01 tff(1072,plain,
% 2.74/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.74/3.01 inference(rewrite,[status(thm)],[])).
% 2.74/3.01 tff(1073,plain,
% 2.74/3.01 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.74/3.01 inference(rewrite,[status(thm)],[])).
% 2.74/3.01 tff(1074,plain,
% 2.74/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 2.74/3.01 inference(monotonicity,[status(thm)],[1073])).
% 2.74/3.01 tff(1075,plain,
% 2.74/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.74/3.01 inference(transitivity,[status(thm)],[1074, 1072])).
% 2.74/3.01 tff(1076,plain,
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% 2.74/3.01 inference(modus_ponens,[status(thm)],[1082, 1081])).
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% 2.74/3.01 inference(unit_resolution,[status(thm)],[1084, 1080, 926])).
% 2.74/3.01 tff(1086,plain,
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% 2.74/3.01 inference(monotonicity,[status(thm)],[1088])).
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% 2.74/3.01 inference(monotonicity,[status(thm)],[1088])).
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% 2.74/3.01 inference(monotonicity,[status(thm)],[1092])).
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% 2.74/3.01 tff(1095,plain,
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% 2.74/3.01 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
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% 2.74/3.01 inference(modus_ponens,[status(thm)],[1112, 1111])).
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% 2.74/3.01 inference(modus_ponens,[status(thm)],[1113, 1110])).
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% 2.74/3.01 (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))),
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% 2.74/3.01 inference(monotonicity,[status(thm)],[1119])).
% 2.74/3.01 tff(1121,plain,
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% 2.74/3.01 inference(monotonicity,[status(thm)],[1120])).
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% 2.74/3.01 inference(monotonicity,[status(thm)],[1120])).
% 2.74/3.01 tff(1123,plain,
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% 2.74/3.01 inference(monotonicity,[status(thm)],[1123])).
% 2.74/3.01 tff(1125,assumption,(r(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 2.74/3.01 tff(1126,assumption,(b(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 2.74/3.01 tff(1127,assumption,(b(s(s(s(z))), z)), introduced(assumption)).
% 2.74/3.01 tff(1128,plain,
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% 2.74/3.01 inference(symmetry,[status(thm)],[1121])).
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% 2.74/3.01 ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) <=> (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 2.74/3.01 inference(monotonicity,[status(thm)],[1128])).
% 2.74/3.01 tff(1130,assumption,(r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))), introduced(assumption)).
% 2.74/3.01 tff(1131,plain,
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% 2.74/3.01 inference(modus_ponens,[status(thm)],[1135, 1134])).
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% 2.74/3.01 tff(1138,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.01 tff(1139,plain,
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% 2.74/3.01 tff(1140,plain,
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% 2.74/3.01 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.74/3.01 inference(modus_ponens,[status(thm)],[1142, 1141])).
% 2.74/3.01 tff(1144,plain,
% 2.74/3.01 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[1143, 118, 1130, 145])).
% 2.74/3.01 tff(1145,plain,
% 2.74/3.01 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[271, 1144])).
% 2.74/3.01 tff(1146,assumption,(b(s(s(s(s(s(s(s(z))))))), s(s(z)))), introduced(assumption)).
% 2.74/3.01 tff(1147,plain,
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% 2.74/3.01 tff(1148,plain,
% 2.74/3.01 (((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z))) <=> ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), 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))))))), z)))),
% 2.74/3.01 inference(rewrite,[status(thm)],[])).
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% 2.74/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), 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))))))), z))))),
% 2.74/3.01 inference(monotonicity,[status(thm)],[1148])).
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% 2.74/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.74/3.01 inference(transitivity,[status(thm)],[1149, 1147])).
% 2.74/3.01 tff(1151,plain,
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% 2.74/3.01 inference(quant_inst,[status(thm)],[])).
% 2.74/3.01 tff(1152,plain,
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% 2.74/3.01 inference(modus_ponens,[status(thm)],[1151, 1150])).
% 2.74/3.01 tff(1153,plain,
% 2.74/3.01 ($false),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[1152, 178, 273, 166, 595, 146, 1146])).
% 2.74/3.01 tff(1154,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(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,[]))).
% 2.74/3.01 tff(1155,plain,
% 2.74/3.01 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[1154, 1145, 166, 273, 1140])).
% 2.74/3.01 tff(1156,plain,
% 2.74/3.01 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.74/3.01 inference(modus_ponens,[status(thm)],[1155, 1129])).
% 2.74/3.01 tff(1157,assumption,(s(s(s(s(elem!1)))) = s(s(z))), introduced(assumption)).
% 2.74/3.01 tff(1158,plain,
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% 2.74/3.01 tff(1159,plain,
% 2.74/3.01 (inj_0(s(s(z))) = inj_0(s(s(s(s(elem!1)))))),
% 2.74/3.01 inference(monotonicity,[status(thm)],[1158])).
% 2.74/3.01 tff(1160,plain,
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% 2.74/3.01 inference(transitivity,[status(thm)],[71, 1159, 946])).
% 2.74/3.01 tff(1161,plain,
% 2.74/3.01 (inj_0(s(z)) = inj_0(s(s(s(elem!1))))),
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% 2.74/3.01 tff(1162,plain,
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% 2.74/3.01 inference(symmetry,[status(thm)],[1161])).
% 2.74/3.01 tff(1163,plain,
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% 2.74/3.01 tff(1164,plain,
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% 2.74/3.01 inference(unit_resolution,[status(thm)],[970, 1163])).
% 2.74/3.01 tff(1165,plain,(~(s(s(s(s(elem!1)))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.01 tff(1166,plain,
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% 2.74/3.01 tff(1167,plain,
% 2.74/3.01 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(z))) | b(s(s(s(s(elem!1)))), s(s(z))) | r(s(s(s(s(elem!1)))), s(s(z))))),
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% 2.74/3.01 tff(1168,plain,
% 2.74/3.01 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(z))) | b(s(s(s(s(elem!1)))), s(s(z))) | r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.74/3.01 inference(modus_ponens,[status(thm)],[1167, 1166])).
% 2.74/3.01 tff(1169,plain,
% 2.74/3.01 ((s(s(s(s(elem!1)))) = s(s(z))) | b(s(s(s(s(elem!1)))), s(s(z))) | r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[1168, 41])).
% 2.74/3.01 tff(1170,plain,
% 2.74/3.01 (b(s(s(s(s(elem!1)))), s(s(z))) | r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[1169, 1165])).
% 2.74/3.01 tff(1171,plain,
% 2.74/3.01 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[1170, 1156])).
% 2.74/3.01 tff(1172,plain,
% 2.74/3.01 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.74/3.01 inference(modus_ponens,[status(thm)],[1171, 1122])).
% 2.74/3.01 tff(1173,plain,
% 2.74/3.01 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
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% 2.74/3.01 tff(1174,plain,
% 2.74/3.01 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(s(s(z))))))),
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% 2.74/3.01 tff(1175,plain,
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% 2.74/3.02 tff(1178,plain,
% 2.74/3.02 ((~![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)))))),
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% 2.74/3.02 tff(1179,plain,
% 2.74/3.02 ((~![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))))),
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% 2.74/3.02 tff(1180,plain,
% 2.74/3.02 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 1176])).
% 2.74/3.02 tff(1181,plain,
% 2.74/3.02 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 2.74/3.02 inference(monotonicity,[status(thm)],[1117])).
% 2.74/3.02 tff(1182,plain,
% 2.74/3.02 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
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% 2.74/3.02 tff(1183,plain,
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% 2.74/3.02 tff(1184,plain,
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% 2.74/3.02 inference(monotonicity,[status(thm)],[1183])).
% 2.74/3.02 tff(1185,plain,
% 2.74/3.02 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.74/3.02 inference(symmetry,[status(thm)],[1184])).
% 2.74/3.02 tff(1186,plain,
% 2.74/3.02 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.74/3.02 inference(monotonicity,[status(thm)],[1183])).
% 2.74/3.02 tff(1187,plain,
% 2.74/3.02 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.74/3.02 inference(transitivity,[status(thm)],[1186, 836])).
% 2.74/3.02 tff(1188,plain,
% 2.74/3.02 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(s(s(s(s(z)))))))))),
% 2.74/3.02 inference(monotonicity,[status(thm)],[1187])).
% 2.74/3.02 tff(1189,plain,
% 2.74/3.02 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.74/3.02 inference(modus_ponens,[status(thm)],[1104, 1188])).
% 2.74/3.02 tff(1190,plain,
% 2.74/3.02 (r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.74/3.02 inference(monotonicity,[status(thm)],[1183])).
% 2.74/3.02 tff(1191,plain,
% 2.74/3.02 ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) <=> (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 2.74/3.02 inference(monotonicity,[status(thm)],[1190])).
% 2.74/3.02 tff(1192,plain,
% 2.74/3.02 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.74/3.02 inference(rewrite,[status(thm)],[])).
% 2.74/3.02 tff(1193,plain,
% 2.74/3.02 (((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(z)))))),
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% 2.74/3.02 tff(1194,plain,
% 2.74/3.02 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(z))))))),
% 2.74/3.02 inference(monotonicity,[status(thm)],[1193])).
% 2.74/3.02 tff(1195,plain,
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% 2.74/3.02 inference(transitivity,[status(thm)],[1194, 1192])).
% 2.74/3.02 tff(1196,plain,
% 2.74/3.02 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.74/3.02 inference(quant_inst,[status(thm)],[])).
% 2.74/3.02 tff(1197,plain,
% 2.74/3.02 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(z))))),
% 2.74/3.02 inference(modus_ponens,[status(thm)],[1196, 1195])).
% 2.74/3.02 tff(1198,plain,
% 2.74/3.02 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[1197, 118, 1125, 1172])).
% 2.74/3.02 tff(1199,plain,
% 2.74/3.02 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.74/3.02 inference(modus_ponens,[status(thm)],[1198, 1191])).
% 2.74/3.02 tff(1200,plain,
% 2.74/3.02 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[691, 1199, 1189])).
% 2.74/3.02 tff(1201,plain,
% 2.74/3.02 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.74/3.02 inference(modus_ponens,[status(thm)],[1200, 1185])).
% 2.74/3.02 tff(1202,plain,
% 2.74/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)))),
% 2.74/3.02 inference(rewrite,[status(thm)],[])).
% 2.74/3.02 tff(1203,plain,
% 2.74/3.02 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)))),
% 2.74/3.02 inference(rewrite,[status(thm)],[])).
% 2.74/3.02 tff(1204,plain,
% 2.74/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z))))),
% 2.74/3.02 inference(monotonicity,[status(thm)],[1203])).
% 2.74/3.02 tff(1205,plain,
% 2.74/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)))),
% 2.74/3.02 inference(transitivity,[status(thm)],[1204, 1202])).
% 2.74/3.02 tff(1206,plain,
% 2.74/3.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.74/3.02 inference(quant_inst,[status(thm)],[])).
% 2.74/3.02 tff(1207,plain,
% 2.74/3.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z))),
% 2.74/3.02 inference(modus_ponens,[status(thm)],[1206, 1205])).
% 2.74/3.02 tff(1208,plain,
% 2.74/3.02 ($false),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[1207, 178, 1145, 1140, 1127, 1201, 1180])).
% 2.74/3.02 tff(1209,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~(s(elem!1) = s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.02 tff(1210,plain,
% 2.74/3.02 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[1209, 166, 1117, 1125, 1127, 273, 145])).
% 2.74/3.02 tff(1211,plain,
% 2.74/3.02 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[84, 1210])).
% 2.74/3.02 tff(1212,plain,
% 2.74/3.02 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[1197, 118, 1125, 107])).
% 2.74/3.02 tff(1213,plain,
% 2.74/3.02 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.74/3.02 inference(modus_ponens,[status(thm)],[1212, 1191])).
% 2.74/3.02 tff(1214,plain,
% 2.74/3.02 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[691, 1213, 1189])).
% 2.74/3.02 tff(1215,plain,
% 2.74/3.02 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.74/3.02 inference(modus_ponens,[status(thm)],[1214, 1185])).
% 2.74/3.02 tff(1216,plain,
% 2.74/3.02 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[1175, 118, 1125, 107])).
% 2.74/3.02 tff(1217,plain,
% 2.74/3.02 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 1216])).
% 2.74/3.02 tff(1218,plain,
% 2.74/3.02 (elem!1 = s(s(s(z)))),
% 2.74/3.02 inference(transitivity,[status(thm)],[517, 1181, 11])).
% 2.74/3.02 tff(1219,plain,
% 2.74/3.02 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(z))))),
% 2.74/3.02 inference(monotonicity,[status(thm)],[1218])).
% 2.74/3.02 tff(1220,plain,
% 2.74/3.02 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), elem!1)),
% 2.74/3.02 inference(symmetry,[status(thm)],[1219])).
% 2.74/3.02 tff(1221,plain,
% 2.74/3.02 ((~b(s(s(z)), s(s(s(z))))) <=> (~b(s(s(z)), elem!1))),
% 2.74/3.02 inference(monotonicity,[status(thm)],[1220])).
% 2.74/3.02 tff(1222,plain,
% 2.74/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.74/3.02 inference(rewrite,[status(thm)],[])).
% 2.74/3.02 tff(1223,plain,
% 2.74/3.02 (((~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(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.74/3.02 inference(rewrite,[status(thm)],[])).
% 2.74/3.02 tff(1224,plain,
% 2.74/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 2.74/3.02 inference(monotonicity,[status(thm)],[1223])).
% 2.74/3.02 tff(1225,plain,
% 2.74/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.74/3.02 inference(transitivity,[status(thm)],[1224, 1222])).
% 2.74/3.02 tff(1226,plain,
% 2.74/3.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.74/3.02 inference(quant_inst,[status(thm)],[])).
% 2.74/3.02 tff(1227,plain,
% 2.74/3.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z)))))),
% 2.74/3.02 inference(modus_ponens,[status(thm)],[1226, 1225])).
% 2.74/3.02 tff(1228,plain,
% 2.74/3.02 ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z)))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[1227, 178, 104, 166, 1126])).
% 2.74/3.02 tff(1229,plain,
% 2.74/3.02 (~b(s(s(z)), s(s(s(z))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[1228, 1215])).
% 2.74/3.02 tff(1230,plain,
% 2.74/3.02 (~b(s(s(z)), elem!1)),
% 2.74/3.02 inference(modus_ponens,[status(thm)],[1229, 1221])).
% 2.74/3.02 tff(1231,plain,
% 2.74/3.02 (r(s(s(z)), elem!1)),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[448, 1230, 12])).
% 2.74/3.02 tff(1232,plain,
% 2.74/3.02 (~r(z, elem!1)),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[541, 1231, 106])).
% 2.74/3.02 tff(1233,plain,
% 2.74/3.02 (b(z, elem!1)),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[585, 1232, 507])).
% 2.74/3.02 tff(1234,plain,
% 2.74/3.02 (b(z, elem!1) <=> b(z, s(s(s(z))))),
% 2.74/3.02 inference(monotonicity,[status(thm)],[1218])).
% 2.74/3.02 tff(1235,plain,
% 2.74/3.02 (b(z, s(s(s(z))))),
% 2.74/3.02 inference(modus_ponens,[status(thm)],[818, 1234])).
% 2.74/3.02 tff(1236,assumption,(~b(z, s(s(s(z))))), introduced(assumption)).
% 2.74/3.02 tff(1237,plain,
% 2.74/3.02 ($false),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[1236, 1235])).
% 2.74/3.02 tff(1238,plain,((~b(z, elem!1)) | b(z, s(s(s(z)))) | (~(s(elem!1) = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.02 tff(1239,plain,
% 2.74/3.02 (b(z, s(s(s(z))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[1238, 1233, 1117])).
% 2.74/3.02 tff(1240,plain,
% 2.74/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)))),
% 2.74/3.02 inference(rewrite,[status(thm)],[])).
% 2.74/3.02 tff(1241,plain,
% 2.74/3.02 (((~b(z, s(s(s(z))))) | (~b(z, 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))))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)))),
% 2.74/3.02 inference(rewrite,[status(thm)],[])).
% 2.74/3.02 tff(1242,plain,
% 2.74/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z))))),
% 2.74/3.02 inference(monotonicity,[status(thm)],[1241])).
% 2.74/3.02 tff(1243,plain,
% 2.74/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)))),
% 2.74/3.02 inference(transitivity,[status(thm)],[1242, 1240])).
% 2.74/3.02 tff(1244,plain,
% 2.74/3.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.74/3.02 inference(quant_inst,[status(thm)],[])).
% 2.74/3.02 tff(1245,plain,
% 2.74/3.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z))),
% 2.74/3.02 inference(modus_ponens,[status(thm)],[1244, 1243])).
% 2.74/3.02 tff(1246,plain,
% 2.74/3.02 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[1245, 178, 1239, 1127, 1217, 1215])).
% 2.74/3.02 tff(1247,plain,
% 2.74/3.02 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[133, 1246])).
% 2.74/3.02 tff(1248,plain,
% 2.74/3.02 ($false),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[121, 118, 106, 1247, 107])).
% 2.74/3.02 tff(1249,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~(s(elem!1) = s(s(s(s(z)))))) | (z = elem!1) | (s(s(z)) = elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.02 tff(1250,plain,
% 2.74/3.02 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[1249, 1211, 1127, 1117, 507, 12, 106, 166, 1126, 1125])).
% 2.74/3.02 tff(1251,plain,
% 2.74/3.02 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.74/3.02 inference(modus_ponens,[status(thm)],[1250, 1124])).
% 2.74/3.02 tff(1252,plain,
% 2.74/3.02 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[1170, 1251])).
% 2.74/3.02 tff(1253,plain,
% 2.74/3.02 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.74/3.02 inference(modus_ponens,[status(thm)],[1252, 1121])).
% 2.74/3.02 tff(1254,plain,
% 2.74/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), 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(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), 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(z)))), s(s(z)))))),
% 2.87/3.03 inference(rewrite,[status(thm)],[])).
% 2.87/3.03 tff(1255,plain,
% 2.87/3.03 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(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(s(z)))))) | (~b(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(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(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(z)), 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(z)))), s(s(z)))))),
% 2.87/3.03 inference(rewrite,[status(thm)],[])).
% 2.87/3.03 tff(1256,plain,
% 2.87/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(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(s(z))))))), s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), 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(z)))), s(s(z))))))),
% 2.87/3.03 inference(monotonicity,[status(thm)],[1255])).
% 2.87/3.03 tff(1257,plain,
% 2.87/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(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(s(z))))))), s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), 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(z)))), s(s(z)))))),
% 2.87/3.03 inference(transitivity,[status(thm)],[1256, 1254])).
% 2.87/3.03 tff(1258,plain,
% 2.87/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(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(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.87/3.03 inference(quant_inst,[status(thm)],[])).
% 2.87/3.03 tff(1259,plain,
% 2.87/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 2.87/3.03 inference(modus_ponens,[status(thm)],[1258, 1257])).
% 2.87/3.03 tff(1260,plain,
% 2.87/3.03 ($false),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[1259, 178, 1211, 166, 165, 202, 1253])).
% 2.87/3.03 tff(1261,plain,((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~(s(elem!1) = s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (z = elem!1) | (s(s(z)) = elem!1) | (~r(s(s(z)), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.03 tff(1262,plain,
% 2.87/3.03 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[1261, 1085, 202, 1116, 1040, 12, 106, 1114, 1108, 273, 145])).
% 2.87/3.03 tff(1263,plain,
% 2.87/3.03 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[249, 1262])).
% 2.87/3.03 tff(1264,plain,
% 2.87/3.03 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.87/3.03 inference(symmetry,[status(thm)],[1190])).
% 2.87/3.03 tff(1265,assumption,(r(elem!1, s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.87/3.03 tff(1266,plain,
% 2.87/3.03 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.87/3.03 inference(modus_ponens,[status(thm)],[1265, 1264])).
% 2.87/3.03 tff(1267,plain,
% 2.87/3.03 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.87/3.03 inference(rewrite,[status(thm)],[])).
% 2.87/3.03 tff(1268,plain,
% 2.87/3.03 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.87/3.03 inference(quant_inst,[status(thm)],[])).
% 2.87/3.03 tff(1269,plain,
% 2.87/3.03 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(z))))),
% 2.87/3.03 inference(modus_ponens,[status(thm)],[1268, 1267])).
% 2.87/3.03 tff(1270,plain,
% 2.87/3.03 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[1269, 118, 224, 1125])).
% 2.87/3.03 tff(1271,plain,
% 2.87/3.03 ($false),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[1270, 1266])).
% 2.87/3.03 tff(1272,plain,((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~(s(elem!1) = s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.03 tff(1273,plain,
% 2.87/3.03 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[1272, 1085, 1263, 1108])).
% 2.87/3.03 tff(1274,plain,
% 2.87/3.03 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[691, 1273, 1105])).
% 2.87/3.03 tff(1275,plain,
% 2.87/3.03 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.87/3.03 inference(modus_ponens,[status(thm)],[1274, 1090])).
% 2.87/3.03 tff(1276,plain,
% 2.87/3.03 (b(s(s(z)), s(s(s(z))))),
% 2.87/3.03 inference(modus_ponens,[status(thm)],[543, 1219])).
% 2.87/3.03 tff(1277,plain,
% 2.87/3.03 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), elem!1)),
% 2.87/3.03 inference(monotonicity,[status(thm)],[1183])).
% 2.87/3.03 tff(1278,plain,
% 2.87/3.03 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 2.87/3.03 inference(symmetry,[status(thm)],[1277])).
% 2.87/3.03 tff(1279,plain,
% 2.87/3.03 (b(s(elem!1), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 2.87/3.03 inference(monotonicity,[status(thm)],[1117])).
% 2.87/3.03 tff(1280,plain,
% 2.87/3.03 (b(s(elem!1), elem!1) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 2.87/3.03 inference(transitivity,[status(thm)],[1279, 1278])).
% 2.87/3.03 tff(1281,plain,
% 2.87/3.03 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 2.87/3.03 inference(rewrite,[status(thm)],[])).
% 2.87/3.03 tff(1282,plain,
% 2.87/3.03 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 2.87/3.03 inference(quant_inst,[status(thm)],[])).
% 2.87/3.03 tff(1283,plain,
% 2.87/3.03 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))),
% 2.87/3.03 inference(modus_ponens,[status(thm)],[1282, 1281])).
% 2.87/3.03 tff(1284,plain,
% 2.87/3.03 ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[1283, 118])).
% 2.87/3.03 tff(1285,plain,
% 2.87/3.03 (~r(s(elem!1), elem!1)),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[1284, 521, 844])).
% 2.87/3.03 tff(1286,plain,
% 2.87/3.03 (b(s(elem!1), elem!1)),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[677, 1285, 725])).
% 2.87/3.03 tff(1287,plain,
% 2.87/3.03 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.87/3.03 inference(modus_ponens,[status(thm)],[1286, 1280])).
% 2.87/3.03 tff(1288,plain,
% 2.87/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), 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(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), 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(z))))))),
% 2.87/3.03 inference(rewrite,[status(thm)],[])).
% 2.87/3.03 tff(1289,plain,
% 2.87/3.03 (((~b(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(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(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(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.87/3.03 inference(rewrite,[status(thm)],[])).
% 2.87/3.03 tff(1290,plain,
% 2.87/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), 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(z)))))))),
% 2.87/3.03 inference(monotonicity,[status(thm)],[1289])).
% 2.87/3.03 tff(1291,plain,
% 2.87/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), 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(z))))))),
% 2.87/3.03 inference(transitivity,[status(thm)],[1290, 1288])).
% 2.87/3.03 tff(1292,plain,
% 2.87/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.87/3.03 inference(quant_inst,[status(thm)],[])).
% 2.87/3.03 tff(1293,plain,
% 2.87/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))),
% 2.87/3.03 inference(modus_ponens,[status(thm)],[1292, 1291])).
% 2.87/3.03 tff(1294,plain,
% 2.87/3.03 ($false),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[1293, 178, 167, 202, 1126, 1287, 1276])).
% 2.87/3.03 tff(1295,plain,((~r(z, elem!1)) | (~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)))))) | (~(s(elem!1) = s(s(s(s(z)))))) | (s(elem!1) = elem!1) | (s(s(z)) = elem!1) | (~r(s(elem!1), z)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.03 tff(1296,plain,
% 2.87/3.03 (~r(z, elem!1)),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[1295, 1114, 202, 165, 1085, 725, 12, 844, 106])).
% 2.87/3.03 tff(1297,plain,
% 2.87/3.03 (b(z, elem!1)),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[585, 1296, 1040])).
% 2.87/3.03 tff(1298,plain,
% 2.87/3.03 (b(z, s(s(s(z))))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[1238, 1297, 1085])).
% 2.87/3.03 tff(1299,plain,
% 2.87/3.03 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[232, 1263, 106])).
% 2.87/3.03 tff(1300,plain,
% 2.87/3.03 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[271, 1299])).
% 2.87/3.03 tff(1301,assumption,(b(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 2.87/3.03 tff(1302,plain,
% 2.87/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.87/3.03 inference(rewrite,[status(thm)],[])).
% 2.87/3.03 tff(1303,plain,
% 2.87/3.03 (((~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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.87/3.03 inference(rewrite,[status(thm)],[])).
% 2.87/3.03 tff(1304,plain,
% 2.87/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 2.87/3.03 inference(monotonicity,[status(thm)],[1303])).
% 2.87/3.03 tff(1305,plain,
% 2.87/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.87/3.03 inference(transitivity,[status(thm)],[1304, 1302])).
% 2.87/3.03 tff(1306,plain,
% 2.87/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)))),
% 2.87/3.03 inference(quant_inst,[status(thm)],[])).
% 2.87/3.03 tff(1307,plain,
% 2.87/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 2.87/3.03 inference(modus_ponens,[status(thm)],[1306, 1305])).
% 2.87/3.03 tff(1308,plain,
% 2.87/3.03 ($false),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[1307, 178, 818, 104, 869, 1301, 595])).
% 2.87/3.03 tff(1309,plain,((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.03 tff(1310,plain,
% 2.87/3.03 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[1309, 1274, 1300, 1113, 1297])).
% 2.87/3.03 tff(1311,plain,
% 2.87/3.03 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[84, 1310])).
% 2.87/3.03 tff(1312,plain,
% 2.87/3.03 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[1138, 1311, 145])).
% 2.87/3.03 tff(1313,plain,
% 2.87/3.03 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[133, 1312])).
% 2.87/3.03 tff(1314,plain,
% 2.87/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)))),
% 2.87/3.03 inference(rewrite,[status(thm)],[])).
% 2.87/3.03 tff(1315,plain,
% 2.87/3.03 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)))),
% 2.87/3.03 inference(rewrite,[status(thm)],[])).
% 2.87/3.03 tff(1316,plain,
% 2.87/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z))))),
% 2.87/3.03 inference(monotonicity,[status(thm)],[1315])).
% 2.87/3.03 tff(1317,plain,
% 2.87/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)))),
% 2.87/3.03 inference(transitivity,[status(thm)],[1316, 1314])).
% 2.87/3.03 tff(1318,plain,
% 2.87/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))))),
% 2.87/3.03 inference(quant_inst,[status(thm)],[])).
% 2.87/3.03 tff(1319,plain,
% 2.87/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z))),
% 2.87/3.03 inference(modus_ponens,[status(thm)],[1318, 1317])).
% 2.87/3.03 tff(1320,plain,
% 2.87/3.03 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[1319, 178, 1300, 1313, 1298, 1116])).
% 2.87/3.03 tff(1321,plain,
% 2.87/3.03 ($false),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[1320, 1275])).
% 2.87/3.03 tff(1322,plain,((s(s(z)) = elem!1) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (s(elem!1) = elem!1) | (~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | r(s(elem!1), s(s(s(s(z))))) | r(s(elem!1), s(s(z))) | r(elem!1, s(elem!1)) | b(elem!1, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.03 tff(1323,plain,
% 2.87/3.03 (s(s(z)) = elem!1),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[1322, 461, 202, 725, 844, 106, 273, 506, 926, 927, 744, 145])).
% 2.87/3.03 tff(1324,assumption,(s(s(z)) = elem!1), introduced(assumption)).
% 2.87/3.03 tff(1325,plain,
% 2.87/3.03 (r(s(s(z)), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 2.87/3.03 inference(monotonicity,[status(thm)],[1324])).
% 2.87/3.03 tff(1326,plain,
% 2.87/3.03 (r(elem!1, s(elem!1)) <=> r(s(s(z)), s(elem!1))),
% 2.87/3.03 inference(symmetry,[status(thm)],[1325])).
% 2.87/3.03 tff(1327,plain,
% 2.87/3.03 ((~r(elem!1, s(elem!1))) <=> (~r(s(s(z)), s(elem!1)))),
% 2.87/3.03 inference(monotonicity,[status(thm)],[1326])).
% 2.87/3.03 tff(1328,plain,
% 2.87/3.03 (~r(s(s(z)), s(elem!1))),
% 2.87/3.03 inference(modus_ponens,[status(thm)],[744, 1327])).
% 2.87/3.03 tff(1329,assumption,(r(s(s(z)), s(elem!1))), introduced(assumption)).
% 2.87/3.03 tff(1330,plain,
% 2.87/3.03 ($false),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[1329, 1328])).
% 2.87/3.03 tff(1331,plain,(r(elem!1, s(elem!1)) | (~r(s(s(z)), s(elem!1))) | (~(s(s(z)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.03 tff(1332,plain,
% 2.87/3.03 (~r(s(s(z)), s(elem!1))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[1331, 1324, 744])).
% 2.87/3.03 tff(1333,plain,
% 2.87/3.03 (s(s(z)) = s(elem!1)),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[1067, 1332, 1061])).
% 2.87/3.03 tff(1334,plain,
% 2.87/3.03 (s(elem!1) = s(s(z))),
% 2.87/3.03 inference(symmetry,[status(thm)],[1333])).
% 2.87/3.03 tff(1335,plain,
% 2.87/3.03 (s(elem!1) = elem!1),
% 2.87/3.03 inference(transitivity,[status(thm)],[1334, 1324])).
% 2.87/3.03 tff(1336,plain,
% 2.87/3.03 ($false),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[725, 1335])).
% 2.87/3.03 tff(1337,plain,((~(s(s(z)) = elem!1)) | (s(elem!1) = elem!1) | b(s(s(z)), s(elem!1)) | r(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.03 tff(1338,plain,
% 2.87/3.03 (b(s(s(z)), s(elem!1))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[1337, 1323, 744, 725])).
% 2.87/3.03 tff(1339,plain,
% 2.87/3.03 (r(s(s(z)), z) <=> r(elem!1, z)),
% 2.87/3.03 inference(monotonicity,[status(thm)],[1324])).
% 2.87/3.03 tff(1340,plain,
% 2.87/3.03 (r(elem!1, z) <=> r(s(s(z)), z)),
% 2.87/3.03 inference(symmetry,[status(thm)],[1339])).
% 2.87/3.03 tff(1341,plain,
% 2.87/3.03 ((~r(elem!1, z)) <=> (~r(s(s(z)), z))),
% 2.87/3.03 inference(monotonicity,[status(thm)],[1340])).
% 2.87/3.03 tff(1342,assumption,(~r(elem!1, z)), introduced(assumption)).
% 2.87/3.03 tff(1343,plain,
% 2.87/3.03 (~r(s(s(z)), z)),
% 2.87/3.03 inference(modus_ponens,[status(thm)],[1342, 1341])).
% 2.87/3.03 tff(1344,plain,
% 2.87/3.03 ($false),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[106, 1343])).
% 2.87/3.03 tff(1345,plain,((~(s(s(z)) = elem!1)) | (~r(s(s(z)), z)) | r(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 2.87/3.03 tff(1346,plain,
% 2.87/3.03 (r(elem!1, z)),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[1345, 1323, 106])).
% 2.87/3.03 tff(1347,plain,
% 2.87/3.03 (~r(elem!1, s(s(z)))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[458, 1346, 106])).
% 2.87/3.03 tff(1348,plain,
% 2.87/3.03 (elem!1 = s(s(z))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[467, 1347, 461])).
% 2.87/3.03 tff(1349,plain,
% 2.87/3.03 (s(s(s(z))) = s(s(z))),
% 2.87/3.03 inference(transitivity,[status(thm)],[61, 1182, 304, 308])).
% 2.87/3.03 tff(1350,plain,
% 2.87/3.03 (s(s(s(s(z)))) = s(s(s(z)))),
% 2.87/3.03 inference(monotonicity,[status(thm)],[1349])).
% 2.87/3.03 tff(1351,plain,
% 2.87/3.03 (s(s(s(s(z)))) = elem!1),
% 2.87/3.03 inference(transitivity,[status(thm)],[1350, 61, 1182, 304])).
% 2.87/3.03 tff(1352,plain,
% 2.87/3.03 ($false),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[323, 1351])).
% 2.87/3.03 tff(1353,plain,((~(elem!1 = s(s(z)))) | (s(s(s(s(z)))) = elem!1) | (~(s(elem!1) = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.04 tff(1354,plain,
% 2.87/3.04 (~(s(elem!1) = s(s(s(s(z)))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[1353, 1348, 323])).
% 2.87/3.04 tff(1355,plain,
% 2.87/3.04 (b(s(elem!1), s(s(s(s(z)))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[1084, 1354, 926])).
% 2.87/3.04 tff(1356,plain,
% 2.87/3.04 (~b(s(elem!1), s(s(z)))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[1079, 1355, 165, 202, 1338])).
% 2.87/3.04 tff(1357,plain,
% 2.87/3.04 (s(elem!1) = s(s(z))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[421, 1356, 927])).
% 2.87/3.04 tff(1358,plain,
% 2.87/3.04 ((s(s(z)) = s(elem!1)) <=> (s(elem!1) = s(s(z)))),
% 2.87/3.04 inference(commutativity,[status(thm)],[])).
% 2.87/3.04 tff(1359,plain,
% 2.87/3.04 ((s(elem!1) = s(s(z))) <=> (s(s(z)) = s(elem!1))),
% 2.87/3.04 inference(symmetry,[status(thm)],[1358])).
% 2.87/3.04 tff(1360,plain,
% 2.87/3.04 (s(s(z)) = s(elem!1)),
% 2.87/3.04 inference(modus_ponens,[status(thm)],[515, 1359])).
% 2.87/3.04 tff(1361,plain,
% 2.87/3.04 ($false),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[1060, 1360])).
% 2.87/3.04 tff(1362,plain,((~(s(elem!1) = s(s(z)))) | (s(s(z)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.04 tff(1363,plain,
% 2.87/3.04 (s(s(z)) = s(elem!1)),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[1362, 1357])).
% 2.87/3.04 tff(1364,plain,
% 2.87/3.04 (s(elem!1) = s(s(z))),
% 2.87/3.04 inference(symmetry,[status(thm)],[1363])).
% 2.87/3.04 tff(1365,plain,
% 2.87/3.04 (s(elem!1) = elem!1),
% 2.87/3.04 inference(transitivity,[status(thm)],[1364, 1323])).
% 2.87/3.04 tff(1366,plain,
% 2.87/3.04 ($false),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[725, 1365])).
% 2.87/3.04 tff(1367,plain,(b(elem!1, s(s(z))) | (s(elem!1) = elem!1) | r(s(elem!1), s(s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | r(s(elem!1), s(s(s(s(z))))) | (s(s(s(s(z)))) = elem!1) | (~r(s(s(z)), z)) | r(elem!1, s(elem!1)) | (~r(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.04 tff(1368,plain,
% 2.87/3.04 (b(elem!1, s(s(z)))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[1367, 744, 927, 202, 926, 551, 106, 725, 844, 273, 506, 145])).
% 2.87/3.04 tff(1369,assumption,(~(s(elem!1) = s(s(s(s(z)))))), introduced(assumption)).
% 2.87/3.04 tff(1370,plain,
% 2.87/3.04 (b(s(elem!1), s(s(s(s(z)))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[1084, 1369, 926])).
% 2.87/3.04 tff(1371,plain,
% 2.87/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(z)))) | (~b(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.87/3.04 inference(rewrite,[status(thm)],[])).
% 2.87/3.04 tff(1372,plain,
% 2.87/3.04 (((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(s(z))))) <=> ((~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.87/3.04 inference(rewrite,[status(thm)],[])).
% 2.87/3.04 tff(1373,plain,
% 2.87/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 2.87/3.04 inference(monotonicity,[status(thm)],[1372])).
% 2.87/3.04 tff(1374,plain,
% 2.87/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.87/3.04 inference(transitivity,[status(thm)],[1373, 1371])).
% 2.87/3.04 tff(1375,plain,
% 2.87/3.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(s(z)))))),
% 2.87/3.04 inference(quant_inst,[status(thm)],[])).
% 2.87/3.04 tff(1376,plain,
% 2.87/3.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 2.87/3.04 inference(modus_ponens,[status(thm)],[1375, 1374])).
% 2.87/3.04 tff(1377,plain,
% 2.87/3.04 (~b(s(s(z)), s(elem!1))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[1376, 178, 854, 812, 1370, 165])).
% 2.87/3.04 tff(1378,plain,
% 2.87/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.87/3.04 inference(rewrite,[status(thm)],[])).
% 2.87/3.04 tff(1379,plain,
% 2.87/3.04 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.87/3.04 inference(rewrite,[status(thm)],[])).
% 2.87/3.04 tff(1380,plain,
% 2.87/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 2.87/3.04 inference(monotonicity,[status(thm)],[1379])).
% 2.87/3.04 tff(1381,plain,
% 2.87/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.87/3.04 inference(transitivity,[status(thm)],[1380, 1378])).
% 2.87/3.04 tff(1382,plain,
% 2.87/3.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(elem!1))))),
% 2.87/3.04 inference(quant_inst,[status(thm)],[])).
% 2.87/3.04 tff(1383,plain,
% 2.87/3.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 2.87/3.04 inference(modus_ponens,[status(thm)],[1382, 1381])).
% 2.87/3.04 tff(1384,plain,
% 2.87/3.04 (~b(s(elem!1), s(s(z)))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[1383, 178, 854, 812, 1370, 165])).
% 2.87/3.04 tff(1385,plain,
% 2.87/3.04 (s(elem!1) = s(s(z))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[421, 1384, 927])).
% 2.87/3.04 tff(1386,plain,
% 2.87/3.04 (b(z, s(elem!1)) <=> b(z, s(s(z)))),
% 2.87/3.04 inference(monotonicity,[status(thm)],[515])).
% 2.87/3.04 tff(1387,plain,
% 2.87/3.04 (b(z, s(s(z))) <=> b(z, s(elem!1))),
% 2.87/3.04 inference(symmetry,[status(thm)],[1386])).
% 2.87/3.04 tff(1388,plain,
% 2.87/3.04 (b(z, s(elem!1))),
% 2.87/3.04 inference(modus_ponens,[status(thm)],[273, 1387])).
% 2.87/3.04 tff(1389,plain,
% 2.87/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, z)))),
% 2.87/3.04 inference(rewrite,[status(thm)],[])).
% 2.87/3.04 tff(1390,plain,
% 2.87/3.04 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, z))) <=> ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, z)))),
% 2.87/3.04 inference(rewrite,[status(thm)],[])).
% 2.87/3.04 tff(1391,plain,
% 2.87/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, z))))),
% 2.87/3.04 inference(monotonicity,[status(thm)],[1390])).
% 2.87/3.04 tff(1392,plain,
% 2.87/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, z)))),
% 2.87/3.04 inference(transitivity,[status(thm)],[1391, 1389])).
% 2.87/3.04 tff(1393,plain,
% 2.87/3.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, z)))),
% 2.87/3.04 inference(quant_inst,[status(thm)],[])).
% 2.87/3.04 tff(1394,plain,
% 2.87/3.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, z))),
% 2.87/3.04 inference(modus_ponens,[status(thm)],[1393, 1392])).
% 2.87/3.04 tff(1395,plain,
% 2.87/3.04 ($false),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[1394, 178, 818, 506, 855, 683, 854])).
% 2.87/3.04 tff(1396,plain,((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.04 tff(1397,plain,
% 2.87/3.04 (~b(s(elem!1), elem!1)),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[1396, 818, 506, 854, 1388])).
% 2.87/3.04 tff(1398,plain,
% 2.87/3.04 (r(s(elem!1), elem!1)),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[677, 1397, 725])).
% 2.87/3.04 tff(1399,plain,
% 2.87/3.04 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 2.87/3.04 inference(monotonicity,[status(thm)],[546])).
% 2.87/3.04 tff(1400,plain,
% 2.87/3.04 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 2.87/3.04 inference(symmetry,[status(thm)],[1399])).
% 2.87/3.04 tff(1401,plain,
% 2.87/3.04 (r(s(s(z)), s(s(s(s(s(z)))))) <=> r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.87/3.04 inference(monotonicity,[status(thm)],[1400])).
% 2.87/3.04 tff(1402,plain,
% 2.87/3.04 (r(s(s(z)), s(s(s(s(elem!1))))) <=> r(s(s(z)), s(s(s(s(s(z))))))),
% 2.87/3.04 inference(symmetry,[status(thm)],[1401])).
% 2.87/3.04 tff(1403,assumption,(r(s(s(z)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.87/3.04 tff(1404,plain,
% 2.87/3.04 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.87/3.04 inference(modus_ponens,[status(thm)],[1403, 1402])).
% 2.87/3.04 tff(1405,plain,
% 2.87/3.04 ((z = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = z)),
% 2.87/3.04 inference(commutativity,[status(thm)],[])).
% 2.87/3.04 tff(1406,plain,
% 2.87/3.04 ((s(s(s(s(s(z))))) = z) <=> (z = s(s(s(s(s(z))))))),
% 2.87/3.04 inference(symmetry,[status(thm)],[1405])).
% 2.87/3.04 tff(1407,plain,
% 2.87/3.04 ((~(s(s(s(s(s(z))))) = z)) <=> (~(z = s(s(s(s(s(z)))))))),
% 2.87/3.04 inference(monotonicity,[status(thm)],[1406])).
% 2.87/3.04 tff(1408,plain,
% 2.87/3.04 (~(z = s(s(s(s(s(z))))))),
% 2.87/3.04 inference(modus_ponens,[status(thm)],[242, 1407])).
% 2.87/3.04 tff(1409,plain,
% 2.87/3.04 ((s(s(s(s(elem!1)))) = elem!1) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 2.87/3.04 inference(commutativity,[status(thm)],[])).
% 2.87/3.04 tff(1410,plain,
% 2.87/3.04 ((s(s(s(s(s(z))))) = s(z)) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.87/3.04 inference(monotonicity,[status(thm)],[1400, 534])).
% 2.87/3.04 tff(1411,plain,
% 2.87/3.04 ((s(s(s(s(s(z))))) = s(z)) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 2.87/3.04 inference(transitivity,[status(thm)],[1410, 1409])).
% 2.87/3.04 tff(1412,plain,
% 2.87/3.04 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(s(z))))) = s(z))),
% 2.87/3.04 inference(symmetry,[status(thm)],[1411])).
% 2.87/3.04 tff(1413,plain,
% 2.87/3.04 ((~(elem!1 = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(s(z))))) = s(z)))),
% 2.87/3.04 inference(monotonicity,[status(thm)],[1412])).
% 2.87/3.04 tff(1414,assumption,(elem!1 = s(s(s(s(elem!1))))), introduced(assumption)).
% 2.87/3.04 tff(1415,plain,
% 2.87/3.04 (s(s(z)) = s(elem!1)),
% 2.87/3.04 inference(symmetry,[status(thm)],[515])).
% 2.87/3.04 tff(1416,plain,
% 2.87/3.04 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 2.87/3.04 inference(monotonicity,[status(thm)],[1415])).
% 2.87/3.04 tff(1417,plain,
% 2.87/3.04 (s(z) = s(s(s(s(s(z)))))),
% 2.87/3.04 inference(transitivity,[status(thm)],[71, 1416, 304, 1414, 1399])).
% 2.87/3.04 tff(1418,plain,
% 2.87/3.04 (inj_0(s(z)) = inj_0(s(s(s(s(s(z))))))),
% 2.87/3.04 inference(monotonicity,[status(thm)],[1417])).
% 2.87/3.04 tff(1419,plain,
% 2.87/3.04 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(z))),
% 2.87/3.04 inference(symmetry,[status(thm)],[1418])).
% 2.87/3.04 tff(1420,plain,
% 2.87/3.04 (s(s(s(s(z)))) = z),
% 2.87/3.04 inference(transitivity,[status(thm)],[663, 1419, 51])).
% 2.87/3.04 tff(1421,plain,
% 2.87/3.04 ($false),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[30, 1420])).
% 2.87/3.04 tff(1422,plain,((~(elem!1 = s(s(s(s(elem!1)))))) | (~(s(elem!1) = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.04 tff(1423,plain,
% 2.87/3.04 (~(elem!1 = s(s(s(s(elem!1)))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[1422, 515])).
% 2.87/3.04 tff(1424,plain,
% 2.87/3.04 (~(s(s(s(s(s(z))))) = s(z))),
% 2.87/3.04 inference(modus_ponens,[status(thm)],[1423, 1413])).
% 2.87/3.04 tff(1425,plain,
% 2.87/3.04 (r(s(elem!1), elem!1) <=> r(s(s(z)), elem!1)),
% 2.87/3.04 inference(monotonicity,[status(thm)],[515])).
% 2.87/3.04 tff(1426,assumption,(r(s(elem!1), elem!1)), introduced(assumption)).
% 2.87/3.04 tff(1427,plain,
% 2.87/3.04 (r(s(s(z)), elem!1)),
% 2.87/3.04 inference(modus_ponens,[status(thm)],[1426, 1425])).
% 2.87/3.04 tff(1428,plain,
% 2.87/3.04 (r(s(s(z)), s(z)) <=> r(s(s(z)), elem!1)),
% 2.87/3.04 inference(monotonicity,[status(thm)],[534])).
% 2.87/3.04 tff(1429,plain,
% 2.87/3.04 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(z))),
% 2.87/3.04 inference(symmetry,[status(thm)],[1428])).
% 2.87/3.04 tff(1430,plain,
% 2.87/3.04 (r(s(s(z)), s(z))),
% 2.87/3.04 inference(modus_ponens,[status(thm)],[438, 1429])).
% 2.87/3.04 tff(1431,assumption,(r(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 2.87/3.04 tff(1432,plain,
% 2.87/3.04 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.87/3.04 inference(rewrite,[status(thm)],[])).
% 2.87/3.04 tff(1433,plain,
% 2.87/3.04 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.87/3.04 inference(quant_inst,[status(thm)],[])).
% 2.87/3.04 tff(1434,plain,
% 2.87/3.04 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 2.87/3.04 inference(modus_ponens,[status(thm)],[1433, 1432])).
% 2.87/3.04 tff(1435,plain,
% 2.87/3.04 ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[1434, 118, 1431])).
% 2.87/3.04 tff(1436,plain,
% 2.87/3.04 ($false),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[1435, 1404, 1430])).
% 2.87/3.04 tff(1437,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~(s(elem!1) = s(s(z)))) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.04 tff(1438,plain,
% 2.87/3.04 (~r(s(s(s(s(s(z))))), s(z))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[1437, 1403, 515, 1427])).
% 2.87/3.04 tff(1439,plain,
% 2.87/3.04 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z)))),
% 2.87/3.04 inference(rewrite,[status(thm)],[])).
% 2.87/3.04 tff(1440,plain,
% 2.87/3.04 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z)))),
% 2.87/3.04 inference(quant_inst,[status(thm)],[])).
% 2.87/3.04 tff(1441,plain,
% 2.87/3.04 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z))),
% 2.87/3.04 inference(modus_ponens,[status(thm)],[1440, 1439])).
% 2.87/3.04 tff(1442,plain,
% 2.87/3.04 ((s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[1441, 41, 1438])).
% 2.87/3.04 tff(1443,plain,
% 2.87/3.04 (b(s(s(s(s(s(z))))), s(z))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[1442, 1424])).
% 2.87/3.04 tff(1444,plain,
% 2.87/3.04 (b(s(z), s(s(s(s(s(z)))))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 2.87/3.04 inference(monotonicity,[status(thm)],[1400])).
% 2.87/3.04 tff(1445,plain,
% 2.87/3.04 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(s(z))))))),
% 2.87/3.04 inference(symmetry,[status(thm)],[1444])).
% 2.87/3.04 tff(1446,plain,
% 2.87/3.04 (b(elem!1, s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 2.87/3.04 inference(monotonicity,[status(thm)],[518])).
% 2.87/3.04 tff(1447,plain,
% 2.87/3.04 (b(elem!1, s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(s(z))))))),
% 2.87/3.04 inference(transitivity,[status(thm)],[1446, 1445])).
% 2.87/3.04 tff(1448,plain,
% 2.87/3.04 (r(s(elem!1), s(s(s(s(elem!1))))) <=> r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.87/3.04 inference(monotonicity,[status(thm)],[515])).
% 2.87/3.04 tff(1449,plain,
% 2.87/3.04 (r(s(s(z)), s(s(s(s(elem!1))))) <=> r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.87/3.04 inference(symmetry,[status(thm)],[1448])).
% 2.87/3.04 tff(1450,plain,
% 2.87/3.04 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.87/3.04 inference(modus_ponens,[status(thm)],[1403, 1449])).
% 2.87/3.04 tff(1451,assumption,(r(s(elem!1), s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.87/3.04 tff(1452,assumption,(r(elem!1, s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.87/3.04 tff(1453,plain,
% 2.87/3.04 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.87/3.04 inference(rewrite,[status(thm)],[])).
% 2.87/3.04 tff(1454,plain,
% 2.87/3.04 (((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.87/3.04 inference(rewrite,[status(thm)],[])).
% 2.87/3.04 tff(1455,plain,
% 2.87/3.04 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1))))))))),
% 2.87/3.04 inference(monotonicity,[status(thm)],[1454])).
% 2.87/3.04 tff(1456,plain,
% 2.87/3.04 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.87/3.04 inference(transitivity,[status(thm)],[1455, 1453])).
% 2.87/3.04 tff(1457,plain,
% 2.87/3.04 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)))),
% 2.87/3.04 inference(quant_inst,[status(thm)],[])).
% 2.87/3.04 tff(1458,plain,
% 2.87/3.04 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1))))))),
% 2.87/3.04 inference(modus_ponens,[status(thm)],[1457, 1456])).
% 2.87/3.04 tff(1459,plain,
% 2.87/3.04 ($false),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[1458, 118, 1452, 1426, 1451])).
% 2.87/3.04 tff(1460,plain,((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.04 tff(1461,plain,
% 2.87/3.04 (~r(elem!1, s(s(s(s(elem!1)))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[1460, 1450, 1426])).
% 2.87/3.04 tff(1462,plain,
% 2.87/3.04 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1))))))),
% 2.87/3.04 inference(rewrite,[status(thm)],[])).
% 2.87/3.04 tff(1463,plain,
% 2.87/3.04 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1))))))),
% 2.87/3.04 inference(quant_inst,[status(thm)],[])).
% 2.87/3.04 tff(1464,plain,
% 2.87/3.04 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1)))))),
% 2.87/3.04 inference(modus_ponens,[status(thm)],[1463, 1462])).
% 2.87/3.04 tff(1465,plain,
% 2.87/3.04 ((elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1)))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[1464, 41])).
% 2.87/3.04 tff(1466,plain,
% 2.87/3.04 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[1465, 1461, 1423])).
% 2.87/3.04 tff(1467,plain,
% 2.87/3.04 (b(s(z), s(s(s(s(s(z))))))),
% 2.87/3.04 inference(modus_ponens,[status(thm)],[1466, 1447])).
% 2.87/3.04 tff(1468,plain,
% 2.87/3.04 (b(z, s(z)) <=> b(z, elem!1)),
% 2.87/3.04 inference(monotonicity,[status(thm)],[534])).
% 2.87/3.04 tff(1469,plain,
% 2.87/3.04 (b(z, elem!1) <=> b(z, s(z))),
% 2.87/3.04 inference(symmetry,[status(thm)],[1468])).
% 2.87/3.04 tff(1470,plain,
% 2.87/3.04 (b(z, s(z))),
% 2.87/3.04 inference(modus_ponens,[status(thm)],[818, 1469])).
% 2.87/3.04 tff(1471,plain,
% 2.87/3.04 ((s(z) = z) <=> (elem!1 = z)),
% 2.87/3.04 inference(monotonicity,[status(thm)],[534])).
% 2.87/3.04 tff(1472,plain,
% 2.87/3.04 ((s(z) = z) <=> (z = elem!1)),
% 2.87/3.04 inference(transitivity,[status(thm)],[1471, 313])).
% 2.87/3.04 tff(1473,plain,
% 2.87/3.04 ((s(z) = z) <=> (elem!1 = z)),
% 2.87/3.04 inference(transitivity,[status(thm)],[1472, 314])).
% 2.87/3.04 tff(1474,plain,
% 2.87/3.04 ((~(s(z) = z)) <=> (~(elem!1 = z))),
% 2.87/3.04 inference(monotonicity,[status(thm)],[1473])).
% 2.87/3.04 tff(1475,plain,
% 2.87/3.04 ((~![X: $i] : (~(s(X) = z))) | (~(s(z) = z))),
% 2.87/3.04 inference(quant_inst,[status(thm)],[])).
% 2.87/3.05 tff(1476,plain,
% 2.87/3.05 (~(s(z) = z)),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[1475, 28])).
% 2.87/3.05 tff(1477,plain,
% 2.87/3.05 (~(elem!1 = z)),
% 2.87/3.05 inference(modus_ponens,[status(thm)],[1476, 1474])).
% 2.87/3.05 tff(1478,plain,
% 2.87/3.05 (~r(elem!1, z)),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[443, 106, 1427])).
% 2.87/3.05 tff(1479,plain,
% 2.87/3.05 (b(elem!1, z)),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[498, 1478, 1477])).
% 2.87/3.05 tff(1480,plain,
% 2.87/3.05 (b(s(z), z)),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[593, 1479, 515])).
% 2.87/3.05 tff(1481,plain,
% 2.87/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(z, s(z))))),
% 2.87/3.05 inference(rewrite,[status(thm)],[])).
% 2.87/3.05 tff(1482,plain,
% 2.87/3.05 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z))) <=> ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(z, s(z))))),
% 2.87/3.05 inference(rewrite,[status(thm)],[])).
% 2.87/3.05 tff(1483,plain,
% 2.87/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(z, s(z)))))),
% 2.87/3.05 inference(monotonicity,[status(thm)],[1482])).
% 2.87/3.05 tff(1484,plain,
% 2.87/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(z, s(z))))),
% 2.87/3.05 inference(transitivity,[status(thm)],[1483, 1481])).
% 2.87/3.05 tff(1485,plain,
% 2.87/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)))),
% 2.87/3.05 inference(quant_inst,[status(thm)],[])).
% 2.87/3.05 tff(1486,plain,
% 2.87/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(z, s(z)))),
% 2.87/3.05 inference(modus_ponens,[status(thm)],[1485, 1484])).
% 2.87/3.05 tff(1487,plain,
% 2.87/3.05 (~b(z, s(s(s(s(s(z))))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[1486, 178, 1480, 1470, 1467, 1443])).
% 2.87/3.05 tff(1488,plain,
% 2.87/3.05 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z)))))))),
% 2.87/3.05 inference(rewrite,[status(thm)],[])).
% 2.87/3.05 tff(1489,plain,
% 2.87/3.05 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z)))))))),
% 2.87/3.05 inference(quant_inst,[status(thm)],[])).
% 2.87/3.05 tff(1490,plain,
% 2.87/3.05 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z))))))),
% 2.87/3.05 inference(modus_ponens,[status(thm)],[1489, 1488])).
% 2.87/3.05 tff(1491,plain,
% 2.87/3.05 ((z = s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z))))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[1490, 41, 1487])).
% 2.87/3.05 tff(1492,plain,
% 2.87/3.05 (r(z, s(s(s(s(s(z))))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[1491, 1408])).
% 2.87/3.05 tff(1493,plain,
% 2.87/3.05 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.87/3.05 inference(rewrite,[status(thm)],[])).
% 2.87/3.05 tff(1494,plain,
% 2.87/3.05 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.87/3.05 inference(rewrite,[status(thm)],[])).
% 2.87/3.05 tff(1495,plain,
% 2.87/3.05 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.87/3.05 inference(monotonicity,[status(thm)],[1494])).
% 2.87/3.05 tff(1496,plain,
% 2.87/3.05 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.87/3.05 inference(transitivity,[status(thm)],[1495, 1493])).
% 2.87/3.05 tff(1497,plain,
% 2.87/3.05 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), z)))),
% 2.87/3.05 inference(quant_inst,[status(thm)],[])).
% 2.87/3.05 tff(1498,plain,
% 2.87/3.05 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 2.87/3.05 inference(modus_ponens,[status(thm)],[1497, 1496])).
% 2.87/3.05 tff(1499,plain,
% 2.87/3.05 ($false),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[1498, 118, 106, 1492, 1404])).
% 2.87/3.05 tff(1500,plain,((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~(s(elem!1) = s(s(z)))) | (~r(s(elem!1), elem!1)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.05 tff(1501,plain,
% 2.87/3.05 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[1500, 1398, 106, 515, 818])).
% 2.87/3.05 tff(1502,plain,
% 2.87/3.05 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.87/3.05 inference(monotonicity,[status(thm)],[340])).
% 2.87/3.05 tff(1503,plain,
% 2.87/3.05 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 2.87/3.05 inference(symmetry,[status(thm)],[1502])).
% 2.87/3.05 tff(1504,plain,
% 2.87/3.05 (s(s(elem!1)) = elem!1),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[348, 340])).
% 2.87/3.05 tff(1505,plain,
% 2.87/3.05 (elem!1 = s(s(elem!1))),
% 2.87/3.05 inference(symmetry,[status(thm)],[1504])).
% 2.87/3.05 tff(1506,plain,
% 2.87/3.05 (elem!1 = s(s(s(s(elem!1))))),
% 2.87/3.05 inference(transitivity,[status(thm)],[1505, 1503])).
% 2.87/3.05 tff(1507,assumption,(~(elem!1 = s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.87/3.05 tff(1508,plain,
% 2.87/3.05 ($false),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[1507, 1506])).
% 2.87/3.05 tff(1509,plain,((~(s(s(s(elem!1))) = s(elem!1))) | (elem!1 = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.05 tff(1510,plain,
% 2.87/3.05 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[1509, 1423])).
% 2.87/3.05 tff(1511,plain,
% 2.87/3.05 (r(s(s(s(s(s(z))))), z) <=> r(s(s(s(s(elem!1)))), z)),
% 2.87/3.05 inference(monotonicity,[status(thm)],[1400])).
% 2.87/3.05 tff(1512,plain,
% 2.87/3.05 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(s(z))))), z)),
% 2.87/3.05 inference(symmetry,[status(thm)],[1511])).
% 2.87/3.05 tff(1513,plain,
% 2.87/3.05 (b(s(s(s(s(s(z))))), z) <=> b(s(s(s(s(elem!1)))), z)),
% 2.87/3.05 inference(monotonicity,[status(thm)],[1400])).
% 2.87/3.05 tff(1514,plain,
% 2.87/3.05 ((~b(s(s(s(s(s(z))))), z)) <=> (~b(s(s(s(s(elem!1)))), z))),
% 2.87/3.05 inference(monotonicity,[status(thm)],[1513])).
% 2.87/3.05 tff(1515,plain,
% 2.87/3.05 (r(s(z), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 2.87/3.05 inference(monotonicity,[status(thm)],[534])).
% 2.87/3.05 tff(1516,plain,
% 2.87/3.05 (r(elem!1, s(s(s(s(z))))) <=> r(s(z), s(s(s(s(z)))))),
% 2.87/3.05 inference(symmetry,[status(thm)],[1515])).
% 2.87/3.05 tff(1517,plain,
% 2.87/3.05 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(s(z)))))),
% 2.87/3.05 inference(monotonicity,[status(thm)],[546])).
% 2.87/3.05 tff(1518,assumption,(b(s(s(z)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.87/3.05 tff(1519,assumption,(s(s(s(elem!1))) = elem!1), introduced(assumption)).
% 2.87/3.05 tff(1520,plain,
% 2.87/3.05 (s(s(s(s(elem!1)))) = s(elem!1)),
% 2.87/3.05 inference(monotonicity,[status(thm)],[1519])).
% 2.87/3.05 tff(1521,plain,
% 2.87/3.05 (b(s(s(z)), s(s(s(s(elem!1))))) <=> b(s(s(z)), s(elem!1))),
% 2.87/3.05 inference(monotonicity,[status(thm)],[1520])).
% 2.87/3.05 tff(1522,plain,
% 2.87/3.05 (b(s(s(z)), s(elem!1))),
% 2.87/3.05 inference(modus_ponens,[status(thm)],[1518, 1521])).
% 2.87/3.05 tff(1523,plain,
% 2.87/3.05 ($false),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[1061, 1522])).
% 2.87/3.05 tff(1524,plain,((~b(s(s(z)), s(s(s(s(elem!1)))))) | b(s(s(z)), s(elem!1)) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.05 tff(1525,plain,
% 2.87/3.05 (~(s(s(s(elem!1))) = elem!1)),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[1524, 1518, 1061])).
% 2.87/3.05 tff(1526,plain,
% 2.87/3.05 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 2.87/3.05 inference(commutativity,[status(thm)],[])).
% 2.87/3.05 tff(1527,assumption,(elem!1 = s(s(s(elem!1)))), introduced(assumption)).
% 2.87/3.05 tff(1528,plain,
% 2.87/3.05 (s(s(s(elem!1))) = elem!1),
% 2.87/3.05 inference(modus_ponens,[status(thm)],[1527, 1526])).
% 2.87/3.05 tff(1529,plain,
% 2.87/3.05 ($false),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[949, 1528])).
% 2.87/3.05 tff(1530,plain,((~(elem!1 = s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.87/3.05 tff(1531,plain,
% 2.87/3.05 (~(elem!1 = s(s(s(elem!1))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[1530, 1525])).
% 2.87/3.05 tff(1532,plain,
% 2.87/3.05 (r(s(elem!1), z)),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[906, 106, 515])).
% 2.87/3.05 tff(1533,plain,
% 2.87/3.05 ((s(elem!1) = elem!1) <=> (s(s(z)) = elem!1)),
% 2.87/3.05 inference(monotonicity,[status(thm)],[515])).
% 2.87/3.05 tff(1534,plain,
% 2.87/3.05 ((~(s(elem!1) = elem!1)) <=> (~(s(s(z)) = elem!1))),
% 2.87/3.05 inference(monotonicity,[status(thm)],[1533])).
% 2.87/3.05 tff(1535,assumption,(elem!1 = s(s(elem!1))), introduced(assumption)).
% 2.87/3.05 tff(1536,plain,
% 2.87/3.05 (s(elem!1) = s(s(s(elem!1)))),
% 2.87/3.05 inference(monotonicity,[status(thm)],[1535])).
% 2.87/3.05 tff(1537,plain,
% 2.87/3.05 (s(s(s(elem!1))) = s(elem!1)),
% 2.87/3.05 inference(symmetry,[status(thm)],[1536])).
% 2.87/3.05 tff(1538,plain,
% 2.87/3.05 ($false),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[356, 1537])).
% 2.87/3.05 tff(1539,plain,((~(elem!1 = s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.05 tff(1540,plain,
% 2.87/3.05 (~(elem!1 = s(s(elem!1)))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[1539, 356])).
% 2.87/3.05 tff(1541,plain,
% 2.87/3.05 ((elem!1 = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 2.87/3.05 inference(commutativity,[status(thm)],[])).
% 2.87/3.05 tff(1542,plain,
% 2.87/3.05 ((s(s(elem!1)) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 2.87/3.05 inference(symmetry,[status(thm)],[1541])).
% 2.87/3.05 tff(1543,plain,
% 2.87/3.05 (elem!1 = s(s(elem!1))),
% 2.87/3.05 inference(modus_ponens,[status(thm)],[329, 1542])).
% 2.87/3.05 tff(1544,assumption,(~(elem!1 = s(s(elem!1)))), introduced(assumption)).
% 2.87/3.05 tff(1545,plain,
% 2.87/3.05 ($false),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[1544, 1543])).
% 2.87/3.05 tff(1546,plain,((~(s(s(elem!1)) = elem!1)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.05 tff(1547,plain,
% 2.87/3.05 (~(s(s(elem!1)) = elem!1)),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[1546, 1540])).
% 2.87/3.05 tff(1548,plain,
% 2.87/3.05 (~(s(elem!1) = elem!1)),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[672, 1547])).
% 2.87/3.05 tff(1549,plain,
% 2.87/3.05 (~(s(s(z)) = elem!1)),
% 2.87/3.05 inference(modus_ponens,[status(thm)],[1548, 1534])).
% 2.87/3.05 tff(1550,plain,
% 2.87/3.05 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(z)))), z)),
% 2.87/3.05 inference(monotonicity,[status(thm)],[546])).
% 2.87/3.05 tff(1551,assumption,(r(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 2.87/3.05 tff(1552,assumption,(r(s(s(s(elem!1))), z)), introduced(assumption)).
% 2.87/3.05 tff(1553,plain,
% 2.87/3.05 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 2.87/3.05 inference(rewrite,[status(thm)],[])).
% 2.87/3.05 tff(1554,plain,
% 2.87/3.05 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 2.87/3.05 inference(quant_inst,[status(thm)],[])).
% 2.87/3.05 tff(1555,plain,
% 2.87/3.05 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 2.87/3.05 inference(modus_ponens,[status(thm)],[1554, 1553])).
% 2.87/3.05 tff(1556,plain,
% 2.87/3.05 ($false),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[1555, 118, 1551, 844, 1552])).
% 2.87/3.05 tff(1557,plain,((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.05 tff(1558,plain,
% 2.87/3.05 (~r(s(s(s(elem!1))), z)),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[1557, 1551, 844])).
% 2.87/3.05 tff(1559,assumption,(~b(s(s(s(elem!1))), z)), introduced(assumption)).
% 2.87/3.05 tff(1560,assumption,(~r(s(s(s(elem!1))), z)), introduced(assumption)).
% 2.87/3.05 tff(1561,plain,
% 2.87/3.05 (((~![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))),
% 2.87/3.05 inference(rewrite,[status(thm)],[])).
% 2.87/3.05 tff(1562,plain,
% 2.87/3.05 ((~![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))),
% 2.87/3.05 inference(quant_inst,[status(thm)],[])).
% 2.87/3.05 tff(1563,plain,
% 2.87/3.05 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = z) | b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z)),
% 2.87/3.05 inference(modus_ponens,[status(thm)],[1562, 1561])).
% 2.87/3.05 tff(1564,plain,
% 2.87/3.05 ($false),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[1563, 41, 940, 1560, 1559])).
% 2.87/3.05 tff(1565,plain,(b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 2.87/3.05 tff(1566,plain,
% 2.87/3.05 (b(s(s(s(elem!1))), z)),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[1565, 1558])).
% 2.87/3.05 tff(1567,plain,
% 2.87/3.05 (b(s(s(s(s(z)))), z)),
% 2.87/3.05 inference(modus_ponens,[status(thm)],[1566, 1550])).
% 2.87/3.05 tff(1568,plain,
% 2.87/3.05 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(z)))), elem!1)),
% 2.87/3.05 inference(monotonicity,[status(thm)],[534])).
% 2.87/3.05 tff(1569,plain,
% 2.87/3.05 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 2.87/3.05 inference(symmetry,[status(thm)],[1568])).
% 2.87/3.05 tff(1570,plain,
% 2.87/3.05 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 2.87/3.05 inference(monotonicity,[status(thm)],[546])).
% 2.87/3.05 tff(1571,plain,
% 2.87/3.05 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 2.87/3.05 inference(transitivity,[status(thm)],[1570, 1569])).
% 2.87/3.05 tff(1572,plain,
% 2.87/3.05 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 2.87/3.05 inference(rewrite,[status(thm)],[])).
% 2.87/3.05 tff(1573,plain,
% 2.87/3.05 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 2.87/3.05 inference(quant_inst,[status(thm)],[])).
% 2.87/3.05 tff(1574,plain,
% 2.87/3.05 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 2.87/3.05 inference(modus_ponens,[status(thm)],[1573, 1572])).
% 2.87/3.05 tff(1575,plain,
% 2.87/3.05 ($false),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[1574, 118, 1551, 1426, 556])).
% 2.87/3.05 tff(1576,plain,((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.05 tff(1577,plain,
% 2.87/3.05 (~r(s(s(s(elem!1))), elem!1)),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[1576, 1551, 1426])).
% 2.87/3.05 tff(1578,plain,
% 2.87/3.05 (b(s(s(s(elem!1))), elem!1)),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[570, 1577, 949])).
% 2.87/3.05 tff(1579,plain,
% 2.87/3.05 (b(s(s(s(s(z)))), s(z))),
% 2.87/3.05 inference(modus_ponens,[status(thm)],[1578, 1571])).
% 2.87/3.05 tff(1580,plain,
% 2.87/3.05 (b(s(z), z)),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[593, 506, 515])).
% 2.87/3.05 tff(1581,plain,
% 2.87/3.05 (r(s(z), s(s(z))) <=> r(elem!1, s(s(z)))),
% 2.87/3.05 inference(monotonicity,[status(thm)],[534])).
% 2.87/3.05 tff(1582,plain,
% 2.87/3.05 (r(elem!1, s(s(z))) <=> r(s(z), s(s(z)))),
% 2.87/3.05 inference(symmetry,[status(thm)],[1581])).
% 2.87/3.05 tff(1583,plain,
% 2.87/3.05 ((~r(elem!1, s(s(z)))) <=> (~r(s(z), s(s(z))))),
% 2.87/3.05 inference(monotonicity,[status(thm)],[1582])).
% 2.87/3.05 tff(1584,plain,
% 2.87/3.05 ((~r(elem!1, s(elem!1))) <=> (~r(elem!1, s(s(z))))),
% 2.87/3.05 inference(monotonicity,[status(thm)],[1043])).
% 2.87/3.05 tff(1585,plain,
% 2.87/3.05 (~(elem!1 = s(s(s(elem!1))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[1530, 949])).
% 2.87/3.05 tff(1586,assumption,(~(elem!1 = s(s(s(elem!1))))), introduced(assumption)).
% 2.87/3.05 tff(1587,assumption,(r(elem!1, s(elem!1))), introduced(assumption)).
% 2.87/3.05 tff(1588,plain,
% 2.87/3.05 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))),
% 2.87/3.05 inference(rewrite,[status(thm)],[])).
% 2.87/3.05 tff(1589,plain,
% 2.87/3.05 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))),
% 2.87/3.05 inference(quant_inst,[status(thm)],[])).
% 2.87/3.05 tff(1590,plain,
% 2.87/3.05 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1)))))),
% 2.87/3.05 inference(modus_ponens,[status(thm)],[1589, 1588])).
% 2.87/3.05 tff(1591,plain,
% 2.87/3.05 ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1)))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[1590, 118])).
% 2.87/3.05 tff(1592,plain,
% 2.87/3.05 (~r(elem!1, s(s(s(elem!1))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[1591, 1551, 1587])).
% 2.87/3.05 tff(1593,plain,
% 2.87/3.05 (((~![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)))))),
% 2.87/3.05 inference(rewrite,[status(thm)],[])).
% 2.87/3.05 tff(1594,plain,
% 2.87/3.05 ((~![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)))))),
% 2.87/3.05 inference(quant_inst,[status(thm)],[])).
% 2.87/3.05 tff(1595,plain,
% 2.87/3.05 ((~![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))))),
% 2.87/3.05 inference(modus_ponens,[status(thm)],[1594, 1593])).
% 2.87/3.05 tff(1596,plain,
% 2.87/3.05 (b(elem!1, s(s(s(elem!1))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[1595, 41, 1592, 1586])).
% 2.87/3.05 tff(1597,assumption,(b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 2.87/3.05 tff(1598,plain,
% 2.87/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.87/3.05 inference(rewrite,[status(thm)],[])).
% 2.87/3.05 tff(1599,plain,
% 2.87/3.05 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(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(elem!1, s(s(s(elem!1))))))),
% 2.87/3.05 inference(rewrite,[status(thm)],[])).
% 2.87/3.05 tff(1600,plain,
% 2.87/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))))),
% 2.87/3.05 inference(monotonicity,[status(thm)],[1599])).
% 2.87/3.05 tff(1601,plain,
% 2.87/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.87/3.05 inference(transitivity,[status(thm)],[1600, 1598])).
% 2.87/3.05 tff(1602,plain,
% 2.87/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.87/3.05 inference(quant_inst,[status(thm)],[])).
% 2.87/3.05 tff(1603,plain,
% 2.87/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))),
% 2.87/3.05 inference(modus_ponens,[status(thm)],[1602, 1601])).
% 2.87/3.05 tff(1604,plain,
% 2.87/3.05 ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1)))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[1603, 178, 818, 506, 1597])).
% 2.87/3.05 tff(1605,plain,
% 2.87/3.05 (~b(s(s(s(elem!1))), z)),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[1604, 1596])).
% 2.87/3.05 tff(1606,plain,
% 2.87/3.05 ($false),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[1563, 41, 940, 1558, 1605])).
% 2.87/3.05 tff(1607,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (elem!1 = s(s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.05 tff(1608,plain,
% 2.87/3.05 (~r(elem!1, s(elem!1))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[1607, 1578, 506, 818, 1585, 844, 1551])).
% 2.87/3.05 tff(1609,plain,
% 2.87/3.05 (~r(elem!1, s(s(z)))),
% 2.87/3.05 inference(modus_ponens,[status(thm)],[1608, 1584])).
% 2.87/3.05 tff(1610,plain,
% 2.87/3.05 (~r(s(z), s(s(z)))),
% 2.87/3.05 inference(modus_ponens,[status(thm)],[1609, 1583])).
% 2.87/3.05 tff(1611,plain,
% 2.87/3.05 ((elem!1 = s(s(z))) <=> (s(s(z)) = elem!1)),
% 2.87/3.05 inference(commutativity,[status(thm)],[])).
% 2.87/3.05 tff(1612,plain,
% 2.87/3.05 ((s(z) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 2.87/3.05 inference(monotonicity,[status(thm)],[534])).
% 2.87/3.05 tff(1613,plain,
% 2.87/3.05 ((s(z) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 2.87/3.05 inference(transitivity,[status(thm)],[1612, 1611])).
% 2.87/3.05 tff(1614,plain,
% 2.87/3.05 ((s(s(z)) = elem!1) <=> (s(z) = s(s(z)))),
% 2.87/3.05 inference(symmetry,[status(thm)],[1613])).
% 2.87/3.05 tff(1615,plain,
% 2.87/3.05 ((~(s(s(z)) = elem!1)) <=> (~(s(z) = s(s(z))))),
% 2.87/3.05 inference(monotonicity,[status(thm)],[1614])).
% 2.87/3.05 tff(1616,plain,
% 2.87/3.06 (~(s(z) = s(s(z)))),
% 2.87/3.06 inference(modus_ponens,[status(thm)],[12, 1615])).
% 2.87/3.06 tff(1617,plain,
% 2.87/3.06 (((~![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))))),
% 2.87/3.06 inference(rewrite,[status(thm)],[])).
% 2.87/3.06 tff(1618,plain,
% 2.87/3.06 ((~![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))))),
% 2.87/3.06 inference(quant_inst,[status(thm)],[])).
% 2.87/3.06 tff(1619,plain,
% 2.87/3.06 ((~![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)))),
% 2.87/3.06 inference(modus_ponens,[status(thm)],[1618, 1617])).
% 2.87/3.06 tff(1620,plain,
% 2.87/3.06 ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[1619, 41])).
% 2.87/3.06 tff(1621,plain,
% 2.87/3.06 (b(s(z), s(s(z)))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[1620, 1616, 1610])).
% 2.87/3.06 tff(1622,plain,
% 2.87/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.87/3.06 inference(rewrite,[status(thm)],[])).
% 2.87/3.06 tff(1623,plain,
% 2.87/3.06 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.87/3.06 inference(rewrite,[status(thm)],[])).
% 2.87/3.06 tff(1624,plain,
% 2.87/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.87/3.06 inference(monotonicity,[status(thm)],[1623])).
% 2.87/3.06 tff(1625,plain,
% 2.87/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.87/3.06 inference(transitivity,[status(thm)],[1624, 1622])).
% 2.87/3.06 tff(1626,plain,
% 2.87/3.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.87/3.06 inference(quant_inst,[status(thm)],[])).
% 2.87/3.06 tff(1627,plain,
% 2.87/3.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z)))),
% 2.87/3.06 inference(modus_ponens,[status(thm)],[1626, 1625])).
% 2.87/3.06 tff(1628,plain,
% 2.87/3.06 ($false),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[1627, 178, 273, 1621, 168, 1580, 1579])).
% 2.87/3.06 tff(1629,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~(s(elem!1) = s(s(z)))) | (s(s(z)) = elem!1) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~r(s(elem!1), z)) | (s(s(s(elem!1))) = elem!1) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.06 tff(1630,plain,
% 2.87/3.06 (~b(s(s(s(s(z)))), z)),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[1629, 1551, 273, 515, 12, 506, 818, 844, 949, 1426])).
% 2.87/3.06 tff(1631,plain,
% 2.87/3.06 ($false),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[1630, 1567])).
% 2.87/3.06 tff(1632,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~(s(elem!1) = s(s(z)))) | (~b(z, s(s(z)))) | (s(s(z)) = elem!1) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~r(s(elem!1), z)) | (s(s(s(elem!1))) = elem!1) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.06 tff(1633,plain,
% 2.87/3.06 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[1632, 1525, 273, 1549, 1479, 818, 1532, 515, 1426])).
% 2.87/3.06 tff(1634,plain,
% 2.87/3.06 (b(s(s(s(elem!1))), s(elem!1))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[373, 1633, 356])).
% 2.87/3.06 tff(1635,plain,
% 2.87/3.06 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(s(z)))))),
% 2.87/3.06 inference(monotonicity,[status(thm)],[546])).
% 2.87/3.06 tff(1636,plain,
% 2.87/3.06 (b(z, s(s(s(s(z))))) <=> b(z, s(s(s(elem!1))))),
% 2.87/3.06 inference(symmetry,[status(thm)],[1635])).
% 2.87/3.06 tff(1637,plain,
% 2.87/3.06 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.87/3.06 inference(symmetry,[status(thm)],[546])).
% 2.87/3.06 tff(1638,plain,
% 2.87/3.06 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.87/3.06 inference(monotonicity,[status(thm)],[1400, 1637])).
% 2.87/3.06 tff(1639,plain,
% 2.87/3.06 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.87/3.06 inference(symmetry,[status(thm)],[1638])).
% 2.87/3.06 tff(1640,assumption,(s(s(elem!1)) = s(s(s(elem!1)))), introduced(assumption)).
% 2.87/3.06 tff(1641,plain,
% 2.87/3.06 (s(s(s(elem!1))) = s(s(elem!1))),
% 2.87/3.06 inference(symmetry,[status(thm)],[1640])).
% 2.87/3.06 tff(1642,plain,
% 2.87/3.06 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(elem!1)) = s(elem!1))),
% 2.87/3.06 inference(monotonicity,[status(thm)],[1641])).
% 2.87/3.06 tff(1643,plain,
% 2.87/3.06 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(s(elem!1))) = s(elem!1))),
% 2.87/3.06 inference(symmetry,[status(thm)],[1642])).
% 2.87/3.06 tff(1644,plain,
% 2.87/3.06 (inj_0(s(s(elem!1))) = inj_0(s(s(s(elem!1))))),
% 2.87/3.06 inference(monotonicity,[status(thm)],[1640])).
% 2.87/3.06 tff(1645,plain,
% 2.87/3.06 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(elem!1)))),
% 2.87/3.06 inference(symmetry,[status(thm)],[1644])).
% 2.87/3.06 tff(1646,plain,
% 2.87/3.06 (s(s(elem!1)) = s(elem!1)),
% 2.87/3.06 inference(transitivity,[status(thm)],[344, 1645, 328])).
% 2.87/3.06 tff(1647,plain,
% 2.87/3.06 (s(s(s(elem!1))) = s(elem!1)),
% 2.87/3.06 inference(modus_ponens,[status(thm)],[1646, 1643])).
% 2.87/3.06 tff(1648,plain,
% 2.87/3.06 ($false),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[356, 1647])).
% 2.87/3.06 tff(1649,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.06 tff(1650,plain,
% 2.87/3.06 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[1649, 356])).
% 2.87/3.06 tff(1651,assumption,(s(s(s(s(elem!1)))) = s(s(s(elem!1)))), introduced(assumption)).
% 2.87/3.06 tff(1652,plain,
% 2.87/3.06 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 2.87/3.06 inference(symmetry,[status(thm)],[1651])).
% 2.87/3.06 tff(1653,plain,
% 2.87/3.06 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(elem!1)))))),
% 2.87/3.06 inference(monotonicity,[status(thm)],[1652])).
% 2.87/3.06 tff(1654,plain,
% 2.87/3.06 (s(s(elem!1)) = s(s(s(elem!1)))),
% 2.87/3.06 inference(transitivity,[status(thm)],[344, 1653, 946])).
% 2.87/3.06 tff(1655,assumption,(~(s(s(elem!1)) = s(s(s(elem!1))))), introduced(assumption)).
% 2.87/3.06 tff(1656,plain,
% 2.87/3.06 ($false),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[1655, 1654])).
% 2.87/3.06 tff(1657,plain,((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.06 tff(1658,plain,
% 2.87/3.06 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[1657, 1650])).
% 2.87/3.06 tff(1659,plain,
% 2.87/3.06 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.87/3.06 inference(monotonicity,[status(thm)],[1400, 1637])).
% 2.87/3.06 tff(1660,plain,
% 2.87/3.06 ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) <=> (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.87/3.06 inference(monotonicity,[status(thm)],[1659])).
% 2.87/3.06 tff(1661,plain,
% 2.87/3.06 (b(s(s(z)), s(s(s(s(s(z)))))) <=> b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.87/3.06 inference(monotonicity,[status(thm)],[1400])).
% 2.87/3.06 tff(1662,plain,
% 2.87/3.06 (b(s(s(z)), s(s(s(s(elem!1))))) <=> b(s(s(z)), s(s(s(s(s(z))))))),
% 2.87/3.06 inference(symmetry,[status(thm)],[1661])).
% 2.87/3.06 tff(1663,plain,
% 2.87/3.06 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.87/3.06 inference(modus_ponens,[status(thm)],[1518, 1662])).
% 2.87/3.06 tff(1664,assumption,(b(s(s(s(s(s(z))))), s(s(s(s(z)))))), introduced(assumption)).
% 2.87/3.06 tff(1665,assumption,(b(s(s(z)), s(s(s(s(s(z))))))), introduced(assumption)).
% 2.87/3.06 tff(1666,plain,
% 2.87/3.06 ((s(s(z)) = elem!1) <=> (elem!1 = s(s(z)))),
% 2.87/3.06 inference(symmetry,[status(thm)],[1611])).
% 2.87/3.06 tff(1667,plain,
% 2.87/3.06 ((s(elem!1) = elem!1) <=> (elem!1 = s(s(z)))),
% 2.87/3.06 inference(transitivity,[status(thm)],[1533, 1666])).
% 2.87/3.06 tff(1668,plain,
% 2.87/3.06 ((~(s(elem!1) = elem!1)) <=> (~(elem!1 = s(s(z))))),
% 2.87/3.06 inference(monotonicity,[status(thm)],[1667])).
% 2.87/3.06 tff(1669,plain,
% 2.87/3.06 (~(elem!1 = s(s(z)))),
% 2.87/3.06 inference(modus_ponens,[status(thm)],[1548, 1668])).
% 2.87/3.06 tff(1670,plain,
% 2.87/3.06 (r(s(s(s(s(s(z))))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.87/3.06 inference(monotonicity,[status(thm)],[1400])).
% 2.87/3.06 tff(1671,plain,
% 2.87/3.06 (r(s(s(s(s(elem!1)))), s(s(z))) <=> r(s(s(s(s(s(z))))), s(s(z)))),
% 2.87/3.06 inference(symmetry,[status(thm)],[1670])).
% 2.87/3.06 tff(1672,plain,
% 2.87/3.06 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.87/3.06 inference(monotonicity,[status(thm)],[1400])).
% 2.87/3.06 tff(1673,plain,
% 2.87/3.06 ((~b(s(s(s(s(s(z))))), s(s(z)))) <=> (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 2.87/3.06 inference(monotonicity,[status(thm)],[1672])).
% 2.87/3.06 tff(1674,plain,
% 2.87/3.06 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 2.87/3.06 inference(monotonicity,[status(thm)],[546])).
% 2.87/3.06 tff(1675,plain,
% 2.87/3.06 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(z)) = s(s(s(s(z))))))),
% 2.87/3.06 inference(monotonicity,[status(thm)],[1674])).
% 2.87/3.06 tff(1676,assumption,(s(s(z)) = s(s(s(elem!1)))), introduced(assumption)).
% 2.87/3.06 tff(1677,plain,
% 2.87/3.06 (inj_0(s(s(z))) = inj_0(s(s(s(elem!1))))),
% 2.87/3.06 inference(monotonicity,[status(thm)],[1676])).
% 2.87/3.06 tff(1678,plain,
% 2.87/3.06 (s(z) = s(s(elem!1))),
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% 2.87/3.06 tff(1679,plain,
% 2.87/3.06 (inj_0(s(z)) = inj_0(s(s(elem!1)))),
% 2.87/3.06 inference(monotonicity,[status(thm)],[1678])).
% 2.87/3.06 tff(1680,plain,
% 2.87/3.06 (inj_0(s(s(elem!1))) = inj_0(s(z))),
% 2.87/3.06 inference(symmetry,[status(thm)],[1679])).
% 2.87/3.06 tff(1681,plain,
% 2.87/3.06 (s(elem!1) = z),
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% 2.87/3.06 tff(1682,plain,
% 2.87/3.06 ($false),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[769, 1681])).
% 2.87/3.06 tff(1683,plain,(~(s(s(z)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.06 tff(1684,plain,
% 2.87/3.06 (~(s(s(z)) = s(s(s(s(z)))))),
% 2.87/3.06 inference(modus_ponens,[status(thm)],[1683, 1675])).
% 2.87/3.06 tff(1685,plain,
% 2.87/3.06 (b(s(s(s(s(elem!1)))), s(s(z))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 2.87/3.06 inference(symmetry,[status(thm)],[1672])).
% 2.87/3.06 tff(1686,plain,
% 2.87/3.06 ((~r(s(s(s(s(s(z))))), s(s(z)))) <=> (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 2.87/3.06 inference(monotonicity,[status(thm)],[1670])).
% 2.87/3.06 tff(1687,assumption,(b(z, s(s(s(s(z)))))), introduced(assumption)).
% 2.87/3.06 tff(1688,plain,
% 2.87/3.06 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.87/3.06 inference(monotonicity,[status(thm)],[1637, 1400])).
% 2.87/3.06 tff(1689,plain,
% 2.87/3.06 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.87/3.06 inference(symmetry,[status(thm)],[1688])).
% 2.87/3.06 tff(1690,plain,
% 2.87/3.06 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.87/3.06 inference(commutativity,[status(thm)],[])).
% 2.87/3.06 tff(1691,assumption,(s(s(s(elem!1))) = s(s(s(s(elem!1))))), introduced(assumption)).
% 2.87/3.06 tff(1692,plain,
% 2.87/3.06 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 2.87/3.06 inference(modus_ponens,[status(thm)],[1691, 1690])).
% 2.87/3.06 tff(1693,assumption,(~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))), introduced(assumption)).
% 2.87/3.06 tff(1694,plain,
% 2.87/3.06 ($false),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[1693, 1692])).
% 2.87/3.06 tff(1695,plain,((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.06 tff(1696,plain,
% 2.87/3.06 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[1695, 1658])).
% 2.87/3.06 tff(1697,plain,
% 2.87/3.06 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.87/3.06 inference(monotonicity,[status(thm)],[1637, 1400])).
% 2.87/3.06 tff(1698,plain,
% 2.87/3.06 ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) <=> (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 2.87/3.06 inference(monotonicity,[status(thm)],[1697])).
% 2.87/3.06 tff(1699,plain,
% 2.87/3.06 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(z)))),
% 2.87/3.06 inference(monotonicity,[status(thm)],[546, 515])).
% 2.87/3.06 tff(1700,plain,
% 2.87/3.06 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[1576, 556, 1426])).
% 2.87/3.06 tff(1701,plain,
% 2.87/3.06 (b(s(s(s(elem!1))), s(elem!1))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[373, 1700, 356])).
% 2.87/3.06 tff(1702,plain,
% 2.87/3.06 (b(s(s(s(s(z)))), s(s(z)))),
% 2.87/3.06 inference(modus_ponens,[status(thm)],[1701, 1699])).
% 2.87/3.06 tff(1703,plain,
% 2.87/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 2.87/3.06 inference(rewrite,[status(thm)],[])).
% 2.87/3.06 tff(1704,plain,
% 2.87/3.06 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 2.87/3.06 inference(rewrite,[status(thm)],[])).
% 2.87/3.06 tff(1705,plain,
% 2.87/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))))),
% 2.87/3.06 inference(monotonicity,[status(thm)],[1704])).
% 2.87/3.06 tff(1706,plain,
% 2.87/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 2.87/3.06 inference(transitivity,[status(thm)],[1705, 1703])).
% 2.87/3.06 tff(1707,plain,
% 2.87/3.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.87/3.06 inference(quant_inst,[status(thm)],[])).
% 2.87/3.06 tff(1708,plain,
% 2.87/3.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))),
% 2.87/3.06 inference(modus_ponens,[status(thm)],[1707, 1706])).
% 2.87/3.06 tff(1709,plain,
% 2.87/3.06 (~b(s(s(s(s(s(z))))), z)),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[1708, 178, 273, 1687, 1702, 1664])).
% 2.87/3.06 tff(1710,plain,
% 2.87/3.06 (~b(s(s(s(s(elem!1)))), z)),
% 2.87/3.06 inference(modus_ponens,[status(thm)],[1709, 1514])).
% 2.87/3.06 tff(1711,plain,
% 2.87/3.06 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(elem!1)))) = z))),
% 2.87/3.06 inference(quant_inst,[status(thm)],[])).
% 2.87/3.06 tff(1712,plain,
% 2.87/3.06 (~(s(s(s(s(elem!1)))) = z)),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[1711, 28])).
% 2.87/3.06 tff(1713,plain,
% 2.87/3.06 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z))),
% 2.87/3.06 inference(rewrite,[status(thm)],[])).
% 2.87/3.06 tff(1714,plain,
% 2.87/3.06 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z))),
% 2.87/3.06 inference(quant_inst,[status(thm)],[])).
% 2.87/3.06 tff(1715,plain,
% 2.87/3.06 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z)),
% 2.87/3.06 inference(modus_ponens,[status(thm)],[1714, 1713])).
% 2.87/3.06 tff(1716,plain,
% 2.87/3.06 (b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z)),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[1715, 41, 1712])).
% 2.87/3.06 tff(1717,plain,
% 2.87/3.06 (r(s(s(s(s(elem!1)))), z)),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[1716, 1710])).
% 2.87/3.06 tff(1718,plain,
% 2.87/3.06 (r(s(s(s(s(s(z))))), z)),
% 2.87/3.06 inference(modus_ponens,[status(thm)],[1717, 1512])).
% 2.87/3.06 tff(1719,plain,
% 2.87/3.06 (r(s(s(z)), s(z))),
% 2.87/3.06 inference(modus_ponens,[status(thm)],[1427, 1429])).
% 2.87/3.06 tff(1720,plain,
% 2.87/3.06 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(z)))), elem!1)),
% 2.87/3.06 inference(monotonicity,[status(thm)],[534])).
% 2.87/3.06 tff(1721,plain,
% 2.87/3.06 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(z))),
% 2.87/3.06 inference(symmetry,[status(thm)],[1720])).
% 2.87/3.06 tff(1722,plain,
% 2.87/3.06 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 2.87/3.06 inference(monotonicity,[status(thm)],[546])).
% 2.87/3.06 tff(1723,plain,
% 2.87/3.06 (r(s(s(s(s(z)))), elem!1)),
% 2.87/3.06 inference(modus_ponens,[status(thm)],[556, 1722])).
% 2.87/3.06 tff(1724,plain,
% 2.87/3.06 (r(s(s(s(s(z)))), s(z))),
% 2.87/3.06 inference(modus_ponens,[status(thm)],[1723, 1721])).
% 2.87/3.06 tff(1725,plain,
% 2.87/3.06 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.87/3.06 inference(rewrite,[status(thm)],[])).
% 2.87/3.06 tff(1726,plain,
% 2.87/3.06 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.87/3.06 inference(quant_inst,[status(thm)],[])).
% 2.87/3.06 tff(1727,plain,
% 2.87/3.06 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 2.87/3.06 inference(modus_ponens,[status(thm)],[1726, 1725])).
% 2.87/3.06 tff(1728,plain,
% 2.87/3.06 ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[1727, 118])).
% 2.87/3.06 tff(1729,plain,
% 2.87/3.06 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[1728, 1724, 1719])).
% 2.87/3.06 tff(1730,plain,
% 2.87/3.06 (b(s(s(z)), s(s(s(s(z)))))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[163, 1729, 1684])).
% 2.87/3.06 tff(1731,plain,
% 2.87/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 2.87/3.06 inference(rewrite,[status(thm)],[])).
% 2.87/3.06 tff(1732,plain,
% 2.87/3.06 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 2.87/3.06 inference(rewrite,[status(thm)],[])).
% 2.87/3.06 tff(1733,plain,
% 2.87/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))))),
% 2.87/3.06 inference(monotonicity,[status(thm)],[1732])).
% 2.87/3.06 tff(1734,plain,
% 2.87/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 2.87/3.06 inference(transitivity,[status(thm)],[1733, 1731])).
% 2.87/3.06 tff(1735,plain,
% 2.87/3.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 2.87/3.06 inference(quant_inst,[status(thm)],[])).
% 2.87/3.06 tff(1736,plain,
% 2.87/3.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))),
% 2.87/3.06 inference(modus_ponens,[status(thm)],[1735, 1734])).
% 2.87/3.06 tff(1737,plain,
% 2.87/3.06 (~b(s(s(s(s(z)))), z)),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[1736, 178, 273, 1687, 1730, 1702])).
% 2.87/3.06 tff(1738,plain,
% 2.87/3.06 (r(s(s(s(s(z)))), z)),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[191, 1737])).
% 2.87/3.06 tff(1739,plain,
% 2.87/3.06 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)))),
% 2.87/3.06 inference(rewrite,[status(thm)],[])).
% 2.87/3.06 tff(1740,plain,
% 2.87/3.06 (((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)))),
% 2.87/3.06 inference(rewrite,[status(thm)],[])).
% 2.87/3.06 tff(1741,plain,
% 2.87/3.06 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z))))),
% 2.87/3.06 inference(monotonicity,[status(thm)],[1740])).
% 2.87/3.06 tff(1742,plain,
% 2.87/3.06 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)))),
% 2.87/3.06 inference(transitivity,[status(thm)],[1741, 1739])).
% 2.87/3.06 tff(1743,plain,
% 2.87/3.06 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.87/3.06 inference(quant_inst,[status(thm)],[])).
% 2.87/3.06 tff(1744,plain,
% 2.87/3.06 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z))),
% 2.87/3.06 inference(modus_ponens,[status(thm)],[1743, 1742])).
% 2.87/3.06 tff(1745,plain,
% 2.87/3.06 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[1744, 118, 1738, 1718])).
% 2.87/3.06 tff(1746,plain,
% 2.87/3.06 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.87/3.06 inference(modus_ponens,[status(thm)],[1745, 1698])).
% 2.87/3.06 tff(1747,plain,
% 2.87/3.06 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 2.87/3.06 inference(rewrite,[status(thm)],[])).
% 2.87/3.06 tff(1748,plain,
% 2.87/3.06 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 2.87/3.06 inference(quant_inst,[status(thm)],[])).
% 2.87/3.06 tff(1749,plain,
% 2.87/3.06 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.87/3.06 inference(modus_ponens,[status(thm)],[1748, 1747])).
% 2.87/3.06 tff(1750,plain,
% 2.87/3.06 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[1749, 41])).
% 2.87/3.06 tff(1751,plain,
% 2.87/3.06 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[1750, 1746, 1696])).
% 2.87/3.06 tff(1752,plain,
% 2.87/3.06 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.87/3.06 inference(modus_ponens,[status(thm)],[1751, 1689])).
% 2.87/3.06 tff(1753,plain,
% 2.87/3.06 ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[414, 118, 106])).
% 2.87/3.06 tff(1754,plain,
% 2.87/3.06 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[1753, 1718])).
% 2.87/3.06 tff(1755,plain,
% 2.87/3.06 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.87/3.06 inference(modus_ponens,[status(thm)],[1754, 1686])).
% 2.87/3.06 tff(1756,plain,
% 2.87/3.06 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[1170, 1755])).
% 2.87/3.06 tff(1757,plain,
% 2.87/3.06 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.87/3.06 inference(modus_ponens,[status(thm)],[1756, 1685])).
% 2.87/3.06 tff(1758,plain,
% 2.87/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.87/3.06 inference(rewrite,[status(thm)],[])).
% 2.87/3.06 tff(1759,plain,
% 2.87/3.06 (((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.87/3.07 inference(rewrite,[status(thm)],[])).
% 2.87/3.07 tff(1760,plain,
% 2.87/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 2.87/3.07 inference(monotonicity,[status(thm)],[1759])).
% 2.87/3.07 tff(1761,plain,
% 2.87/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.87/3.07 inference(transitivity,[status(thm)],[1760, 1758])).
% 2.87/3.07 tff(1762,plain,
% 2.87/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.87/3.07 inference(quant_inst,[status(thm)],[])).
% 2.87/3.07 tff(1763,plain,
% 2.87/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 2.87/3.07 inference(modus_ponens,[status(thm)],[1762, 1761])).
% 2.87/3.07 tff(1764,plain,
% 2.87/3.07 ($false),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[1763, 178, 1702, 1757, 1665, 1664, 1752])).
% 2.87/3.07 tff(1765,plain,((~r(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~(s(elem!1) = s(s(z)))) | (~r(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.07 tff(1766,plain,
% 2.87/3.07 (~r(s(s(s(elem!1))), elem!1)),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[1765, 1687, 1664, 515, 106, 273, 1665, 356, 1426])).
% 2.87/3.07 tff(1767,plain,
% 2.87/3.07 (b(s(s(s(elem!1))), elem!1)),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[570, 1766, 949])).
% 2.87/3.07 tff(1768,plain,
% 2.87/3.07 (b(s(s(s(s(z)))), elem!1)),
% 2.87/3.07 inference(modus_ponens,[status(thm)],[1767, 1570])).
% 2.87/3.07 tff(1769,plain,
% 2.87/3.07 (b(s(s(s(s(z)))), s(z))),
% 2.87/3.07 inference(modus_ponens,[status(thm)],[1768, 1569])).
% 2.87/3.07 tff(1770,plain,
% 2.87/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.87/3.07 inference(rewrite,[status(thm)],[])).
% 2.87/3.07 tff(1771,plain,
% 2.87/3.07 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.87/3.07 inference(rewrite,[status(thm)],[])).
% 2.87/3.07 tff(1772,plain,
% 2.87/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.87/3.07 inference(monotonicity,[status(thm)],[1771])).
% 2.87/3.07 tff(1773,plain,
% 2.87/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.87/3.07 inference(transitivity,[status(thm)],[1772, 1770])).
% 2.87/3.07 tff(1774,plain,
% 2.87/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.87/3.07 inference(quant_inst,[status(thm)],[])).
% 2.87/3.07 tff(1775,plain,
% 2.87/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.87/3.07 inference(modus_ponens,[status(thm)],[1774, 1773])).
% 2.87/3.07 tff(1776,plain,
% 2.87/3.07 ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(z)))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[1775, 178, 1687, 1664])).
% 2.87/3.07 tff(1777,plain,
% 2.87/3.07 (~b(s(s(s(s(s(z))))), z)),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[1776, 1470, 1769])).
% 2.87/3.07 tff(1778,plain,
% 2.87/3.07 (~b(s(s(s(s(elem!1)))), z)),
% 2.87/3.07 inference(modus_ponens,[status(thm)],[1777, 1514])).
% 2.87/3.07 tff(1779,plain,
% 2.87/3.07 (r(s(s(s(s(elem!1)))), z)),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[1716, 1778])).
% 2.87/3.07 tff(1780,plain,
% 2.87/3.07 (r(s(s(s(s(s(z))))), z)),
% 2.87/3.07 inference(modus_ponens,[status(thm)],[1779, 1512])).
% 2.87/3.07 tff(1781,plain,
% 2.87/3.07 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[1753, 1780])).
% 2.87/3.07 tff(1782,plain,
% 2.87/3.07 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.87/3.07 inference(modus_ponens,[status(thm)],[1781, 1686])).
% 2.87/3.07 tff(1783,plain,
% 2.87/3.07 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[1170, 1782])).
% 2.87/3.07 tff(1784,plain,
% 2.87/3.07 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.87/3.07 inference(modus_ponens,[status(thm)],[1783, 1685])).
% 2.87/3.07 tff(1785,plain,
% 2.87/3.07 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 2.87/3.07 inference(symmetry,[status(thm)],[157])).
% 2.87/3.07 tff(1786,plain,
% 2.87/3.07 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 2.87/3.07 inference(transitivity,[status(thm)],[1674, 1785])).
% 2.87/3.07 tff(1787,plain,
% 2.87/3.07 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(s(z)))) = s(s(z))))),
% 2.87/3.07 inference(monotonicity,[status(thm)],[1786])).
% 2.87/3.07 tff(1788,plain,
% 2.87/3.07 (~(s(s(s(s(z)))) = s(s(z)))),
% 2.87/3.07 inference(modus_ponens,[status(thm)],[1683, 1787])).
% 2.87/3.07 tff(1789,assumption,(b(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 2.87/3.07 tff(1790,assumption,(b(z, s(z))), introduced(assumption)).
% 2.87/3.07 tff(1791,assumption,(b(s(z), z)), introduced(assumption)).
% 2.87/3.07 tff(1792,plain,
% 2.87/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.87/3.07 inference(rewrite,[status(thm)],[])).
% 2.87/3.07 tff(1793,plain,
% 2.87/3.07 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.87/3.07 inference(rewrite,[status(thm)],[])).
% 2.87/3.07 tff(1794,plain,
% 2.87/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.87/3.07 inference(monotonicity,[status(thm)],[1793])).
% 2.87/3.07 tff(1795,plain,
% 2.87/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.87/3.07 inference(transitivity,[status(thm)],[1794, 1792])).
% 2.87/3.07 tff(1796,plain,
% 2.87/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.87/3.07 inference(quant_inst,[status(thm)],[])).
% 2.87/3.07 tff(1797,plain,
% 2.87/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.87/3.07 inference(modus_ponens,[status(thm)],[1796, 1795])).
% 2.87/3.07 tff(1798,plain,
% 2.87/3.07 ($false),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[1797, 178, 1687, 168, 1791, 1790, 1789])).
% 2.87/3.07 tff(1799,plain,((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.07 tff(1800,plain,
% 2.87/3.07 (~b(s(s(s(s(z)))), z)),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[1799, 1687, 1480, 1470, 1769])).
% 2.87/3.07 tff(1801,plain,
% 2.87/3.07 (r(s(s(s(s(z)))), z)),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[191, 1800])).
% 2.87/3.07 tff(1802,plain,
% 2.87/3.07 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[197, 118, 106, 1801])).
% 2.87/3.07 tff(1803,plain,
% 2.87/3.07 (b(s(s(s(s(z)))), s(s(z)))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[101, 1802, 1788])).
% 2.87/3.07 tff(1804,plain,
% 2.87/3.07 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.87/3.07 inference(rewrite,[status(thm)],[])).
% 2.87/3.07 tff(1805,plain,
% 2.87/3.07 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.87/3.07 inference(rewrite,[status(thm)],[])).
% 2.87/3.07 tff(1806,plain,
% 2.87/3.07 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 2.87/3.07 inference(monotonicity,[status(thm)],[1805])).
% 2.87/3.07 tff(1807,plain,
% 2.87/3.07 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.87/3.07 inference(transitivity,[status(thm)],[1806, 1804])).
% 2.87/3.07 tff(1808,plain,
% 2.87/3.07 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.87/3.07 inference(quant_inst,[status(thm)],[])).
% 2.87/3.07 tff(1809,plain,
% 2.87/3.07 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z))))))),
% 2.87/3.07 inference(modus_ponens,[status(thm)],[1808, 1807])).
% 2.87/3.07 tff(1810,plain,
% 2.87/3.07 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[1809, 118, 106, 1801])).
% 2.87/3.07 tff(1811,plain,
% 2.87/3.07 (b(s(s(z)), s(s(s(s(z)))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[163, 1810, 1684])).
% 2.87/3.07 tff(1812,plain,
% 2.87/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.87/3.07 inference(rewrite,[status(thm)],[])).
% 2.87/3.07 tff(1813,plain,
% 2.87/3.07 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.87/3.07 inference(rewrite,[status(thm)],[])).
% 2.87/3.07 tff(1814,plain,
% 2.87/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 2.87/3.07 inference(monotonicity,[status(thm)],[1813])).
% 2.87/3.07 tff(1815,plain,
% 2.87/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.87/3.07 inference(transitivity,[status(thm)],[1814, 1812])).
% 2.87/3.07 tff(1816,plain,
% 2.87/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.87/3.07 inference(quant_inst,[status(thm)],[])).
% 2.87/3.07 tff(1817,plain,
% 2.87/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 2.87/3.07 inference(modus_ponens,[status(thm)],[1816, 1815])).
% 2.87/3.07 tff(1818,plain,
% 2.87/3.07 ($false),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[1817, 178, 1811, 1803, 1784, 1665, 1664])).
% 2.87/3.07 tff(1819,plain,((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~(s(elem!1) = s(s(z)))) | (~b(z, elem!1)) | (s(s(s(elem!1))) = elem!1) | (~b(z, s(s(z)))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.07 tff(1820,plain,
% 2.87/3.07 (~b(z, s(s(s(s(z)))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[1819, 1664, 1665, 106, 515, 818, 949, 273, 356, 1426])).
% 2.87/3.07 tff(1821,plain,
% 2.87/3.07 (r(z, s(s(s(s(z)))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[46, 1820])).
% 2.87/3.07 tff(1822,plain,
% 2.87/3.07 (r(z, s(s(s(elem!1))))),
% 2.87/3.07 inference(modus_ponens,[status(thm)],[1821, 554])).
% 2.87/3.07 tff(1823,assumption,(r(s(s(z)), s(s(s(elem!1))))), introduced(assumption)).
% 2.87/3.07 tff(1824,plain,
% 2.87/3.07 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)))),
% 2.87/3.07 inference(rewrite,[status(thm)],[])).
% 2.87/3.07 tff(1825,plain,
% 2.87/3.07 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)))),
% 2.87/3.07 inference(rewrite,[status(thm)],[])).
% 2.87/3.07 tff(1826,plain,
% 2.87/3.07 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z))))),
% 2.87/3.07 inference(monotonicity,[status(thm)],[1825])).
% 2.87/3.07 tff(1827,plain,
% 2.87/3.07 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)))),
% 2.87/3.07 inference(transitivity,[status(thm)],[1826, 1824])).
% 2.87/3.07 tff(1828,plain,
% 2.87/3.07 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z)))),
% 2.87/3.07 inference(quant_inst,[status(thm)],[])).
% 2.87/3.07 tff(1829,plain,
% 2.87/3.08 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z))),
% 2.87/3.08 inference(modus_ponens,[status(thm)],[1828, 1827])).
% 2.87/3.08 tff(1830,plain,
% 2.87/3.08 ($false),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[1829, 118, 557, 106, 1823])).
% 2.87/3.08 tff(1831,plain,((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.08 tff(1832,plain,
% 2.87/3.08 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[1831, 1822, 106])).
% 2.87/3.08 tff(1833,plain,
% 2.87/3.08 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 2.87/3.08 inference(monotonicity,[status(thm)],[546])).
% 2.87/3.08 tff(1834,plain,
% 2.87/3.08 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 2.87/3.08 inference(symmetry,[status(thm)],[1833])).
% 2.87/3.08 tff(1835,plain,
% 2.87/3.08 (r(s(s(z)), s(s(s(elem!1))))),
% 2.87/3.08 inference(modus_ponens,[status(thm)],[147, 1834])).
% 2.87/3.08 tff(1836,assumption,(~r(s(s(z)), s(s(s(elem!1))))), introduced(assumption)).
% 2.87/3.08 tff(1837,plain,
% 2.87/3.08 ($false),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[1836, 1835])).
% 2.87/3.08 tff(1838,plain,((~r(s(s(z)), s(s(s(s(z)))))) | r(s(s(z)), s(s(s(elem!1)))) | (~(s(elem!1) = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.08 tff(1839,plain,
% 2.87/3.08 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[1838, 1832, 515])).
% 2.87/3.08 tff(1840,plain,
% 2.87/3.08 (b(s(s(z)), s(s(s(s(z)))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[163, 1839, 1684])).
% 2.87/3.08 tff(1841,plain,
% 2.87/3.08 (s(s(s(s(z)))) = elem!1),
% 2.87/3.08 inference(symmetry,[status(thm)],[319])).
% 2.87/3.08 tff(1842,plain,
% 2.87/3.08 (b(z, s(s(s(s(z))))) <=> b(z, elem!1)),
% 2.87/3.08 inference(monotonicity,[status(thm)],[1841])).
% 2.87/3.08 tff(1843,plain,
% 2.87/3.08 (b(z, elem!1) <=> b(z, s(s(s(s(z)))))),
% 2.87/3.08 inference(symmetry,[status(thm)],[1842])).
% 2.87/3.08 tff(1844,plain,
% 2.87/3.08 (b(z, s(s(s(s(z)))))),
% 2.87/3.08 inference(modus_ponens,[status(thm)],[818, 1843])).
% 2.87/3.08 tff(1845,plain,
% 2.87/3.08 ($false),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[1, 1844])).
% 2.87/3.08 tff(1846,plain,((~(elem!1 = s(s(s(s(z)))))) | b(z, s(s(s(s(z))))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.08 tff(1847,plain,
% 2.87/3.08 (~(elem!1 = s(s(s(s(z)))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[1846, 1820, 818])).
% 2.87/3.08 tff(1848,plain,
% 2.87/3.08 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[1809, 118, 106, 194])).
% 2.87/3.08 tff(1849,plain,
% 2.87/3.08 (b(s(s(z)), s(s(s(s(z)))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[163, 1848, 1684])).
% 2.87/3.08 tff(1850,plain,
% 2.87/3.08 (b(s(s(s(s(z)))), s(s(z)))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[101, 306, 1788])).
% 2.87/3.08 tff(1851,assumption,(b(s(s(s(s(s(z))))), s(s(z)))), introduced(assumption)).
% 2.87/3.08 tff(1852,plain,
% 2.87/3.08 ($false),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[1817, 178, 167, 202, 1851, 1665, 1664])).
% 2.87/3.08 tff(1853,plain,((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.08 tff(1854,plain,
% 2.87/3.08 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[1853, 1849, 1850, 1665, 1664])).
% 2.87/3.08 tff(1855,plain,
% 2.87/3.08 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.87/3.08 inference(modus_ponens,[status(thm)],[1854, 1673])).
% 2.87/3.08 tff(1856,plain,
% 2.87/3.08 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[1170, 1855])).
% 2.87/3.08 tff(1857,plain,
% 2.87/3.08 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.87/3.08 inference(modus_ponens,[status(thm)],[1856, 1671])).
% 2.87/3.08 tff(1858,assumption,(~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.87/3.08 tff(1859,plain,
% 2.87/3.08 ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) <=> (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 2.87/3.08 inference(monotonicity,[status(thm)],[1688])).
% 2.87/3.08 tff(1860,assumption,(b(s(s(s(s(z)))), s(s(s(s(s(z))))))), introduced(assumption)).
% 2.87/3.08 tff(1861,plain,
% 2.87/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.87/3.08 inference(rewrite,[status(thm)],[])).
% 2.87/3.08 tff(1862,plain,
% 2.87/3.08 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.87/3.08 inference(rewrite,[status(thm)],[])).
% 2.87/3.08 tff(1863,plain,
% 2.87/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 2.87/3.08 inference(monotonicity,[status(thm)],[1862])).
% 2.87/3.08 tff(1864,plain,
% 2.87/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.87/3.08 inference(transitivity,[status(thm)],[1863, 1861])).
% 2.87/3.08 tff(1865,plain,
% 2.87/3.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.87/3.08 inference(quant_inst,[status(thm)],[])).
% 2.87/3.08 tff(1866,plain,
% 2.87/3.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 2.87/3.08 inference(modus_ponens,[status(thm)],[1865, 1864])).
% 2.87/3.08 tff(1867,plain,
% 2.87/3.08 ($false),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[1866, 178, 167, 202, 1665, 1664, 1860])).
% 2.87/3.08 tff(1868,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.08 tff(1869,plain,
% 2.87/3.08 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[1868, 1849, 1850, 1665, 1664])).
% 2.87/3.08 tff(1870,plain,
% 2.87/3.08 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.87/3.08 inference(modus_ponens,[status(thm)],[1869, 1859])).
% 2.87/3.08 tff(1871,plain,
% 2.87/3.08 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[1750, 1870, 1858])).
% 2.87/3.08 tff(1872,plain,
% 2.87/3.08 (b(s(z), s(s(z))) <=> b(elem!1, s(s(z)))),
% 2.87/3.08 inference(monotonicity,[status(thm)],[534])).
% 2.87/3.08 tff(1873,plain,
% 2.87/3.08 ((~b(s(z), s(s(z)))) <=> (~b(elem!1, s(s(z))))),
% 2.87/3.08 inference(monotonicity,[status(thm)],[1872])).
% 2.87/3.08 tff(1874,plain,
% 2.87/3.08 (b(s(z), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.87/3.08 inference(monotonicity,[status(thm)],[534])).
% 2.87/3.08 tff(1875,plain,
% 2.87/3.08 (b(elem!1, s(s(s(s(z))))) <=> b(s(z), s(s(s(s(z)))))),
% 2.87/3.08 inference(symmetry,[status(thm)],[1874])).
% 2.87/3.08 tff(1876,assumption,(r(s(s(s(elem!1))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.87/3.08 tff(1877,plain,
% 2.87/3.08 (r(s(z), s(s(s(s(z)))))),
% 2.87/3.08 inference(modus_ponens,[status(thm)],[470, 1516])).
% 2.87/3.08 tff(1878,plain,
% 2.87/3.08 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.87/3.08 inference(symmetry,[status(thm)],[1697])).
% 2.87/3.08 tff(1879,plain,
% 2.87/3.08 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.87/3.08 inference(modus_ponens,[status(thm)],[1876, 1878])).
% 2.87/3.08 tff(1880,plain,
% 2.87/3.08 (r(s(z), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 2.87/3.08 inference(monotonicity,[status(thm)],[534, 1400])).
% 2.87/3.08 tff(1881,plain,
% 2.87/3.08 (r(elem!1, s(s(s(s(elem!1))))) <=> r(s(z), s(s(s(s(s(z))))))),
% 2.87/3.08 inference(symmetry,[status(thm)],[1880])).
% 2.87/3.08 tff(1882,plain,
% 2.87/3.08 (r(s(z), s(s(s(s(s(z))))))),
% 2.87/3.08 inference(modus_ponens,[status(thm)],[1452, 1881])).
% 2.87/3.08 tff(1883,plain,
% 2.87/3.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.87/3.08 inference(rewrite,[status(thm)],[])).
% 2.87/3.08 tff(1884,plain,
% 2.87/3.08 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.87/3.08 inference(quant_inst,[status(thm)],[])).
% 2.87/3.08 tff(1885,plain,
% 2.87/3.08 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z))))))),
% 2.87/3.08 inference(modus_ponens,[status(thm)],[1884, 1883])).
% 2.87/3.08 tff(1886,plain,
% 2.87/3.08 ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z))))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[1885, 118])).
% 2.87/3.08 tff(1887,plain,
% 2.87/3.08 ($false),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[1886, 1882, 1879, 1877])).
% 2.87/3.08 tff(1888,plain,((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~(s(elem!1) = s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.08 tff(1889,plain,
% 2.87/3.08 (~r(elem!1, s(s(s(s(z)))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[1888, 1452, 515, 1876])).
% 2.87/3.08 tff(1890,plain,
% 2.87/3.08 (b(elem!1, s(s(s(s(z)))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[483, 1889, 469])).
% 2.87/3.08 tff(1891,plain,
% 2.87/3.08 (b(s(z), s(s(s(s(z)))))),
% 2.87/3.08 inference(modus_ponens,[status(thm)],[1890, 1875])).
% 2.87/3.08 tff(1892,plain,
% 2.87/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.87/3.08 inference(rewrite,[status(thm)],[])).
% 2.87/3.08 tff(1893,plain,
% 2.87/3.08 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z)))) <=> ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.87/3.08 inference(rewrite,[status(thm)],[])).
% 2.87/3.08 tff(1894,plain,
% 2.87/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 2.87/3.08 inference(monotonicity,[status(thm)],[1893])).
% 2.87/3.08 tff(1895,plain,
% 2.87/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.87/3.08 inference(transitivity,[status(thm)],[1894, 1892])).
% 2.87/3.08 tff(1896,plain,
% 2.87/3.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))),
% 2.87/3.08 inference(quant_inst,[status(thm)],[])).
% 2.87/3.08 tff(1897,plain,
% 2.87/3.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 2.87/3.08 inference(modus_ponens,[status(thm)],[1896, 1895])).
% 2.87/3.08 tff(1898,plain,
% 2.87/3.08 (~b(s(z), s(s(z)))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[1897, 178, 273, 167, 1790, 1891])).
% 2.87/3.08 tff(1899,plain,
% 2.87/3.08 (~b(elem!1, s(s(z)))),
% 2.87/3.08 inference(modus_ponens,[status(thm)],[1898, 1873])).
% 2.87/3.08 tff(1900,plain,
% 2.87/3.08 (r(elem!1, s(s(z)))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[467, 1899, 462])).
% 2.87/3.08 tff(1901,plain,
% 2.87/3.08 (r(s(z), s(s(z)))),
% 2.87/3.08 inference(modus_ponens,[status(thm)],[1900, 1582])).
% 2.87/3.08 tff(1902,assumption,(r(s(s(s(s(s(z))))), s(s(z)))), introduced(assumption)).
% 2.87/3.08 tff(1903,plain,
% 2.87/3.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.87/3.08 inference(rewrite,[status(thm)],[])).
% 2.87/3.08 tff(1904,plain,
% 2.87/3.08 (((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.87/3.08 inference(rewrite,[status(thm)],[])).
% 2.87/3.08 tff(1905,plain,
% 2.87/3.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 2.87/3.08 inference(monotonicity,[status(thm)],[1904])).
% 2.87/3.08 tff(1906,plain,
% 2.87/3.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.87/3.08 inference(transitivity,[status(thm)],[1905, 1903])).
% 2.87/3.08 tff(1907,plain,
% 2.87/3.08 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.87/3.08 inference(quant_inst,[status(thm)],[])).
% 2.87/3.08 tff(1908,plain,
% 2.87/3.08 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.87/3.08 inference(modus_ponens,[status(thm)],[1907, 1906])).
% 2.87/3.08 tff(1909,plain,
% 2.87/3.08 ($false),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[1908, 118, 1902, 1882, 1901])).
% 2.87/3.08 tff(1910,plain,((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~(s(elem!1) = s(s(z)))) | (elem!1 = s(s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (elem!1 = s(s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.08 tff(1911,plain,
% 2.87/3.08 (~r(elem!1, s(s(s(s(elem!1)))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[1910, 1857, 515, 462, 273, 1849, 1790, 469, 1871])).
% 2.87/3.08 tff(1912,plain,
% 2.87/3.08 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[1465, 1911, 1423])).
% 2.87/3.08 tff(1913,plain,
% 2.87/3.08 (b(s(z), s(s(s(s(elem!1)))))),
% 2.87/3.08 inference(modus_ponens,[status(thm)],[1912, 1446])).
% 2.87/3.08 tff(1914,plain,
% 2.87/3.08 (b(s(z), s(s(s(s(s(z))))))),
% 2.87/3.08 inference(modus_ponens,[status(thm)],[1913, 1445])).
% 2.87/3.08 tff(1915,assumption,(b(s(z), s(s(s(s(s(z))))))), introduced(assumption)).
% 2.87/3.08 tff(1916,assumption,(b(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 2.87/3.08 tff(1917,plain,
% 2.87/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.87/3.08 inference(rewrite,[status(thm)],[])).
% 2.87/3.08 tff(1918,plain,
% 2.87/3.08 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.87/3.08 inference(rewrite,[status(thm)],[])).
% 2.87/3.08 tff(1919,plain,
% 2.87/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.87/3.08 inference(monotonicity,[status(thm)],[1918])).
% 2.87/3.08 tff(1920,plain,
% 2.87/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.87/3.08 inference(transitivity,[status(thm)],[1919, 1917])).
% 2.87/3.08 tff(1921,plain,
% 2.87/3.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))))),
% 2.87/3.08 inference(quant_inst,[status(thm)],[])).
% 2.87/3.08 tff(1922,plain,
% 2.87/3.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 2.87/3.08 inference(modus_ponens,[status(thm)],[1921, 1920])).
% 2.87/3.08 tff(1923,plain,
% 2.87/3.08 (~b(s(z), s(s(z)))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[1922, 178, 167, 1665, 1664, 1915])).
% 2.87/3.08 tff(1924,plain,
% 2.87/3.08 (~b(elem!1, s(s(z)))),
% 2.87/3.08 inference(modus_ponens,[status(thm)],[1923, 1873])).
% 2.87/3.08 tff(1925,plain,
% 2.87/3.08 (r(elem!1, s(s(z)))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[467, 1924, 462])).
% 2.87/3.08 tff(1926,plain,
% 2.87/3.08 (r(s(z), s(s(z)))),
% 2.87/3.08 inference(modus_ponens,[status(thm)],[1925, 1582])).
% 2.87/3.08 tff(1927,plain,
% 2.87/3.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.87/3.08 inference(rewrite,[status(thm)],[])).
% 2.87/3.08 tff(1928,plain,
% 2.87/3.08 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.87/3.08 inference(rewrite,[status(thm)],[])).
% 2.87/3.08 tff(1929,plain,
% 2.87/3.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 2.87/3.08 inference(monotonicity,[status(thm)],[1928])).
% 2.87/3.08 tff(1930,plain,
% 2.87/3.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.87/3.08 inference(transitivity,[status(thm)],[1929, 1927])).
% 2.87/3.08 tff(1931,plain,
% 2.87/3.08 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.87/3.08 inference(quant_inst,[status(thm)],[])).
% 2.87/3.08 tff(1932,plain,
% 2.87/3.08 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.87/3.08 inference(modus_ponens,[status(thm)],[1931, 1930])).
% 2.87/3.08 tff(1933,plain,
% 2.87/3.08 (~r(s(s(s(s(s(z))))), s(z))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[1932, 118, 1902, 1926])).
% 2.87/3.08 tff(1934,plain,
% 2.87/3.08 ((s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[1441, 41, 1933])).
% 2.87/3.08 tff(1935,plain,
% 2.87/3.08 (b(s(s(s(s(s(z))))), s(z))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[1934, 1424])).
% 2.87/3.08 tff(1936,plain,
% 2.87/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.87/3.09 inference(rewrite,[status(thm)],[])).
% 2.87/3.09 tff(1937,plain,
% 2.87/3.09 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.87/3.09 inference(rewrite,[status(thm)],[])).
% 2.87/3.09 tff(1938,plain,
% 2.87/3.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.87/3.09 inference(monotonicity,[status(thm)],[1937])).
% 2.87/3.09 tff(1939,plain,
% 2.87/3.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.87/3.09 inference(transitivity,[status(thm)],[1938, 1936])).
% 2.87/3.09 tff(1940,plain,
% 2.87/3.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.87/3.09 inference(quant_inst,[status(thm)],[])).
% 2.87/3.09 tff(1941,plain,
% 2.87/3.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z))),
% 2.87/3.09 inference(modus_ponens,[status(thm)],[1940, 1939])).
% 2.87/3.09 tff(1942,plain,
% 2.87/3.09 ($false),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[1941, 178, 1791, 1790, 1935, 1916, 1915])).
% 2.87/3.09 tff(1943,plain,((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~(s(elem!1) = s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (elem!1 = s(s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.09 tff(1944,plain,
% 2.87/3.09 (~b(s(s(s(s(s(z))))), z)),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[1943, 1914, 1790, 1791, 515, 1857, 462, 1849, 1665, 1664])).
% 2.87/3.09 tff(1945,plain,
% 2.87/3.09 (~b(s(s(s(s(elem!1)))), z)),
% 2.87/3.09 inference(modus_ponens,[status(thm)],[1944, 1514])).
% 2.87/3.09 tff(1946,plain,
% 2.87/3.09 (r(s(s(s(s(elem!1)))), z)),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[1716, 1945])).
% 2.87/3.09 tff(1947,plain,
% 2.87/3.09 (r(s(s(s(s(s(z))))), z)),
% 2.87/3.09 inference(modus_ponens,[status(thm)],[1946, 1512])).
% 2.87/3.09 tff(1948,plain,
% 2.87/3.09 (~r(s(s(s(s(s(z))))), z)),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[414, 118, 106, 1857])).
% 2.87/3.09 tff(1949,plain,
% 2.87/3.09 ($false),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[1948, 1947])).
% 2.87/3.09 tff(1950,plain,((~r(s(s(s(s(z)))), z)) | (~(s(elem!1) = s(s(z)))) | (~r(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (elem!1 = s(s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (elem!1 = s(s(s(s(z))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.09 tff(1951,plain,
% 2.87/3.09 (~r(s(s(s(s(z)))), z)),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[1950, 1470, 106, 515, 1480, 1669, 1665, 1664, 273, 1847, 1696])).
% 2.87/3.09 tff(1952,plain,
% 2.87/3.09 (b(s(s(s(s(z)))), z)),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[191, 1951])).
% 2.87/3.09 tff(1953,plain,
% 2.87/3.09 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[1629, 1952, 273, 515, 1549, 1479, 818, 1532, 949, 1426])).
% 2.87/3.09 tff(1954,plain,
% 2.87/3.09 (b(s(s(s(elem!1))), s(elem!1))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[373, 1953, 356])).
% 2.87/3.09 tff(1955,plain,
% 2.87/3.09 (b(s(s(s(s(z)))), s(s(z)))),
% 2.87/3.09 inference(modus_ponens,[status(thm)],[1954, 1699])).
% 2.87/3.09 tff(1956,plain,
% 2.87/3.09 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[1853, 1955, 1840, 1665, 1664])).
% 2.87/3.09 tff(1957,plain,
% 2.87/3.09 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.87/3.09 inference(modus_ponens,[status(thm)],[1956, 1673])).
% 2.87/3.09 tff(1958,plain,
% 2.87/3.09 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[1170, 1957])).
% 2.87/3.09 tff(1959,plain,
% 2.87/3.09 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.87/3.09 inference(modus_ponens,[status(thm)],[1958, 1671])).
% 2.87/3.09 tff(1960,plain,
% 2.87/3.09 ((~b(s(z), s(s(s(s(z)))))) <=> (~b(elem!1, s(s(s(s(z))))))),
% 2.87/3.09 inference(monotonicity,[status(thm)],[1874])).
% 2.87/3.09 tff(1961,plain,
% 2.87/3.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.87/3.09 inference(rewrite,[status(thm)],[])).
% 2.87/3.09 tff(1962,plain,
% 2.87/3.09 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.87/3.09 inference(rewrite,[status(thm)],[])).
% 2.87/3.09 tff(1963,plain,
% 2.87/3.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 2.87/3.09 inference(monotonicity,[status(thm)],[1962])).
% 2.87/3.09 tff(1964,plain,
% 2.87/3.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.87/3.09 inference(transitivity,[status(thm)],[1963, 1961])).
% 2.87/3.09 tff(1965,plain,
% 2.87/3.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 2.87/3.09 inference(quant_inst,[status(thm)],[])).
% 2.87/3.09 tff(1966,plain,
% 2.87/3.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 2.87/3.09 inference(modus_ponens,[status(thm)],[1965, 1964])).
% 2.87/3.09 tff(1967,plain,
% 2.87/3.09 (~b(s(z), s(s(s(s(z)))))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[1966, 178, 273, 1952, 1955, 1480])).
% 2.87/3.09 tff(1968,plain,
% 2.87/3.09 (~b(elem!1, s(s(s(s(z)))))),
% 2.87/3.09 inference(modus_ponens,[status(thm)],[1967, 1960])).
% 2.87/3.09 tff(1969,plain,
% 2.87/3.09 (r(elem!1, s(s(s(s(z)))))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[483, 1968, 1847])).
% 2.87/3.09 tff(1970,plain,
% 2.87/3.09 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[1868, 1955, 1840, 1665, 1664])).
% 2.87/3.09 tff(1971,plain,
% 2.87/3.09 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.87/3.09 inference(modus_ponens,[status(thm)],[1970, 1859])).
% 2.87/3.09 tff(1972,plain,
% 2.87/3.09 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[1750, 1971, 1696])).
% 2.87/3.09 tff(1973,plain,
% 2.87/3.09 (~r(elem!1, s(s(s(s(elem!1)))))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[1888, 1972, 515, 1969])).
% 2.87/3.09 tff(1974,plain,
% 2.87/3.09 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[1465, 1973, 1423])).
% 2.87/3.09 tff(1975,plain,
% 2.87/3.09 (b(s(z), s(s(s(s(s(z))))))),
% 2.87/3.09 inference(modus_ponens,[status(thm)],[1974, 1447])).
% 2.87/3.09 tff(1976,plain,
% 2.87/3.09 (~b(s(s(s(s(s(z))))), z)),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[1943, 1975, 1470, 1840, 515, 1959, 1669, 1480, 1665, 1664])).
% 2.87/3.09 tff(1977,plain,
% 2.87/3.09 (~b(s(s(s(s(elem!1)))), z)),
% 2.87/3.09 inference(modus_ponens,[status(thm)],[1976, 1514])).
% 2.87/3.09 tff(1978,plain,
% 2.87/3.09 (r(s(s(s(s(elem!1)))), z)),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[1716, 1977])).
% 2.87/3.09 tff(1979,plain,
% 2.87/3.09 (r(s(s(s(s(s(z))))), z)),
% 2.87/3.09 inference(modus_ponens,[status(thm)],[1978, 1512])).
% 2.87/3.09 tff(1980,plain,
% 2.87/3.09 (~r(s(s(s(s(s(z))))), z)),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[414, 118, 106, 1959])).
% 2.87/3.09 tff(1981,plain,
% 2.87/3.09 ($false),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[1980, 1979])).
% 2.87/3.09 tff(1982,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~(s(elem!1) = s(s(z)))) | (~r(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(z, elem!1)) | (s(s(s(elem!1))) = elem!1) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.09 tff(1983,plain,
% 2.87/3.09 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[1982, 1663, 106, 515, 273, 356, 818, 1525, 1426])).
% 2.87/3.09 tff(1984,plain,
% 2.87/3.09 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.87/3.09 inference(modus_ponens,[status(thm)],[1983, 1660])).
% 2.87/3.09 tff(1985,plain,
% 2.87/3.09 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.87/3.09 inference(rewrite,[status(thm)],[])).
% 2.87/3.09 tff(1986,plain,
% 2.87/3.09 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.87/3.09 inference(quant_inst,[status(thm)],[])).
% 2.87/3.09 tff(1987,plain,
% 2.87/3.09 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.87/3.09 inference(modus_ponens,[status(thm)],[1986, 1985])).
% 2.87/3.09 tff(1988,plain,
% 2.87/3.09 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[1987, 41])).
% 2.87/3.09 tff(1989,plain,
% 2.87/3.09 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[1988, 1984, 1658])).
% 2.87/3.09 tff(1990,plain,
% 2.87/3.09 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.87/3.09 inference(modus_ponens,[status(thm)],[1989, 1639])).
% 2.87/3.09 tff(1991,assumption,(r(s(s(s(s(s(z))))), s(s(s(s(z)))))), introduced(assumption)).
% 2.87/3.09 tff(1992,plain,
% 2.87/3.09 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))),
% 2.87/3.09 inference(rewrite,[status(thm)],[])).
% 2.87/3.09 tff(1993,plain,
% 2.87/3.09 (((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))),
% 2.87/3.09 inference(rewrite,[status(thm)],[])).
% 2.87/3.09 tff(1994,plain,
% 2.87/3.09 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z))))))))),
% 2.87/3.09 inference(monotonicity,[status(thm)],[1993])).
% 2.87/3.09 tff(1995,plain,
% 2.87/3.09 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))),
% 2.87/3.09 inference(transitivity,[status(thm)],[1994, 1992])).
% 2.87/3.09 tff(1996,plain,
% 2.87/3.09 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.87/3.09 inference(quant_inst,[status(thm)],[])).
% 2.87/3.09 tff(1997,plain,
% 2.87/3.09 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z))))))),
% 2.87/3.09 inference(modus_ponens,[status(thm)],[1996, 1995])).
% 2.87/3.09 tff(1998,plain,
% 2.87/3.09 (~r(z, s(s(s(s(s(z))))))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[1997, 118, 145, 1991])).
% 2.87/3.09 tff(1999,plain,
% 2.87/3.09 ((z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z))))))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[1490, 41, 1998])).
% 2.87/3.09 tff(2000,plain,
% 2.87/3.09 (b(z, s(s(s(s(s(z))))))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[1999, 1408])).
% 2.87/3.09 tff(2001,plain,
% 2.87/3.09 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(s(z))))), z)),
% 2.87/3.09 inference(symmetry,[status(thm)],[1513])).
% 2.87/3.09 tff(2002,plain,
% 2.87/3.09 ((~r(s(s(s(s(s(z))))), z)) <=> (~r(s(s(s(s(elem!1)))), z))),
% 2.87/3.09 inference(monotonicity,[status(thm)],[1511])).
% 2.87/3.09 tff(2003,plain,
% 2.87/3.09 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 2.87/3.09 inference(rewrite,[status(thm)],[])).
% 2.87/3.09 tff(2004,plain,
% 2.87/3.09 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 2.87/3.09 inference(rewrite,[status(thm)],[])).
% 2.87/3.09 tff(2005,plain,
% 2.87/3.09 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))))),
% 2.87/3.09 inference(monotonicity,[status(thm)],[2004])).
% 2.87/3.09 tff(2006,plain,
% 2.87/3.09 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 2.87/3.09 inference(transitivity,[status(thm)],[2005, 2003])).
% 2.87/3.09 tff(2007,plain,
% 2.87/3.09 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.87/3.09 inference(quant_inst,[status(thm)],[])).
% 2.87/3.09 tff(2008,plain,
% 2.87/3.09 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))),
% 2.87/3.09 inference(modus_ponens,[status(thm)],[2007, 2006])).
% 2.87/3.09 tff(2009,plain,
% 2.87/3.09 (~r(s(s(s(s(s(z))))), z)),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[2008, 118, 145, 1991])).
% 2.87/3.09 tff(2010,plain,
% 2.87/3.09 (~r(s(s(s(s(elem!1)))), z)),
% 2.87/3.09 inference(modus_ponens,[status(thm)],[2009, 2002])).
% 2.87/3.09 tff(2011,plain,
% 2.87/3.09 (b(s(s(s(s(elem!1)))), z)),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[1716, 2010])).
% 2.87/3.09 tff(2012,plain,
% 2.87/3.09 (b(s(s(s(s(s(z))))), z)),
% 2.87/3.09 inference(modus_ponens,[status(thm)],[2011, 2001])).
% 2.87/3.09 tff(2013,plain,
% 2.87/3.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.87/3.09 inference(rewrite,[status(thm)],[])).
% 2.87/3.09 tff(2014,plain,
% 2.87/3.09 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(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))))), z)))),
% 2.87/3.09 inference(rewrite,[status(thm)],[])).
% 2.87/3.09 tff(2015,plain,
% 2.87/3.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.87/3.09 inference(monotonicity,[status(thm)],[2014])).
% 2.87/3.09 tff(2016,plain,
% 2.87/3.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.87/3.09 inference(transitivity,[status(thm)],[2015, 2013])).
% 2.87/3.09 tff(2017,plain,
% 2.87/3.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.87/3.09 inference(quant_inst,[status(thm)],[])).
% 2.87/3.09 tff(2018,plain,
% 2.87/3.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z))),
% 2.87/3.09 inference(modus_ponens,[status(thm)],[2017, 2016])).
% 2.87/3.09 tff(2019,plain,
% 2.87/3.09 ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z)))))))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[2018, 178, 1791, 1790, 2012])).
% 2.87/3.10 tff(2020,plain,
% 2.87/3.10 (~b(s(s(s(s(s(z))))), s(z))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[2019, 2000])).
% 2.87/3.10 tff(2021,plain,
% 2.87/3.10 ((s(s(s(s(s(z))))) = s(z)) | r(s(s(s(s(s(z))))), s(z))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[1441, 41, 2020])).
% 2.87/3.10 tff(2022,plain,
% 2.87/3.10 (r(s(s(s(s(s(z))))), s(z))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[2021, 1424])).
% 2.87/3.10 tff(2023,plain,
% 2.87/3.10 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.87/3.10 inference(rewrite,[status(thm)],[])).
% 2.87/3.10 tff(2024,plain,
% 2.87/3.10 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.87/3.10 inference(quant_inst,[status(thm)],[])).
% 2.87/3.10 tff(2025,plain,
% 2.87/3.10 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.87/3.10 inference(modus_ponens,[status(thm)],[2024, 2023])).
% 2.87/3.10 tff(2026,plain,
% 2.87/3.10 ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[2025, 118, 2022])).
% 2.87/3.10 tff(2027,plain,
% 2.87/3.10 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[2026, 1430])).
% 2.87/3.10 tff(2028,plain,
% 2.87/3.10 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.87/3.10 inference(modus_ponens,[status(thm)],[2027, 1686])).
% 2.87/3.10 tff(2029,plain,
% 2.87/3.10 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[1170, 2028])).
% 2.87/3.10 tff(2030,plain,
% 2.87/3.10 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.87/3.10 inference(modus_ponens,[status(thm)],[2029, 1685])).
% 2.87/3.10 tff(2031,plain,
% 2.87/3.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.87/3.10 inference(rewrite,[status(thm)],[])).
% 2.87/3.10 tff(2032,plain,
% 2.87/3.10 (((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.87/3.10 inference(rewrite,[status(thm)],[])).
% 2.87/3.10 tff(2033,plain,
% 2.87/3.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.87/3.10 inference(monotonicity,[status(thm)],[2032])).
% 2.87/3.10 tff(2034,plain,
% 2.87/3.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.87/3.10 inference(transitivity,[status(thm)],[2033, 2031])).
% 2.87/3.10 tff(2035,plain,
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% 2.87/3.10 inference(quant_inst,[status(thm)],[])).
% 2.87/3.10 tff(2036,plain,
% 2.87/3.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 2.87/3.10 inference(modus_ponens,[status(thm)],[2035, 2034])).
% 2.87/3.10 tff(2037,plain,
% 2.87/3.10 ($false),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[2036, 178, 273, 2030, 1665, 2012, 2000])).
% 2.87/3.10 tff(2038,plain,((~r(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~(s(elem!1) = s(s(z)))) | (~r(s(s(z)), elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.10 tff(2039,plain,
% 2.87/3.10 (~r(z, s(s(s(s(z)))))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[2038, 1663, 273, 515, 1427, 1480, 1470, 1990])).
% 2.87/3.10 tff(2040,plain,
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% 2.87/3.10 inference(unit_resolution,[status(thm)],[46, 2039])).
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% 2.87/3.10 (b(z, s(s(s(elem!1))))),
% 2.87/3.10 inference(modus_ponens,[status(thm)],[2040, 1636])).
% 2.87/3.10 tff(2042,assumption,(b(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 2.87/3.10 tff(2043,assumption,(b(z, s(s(s(elem!1))))), introduced(assumption)).
% 2.87/3.10 tff(2044,assumption,(b(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 2.87/3.10 tff(2045,plain,
% 2.87/3.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.87/3.10 inference(rewrite,[status(thm)],[])).
% 2.87/3.10 tff(2046,plain,
% 2.87/3.10 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.87/3.10 inference(rewrite,[status(thm)],[])).
% 2.87/3.10 tff(2047,plain,
% 2.87/3.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1)))))))),
% 2.87/3.10 inference(monotonicity,[status(thm)],[2046])).
% 2.87/3.10 tff(2048,plain,
% 2.87/3.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.87/3.10 inference(transitivity,[status(thm)],[2047, 2045])).
% 2.87/3.10 tff(2049,plain,
% 2.87/3.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)))),
% 2.87/3.10 inference(quant_inst,[status(thm)],[])).
% 2.87/3.10 tff(2050,plain,
% 2.87/3.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1)))))),
% 2.87/3.10 inference(modus_ponens,[status(thm)],[2049, 2048])).
% 2.87/3.10 tff(2051,plain,
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% 2.87/3.10 inference(unit_resolution,[status(thm)],[2050, 178, 506, 2044, 855, 2043, 2042])).
% 2.87/3.10 tff(2052,plain,((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.10 tff(2053,plain,
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% 2.87/3.10 tff(2054,plain,
% 2.87/3.10 ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1))))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[1595, 41])).
% 2.87/3.10 tff(2055,plain,
% 2.87/3.10 (r(elem!1, s(s(s(elem!1))))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[2054, 2053, 1531])).
% 2.87/3.10 tff(2056,plain,
% 2.87/3.10 (r(elem!1, s(s(s(s(z)))))),
% 2.87/3.10 inference(modus_ponens,[status(thm)],[2055, 1517])).
% 2.87/3.10 tff(2057,plain,
% 2.87/3.10 (r(s(z), s(s(s(s(z)))))),
% 2.87/3.10 inference(modus_ponens,[status(thm)],[2056, 1516])).
% 2.87/3.10 tff(2058,plain,
% 2.87/3.10 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.87/3.10 inference(rewrite,[status(thm)],[])).
% 2.87/3.10 tff(2059,plain,
% 2.87/3.10 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.87/3.10 inference(rewrite,[status(thm)],[])).
% 2.87/3.10 tff(2060,plain,
% 2.87/3.10 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(z))))))))),
% 2.87/3.10 inference(monotonicity,[status(thm)],[2059])).
% 2.87/3.10 tff(2061,plain,
% 2.87/3.10 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.87/3.10 inference(transitivity,[status(thm)],[2060, 2058])).
% 2.87/3.10 tff(2062,plain,
% 2.87/3.10 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.87/3.10 inference(quant_inst,[status(thm)],[])).
% 2.87/3.10 tff(2063,plain,
% 2.87/3.10 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(z))))))),
% 2.87/3.10 inference(modus_ponens,[status(thm)],[2062, 2061])).
% 2.87/3.10 tff(2064,plain,
% 2.87/3.10 ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(z))))))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[2063, 118, 1990])).
% 2.87/3.10 tff(2065,plain,
% 2.87/3.10 (~r(s(s(s(s(s(z))))), s(z))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[2064, 2057])).
% 2.87/3.10 tff(2066,plain,
% 2.87/3.10 ((s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[1441, 41, 2065])).
% 2.87/3.10 tff(2067,plain,
% 2.87/3.10 (b(s(s(s(s(s(z))))), s(z))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[2066, 1424])).
% 2.87/3.10 tff(2068,plain,
% 2.87/3.10 ((~r(s(z), s(s(s(s(s(z))))))) <=> (~r(elem!1, s(s(s(s(elem!1))))))),
% 2.87/3.10 inference(monotonicity,[status(thm)],[1880])).
% 2.87/3.10 tff(2069,plain,
% 2.87/3.10 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.87/3.10 inference(rewrite,[status(thm)],[])).
% 2.87/3.10 tff(2070,plain,
% 2.87/3.10 (((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.87/3.10 inference(rewrite,[status(thm)],[])).
% 2.87/3.10 tff(2071,plain,
% 2.87/3.10 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z))))))))),
% 2.87/3.10 inference(monotonicity,[status(thm)],[2070])).
% 2.87/3.10 tff(2072,plain,
% 2.87/3.10 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.87/3.10 inference(transitivity,[status(thm)],[2071, 2069])).
% 2.87/3.10 tff(2073,plain,
% 2.87/3.10 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.87/3.10 inference(quant_inst,[status(thm)],[])).
% 2.87/3.10 tff(2074,plain,
% 2.87/3.10 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z))))))),
% 2.87/3.10 inference(modus_ponens,[status(thm)],[2073, 2072])).
% 2.87/3.10 tff(2075,plain,
% 2.87/3.10 ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z))))))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[2074, 118, 1990])).
% 2.87/3.10 tff(2076,plain,
% 2.87/3.10 (~r(s(z), s(s(s(s(s(z))))))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[2075, 2057])).
% 2.87/3.10 tff(2077,plain,
% 2.87/3.10 (~r(elem!1, s(s(s(s(elem!1)))))),
% 2.87/3.10 inference(modus_ponens,[status(thm)],[2076, 2068])).
% 2.87/3.10 tff(2078,plain,
% 2.87/3.10 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[1465, 2077, 1423])).
% 2.87/3.10 tff(2079,plain,
% 2.87/3.10 (b(s(z), s(s(s(s(s(z))))))),
% 2.87/3.10 inference(modus_ponens,[status(thm)],[2078, 1447])).
% 2.87/3.10 tff(2080,plain,
% 2.87/3.10 (~b(s(s(s(s(s(z))))), z)),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[1941, 178, 1480, 1470, 2079, 2067])).
% 2.87/3.10 tff(2081,plain,
% 2.87/3.10 (~b(s(s(s(s(elem!1)))), z)),
% 2.87/3.10 inference(modus_ponens,[status(thm)],[2080, 1514])).
% 2.87/3.10 tff(2082,plain,
% 2.87/3.10 (r(s(s(s(s(elem!1)))), z)),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[1716, 2081])).
% 2.87/3.10 tff(2083,plain,
% 2.87/3.10 (r(s(s(s(s(s(z))))), z)),
% 2.87/3.10 inference(modus_ponens,[status(thm)],[2082, 1512])).
% 2.87/3.10 tff(2084,plain,
% 2.87/3.10 (b(s(s(s(s(z)))), s(s(z)))),
% 2.87/3.10 inference(modus_ponens,[status(thm)],[1634, 1699])).
% 2.87/3.10 tff(2085,plain,
% 2.87/3.10 (r(s(s(z)), s(s(s(elem!1))))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[1838, 147, 515])).
% 2.87/3.10 tff(2086,plain,
% 2.87/3.10 (~r(z, s(s(s(elem!1))))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[1831, 2085, 106])).
% 2.87/3.10 tff(2087,plain,
% 2.87/3.10 ((z = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = z)),
% 2.87/3.10 inference(commutativity,[status(thm)],[])).
% 2.87/3.10 tff(2088,plain,
% 2.87/3.10 ((s(s(s(elem!1))) = z) <=> (z = s(s(s(elem!1))))),
% 2.87/3.10 inference(symmetry,[status(thm)],[2087])).
% 2.87/3.10 tff(2089,plain,
% 2.87/3.10 ((~(s(s(s(elem!1))) = z)) <=> (~(z = s(s(s(elem!1)))))),
% 2.87/3.10 inference(monotonicity,[status(thm)],[2088])).
% 2.87/3.10 tff(2090,plain,
% 2.87/3.10 (~(z = s(s(s(elem!1))))),
% 2.87/3.10 inference(modus_ponens,[status(thm)],[940, 2089])).
% 2.87/3.10 tff(2091,plain,
% 2.87/3.10 (((~![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)))))),
% 2.87/3.10 inference(rewrite,[status(thm)],[])).
% 2.87/3.10 tff(2092,plain,
% 2.87/3.10 ((~![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)))))),
% 2.87/3.10 inference(quant_inst,[status(thm)],[])).
% 2.87/3.10 tff(2093,plain,
% 2.87/3.10 ((~![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))))),
% 2.87/3.10 inference(modus_ponens,[status(thm)],[2092, 2091])).
% 2.87/3.10 tff(2094,plain,
% 2.87/3.10 ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[2093, 41])).
% 2.87/3.10 tff(2095,plain,
% 2.87/3.10 (b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[2094, 2090])).
% 2.87/3.10 tff(2096,plain,
% 2.87/3.10 (b(z, s(s(s(elem!1))))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[2095, 2086])).
% 2.87/3.10 tff(2097,plain,
% 2.87/3.10 (b(z, s(s(s(s(z)))))),
% 2.87/3.10 inference(modus_ponens,[status(thm)],[2096, 1635])).
% 2.87/3.10 tff(2098,plain,
% 2.87/3.10 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 2.87/3.10 inference(monotonicity,[status(thm)],[515])).
% 2.87/3.10 tff(2099,plain,
% 2.87/3.10 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 2.87/3.10 inference(symmetry,[status(thm)],[2098])).
% 2.87/3.10 tff(2100,plain,
% 2.87/3.10 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 2.87/3.10 inference(transitivity,[status(thm)],[1834, 2099])).
% 2.87/3.10 tff(2101,plain,
% 2.87/3.10 (r(s(elem!1), s(s(s(elem!1))))),
% 2.87/3.10 inference(modus_ponens,[status(thm)],[147, 2100])).
% 2.87/3.10 tff(2102,assumption,(r(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 2.87/3.10 tff(2103,plain,
% 2.87/3.10 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.87/3.10 inference(rewrite,[status(thm)],[])).
% 2.87/3.10 tff(2104,plain,
% 2.87/3.10 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.87/3.10 inference(rewrite,[status(thm)],[])).
% 2.87/3.10 tff(2105,plain,
% 2.87/3.10 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1))))),
% 2.87/3.10 inference(monotonicity,[status(thm)],[2104])).
% 2.87/3.10 tff(2106,plain,
% 2.87/3.10 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.87/3.10 inference(transitivity,[status(thm)],[2105, 2103])).
% 2.87/3.10 tff(2107,plain,
% 2.87/3.10 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 2.87/3.10 inference(quant_inst,[status(thm)],[])).
% 2.87/3.10 tff(2108,plain,
% 2.87/3.10 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1))),
% 2.87/3.10 inference(modus_ponens,[status(thm)],[2107, 2106])).
% 2.87/3.10 tff(2109,plain,
% 2.87/3.10 ($false),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[2108, 118, 1426, 556, 2102])).
% 2.87/3.10 tff(2110,plain,((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.10 tff(2111,plain,
% 2.87/3.10 (~r(s(s(s(elem!1))), elem!1)),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[2110, 2101, 1426])).
% 2.87/3.10 tff(2112,plain,
% 2.87/3.10 (b(s(s(s(elem!1))), elem!1)),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[570, 2111, 949])).
% 2.87/3.10 tff(2113,plain,
% 2.87/3.10 (b(s(s(s(s(z)))), s(z))),
% 2.87/3.10 inference(modus_ponens,[status(thm)],[2112, 1571])).
% 2.87/3.10 tff(2114,plain,
% 2.87/3.10 (~b(s(s(s(s(z)))), z)),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[1799, 2113, 1480, 1790, 2097])).
% 2.87/3.10 tff(2115,plain,
% 2.87/3.10 (r(s(s(s(s(z)))), z)),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[191, 2114])).
% 2.87/3.10 tff(2116,plain,
% 2.87/3.10 ($false),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[1809, 118, 106, 2115, 147])).
% 2.87/3.10 tff(2117,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~b(z, s(z))) | (~(s(elem!1) = s(s(z)))) | (s(s(s(elem!1))) = elem!1) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.10 tff(2118,plain,
% 2.87/3.10 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[2117, 1470, 106, 515, 1525, 1426])).
% 2.87/3.10 tff(2119,plain,
% 2.87/3.10 (b(s(s(z)), s(s(s(s(z)))))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[163, 2118, 1684])).
% 2.87/3.10 tff(2120,plain,
% 2.87/3.10 (~b(s(s(s(s(z)))), z)),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[1736, 178, 273, 2040, 2119, 2084])).
% 2.87/3.10 tff(2121,plain,
% 2.87/3.10 (r(s(s(s(s(z)))), z)),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[191, 2120])).
% 2.87/3.10 tff(2122,plain,
% 2.87/3.10 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.87/3.10 inference(rewrite,[status(thm)],[])).
% 2.87/3.10 tff(2123,plain,
% 2.87/3.10 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.87/3.10 inference(quant_inst,[status(thm)],[])).
% 2.87/3.10 tff(2124,plain,
% 2.87/3.10 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.87/3.10 inference(modus_ponens,[status(thm)],[2123, 2122])).
% 2.87/3.10 tff(2125,plain,
% 2.87/3.10 (~r(s(s(s(s(s(z))))), z)),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[2124, 118, 2121, 1990])).
% 2.87/3.10 tff(2126,plain,
% 2.87/3.10 ($false),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[2125, 2083])).
% 2.87/3.10 tff(2127,plain,((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~(s(elem!1) = s(s(z)))) | (~b(z, s(s(z)))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), z)) | b(s(s(z)), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.10 tff(2128,plain,
% 2.87/3.10 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[2127, 1398, 273, 515, 1510, 818, 106, 1061])).
% 2.87/3.10 tff(2129,plain,
% 2.87/3.10 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(elem!1)))))),
% 2.87/3.10 inference(commutativity,[status(thm)],[])).
% 2.87/3.10 tff(2130,plain,
% 2.87/3.10 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(elem!1))))))),
% 2.87/3.10 inference(monotonicity,[status(thm)],[2129])).
% 2.87/3.10 tff(2131,plain,
% 2.87/3.10 (~(s(s(z)) = s(s(s(s(elem!1)))))),
% 2.87/3.10 inference(modus_ponens,[status(thm)],[1165, 2130])).
% 2.87/3.10 tff(2132,plain,
% 2.87/3.10 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(elem!1))))) | b(s(s(z)), s(s(s(s(elem!1))))) | r(s(s(z)), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(elem!1))))) | b(s(s(z)), s(s(s(s(elem!1))))) | r(s(s(z)), s(s(s(s(elem!1))))))),
% 2.87/3.10 inference(rewrite,[status(thm)],[])).
% 2.87/3.10 tff(2133,plain,
% 2.87/3.10 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(elem!1))))) | b(s(s(z)), s(s(s(s(elem!1))))) | r(s(s(z)), s(s(s(s(elem!1))))))),
% 2.87/3.10 inference(quant_inst,[status(thm)],[])).
% 2.87/3.10 tff(2134,plain,
% 2.87/3.10 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(elem!1))))) | b(s(s(z)), s(s(s(s(elem!1))))) | r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.87/3.10 inference(modus_ponens,[status(thm)],[2133, 2132])).
% 2.87/3.10 tff(2135,plain,
% 2.87/3.10 ((s(s(z)) = s(s(s(s(elem!1))))) | b(s(s(z)), s(s(s(s(elem!1))))) | r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[2134, 41])).
% 2.87/3.10 tff(2136,plain,
% 2.87/3.10 (b(s(s(z)), s(s(s(s(elem!1))))) | r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[2135, 2131])).
% 2.87/3.10 tff(2137,plain,
% 2.87/3.10 ($false),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[2136, 2128, 1501])).
% 2.87/3.10 tff(2138,plain,((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~(s(elem!1) = s(s(z)))) | (~r(s(s(z)), z)) | b(s(s(z)), s(elem!1)) | (s(elem!1) = elem!1) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.10 tff(2139,plain,
% 2.87/3.10 (~b(z, elem!1)),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[2138, 1385, 273, 106, 1377, 725, 506, 854])).
% 2.87/3.10 tff(2140,plain,
% 2.87/3.10 (r(z, elem!1)),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[585, 2139, 507])).
% 2.87/3.10 tff(2141,assumption,(~b(s(elem!1), elem!1)), introduced(assumption)).
% 2.87/3.10 tff(2142,plain,
% 2.87/3.10 (s(s(z)) = s(elem!1)),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[1067, 1061, 1062])).
% 2.87/3.10 tff(2143,plain,
% 2.87/3.10 (s(elem!1) = s(s(z))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[1058, 2142])).
% 2.87/3.10 tff(2144,plain,
% 2.87/3.10 (r(s(elem!1), z)),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[906, 2143, 106])).
% 2.87/3.10 tff(2145,plain,
% 2.87/3.10 (~r(s(elem!1), elem!1)),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[1284, 2144, 521])).
% 2.87/3.10 tff(2146,plain,
% 2.87/3.10 (s(elem!1) = elem!1),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[677, 2145, 2141])).
% 2.87/3.10 tff(2147,plain,
% 2.87/3.10 (s(s(s(elem!1))) = s(elem!1)),
% 2.87/3.10 inference(monotonicity,[status(thm)],[670])).
% 2.87/3.10 tff(2148,plain,
% 2.87/3.10 (s(s(s(elem!1))) = elem!1),
% 2.87/3.10 inference(transitivity,[status(thm)],[2147, 668])).
% 2.87/3.10 tff(2149,plain,
% 2.87/3.10 ($false),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[949, 2148])).
% 2.87/3.10 tff(2150,plain,((~(s(elem!1) = elem!1)) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.87/3.10 tff(2151,plain,
% 2.87/3.10 (s(s(s(elem!1))) = elem!1),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[2150, 2146])).
% 2.87/3.10 tff(2152,plain,
% 2.87/3.10 (r(s(s(z)), s(s(s(s(elem!1))))) <=> r(s(s(z)), s(elem!1))),
% 2.87/3.10 inference(monotonicity,[status(thm)],[1520])).
% 2.87/3.10 tff(2153,plain,
% 2.87/3.10 (r(s(s(z)), s(elem!1))),
% 2.87/3.10 inference(modus_ponens,[status(thm)],[1403, 2152])).
% 2.87/3.10 tff(2154,plain,
% 2.87/3.10 ($false),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[1062, 2153])).
% 2.87/3.10 tff(2155,plain,((~r(s(s(z)), s(s(s(s(elem!1)))))) | r(s(s(z)), s(elem!1)) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.10 tff(2156,plain,
% 2.87/3.10 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[2155, 2151, 1062])).
% 2.87/3.10 tff(2157,plain,
% 2.87/3.10 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[1524, 2151, 1061])).
% 2.87/3.10 tff(2158,plain,
% 2.87/3.10 ($false),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[2136, 2157, 2156])).
% 2.87/3.10 tff(2159,plain,(b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1)) | b(s(elem!1), elem!1) | (~r(z, elem!1)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.10 tff(2160,plain,
% 2.87/3.10 (b(s(elem!1), elem!1)),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[2159, 2140, 106, 1377, 1062])).
% 2.87/3.10 tff(2161,plain,
% 2.87/3.10 (~r(elem!1, s(s(s(s(z)))))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[529, 2140, 145])).
% 2.87/3.10 tff(2162,plain,
% 2.87/3.10 (b(elem!1, s(s(s(s(z)))))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[483, 2161, 469])).
% 2.87/3.10 tff(2163,plain,
% 2.87/3.10 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 2.87/3.10 inference(commutativity,[status(thm)],[])).
% 2.87/3.10 tff(2164,plain,
% 2.87/3.10 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(z)))))),
% 2.87/3.10 inference(symmetry,[status(thm)],[2163])).
% 2.87/3.10 tff(2165,assumption,(s(s(s(s(z)))) = s(elem!1)), introduced(assumption)).
% 2.87/3.11 tff(2166,plain,
% 2.87/3.11 (s(elem!1) = s(s(s(s(z))))),
% 2.87/3.11 inference(modus_ponens,[status(thm)],[2165, 2164])).
% 2.87/3.11 tff(2167,plain,
% 2.87/3.11 ($false),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[1369, 2166])).
% 2.87/3.11 tff(2168,plain,((~(s(s(s(s(z)))) = s(elem!1))) | (s(elem!1) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.11 tff(2169,plain,
% 2.87/3.11 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[2168, 1369])).
% 2.87/3.11 tff(2170,plain,
% 2.87/3.11 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1)))),
% 2.87/3.11 inference(rewrite,[status(thm)],[])).
% 2.87/3.11 tff(2171,plain,
% 2.87/3.11 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1)))),
% 2.87/3.11 inference(quant_inst,[status(thm)],[])).
% 2.87/3.11 tff(2172,plain,
% 2.87/3.11 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1))),
% 2.87/3.11 inference(modus_ponens,[status(thm)],[2171, 2170])).
% 2.87/3.11 tff(2173,plain,
% 2.87/3.11 ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1))),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[2172, 41])).
% 2.87/3.11 tff(2174,plain,
% 2.87/3.11 (b(s(s(s(s(z)))), s(elem!1))),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[2173, 2169, 1041])).
% 2.87/3.11 tff(2175,plain,
% 2.87/3.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(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))))),
% 2.87/3.11 inference(rewrite,[status(thm)],[])).
% 2.87/3.11 tff(2176,plain,
% 2.87/3.11 (((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(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))))),
% 2.87/3.11 inference(rewrite,[status(thm)],[])).
% 2.87/3.11 tff(2177,plain,
% 2.87/3.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(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)))))),
% 2.87/3.11 inference(monotonicity,[status(thm)],[2176])).
% 2.87/3.11 tff(2178,plain,
% 2.87/3.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(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))))),
% 2.87/3.11 inference(transitivity,[status(thm)],[2177, 2175])).
% 2.87/3.11 tff(2179,plain,
% 2.87/3.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)))),
% 2.87/3.11 inference(quant_inst,[status(thm)],[])).
% 2.87/3.11 tff(2180,plain,
% 2.87/3.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 2.87/3.11 inference(modus_ponens,[status(thm)],[2179, 2178])).
% 2.87/3.11 tff(2181,plain,
% 2.87/3.11 ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z))))))),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[2180, 178, 854, 2174, 1370])).
% 2.87/3.11 tff(2182,plain,
% 2.87/3.11 ($false),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[2181, 2162, 2160])).
% 2.87/3.11 tff(2183,plain,((s(elem!1) = s(s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (elem!1 = s(s(s(s(z))))) | (~r(s(s(z)), z)) | r(s(s(z)), s(elem!1)) | (~r(z, s(s(s(s(z)))))) | (z = elem!1) | (~b(z, s(s(z)))) | (s(elem!1) = elem!1) | (~b(elem!1, z)) | r(s(elem!1), s(s(z))) | (~b(elem!1, s(s(z)))) | r(s(s(s(s(z)))), s(elem!1)) | r(s(elem!1), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.11 tff(2184,plain,
% 2.87/3.11 (s(elem!1) = s(s(s(s(z))))),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[2183, 1112, 469, 106, 1053, 145, 1040, 273, 725, 506, 927, 1368, 1041, 926])).
% 2.87/3.11 tff(2185,plain,
% 2.87/3.11 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 2.87/3.11 inference(monotonicity,[status(thm)],[2184])).
% 2.87/3.11 tff(2186,plain,
% 2.87/3.11 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 2.87/3.11 inference(symmetry,[status(thm)],[2185])).
% 2.87/3.11 tff(2187,plain,
% 2.87/3.11 (s(s(s(z))) = elem!1),
% 2.87/3.11 inference(transitivity,[status(thm)],[61, 2186, 304])).
% 2.87/3.11 tff(2188,plain,
% 2.87/3.11 ((s(s(z)) = s(s(s(z)))) <=> (s(s(z)) = elem!1)),
% 2.87/3.11 inference(monotonicity,[status(thm)],[2187])).
% 2.87/3.11 tff(2189,plain,
% 2.87/3.11 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(z)) = elem!1))),
% 2.87/3.11 inference(monotonicity,[status(thm)],[2188])).
% 2.87/3.11 tff(2190,plain,
% 2.87/3.11 (~(elem!1 = s(s(z)))),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[1353, 2184, 551])).
% 2.87/3.11 tff(2191,plain,
% 2.87/3.11 ((s(s(z)) = s(s(s(z)))) <=> (s(s(z)) = elem!1)),
% 2.87/3.11 inference(monotonicity,[status(thm)],[1183])).
% 2.87/3.11 tff(2192,plain,
% 2.87/3.11 ((s(s(z)) = s(s(s(z)))) <=> (elem!1 = s(s(z)))),
% 2.87/3.11 inference(transitivity,[status(thm)],[2191, 1666])).
% 2.87/3.11 tff(2193,assumption,(s(s(z)) = s(s(s(z)))), introduced(assumption)).
% 2.87/3.11 tff(2194,plain,
% 2.87/3.11 (elem!1 = s(s(z))),
% 2.87/3.11 inference(modus_ponens,[status(thm)],[2193, 2192])).
% 2.87/3.11 tff(2195,plain,
% 2.87/3.11 ($false),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[462, 2194])).
% 2.87/3.11 tff(2196,plain,((~(s(s(z)) = s(s(s(z))))) | (elem!1 = s(s(z))) | (~(s(elem!1) = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.11 tff(2197,plain,
% 2.87/3.11 (~(s(s(z)) = s(s(s(z))))),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[2196, 2184, 2190])).
% 2.87/3.11 tff(2198,plain,
% 2.87/3.11 (~(s(s(z)) = elem!1)),
% 2.87/3.11 inference(modus_ponens,[status(thm)],[2197, 2189])).
% 2.87/3.11 tff(2199,plain,
% 2.87/3.11 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.87/3.11 inference(monotonicity,[status(thm)],[2187])).
% 2.87/3.11 tff(2200,plain,
% 2.87/3.11 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 2.87/3.11 inference(symmetry,[status(thm)],[2199])).
% 2.87/3.11 tff(2201,plain,
% 2.87/3.11 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(s(z)))))),
% 2.87/3.11 inference(monotonicity,[status(thm)],[2184])).
% 2.87/3.11 tff(2202,plain,
% 2.87/3.11 (b(elem!1, s(s(s(s(z)))))),
% 2.87/3.11 inference(modus_ponens,[status(thm)],[1112, 2201])).
% 2.87/3.11 tff(2203,plain,
% 2.87/3.11 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.87/3.11 inference(modus_ponens,[status(thm)],[2202, 2200])).
% 2.87/3.11 tff(2204,plain,
% 2.87/3.11 (~r(z, elem!1)),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[1295, 2203, 202, 165, 2184, 725, 2198, 844, 106])).
% 2.87/3.11 tff(2205,plain,
% 2.87/3.11 (elem!1 = s(s(s(z)))),
% 2.87/3.11 inference(transitivity,[status(thm)],[517, 2185, 11])).
% 2.87/3.11 tff(2206,plain,
% 2.87/3.11 (b(elem!1, s(s(z))) <=> b(s(s(s(z))), s(s(z)))),
% 2.87/3.11 inference(monotonicity,[status(thm)],[2205])).
% 2.87/3.11 tff(2207,plain,
% 2.87/3.11 (b(s(s(s(z))), s(s(z)))),
% 2.87/3.11 inference(modus_ponens,[status(thm)],[1368, 2206])).
% 2.87/3.11 tff(2208,plain,
% 2.87/3.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.87/3.11 inference(rewrite,[status(thm)],[])).
% 2.87/3.11 tff(2209,plain,
% 2.87/3.11 (((~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(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.87/3.11 inference(rewrite,[status(thm)],[])).
% 2.87/3.11 tff(2210,plain,
% 2.87/3.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(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(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))))),
% 2.87/3.11 inference(monotonicity,[status(thm)],[2209])).
% 2.87/3.11 tff(2211,plain,
% 2.87/3.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(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(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.87/3.11 inference(transitivity,[status(thm)],[2210, 2208])).
% 2.87/3.11 tff(2212,plain,
% 2.87/3.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(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(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 2.87/3.11 inference(quant_inst,[status(thm)],[])).
% 2.87/3.11 tff(2213,plain,
% 2.87/3.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 2.87/3.11 inference(modus_ponens,[status(thm)],[2212, 2211])).
% 2.87/3.11 tff(2214,plain,
% 2.87/3.11 (~b(z, s(s(s(z))))),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[2213, 178, 273, 165, 2203, 2207])).
% 2.87/3.11 tff(2215,plain,
% 2.87/3.11 (~b(z, elem!1)),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[1238, 2214, 2184])).
% 2.87/3.11 tff(2216,plain,
% 2.87/3.11 ($false),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[585, 2215, 2204, 1040])).
% 2.87/3.11 tff(2217,plain,(r(elem!1, s(elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (s(elem!1) = elem!1) | (~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~b(z, s(s(z)))) | (elem!1 = s(s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~b(elem!1, z)) | r(s(elem!1), s(s(z))) | r(s(s(s(s(z)))), s(elem!1)) | r(s(elem!1), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.11 tff(2218,plain,
% 2.87/3.11 ($false),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[2217, 925, 921, 307, 469, 106, 273, 900, 145, 506, 725, 907, 917])).
% 2.87/3.11 tff(2219,plain,((s(elem!1) = elem!1) | (elem!1 = s(s(s(s(z))))) | (~r(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~b(elem!1, z)) | r(elem!1, s(s(z))) | (~r(s(s(s(s(z)))), z)) | b(s(elem!1), s(s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | b(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (s(s(z)) = elem!1) | (~b(z, elem!1)) | r(s(s(s(s(s(s(s(z))))))), z)), inference(lemma,lemma(discharge,[]))).
% 2.87/3.11 tff(2220,plain,
% 2.87/3.11 (s(elem!1) = elem!1),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[2219, 643, 106, 273, 145, 506, 460, 194, 305, 224, 469, 12, 818, 126])).
% 2.87/3.11 tff(2221,plain,
% 2.87/3.11 (s(s(elem!1)) = elem!1),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[672, 2220])).
% 2.87/3.11 tff(2222,plain,
% 2.87/3.11 (elem!1 = s(s(elem!1))),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[1546, 2221])).
% 2.87/3.11 tff(2223,plain,
% 2.87/3.11 (s(s(s(elem!1))) = s(elem!1)),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[1539, 2222])).
% 2.87/3.11 tff(2224,plain,
% 2.87/3.11 (elem!1 = s(s(s(s(elem!1))))),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[1509, 2223])).
% 2.87/3.11 tff(2225,plain,
% 2.87/3.11 (~(s(elem!1) = s(s(z)))),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[1422, 2224])).
% 2.87/3.11 tff(2226,plain,
% 2.87/3.11 (r(s(elem!1), s(s(z)))),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[421, 2225, 305])).
% 2.87/3.11 tff(2227,plain,
% 2.87/3.11 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[390, 2226, 224])).
% 2.87/3.11 tff(2228,plain,
% 2.87/3.11 (s(elem!1) = s(s(s(s(s(s(s(z)))))))),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[395, 2227, 643])).
% 2.87/3.11 tff(2229,plain,
% 2.87/3.11 (s(s(s(s(s(s(s(z))))))) = s(elem!1)),
% 2.87/3.11 inference(modus_ponens,[status(thm)],[2228, 655])).
% 2.87/3.11 tff(2230,plain,
% 2.87/3.11 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[666, 2221, 551])).
% 2.87/3.11 tff(2231,plain,
% 2.87/3.11 ($false),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[2230, 2229])).
% 2.87/3.11 tff(2232,plain,(b(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | b(s(elem!1), s(s(z))) | (~r(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~b(elem!1, z)) | r(elem!1, s(s(z))) | (~r(s(s(s(s(z)))), z)) | (elem!1 = s(s(s(s(z))))) | (s(s(z)) = elem!1) | (~b(z, elem!1)) | r(s(s(s(s(s(s(s(z))))))), z)), inference(lemma,lemma(discharge,[]))).
% 2.87/3.11 tff(2233,plain,
% 2.87/3.11 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[2232, 287, 305, 106, 273, 145, 499, 810, 194, 436, 12, 816, 124])).
% 2.87/3.11 tff(2234,plain,
% 2.87/3.11 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.87/3.11 inference(monotonicity,[status(thm)],[515])).
% 2.87/3.11 tff(2235,plain,
% 2.87/3.11 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.87/3.11 inference(symmetry,[status(thm)],[2234])).
% 2.87/3.11 tff(2236,plain,
% 2.87/3.11 ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.87/3.11 inference(monotonicity,[status(thm)],[2235])).
% 2.87/3.11 tff(2237,plain,
% 2.87/3.11 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.87/3.11 inference(modus_ponens,[status(thm)],[286, 2236])).
% 2.87/3.11 tff(2238,plain,
% 2.87/3.11 ($false),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[727, 2237])).
% 2.87/3.11 tff(2239,plain,((~(s(elem!1) = s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | b(s(s(z)), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.11 tff(2240,plain,
% 2.87/3.11 (~(s(elem!1) = s(s(z)))),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[2239, 2233, 286])).
% 2.87/3.11 tff(2241,plain,
% 2.87/3.11 (r(s(elem!1), s(s(z)))),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[421, 2240, 305])).
% 2.87/3.11 tff(2242,plain,
% 2.87/3.11 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), s(s(z)))))),
% 2.87/3.11 inference(rewrite,[status(thm)],[])).
% 2.87/3.11 tff(2243,plain,
% 2.87/3.11 (((~r(s(s(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(z))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), s(s(z)))))),
% 2.87/3.11 inference(rewrite,[status(thm)],[])).
% 2.87/3.11 tff(2244,plain,
% 2.87/3.11 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), s(s(z))))))),
% 2.87/3.11 inference(monotonicity,[status(thm)],[2243])).
% 2.87/3.11 tff(2245,plain,
% 2.87/3.11 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), s(s(z)))))),
% 2.87/3.11 inference(transitivity,[status(thm)],[2244, 2242])).
% 2.87/3.11 tff(2246,plain,
% 2.87/3.11 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(z)))))),
% 2.87/3.11 inference(quant_inst,[status(thm)],[])).
% 2.87/3.11 tff(2247,plain,
% 2.87/3.11 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), s(s(z))))),
% 2.87/3.11 inference(modus_ponens,[status(thm)],[2246, 2245])).
% 2.87/3.11 tff(2248,plain,
% 2.87/3.11 ($false),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[2247, 118, 1426, 438, 363])).
% 2.87/3.11 tff(2249,plain,((~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.11 tff(2250,plain,
% 2.87/3.11 (~r(s(elem!1), elem!1)),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[2249, 2241, 828])).
% 2.87/3.11 tff(2251,plain,
% 2.87/3.11 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(elem!1), s(s(z)))))),
% 2.87/3.11 inference(rewrite,[status(thm)],[])).
% 2.87/3.11 tff(2252,plain,
% 2.87/3.11 (((~r(s(s(z)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z))))) <=> ((~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(elem!1), s(s(z)))))),
% 2.87/3.11 inference(rewrite,[status(thm)],[])).
% 2.87/3.11 tff(2253,plain,
% 2.87/3.11 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(elem!1), s(s(z))))))),
% 2.87/3.11 inference(monotonicity,[status(thm)],[2252])).
% 2.87/3.11 tff(2254,plain,
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% 2.87/3.11 inference(transitivity,[status(thm)],[2253, 2251])).
% 2.87/3.11 tff(2255,plain,
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% 2.87/3.11 tff(2256,plain,
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% 2.87/3.11 inference(modus_ponens,[status(thm)],[2255, 2254])).
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% 2.87/3.11 inference(unit_resolution,[status(thm)],[2256, 118, 844, 106, 363])).
% 2.87/3.11 tff(2258,plain,((~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(elem!1), s(s(z))))), inference(lemma,lemma(discharge,[]))).
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% 2.87/3.11 inference(unit_resolution,[status(thm)],[2258, 2241, 106])).
% 2.87/3.11 tff(2260,plain,
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% 2.87/3.11 inference(unit_resolution,[status(thm)],[774, 2259])).
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% 2.87/3.11 inference(rewrite,[status(thm)],[])).
% 2.87/3.11 tff(2262,plain,
% 2.87/3.11 (((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z))) <=> ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 2.87/3.11 inference(rewrite,[status(thm)],[])).
% 2.87/3.11 tff(2263,plain,
% 2.87/3.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z))))))),
% 2.87/3.11 inference(monotonicity,[status(thm)],[2262])).
% 2.87/3.11 tff(2264,plain,
% 2.87/3.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 2.87/3.11 inference(transitivity,[status(thm)],[2263, 2261])).
% 2.87/3.11 tff(2265,plain,
% 2.87/3.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)))),
% 2.87/3.11 inference(quant_inst,[status(thm)],[])).
% 2.87/3.11 tff(2266,plain,
% 2.87/3.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z))))),
% 2.87/3.11 inference(modus_ponens,[status(thm)],[2265, 2264])).
% 2.87/3.11 tff(2267,plain,
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% 2.87/3.11 inference(unit_resolution,[status(thm)],[2266, 178, 818, 683, 853, 273, 812])).
% 2.87/3.11 tff(2268,plain,((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.11 tff(2269,plain,
% 2.87/3.11 (~b(s(elem!1), elem!1)),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[2268, 2260, 816, 273, 811])).
% 2.87/3.11 tff(2270,plain,
% 2.87/3.11 (s(elem!1) = elem!1),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[677, 2269, 2250])).
% 2.87/3.11 tff(2271,plain,
% 2.87/3.11 (r(s(elem!1), s(s(z))) <=> r(elem!1, s(s(z)))),
% 2.87/3.11 inference(monotonicity,[status(thm)],[2270])).
% 2.87/3.11 tff(2272,plain,
% 2.87/3.11 (r(elem!1, s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 2.87/3.11 inference(symmetry,[status(thm)],[2271])).
% 2.87/3.11 tff(2273,plain,
% 2.87/3.11 ((~r(elem!1, s(s(z)))) <=> (~r(s(elem!1), s(s(z))))),
% 2.87/3.11 inference(monotonicity,[status(thm)],[2272])).
% 2.87/3.11 tff(2274,plain,
% 2.87/3.11 (~r(s(elem!1), s(s(z)))),
% 2.87/3.11 inference(modus_ponens,[status(thm)],[810, 2273])).
% 2.87/3.11 tff(2275,plain,
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% 2.87/3.11 inference(unit_resolution,[status(thm)],[2241, 2274])).
% 2.87/3.11 tff(2276,plain,(b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | (~b(z, s(s(z)))) | (~r(s(s(z)), z)) | b(s(elem!1), s(s(z))) | (s(s(z)) = elem!1) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.87/3.11 tff(2277,plain,
% 2.87/3.11 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[2276, 305, 106, 273, 12, 145, 194, 167, 107, 290])).
% 2.87/3.12 tff(2278,plain,
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% 2.87/3.12 inference(unit_resolution,[status(thm)],[421, 1056, 305])).
% 2.87/3.12 tff(2279,plain,
% 2.87/3.12 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.87/3.12 inference(modus_ponens,[status(thm)],[2278, 362])).
% 2.87/3.12 tff(2280,plain,
% 2.87/3.12 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[367, 118, 2279, 107])).
% 2.87/3.12 tff(2281,plain,
% 2.87/3.12 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.87/3.12 inference(modus_ponens,[status(thm)],[2280, 361])).
% 2.87/3.12 tff(2282,plain,
% 2.87/3.12 (b(s(s(s(elem!1))), s(elem!1))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[373, 2281, 356])).
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% 2.87/3.12 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.87/3.12 inference(modus_ponens,[status(thm)],[2282, 355])).
% 2.87/3.12 tff(2284,plain,
% 2.87/3.12 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.87/3.12 inference(monotonicity,[status(thm)],[350])).
% 2.87/3.12 tff(2285,plain,
% 2.87/3.12 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.87/3.12 inference(symmetry,[status(thm)],[2284])).
% 2.87/3.12 tff(2286,assumption,(~(s(elem!1) = s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.87/3.12 tff(2287,plain,
% 2.87/3.12 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[395, 643, 2286])).
% 2.87/3.12 tff(2288,plain,
% 2.87/3.12 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.87/3.12 inference(modus_ponens,[status(thm)],[2287, 2285])).
% 2.87/3.12 tff(2289,plain,
% 2.87/3.12 (b(s(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))))))))),
% 2.87/3.12 inference(symmetry,[status(thm)],[376])).
% 2.87/3.12 tff(2290,plain,
% 2.87/3.12 (s(s(z)) = s(s(s(s(s(z)))))),
% 2.87/3.12 inference(transitivity,[status(thm)],[1415, 320])).
% 2.87/3.12 tff(2291,plain,
% 2.87/3.12 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.87/3.12 inference(monotonicity,[status(thm)],[2290])).
% 2.87/3.12 tff(2292,plain,
% 2.87/3.12 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.87/3.12 inference(transitivity,[status(thm)],[2291, 2289])).
% 2.87/3.12 tff(2293,plain,
% 2.87/3.12 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.87/3.12 inference(modus_ponens,[status(thm)],[166, 2292])).
% 2.87/3.12 tff(2294,plain,
% 2.87/3.12 ($false),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[643, 2293])).
% 2.87/3.12 tff(2295,plain,((~(s(elem!1) = s(s(z)))) | b(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.12 tff(2296,plain,
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% 2.87/3.12 inference(unit_resolution,[status(thm)],[2295, 643, 166, 319])).
% 2.87/3.12 tff(2297,plain,
% 2.87/3.12 (r(s(elem!1), s(s(z)))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[421, 2296, 305])).
% 2.87/3.12 tff(2298,plain,
% 2.87/3.12 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.87/3.12 inference(modus_ponens,[status(thm)],[2297, 362])).
% 2.87/3.12 tff(2299,plain,
% 2.87/3.12 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.87/3.12 inference(rewrite,[status(thm)],[])).
% 2.87/3.12 tff(2300,plain,
% 2.87/3.12 (((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.87/3.12 inference(rewrite,[status(thm)],[])).
% 2.87/3.12 tff(2301,plain,
% 2.87/3.12 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 2.87/3.12 inference(monotonicity,[status(thm)],[2300])).
% 2.87/3.12 tff(2302,plain,
% 2.87/3.12 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.87/3.12 inference(transitivity,[status(thm)],[2301, 2299])).
% 2.87/3.12 tff(2303,plain,
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% 2.87/3.12 tff(2304,plain,
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% 2.87/3.12 inference(modus_ponens,[status(thm)],[2303, 2302])).
% 2.87/3.12 tff(2305,plain,
% 2.87/3.12 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[2304, 118, 2298, 107])).
% 2.87/3.12 tff(2306,plain,
% 2.87/3.12 ($false),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[2305, 2288])).
% 2.87/3.12 tff(2307,plain,(b(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~(elem!1 = s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | b(s(elem!1), s(s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.12 tff(2308,plain,
% 2.87/3.12 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
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% 2.87/3.12 tff(2309,plain,
% 2.87/3.12 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.87/3.12 inference(modus_ponens,[status(thm)],[2308, 376])).
% 2.87/3.12 tff(2310,plain,
% 2.87/3.12 (b(z, s(elem!1)) <=> b(z, s(s(s(s(s(z))))))),
% 2.87/3.12 inference(monotonicity,[status(thm)],[320])).
% 2.87/3.12 tff(2311,plain,
% 2.87/3.12 (~(s(s(z)) = s(elem!1))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[1058, 1056])).
% 2.87/3.12 tff(2312,plain,
% 2.87/3.12 (r(s(elem!1), z) <=> r(s(s(s(s(s(z))))), z)),
% 2.87/3.12 inference(monotonicity,[status(thm)],[320])).
% 2.87/3.12 tff(2313,plain,
% 2.87/3.12 ((~r(s(elem!1), z)) <=> (~r(s(s(s(s(s(z))))), z))),
% 2.87/3.12 inference(monotonicity,[status(thm)],[2312])).
% 2.87/3.12 tff(2314,plain,
% 2.87/3.12 (~r(s(elem!1), z)),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[2258, 2278, 106])).
% 2.87/3.12 tff(2315,plain,
% 2.87/3.12 (~r(s(s(s(s(s(z))))), z)),
% 2.87/3.12 inference(modus_ponens,[status(thm)],[2314, 2313])).
% 2.87/3.12 tff(2316,plain,
% 2.87/3.12 (b(s(s(s(s(s(z))))), z)),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[410, 41, 242, 2315])).
% 2.87/3.12 tff(2317,plain,
% 2.87/3.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.87/3.12 inference(rewrite,[status(thm)],[])).
% 2.87/3.12 tff(2318,plain,
% 2.87/3.12 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.87/3.12 inference(rewrite,[status(thm)],[])).
% 2.87/3.12 tff(2319,plain,
% 2.87/3.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.87/3.12 inference(monotonicity,[status(thm)],[2318])).
% 2.87/3.12 tff(2320,plain,
% 2.87/3.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.87/3.12 inference(transitivity,[status(thm)],[2319, 2317])).
% 2.87/3.12 tff(2321,plain,
% 2.87/3.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.87/3.12 inference(quant_inst,[status(thm)],[])).
% 2.87/3.12 tff(2322,plain,
% 2.87/3.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 2.87/3.12 inference(modus_ponens,[status(thm)],[2321, 2320])).
% 2.87/3.12 tff(2323,plain,
% 2.87/3.12 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[2322, 178, 166, 2316, 134, 2309])).
% 2.87/3.12 tff(2324,plain,
% 2.87/3.12 (b(s(s(z)), s(elem!1)) <=> b(s(s(z)), s(s(s(s(s(z))))))),
% 2.87/3.12 inference(monotonicity,[status(thm)],[320])).
% 2.87/3.12 tff(2325,plain,
% 2.87/3.12 (b(s(s(z)), s(s(s(s(s(z)))))) <=> b(s(s(z)), s(elem!1))),
% 2.87/3.12 inference(symmetry,[status(thm)],[2324])).
% 2.87/3.12 tff(2326,plain,
% 2.87/3.12 ((~b(s(s(z)), s(s(s(s(s(z))))))) <=> (~b(s(s(z)), s(elem!1)))),
% 2.87/3.12 inference(monotonicity,[status(thm)],[2325])).
% 2.87/3.12 tff(2327,assumption,(~b(s(s(z)), s(s(s(s(s(z))))))), introduced(assumption)).
% 2.87/3.12 tff(2328,plain,
% 2.87/3.12 (~b(s(s(z)), s(elem!1))),
% 2.87/3.12 inference(modus_ponens,[status(thm)],[2327, 2326])).
% 2.87/3.12 tff(2329,plain,
% 2.87/3.12 ($false),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[1071, 2328])).
% 2.87/3.12 tff(2330,plain,(b(s(s(z)), s(s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))) | (~(elem!1 = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.12 tff(2331,plain,
% 2.87/3.12 (~b(s(s(z)), s(elem!1))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[2330, 2323, 319])).
% 2.87/3.12 tff(2332,plain,
% 2.87/3.12 (r(s(s(z)), s(elem!1))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[1067, 2331, 2311])).
% 2.87/3.12 tff(2333,assumption,(r(z, s(elem!1))), introduced(assumption)).
% 2.87/3.12 tff(2334,plain,
% 2.87/3.12 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1))))),
% 2.87/3.12 inference(rewrite,[status(thm)],[])).
% 2.87/3.12 tff(2335,plain,
% 2.87/3.12 (((~r(z, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), z))) <=> ((~r(z, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1))))),
% 2.87/3.12 inference(rewrite,[status(thm)],[])).
% 2.87/3.12 tff(2336,plain,
% 2.87/3.12 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1)))))),
% 2.87/3.12 inference(monotonicity,[status(thm)],[2335])).
% 2.87/3.12 tff(2337,plain,
% 2.87/3.12 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1))))),
% 2.87/3.12 inference(transitivity,[status(thm)],[2336, 2334])).
% 2.87/3.12 tff(2338,plain,
% 2.87/3.12 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), z)))),
% 2.87/3.12 inference(quant_inst,[status(thm)],[])).
% 2.87/3.12 tff(2339,plain,
% 2.87/3.12 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1)))),
% 2.87/3.12 inference(modus_ponens,[status(thm)],[2338, 2337])).
% 2.87/3.12 tff(2340,plain,
% 2.87/3.12 ($false),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[2339, 118, 2333, 106, 1329])).
% 2.87/3.12 tff(2341,plain,((~r(s(s(z)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.12 tff(2342,plain,
% 2.87/3.12 (~r(z, s(elem!1))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[2341, 2332, 106])).
% 2.87/3.12 tff(2343,plain,
% 2.87/3.12 ((z = s(elem!1)) <=> (s(elem!1) = z)),
% 2.87/3.12 inference(commutativity,[status(thm)],[])).
% 2.87/3.12 tff(2344,plain,
% 2.87/3.12 ((s(elem!1) = z) <=> (z = s(elem!1))),
% 2.87/3.12 inference(symmetry,[status(thm)],[2343])).
% 2.87/3.12 tff(2345,plain,
% 2.87/3.12 ((~(s(elem!1) = z)) <=> (~(z = s(elem!1)))),
% 2.87/3.12 inference(monotonicity,[status(thm)],[2344])).
% 2.87/3.12 tff(2346,plain,
% 2.87/3.12 (~(z = s(elem!1))),
% 2.87/3.12 inference(modus_ponens,[status(thm)],[769, 2345])).
% 2.87/3.12 tff(2347,plain,
% 2.87/3.12 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1)))),
% 2.87/3.12 inference(rewrite,[status(thm)],[])).
% 2.87/3.12 tff(2348,plain,
% 2.87/3.12 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1)))),
% 2.87/3.12 inference(quant_inst,[status(thm)],[])).
% 2.87/3.12 tff(2349,plain,
% 2.87/3.12 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1))),
% 2.87/3.12 inference(modus_ponens,[status(thm)],[2348, 2347])).
% 2.87/3.12 tff(2350,plain,
% 2.87/3.12 ((z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[2349, 41])).
% 2.87/3.12 tff(2351,plain,
% 2.87/3.12 (b(z, s(elem!1)) | r(z, s(elem!1))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[2350, 2346])).
% 2.87/3.12 tff(2352,plain,
% 2.87/3.12 (b(z, s(elem!1))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[2351, 2342])).
% 2.87/3.12 tff(2353,plain,
% 2.87/3.12 (b(z, s(s(s(s(s(z))))))),
% 2.87/3.12 inference(modus_ponens,[status(thm)],[2352, 2310])).
% 2.87/3.12 tff(2354,plain,
% 2.87/3.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.87/3.12 inference(rewrite,[status(thm)],[])).
% 2.87/3.12 tff(2355,plain,
% 2.87/3.12 (((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.87/3.12 inference(rewrite,[status(thm)],[])).
% 2.87/3.12 tff(2356,plain,
% 2.87/3.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 2.87/3.12 inference(monotonicity,[status(thm)],[2355])).
% 2.87/3.12 tff(2357,plain,
% 2.87/3.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.87/3.12 inference(transitivity,[status(thm)],[2356, 2354])).
% 2.87/3.12 tff(2358,plain,
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% 2.87/3.12 tff(2359,plain,
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% 2.87/3.12 inference(modus_ponens,[status(thm)],[2358, 2357])).
% 2.87/3.12 tff(2360,plain,
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% 2.87/3.12 inference(unit_resolution,[status(thm)],[2359, 178, 2316, 2353, 134, 2309, 2283])).
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% 2.87/3.12 tff(2362,plain,
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% 2.87/3.12 tff(2363,plain,
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% 2.87/3.12 inference(symmetry,[status(thm)],[2362])).
% 2.87/3.12 tff(2364,plain,
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% 2.87/3.12 tff(2365,plain,
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% 2.87/3.12 inference(monotonicity,[status(thm)],[2364])).
% 2.87/3.12 tff(2366,plain,
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% 2.87/3.12 inference(transitivity,[status(thm)],[71, 2365, 53])).
% 2.87/3.12 tff(2367,plain,
% 2.87/3.12 (inj_0(s(z)) = inj_0(s(s(s(s(z)))))),
% 2.87/3.12 inference(monotonicity,[status(thm)],[2366])).
% 2.87/3.12 tff(2368,plain,
% 2.87/3.12 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 2.87/3.12 inference(symmetry,[status(thm)],[2367])).
% 2.87/3.12 tff(2369,plain,
% 2.87/3.12 (s(s(s(z))) = s(s(s(s(s(s(z))))))),
% 2.87/3.12 inference(monotonicity,[status(thm)],[2364])).
% 2.87/3.12 tff(2370,plain,
% 2.87/3.12 (s(s(s(s(s(s(z)))))) = s(s(s(z)))),
% 2.87/3.12 inference(symmetry,[status(thm)],[2369])).
% 2.87/3.12 tff(2371,plain,
% 2.87/3.12 (s(s(s(s(s(s(z)))))) = z),
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% 2.87/3.12 tff(2372,plain,
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% 2.87/3.12 inference(unit_resolution,[status(thm)],[433, 2371])).
% 2.87/3.12 tff(2373,plain,((~(elem!1 = s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | b(s(elem!1), s(s(z))) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.87/3.12 tff(2374,plain,
% 2.87/3.12 (~(elem!1 = s(s(s(s(z)))))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[2373, 2277, 106, 107, 305, 12])).
% 2.87/3.12 tff(2375,plain,
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% 2.87/3.12 tff(2376,plain,
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% 2.87/3.12 inference(unit_resolution,[status(thm)],[498, 2375, 290])).
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% 2.87/3.12 (~(elem!1 = s(s(s(s(z)))))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[2373, 166, 106, 107, 305, 12])).
% 2.87/3.12 tff(2378,assumption,(s(s(elem!1)) = s(s(z))), introduced(assumption)).
% 2.87/3.12 tff(2379,plain,
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% 2.87/3.12 tff(2380,plain,
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% 2.87/3.12 inference(monotonicity,[status(thm)],[2379])).
% 2.87/3.12 tff(2381,plain,
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% 2.87/3.12 tff(2382,plain,
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% 2.87/3.12 inference(monotonicity,[status(thm)],[2381])).
% 2.87/3.12 tff(2383,plain,
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% 2.87/3.12 inference(symmetry,[status(thm)],[51])).
% 2.87/3.12 tff(2384,plain,
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% 2.87/3.12 tff(2385,plain,
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% 2.87/3.12 inference(unit_resolution,[status(thm)],[507, 2384])).
% 2.87/3.12 tff(2386,plain,((~(s(s(elem!1)) = s(s(z)))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.87/3.12 tff(2387,plain,
% 2.87/3.12 (~(s(s(elem!1)) = s(s(z)))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[2386, 507])).
% 2.87/3.12 tff(2388,plain,
% 2.87/3.12 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), 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(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), 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(s(z)))))),
% 2.87/3.12 inference(rewrite,[status(thm)],[])).
% 2.87/3.12 tff(2389,plain,
% 2.87/3.12 (((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(elem!1), 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(s(z)))))),
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% 2.87/3.12 tff(2390,plain,
% 2.87/3.12 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), 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(s(z))))))),
% 2.87/3.12 inference(monotonicity,[status(thm)],[2389])).
% 2.87/3.12 tff(2391,plain,
% 2.87/3.12 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), 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(s(z)))))),
% 2.87/3.12 inference(transitivity,[status(thm)],[2390, 2388])).
% 2.87/3.12 tff(2392,plain,
% 2.87/3.12 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.87/3.12 inference(quant_inst,[status(thm)],[])).
% 2.87/3.12 tff(2393,plain,
% 2.87/3.12 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), 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(s(z))))),
% 2.87/3.12 inference(modus_ponens,[status(thm)],[2392, 2391])).
% 2.87/3.12 tff(2394,plain,
% 2.87/3.12 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[2393, 118, 2278, 107])).
% 2.87/3.12 tff(2395,plain,
% 2.97/3.13 (r(elem!1, s(s(z))) <=> r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[694])).
% 2.97/3.13 tff(2396,plain,
% 2.97/3.13 (r(s(s(s(s(s(s(z)))))), s(s(z))) <=> r(elem!1, s(s(z)))),
% 2.97/3.13 inference(symmetry,[status(thm)],[2395])).
% 2.97/3.13 tff(2397,plain,
% 2.97/3.13 ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) <=> (~r(elem!1, s(s(z))))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[2396])).
% 2.97/3.13 tff(2398,plain,
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% 2.97/3.13 inference(unit_resolution,[status(thm)],[666, 656, 551])).
% 2.97/3.13 tff(2399,plain,
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% 2.97/3.13 inference(unit_resolution,[status(thm)],[672, 2398])).
% 2.97/3.13 tff(2400,plain,
% 2.97/3.13 (~r(s(elem!1), z)),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[2258, 363, 106])).
% 2.97/3.13 tff(2401,plain,
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% 2.97/3.13 inference(unit_resolution,[status(thm)],[774, 2400])).
% 2.97/3.13 tff(2402,plain,
% 2.97/3.13 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.97/3.13 inference(monotonicity,[status(thm)],[648])).
% 2.97/3.13 tff(2403,plain,
% 2.97/3.13 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))) <=> r(s(elem!1), elem!1)),
% 2.97/3.13 inference(transitivity,[status(thm)],[2402, 652])).
% 2.97/3.13 tff(2404,plain,
% 2.97/3.13 ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) <=> (~r(s(elem!1), elem!1))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[2403])).
% 2.97/3.13 tff(2405,assumption,(r(s(s(s(s(s(s(z)))))), s(s(z)))), introduced(assumption)).
% 2.97/3.13 tff(2406,plain,
% 2.97/3.13 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(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(s(s(s(s(s(z)))))))))),
% 2.97/3.13 inference(rewrite,[status(thm)],[])).
% 2.97/3.13 tff(2407,plain,
% 2.97/3.13 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))),
% 2.97/3.13 inference(quant_inst,[status(thm)],[])).
% 2.97/3.13 tff(2408,plain,
% 2.97/3.13 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))))),
% 2.97/3.13 inference(modus_ponens,[status(thm)],[2407, 2406])).
% 2.97/3.13 tff(2409,plain,
% 2.97/3.13 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[2408, 118, 2405, 107])).
% 2.97/3.13 tff(2410,plain,
% 2.97/3.13 (~r(s(elem!1), elem!1)),
% 2.97/3.13 inference(modus_ponens,[status(thm)],[2409, 2404])).
% 2.97/3.13 tff(2411,plain,
% 2.97/3.13 (b(s(elem!1), elem!1)),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[677, 2410, 725])).
% 2.97/3.13 tff(2412,plain,
% 2.97/3.13 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[645])).
% 2.97/3.13 tff(2413,plain,
% 2.97/3.13 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(elem!1))),
% 2.97/3.13 inference(symmetry,[status(thm)],[2412])).
% 2.97/3.13 tff(2414,plain,
% 2.97/3.13 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(elem!1))),
% 2.97/3.13 inference(transitivity,[status(thm)],[834, 2413])).
% 2.97/3.13 tff(2415,plain,
% 2.97/3.13 ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) <=> (~r(elem!1, s(elem!1)))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[2414])).
% 2.97/3.13 tff(2416,plain,
% 2.97/3.13 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.13 inference(rewrite,[status(thm)],[])).
% 2.97/3.13 tff(2417,plain,
% 2.97/3.13 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.13 inference(quant_inst,[status(thm)],[])).
% 2.97/3.13 tff(2418,plain,
% 2.97/3.13 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.13 inference(modus_ponens,[status(thm)],[2417, 2416])).
% 2.97/3.13 tff(2419,plain,
% 2.97/3.13 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[2418, 118, 2405, 107])).
% 2.97/3.13 tff(2420,plain,
% 2.97/3.13 (~r(elem!1, s(elem!1))),
% 2.97/3.13 inference(modus_ponens,[status(thm)],[2419, 2415])).
% 2.97/3.13 tff(2421,plain,
% 2.97/3.13 (b(elem!1, s(elem!1))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[756, 2420, 749])).
% 2.97/3.13 tff(2422,plain,
% 2.97/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z)))),
% 2.97/3.13 inference(rewrite,[status(thm)],[])).
% 2.97/3.13 tff(2423,plain,
% 2.97/3.13 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z)))),
% 2.97/3.13 inference(rewrite,[status(thm)],[])).
% 2.97/3.13 tff(2424,plain,
% 2.97/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z))))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[2423])).
% 2.97/3.13 tff(2425,plain,
% 2.97/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z)))),
% 2.97/3.13 inference(transitivity,[status(thm)],[2424, 2422])).
% 2.97/3.13 tff(2426,plain,
% 2.97/3.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))),
% 2.97/3.13 inference(quant_inst,[status(thm)],[])).
% 2.97/3.13 tff(2427,plain,
% 2.97/3.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z))),
% 2.97/3.13 inference(modus_ponens,[status(thm)],[2426, 2425])).
% 2.97/3.13 tff(2428,plain,
% 2.97/3.13 ($false),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[2427, 178, 818, 506, 683, 854, 853])).
% 2.97/3.13 tff(2429,plain,((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.13 tff(2430,plain,
% 2.97/3.13 (~b(z, elem!1)),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[2429, 2421, 853, 2411, 506])).
% 2.97/3.13 tff(2431,plain,
% 2.97/3.13 (r(z, elem!1)),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[585, 2430, 507])).
% 2.97/3.13 tff(2432,plain,
% 2.97/3.13 (~r(s(s(z)), elem!1)),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[541, 2431, 106])).
% 2.97/3.13 tff(2433,plain,
% 2.97/3.13 (b(s(s(z)), elem!1)),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[448, 2432, 12])).
% 2.97/3.13 tff(2434,plain,
% 2.97/3.13 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.97/3.13 inference(modus_ponens,[status(thm)],[2433, 830])).
% 2.97/3.13 tff(2435,plain,
% 2.97/3.13 (b(s(elem!1), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.97/3.13 inference(monotonicity,[status(thm)],[645])).
% 2.97/3.13 tff(2436,plain,
% 2.97/3.13 (b(s(elem!1), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 2.97/3.13 inference(transitivity,[status(thm)],[2435, 698])).
% 2.97/3.13 tff(2437,plain,
% 2.97/3.13 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 2.97/3.13 inference(modus_ponens,[status(thm)],[2411, 2436])).
% 2.97/3.13 tff(2438,plain,
% 2.97/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.97/3.13 inference(rewrite,[status(thm)],[])).
% 2.97/3.13 tff(2439,plain,
% 2.97/3.13 (((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.97/3.13 inference(rewrite,[status(thm)],[])).
% 2.97/3.13 tff(2440,plain,
% 2.97/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[2439])).
% 2.97/3.13 tff(2441,plain,
% 2.97/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.97/3.13 inference(transitivity,[status(thm)],[2440, 2438])).
% 2.97/3.13 tff(2442,plain,
% 2.97/3.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.13 inference(quant_inst,[status(thm)],[])).
% 2.97/3.13 tff(2443,plain,
% 2.97/3.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 2.97/3.13 inference(modus_ponens,[status(thm)],[2442, 2441])).
% 2.97/3.13 tff(2444,plain,
% 2.97/3.13 ($false),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[2443, 178, 166, 2437, 134, 2434, 696])).
% 2.97/3.13 tff(2445,plain,((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) | (s(s(z)) = elem!1) | (~r(s(s(z)), z)) | (z = elem!1) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (s(elem!1) = elem!1) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.13 tff(2446,plain,
% 2.97/3.13 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[2445, 645, 166, 12, 106, 507, 2401, 506, 2399, 107])).
% 2.97/3.13 tff(2447,plain,
% 2.97/3.13 (~r(elem!1, s(s(z)))),
% 2.97/3.13 inference(modus_ponens,[status(thm)],[2446, 2397])).
% 2.97/3.13 tff(2448,plain,
% 2.97/3.13 (b(elem!1, s(s(z)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[467, 2447, 312])).
% 2.97/3.13 tff(2449,plain,
% 2.97/3.13 (~r(z, elem!1)),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[814, 2448, 167, 202, 469, 12, 145, 106])).
% 2.97/3.13 tff(2450,plain,
% 2.97/3.13 (b(z, elem!1)),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[585, 2449, 507])).
% 2.97/3.13 tff(2451,plain,
% 2.97/3.13 (~b(s(s(z)), elem!1)),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[826, 2450, 506, 273, 2448])).
% 2.97/3.13 tff(2452,plain,
% 2.97/3.13 (r(s(s(z)), elem!1)),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[448, 2451, 12])).
% 2.97/3.13 tff(2453,plain,
% 2.97/3.13 (~b(s(elem!1), elem!1)),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[2268, 2450, 2401, 273, 2448])).
% 2.97/3.13 tff(2454,plain,
% 2.97/3.13 (r(s(elem!1), elem!1)),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[677, 2453, 2399])).
% 2.97/3.13 tff(2455,plain,
% 2.97/3.13 ($false),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[2249, 2454, 2452, 363])).
% 2.97/3.13 tff(2456,plain,((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(z)))) | (s(s(z)) = elem!1) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (z = elem!1) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (elem!1 = s(s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.13 tff(2457,plain,
% 2.97/3.13 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[2456, 2278, 12, 273, 506, 507, 167, 202, 2377, 145, 106, 166, 107])).
% 2.97/3.13 tff(2458,plain,
% 2.97/3.13 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[395, 2457, 2394])).
% 2.97/3.13 tff(2459,plain,
% 2.97/3.13 (~b(elem!1, s(s(z)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[814, 521, 167, 202, 469, 12, 145, 106])).
% 2.97/3.13 tff(2460,plain,
% 2.97/3.13 (r(elem!1, s(s(z)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[467, 2459, 312])).
% 2.97/3.13 tff(2461,plain,
% 2.97/3.13 (~r(s(elem!1), elem!1)),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[625, 118, 2460, 363])).
% 2.97/3.13 tff(2462,plain,
% 2.97/3.13 (~r(elem!1, s(elem!1))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[632, 118, 2460, 363])).
% 2.97/3.13 tff(2463,plain,
% 2.97/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)))),
% 2.97/3.13 inference(rewrite,[status(thm)],[])).
% 2.97/3.13 tff(2464,plain,
% 2.97/3.13 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)))),
% 2.97/3.13 inference(rewrite,[status(thm)],[])).
% 2.97/3.13 tff(2465,plain,
% 2.97/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1))))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[2464])).
% 2.97/3.13 tff(2466,plain,
% 2.97/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)))),
% 2.97/3.13 inference(transitivity,[status(thm)],[2465, 2463])).
% 2.97/3.13 tff(2467,plain,
% 2.97/3.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))))),
% 2.97/3.13 inference(quant_inst,[status(thm)],[])).
% 2.97/3.13 tff(2468,plain,
% 2.97/3.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1))),
% 2.97/3.13 inference(modus_ponens,[status(thm)],[2467, 2466])).
% 2.97/3.13 tff(2469,plain,
% 2.97/3.13 ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[2468, 178, 506, 817, 853])).
% 2.97/3.13 tff(2470,plain,
% 2.97/3.13 (~b(s(s(z)), s(elem!1))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[2469, 726])).
% 2.97/3.13 tff(2471,plain,
% 2.97/3.13 (r(s(s(z)), s(elem!1))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[1067, 2470, 1060])).
% 2.97/3.13 tff(2472,plain,
% 2.97/3.13 (~r(z, s(elem!1))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[2341, 2471, 106])).
% 2.97/3.13 tff(2473,plain,
% 2.97/3.13 (b(z, s(elem!1))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[2351, 2472])).
% 2.97/3.13 tff(2474,plain,
% 2.97/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)))),
% 2.97/3.13 inference(rewrite,[status(thm)],[])).
% 2.97/3.13 tff(2475,plain,
% 2.97/3.13 (((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)))),
% 2.97/3.13 inference(rewrite,[status(thm)],[])).
% 2.97/3.13 tff(2476,plain,
% 2.97/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z))))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[2475])).
% 2.97/3.13 tff(2477,plain,
% 2.97/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)))),
% 2.97/3.13 inference(transitivity,[status(thm)],[2476, 2474])).
% 2.97/3.13 tff(2478,plain,
% 2.97/3.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)))),
% 2.97/3.13 inference(quant_inst,[status(thm)],[])).
% 2.97/3.13 tff(2479,plain,
% 2.97/3.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z))),
% 2.97/3.13 inference(modus_ponens,[status(thm)],[2478, 2477])).
% 2.97/3.13 tff(2480,plain,
% 2.97/3.13 ($false),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[2479, 178, 506, 2473, 726, 757, 853])).
% 2.97/3.13 tff(2481,plain,((s(elem!1) = elem!1) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~r(s(s(z)), z)) | (s(s(z)) = s(elem!1)) | (~b(s(s(z)), elem!1)) | r(elem!1, s(elem!1)) | r(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.97/3.13 tff(2482,plain,
% 2.97/3.13 (s(elem!1) = elem!1),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[2481, 543, 2401, 106, 1060, 506, 2462, 2461])).
% 2.97/3.13 tff(2483,plain,
% 2.97/3.13 (s(s(elem!1)) = elem!1),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[672, 2482])).
% 2.97/3.13 tff(2484,assumption,(~(s(s(elem!1)) = s(s(z)))), introduced(assumption)).
% 2.97/3.13 tff(2485,plain,
% 2.97/3.13 (s(s(s(elem!1))) = elem!1),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[2150, 2482])).
% 2.97/3.13 tff(2486,plain,
% 2.97/3.13 ((s(s(s(elem!1))) = elem!1) <=> (elem!1 = s(s(s(elem!1))))),
% 2.97/3.13 inference(symmetry,[status(thm)],[1526])).
% 2.97/3.13 tff(2487,plain,
% 2.97/3.13 (elem!1 = s(s(s(elem!1)))),
% 2.97/3.13 inference(modus_ponens,[status(thm)],[1519, 2486])).
% 2.97/3.13 tff(2488,plain,
% 2.97/3.13 ($false),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[1586, 2487])).
% 2.97/3.13 tff(2489,plain,((~(s(s(s(elem!1))) = elem!1)) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.13 tff(2490,plain,
% 2.97/3.13 (elem!1 = s(s(s(elem!1)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[2489, 2485])).
% 2.97/3.13 tff(2491,plain,
% 2.97/3.13 (s(s(s(s(z)))) = s(elem!1)),
% 2.97/3.13 inference(symmetry,[status(thm)],[1117])).
% 2.97/3.13 tff(2492,plain,
% 2.97/3.13 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[2491])).
% 2.97/3.13 tff(2493,plain,
% 2.97/3.13 (s(s(s(z))) = s(s(s(s(s(s(z))))))),
% 2.97/3.13 inference(transitivity,[status(thm)],[61, 2492, 304, 1527, 1119])).
% 2.97/3.13 tff(2494,plain,
% 2.97/3.13 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(s(z)))))))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[2493])).
% 2.97/3.13 tff(2495,plain,
% 2.97/3.13 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(s(z))))),
% 2.97/3.13 inference(symmetry,[status(thm)],[2494])).
% 2.97/3.13 tff(2496,plain,
% 2.97/3.13 (s(s(elem!1)) = s(s(z))),
% 2.97/3.13 inference(transitivity,[status(thm)],[1118, 239, 2495, 65])).
% 2.97/3.13 tff(2497,plain,
% 2.97/3.13 ($false),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[2484, 2496])).
% 2.97/3.13 tff(2498,plain,((~(elem!1 = s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(z))) | (~(s(elem!1) = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.13 tff(2499,plain,
% 2.97/3.13 (~(s(elem!1) = s(s(s(s(z)))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[2498, 2490, 2484])).
% 2.97/3.13 tff(2500,plain,
% 2.97/3.13 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[2168, 2499])).
% 2.97/3.14 tff(2501,plain,
% 2.97/3.14 (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))),
% 2.97/3.14 inference(transitivity,[status(thm)],[680, 330])).
% 2.97/3.14 tff(2502,plain,
% 2.97/3.14 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(elem!1)))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[2501])).
% 2.97/3.14 tff(2503,plain,
% 2.97/3.14 (s(s(s(s(s(s(z)))))) = s(elem!1)),
% 2.97/3.14 inference(transitivity,[status(thm)],[609, 2502, 328])).
% 2.97/3.14 tff(2504,plain,
% 2.97/3.14 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(elem!1))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[2503])).
% 2.97/3.14 tff(2505,plain,
% 2.97/3.14 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 2.97/3.14 inference(transitivity,[status(thm)],[239, 2504, 304, 330])).
% 2.97/3.14 tff(2506,plain,
% 2.97/3.14 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(elem!1)))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[2505])).
% 2.97/3.14 tff(2507,plain,
% 2.97/3.14 (s(s(s(s(z)))) = s(elem!1)),
% 2.97/3.14 inference(transitivity,[status(thm)],[663, 2506, 328])).
% 2.97/3.14 tff(2508,assumption,(~(s(s(s(s(z)))) = s(elem!1))), introduced(assumption)).
% 2.97/3.14 tff(2509,plain,
% 2.97/3.14 ($false),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[2508, 2507])).
% 2.97/3.14 tff(2510,plain,((~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(z)))) = s(elem!1)) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.14 tff(2511,plain,
% 2.97/3.14 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[2510, 2500, 2483])).
% 2.97/3.14 tff(2512,plain,
% 2.97/3.14 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[703, 2511])).
% 2.97/3.14 tff(2513,plain,
% 2.97/3.14 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[513, 118, 2460, 107])).
% 2.97/3.14 tff(2514,plain,
% 2.97/3.14 ((s(s(s(s(s(s(s(z))))))) = elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[707, 41, 2513])).
% 2.97/3.14 tff(2515,plain,
% 2.97/3.14 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[2514, 2512])).
% 2.97/3.14 tff(2516,plain,
% 2.97/3.14 (b(s(elem!1), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[2482])).
% 2.97/3.14 tff(2517,plain,
% 2.97/3.14 (b(elem!1, s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 2.97/3.14 inference(symmetry,[status(thm)],[2516])).
% 2.97/3.14 tff(2518,plain,
% 2.97/3.14 (b(s(elem!1), s(s(s(s(z)))))),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[531, 2517])).
% 2.97/3.14 tff(2519,plain,
% 2.97/3.14 (b(s(s(z)), s(elem!1)) <=> b(s(s(z)), elem!1)),
% 2.97/3.14 inference(monotonicity,[status(thm)],[2482])).
% 2.97/3.14 tff(2520,plain,
% 2.97/3.14 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(elem!1))),
% 2.97/3.14 inference(symmetry,[status(thm)],[2519])).
% 2.97/3.14 tff(2521,plain,
% 2.97/3.14 (b(s(s(z)), s(elem!1))),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[543, 2520])).
% 2.97/3.14 tff(2522,plain,
% 2.97/3.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.97/3.14 inference(rewrite,[status(thm)],[])).
% 2.97/3.14 tff(2523,plain,
% 2.97/3.14 (((~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(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(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(z)), s(elem!1)))) <=> ((~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.97/3.14 inference(rewrite,[status(thm)],[])).
% 2.97/3.14 tff(2524,plain,
% 2.97/3.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~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(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(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(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[2523])).
% 2.97/3.14 tff(2525,plain,
% 2.97/3.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~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(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(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(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.97/3.14 inference(transitivity,[status(thm)],[2524, 2522])).
% 2.97/3.14 tff(2526,plain,
% 2.97/3.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~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(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(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(z)), s(elem!1))))),
% 2.97/3.14 inference(quant_inst,[status(thm)],[])).
% 2.97/3.14 tff(2527,plain,
% 2.97/3.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[2526, 2525])).
% 2.97/3.14 tff(2528,plain,
% 2.97/3.14 ($false),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[2527, 178, 1071, 104, 166, 1069, 727])).
% 2.97/3.14 tff(2529,plain,((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(elem!1))) | (~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(elem!1), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.14 tff(2530,plain,
% 2.97/3.14 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[2529, 2521, 166, 727, 2518])).
% 2.97/3.14 tff(2531,plain,
% 2.97/3.14 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[84, 2530])).
% 2.97/3.14 tff(2532,plain,
% 2.97/3.14 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[1143, 118, 2531, 145])).
% 2.97/3.14 tff(2533,plain,
% 2.97/3.14 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[271, 2532])).
% 2.97/3.14 tff(2534,plain,
% 2.97/3.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.14 inference(rewrite,[status(thm)],[])).
% 2.97/3.14 tff(2535,plain,
% 2.97/3.14 (((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.14 inference(rewrite,[status(thm)],[])).
% 2.97/3.14 tff(2536,plain,
% 2.97/3.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[2535])).
% 2.97/3.14 tff(2537,plain,
% 2.97/3.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.14 inference(transitivity,[status(thm)],[2536, 2534])).
% 2.97/3.14 tff(2538,plain,
% 2.97/3.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))))),
% 2.97/3.14 inference(quant_inst,[status(thm)],[])).
% 2.97/3.14 tff(2539,plain,
% 2.97/3.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[2538, 2537])).
% 2.97/3.14 tff(2540,plain,
% 2.97/3.14 ($false),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[2539, 178, 543, 273, 166, 2533, 2515])).
% 2.97/3.14 tff(2541,plain,((~r(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (s(s(elem!1)) = s(s(z))) | (~r(s(s(z)), z)) | (s(s(z)) = s(elem!1)) | (~b(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (elem!1 = s(s(s(s(z))))) | (s(s(z)) = elem!1) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.14 tff(2542,plain,
% 2.97/3.14 (~r(z, elem!1)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[2541, 2458, 166, 145, 273, 2387, 106, 2311, 506, 107, 2278, 2377, 12, 167, 202])).
% 2.97/3.14 tff(2543,plain,
% 2.97/3.14 (b(z, elem!1)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[585, 2542, 507])).
% 2.97/3.14 tff(2544,plain,
% 2.97/3.14 (b(s(elem!1), z)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[774, 2314])).
% 2.97/3.14 tff(2545,plain,
% 2.97/3.14 (~r(elem!1, s(elem!1))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[632, 118, 450, 363])).
% 2.97/3.14 tff(2546,plain,
% 2.97/3.14 (b(elem!1, s(elem!1))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[756, 2545, 749])).
% 2.97/3.14 tff(2547,plain,
% 2.97/3.14 (~r(s(elem!1), elem!1)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[625, 118, 450, 363])).
% 2.97/3.14 tff(2548,plain,
% 2.97/3.14 (b(s(elem!1), elem!1)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[677, 2547, 725])).
% 2.97/3.14 tff(2549,plain,
% 2.97/3.14 ($false),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[2429, 2548, 2546, 853, 818, 506])).
% 2.97/3.14 tff(2550,plain,((~r(elem!1, s(s(z)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(elem!1) = elem!1) | (~r(s(elem!1), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.14 tff(2551,plain,
% 2.97/3.14 (~r(elem!1, s(s(z)))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[2550, 725, 818, 506, 853, 363])).
% 2.97/3.14 tff(2552,plain,
% 2.97/3.14 (b(elem!1, s(s(z)))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[467, 2551, 312])).
% 2.97/3.14 tff(2553,plain,
% 2.97/3.14 (~b(s(s(z)), elem!1)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[826, 2552, 506, 273, 818])).
% 2.97/3.14 tff(2554,plain,
% 2.97/3.14 (r(s(s(z)), elem!1)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[448, 2553, 12])).
% 2.97/3.14 tff(2555,plain,
% 2.97/3.14 (~b(s(elem!1), elem!1)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[2268, 2552, 853, 273, 818])).
% 2.97/3.14 tff(2556,plain,
% 2.97/3.14 (r(s(elem!1), elem!1)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[677, 2555, 725])).
% 2.97/3.14 tff(2557,plain,
% 2.97/3.14 ($false),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[2249, 2556, 2554, 363])).
% 2.97/3.14 tff(2558,plain,((s(elem!1) = elem!1) | (~r(s(elem!1), s(s(z)))) | (s(s(z)) = elem!1) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(z, elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.14 tff(2559,plain,
% 2.97/3.14 (s(elem!1) = elem!1),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[2558, 2278, 12, 2544, 273, 2543, 506])).
% 2.97/3.14 tff(2560,plain,
% 2.97/3.14 (b(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.97/3.14 inference(monotonicity,[status(thm)],[2559])).
% 2.97/3.14 tff(2561,plain,
% 2.97/3.14 ((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[655])).
% 2.97/3.14 tff(2562,plain,
% 2.97/3.14 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[2457, 2561])).
% 2.97/3.14 tff(2563,plain,
% 2.97/3.14 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[802, 118, 2278, 107])).
% 2.97/3.14 tff(2564,plain,
% 2.97/3.14 ((s(s(s(s(s(s(s(z))))))) = s(elem!1)) | b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[806, 41, 2563])).
% 2.97/3.14 tff(2565,plain,
% 2.97/3.14 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[2564, 2562])).
% 2.97/3.14 tff(2566,plain,
% 2.97/3.14 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[2565, 2560])).
% 2.97/3.14 tff(2567,plain,
% 2.97/3.14 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[2559])).
% 2.97/3.14 tff(2568,plain,
% 2.97/3.14 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[2458, 2567])).
% 2.97/3.14 tff(2569,plain,
% 2.97/3.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.97/3.14 inference(rewrite,[status(thm)],[])).
% 2.97/3.14 tff(2570,plain,
% 2.97/3.14 (((~b(z, 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, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, 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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.97/3.14 inference(rewrite,[status(thm)],[])).
% 2.97/3.14 tff(2571,plain,
% 2.97/3.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[2570])).
% 2.97/3.14 tff(2572,plain,
% 2.97/3.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.97/3.14 inference(transitivity,[status(thm)],[2571, 2569])).
% 2.97/3.14 tff(2573,plain,
% 2.97/3.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.14 inference(quant_inst,[status(thm)],[])).
% 2.97/3.14 tff(2574,plain,
% 2.97/3.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[2573, 2572])).
% 2.97/3.14 tff(2575,plain,
% 2.97/3.14 ($false),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[2574, 178, 2543, 506, 2568, 134, 2566])).
% 2.97/3.14 tff(2576,plain,((s(elem!1) = s(s(z))) | (~b(elem!1, z)) | (s(s(z)) = elem!1) | (~b(z, s(s(z)))) | (z = elem!1) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(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(z)))) | b(s(elem!1), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.14 tff(2577,plain,
% 2.97/3.14 (s(elem!1) = s(s(z))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[2576, 2376, 12, 273, 318, 2277, 145, 106, 107, 167, 307, 305])).
% 2.97/3.14 tff(2578,plain,
% 2.97/3.14 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[2577])).
% 2.97/3.14 tff(2579,plain,
% 2.97/3.14 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 2.97/3.14 inference(symmetry,[status(thm)],[2578])).
% 2.97/3.14 tff(2580,plain,
% 2.97/3.14 (s(z) = elem!1),
% 2.97/3.14 inference(transitivity,[status(thm)],[71, 2579, 304])).
% 2.97/3.14 tff(2581,plain,
% 2.97/3.14 (b(s(z), s(s(z))) <=> b(elem!1, s(s(z)))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[2580])).
% 2.97/3.14 tff(2582,plain,
% 2.97/3.14 (b(elem!1, s(s(z))) <=> b(s(z), s(s(z)))),
% 2.97/3.14 inference(symmetry,[status(thm)],[2581])).
% 2.97/3.14 tff(2583,plain,
% 2.97/3.14 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(z)))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[2577])).
% 2.97/3.14 tff(2584,plain,
% 2.97/3.14 (b(elem!1, s(elem!1)) <=> b(s(z), s(s(z)))),
% 2.97/3.14 inference(transitivity,[status(thm)],[2583, 2582])).
% 2.97/3.14 tff(2585,plain,
% 2.97/3.14 ((~b(elem!1, s(elem!1))) <=> (~b(s(z), s(s(z))))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[2584])).
% 2.97/3.14 tff(2586,plain,
% 2.97/3.14 (~r(z, elem!1)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[580, 2577, 307, 2374, 12, 145, 106])).
% 2.97/3.14 tff(2587,plain,
% 2.97/3.14 (b(z, elem!1)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[585, 2586, 318])).
% 2.97/3.14 tff(2588,plain,
% 2.97/3.14 (~(elem!1 = s(s(s(s(elem!1)))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[1422, 2577])).
% 2.97/3.14 tff(2589,plain,
% 2.97/3.14 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[1509, 2588])).
% 2.97/3.14 tff(2590,plain,
% 2.97/3.14 (~(elem!1 = s(s(elem!1)))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[1539, 2589])).
% 2.97/3.14 tff(2591,plain,
% 2.97/3.14 (~(s(s(elem!1)) = elem!1)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[1546, 2590])).
% 2.97/3.14 tff(2592,plain,
% 2.97/3.14 (~(s(elem!1) = elem!1)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[672, 2591])).
% 2.97/3.14 tff(2593,plain,
% 2.97/3.14 (b(s(s(z)), s(elem!1)) <=> b(s(s(z)), s(s(z)))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[2577])).
% 2.97/3.14 tff(2594,plain,
% 2.97/3.14 (b(s(s(z)), s(s(z))) <=> b(s(s(z)), s(elem!1))),
% 2.97/3.14 inference(symmetry,[status(thm)],[2593])).
% 2.97/3.14 tff(2595,plain,
% 2.97/3.14 ((~b(s(s(z)), s(s(z)))) <=> (~b(s(s(z)), s(elem!1)))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[2594])).
% 2.97/3.14 tff(2596,plain,
% 2.97/3.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.97/3.14 inference(rewrite,[status(thm)],[])).
% 2.97/3.14 tff(2597,plain,
% 2.97/3.14 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(z)))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.97/3.14 inference(rewrite,[status(thm)],[])).
% 2.97/3.14 tff(2598,plain,
% 2.97/3.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(z)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[2597])).
% 2.97/3.14 tff(2599,plain,
% 2.97/3.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(z)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.97/3.14 inference(transitivity,[status(thm)],[2598, 2596])).
% 2.97/3.14 tff(2600,plain,
% 2.97/3.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(z)))) | (~b(z, s(s(z)))))),
% 2.97/3.14 inference(quant_inst,[status(thm)],[])).
% 2.97/3.14 tff(2601,plain,
% 2.97/3.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[2600, 2599])).
% 2.97/3.14 tff(2602,plain,
% 2.97/3.14 (~b(s(s(z)), s(s(z)))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[2601, 178, 273, 167])).
% 2.97/3.14 tff(2603,plain,
% 2.97/3.14 (~b(s(s(z)), s(elem!1))),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[2602, 2595])).
% 2.97/3.14 tff(2604,plain,
% 2.97/3.14 (~b(elem!1, s(elem!1))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[2138, 2603, 273, 106, 2376, 2577, 2592, 2587])).
% 2.97/3.14 tff(2605,plain,
% 2.97/3.14 (~b(s(z), s(s(z)))),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[2604, 2585])).
% 2.97/3.14 tff(2606,assumption,(s(z) = s(s(z))), introduced(assumption)).
% 2.97/3.14 tff(2607,plain,
% 2.97/3.14 (s(s(z)) = s(z)),
% 2.97/3.14 inference(symmetry,[status(thm)],[2606])).
% 2.97/3.14 tff(2608,plain,
% 2.97/3.14 (s(s(z)) = elem!1),
% 2.97/3.14 inference(transitivity,[status(thm)],[2607, 71, 533, 304])).
% 2.97/3.14 tff(2609,plain,
% 2.97/3.14 ($false),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[12, 2608])).
% 2.97/3.14 tff(2610,plain,((~(s(z) = s(s(z)))) | (s(s(z)) = elem!1) | (~(s(elem!1) = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.15 tff(2611,plain,
% 2.97/3.15 (~(s(z) = s(s(z)))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[2610, 2577, 12])).
% 2.97/3.15 tff(2612,plain,
% 2.97/3.15 (b(s(z), z)),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[593, 2577, 2376])).
% 2.97/3.15 tff(2613,plain,
% 2.97/3.15 (elem!1 = s(z)),
% 2.97/3.15 inference(transitivity,[status(thm)],[517, 2578, 70])).
% 2.97/3.15 tff(2614,plain,
% 2.97/3.15 (b(z, elem!1) <=> b(z, s(z))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[2613])).
% 2.97/3.15 tff(2615,plain,
% 2.97/3.15 (b(z, s(z))),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[2587, 2614])).
% 2.97/3.15 tff(2616,plain,
% 2.97/3.15 (b(s(z), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[534])).
% 2.97/3.15 tff(2617,plain,
% 2.97/3.15 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.15 inference(symmetry,[status(thm)],[2616])).
% 2.97/3.15 tff(2618,plain,
% 2.97/3.15 ((s(s(s(s(s(s(s(z))))))) = s(z)) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.97/3.15 inference(monotonicity,[status(thm)],[534])).
% 2.97/3.15 tff(2619,plain,
% 2.97/3.15 ((s(s(s(s(s(s(s(z))))))) = s(z)) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.97/3.15 inference(transitivity,[status(thm)],[2618, 836])).
% 2.97/3.15 tff(2620,plain,
% 2.97/3.15 ((~(s(s(s(s(s(s(s(z))))))) = s(z))) <=> (~(elem!1 = s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[2619])).
% 2.97/3.15 tff(2621,plain,
% 2.97/3.15 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[612, 2620])).
% 2.97/3.15 tff(2622,plain,
% 2.97/3.15 (r(s(z), s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[534])).
% 2.97/3.15 tff(2623,plain,
% 2.97/3.15 ((~r(s(z), s(s(s(s(s(s(s(z))))))))) <=> (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[2622])).
% 2.97/3.15 tff(2624,assumption,(r(s(z), s(s(z)))), introduced(assumption)).
% 2.97/3.15 tff(2625,plain,
% 2.97/3.15 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(z)))))),
% 2.97/3.15 inference(rewrite,[status(thm)],[])).
% 2.97/3.15 tff(2626,plain,
% 2.97/3.15 (((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(z)))))),
% 2.97/3.15 inference(rewrite,[status(thm)],[])).
% 2.97/3.15 tff(2627,plain,
% 2.97/3.15 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(z))))))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[2626])).
% 2.97/3.15 tff(2628,plain,
% 2.97/3.15 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(z)))))),
% 2.97/3.15 inference(transitivity,[status(thm)],[2627, 2625])).
% 2.97/3.15 tff(2629,plain,
% 2.97/3.15 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.15 inference(quant_inst,[status(thm)],[])).
% 2.97/3.15 tff(2630,plain,
% 2.97/3.15 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(z))))),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[2629, 2628])).
% 2.97/3.15 tff(2631,plain,
% 2.97/3.15 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[2630, 118, 2624, 107])).
% 2.97/3.15 tff(2632,plain,
% 2.97/3.15 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[2631, 2623])).
% 2.97/3.15 tff(2633,plain,
% 2.97/3.15 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[691, 2632, 2621])).
% 2.97/3.15 tff(2634,plain,
% 2.97/3.15 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[2633, 2617])).
% 2.97/3.15 tff(2635,plain,
% 2.97/3.15 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(z)))))),
% 2.97/3.15 inference(rewrite,[status(thm)],[])).
% 2.97/3.15 tff(2636,plain,
% 2.97/3.15 (((~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)))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(z)))))),
% 2.97/3.15 inference(rewrite,[status(thm)],[])).
% 2.97/3.15 tff(2637,plain,
% 2.97/3.15 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(z))))))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[2636])).
% 2.97/3.15 tff(2638,plain,
% 2.97/3.15 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(z)))))),
% 2.97/3.15 inference(transitivity,[status(thm)],[2637, 2635])).
% 2.97/3.15 tff(2639,plain,
% 2.97/3.15 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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))))),
% 2.97/3.15 inference(quant_inst,[status(thm)],[])).
% 2.97/3.15 tff(2640,plain,
% 2.97/3.15 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(z))))),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[2639, 2638])).
% 2.97/3.15 tff(2641,plain,
% 2.97/3.15 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[2640, 118, 2624, 107])).
% 2.97/3.15 tff(2642,plain,
% 2.97/3.15 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[615, 41, 612, 2641])).
% 2.97/3.15 tff(2643,plain,
% 2.97/3.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.15 inference(rewrite,[status(thm)],[])).
% 2.97/3.15 tff(2644,plain,
% 2.97/3.15 (((~b(z, 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(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(z), z)) | (~b(z, s(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), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.15 inference(rewrite,[status(thm)],[])).
% 2.97/3.15 tff(2645,plain,
% 2.97/3.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[2644])).
% 2.97/3.15 tff(2646,plain,
% 2.97/3.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.15 inference(transitivity,[status(thm)],[2645, 2643])).
% 2.97/3.15 tff(2647,plain,
% 2.97/3.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.15 inference(quant_inst,[status(thm)],[])).
% 2.97/3.15 tff(2648,plain,
% 2.97/3.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[2647, 2646])).
% 2.97/3.15 tff(2649,plain,
% 2.97/3.15 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[2648, 178, 1791, 1790, 146, 2642])).
% 2.97/3.15 tff(2650,plain,
% 2.97/3.15 ($false),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[2649, 2634])).
% 2.97/3.15 tff(2651,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~(s(elem!1) = s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.15 tff(2652,plain,
% 2.97/3.15 (~r(s(z), s(s(z)))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[2651, 2615, 107, 134, 2577, 2612])).
% 2.97/3.15 tff(2653,assumption,(~(s(z) = s(s(z)))), introduced(assumption)).
% 2.97/3.15 tff(2654,assumption,(~r(s(z), s(s(z)))), introduced(assumption)).
% 2.97/3.15 tff(2655,assumption,(~b(s(z), s(s(z)))), introduced(assumption)).
% 2.97/3.15 tff(2656,plain,
% 2.97/3.15 ($false),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[1619, 41, 2655, 2654, 2653])).
% 2.97/3.15 tff(2657,plain,(b(s(z), s(s(z))) | r(s(z), s(s(z))) | (s(z) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.15 tff(2658,plain,
% 2.97/3.15 (b(s(z), s(s(z)))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[2657, 2652, 2611])).
% 2.97/3.15 tff(2659,plain,
% 2.97/3.15 ($false),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[2658, 2605])).
% 2.97/3.15 tff(2660,plain,(b(s(elem!1), s(s(z))) | (s(s(z)) = elem!1) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (elem!1 = z) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.15 tff(2661,plain,
% 2.97/3.15 (b(s(elem!1), s(s(z)))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[2660, 12, 273, 106, 300, 47, 302, 290, 107])).
% 2.97/3.15 tff(2662,plain,
% 2.97/3.15 (elem!1 = s(s(s(s(z))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[493, 437, 307, 167, 12, 145, 106])).
% 2.97/3.15 tff(2663,plain,
% 2.97/3.15 (s(elem!1) = s(s(s(s(s(z)))))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[2662])).
% 2.97/3.15 tff(2664,plain,
% 2.97/3.15 (s(s(s(s(s(z))))) = s(elem!1)),
% 2.97/3.15 inference(symmetry,[status(thm)],[2663])).
% 2.97/3.15 tff(2665,plain,
% 2.97/3.15 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) <=> r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[2664])).
% 2.97/3.15 tff(2666,plain,
% 2.97/3.15 (r(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.97/3.15 inference(symmetry,[status(thm)],[2665])).
% 2.97/3.15 tff(2667,plain,
% 2.97/3.15 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[2663])).
% 2.97/3.15 tff(2668,plain,
% 2.97/3.15 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[2667])).
% 2.97/3.15 tff(2669,plain,
% 2.97/3.15 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[2668])).
% 2.97/3.15 tff(2670,plain,
% 2.97/3.15 (s(s(s(s(z)))) = elem!1),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[325, 2662])).
% 2.97/3.15 tff(2671,plain,
% 2.97/3.15 (~(s(s(elem!1)) = elem!1)),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[338, 2670, 12])).
% 2.97/3.15 tff(2672,plain,
% 2.97/3.15 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[348, 2671])).
% 2.97/3.15 tff(2673,plain,
% 2.97/3.15 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 2.97/3.15 inference(symmetry,[status(thm)],[2668])).
% 2.97/3.15 tff(2674,plain,
% 2.97/3.15 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[2673, 2664])).
% 2.97/3.15 tff(2675,plain,
% 2.97/3.15 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[2674])).
% 2.97/3.15 tff(2676,plain,
% 2.97/3.15 (r(s(elem!1), z) <=> r(s(s(s(s(s(z))))), z)),
% 2.97/3.15 inference(monotonicity,[status(thm)],[2663])).
% 2.97/3.15 tff(2677,plain,
% 2.97/3.15 ((~r(s(elem!1), z)) <=> (~r(s(s(s(s(s(z))))), z))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[2676])).
% 2.97/3.15 tff(2678,plain,
% 2.97/3.15 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(s(s(z)))))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[2662])).
% 2.97/3.15 tff(2679,plain,
% 2.97/3.15 ((s(elem!1) = elem!1) <=> (s(s(s(s(z)))) = s(elem!1))),
% 2.97/3.15 inference(transitivity,[status(thm)],[2678, 2163])).
% 2.97/3.15 tff(2680,plain,
% 2.97/3.15 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(s(s(z)))))),
% 2.97/3.15 inference(transitivity,[status(thm)],[2679, 2164])).
% 2.97/3.15 tff(2681,plain,
% 2.97/3.15 ((~(s(elem!1) = elem!1)) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[2680])).
% 2.97/3.15 tff(2682,plain,
% 2.97/3.15 (~(s(elem!1) = elem!1)),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[672, 2671])).
% 2.97/3.15 tff(2683,plain,
% 2.97/3.15 (~(s(elem!1) = s(s(s(s(z)))))),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[2682, 2681])).
% 2.97/3.15 tff(2684,plain,
% 2.97/3.15 (~(elem!1 = s(elem!1))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[748, 2682])).
% 2.97/3.15 tff(2685,plain,
% 2.97/3.15 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[2663])).
% 2.97/3.15 tff(2686,plain,
% 2.97/3.15 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[1070, 2685])).
% 2.97/3.15 tff(2687,plain,
% 2.97/3.15 (b(elem!1, s(elem!1)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[319])).
% 2.97/3.15 tff(2688,plain,
% 2.97/3.15 (b(s(s(s(s(z)))), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 2.97/3.15 inference(symmetry,[status(thm)],[2687])).
% 2.97/3.15 tff(2689,plain,
% 2.97/3.15 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[350])).
% 2.97/3.15 tff(2690,plain,
% 2.97/3.15 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(elem!1, s(elem!1))),
% 2.97/3.15 inference(transitivity,[status(thm)],[2689, 2688])).
% 2.97/3.15 tff(2691,plain,
% 2.97/3.15 ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) <=> (~b(elem!1, s(elem!1)))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[2690])).
% 2.97/3.15 tff(2692,plain,
% 2.97/3.15 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[350])).
% 2.97/3.15 tff(2693,plain,
% 2.97/3.15 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.97/3.15 inference(symmetry,[status(thm)],[2692])).
% 2.97/3.15 tff(2694,plain,
% 2.97/3.15 (~r(s(elem!1), s(s(s(s(z)))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[916, 844, 194])).
% 2.97/3.15 tff(2695,plain,
% 2.97/3.15 (b(s(elem!1), s(s(s(s(z)))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[1084, 2694, 1369])).
% 2.97/3.15 tff(2696,plain,
% 2.97/3.15 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[2695, 2693])).
% 2.97/3.15 tff(2697,plain,
% 2.97/3.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.97/3.15 inference(rewrite,[status(thm)],[])).
% 2.97/3.15 tff(2698,plain,
% 2.97/3.15 (((~b(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(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.97/3.15 inference(rewrite,[status(thm)],[])).
% 2.97/3.15 tff(2699,plain,
% 2.97/3.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[2698])).
% 2.97/3.15 tff(2700,plain,
% 2.97/3.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.97/3.15 inference(transitivity,[status(thm)],[2699, 2697])).
% 2.97/3.15 tff(2701,plain,
% 2.97/3.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.97/3.15 inference(quant_inst,[status(thm)],[])).
% 2.97/3.15 tff(2702,plain,
% 2.97/3.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[2701, 2700])).
% 2.97/3.15 tff(2703,plain,
% 2.97/3.15 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[2702, 178, 167, 202, 1851, 2696])).
% 2.97/3.15 tff(2704,plain,
% 2.97/3.15 (~b(elem!1, s(elem!1))),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[2703, 2691])).
% 2.97/3.15 tff(2705,plain,
% 2.97/3.15 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)))),
% 2.97/3.15 inference(rewrite,[status(thm)],[])).
% 2.97/3.15 tff(2706,plain,
% 2.97/3.15 (((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)))),
% 2.97/3.15 inference(rewrite,[status(thm)],[])).
% 2.97/3.15 tff(2707,plain,
% 2.97/3.15 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z))))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[2706])).
% 2.97/3.15 tff(2708,plain,
% 2.97/3.15 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)))),
% 2.97/3.15 inference(transitivity,[status(thm)],[2707, 2705])).
% 2.97/3.15 tff(2709,plain,
% 2.97/3.15 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))),
% 2.97/3.15 inference(quant_inst,[status(thm)],[])).
% 2.97/3.15 tff(2710,plain,
% 2.97/3.15 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z))),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[2709, 2708])).
% 2.97/3.15 tff(2711,plain,
% 2.97/3.15 ((~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[2710, 118])).
% 2.97/3.15 tff(2712,plain,
% 2.97/3.15 (~r(elem!1, s(elem!1))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[2711, 844, 437])).
% 2.97/3.15 tff(2713,plain,
% 2.97/3.15 (b(elem!1, s(elem!1))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[756, 2712, 750])).
% 2.97/3.15 tff(2714,plain,
% 2.97/3.15 ($false),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[2713, 2704])).
% 2.97/3.15 tff(2715,plain,((~r(s(elem!1), z)) | (~(elem!1 = s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (elem!1 = s(elem!1)) | (s(elem!1) = s(s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.15 tff(2716,plain,
% 2.97/3.15 (~r(s(elem!1), z)),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[2715, 2662, 167, 307, 2686, 2684, 2683, 437, 194])).
% 2.97/3.15 tff(2717,plain,
% 2.97/3.15 (~r(s(s(s(s(s(z))))), z)),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[2716, 2677])).
% 2.97/3.15 tff(2718,plain,
% 2.97/3.15 (b(s(s(s(s(s(z))))), z)),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[410, 41, 242, 2717])).
% 2.97/3.15 tff(2719,plain,
% 2.97/3.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.97/3.15 inference(rewrite,[status(thm)],[])).
% 2.97/3.15 tff(2720,plain,
% 2.97/3.15 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.97/3.15 inference(rewrite,[status(thm)],[])).
% 2.97/3.15 tff(2721,plain,
% 2.97/3.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[2720])).
% 2.97/3.15 tff(2722,plain,
% 2.97/3.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.97/3.16 inference(transitivity,[status(thm)],[2721, 2719])).
% 2.97/3.16 tff(2723,plain,
% 2.97/3.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.97/3.16 inference(quant_inst,[status(thm)],[])).
% 2.97/3.16 tff(2724,plain,
% 2.97/3.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[2723, 2722])).
% 2.97/3.16 tff(2725,plain,
% 2.97/3.16 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[2724, 178, 273, 2686, 134])).
% 2.97/3.16 tff(2726,plain,
% 2.97/3.16 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[2725, 2718])).
% 2.97/3.16 tff(2727,plain,
% 2.97/3.16 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[2726, 2675])).
% 2.97/3.16 tff(2728,plain,
% 2.97/3.16 (r(s(s(s(elem!1))), s(elem!1))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[373, 2727, 2672])).
% 2.97/3.16 tff(2729,plain,
% 2.97/3.16 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[2728, 2669])).
% 2.97/3.16 tff(2730,plain,
% 2.97/3.16 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[2729, 2666])).
% 2.97/3.16 tff(2731,plain,
% 2.97/3.16 ((s(s(z)) = s(s(s(s(s(z)))))) <=> (s(s(z)) = s(elem!1))),
% 2.97/3.16 inference(monotonicity,[status(thm)],[2664])).
% 2.97/3.16 tff(2732,plain,
% 2.97/3.16 ((s(s(z)) = s(s(s(s(s(z)))))) <=> (s(elem!1) = s(s(z)))),
% 2.97/3.16 inference(transitivity,[status(thm)],[2731, 1358])).
% 2.97/3.16 tff(2733,plain,
% 2.97/3.16 ((s(elem!1) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(z))))))),
% 2.97/3.16 inference(symmetry,[status(thm)],[2732])).
% 2.97/3.16 tff(2734,plain,
% 2.97/3.16 ((~(s(elem!1) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(s(z)))))))),
% 2.97/3.16 inference(monotonicity,[status(thm)],[2733])).
% 2.97/3.16 tff(2735,plain,
% 2.97/3.16 (~(s(elem!1) = s(s(z)))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[906, 2716, 106])).
% 2.97/3.16 tff(2736,plain,
% 2.97/3.16 (~(s(s(z)) = s(s(s(s(s(z))))))),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[2735, 2734])).
% 2.97/3.16 tff(2737,plain,
% 2.97/3.16 (b(s(s(z)), s(elem!1)) <=> b(s(s(z)), s(s(s(s(s(z))))))),
% 2.97/3.16 inference(monotonicity,[status(thm)],[2663])).
% 2.97/3.16 tff(2738,plain,
% 2.97/3.16 ((~b(s(s(z)), s(elem!1))) <=> (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 2.97/3.16 inference(monotonicity,[status(thm)],[2737])).
% 2.97/3.16 tff(2739,plain,
% 2.97/3.16 (b(s(elem!1), z)),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[774, 2716])).
% 2.97/3.16 tff(2740,plain,
% 2.97/3.16 (~(s(s(z)) = s(elem!1))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[1058, 2735])).
% 2.97/3.16 tff(2741,plain,
% 2.97/3.16 (~b(s(s(z)), s(elem!1))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[1079, 1069, 167, 202, 1070])).
% 2.97/3.16 tff(2742,plain,
% 2.97/3.16 (r(s(s(z)), s(elem!1))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[1067, 2741, 1060])).
% 2.97/3.16 tff(2743,plain,
% 2.97/3.16 (~r(z, s(elem!1))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[2341, 2742, 106])).
% 2.97/3.16 tff(2744,plain,
% 2.97/3.16 (b(z, s(elem!1))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[2351, 2743])).
% 2.97/3.16 tff(2745,plain,
% 2.97/3.16 (b(z, s(s(s(s(s(z))))))),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[2744, 2310])).
% 2.97/3.16 tff(2746,plain,
% 2.97/3.16 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[1069, 2693])).
% 2.97/3.16 tff(2747,plain,
% 2.97/3.16 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 2.97/3.16 inference(monotonicity,[status(thm)],[320])).
% 2.97/3.16 tff(2748,plain,
% 2.97/3.16 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[1070, 2747])).
% 2.97/3.16 tff(2749,plain,
% 2.97/3.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.97/3.16 inference(rewrite,[status(thm)],[])).
% 2.97/3.16 tff(2750,plain,
% 2.97/3.16 (((~b(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(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.97/3.16 inference(rewrite,[status(thm)],[])).
% 2.97/3.16 tff(2751,plain,
% 2.97/3.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(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(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 2.97/3.16 inference(monotonicity,[status(thm)],[2750])).
% 2.97/3.16 tff(2752,plain,
% 2.97/3.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(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(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.97/3.16 inference(transitivity,[status(thm)],[2751, 2749])).
% 2.97/3.16 tff(2753,plain,
% 2.97/3.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(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(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.97/3.16 inference(quant_inst,[status(thm)],[])).
% 2.97/3.16 tff(2754,plain,
% 2.97/3.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[2753, 2752])).
% 2.97/3.16 tff(2755,plain,
% 2.97/3.16 ($false),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[2754, 178, 273, 167, 2748, 2746, 2745])).
% 2.97/3.16 tff(2756,plain,((~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~(elem!1 = s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (s(s(z)) = s(elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(elem!1), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.16 tff(2757,plain,
% 2.97/3.16 (~b(s(elem!1), s(s(s(s(z)))))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[2756, 2740, 167, 2662, 106, 273, 307, 1070])).
% 2.97/3.16 tff(2758,plain,
% 2.97/3.16 (r(s(elem!1), s(s(s(s(z)))))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[1084, 2757, 2683])).
% 2.97/3.16 tff(2759,plain,
% 2.97/3.16 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.97/3.16 inference(rewrite,[status(thm)],[])).
% 2.97/3.16 tff(2760,plain,
% 2.97/3.16 (((~r(s(elem!1), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(elem!1))) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.97/3.16 inference(rewrite,[status(thm)],[])).
% 2.97/3.16 tff(2761,plain,
% 2.97/3.16 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 2.97/3.16 inference(monotonicity,[status(thm)],[2760])).
% 2.97/3.16 tff(2762,plain,
% 2.97/3.16 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.97/3.16 inference(transitivity,[status(thm)],[2761, 2759])).
% 2.97/3.16 tff(2763,plain,
% 2.97/3.16 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(elem!1))))),
% 2.97/3.16 inference(quant_inst,[status(thm)],[])).
% 2.97/3.16 tff(2764,plain,
% 2.97/3.16 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[2763, 2762])).
% 2.97/3.16 tff(2765,plain,
% 2.97/3.16 ($false),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[2764, 118, 2333, 145, 908])).
% 2.97/3.16 tff(2766,plain,((~r(z, s(s(s(s(z)))))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.16 tff(2767,plain,
% 2.97/3.16 (~r(z, s(elem!1))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[2766, 2758, 145])).
% 2.97/3.16 tff(2768,plain,
% 2.97/3.16 (b(z, s(elem!1))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[2351, 2767])).
% 2.97/3.16 tff(2769,plain,
% 2.97/3.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))))),
% 2.97/3.16 inference(rewrite,[status(thm)],[])).
% 2.97/3.16 tff(2770,plain,
% 2.97/3.16 (((~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z))) <=> ((~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))))),
% 2.97/3.16 inference(rewrite,[status(thm)],[])).
% 2.97/3.16 tff(2771,plain,
% 2.97/3.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z))))))),
% 2.97/3.16 inference(monotonicity,[status(thm)],[2770])).
% 2.97/3.16 tff(2772,plain,
% 2.97/3.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))))),
% 2.97/3.16 inference(transitivity,[status(thm)],[2771, 2769])).
% 2.97/3.16 tff(2773,plain,
% 2.97/3.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)))),
% 2.97/3.16 inference(quant_inst,[status(thm)],[])).
% 2.97/3.16 tff(2774,plain,
% 2.97/3.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z))))),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[2773, 2772])).
% 2.97/3.16 tff(2775,plain,
% 2.97/3.16 ($false),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[2774, 178, 855, 853, 273, 1071, 1070])).
% 2.97/3.16 tff(2776,plain,((~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.16 tff(2777,plain,
% 2.97/3.16 (~b(s(s(z)), s(elem!1))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[2776, 2768, 273, 1070, 2739])).
% 2.97/3.16 tff(2778,plain,
% 2.97/3.16 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[2777, 2738])).
% 2.97/3.16 tff(2779,plain,
% 2.97/3.16 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z)))))))),
% 2.97/3.16 inference(rewrite,[status(thm)],[])).
% 2.97/3.16 tff(2780,plain,
% 2.97/3.16 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z)))))))),
% 2.97/3.16 inference(quant_inst,[status(thm)],[])).
% 2.97/3.16 tff(2781,plain,
% 2.97/3.16 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z))))))),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[2780, 2779])).
% 2.97/3.16 tff(2782,plain,
% 2.97/3.16 ((s(s(z)) = s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z))))))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[2781, 41, 2778])).
% 2.97/3.16 tff(2783,plain,
% 2.97/3.16 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[2782, 2736])).
% 2.97/3.16 tff(2784,plain,
% 2.97/3.16 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.97/3.16 inference(rewrite,[status(thm)],[])).
% 2.97/3.16 tff(2785,plain,
% 2.97/3.16 (((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.97/3.16 inference(rewrite,[status(thm)],[])).
% 2.97/3.16 tff(2786,plain,
% 2.97/3.16 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))))),
% 2.97/3.16 inference(monotonicity,[status(thm)],[2785])).
% 2.97/3.16 tff(2787,plain,
% 2.97/3.16 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.97/3.16 inference(transitivity,[status(thm)],[2786, 2784])).
% 2.97/3.16 tff(2788,plain,
% 2.97/3.16 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.97/3.16 inference(quant_inst,[status(thm)],[])).
% 2.97/3.16 tff(2789,plain,
% 2.97/3.16 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[2788, 2787])).
% 2.97/3.16 tff(2790,plain,
% 2.97/3.16 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[2789, 118, 2783, 107])).
% 2.97/3.16 tff(2791,plain,
% 2.97/3.16 ($false),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[2790, 2730])).
% 2.97/3.16 tff(2792,plain,((~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.97/3.16 tff(2793,plain,
% 2.97/3.16 (~r(elem!1, z)),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[2792, 2661, 273, 106, 47, 302, 107, 300, 12])).
% 2.97/3.16 tff(2794,plain,
% 2.97/3.16 (~r(elem!1, z)),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[443, 438, 106])).
% 2.97/3.16 tff(2795,plain,
% 2.97/3.16 (b(elem!1, z)),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[498, 2794, 290])).
% 2.97/3.16 tff(2796,plain,
% 2.97/3.16 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.16 inference(rewrite,[status(thm)],[])).
% 2.97/3.16 tff(2797,plain,
% 2.97/3.16 (((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), elem!1))) <=> ((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.16 inference(rewrite,[status(thm)],[])).
% 2.97/3.16 tff(2798,plain,
% 2.97/3.16 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.16 inference(monotonicity,[status(thm)],[2797])).
% 2.97/3.16 tff(2799,plain,
% 2.97/3.16 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.16 inference(transitivity,[status(thm)],[2798, 2796])).
% 2.97/3.16 tff(2800,plain,
% 2.97/3.16 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), elem!1)))),
% 2.97/3.16 inference(quant_inst,[status(thm)],[])).
% 2.97/3.16 tff(2801,plain,
% 2.97/3.16 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[2800, 2799])).
% 2.97/3.16 tff(2802,plain,
% 2.97/3.16 ($false),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[2801, 118, 438, 224, 1265])).
% 2.97/3.16 tff(2803,plain,((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.16 tff(2804,plain,
% 2.97/3.16 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[2803, 438, 224])).
% 2.97/3.16 tff(2805,plain,
% 2.97/3.16 (~r(z, elem!1)),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[541, 438, 106])).
% 2.97/3.16 tff(2806,plain,
% 2.97/3.16 (z = elem!1),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[928, 313])).
% 2.97/3.16 tff(2807,plain,
% 2.97/3.16 ($false),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[507, 2806])).
% 2.97/3.16 tff(2808,plain,((~(elem!1 = z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.97/3.16 tff(2809,plain,
% 2.97/3.16 (~(elem!1 = z)),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[2808, 507])).
% 2.97/3.16 tff(2810,plain,
% 2.97/3.16 (b(elem!1, z)),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[498, 2809, 1342])).
% 2.97/3.16 tff(2811,assumption,(~r(z, elem!1)), introduced(assumption)).
% 2.97/3.16 tff(2812,plain,
% 2.97/3.16 (b(z, elem!1)),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[585, 507, 2811])).
% 2.97/3.16 tff(2813,plain,
% 2.97/3.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.97/3.16 inference(rewrite,[status(thm)],[])).
% 2.97/3.16 tff(2814,plain,
% 2.97/3.17 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.97/3.17 inference(rewrite,[status(thm)],[])).
% 2.97/3.17 tff(2815,plain,
% 2.97/3.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[2814])).
% 2.97/3.17 tff(2816,plain,
% 2.97/3.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.97/3.17 inference(transitivity,[status(thm)],[2815, 2813])).
% 2.97/3.17 tff(2817,plain,
% 2.97/3.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)))),
% 2.97/3.17 inference(quant_inst,[status(thm)],[])).
% 2.97/3.17 tff(2818,plain,
% 2.97/3.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[2817, 2816])).
% 2.97/3.17 tff(2819,plain,
% 2.97/3.17 ($false),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[2818, 178, 2812, 2810, 869, 595, 146])).
% 2.97/3.17 tff(2820,plain,((z = elem!1) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | r(elem!1, z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.97/3.17 tff(2821,plain,
% 2.97/3.17 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[2820, 2805, 134, 399, 2794, 318])).
% 2.97/3.17 tff(2822,plain,
% 2.97/3.17 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[691, 2821, 2804])).
% 2.97/3.17 tff(2823,plain,
% 2.97/3.17 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[679])).
% 2.97/3.17 tff(2824,plain,
% 2.97/3.17 (s(s(z)) = s(s(s(s(s(s(s(s(z))))))))),
% 2.97/3.17 inference(transitivity,[status(thm)],[1415, 2823])).
% 2.97/3.17 tff(2825,plain,
% 2.97/3.17 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[2824])).
% 2.97/3.17 tff(2826,plain,
% 2.97/3.17 (inj_0(s(s(s(s(s(s(s(s(z))))))))) = inj_0(s(s(z)))),
% 2.97/3.17 inference(symmetry,[status(thm)],[2825])).
% 2.97/3.17 tff(2827,plain,
% 2.97/3.17 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(s(s(z))))))))) = s(s(s(s(s(s(s(z))))))))),
% 2.97/3.17 inference(quant_inst,[status(thm)],[])).
% 2.97/3.17 tff(2828,plain,
% 2.97/3.17 (inj_0(s(s(s(s(s(s(s(s(z))))))))) = s(s(s(s(s(s(s(z)))))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[2827, 9])).
% 2.97/3.17 tff(2829,plain,
% 2.97/3.17 (s(s(s(s(s(s(s(z))))))) = inj_0(s(s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.17 inference(symmetry,[status(thm)],[2828])).
% 2.97/3.17 tff(2830,plain,
% 2.97/3.17 (s(s(s(s(s(s(s(z))))))) = s(z)),
% 2.97/3.17 inference(transitivity,[status(thm)],[2829, 2826, 70])).
% 2.97/3.17 tff(2831,plain,
% 2.97/3.17 ($false),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[612, 2830])).
% 2.97/3.17 tff(2832,plain,((~(s(elem!1) = s(s(z)))) | (~(elem!1 = s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.17 tff(2833,plain,
% 2.97/3.17 (~(s(elem!1) = s(s(z)))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[2832, 2822])).
% 2.97/3.17 tff(2834,assumption,(s(s(s(elem!1))) = s(s(s(s(z))))), introduced(assumption)).
% 2.97/3.17 tff(2835,plain,
% 2.97/3.17 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(z)))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[2834])).
% 2.97/3.17 tff(2836,plain,
% 2.97/3.17 (s(s(elem!1)) = s(s(s(z)))),
% 2.97/3.17 inference(transitivity,[status(thm)],[344, 2835, 11])).
% 2.97/3.17 tff(2837,plain,
% 2.97/3.17 (inj_0(s(s(elem!1))) = inj_0(s(s(s(z))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[2836])).
% 2.97/3.17 tff(2838,plain,
% 2.97/3.17 (s(elem!1) = s(s(z))),
% 2.97/3.17 inference(transitivity,[status(thm)],[975, 2837, 65])).
% 2.97/3.17 tff(2839,plain,
% 2.97/3.17 ($false),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[1056, 2838])).
% 2.97/3.17 tff(2840,plain,((~(s(s(s(elem!1))) = s(s(s(s(z)))))) | (s(elem!1) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.17 tff(2841,plain,
% 2.97/3.17 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[2840, 2833])).
% 2.97/3.17 tff(2842,plain,
% 2.97/3.17 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.17 inference(quant_inst,[status(thm)],[])).
% 2.97/3.17 tff(2843,plain,
% 2.97/3.17 (inj_0(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(s(s(s(s(s(s(z))))))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[2842, 9])).
% 2.97/3.17 tff(2844,plain,
% 2.97/3.17 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(s(s(s(s(z))))))))))) = s(s(s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.17 inference(quant_inst,[status(thm)],[])).
% 2.97/3.17 tff(2845,plain,
% 2.97/3.17 (inj_0(s(s(s(s(s(s(s(s(s(s(z))))))))))) = s(s(s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[2844, 9])).
% 2.97/3.17 tff(2846,plain,
% 2.97/3.17 (s(s(elem!1)) = s(s(s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[2823])).
% 2.97/3.17 tff(2847,plain,
% 2.97/3.17 (s(s(s(elem!1))) = s(s(s(s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[2846])).
% 2.97/3.17 tff(2848,plain,
% 2.97/3.17 (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.17 inference(transitivity,[status(thm)],[680, 1527, 2847])).
% 2.97/3.17 tff(2849,plain,
% 2.97/3.17 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[2848])).
% 2.97/3.17 tff(2850,plain,
% 2.97/3.17 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.17 inference(transitivity,[status(thm)],[609, 2849, 2845])).
% 2.97/3.17 tff(2851,plain,
% 2.97/3.17 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[2850])).
% 2.97/3.17 tff(2852,plain,
% 2.97/3.17 (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(s(z))))))))),
% 2.97/3.17 inference(transitivity,[status(thm)],[239, 2851, 2843])).
% 2.97/3.17 tff(2853,plain,
% 2.97/3.17 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[2852])).
% 2.97/3.17 tff(2854,plain,
% 2.97/3.17 (inj_0(s(s(s(s(s(s(s(s(z))))))))) = inj_0(s(s(s(s(s(z))))))),
% 2.97/3.17 inference(symmetry,[status(thm)],[2853])).
% 2.97/3.17 tff(2855,plain,
% 2.97/3.17 (s(s(s(elem!1))) = elem!1),
% 2.97/3.17 inference(symmetry,[status(thm)],[1527])).
% 2.97/3.17 tff(2856,plain,
% 2.97/3.17 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.97/3.17 inference(transitivity,[status(thm)],[2855, 679, 2829, 2854, 53])).
% 2.97/3.17 tff(2857,assumption,(~(s(s(s(elem!1))) = s(s(s(s(z)))))), introduced(assumption)).
% 2.97/3.17 tff(2858,plain,
% 2.97/3.17 ($false),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[2857, 2856])).
% 2.97/3.17 tff(2859,plain,((~(elem!1 = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~(elem!1 = s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.17 tff(2860,plain,
% 2.97/3.17 (~(elem!1 = s(s(s(elem!1))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[2859, 2841, 2822])).
% 2.97/3.17 tff(2861,plain,
% 2.97/3.17 (~(s(s(s(elem!1))) = elem!1)),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[2489, 2860])).
% 2.97/3.17 tff(2862,plain,
% 2.97/3.17 (~(s(elem!1) = elem!1)),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[2150, 2861])).
% 2.97/3.17 tff(2863,plain,
% 2.97/3.17 (b(z, elem!1)),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[585, 2805, 318])).
% 2.97/3.17 tff(2864,plain,
% 2.97/3.17 (~(elem!1 = s(s(s(s(z)))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[1846, 2863, 1])).
% 2.97/3.17 tff(2865,plain,
% 2.97/3.17 (r(elem!1, s(s(z))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[2822])).
% 2.97/3.17 tff(2866,plain,
% 2.97/3.17 (r(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> r(elem!1, s(s(z)))),
% 2.97/3.17 inference(symmetry,[status(thm)],[2865])).
% 2.97/3.17 tff(2867,plain,
% 2.97/3.17 (r(elem!1, s(s(z)))),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[107, 2866])).
% 2.97/3.17 tff(2868,plain,
% 2.97/3.17 (b(s(elem!1), s(s(z)))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[809, 2867, 106, 107, 2795, 224, 318, 202, 12, 47])).
% 2.97/3.17 tff(2869,plain,
% 2.97/3.17 (~b(s(s(s(s(z)))), z)),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[296, 178, 273, 104, 202, 134])).
% 2.97/3.17 tff(2870,plain,
% 2.97/3.17 (r(s(s(s(s(z)))), z)),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[191, 2869])).
% 2.97/3.17 tff(2871,plain,
% 2.97/3.17 (b(s(elem!1), s(s(z))) <=> b(s(elem!1), s(elem!1))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[2142])).
% 2.97/3.17 tff(2872,plain,
% 2.97/3.17 (b(s(elem!1), s(elem!1)) <=> b(s(elem!1), s(s(z)))),
% 2.97/3.17 inference(symmetry,[status(thm)],[2871])).
% 2.97/3.17 tff(2873,plain,
% 2.97/3.17 ((~b(s(elem!1), s(elem!1))) <=> (~b(s(elem!1), s(s(z))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[2872])).
% 2.97/3.17 tff(2874,plain,
% 2.97/3.17 (b(s(s(z)), s(elem!1)) <=> b(s(elem!1), s(elem!1))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[2142])).
% 2.97/3.17 tff(2875,plain,
% 2.97/3.17 ((~b(s(s(z)), s(elem!1))) <=> (~b(s(elem!1), s(elem!1)))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[2874])).
% 2.97/3.17 tff(2876,plain,
% 2.97/3.17 (~b(s(elem!1), s(elem!1))),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[1061, 2875])).
% 2.97/3.17 tff(2877,plain,
% 2.97/3.17 (~b(s(elem!1), s(s(z)))),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[2876, 2873])).
% 2.97/3.17 tff(2878,plain,
% 2.97/3.17 ($false),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[1070, 2877])).
% 2.97/3.17 tff(2879,plain,(b(s(s(z)), s(elem!1)) | (~b(s(elem!1), s(s(z)))) | r(s(s(z)), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.17 tff(2880,plain,
% 2.97/3.17 (b(s(s(z)), s(elem!1))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[2879, 1053, 1070])).
% 2.97/3.17 tff(2881,plain,
% 2.97/3.17 (~b(s(elem!1), s(s(s(s(z)))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[1079, 2880, 167, 307, 1070])).
% 2.97/3.17 tff(2882,plain,
% 2.97/3.17 (s(elem!1) = s(s(s(s(z))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[1084, 2881, 2694])).
% 2.97/3.17 tff(2883,plain,
% 2.97/3.17 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[2882])).
% 2.97/3.17 tff(2884,plain,
% 2.97/3.17 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 2.97/3.17 inference(symmetry,[status(thm)],[2883])).
% 2.97/3.17 tff(2885,plain,
% 2.97/3.17 (s(s(s(z))) = elem!1),
% 2.97/3.17 inference(transitivity,[status(thm)],[61, 2884, 304])).
% 2.97/3.17 tff(2886,plain,
% 2.97/3.17 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[2885])).
% 2.97/3.17 tff(2887,plain,
% 2.97/3.17 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 2.97/3.17 inference(symmetry,[status(thm)],[2886])).
% 2.97/3.17 tff(2888,plain,
% 2.97/3.17 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(s(z)))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[2882])).
% 2.97/3.17 tff(2889,plain,
% 2.97/3.17 (~r(s(elem!1), s(s(z)))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[2258, 844, 106])).
% 2.97/3.17 tff(2890,plain,
% 2.97/3.17 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 2.97/3.17 inference(rewrite,[status(thm)],[])).
% 2.97/3.17 tff(2891,plain,
% 2.97/3.17 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 2.97/3.17 inference(quant_inst,[status(thm)],[])).
% 2.97/3.17 tff(2892,plain,
% 2.97/3.17 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[2891, 2890])).
% 2.97/3.17 tff(2893,plain,
% 2.97/3.17 (~r(s(s(s(s(z)))), s(elem!1))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[2892, 118, 844, 194])).
% 2.97/3.17 tff(2894,plain,
% 2.97/3.17 (r(elem!1, s(elem!1))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[2217, 2893, 307, 469, 106, 273, 2889, 145, 506, 725, 844, 2694])).
% 2.97/3.17 tff(2895,plain,
% 2.97/3.17 (r(elem!1, s(s(s(s(z)))))),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[2894, 2888])).
% 2.97/3.17 tff(2896,plain,
% 2.97/3.17 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[2895, 2887])).
% 2.97/3.17 tff(2897,plain,
% 2.97/3.17 (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))))))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[2882])).
% 2.97/3.17 tff(2898,plain,
% 2.97/3.17 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[847, 844, 124])).
% 2.97/3.17 tff(2899,plain,
% 2.97/3.17 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.97/3.17 inference(monotonicity,[status(thm)],[2885])).
% 2.97/3.17 tff(2900,plain,
% 2.97/3.17 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.97/3.17 inference(transitivity,[status(thm)],[2899, 836])).
% 2.97/3.17 tff(2901,plain,
% 2.97/3.17 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[2900])).
% 2.97/3.17 tff(2902,plain,
% 2.97/3.17 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[1104, 2901])).
% 2.97/3.17 tff(2903,plain,
% 2.97/3.17 (b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[2885])).
% 2.97/3.17 tff(2904,plain,
% 2.97/3.17 ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) <=> (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[2903])).
% 2.97/3.17 tff(2905,plain,
% 2.97/3.17 (~b(s(elem!1), s(s(s(s(z)))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[1079, 1071, 167, 202, 1070])).
% 2.97/3.17 tff(2906,plain,
% 2.97/3.17 (s(elem!1) = s(s(s(s(z))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[1084, 2905, 926])).
% 2.97/3.17 tff(2907,plain,
% 2.97/3.17 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[2906])).
% 2.97/3.17 tff(2908,plain,
% 2.97/3.17 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 2.97/3.17 inference(symmetry,[status(thm)],[2907])).
% 2.97/3.17 tff(2909,plain,
% 2.97/3.17 (s(s(s(z))) = elem!1),
% 2.97/3.17 inference(transitivity,[status(thm)],[61, 2908, 304])).
% 2.97/3.17 tff(2910,plain,
% 2.97/3.17 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.97/3.17 inference(monotonicity,[status(thm)],[2909])).
% 2.97/3.17 tff(2911,plain,
% 2.97/3.17 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.97/3.17 inference(transitivity,[status(thm)],[2910, 836])).
% 2.97/3.17 tff(2912,plain,
% 2.97/3.17 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[2911])).
% 2.97/3.17 tff(2913,plain,
% 2.97/3.17 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[1104, 2912])).
% 2.97/3.17 tff(2914,plain,
% 2.97/3.17 (b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[2909])).
% 2.97/3.17 tff(2915,plain,
% 2.97/3.17 ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) <=> (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[2914])).
% 2.97/3.17 tff(2916,plain,
% 2.97/3.17 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(s(z)))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[2906])).
% 2.97/3.17 tff(2917,plain,
% 2.97/3.17 (r(elem!1, s(s(s(s(z)))))),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[1587, 2916])).
% 2.97/3.17 tff(2918,plain,
% 2.97/3.17 (~r(z, elem!1)),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[529, 2917, 145])).
% 2.97/3.17 tff(2919,plain,
% 2.97/3.17 (b(z, elem!1)),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[585, 2918, 507])).
% 2.97/3.17 tff(2920,plain,
% 2.97/3.17 (b(z, s(s(s(z))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[1238, 2919, 2906])).
% 2.97/3.17 tff(2921,plain,
% 2.97/3.17 (elem!1 = s(s(s(z)))),
% 2.97/3.17 inference(transitivity,[status(thm)],[517, 2907, 11])).
% 2.97/3.17 tff(2922,plain,
% 2.97/3.17 (b(elem!1, z) <=> b(s(s(s(z))), z)),
% 2.97/3.17 inference(monotonicity,[status(thm)],[2921])).
% 2.97/3.17 tff(2923,plain,
% 2.97/3.17 (b(s(s(s(z))), z)),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[506, 2922])).
% 2.97/3.17 tff(2924,plain,
% 2.97/3.17 ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[1319, 178, 595, 146, 2923])).
% 2.97/3.17 tff(2925,plain,
% 2.97/3.17 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[2924, 2920])).
% 2.97/3.17 tff(2926,plain,
% 2.97/3.17 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[2925, 2915])).
% 2.97/3.17 tff(2927,plain,
% 2.97/3.17 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[691, 2926, 2913])).
% 2.97/3.17 tff(2928,plain,
% 2.97/3.17 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.17 inference(rewrite,[status(thm)],[])).
% 2.97/3.17 tff(2929,plain,
% 2.97/3.17 (((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.17 inference(rewrite,[status(thm)],[])).
% 2.97/3.17 tff(2930,plain,
% 2.97/3.17 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[2929])).
% 2.97/3.17 tff(2931,plain,
% 2.97/3.17 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.17 inference(transitivity,[status(thm)],[2930, 2928])).
% 2.97/3.17 tff(2932,plain,
% 2.97/3.17 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(elem!1))))),
% 2.97/3.17 inference(quant_inst,[status(thm)],[])).
% 2.97/3.17 tff(2933,plain,
% 2.97/3.17 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[2932, 2931])).
% 2.97/3.17 tff(2934,plain,
% 2.97/3.17 ($false),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[2933, 118, 1587, 1265, 382])).
% 2.97/3.17 tff(2935,plain,((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.17 tff(2936,plain,
% 2.97/3.17 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[2935, 2927, 1587])).
% 2.97/3.17 tff(2937,plain,
% 2.97/3.17 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[395, 2936, 2286])).
% 2.97/3.17 tff(2938,plain,
% 2.97/3.17 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.97/3.17 inference(monotonicity,[status(thm)],[2909])).
% 2.97/3.17 tff(2939,plain,
% 2.97/3.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.97/3.17 inference(rewrite,[status(thm)],[])).
% 2.97/3.17 tff(2940,plain,
% 2.97/3.17 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.97/3.17 inference(rewrite,[status(thm)],[])).
% 2.97/3.17 tff(2941,plain,
% 2.97/3.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[2940])).
% 2.97/3.17 tff(2942,plain,
% 2.97/3.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.97/3.17 inference(transitivity,[status(thm)],[2941, 2939])).
% 2.97/3.17 tff(2943,plain,
% 2.97/3.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.17 inference(quant_inst,[status(thm)],[])).
% 2.97/3.17 tff(2944,plain,
% 2.97/3.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[2943, 2942])).
% 2.97/3.17 tff(2945,plain,
% 2.97/3.17 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[2944, 178, 595, 146, 2920, 2923])).
% 2.97/3.17 tff(2946,plain,
% 2.97/3.17 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 2945])).
% 2.97/3.17 tff(2947,plain,
% 2.97/3.17 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[2946, 2938])).
% 2.97/3.17 tff(2948,plain,
% 2.97/3.17 ((s(s(s(s(s(s(s(z))))))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(s(s(z))))))))),
% 2.97/3.17 inference(commutativity,[status(thm)],[])).
% 2.97/3.17 tff(2949,plain,
% 2.97/3.17 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(z)))),
% 2.97/3.17 inference(symmetry,[status(thm)],[2948])).
% 2.97/3.17 tff(2950,plain,
% 2.97/3.17 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(z))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[2949])).
% 2.97/3.17 tff(2951,assumption,(~(s(s(z)) = s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.97/3.17 tff(2952,plain,
% 2.97/3.17 (~(s(s(s(s(s(s(s(z))))))) = s(s(z)))),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[2951, 2950])).
% 2.97/3.17 tff(2953,assumption,(r(s(s(s(s(s(s(s(z))))))), elem!1)), introduced(assumption)).
% 2.97/3.17 tff(2954,plain,
% 2.97/3.17 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.97/3.17 inference(rewrite,[status(thm)],[])).
% 2.97/3.17 tff(2955,plain,
% 2.97/3.17 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.97/3.17 inference(quant_inst,[status(thm)],[])).
% 2.97/3.17 tff(2956,plain,
% 2.97/3.17 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[2955, 2954])).
% 2.97/3.17 tff(2957,plain,
% 2.97/3.17 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[2956, 118, 438, 2953])).
% 2.97/3.17 tff(2958,plain,
% 2.97/3.17 (((~![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))))),
% 2.97/3.17 inference(rewrite,[status(thm)],[])).
% 2.97/3.17 tff(2959,plain,
% 2.97/3.17 ((~![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))))),
% 2.97/3.17 inference(quant_inst,[status(thm)],[])).
% 2.97/3.17 tff(2960,plain,
% 2.97/3.17 ((~![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)))),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[2959, 2958])).
% 2.97/3.17 tff(2961,plain,
% 2.97/3.17 ((s(s(s(s(s(s(s(z))))))) = s(s(z))) | b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[2960, 41, 2957])).
% 2.97/3.17 tff(2962,plain,
% 2.97/3.17 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[2961, 2952])).
% 2.97/3.17 tff(2963,plain,
% 2.97/3.17 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.18 inference(rewrite,[status(thm)],[])).
% 2.97/3.18 tff(2964,plain,
% 2.97/3.18 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.18 inference(rewrite,[status(thm)],[])).
% 2.97/3.18 tff(2965,plain,
% 2.97/3.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.18 inference(monotonicity,[status(thm)],[2964])).
% 2.97/3.18 tff(2966,plain,
% 2.97/3.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.18 inference(transitivity,[status(thm)],[2965, 2963])).
% 2.97/3.18 tff(2967,plain,
% 2.97/3.18 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.18 inference(quant_inst,[status(thm)],[])).
% 2.97/3.18 tff(2968,plain,
% 2.97/3.18 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.18 inference(modus_ponens,[status(thm)],[2967, 2966])).
% 2.97/3.18 tff(2969,plain,
% 2.97/3.18 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[2968, 118, 438, 2953])).
% 2.97/3.18 tff(2970,plain,
% 2.97/3.18 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[248, 2969, 2951])).
% 2.97/3.18 tff(2971,plain,
% 2.97/3.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.97/3.18 inference(rewrite,[status(thm)],[])).
% 2.97/3.18 tff(2972,plain,
% 2.97/3.18 (((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(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(z)), s(elem!1)))) <=> ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.97/3.18 inference(rewrite,[status(thm)],[])).
% 2.97/3.18 tff(2973,plain,
% 2.97/3.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(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(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))))),
% 2.97/3.18 inference(monotonicity,[status(thm)],[2972])).
% 2.97/3.18 tff(2974,plain,
% 2.97/3.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(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(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.97/3.18 inference(transitivity,[status(thm)],[2973, 2971])).
% 2.97/3.18 tff(2975,plain,
% 2.97/3.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(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(z)), s(elem!1))))),
% 2.97/3.18 inference(quant_inst,[status(thm)],[])).
% 2.97/3.18 tff(2976,plain,
% 2.97/3.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 2.97/3.18 inference(modus_ponens,[status(thm)],[2975, 2974])).
% 2.97/3.18 tff(2977,plain,
% 2.97/3.18 ($false),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[2976, 178, 1071, 1070, 2970, 727, 2962])).
% 2.97/3.18 tff(2978,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (s(s(z)) = s(s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.18 tff(2979,plain,
% 2.97/3.18 ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), elem!1))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[2978, 244])).
% 2.97/3.18 tff(2980,plain,
% 2.97/3.18 (~r(s(s(z)), elem!1)),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[2979, 2947, 1070, 1071, 2937])).
% 2.97/3.18 tff(2981,plain,
% 2.97/3.18 (r(elem!1, s(s(z))) <=> r(s(s(s(z))), s(s(z)))),
% 2.97/3.18 inference(monotonicity,[status(thm)],[2921])).
% 2.97/3.18 tff(2982,plain,
% 2.97/3.18 (r(s(s(s(z))), s(s(z))) <=> r(elem!1, s(s(z)))),
% 2.97/3.18 inference(symmetry,[status(thm)],[2981])).
% 2.97/3.18 tff(2983,plain,
% 2.97/3.18 ((~r(s(s(s(z))), s(s(z)))) <=> (~r(elem!1, s(s(z))))),
% 2.97/3.18 inference(monotonicity,[status(thm)],[2982])).
% 2.97/3.18 tff(2984,plain,
% 2.97/3.18 (~r(s(s(s(z))), s(s(z)))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[1272, 2927, 224, 2906])).
% 2.97/3.18 tff(2985,plain,
% 2.97/3.18 (~r(elem!1, s(s(z)))),
% 2.97/3.18 inference(modus_ponens,[status(thm)],[2984, 2983])).
% 2.97/3.18 tff(2986,plain,
% 2.97/3.18 (b(elem!1, s(s(z)))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[467, 2985, 312])).
% 2.97/3.18 tff(2987,plain,
% 2.97/3.18 (~b(s(s(z)), elem!1)),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[826, 2986, 506, 273, 2919])).
% 2.97/3.18 tff(2988,plain,
% 2.97/3.18 ($false),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[448, 2987, 2980, 12])).
% 2.97/3.18 tff(2989,plain,((~b(s(s(z)), s(elem!1))) | (s(s(z)) = elem!1) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (z = elem!1) | (~r(z, s(s(s(s(z)))))) | r(s(elem!1), s(s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.18 tff(2990,plain,
% 2.97/3.18 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[2989, 224, 506, 273, 1070, 2286, 1587, 12, 1071, 146, 507, 145, 926, 167, 202])).
% 2.97/3.18 tff(2991,plain,
% 2.97/3.18 ($false),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[271, 2990, 398])).
% 2.97/3.18 tff(2992,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(elem!1))) | (s(s(z)) = elem!1) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (z = elem!1) | (~r(z, s(s(s(s(z)))))) | r(s(elem!1), s(s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.18 tff(2993,plain,
% 2.97/3.18 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[2992, 2898, 273, 1070, 506, 2894, 12, 2880, 134, 507, 145, 2694, 167, 307, 106])).
% 2.97/3.18 tff(2994,plain,
% 2.97/3.18 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[249, 2993])).
% 2.97/3.18 tff(2995,plain,
% 2.97/3.18 (~(s(s(z)) = s(s(s(z))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[2196, 2882, 312])).
% 2.97/3.18 tff(2996,plain,
% 2.97/3.18 (elem!1 = s(s(s(z)))),
% 2.97/3.18 inference(transitivity,[status(thm)],[517, 2883, 11])).
% 2.97/3.18 tff(2997,plain,
% 2.97/3.18 (b(elem!1, z) <=> b(s(s(s(z))), z)),
% 2.97/3.18 inference(monotonicity,[status(thm)],[2996])).
% 2.97/3.18 tff(2998,plain,
% 2.97/3.18 (b(s(s(s(z))), z)),
% 2.97/3.18 inference(modus_ponens,[status(thm)],[506, 2997])).
% 2.97/3.18 tff(2999,plain,
% 2.97/3.18 (~r(z, elem!1)),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[529, 2895, 145])).
% 2.97/3.18 tff(3000,plain,
% 2.97/3.18 (b(z, elem!1)),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[585, 2999, 507])).
% 2.97/3.18 tff(3001,plain,
% 2.97/3.18 (b(z, s(s(s(z))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[1238, 3000, 2882])).
% 2.97/3.18 tff(3002,assumption,(b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.97/3.18 tff(3003,plain,
% 2.97/3.18 ((s(s(s(z))) = s(s(z))) <=> (s(s(z)) = s(s(s(z))))),
% 2.97/3.18 inference(commutativity,[status(thm)],[])).
% 2.97/3.18 tff(3004,plain,
% 2.97/3.18 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(z)))),
% 2.97/3.18 inference(symmetry,[status(thm)],[3003])).
% 2.97/3.18 tff(3005,plain,
% 2.97/3.18 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(z))))),
% 2.97/3.18 inference(monotonicity,[status(thm)],[3004])).
% 2.97/3.18 tff(3006,assumption,(~(s(s(z)) = s(s(s(z))))), introduced(assumption)).
% 2.97/3.18 tff(3007,plain,
% 2.97/3.18 (~(s(s(s(z))) = s(s(z)))),
% 2.97/3.18 inference(modus_ponens,[status(thm)],[3006, 3005])).
% 2.97/3.18 tff(3008,assumption,(b(z, s(s(s(z))))), introduced(assumption)).
% 2.97/3.18 tff(3009,plain,
% 2.97/3.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.97/3.18 inference(rewrite,[status(thm)],[])).
% 2.97/3.18 tff(3010,plain,
% 2.97/3.18 (((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.97/3.18 inference(rewrite,[status(thm)],[])).
% 2.97/3.18 tff(3011,plain,
% 2.97/3.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z))))))),
% 2.97/3.18 inference(monotonicity,[status(thm)],[3010])).
% 2.97/3.18 tff(3012,plain,
% 2.97/3.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.97/3.18 inference(transitivity,[status(thm)],[3011, 3009])).
% 2.97/3.18 tff(3013,plain,
% 2.97/3.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 2.97/3.18 inference(quant_inst,[status(thm)],[])).
% 2.97/3.18 tff(3014,plain,
% 2.97/3.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z))))),
% 2.97/3.18 inference(modus_ponens,[status(thm)],[3013, 3012])).
% 2.97/3.18 tff(3015,plain,
% 2.97/3.18 (~b(s(s(s(z))), s(s(z)))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[3014, 178, 273, 166, 3008, 3002])).
% 2.97/3.18 tff(3016,plain,
% 2.97/3.18 (((~![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))))),
% 2.97/3.18 inference(rewrite,[status(thm)],[])).
% 2.97/3.18 tff(3017,plain,
% 2.97/3.18 ((~![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))))),
% 2.97/3.18 inference(quant_inst,[status(thm)],[])).
% 2.97/3.18 tff(3018,plain,
% 2.97/3.18 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 2.97/3.18 inference(modus_ponens,[status(thm)],[3017, 3016])).
% 2.97/3.18 tff(3019,plain,
% 2.97/3.18 ((s(s(s(z))) = s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[3018, 41, 3015])).
% 2.97/3.18 tff(3020,plain,
% 2.97/3.18 (r(s(s(s(z))), s(s(z)))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[3019, 3007])).
% 2.97/3.18 tff(3021,plain,
% 2.97/3.18 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[1175, 118, 3020, 107])).
% 2.97/3.18 tff(3022,plain,
% 2.97/3.18 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 3021])).
% 2.97/3.18 tff(3023,plain,
% 2.97/3.18 ($false),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[1245, 178, 146, 3008, 1127, 3022, 3002])).
% 2.97/3.18 tff(3024,plain,((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (s(s(z)) = s(s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.18 tff(3025,plain,
% 2.97/3.18 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[3024, 3001, 134, 2998, 107, 2995, 273, 2994])).
% 2.97/3.18 tff(3026,plain,
% 2.97/3.18 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.18 inference(modus_ponens,[status(thm)],[3025, 2904])).
% 2.97/3.18 tff(3027,plain,
% 2.97/3.18 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[691, 3026, 2902])).
% 2.97/3.18 tff(3028,plain,
% 2.97/3.18 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[2935, 3027, 2894])).
% 2.97/3.18 tff(3029,plain,
% 2.97/3.18 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[395, 3028, 2898])).
% 2.97/3.18 tff(3030,plain,
% 2.97/3.18 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.18 inference(modus_ponens,[status(thm)],[3029, 2897])).
% 2.97/3.18 tff(3031,plain,
% 2.97/3.18 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[259, 2994, 167, 3030, 307])).
% 2.97/3.18 tff(3032,plain,
% 2.97/3.18 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[84, 3031])).
% 2.97/3.18 tff(3033,plain,
% 2.97/3.18 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[1143, 118, 3032, 145])).
% 2.97/3.18 tff(3034,plain,
% 2.97/3.18 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[271, 3033])).
% 2.97/3.18 tff(3035,plain,
% 2.97/3.18 ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[2944, 178, 134, 3001, 2998])).
% 2.97/3.18 tff(3036,plain,
% 2.97/3.18 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[3035, 3034])).
% 2.97/3.18 tff(3037,plain,
% 2.97/3.18 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 3036])).
% 2.97/3.18 tff(3038,plain,
% 2.97/3.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.97/3.18 inference(rewrite,[status(thm)],[])).
% 2.97/3.18 tff(3039,plain,
% 2.97/3.18 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.97/3.18 inference(rewrite,[status(thm)],[])).
% 2.97/3.18 tff(3040,plain,
% 2.97/3.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 2.97/3.18 inference(monotonicity,[status(thm)],[3039])).
% 2.97/3.18 tff(3041,plain,
% 2.97/3.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.97/3.18 inference(transitivity,[status(thm)],[3040, 3038])).
% 2.97/3.18 tff(3042,plain,
% 2.97/3.18 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.97/3.18 inference(quant_inst,[status(thm)],[])).
% 2.97/3.18 tff(3043,plain,
% 2.97/3.18 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 2.97/3.18 inference(modus_ponens,[status(thm)],[3042, 3041])).
% 2.97/3.18 tff(3044,plain,
% 2.97/3.18 ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[3043, 118, 3032])).
% 2.97/3.18 tff(3045,plain,
% 2.97/3.18 ($false),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[3044, 3037, 2896])).
% 2.97/3.18 tff(3046,plain,((~r(s(elem!1), z)) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, z)) | (s(s(z)) = elem!1) | (z = elem!1) | (~r(s(s(z)), z)) | (elem!1 = s(s(s(s(z))))) | (s(elem!1) = elem!1) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.18 tff(3047,plain,
% 2.97/3.18 (~r(s(elem!1), z)),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[3046, 725, 167, 107, 273, 1070, 506, 12, 507, 106, 469, 145, 194])).
% 2.97/3.18 tff(3048,plain,
% 2.97/3.18 (b(s(elem!1), z)),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[774, 3047])).
% 2.97/3.18 tff(3049,plain,
% 2.97/3.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, z)))),
% 2.97/3.18 inference(rewrite,[status(thm)],[])).
% 2.97/3.18 tff(3050,plain,
% 2.97/3.18 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, z)))),
% 2.97/3.18 inference(rewrite,[status(thm)],[])).
% 2.97/3.18 tff(3051,plain,
% 2.97/3.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, z))))),
% 2.97/3.18 inference(monotonicity,[status(thm)],[3050])).
% 2.97/3.18 tff(3052,plain,
% 2.97/3.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, z)))),
% 2.97/3.18 inference(transitivity,[status(thm)],[3051, 3049])).
% 2.97/3.18 tff(3053,plain,
% 2.97/3.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))),
% 2.97/3.18 inference(quant_inst,[status(thm)],[])).
% 2.97/3.18 tff(3054,plain,
% 2.97/3.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, z))),
% 2.97/3.18 inference(modus_ponens,[status(thm)],[3053, 3052])).
% 2.97/3.18 tff(3055,plain,
% 2.97/3.18 ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), z))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[3054, 178, 506, 273, 1070])).
% 2.97/3.18 tff(3056,plain,
% 2.97/3.18 (~b(elem!1, s(elem!1))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[3055, 3048])).
% 2.97/3.18 tff(3057,plain,
% 2.97/3.18 (r(elem!1, s(elem!1))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[756, 3056, 749])).
% 2.97/3.18 tff(3058,plain,
% 2.97/3.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1))))),
% 2.97/3.18 inference(rewrite,[status(thm)],[])).
% 2.97/3.18 tff(3059,plain,
% 2.97/3.18 (((~r(elem!1, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1))))),
% 2.97/3.18 inference(rewrite,[status(thm)],[])).
% 2.97/3.18 tff(3060,plain,
% 2.97/3.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1)))))),
% 2.97/3.19 inference(monotonicity,[status(thm)],[3059])).
% 2.97/3.19 tff(3061,plain,
% 2.97/3.19 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1))))),
% 2.97/3.19 inference(transitivity,[status(thm)],[3060, 3058])).
% 2.97/3.19 tff(3062,plain,
% 2.97/3.19 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), elem!1)))),
% 2.97/3.19 inference(quant_inst,[status(thm)],[])).
% 2.97/3.19 tff(3063,plain,
% 2.97/3.19 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1)))),
% 2.97/3.19 inference(modus_ponens,[status(thm)],[3062, 3061])).
% 2.97/3.19 tff(3064,plain,
% 2.97/3.19 (~r(s(s(z)), elem!1)),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[3063, 118, 1587, 1329])).
% 2.97/3.19 tff(3065,plain,
% 2.97/3.19 (b(s(s(z)), elem!1)),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[448, 3064, 12])).
% 2.97/3.19 tff(3066,plain,
% 2.97/3.19 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(elem!1))))),
% 2.97/3.19 inference(rewrite,[status(thm)],[])).
% 2.97/3.19 tff(3067,plain,
% 2.97/3.19 (((~r(s(s(z)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(z))))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(elem!1))))),
% 2.97/3.19 inference(rewrite,[status(thm)],[])).
% 2.97/3.19 tff(3068,plain,
% 2.97/3.19 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(elem!1)))))),
% 2.97/3.19 inference(monotonicity,[status(thm)],[3067])).
% 2.97/3.19 tff(3069,plain,
% 2.97/3.19 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(elem!1))))),
% 2.97/3.19 inference(transitivity,[status(thm)],[3068, 3066])).
% 2.97/3.19 tff(3070,plain,
% 2.97/3.19 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(z)))))),
% 2.97/3.19 inference(quant_inst,[status(thm)],[])).
% 2.97/3.19 tff(3071,plain,
% 2.97/3.19 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(elem!1)))),
% 2.97/3.19 inference(modus_ponens,[status(thm)],[3070, 3069])).
% 2.97/3.19 tff(3072,plain,
% 2.97/3.19 (~r(elem!1, s(s(z)))),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[3071, 118, 1587, 1329])).
% 2.97/3.19 tff(3073,plain,
% 2.97/3.19 (b(elem!1, s(s(z)))),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[467, 3072, 312])).
% 2.97/3.19 tff(3074,plain,
% 2.97/3.19 (~b(z, elem!1)),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[826, 3073, 506, 273, 3065])).
% 2.97/3.19 tff(3075,plain,
% 2.97/3.19 (~r(z, elem!1)),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[814, 3073, 167, 202, 469, 12, 145, 106])).
% 2.97/3.19 tff(3076,plain,
% 2.97/3.19 ($false),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[585, 3075, 3074, 507])).
% 2.97/3.19 tff(3077,plain,((~r(s(s(z)), s(elem!1))) | (z = elem!1) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (elem!1 = s(s(s(s(z))))) | (s(s(z)) = elem!1) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.19 tff(3078,plain,
% 2.97/3.19 (~r(s(s(z)), s(elem!1))),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[3077, 3057, 167, 307, 469, 12, 145, 106, 506, 273, 507])).
% 2.97/3.19 tff(3079,plain,
% 2.97/3.19 (b(s(s(z)), s(elem!1))),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[2879, 3078, 1070])).
% 2.97/3.19 tff(3080,plain,
% 2.97/3.19 (~b(s(elem!1), s(s(s(s(z)))))),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[1079, 3079, 167, 307, 1070])).
% 2.97/3.19 tff(3081,plain,
% 2.97/3.19 (~b(z, s(elem!1))),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[2776, 3079, 273, 1070, 3048])).
% 2.97/3.19 tff(3082,plain,
% 2.97/3.19 (r(z, s(elem!1))),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[2351, 3081])).
% 2.97/3.19 tff(3083,plain,
% 2.97/3.19 (~r(s(elem!1), s(s(s(s(z)))))),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[2766, 3082, 145])).
% 2.97/3.19 tff(3084,plain,
% 2.97/3.19 (s(elem!1) = s(s(s(s(z))))),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[1084, 3083, 3080])).
% 2.97/3.19 tff(3085,plain,
% 2.97/3.19 (r(s(elem!1), z) <=> r(s(s(s(s(z)))), z)),
% 2.97/3.19 inference(monotonicity,[status(thm)],[3084])).
% 2.97/3.19 tff(3086,plain,
% 2.97/3.19 (r(s(s(s(s(z)))), z) <=> r(s(elem!1), z)),
% 2.97/3.19 inference(symmetry,[status(thm)],[3085])).
% 2.97/3.19 tff(3087,plain,
% 2.97/3.19 (r(s(elem!1), z)),
% 2.97/3.19 inference(modus_ponens,[status(thm)],[194, 3086])).
% 2.97/3.19 tff(3088,plain,
% 2.97/3.19 ($false),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[3047, 3087])).
% 2.97/3.19 tff(3089,plain,((s(elem!1) = elem!1) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (elem!1 = s(s(s(s(z))))) | (s(s(z)) = elem!1) | (~r(s(s(z)), z)) | (~b(elem!1, z)) | (z = elem!1) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.19 tff(3090,plain,
% 2.97/3.19 ($false),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[3089, 2870, 2868, 273, 47, 2864, 12, 106, 2862, 107, 2795, 318, 302])).
% 2.97/3.19 tff(3091,plain,((~r(s(s(z)), elem!1)) | (~b(z, s(s(z)))) | (s(s(z)) = elem!1) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | b(z, s(s(s(s(z))))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.97/3.19 tff(3092,plain,
% 2.97/3.19 (~r(s(s(z)), elem!1)),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[3091, 12, 273, 106, 107, 287, 202, 104, 1, 290])).
% 2.97/3.19 tff(3093,plain,
% 2.97/3.19 (~r(elem!1, z)),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[493, 469, 106, 202, 12, 145, 165])).
% 2.97/3.19 tff(3094,plain,
% 2.97/3.19 (b(elem!1, z)),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[498, 3093, 290])).
% 2.97/3.19 tff(3095,plain,
% 2.97/3.19 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.19 inference(rewrite,[status(thm)],[])).
% 2.97/3.19 tff(3096,plain,
% 2.97/3.19 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.19 inference(rewrite,[status(thm)],[])).
% 2.97/3.19 tff(3097,plain,
% 2.97/3.19 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.19 inference(monotonicity,[status(thm)],[3096])).
% 2.97/3.19 tff(3098,plain,
% 2.97/3.19 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.19 inference(transitivity,[status(thm)],[3097, 3095])).
% 2.97/3.19 tff(3099,plain,
% 2.97/3.19 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.19 inference(quant_inst,[status(thm)],[])).
% 2.97/3.19 tff(3100,plain,
% 2.97/3.19 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.19 inference(modus_ponens,[status(thm)],[3099, 3098])).
% 2.97/3.19 tff(3101,plain,
% 2.97/3.19 ($false),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[3100, 118, 106, 224, 108])).
% 2.97/3.19 tff(3102,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.19 tff(3103,plain,
% 2.97/3.19 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[3102, 287, 106])).
% 2.97/3.19 tff(3104,plain,
% 2.97/3.19 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[133, 3103])).
% 2.97/3.19 tff(3105,plain,
% 2.97/3.19 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[2820, 3104, 595, 2811, 1342, 507])).
% 2.97/3.19 tff(3106,plain,
% 2.97/3.19 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.19 inference(rewrite,[status(thm)],[])).
% 2.97/3.19 tff(3107,plain,
% 2.97/3.19 (((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(z))))) <=> ((~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.19 inference(rewrite,[status(thm)],[])).
% 2.97/3.19 tff(3108,plain,
% 2.97/3.19 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.19 inference(monotonicity,[status(thm)],[3107])).
% 2.97/3.19 tff(3109,plain,
% 2.97/3.19 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.19 inference(transitivity,[status(thm)],[3108, 3106])).
% 2.97/3.19 tff(3110,plain,
% 2.97/3.19 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(z)))))),
% 2.97/3.19 inference(quant_inst,[status(thm)],[])).
% 2.97/3.19 tff(3111,plain,
% 2.97/3.19 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.19 inference(modus_ponens,[status(thm)],[3110, 3109])).
% 2.97/3.19 tff(3112,plain,
% 2.97/3.19 ($false),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[3111, 118, 450, 224, 1265])).
% 2.97/3.19 tff(3113,plain,((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.19 tff(3114,plain,
% 2.97/3.19 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[3113, 287, 450])).
% 2.97/3.19 tff(3115,plain,
% 2.97/3.19 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[691, 3114, 3105])).
% 2.97/3.19 tff(3116,plain,
% 2.97/3.19 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.19 inference(monotonicity,[status(thm)],[3115])).
% 2.97/3.19 tff(3117,plain,
% 2.97/3.19 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(z)), elem!1)),
% 2.97/3.19 inference(symmetry,[status(thm)],[3116])).
% 2.97/3.19 tff(3118,plain,
% 2.97/3.19 ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(s(z)), elem!1))),
% 2.97/3.19 inference(monotonicity,[status(thm)],[3117])).
% 2.97/3.19 tff(3119,plain,
% 2.97/3.19 (~b(s(s(z)), elem!1)),
% 2.97/3.19 inference(modus_ponens,[status(thm)],[286, 3118])).
% 2.97/3.19 tff(3120,plain,
% 2.97/3.19 ($false),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[817, 3119])).
% 2.97/3.19 tff(3121,plain,(b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | r(z, elem!1) | r(elem!1, z) | (z = elem!1) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.19 tff(3122,plain,
% 2.97/3.19 (~r(elem!1, s(s(z)))),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[3121, 2811, 106, 817, 289, 507, 1342, 286])).
% 2.97/3.19 tff(3123,plain,
% 2.97/3.19 (b(z, elem!1)),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[585, 2811, 507])).
% 2.97/3.19 tff(3124,plain,
% 2.97/3.19 (~b(elem!1, s(s(z)))),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[826, 3123, 273, 817, 506])).
% 2.97/3.19 tff(3125,plain,
% 2.97/3.19 ($false),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[467, 3124, 3122, 462])).
% 2.97/3.19 tff(3126,plain,(r(z, elem!1) | (elem!1 = s(s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~r(s(s(z)), z)) | (z = elem!1) | r(elem!1, z) | b(s(s(z)), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.19 tff(3127,plain,
% 2.97/3.19 (r(z, elem!1)),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[3126, 3094, 273, 817, 312, 106, 318, 3093, 286])).
% 2.97/3.19 tff(3128,plain,
% 2.97/3.19 (~r(elem!1, s(s(s(s(z)))))),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[529, 3127, 145])).
% 2.97/3.19 tff(3129,plain,
% 2.97/3.19 (b(elem!1, s(s(s(s(z)))))),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[483, 3128, 469])).
% 2.97/3.19 tff(3130,plain,
% 2.97/3.19 (~(elem!1 = s(s(s(s(z)))))),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[325, 323])).
% 2.97/3.19 tff(3131,plain,
% 2.97/3.19 (b(elem!1, s(s(s(s(z)))))),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[483, 530, 3130])).
% 2.97/3.19 tff(3132,assumption,(r(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 2.97/3.19 tff(3133,plain,
% 2.97/3.19 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 2.97/3.19 inference(rewrite,[status(thm)],[])).
% 2.97/3.19 tff(3134,plain,
% 2.97/3.19 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 2.97/3.19 inference(quant_inst,[status(thm)],[])).
% 2.97/3.19 tff(3135,plain,
% 2.97/3.19 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z))),
% 2.97/3.19 inference(modus_ponens,[status(thm)],[3134, 3133])).
% 2.97/3.19 tff(3136,plain,
% 2.97/3.19 ($false),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[3135, 118, 521, 3132, 194])).
% 2.97/3.19 tff(3137,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.19 tff(3138,plain,
% 2.97/3.19 (~r(s(s(s(s(z)))), elem!1)),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[3137, 521, 194])).
% 2.97/3.19 tff(3139,plain,
% 2.97/3.19 (((~![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))),
% 2.97/3.19 inference(rewrite,[status(thm)],[])).
% 2.97/3.19 tff(3140,plain,
% 2.97/3.19 ((~![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))),
% 2.97/3.19 inference(quant_inst,[status(thm)],[])).
% 2.97/3.19 tff(3141,plain,
% 2.97/3.19 ((~![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)),
% 2.97/3.19 inference(modus_ponens,[status(thm)],[3140, 3139])).
% 2.97/3.19 tff(3142,plain,
% 2.97/3.19 ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1)),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[3141, 41])).
% 2.97/3.19 tff(3143,plain,
% 2.97/3.19 (b(s(s(s(s(z)))), elem!1)),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[3142, 3138, 323])).
% 2.97/3.19 tff(3144,plain,
% 2.97/3.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.97/3.19 inference(rewrite,[status(thm)],[])).
% 2.97/3.19 tff(3145,plain,
% 2.97/3.19 (((~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(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.97/3.19 inference(rewrite,[status(thm)],[])).
% 2.97/3.19 tff(3146,plain,
% 2.97/3.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 2.97/3.19 inference(monotonicity,[status(thm)],[3145])).
% 2.97/3.19 tff(3147,plain,
% 2.97/3.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.97/3.19 inference(transitivity,[status(thm)],[3146, 3144])).
% 2.97/3.19 tff(3148,plain,
% 2.97/3.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.97/3.19 inference(quant_inst,[status(thm)],[])).
% 2.97/3.19 tff(3149,plain,
% 2.97/3.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z))))),
% 2.97/3.19 inference(modus_ponens,[status(thm)],[3148, 3147])).
% 2.97/3.19 tff(3150,plain,
% 2.97/3.19 ($false),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[3149, 178, 817, 3143, 3131, 167, 202])).
% 2.97/3.19 tff(3151,plain,((~r(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (s(s(s(s(z)))) = elem!1) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.19 tff(3152,plain,
% 2.97/3.19 (~r(s(s(s(s(z)))), z)),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[3151, 3127, 165, 202, 817, 551, 145])).
% 2.97/3.19 tff(3153,plain,
% 2.97/3.19 (b(s(s(s(s(z)))), z)),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[191, 3152])).
% 2.97/3.19 tff(3154,plain,
% 2.97/3.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.97/3.19 inference(rewrite,[status(thm)],[])).
% 2.97/3.19 tff(3155,plain,
% 2.97/3.19 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.97/3.19 inference(rewrite,[status(thm)],[])).
% 2.97/3.19 tff(3156,plain,
% 2.97/3.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 2.97/3.19 inference(monotonicity,[status(thm)],[3155])).
% 2.97/3.19 tff(3157,plain,
% 2.97/3.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.97/3.19 inference(transitivity,[status(thm)],[3156, 3154])).
% 2.97/3.19 tff(3158,plain,
% 2.97/3.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.97/3.19 inference(quant_inst,[status(thm)],[])).
% 2.97/3.19 tff(3159,plain,
% 2.97/3.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))),
% 2.97/3.19 inference(modus_ponens,[status(thm)],[3158, 3157])).
% 2.97/3.19 tff(3160,plain,
% 2.97/3.19 ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[3159, 178, 3094, 273, 202])).
% 2.97/3.19 tff(3161,plain,
% 2.97/3.19 ($false),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[3160, 3153, 3129])).
% 2.97/3.19 tff(3162,plain,((elem!1 = s(s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | (elem!1 = z) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.97/3.19 tff(3163,plain,
% 2.97/3.19 (~b(s(s(z)), elem!1)),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[3162, 12, 202, 273, 47, 106, 286, 290, 469])).
% 2.97/3.19 tff(3164,plain,
% 2.97/3.19 ($false),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[448, 3163, 3092, 12])).
% 2.97/3.19 tff(3165,plain,((s(s(z)) = elem!1) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~r(s(s(z)), z)) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | (elem!1 = z) | (elem!1 = s(s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.19 tff(3166,plain,
% 2.97/3.19 (elem!1 = s(s(s(s(z))))),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[3165, 12, 273, 106, 286, 290, 202, 107, 104, 1])).
% 2.97/3.19 tff(3167,plain,
% 2.97/3.19 (b(s(s(s(s(z)))), z) <=> b(elem!1, z)),
% 2.97/3.19 inference(monotonicity,[status(thm)],[1841])).
% 2.97/3.19 tff(3168,plain,
% 2.97/3.19 (b(elem!1, z) <=> b(s(s(s(s(z)))), z)),
% 2.97/3.19 inference(symmetry,[status(thm)],[3167])).
% 2.97/3.20 tff(3169,plain,
% 2.97/3.20 (b(s(s(s(s(z)))), z)),
% 2.97/3.20 inference(modus_ponens,[status(thm)],[506, 3168])).
% 2.97/3.20 tff(3170,assumption,(~b(s(s(s(s(z)))), z)), introduced(assumption)).
% 2.97/3.20 tff(3171,plain,
% 2.97/3.20 ($false),
% 2.97/3.20 inference(unit_resolution,[status(thm)],[3170, 3169])).
% 2.97/3.20 tff(3172,plain,((~(elem!1 = s(s(s(s(z)))))) | b(s(s(s(s(z)))), z) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.20 tff(3173,plain,
% 2.97/3.20 (~b(elem!1, z)),
% 2.97/3.20 inference(unit_resolution,[status(thm)],[3172, 3166, 299])).
% 2.97/3.20 tff(3174,plain,
% 2.97/3.20 ($false),
% 2.97/3.20 inference(unit_resolution,[status(thm)],[498, 3173, 2793, 290])).
% 2.97/3.20 tff(3175,plain,((s(s(z)) = elem!1) | (elem!1 = z) | (~b(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.20 tff(3176,plain,
% 2.97/3.20 (s(s(z)) = elem!1),
% 2.97/3.20 inference(unit_resolution,[status(thm)],[3175, 202, 144, 106, 107, 286, 290, 104, 1])).
% 2.97/3.20 tff(3177,plain,
% 2.97/3.20 (r(z, s(s(z))) <=> r(z, elem!1)),
% 2.97/3.20 inference(monotonicity,[status(thm)],[3176])).
% 2.97/3.20 tff(3178,plain,
% 2.97/3.20 (r(z, elem!1) <=> r(z, s(s(z)))),
% 2.97/3.20 inference(symmetry,[status(thm)],[3177])).
% 2.97/3.20 tff(3179,plain,
% 2.97/3.20 (~(elem!1 = s(s(s(s(z)))))),
% 2.97/3.20 inference(unit_resolution,[status(thm)],[1846, 818, 1])).
% 2.97/3.20 tff(3180,plain,
% 2.97/3.20 (s(s(z)) = elem!1),
% 2.97/3.20 inference(unit_resolution,[status(thm)],[3165, 3179, 273, 106, 286, 290, 202, 107, 104, 1])).
% 2.97/3.20 tff(3181,plain,
% 2.97/3.20 (s(s(s(z))) = s(elem!1)),
% 2.97/3.20 inference(monotonicity,[status(thm)],[3180])).
% 2.97/3.20 tff(3182,plain,
% 2.97/3.20 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.97/3.20 inference(monotonicity,[status(thm)],[3181])).
% 2.97/3.20 tff(3183,plain,
% 2.97/3.20 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(elem!1)))),
% 2.97/3.20 inference(monotonicity,[status(thm)],[3182])).
% 2.97/3.20 tff(3184,plain,
% 2.97/3.20 (r(elem!1, z)),
% 2.97/3.20 inference(unit_resolution,[status(thm)],[1345, 3180, 106])).
% 2.97/3.20 tff(3185,plain,
% 2.97/3.20 (~r(elem!1, s(s(s(s(z)))))),
% 2.97/3.20 inference(unit_resolution,[status(thm)],[478, 3184, 47])).
% 2.97/3.20 tff(3186,plain,
% 2.97/3.20 (b(elem!1, s(s(s(s(z)))))),
% 2.97/3.20 inference(unit_resolution,[status(thm)],[483, 3185, 3179])).
% 2.97/3.20 tff(3187,plain,
% 2.97/3.20 (b(elem!1, s(s(elem!1)))),
% 2.97/3.20 inference(modus_ponens,[status(thm)],[3186, 3183])).
% 2.97/3.20 tff(3188,plain,
% 2.97/3.20 ((s(elem!1) = s(s(z))) <=> (s(elem!1) = elem!1)),
% 2.97/3.20 inference(monotonicity,[status(thm)],[3180])).
% 2.97/3.20 tff(3189,plain,
% 2.97/3.20 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(z)))),
% 2.97/3.20 inference(symmetry,[status(thm)],[3188])).
% 2.97/3.20 tff(3190,plain,
% 2.97/3.20 ((elem!1 = s(elem!1)) <=> (s(elem!1) = elem!1)),
% 2.97/3.20 inference(commutativity,[status(thm)],[])).
% 2.97/3.20 tff(3191,plain,
% 2.97/3.20 ((elem!1 = s(s(s(z)))) <=> (elem!1 = s(elem!1))),
% 2.97/3.20 inference(monotonicity,[status(thm)],[3181])).
% 2.97/3.20 tff(3192,plain,
% 2.97/3.20 ((elem!1 = s(s(s(z)))) <=> (s(elem!1) = elem!1)),
% 2.97/3.20 inference(transitivity,[status(thm)],[3191, 3190])).
% 2.97/3.20 tff(3193,plain,
% 2.97/3.20 ((elem!1 = s(s(s(z)))) <=> (s(elem!1) = s(s(z)))),
% 2.97/3.20 inference(transitivity,[status(thm)],[3192, 3189])).
% 2.97/3.20 tff(3194,plain,
% 2.97/3.20 ((~(elem!1 = s(s(s(z))))) <=> (~(s(elem!1) = s(s(z))))),
% 2.97/3.20 inference(monotonicity,[status(thm)],[3193])).
% 2.97/3.20 tff(3195,plain,
% 2.97/3.20 ((s(s(z)) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 2.97/3.20 inference(monotonicity,[status(thm)],[3180])).
% 2.97/3.20 tff(3196,plain,
% 2.97/3.20 ((~(s(s(z)) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 2.97/3.20 inference(monotonicity,[status(thm)],[3195])).
% 2.97/3.20 tff(3197,plain,
% 2.97/3.20 ((~(s(s(s(z))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(z)))))),
% 2.97/3.20 inference(monotonicity,[status(thm)],[3003])).
% 2.97/3.20 tff(3198,assumption,(s(s(s(z))) = s(s(z))), introduced(assumption)).
% 2.97/3.20 tff(3199,plain,
% 2.97/3.20 (s(s(s(s(z)))) = s(s(s(z)))),
% 2.97/3.20 inference(monotonicity,[status(thm)],[3198])).
% 2.97/3.20 tff(3200,plain,
% 2.97/3.20 (s(s(s(z))) = s(s(s(s(z))))),
% 2.97/3.20 inference(symmetry,[status(thm)],[3199])).
% 2.97/3.20 tff(3201,plain,
% 2.97/3.20 (s(s(z)) = s(s(s(z)))),
% 2.97/3.20 inference(symmetry,[status(thm)],[3198])).
% 2.97/3.20 tff(3202,plain,
% 2.97/3.20 (s(s(z)) = s(s(s(s(z))))),
% 2.97/3.20 inference(transitivity,[status(thm)],[3201, 3200])).
% 2.97/3.20 tff(3203,plain,
% 2.97/3.20 ($false),
% 2.97/3.20 inference(unit_resolution,[status(thm)],[159, 3202])).
% 2.97/3.20 tff(3204,plain,(~(s(s(s(z))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.20 tff(3205,plain,
% 3.04/3.20 (~(s(s(z)) = s(s(s(z))))),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[3204, 3197])).
% 3.04/3.20 tff(3206,plain,
% 3.04/3.20 (~(elem!1 = s(s(s(z))))),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[3205, 3196])).
% 3.04/3.20 tff(3207,plain,
% 3.04/3.20 (~(s(elem!1) = s(s(z)))),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[3206, 3194])).
% 3.04/3.20 tff(3208,plain,
% 3.04/3.20 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[2840, 3207])).
% 3.04/3.20 tff(3209,plain,
% 3.04/3.20 (b(elem!1, s(s(z))) <=> b(elem!1, elem!1)),
% 3.04/3.20 inference(monotonicity,[status(thm)],[1324])).
% 3.04/3.20 tff(3210,plain,
% 3.04/3.20 (b(elem!1, elem!1) <=> b(elem!1, s(s(z)))),
% 3.04/3.20 inference(symmetry,[status(thm)],[3209])).
% 3.04/3.20 tff(3211,plain,
% 3.04/3.20 ((~b(elem!1, elem!1)) <=> (~b(elem!1, s(s(z))))),
% 3.04/3.20 inference(monotonicity,[status(thm)],[3210])).
% 3.04/3.20 tff(3212,plain,
% 3.04/3.20 (^[X: $i] : refl((~b(X, X)) <=> (~b(X, X)))),
% 3.04/3.20 inference(bind,[status(th)],[])).
% 3.04/3.20 tff(3213,plain,
% 3.04/3.20 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 3.04/3.20 inference(quant_intro,[status(thm)],[3212])).
% 3.04/3.20 tff(3214,plain,
% 3.04/3.20 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 3.04/3.20 inference(rewrite,[status(thm)],[])).
% 3.04/3.20 tff(3215,axiom,(![X: $i] : (~b(X, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bi')).
% 3.04/3.20 tff(3216,plain,
% 3.04/3.20 (![X: $i] : (~b(X, X))),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[3215, 3214])).
% 3.04/3.20 tff(3217,plain,(
% 3.04/3.20 ![X: $i] : (~b(X, X))),
% 3.04/3.20 inference(skolemize,[status(sab)],[3216])).
% 3.04/3.20 tff(3218,plain,
% 3.04/3.20 (![X: $i] : (~b(X, X))),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[3217, 3213])).
% 3.04/3.20 tff(3219,plain,
% 3.04/3.20 ((~![X: $i] : (~b(X, X))) | (~b(elem!1, elem!1))),
% 3.04/3.20 inference(quant_inst,[status(thm)],[])).
% 3.04/3.20 tff(3220,plain,
% 3.04/3.20 (~b(elem!1, elem!1)),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[3219, 3218])).
% 3.04/3.20 tff(3221,plain,
% 3.04/3.20 (~b(elem!1, s(s(z)))),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[3220, 3211])).
% 3.04/3.20 tff(3222,plain,
% 3.04/3.20 ($false),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[812, 3221])).
% 3.04/3.20 tff(3223,plain,((~(s(s(z)) = elem!1)) | (~b(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.20 tff(3224,plain,
% 3.04/3.20 (~b(elem!1, s(s(z)))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[3223, 3180])).
% 3.04/3.20 tff(3225,plain,
% 3.04/3.20 (b(s(s(z)), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 3.04/3.20 inference(monotonicity,[status(thm)],[3180])).
% 3.04/3.20 tff(3226,plain,
% 3.04/3.20 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 3.04/3.20 inference(symmetry,[status(thm)],[3225])).
% 3.04/3.20 tff(3227,plain,
% 3.04/3.20 (~b(s(s(z)), s(s(z)))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[2601, 178, 273, 302])).
% 3.04/3.20 tff(3228,plain,
% 3.04/3.20 (elem!1 = s(s(z))),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[1324, 1666])).
% 3.04/3.20 tff(3229,plain,
% 3.04/3.20 ($false),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[462, 3228])).
% 3.04/3.20 tff(3230,plain,((~(s(s(z)) = elem!1)) | (elem!1 = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.20 tff(3231,plain,
% 3.04/3.20 (elem!1 = s(s(z))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[3230, 3180])).
% 3.04/3.20 tff(3232,plain,
% 3.04/3.20 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(z)))),
% 3.04/3.20 inference(monotonicity,[status(thm)],[308])).
% 3.04/3.20 tff(3233,plain,
% 3.04/3.20 (b(s(s(z)), s(s(z))) <=> b(s(s(z)), elem!1)),
% 3.04/3.20 inference(symmetry,[status(thm)],[3232])).
% 3.04/3.20 tff(3234,plain,
% 3.04/3.20 ((~b(s(s(z)), s(s(z)))) <=> (~b(s(s(z)), elem!1))),
% 3.04/3.20 inference(monotonicity,[status(thm)],[3233])).
% 3.04/3.20 tff(3235,assumption,(~b(s(s(z)), s(s(z)))), introduced(assumption)).
% 3.04/3.20 tff(3236,plain,
% 3.04/3.20 (~b(s(s(z)), elem!1)),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[3235, 3234])).
% 3.04/3.20 tff(3237,plain,
% 3.04/3.20 ($false),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[817, 3236])).
% 3.04/3.20 tff(3238,plain,((~(elem!1 = s(s(z)))) | (~b(s(s(z)), elem!1)) | b(s(s(z)), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.20 tff(3239,plain,
% 3.04/3.20 (~b(s(s(z)), elem!1)),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[3238, 3231, 3227])).
% 3.04/3.20 tff(3240,assumption,(~b(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 3.04/3.20 tff(3241,assumption,(~b(s(s(z)), elem!1)), introduced(assumption)).
% 3.04/3.20 tff(3242,assumption,(~b(z, s(s(s(elem!1))))), introduced(assumption)).
% 3.04/3.20 tff(3243,plain,
% 3.04/3.20 (r(z, s(s(s(elem!1))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[2095, 3242])).
% 3.04/3.20 tff(3244,plain,
% 3.04/3.20 (r(s(s(s(s(z)))), z)),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[191, 3170])).
% 3.04/3.20 tff(3245,plain,
% 3.04/3.20 (~r(s(s(z)), z)),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[199, 103, 194])).
% 3.04/3.20 tff(3246,plain,
% 3.04/3.20 (((~![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))),
% 3.04/3.20 inference(rewrite,[status(thm)],[])).
% 3.04/3.20 tff(3247,plain,
% 3.04/3.20 ((~![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))),
% 3.04/3.20 inference(quant_inst,[status(thm)],[])).
% 3.04/3.20 tff(3248,plain,
% 3.04/3.20 ((~![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)),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[3247, 3246])).
% 3.04/3.20 tff(3249,plain,
% 3.04/3.20 (b(s(s(z)), z) | r(s(s(z)), z)),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[3248, 41, 95])).
% 3.04/3.20 tff(3250,plain,
% 3.04/3.20 (b(s(s(z)), z)),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[3249, 3245])).
% 3.04/3.20 tff(3251,assumption,(r(s(s(s(elem!1))), s(s(s(s(z)))))), introduced(assumption)).
% 3.04/3.20 tff(3252,plain,
% 3.04/3.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.04/3.20 inference(rewrite,[status(thm)],[])).
% 3.04/3.20 tff(3253,plain,
% 3.04/3.20 (((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.04/3.20 inference(rewrite,[status(thm)],[])).
% 3.04/3.20 tff(3254,plain,
% 3.04/3.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 3.04/3.20 inference(monotonicity,[status(thm)],[3253])).
% 3.04/3.20 tff(3255,plain,
% 3.04/3.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.04/3.20 inference(transitivity,[status(thm)],[3254, 3252])).
% 3.04/3.20 tff(3256,plain,
% 3.04/3.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))))),
% 3.04/3.20 inference(quant_inst,[status(thm)],[])).
% 3.04/3.20 tff(3257,plain,
% 3.04/3.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[3256, 3255])).
% 3.04/3.20 tff(3258,plain,
% 3.04/3.20 ($false),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[3257, 118, 557, 145, 3251])).
% 3.04/3.20 tff(3259,plain,((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.20 tff(3260,plain,
% 3.04/3.20 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[3259, 3243, 47])).
% 3.04/3.20 tff(3261,assumption,(r(z, s(s(z)))), introduced(assumption)).
% 3.04/3.20 tff(3262,plain,
% 3.04/3.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 3.04/3.20 inference(rewrite,[status(thm)],[])).
% 3.04/3.20 tff(3263,plain,
% 3.04/3.20 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 3.04/3.20 inference(rewrite,[status(thm)],[])).
% 3.04/3.20 tff(3264,plain,
% 3.04/3.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 3.04/3.20 inference(monotonicity,[status(thm)],[3263])).
% 3.04/3.20 tff(3265,plain,
% 3.04/3.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 3.04/3.20 inference(transitivity,[status(thm)],[3264, 3262])).
% 3.04/3.20 tff(3266,plain,
% 3.04/3.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))))),
% 3.04/3.20 inference(quant_inst,[status(thm)],[])).
% 3.04/3.20 tff(3267,plain,
% 3.04/3.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[3266, 3265])).
% 3.04/3.20 tff(3268,plain,
% 3.04/3.20 ($false),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[3267, 118, 3261, 145, 193])).
% 3.04/3.20 tff(3269,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.20 tff(3270,plain,
% 3.04/3.20 (~r(z, s(s(z)))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[3269, 103, 47])).
% 3.04/3.20 tff(3271,plain,
% 3.04/3.20 (b(z, s(s(z)))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[143, 3270])).
% 3.04/3.20 tff(3272,plain,
% 3.04/3.20 (b(elem!1, s(s(z))) <=> b(z, s(s(z)))),
% 3.04/3.20 inference(monotonicity,[status(thm)],[928])).
% 3.04/3.20 tff(3273,plain,
% 3.04/3.20 (b(z, s(s(z))) <=> b(elem!1, s(s(z)))),
% 3.04/3.20 inference(symmetry,[status(thm)],[3272])).
% 3.04/3.20 tff(3274,plain,
% 3.04/3.20 (b(elem!1, s(s(z)))),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[273, 3273])).
% 3.04/3.20 tff(3275,plain,
% 3.04/3.20 ($false),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[461, 3274])).
% 3.04/3.20 tff(3276,plain,((~(elem!1 = z)) | b(elem!1, s(s(z))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.20 tff(3277,plain,
% 3.04/3.20 (~(elem!1 = z)),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[3276, 3271, 461])).
% 3.04/3.20 tff(3278,assumption,(~b(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 3.04/3.20 tff(3279,assumption,(r(s(s(s(s(z)))), s(s(s(elem!1))))), introduced(assumption)).
% 3.04/3.20 tff(3280,plain,
% 3.04/3.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.04/3.20 inference(rewrite,[status(thm)],[])).
% 3.04/3.20 tff(3281,plain,
% 3.04/3.20 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.04/3.20 inference(rewrite,[status(thm)],[])).
% 3.04/3.20 tff(3282,plain,
% 3.04/3.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 3.04/3.20 inference(monotonicity,[status(thm)],[3281])).
% 3.04/3.20 tff(3283,plain,
% 3.04/3.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.04/3.20 inference(transitivity,[status(thm)],[3282, 3280])).
% 3.04/3.20 tff(3284,plain,
% 3.04/3.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))),
% 3.04/3.20 inference(quant_inst,[status(thm)],[])).
% 3.04/3.20 tff(3285,plain,
% 3.04/3.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[3284, 3283])).
% 3.04/3.20 tff(3286,plain,
% 3.04/3.20 ($false),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[3285, 118, 557, 194, 3279])).
% 3.04/3.20 tff(3287,plain,((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.20 tff(3288,plain,
% 3.04/3.20 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[3287, 557, 194])).
% 3.04/3.20 tff(3289,plain,
% 3.04/3.20 ((s(s(s(s(z)))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.04/3.20 inference(commutativity,[status(thm)],[])).
% 3.04/3.20 tff(3290,plain,
% 3.04/3.20 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.04/3.20 inference(monotonicity,[status(thm)],[1527])).
% 3.04/3.20 tff(3291,plain,
% 3.04/3.20 ((~b(s(s(s(s(z)))), elem!1)) <=> (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 3.04/3.20 inference(monotonicity,[status(thm)],[3290])).
% 3.04/3.20 tff(3292,plain,
% 3.04/3.20 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[3278, 3291])).
% 3.04/3.20 tff(3293,assumption,(~r(s(s(s(s(z)))), s(s(s(elem!1))))), introduced(assumption)).
% 3.04/3.20 tff(3294,plain,
% 3.04/3.20 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(elem!1)))) | b(s(s(s(s(z)))), s(s(s(elem!1)))) | r(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | b(s(s(s(s(z)))), s(s(s(elem!1)))) | r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 3.04/3.20 inference(rewrite,[status(thm)],[])).
% 3.04/3.20 tff(3295,plain,
% 3.04/3.20 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(elem!1)))) | b(s(s(s(s(z)))), s(s(s(elem!1)))) | r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 3.04/3.20 inference(quant_inst,[status(thm)],[])).
% 3.04/3.20 tff(3296,plain,
% 3.04/3.20 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | b(s(s(s(s(z)))), s(s(s(elem!1)))) | r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[3295, 3294])).
% 3.04/3.20 tff(3297,plain,
% 3.04/3.20 ((s(s(s(s(z)))) = s(s(s(elem!1)))) | b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[3296, 41, 3293])).
% 3.04/3.20 tff(3298,plain,
% 3.04/3.20 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[3297, 3292])).
% 3.04/3.20 tff(3299,plain,
% 3.04/3.20 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[3298, 3289])).
% 3.04/3.20 tff(3300,plain,
% 3.04/3.20 (s(elem!1) = s(s(s(s(elem!1))))),
% 3.04/3.20 inference(monotonicity,[status(thm)],[1527])).
% 3.04/3.20 tff(3301,plain,
% 3.04/3.20 ((s(elem!1) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(z)))),
% 3.04/3.20 inference(monotonicity,[status(thm)],[3300])).
% 3.04/3.20 tff(3302,plain,
% 3.04/3.20 ((s(elem!1) = s(s(z))) <=> (s(s(z)) = s(s(s(s(elem!1)))))),
% 3.04/3.20 inference(transitivity,[status(thm)],[3301, 2129])).
% 3.04/3.20 tff(3303,plain,
% 3.04/3.20 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(elem!1) = s(s(z)))),
% 3.04/3.20 inference(symmetry,[status(thm)],[3302])).
% 3.04/3.20 tff(3304,plain,
% 3.04/3.20 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(s(elem!1) = s(s(z))))),
% 3.04/3.20 inference(monotonicity,[status(thm)],[3303])).
% 3.04/3.20 tff(3305,plain,
% 3.04/3.20 (~(s(elem!1) = s(s(z)))),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[2131, 3304])).
% 3.04/3.20 tff(3306,plain,
% 3.04/3.20 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[2840, 3305])).
% 3.04/3.20 tff(3307,plain,
% 3.04/3.20 ($false),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[3306, 3299])).
% 3.04/3.20 tff(3308,plain,((~(elem!1 = s(s(s(elem!1))))) | r(s(s(s(s(z)))), s(s(s(elem!1)))) | b(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.04/3.20 tff(3309,plain,
% 3.04/3.20 (~(elem!1 = s(s(s(elem!1))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[3308, 3278, 3288])).
% 3.04/3.20 tff(3310,plain,
% 3.04/3.20 (r(elem!1, s(s(s(elem!1))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[2054, 3309, 3240])).
% 3.04/3.20 tff(3311,assumption,(r(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 3.04/3.20 tff(3312,plain,
% 3.04/3.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 3.04/3.20 inference(rewrite,[status(thm)],[])).
% 3.04/3.20 tff(3313,plain,
% 3.04/3.20 (((~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 3.04/3.20 inference(rewrite,[status(thm)],[])).
% 3.04/3.20 tff(3314,plain,
% 3.04/3.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))))),
% 3.04/3.20 inference(monotonicity,[status(thm)],[3313])).
% 3.04/3.20 tff(3315,plain,
% 3.04/3.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 3.04/3.20 inference(transitivity,[status(thm)],[3314, 3312])).
% 3.04/3.20 tff(3316,plain,
% 3.04/3.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))),
% 3.04/3.20 inference(quant_inst,[status(thm)],[])).
% 3.04/3.20 tff(3317,plain,
% 3.04/3.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[3316, 3315])).
% 3.04/3.20 tff(3318,plain,
% 3.04/3.20 ($false),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[3317, 118, 521, 3311, 557])).
% 3.04/3.20 tff(3319,plain,((~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.20 tff(3320,plain,
% 3.04/3.20 (~r(z, elem!1)),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[3319, 3310, 557])).
% 3.04/3.20 tff(3321,plain,
% 3.04/3.20 (b(z, elem!1)),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[585, 3320, 318])).
% 3.04/3.20 tff(3322,plain,
% 3.04/3.20 (~(elem!1 = s(s(s(s(z)))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[1846, 3321, 1])).
% 3.04/3.20 tff(3323,plain,
% 3.04/3.20 (~(s(s(s(s(z)))) = elem!1)),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[504, 3322])).
% 3.04/3.20 tff(3324,plain,
% 3.04/3.20 (r(s(s(s(s(z)))), elem!1)),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[3142, 3323, 3278])).
% 3.04/3.20 tff(3325,plain,
% 3.04/3.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 3.04/3.20 inference(rewrite,[status(thm)],[])).
% 3.04/3.20 tff(3326,plain,
% 3.04/3.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 3.04/3.20 inference(quant_inst,[status(thm)],[])).
% 3.04/3.20 tff(3327,plain,
% 3.04/3.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z))))),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[3326, 3325])).
% 3.04/3.20 tff(3328,plain,
% 3.04/3.20 ($false),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[3327, 118, 438, 3132, 193])).
% 3.04/3.20 tff(3329,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.20 tff(3330,plain,
% 3.04/3.20 (~r(s(s(z)), elem!1)),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[3329, 3324, 193])).
% 3.04/3.20 tff(3331,plain,
% 3.04/3.20 (s(s(z)) = elem!1),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[448, 3330, 3241])).
% 3.04/3.20 tff(3332,plain,
% 3.04/3.20 (elem!1 = s(s(z))),
% 3.04/3.20 inference(symmetry,[status(thm)],[3331])).
% 3.04/3.20 tff(3333,plain,
% 3.04/3.20 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(elem!1)))), s(s(z)))),
% 3.04/3.20 inference(monotonicity,[status(thm)],[3332])).
% 3.04/3.20 tff(3334,plain,
% 3.04/3.20 (r(s(s(s(s(elem!1)))), s(s(z))) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 3.04/3.20 inference(symmetry,[status(thm)],[3333])).
% 3.04/3.20 tff(3335,plain,
% 3.04/3.20 (b(s(s(s(s(elem!1)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 3.04/3.20 inference(monotonicity,[status(thm)],[3331])).
% 3.04/3.20 tff(3336,plain,
% 3.04/3.20 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(elem!1)))), s(s(z)))),
% 3.04/3.20 inference(symmetry,[status(thm)],[3335])).
% 3.04/3.20 tff(3337,plain,
% 3.04/3.20 ((~b(s(s(s(s(elem!1)))), elem!1)) <=> (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 3.04/3.20 inference(monotonicity,[status(thm)],[3336])).
% 3.04/3.20 tff(3338,plain,
% 3.04/3.20 ((s(s(elem!1)) = s(s(z))) <=> (s(s(elem!1)) = elem!1)),
% 3.04/3.20 inference(monotonicity,[status(thm)],[3331])).
% 3.04/3.20 tff(3339,plain,
% 3.04/3.20 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(elem!1)) = elem!1))),
% 3.04/3.20 inference(monotonicity,[status(thm)],[3338])).
% 3.04/3.20 tff(3340,plain,
% 3.04/3.20 (~(s(s(elem!1)) = s(s(z)))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[2386, 318])).
% 3.04/3.20 tff(3341,plain,
% 3.04/3.20 (~(s(s(elem!1)) = elem!1)),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[3340, 3339])).
% 3.04/3.20 tff(3342,plain,
% 3.04/3.20 (s(s(s(z))) = s(elem!1)),
% 3.04/3.20 inference(monotonicity,[status(thm)],[3331])).
% 3.04/3.20 tff(3343,plain,
% 3.04/3.20 (s(s(s(s(z)))) = s(s(elem!1))),
% 3.04/3.20 inference(monotonicity,[status(thm)],[3342])).
% 3.04/3.20 tff(3344,plain,
% 3.04/3.20 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 3.04/3.20 inference(monotonicity,[status(thm)],[3343])).
% 3.04/3.20 tff(3345,plain,
% 3.04/3.20 ((~b(s(s(s(s(z)))), elem!1)) <=> (~b(s(s(elem!1)), elem!1))),
% 3.04/3.20 inference(monotonicity,[status(thm)],[3344])).
% 3.04/3.20 tff(3346,plain,
% 3.04/3.20 (~b(s(s(elem!1)), elem!1)),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[3278, 3345])).
% 3.04/3.20 tff(3347,assumption,(~b(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 3.04/3.20 tff(3348,plain,
% 3.04/3.20 (~(s(elem!1) = s(s(elem!1)))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[979, 346])).
% 3.04/3.20 tff(3349,plain,
% 3.04/3.20 (s(s(s(elem!1))) = s(elem!1)),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[1649, 1640])).
% 3.04/3.20 tff(3350,plain,
% 3.04/3.20 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(elem!1))),
% 3.04/3.20 inference(monotonicity,[status(thm)],[340])).
% 3.04/3.20 tff(3351,plain,
% 3.04/3.20 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(elem!1)))),
% 3.04/3.20 inference(transitivity,[status(thm)],[3350, 981])).
% 3.04/3.20 tff(3352,plain,
% 3.04/3.20 (s(elem!1) = s(s(elem!1))),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[1640, 3351])).
% 3.04/3.20 tff(3353,plain,
% 3.04/3.20 ($false),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[984, 3352])).
% 3.04/3.20 tff(3354,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | (s(elem!1) = s(s(elem!1))) | (~(s(s(s(elem!1))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.20 tff(3355,plain,
% 3.04/3.20 ($false),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[3354, 3349, 1640, 984])).
% 3.04/3.20 tff(3356,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.20 tff(3357,plain,
% 3.04/3.20 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[3356, 3348])).
% 3.04/3.20 tff(3358,assumption,(~b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 3.04/3.20 tff(3359,plain,
% 3.04/3.20 (((~![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))),
% 3.04/3.20 inference(rewrite,[status(thm)],[])).
% 3.04/3.20 tff(3360,plain,
% 3.04/3.20 ((~![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))),
% 3.04/3.20 inference(quant_inst,[status(thm)],[])).
% 3.04/3.20 tff(3361,plain,
% 3.04/3.20 ((~![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)),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[3360, 3359])).
% 3.04/3.20 tff(3362,plain,
% 3.04/3.20 ((s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1)),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[3361, 41])).
% 3.04/3.20 tff(3363,plain,
% 3.04/3.20 (r(s(s(elem!1)), elem!1)),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[3362, 346, 3358])).
% 3.04/3.20 tff(3364,assumption,(r(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 3.04/3.20 tff(3365,assumption,(r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 3.04/3.21 tff(3366,plain,
% 3.04/3.21 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))),
% 3.04/3.21 inference(rewrite,[status(thm)],[])).
% 3.04/3.21 tff(3367,plain,
% 3.04/3.21 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))),
% 3.04/3.21 inference(quant_inst,[status(thm)],[])).
% 3.04/3.21 tff(3368,plain,
% 3.04/3.21 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1))),
% 3.04/3.21 inference(modus_ponens,[status(thm)],[3367, 3366])).
% 3.04/3.21 tff(3369,plain,
% 3.04/3.21 ($false),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[3368, 118, 3311, 3365, 3364])).
% 3.04/3.21 tff(3370,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.21 tff(3371,plain,
% 3.04/3.21 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[3370, 3363, 3311])).
% 3.04/3.21 tff(3372,plain,
% 3.04/3.21 (((~![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)))))),
% 3.04/3.21 inference(rewrite,[status(thm)],[])).
% 3.04/3.21 tff(3373,plain,
% 3.04/3.21 ((~![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)))))),
% 3.04/3.21 inference(quant_inst,[status(thm)],[])).
% 3.04/3.21 tff(3374,plain,
% 3.04/3.21 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.04/3.21 inference(modus_ponens,[status(thm)],[3373, 3372])).
% 3.04/3.21 tff(3375,plain,
% 3.04/3.21 ((s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[3374, 41])).
% 3.04/3.21 tff(3376,plain,
% 3.04/3.21 ($false),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[3375, 3371, 3357, 3347])).
% 3.04/3.21 tff(3377,plain,((s(s(elem!1)) = elem!1) | b(s(s(elem!1)), s(s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.04/3.21 tff(3378,plain,
% 3.04/3.21 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[3377, 3346, 3341, 3310])).
% 3.04/3.21 tff(3379,plain,
% 3.04/3.21 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.04/3.21 inference(monotonicity,[status(thm)],[3343])).
% 3.04/3.21 tff(3380,plain,
% 3.04/3.21 ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) <=> (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 3.04/3.21 inference(monotonicity,[status(thm)],[3379])).
% 3.04/3.21 tff(3381,plain,
% 3.04/3.21 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[3259, 557, 47])).
% 3.04/3.21 tff(3382,plain,
% 3.04/3.21 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.04/3.21 inference(modus_ponens,[status(thm)],[3381, 3380])).
% 3.04/3.21 tff(3383,plain,
% 3.04/3.21 (b(z, s(s(s(s(z))))) <=> b(z, s(s(elem!1)))),
% 3.04/3.21 inference(monotonicity,[status(thm)],[3343])).
% 3.04/3.21 tff(3384,plain,
% 3.04/3.21 ((~b(z, s(s(s(s(z)))))) <=> (~b(z, s(s(elem!1))))),
% 3.04/3.21 inference(monotonicity,[status(thm)],[3383])).
% 3.04/3.21 tff(3385,plain,
% 3.04/3.21 (~b(z, s(s(elem!1)))),
% 3.04/3.21 inference(modus_ponens,[status(thm)],[1, 3384])).
% 3.04/3.21 tff(3386,plain,
% 3.04/3.21 (s(s(elem!1)) = elem!1),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[348, 3349])).
% 3.04/3.21 tff(3387,plain,
% 3.04/3.21 (elem!1 = s(s(elem!1))),
% 3.04/3.21 inference(symmetry,[status(thm)],[3386])).
% 3.04/3.21 tff(3388,plain,
% 3.04/3.21 (elem!1 = s(s(s(elem!1)))),
% 3.04/3.21 inference(transitivity,[status(thm)],[3387, 1640])).
% 3.04/3.21 tff(3389,plain,
% 3.04/3.21 (b(z, elem!1) <=> b(z, s(s(s(elem!1))))),
% 3.04/3.21 inference(monotonicity,[status(thm)],[3388])).
% 3.04/3.21 tff(3390,plain,
% 3.04/3.21 (b(z, s(s(s(elem!1)))) <=> b(z, elem!1)),
% 3.04/3.21 inference(symmetry,[status(thm)],[3389])).
% 3.04/3.21 tff(3391,plain,
% 3.04/3.21 ((~b(z, s(s(s(elem!1))))) <=> (~b(z, elem!1))),
% 3.04/3.21 inference(monotonicity,[status(thm)],[3390])).
% 3.04/3.21 tff(3392,plain,
% 3.04/3.21 (b(z, s(s(elem!1))) <=> b(z, s(s(s(elem!1))))),
% 3.04/3.21 inference(monotonicity,[status(thm)],[1640])).
% 3.04/3.21 tff(3393,plain,
% 3.04/3.21 ((~b(z, s(s(elem!1)))) <=> (~b(z, s(s(s(elem!1)))))),
% 3.04/3.21 inference(monotonicity,[status(thm)],[3392])).
% 3.04/3.21 tff(3394,assumption,(~b(z, s(s(elem!1)))), introduced(assumption)).
% 3.04/3.21 tff(3395,plain,
% 3.04/3.21 (~b(z, s(s(s(elem!1))))),
% 3.04/3.21 inference(modus_ponens,[status(thm)],[3394, 3393])).
% 3.04/3.21 tff(3396,plain,
% 3.04/3.21 (~b(z, elem!1)),
% 3.04/3.21 inference(modus_ponens,[status(thm)],[3395, 3391])).
% 3.04/3.21 tff(3397,plain,
% 3.04/3.21 ($false),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[818, 3396])).
% 3.04/3.21 tff(3398,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(z, elem!1)) | b(z, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.21 tff(3399,plain,
% 3.04/3.21 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[3398, 3385, 3321])).
% 3.04/3.21 tff(3400,plain,
% 3.04/3.21 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 3.04/3.21 inference(commutativity,[status(thm)],[])).
% 3.04/3.21 tff(3401,assumption,(s(s(s(elem!1))) = s(s(elem!1))), introduced(assumption)).
% 3.04/3.21 tff(3402,plain,
% 3.04/3.21 (s(s(elem!1)) = s(s(s(elem!1)))),
% 3.04/3.21 inference(modus_ponens,[status(thm)],[3401, 3400])).
% 3.04/3.21 tff(3403,plain,
% 3.04/3.21 ($false),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[1655, 3402])).
% 3.04/3.21 tff(3404,plain,((~(s(s(s(elem!1))) = s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.21 tff(3405,plain,
% 3.04/3.21 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[3404, 3399])).
% 3.04/3.21 tff(3406,plain,
% 3.04/3.21 (((~![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))))),
% 3.04/3.21 inference(rewrite,[status(thm)],[])).
% 3.04/3.21 tff(3407,plain,
% 3.04/3.21 ((~![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))))),
% 3.04/3.21 inference(quant_inst,[status(thm)],[])).
% 3.04/3.21 tff(3408,plain,
% 3.04/3.21 ((~![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)))),
% 3.04/3.21 inference(modus_ponens,[status(thm)],[3407, 3406])).
% 3.04/3.21 tff(3409,plain,
% 3.04/3.21 ((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)))),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[3408, 41])).
% 3.04/3.21 tff(3410,plain,
% 3.04/3.21 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[3409, 3405, 3382])).
% 3.04/3.21 tff(3411,plain,
% 3.04/3.21 (s(s(elem!1)) = s(s(s(s(z))))),
% 3.04/3.21 inference(symmetry,[status(thm)],[3343])).
% 3.04/3.21 tff(3412,plain,
% 3.04/3.21 (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)))))),
% 3.04/3.21 inference(monotonicity,[status(thm)],[3411])).
% 3.04/3.21 tff(3413,plain,
% 3.04/3.21 (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)))),
% 3.04/3.21 inference(symmetry,[status(thm)],[3412])).
% 3.04/3.21 tff(3414,plain,
% 3.04/3.21 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 3.04/3.21 inference(rewrite,[status(thm)],[])).
% 3.04/3.21 tff(3415,plain,
% 3.04/3.21 (((~r(z, s(s(s(elem!1))))) | (~r(elem!1, 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))))))),
% 3.04/3.21 inference(rewrite,[status(thm)],[])).
% 3.04/3.21 tff(3416,plain,
% 3.04/3.21 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))))),
% 3.04/3.21 inference(monotonicity,[status(thm)],[3415])).
% 3.04/3.21 tff(3417,plain,
% 3.04/3.21 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 3.04/3.21 inference(transitivity,[status(thm)],[3416, 3414])).
% 3.04/3.21 tff(3418,plain,
% 3.04/3.21 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z)))),
% 3.04/3.21 inference(quant_inst,[status(thm)],[])).
% 3.04/3.21 tff(3419,plain,
% 3.04/3.21 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))),
% 3.04/3.21 inference(modus_ponens,[status(thm)],[3418, 3417])).
% 3.04/3.21 tff(3420,plain,
% 3.04/3.21 ($false),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[3419, 118, 437, 3311, 557])).
% 3.04/3.21 tff(3421,plain,((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.21 tff(3422,plain,
% 3.04/3.21 (~r(elem!1, z)),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[3421, 3310, 557])).
% 3.04/3.21 tff(3423,plain,
% 3.04/3.21 (b(elem!1, z)),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[498, 3422, 290])).
% 3.04/3.21 tff(3424,plain,
% 3.04/3.21 (~r(s(s(z)), z)),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[199, 193, 194])).
% 3.04/3.21 tff(3425,plain,
% 3.04/3.21 (b(s(s(z)), z)),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[3249, 3424])).
% 3.04/3.21 tff(3426,plain,
% 3.04/3.21 (r(s(s(z)), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 3.04/3.21 inference(monotonicity,[status(thm)],[1324])).
% 3.04/3.21 tff(3427,plain,
% 3.04/3.21 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 3.04/3.21 inference(symmetry,[status(thm)],[3426])).
% 3.04/3.21 tff(3428,assumption,(~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))), introduced(assumption)).
% 3.04/3.21 tff(3429,plain,
% 3.04/3.21 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.04/3.21 inference(monotonicity,[status(thm)],[679])).
% 3.04/3.21 tff(3430,plain,
% 3.04/3.21 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 3.04/3.21 inference(symmetry,[status(thm)],[3429])).
% 3.04/3.21 tff(3431,plain,
% 3.04/3.21 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) <=> (~b(elem!1, s(s(s(s(z))))))),
% 3.04/3.21 inference(monotonicity,[status(thm)],[3430])).
% 3.04/3.21 tff(3432,plain,
% 3.04/3.21 (~b(elem!1, s(s(s(s(z)))))),
% 3.04/3.21 inference(modus_ponens,[status(thm)],[3428, 3431])).
% 3.04/3.21 tff(3433,plain,
% 3.04/3.21 ($false),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[1301, 3432])).
% 3.04/3.21 tff(3434,plain,((~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.21 tff(3435,plain,
% 3.04/3.21 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[3434, 3428, 1301])).
% 3.04/3.21 tff(3436,plain,
% 3.04/3.21 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[703, 3435])).
% 3.04/3.21 tff(3437,plain,
% 3.04/3.21 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[84, 3428])).
% 3.04/3.21 tff(3438,plain,
% 3.04/3.21 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), 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)))))))),
% 3.04/3.21 inference(rewrite,[status(thm)],[])).
% 3.04/3.21 tff(3439,plain,
% 3.04/3.21 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 3.04/3.21 inference(quant_inst,[status(thm)],[])).
% 3.04/3.21 tff(3440,plain,
% 3.04/3.21 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 3.04/3.21 inference(modus_ponens,[status(thm)],[3439, 3438])).
% 3.04/3.21 tff(3441,plain,
% 3.04/3.21 ($false),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[3440, 118, 1130, 3132, 2953])).
% 3.04/3.21 tff(3442,plain,((~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)))))) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.21 tff(3443,plain,
% 3.04/3.21 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[3442, 3437, 3132])).
% 3.04/3.21 tff(3444,plain,
% 3.04/3.21 ((s(s(s(s(s(s(s(z))))))) = elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[707, 41])).
% 3.04/3.21 tff(3445,plain,
% 3.04/3.21 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[3444, 3443, 3436])).
% 3.04/3.21 tff(3446,plain,
% 3.04/3.21 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[1138, 3437, 145])).
% 3.04/3.21 tff(3447,plain,
% 3.04/3.21 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[133, 3446])).
% 3.04/3.21 tff(3448,plain,
% 3.04/3.21 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[1143, 118, 3437, 145])).
% 3.04/3.21 tff(3449,plain,
% 3.04/3.21 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[271, 3448])).
% 3.04/3.21 tff(3450,plain,
% 3.04/3.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.04/3.21 inference(rewrite,[status(thm)],[])).
% 3.04/3.21 tff(3451,plain,
% 3.04/3.21 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.04/3.21 inference(rewrite,[status(thm)],[])).
% 3.04/3.21 tff(3452,plain,
% 3.04/3.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 3.04/3.21 inference(monotonicity,[status(thm)],[3451])).
% 3.04/3.21 tff(3453,plain,
% 3.04/3.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.04/3.21 inference(transitivity,[status(thm)],[3452, 3450])).
% 3.04/3.21 tff(3454,plain,
% 3.04/3.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.21 inference(quant_inst,[status(thm)],[])).
% 3.04/3.21 tff(3455,plain,
% 3.04/3.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 3.04/3.21 inference(modus_ponens,[status(thm)],[3454, 3453])).
% 3.04/3.21 tff(3456,plain,
% 3.04/3.21 ($false),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[3455, 178, 818, 506, 3449, 3447, 3445])).
% 3.04/3.21 tff(3457,plain,(b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.21 tff(3458,plain,
% 3.04/3.21 (~b(elem!1, s(s(s(s(z)))))),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[3457, 3428, 506, 145, 818, 3132])).
% 3.04/3.21 tff(3459,plain,
% 3.04/3.21 (r(elem!1, s(s(s(s(z)))))),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[483, 3458, 469])).
% 3.04/3.21 tff(3460,plain,
% 3.04/3.21 (r(s(s(z)), s(s(s(s(z)))))),
% 3.04/3.21 inference(modus_ponens,[status(thm)],[3459, 3427])).
% 3.04/3.21 tff(3461,assumption,(b(s(s(z)), z)), introduced(assumption)).
% 3.04/3.21 tff(3462,plain,
% 3.04/3.21 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[131, 41, 128, 1139])).
% 3.04/3.21 tff(3463,plain,
% 3.04/3.21 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.04/3.21 inference(rewrite,[status(thm)],[])).
% 3.04/3.21 tff(3464,plain,
% 3.04/3.21 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.04/3.21 inference(rewrite,[status(thm)],[])).
% 3.04/3.21 tff(3465,plain,
% 3.04/3.21 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 3.04/3.21 inference(monotonicity,[status(thm)],[3464])).
% 3.04/3.21 tff(3466,plain,
% 3.04/3.21 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.04/3.21 inference(transitivity,[status(thm)],[3465, 3463])).
% 3.04/3.21 tff(3467,plain,
% 3.04/3.21 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.21 inference(quant_inst,[status(thm)],[])).
% 3.04/3.21 tff(3468,plain,
% 3.04/3.21 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 3.04/3.21 inference(modus_ponens,[status(thm)],[3467, 3466])).
% 3.04/3.21 tff(3469,plain,
% 3.04/3.21 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[3468, 118, 1130, 147])).
% 3.04/3.21 tff(3470,plain,
% 3.04/3.21 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[249, 3469])).
% 3.04/3.21 tff(3471,plain,
% 3.04/3.21 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.04/3.21 inference(rewrite,[status(thm)],[])).
% 3.04/3.21 tff(3472,plain,
% 3.04/3.21 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.04/3.21 inference(rewrite,[status(thm)],[])).
% 3.04/3.21 tff(3473,plain,
% 3.04/3.21 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 3.04/3.21 inference(monotonicity,[status(thm)],[3472])).
% 3.04/3.21 tff(3474,plain,
% 3.04/3.21 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.04/3.21 inference(transitivity,[status(thm)],[3473, 3471])).
% 3.04/3.21 tff(3475,plain,
% 3.04/3.21 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))))),
% 3.04/3.21 inference(quant_inst,[status(thm)],[])).
% 3.04/3.21 tff(3476,plain,
% 3.04/3.21 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 3.04/3.21 inference(modus_ponens,[status(thm)],[3475, 3474])).
% 3.04/3.21 tff(3477,plain,
% 3.04/3.21 ($false),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[3476, 118, 3261, 145, 147])).
% 3.04/3.21 tff(3478,plain,((~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.21 tff(3479,plain,
% 3.04/3.21 (~r(z, s(s(z)))),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[3478, 147, 145])).
% 3.04/3.21 tff(3480,plain,
% 3.04/3.21 (b(z, s(s(z)))),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[143, 3479])).
% 3.04/3.21 tff(3481,plain,
% 3.04/3.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.04/3.21 inference(rewrite,[status(thm)],[])).
% 3.04/3.21 tff(3482,plain,
% 3.04/3.21 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.04/3.21 inference(rewrite,[status(thm)],[])).
% 3.04/3.21 tff(3483,plain,
% 3.04/3.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 3.04/3.21 inference(monotonicity,[status(thm)],[3482])).
% 3.04/3.21 tff(3484,plain,
% 3.04/3.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.04/3.22 inference(transitivity,[status(thm)],[3483, 3481])).
% 3.04/3.22 tff(3485,plain,
% 3.04/3.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))))),
% 3.04/3.22 inference(quant_inst,[status(thm)],[])).
% 3.04/3.22 tff(3486,plain,
% 3.04/3.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 3.04/3.22 inference(modus_ponens,[status(thm)],[3485, 3484])).
% 3.04/3.22 tff(3487,plain,
% 3.04/3.22 ($false),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[3486, 178, 3461, 3480, 3470, 1145, 3462])).
% 3.04/3.22 tff(3488,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.22 tff(3489,plain,
% 3.04/3.22 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[3488, 3437, 145, 3461])).
% 3.04/3.22 tff(3490,plain,
% 3.04/3.22 ($false),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[3489, 3460])).
% 3.04/3.22 tff(3491,plain,(b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | (~(s(s(z)) = elem!1)) | (elem!1 = s(s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.22 tff(3492,plain,
% 3.04/3.22 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[3491, 3331, 3322, 47, 3425, 3423, 3321, 3324])).
% 3.04/3.22 tff(3493,plain,
% 3.04/3.22 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.04/3.22 inference(modus_ponens,[status(thm)],[3492, 3413])).
% 3.04/3.22 tff(3494,assumption,(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))), introduced(assumption)).
% 3.04/3.22 tff(3495,plain,
% 3.04/3.22 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(s(elem!1))))),
% 3.04/3.22 inference(monotonicity,[status(thm)],[3494])).
% 3.04/3.22 tff(3496,plain,
% 3.04/3.22 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 3.04/3.22 inference(transitivity,[status(thm)],[609, 3495, 343])).
% 3.04/3.22 tff(3497,plain,
% 3.04/3.22 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(elem!1)))),
% 3.04/3.22 inference(monotonicity,[status(thm)],[3496])).
% 3.04/3.22 tff(3498,plain,
% 3.04/3.22 (s(s(s(s(s(z))))) = s(elem!1)),
% 3.04/3.22 inference(transitivity,[status(thm)],[239, 3497, 328])).
% 3.04/3.22 tff(3499,plain,
% 3.04/3.22 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(elem!1))),
% 3.04/3.22 inference(monotonicity,[status(thm)],[3498])).
% 3.04/3.22 tff(3500,plain,
% 3.04/3.22 (s(s(s(s(z)))) = elem!1),
% 3.04/3.22 inference(transitivity,[status(thm)],[663, 3499, 304])).
% 3.04/3.22 tff(3501,plain,
% 3.04/3.22 ($false),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[323, 3500])).
% 3.04/3.22 tff(3502,plain,((~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.04/3.22 tff(3503,plain,
% 3.04/3.22 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[3502, 3323])).
% 3.04/3.22 tff(3504,assumption,(b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))), introduced(assumption)).
% 3.04/3.22 tff(3505,plain,
% 3.04/3.22 (s(s(s(z))) = s(elem!1)),
% 3.04/3.22 inference(monotonicity,[status(thm)],[1324])).
% 3.04/3.22 tff(3506,plain,
% 3.04/3.22 (s(s(s(s(z)))) = s(s(elem!1))),
% 3.04/3.22 inference(monotonicity,[status(thm)],[3505])).
% 3.04/3.22 tff(3507,plain,
% 3.04/3.22 (s(s(elem!1)) = s(s(s(s(z))))),
% 3.04/3.22 inference(symmetry,[status(thm)],[3506])).
% 3.04/3.22 tff(3508,plain,
% 3.04/3.22 (b(s(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))))))))),
% 3.04/3.22 inference(monotonicity,[status(thm)],[3507])).
% 3.04/3.22 tff(3509,plain,
% 3.04/3.22 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.22 inference(symmetry,[status(thm)],[3508])).
% 3.04/3.22 tff(3510,plain,
% 3.04/3.22 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.22 inference(modus_ponens,[status(thm)],[223, 3509])).
% 3.04/3.22 tff(3511,assumption,(b(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 3.04/3.22 tff(3512,assumption,(b(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 3.04/3.22 tff(3513,plain,
% 3.04/3.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(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(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(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(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.04/3.22 inference(rewrite,[status(thm)],[])).
% 3.04/3.22 tff(3514,plain,
% 3.04/3.22 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(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))))))), s(s(s(elem!1))))) | (~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(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(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(elem!1))))))),
% 3.04/3.22 inference(rewrite,[status(thm)],[])).
% 3.04/3.22 tff(3515,plain,
% 3.04/3.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~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(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(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(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))))),
% 3.04/3.22 inference(monotonicity,[status(thm)],[3514])).
% 3.04/3.22 tff(3516,plain,
% 3.04/3.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~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(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(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(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.04/3.22 inference(transitivity,[status(thm)],[3515, 3513])).
% 3.04/3.22 tff(3517,plain,
% 3.04/3.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~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(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.22 inference(quant_inst,[status(thm)],[])).
% 3.04/3.22 tff(3518,plain,
% 3.04/3.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(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(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 3.04/3.22 inference(modus_ponens,[status(thm)],[3517, 3516])).
% 3.04/3.22 tff(3519,plain,
% 3.04/3.22 ((~b(s(s(elem!1)), s(s(s(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(elem!1)))))),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[3518, 178, 3512, 3511])).
% 3.04/3.22 tff(3520,plain,
% 3.04/3.22 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[3519, 3510, 3504])).
% 3.04/3.22 tff(3521,assumption,(~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))), introduced(assumption)).
% 3.04/3.22 tff(3522,plain,
% 3.04/3.22 (((~![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)))))),
% 3.04/3.22 inference(rewrite,[status(thm)],[])).
% 3.04/3.22 tff(3523,plain,
% 3.04/3.22 ((~![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)))))),
% 3.04/3.22 inference(quant_inst,[status(thm)],[])).
% 3.04/3.22 tff(3524,plain,
% 3.04/3.22 ((~![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))))),
% 3.04/3.22 inference(modus_ponens,[status(thm)],[3523, 3522])).
% 3.04/3.22 tff(3525,plain,
% 3.04/3.22 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[3524, 41, 3521, 3520])).
% 3.04/3.22 tff(3526,plain,
% 3.04/3.22 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.04/3.22 inference(rewrite,[status(thm)],[])).
% 3.04/3.22 tff(3527,plain,
% 3.04/3.22 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.04/3.22 inference(rewrite,[status(thm)],[])).
% 3.04/3.22 tff(3528,plain,
% 3.04/3.22 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))))),
% 3.04/3.22 inference(monotonicity,[status(thm)],[3527])).
% 3.04/3.22 tff(3529,plain,
% 3.04/3.22 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.04/3.22 inference(transitivity,[status(thm)],[3528, 3526])).
% 3.04/3.22 tff(3530,plain,
% 3.04/3.22 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.22 inference(quant_inst,[status(thm)],[])).
% 3.04/3.22 tff(3531,plain,
% 3.04/3.22 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 3.04/3.22 inference(modus_ponens,[status(thm)],[3530, 3529])).
% 3.04/3.22 tff(3532,plain,
% 3.04/3.22 ($false),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[3531, 118, 557, 203, 3525])).
% 3.04/3.22 tff(3533,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(elem!1))))) | (s(s(s(s(s(s(s(z))))))) = 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(elem!1)), s(s(s(elem!1))))) | (~(s(s(z)) = elem!1)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.22 tff(3534,plain,
% 3.04/3.22 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[3533, 3503, 557, 3493, 3410, 3378, 3331, 47])).
% 3.04/3.22 tff(3535,plain,
% 3.04/3.22 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[271, 3534])).
% 3.04/3.22 tff(3536,plain,
% 3.04/3.22 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.04/3.22 inference(monotonicity,[status(thm)],[3331])).
% 3.04/3.22 tff(3537,plain,
% 3.04/3.22 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(elem!1 = s(s(s(s(s(s(s(z)))))))))),
% 3.04/3.22 inference(monotonicity,[status(thm)],[3536])).
% 3.04/3.22 tff(3538,plain,
% 3.04/3.22 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.04/3.22 inference(modus_ponens,[status(thm)],[244, 3537])).
% 3.04/3.22 tff(3539,plain,
% 3.04/3.22 ((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))))),
% 3.04/3.22 inference(commutativity,[status(thm)],[])).
% 3.04/3.22 tff(3540,plain,
% 3.04/3.22 ((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))))))))),
% 3.04/3.22 inference(symmetry,[status(thm)],[3539])).
% 3.04/3.22 tff(3541,plain,
% 3.04/3.22 ((~(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)))))))))),
% 3.04/3.22 inference(monotonicity,[status(thm)],[3540])).
% 3.04/3.22 tff(3542,plain,
% 3.04/3.22 (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 3.04/3.22 inference(modus_ponens,[status(thm)],[3503, 3541])).
% 3.04/3.22 tff(3543,plain,
% 3.04/3.22 (b(s(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))))))))),
% 3.04/3.22 inference(monotonicity,[status(thm)],[3411])).
% 3.04/3.22 tff(3544,plain,
% 3.04/3.22 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.22 inference(symmetry,[status(thm)],[3543])).
% 3.04/3.22 tff(3545,plain,
% 3.04/3.22 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 3.04/3.22 inference(monotonicity,[status(thm)],[3343])).
% 3.04/3.22 tff(3546,plain,
% 3.04/3.22 (r(s(s(elem!1)), elem!1)),
% 3.04/3.22 inference(modus_ponens,[status(thm)],[3324, 3545])).
% 3.04/3.22 tff(3547,plain,
% 3.04/3.22 (r(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.04/3.22 inference(monotonicity,[status(thm)],[1324])).
% 3.04/3.22 tff(3548,plain,
% 3.04/3.22 (~r(z, s(s(z)))),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[3269, 193, 145])).
% 3.04/3.22 tff(3549,plain,
% 3.04/3.22 (b(z, s(s(z)))),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[143, 3548])).
% 3.04/3.22 tff(3550,plain,
% 3.04/3.22 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[212, 204, 145])).
% 3.04/3.22 tff(3551,plain,
% 3.04/3.22 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[271, 3550])).
% 3.04/3.22 tff(3552,plain,
% 3.04/3.22 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 3.04/3.22 inference(rewrite,[status(thm)],[])).
% 3.04/3.22 tff(3553,plain,
% 3.04/3.22 (((~r(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))))))))) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 3.04/3.22 inference(rewrite,[status(thm)],[])).
% 3.04/3.22 tff(3554,plain,
% 3.04/3.22 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))))))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 3.04/3.22 inference(monotonicity,[status(thm)],[3553])).
% 3.04/3.22 tff(3555,plain,
% 3.04/3.22 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))))))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 3.04/3.22 inference(transitivity,[status(thm)],[3554, 3552])).
% 3.04/3.22 tff(3556,plain,
% 3.04/3.22 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))))))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 3.04/3.22 inference(quant_inst,[status(thm)],[])).
% 3.04/3.22 tff(3557,plain,
% 3.04/3.22 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 3.04/3.22 inference(modus_ponens,[status(thm)],[3556, 3555])).
% 3.04/3.22 tff(3558,plain,
% 3.04/3.22 ($false),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[3557, 118, 224, 204, 193])).
% 3.04/3.22 tff(3559,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.22 tff(3560,plain,
% 3.04/3.22 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[3559, 204, 193])).
% 3.04/3.22 tff(3561,plain,
% 3.04/3.22 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[249, 3560])).
% 3.04/3.22 tff(3562,plain,
% 3.04/3.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 3.04/3.22 inference(rewrite,[status(thm)],[])).
% 3.04/3.22 tff(3563,plain,
% 3.04/3.22 (((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 3.04/3.22 inference(rewrite,[status(thm)],[])).
% 3.04/3.22 tff(3564,plain,
% 3.04/3.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))))),
% 3.04/3.22 inference(monotonicity,[status(thm)],[3563])).
% 3.04/3.22 tff(3565,plain,
% 3.04/3.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 3.04/3.22 inference(transitivity,[status(thm)],[3564, 3562])).
% 3.04/3.22 tff(3566,plain,
% 3.04/3.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)))),
% 3.04/3.22 inference(quant_inst,[status(thm)],[])).
% 3.04/3.22 tff(3567,plain,
% 3.04/3.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 3.04/3.22 inference(modus_ponens,[status(thm)],[3566, 3565])).
% 3.04/3.22 tff(3568,plain,
% 3.04/3.22 ($false),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[3567, 178, 3461, 273, 3561, 3551, 1146])).
% 3.04/3.22 tff(3569,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.22 tff(3570,plain,
% 3.04/3.22 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[3569, 204, 145, 193, 3549, 3461])).
% 3.04/3.22 tff(3571,assumption,(s(s(s(s(s(s(s(z))))))) = s(s(z))), introduced(assumption)).
% 3.04/3.22 tff(3572,plain,
% 3.04/3.22 (s(s(z)) = s(s(s(s(s(s(s(z)))))))),
% 3.04/3.22 inference(symmetry,[status(thm)],[3571])).
% 3.04/3.22 tff(3573,plain,
% 3.04/3.22 ($false),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[244, 3572])).
% 3.04/3.22 tff(3574,plain,(~(s(s(s(s(s(s(s(z))))))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.22 tff(3575,assumption,(~r(s(s(s(s(s(s(s(z))))))), s(s(z)))), introduced(assumption)).
% 3.04/3.22 tff(3576,assumption,(~b(s(s(s(s(s(s(s(z))))))), s(s(z)))), introduced(assumption)).
% 3.04/3.22 tff(3577,plain,
% 3.04/3.22 ($false),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[2960, 41, 3576, 3575, 3574])).
% 3.04/3.22 tff(3578,plain,(r(s(s(s(s(s(s(s(z))))))), s(s(z))) | b(s(s(s(s(s(s(s(z))))))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.22 tff(3579,plain,
% 3.04/3.22 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[3578, 3570])).
% 3.04/3.22 tff(3580,plain,
% 3.04/3.22 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.04/3.22 inference(modus_ponens,[status(thm)],[3579, 3547])).
% 3.04/3.22 tff(3581,plain,
% 3.04/3.22 (r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.22 inference(monotonicity,[status(thm)],[3507])).
% 3.04/3.22 tff(3582,plain,
% 3.04/3.22 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.22 inference(symmetry,[status(thm)],[3581])).
% 3.04/3.22 tff(3583,plain,
% 3.04/3.22 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.22 inference(modus_ponens,[status(thm)],[204, 3582])).
% 3.04/3.22 tff(3584,assumption,(~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 3.04/3.22 tff(3585,plain,
% 3.04/3.22 ($false),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[3584, 3583])).
% 3.04/3.22 tff(3586,plain,(r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~(s(s(z)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.22 tff(3587,plain,
% 3.04/3.22 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[3586, 204, 1324])).
% 3.04/3.22 tff(3588,assumption,(r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 3.04/3.22 tff(3589,plain,
% 3.04/3.22 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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))))))))))),
% 3.04/3.22 inference(rewrite,[status(thm)],[])).
% 3.04/3.22 tff(3590,plain,
% 3.04/3.22 (((~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)))))))))) <=> ((~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))))))))))),
% 3.04/3.23 inference(rewrite,[status(thm)],[])).
% 3.04/3.23 tff(3591,plain,
% 3.04/3.23 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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)))))))))))),
% 3.04/3.23 inference(monotonicity,[status(thm)],[3590])).
% 3.04/3.23 tff(3592,plain,
% 3.04/3.23 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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))))))))))),
% 3.04/3.23 inference(transitivity,[status(thm)],[3591, 3589])).
% 3.04/3.23 tff(3593,plain,
% 3.04/3.23 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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))))))))))),
% 3.04/3.23 inference(quant_inst,[status(thm)],[])).
% 3.04/3.23 tff(3594,plain,
% 3.04/3.23 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 3.04/3.23 inference(modus_ponens,[status(thm)],[3593, 3592])).
% 3.04/3.23 tff(3595,plain,
% 3.04/3.23 ($false),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[3594, 118, 3365, 2953, 3588])).
% 3.04/3.23 tff(3596,plain,((~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)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.23 tff(3597,plain,
% 3.04/3.23 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[3596, 3587, 3365])).
% 3.04/3.23 tff(3598,plain,
% 3.04/3.23 ($false),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[3597, 3580])).
% 3.04/3.23 tff(3599,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~(s(s(z)) = elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.23 tff(3600,plain,
% 3.04/3.23 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[3599, 3331, 3546, 47, 193, 3425])).
% 3.04/3.23 tff(3601,plain,
% 3.04/3.23 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[222, 3600])).
% 3.04/3.23 tff(3602,plain,
% 3.04/3.23 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.23 inference(modus_ponens,[status(thm)],[3601, 3544])).
% 3.04/3.23 tff(3603,plain,
% 3.04/3.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), 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(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), 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(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 3.04/3.23 inference(rewrite,[status(thm)],[])).
% 3.04/3.23 tff(3604,plain,
% 3.04/3.23 (((~b(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)))) | (~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(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(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), 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(elem!1)))))),
% 3.04/3.23 inference(rewrite,[status(thm)],[])).
% 3.04/3.23 tff(3605,plain,
% 3.04/3.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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)))) | (~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(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(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), 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(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 3.04/3.23 inference(monotonicity,[status(thm)],[3604])).
% 3.04/3.23 tff(3606,plain,
% 3.04/3.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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)))) | (~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(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(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), 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(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 3.04/3.23 inference(transitivity,[status(thm)],[3605, 3603])).
% 3.04/3.23 tff(3607,plain,
% 3.04/3.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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)))) | (~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(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(elem!1))))))),
% 3.04/3.23 inference(quant_inst,[status(thm)],[])).
% 3.04/3.23 tff(3608,plain,
% 3.04/3.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), 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(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 3.04/3.23 inference(modus_ponens,[status(thm)],[3607, 3606])).
% 3.04/3.23 tff(3609,plain,
% 3.04/3.23 (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[3608, 178, 3410, 3378, 3602, 3493])).
% 3.04/3.23 tff(3610,plain,
% 3.04/3.23 (((~![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)))))))))),
% 3.04/3.23 inference(rewrite,[status(thm)],[])).
% 3.04/3.23 tff(3611,plain,
% 3.04/3.23 ((~![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)))))))))),
% 3.04/3.23 inference(quant_inst,[status(thm)],[])).
% 3.04/3.23 tff(3612,plain,
% 3.04/3.23 ((~![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))))))))),
% 3.04/3.23 inference(modus_ponens,[status(thm)],[3611, 3610])).
% 3.04/3.23 tff(3613,plain,
% 3.04/3.23 ((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))))))))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[3612, 41, 3609])).
% 3.04/3.23 tff(3614,plain,
% 3.04/3.23 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[3613, 3542])).
% 3.04/3.23 tff(3615,assumption,(r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 3.04/3.23 tff(3616,plain,
% 3.04/3.23 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.23 inference(rewrite,[status(thm)],[])).
% 3.04/3.23 tff(3617,plain,
% 3.04/3.23 (((~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.23 inference(rewrite,[status(thm)],[])).
% 3.04/3.23 tff(3618,plain,
% 3.04/3.23 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))))),
% 3.04/3.23 inference(monotonicity,[status(thm)],[3617])).
% 3.04/3.23 tff(3619,plain,
% 3.04/3.23 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.23 inference(transitivity,[status(thm)],[3618, 3616])).
% 3.04/3.23 tff(3620,plain,
% 3.04/3.23 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 3.04/3.23 inference(quant_inst,[status(thm)],[])).
% 3.04/3.23 tff(3621,plain,
% 3.04/3.23 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 3.04/3.23 inference(modus_ponens,[status(thm)],[3620, 3619])).
% 3.04/3.23 tff(3622,plain,
% 3.04/3.23 ($false),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[3621, 118, 3311, 1265, 3615])).
% 3.04/3.23 tff(3623,plain,((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.23 tff(3624,plain,
% 3.04/3.23 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[3623, 3310, 3614])).
% 3.04/3.23 tff(3625,plain,
% 3.04/3.23 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[691, 3624, 3538])).
% 3.04/3.23 tff(3626,plain,
% 3.04/3.23 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[1657, 3399])).
% 3.04/3.23 tff(3627,plain,
% 3.04/3.23 (r(s(s(z)), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 3.04/3.23 inference(monotonicity,[status(thm)],[3331])).
% 3.04/3.23 tff(3628,plain,
% 3.04/3.23 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 3.04/3.23 inference(symmetry,[status(thm)],[3627])).
% 3.04/3.23 tff(3629,plain,
% 3.04/3.23 (r(s(s(z)), s(s(s(elem!1))))),
% 3.04/3.23 inference(modus_ponens,[status(thm)],[3310, 3628])).
% 3.04/3.23 tff(3630,assumption,(r(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 3.04/3.23 tff(3631,plain,
% 3.04/3.23 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 3.04/3.23 inference(rewrite,[status(thm)],[])).
% 3.04/3.23 tff(3632,plain,
% 3.04/3.23 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 3.04/3.23 inference(quant_inst,[status(thm)],[])).
% 3.04/3.23 tff(3633,plain,
% 3.04/3.23 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z))),
% 3.04/3.23 inference(modus_ponens,[status(thm)],[3632, 3631])).
% 3.04/3.23 tff(3634,plain,
% 3.04/3.23 (~r(s(s(s(s(elem!1)))), z)),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[3633, 118, 557, 3630])).
% 3.04/3.23 tff(3635,plain,
% 3.04/3.23 (b(s(s(s(s(elem!1)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 3.04/3.23 inference(monotonicity,[status(thm)],[1324])).
% 3.04/3.23 tff(3636,assumption,(r(s(s(s(s(elem!1)))), s(s(z)))), introduced(assumption)).
% 3.04/3.23 tff(3637,plain,
% 3.04/3.23 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 3.04/3.23 inference(rewrite,[status(thm)],[])).
% 3.04/3.23 tff(3638,plain,
% 3.04/3.23 (((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 3.04/3.23 inference(rewrite,[status(thm)],[])).
% 3.04/3.23 tff(3639,plain,
% 3.04/3.23 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 3.04/3.23 inference(monotonicity,[status(thm)],[3638])).
% 3.04/3.23 tff(3640,plain,
% 3.04/3.23 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 3.04/3.23 inference(transitivity,[status(thm)],[3639, 3637])).
% 3.04/3.23 tff(3641,plain,
% 3.04/3.23 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 3.04/3.23 inference(quant_inst,[status(thm)],[])).
% 3.04/3.23 tff(3642,plain,
% 3.04/3.23 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 3.04/3.23 inference(modus_ponens,[status(thm)],[3641, 3640])).
% 3.04/3.23 tff(3643,plain,
% 3.04/3.23 ($false),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[3642, 118, 3636, 1823, 3630])).
% 3.04/3.23 tff(3644,plain,((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.23 tff(3645,plain,
% 3.04/3.23 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[3644, 3630, 1823])).
% 3.04/3.23 tff(3646,plain,
% 3.04/3.23 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[1170, 3645])).
% 3.04/3.23 tff(3647,plain,
% 3.04/3.23 (b(s(s(s(s(elem!1)))), elem!1)),
% 3.04/3.23 inference(modus_ponens,[status(thm)],[3646, 3635])).
% 3.04/3.23 tff(3648,plain,
% 3.04/3.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.23 inference(rewrite,[status(thm)],[])).
% 3.04/3.23 tff(3649,plain,
% 3.04/3.23 (((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.23 inference(rewrite,[status(thm)],[])).
% 3.04/3.23 tff(3650,plain,
% 3.04/3.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.04/3.23 inference(monotonicity,[status(thm)],[3649])).
% 3.04/3.23 tff(3651,plain,
% 3.04/3.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.23 inference(transitivity,[status(thm)],[3650, 3648])).
% 3.04/3.23 tff(3652,plain,
% 3.04/3.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 3.04/3.23 inference(quant_inst,[status(thm)],[])).
% 3.04/3.23 tff(3653,plain,
% 3.04/3.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.04/3.23 inference(modus_ponens,[status(thm)],[3652, 3651])).
% 3.04/3.23 tff(3654,plain,
% 3.04/3.23 (~b(s(s(s(s(elem!1)))), z)),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[3653, 178, 818, 3647, 869, 595])).
% 3.04/3.23 tff(3655,plain,
% 3.04/3.23 ($false),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[1716, 3654, 3634])).
% 3.04/3.23 tff(3656,plain,((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(elem!1))))) | (~(s(s(z)) = elem!1)) | (~r(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.23 tff(3657,plain,
% 3.04/3.23 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[3656, 3321, 3625, 3535, 557, 3331, 3629])).
% 3.04/3.23 tff(3658,plain,
% 3.04/3.23 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[1988, 3657, 3626])).
% 3.04/3.23 tff(3659,plain,
% 3.04/3.23 (~(s(s(s(elem!1))) = elem!1)),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[2489, 3309])).
% 3.04/3.23 tff(3660,plain,
% 3.04/3.23 ((elem!1 = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 3.04/3.23 inference(symmetry,[status(thm)],[836])).
% 3.04/3.23 tff(3661,plain,
% 3.04/3.23 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 3.04/3.23 inference(transitivity,[status(thm)],[3536, 3660])).
% 3.04/3.23 tff(3662,plain,
% 3.04/3.23 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = elem!1))),
% 3.04/3.23 inference(monotonicity,[status(thm)],[3661])).
% 3.04/3.23 tff(3663,plain,
% 3.04/3.23 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 3.04/3.23 inference(modus_ponens,[status(thm)],[244, 3662])).
% 3.04/3.23 tff(3664,assumption,(b(s(s(s(s(s(s(s(z))))))), elem!1)), introduced(assumption)).
% 3.04/3.23 tff(3665,plain,
% 3.04/3.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.23 inference(rewrite,[status(thm)],[])).
% 3.04/3.23 tff(3666,plain,
% 3.04/3.23 (((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.23 inference(rewrite,[status(thm)],[])).
% 3.04/3.23 tff(3667,plain,
% 3.04/3.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.04/3.23 inference(monotonicity,[status(thm)],[3666])).
% 3.04/3.23 tff(3668,plain,
% 3.04/3.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.23 inference(transitivity,[status(thm)],[3667, 3665])).
% 3.04/3.23 tff(3669,plain,
% 3.04/3.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)))),
% 3.04/3.23 inference(quant_inst,[status(thm)],[])).
% 3.04/3.23 tff(3670,plain,
% 3.04/3.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.04/3.23 inference(modus_ponens,[status(thm)],[3669, 3668])).
% 3.04/3.23 tff(3671,plain,
% 3.04/3.23 ($false),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[3670, 178, 818, 506, 869, 595, 3664])).
% 3.04/3.23 tff(3672,plain,((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.23 tff(3673,plain,
% 3.04/3.23 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[3672, 3625, 3423, 3535, 3321])).
% 3.04/3.23 tff(3674,plain,
% 3.04/3.23 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[3444, 3673, 3663])).
% 3.04/3.23 tff(3675,plain,
% 3.04/3.23 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(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))))))))))),
% 3.04/3.23 inference(rewrite,[status(thm)],[])).
% 3.04/3.23 tff(3676,plain,
% 3.04/3.23 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), 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))))))))))),
% 3.04/3.23 inference(rewrite,[status(thm)],[])).
% 3.04/3.23 tff(3677,plain,
% 3.04/3.23 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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)))))))))))),
% 3.04/3.23 inference(monotonicity,[status(thm)],[3676])).
% 3.04/3.23 tff(3678,plain,
% 3.04/3.23 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(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))))))))))),
% 3.04/3.24 inference(transitivity,[status(thm)],[3677, 3675])).
% 3.04/3.24 tff(3679,plain,
% 3.04/3.24 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.24 inference(quant_inst,[status(thm)],[])).
% 3.04/3.24 tff(3680,plain,
% 3.04/3.24 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 3.04/3.24 inference(modus_ponens,[status(thm)],[3679, 3678])).
% 3.04/3.24 tff(3681,plain,
% 3.04/3.24 ($false),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[3680, 118, 556, 2953, 3615])).
% 3.04/3.24 tff(3682,plain,((~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)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.24 tff(3683,plain,
% 3.04/3.24 (~r(s(s(s(elem!1))), elem!1)),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[3682, 3674, 3614])).
% 3.04/3.24 tff(3684,plain,
% 3.04/3.24 (b(s(s(s(elem!1))), elem!1)),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[570, 3683, 3659])).
% 3.04/3.24 tff(3685,plain,
% 3.04/3.24 ((s(s(elem!1)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 3.04/3.24 inference(commutativity,[status(thm)],[])).
% 3.04/3.24 tff(3686,plain,
% 3.04/3.24 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 3.04/3.24 inference(monotonicity,[status(thm)],[3343])).
% 3.04/3.24 tff(3687,plain,
% 3.04/3.24 (s(s(s(s(s(s(z)))))) = s(s(s(s(elem!1))))),
% 3.04/3.24 inference(monotonicity,[status(thm)],[3686])).
% 3.04/3.24 tff(3688,plain,
% 3.04/3.24 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 3.04/3.24 inference(monotonicity,[status(thm)],[3343, 3687])).
% 3.04/3.24 tff(3689,plain,
% 3.04/3.24 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 3.04/3.24 inference(transitivity,[status(thm)],[3688, 3685])).
% 3.04/3.24 tff(3690,plain,
% 3.04/3.24 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 3.04/3.24 inference(monotonicity,[status(thm)],[3689])).
% 3.04/3.24 tff(3691,assumption,(s(s(s(s(z)))) = s(s(s(s(s(s(z))))))), introduced(assumption)).
% 3.04/3.24 tff(3692,plain,
% 3.04/3.24 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 3.04/3.24 inference(monotonicity,[status(thm)],[3691])).
% 3.04/3.24 tff(3693,plain,
% 3.04/3.24 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(s(s(z)))))),
% 3.04/3.24 inference(symmetry,[status(thm)],[3692])).
% 3.04/3.24 tff(3694,plain,
% 3.04/3.24 (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))),
% 3.04/3.24 inference(monotonicity,[status(thm)],[3691])).
% 3.04/3.24 tff(3695,plain,
% 3.04/3.24 (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))),
% 3.04/3.24 inference(symmetry,[status(thm)],[3694])).
% 3.04/3.24 tff(3696,plain,
% 3.04/3.24 (s(s(s(s(s(s(s(z))))))) = s(s(s(z)))),
% 3.04/3.24 inference(transitivity,[status(thm)],[3695, 239, 3693, 11])).
% 3.04/3.24 tff(3697,plain,
% 3.04/3.24 ($false),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[1104, 3696])).
% 3.04/3.24 tff(3698,plain,(~(s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.24 tff(3699,plain,
% 3.04/3.24 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 3.04/3.24 inference(modus_ponens,[status(thm)],[3698, 3690])).
% 3.04/3.24 tff(3700,assumption,(s(s(elem!1)) = s(s(s(s(elem!1))))), introduced(assumption)).
% 3.04/3.24 tff(3701,plain,
% 3.04/3.24 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 3.04/3.24 inference(symmetry,[status(thm)],[3700])).
% 3.04/3.24 tff(3702,assumption,(~(s(s(s(s(elem!1)))) = s(s(elem!1)))), introduced(assumption)).
% 3.04/3.24 tff(3703,plain,
% 3.04/3.24 ($false),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[3702, 3701])).
% 3.04/3.24 tff(3704,plain,((~(s(s(elem!1)) = s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.24 tff(3705,plain,
% 3.04/3.24 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[3704, 3699])).
% 3.04/3.24 tff(3706,plain,
% 3.04/3.24 (r(s(s(s(s(z)))), z) <=> r(s(s(elem!1)), z)),
% 3.04/3.24 inference(monotonicity,[status(thm)],[3343])).
% 3.04/3.24 tff(3707,plain,
% 3.04/3.24 (r(s(s(elem!1)), z)),
% 3.04/3.24 inference(modus_ponens,[status(thm)],[194, 3706])).
% 3.04/3.24 tff(3708,assumption,(~(s(s(elem!1)) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 3.04/3.24 tff(3709,assumption,(b(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 3.04/3.24 tff(3710,assumption,(b(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 3.04/3.24 tff(3711,plain,
% 3.04/3.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 3.04/3.24 inference(rewrite,[status(thm)],[])).
% 3.04/3.24 tff(3712,plain,
% 3.04/3.24 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 3.04/3.24 inference(rewrite,[status(thm)],[])).
% 3.04/3.24 tff(3713,plain,
% 3.04/3.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 3.04/3.24 inference(monotonicity,[status(thm)],[3712])).
% 3.04/3.24 tff(3714,plain,
% 3.04/3.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 3.04/3.24 inference(transitivity,[status(thm)],[3713, 3711])).
% 3.04/3.24 tff(3715,plain,
% 3.04/3.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 3.04/3.24 inference(quant_inst,[status(thm)],[])).
% 3.04/3.24 tff(3716,plain,
% 3.04/3.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 3.04/3.24 inference(modus_ponens,[status(thm)],[3715, 3714])).
% 3.04/3.24 tff(3717,plain,
% 3.04/3.24 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[3716, 178, 1597, 3710, 3511, 3709])).
% 3.04/3.24 tff(3718,plain,
% 3.04/3.24 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 3.04/3.24 inference(rewrite,[status(thm)],[])).
% 3.04/3.24 tff(3719,plain,
% 3.04/3.24 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 3.04/3.24 inference(quant_inst,[status(thm)],[])).
% 3.04/3.24 tff(3720,plain,
% 3.04/3.24 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 3.04/3.24 inference(modus_ponens,[status(thm)],[3719, 3718])).
% 3.04/3.24 tff(3721,plain,
% 3.04/3.24 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[3720, 41, 3717, 3708])).
% 3.04/3.24 tff(3722,plain,
% 3.04/3.24 (~b(s(s(s(s(elem!1)))), z)),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[3653, 178, 818, 3710, 869, 595])).
% 3.04/3.24 tff(3723,plain,
% 3.04/3.24 (r(s(s(s(s(elem!1)))), z)),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[1716, 3722])).
% 3.04/3.24 tff(3724,plain,
% 3.04/3.24 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), z)))),
% 3.04/3.24 inference(rewrite,[status(thm)],[])).
% 3.04/3.24 tff(3725,plain,
% 3.04/3.24 (((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), z)))),
% 3.04/3.24 inference(rewrite,[status(thm)],[])).
% 3.04/3.24 tff(3726,plain,
% 3.04/3.24 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), z))))),
% 3.04/3.24 inference(monotonicity,[status(thm)],[3725])).
% 3.04/3.24 tff(3727,plain,
% 3.04/3.24 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), z)))),
% 3.04/3.24 inference(transitivity,[status(thm)],[3726, 3724])).
% 3.04/3.24 tff(3728,plain,
% 3.04/3.24 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 3.04/3.24 inference(quant_inst,[status(thm)],[])).
% 3.04/3.24 tff(3729,plain,
% 3.04/3.24 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), z))),
% 3.04/3.24 inference(modus_ponens,[status(thm)],[3728, 3727])).
% 3.04/3.24 tff(3730,plain,
% 3.04/3.24 ($false),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[3729, 118, 3723, 991, 3721])).
% 3.04/3.24 tff(3731,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), z)) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.24 tff(3732,plain,
% 3.04/3.24 (~b(s(s(s(s(elem!1)))), elem!1)),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[3731, 3707, 3705, 3684, 3378, 3658, 3321, 3625, 3535])).
% 3.04/3.24 tff(3733,plain,
% 3.04/3.24 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 3.04/3.24 inference(modus_ponens,[status(thm)],[3732, 3337])).
% 3.04/3.24 tff(3734,plain,
% 3.04/3.24 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[1170, 3733])).
% 3.04/3.24 tff(3735,plain,
% 3.04/3.24 (r(s(s(s(s(elem!1)))), elem!1)),
% 3.04/3.24 inference(modus_ponens,[status(thm)],[3734, 3334])).
% 3.04/3.24 tff(3736,plain,
% 3.04/3.24 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 3.04/3.24 inference(rewrite,[status(thm)],[])).
% 3.04/3.24 tff(3737,plain,
% 3.04/3.24 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 3.04/3.24 inference(quant_inst,[status(thm)],[])).
% 3.04/3.24 tff(3738,plain,
% 3.04/3.24 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 3.04/3.24 inference(modus_ponens,[status(thm)],[3737, 3736])).
% 3.04/3.24 tff(3739,plain,
% 3.04/3.24 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[3738, 118, 3546, 3735])).
% 3.04/3.24 tff(3740,plain,
% 3.04/3.24 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 3.04/3.24 inference(rewrite,[status(thm)],[])).
% 3.04/3.24 tff(3741,plain,
% 3.04/3.24 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 3.04/3.24 inference(quant_inst,[status(thm)],[])).
% 3.04/3.24 tff(3742,plain,
% 3.04/3.24 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.04/3.24 inference(modus_ponens,[status(thm)],[3741, 3740])).
% 3.04/3.24 tff(3743,plain,
% 3.04/3.24 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[3742, 41, 3699, 3739])).
% 3.04/3.24 tff(3744,plain,
% 3.04/3.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 3.04/3.24 inference(rewrite,[status(thm)],[])).
% 3.04/3.24 tff(3745,plain,
% 3.04/3.24 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 3.04/3.24 inference(rewrite,[status(thm)],[])).
% 3.04/3.24 tff(3746,plain,
% 3.04/3.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 3.04/3.24 inference(monotonicity,[status(thm)],[3745])).
% 3.04/3.24 tff(3747,plain,
% 3.04/3.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 3.04/3.24 inference(transitivity,[status(thm)],[3746, 3744])).
% 3.04/3.24 tff(3748,plain,
% 3.04/3.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))),
% 3.04/3.24 inference(quant_inst,[status(thm)],[])).
% 3.04/3.24 tff(3749,plain,
% 3.04/3.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 3.04/3.24 inference(modus_ponens,[status(thm)],[3748, 3747])).
% 3.04/3.24 tff(3750,plain,
% 3.04/3.24 ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1))))))),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[3749, 178, 3378, 3658, 3493])).
% 3.04/3.24 tff(3751,plain,
% 3.04/3.24 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[3750, 3743])).
% 3.04/3.24 tff(3752,plain,
% 3.04/3.24 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), 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(elem!1)))))))),
% 3.04/3.24 inference(rewrite,[status(thm)],[])).
% 3.04/3.24 tff(3753,plain,
% 3.04/3.24 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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(s(elem!1)))))))),
% 3.04/3.24 inference(quant_inst,[status(thm)],[])).
% 3.04/3.24 tff(3754,plain,
% 3.04/3.24 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(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(s(elem!1))))))),
% 3.04/3.24 inference(modus_ponens,[status(thm)],[3753, 3752])).
% 3.04/3.24 tff(3755,plain,
% 3.04/3.24 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[3754, 118, 3674, 3735])).
% 3.04/3.24 tff(3756,plain,
% 3.04/3.24 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1))))))),
% 3.04/3.24 inference(rewrite,[status(thm)],[])).
% 3.04/3.24 tff(3757,plain,
% 3.04/3.24 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1))))))),
% 3.04/3.24 inference(quant_inst,[status(thm)],[])).
% 3.04/3.24 tff(3758,plain,
% 3.04/3.24 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))),
% 3.04/3.24 inference(modus_ponens,[status(thm)],[3757, 3756])).
% 3.04/3.24 tff(3759,plain,
% 3.04/3.24 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[3758, 41, 3755])).
% 3.04/3.24 tff(3760,plain,
% 3.04/3.24 (s(s(s(s(s(s(s(z))))))) = s(s(s(s(elem!1))))),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[3759, 3751])).
% 3.04/3.24 tff(3761,plain,
% 3.04/3.24 (s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(z)))))))),
% 3.04/3.24 inference(symmetry,[status(thm)],[3760])).
% 3.04/3.24 tff(3762,plain,
% 3.04/3.24 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 3.04/3.24 inference(monotonicity,[status(thm)],[3761])).
% 3.04/3.24 tff(3763,plain,
% 3.04/3.24 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(s(s(elem!1)))))),
% 3.04/3.24 inference(symmetry,[status(thm)],[3762])).
% 3.04/3.24 tff(3764,plain,
% 3.04/3.24 (s(s(s(s(elem!1)))) = s(s(s(s(s(s(z))))))),
% 3.04/3.24 inference(symmetry,[status(thm)],[3687])).
% 3.04/3.24 tff(3765,plain,
% 3.04/3.24 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 3.04/3.24 inference(transitivity,[status(thm)],[3764, 609, 3763, 946])).
% 3.04/3.24 tff(3766,plain,
% 3.04/3.24 ($false),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[3626, 3765])).
% 3.04/3.24 tff(3767,plain,(b(s(s(s(s(z)))), elem!1) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | b(z, s(s(s(s(z))))) | b(s(s(z)), elem!1) | (elem!1 = z) | b(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.24 tff(3768,plain,
% 3.04/3.24 (b(s(s(s(s(z)))), elem!1)),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[3767, 103, 3243, 194, 1, 3241, 3277, 3240])).
% 3.04/3.24 tff(3769,plain,
% 3.04/3.24 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), elem!1)),
% 3.04/3.24 inference(monotonicity,[status(thm)],[1324])).
% 3.04/3.24 tff(3770,plain,
% 3.04/3.24 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(z)))),
% 3.04/3.24 inference(symmetry,[status(thm)],[3769])).
% 3.04/3.24 tff(3771,assumption,(b(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 3.04/3.24 tff(3772,plain,
% 3.04/3.24 (b(s(s(s(s(z)))), s(s(z)))),
% 3.04/3.24 inference(modus_ponens,[status(thm)],[3771, 3770])).
% 3.04/3.24 tff(3773,plain,
% 3.04/3.24 ($false),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[86, 3772])).
% 3.04/3.24 tff(3774,plain,((~(s(s(z)) = elem!1)) | b(s(s(s(s(z)))), s(s(z))) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.24 tff(3775,plain,
% 3.04/3.24 (~(s(s(z)) = elem!1)),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[3774, 3768, 86])).
% 3.04/3.24 tff(3776,plain,
% 3.04/3.24 (~(elem!1 = s(s(z)))),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[311, 3775])).
% 3.04/3.24 tff(3777,plain,
% 3.04/3.24 (r(elem!1, s(s(z)))),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[467, 3776, 461])).
% 3.04/3.24 tff(3778,plain,
% 3.04/3.24 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 3.04/3.24 inference(rewrite,[status(thm)],[])).
% 3.04/3.24 tff(3779,plain,
% 3.04/3.24 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 3.04/3.24 inference(rewrite,[status(thm)],[])).
% 3.04/3.24 tff(3780,plain,
% 3.04/3.24 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 3.04/3.24 inference(monotonicity,[status(thm)],[3779])).
% 3.04/3.24 tff(3781,plain,
% 3.04/3.24 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 3.04/3.24 inference(transitivity,[status(thm)],[3780, 3778])).
% 3.04/3.24 tff(3782,plain,
% 3.04/3.24 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))))),
% 3.04/3.24 inference(quant_inst,[status(thm)],[])).
% 3.04/3.24 tff(3783,plain,
% 3.04/3.24 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 3.04/3.24 inference(modus_ponens,[status(thm)],[3782, 3781])).
% 3.04/3.24 tff(3784,plain,
% 3.04/3.24 ($false),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[3783, 118, 450, 470, 193])).
% 3.04/3.24 tff(3785,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.24 tff(3786,plain,
% 3.04/3.24 (~r(elem!1, s(s(s(s(z)))))),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[3785, 3777, 103])).
% 3.04/3.24 tff(3787,plain,
% 3.04/3.24 (~(z = elem!1)),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[317, 3277])).
% 3.04/3.24 tff(3788,plain,
% 3.04/3.24 (r(s(s(z)), elem!1)),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[448, 3775, 3241])).
% 3.04/3.24 tff(3789,plain,
% 3.04/3.24 (~(elem!1 = z)),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[3276, 3549, 461])).
% 3.04/3.24 tff(3790,plain,
% 3.04/3.24 (~(z = elem!1)),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[317, 3789])).
% 3.04/3.24 tff(3791,plain,
% 3.04/3.24 (~(s(s(elem!1)) = s(s(z)))),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[2386, 3790])).
% 3.04/3.24 tff(3792,plain,
% 3.04/3.24 (~r(elem!1, s(s(s(elem!1))))),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[3319, 521, 557])).
% 3.04/3.24 tff(3793,plain,
% 3.04/3.24 (elem!1 = s(s(s(elem!1)))),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[2054, 3792, 3240])).
% 3.04/3.24 tff(3794,plain,
% 3.04/3.24 (~(s(elem!1) = s(s(s(s(z)))))),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[2498, 3793, 3791])).
% 3.04/3.24 tff(3795,plain,
% 3.04/3.24 (~(s(s(s(s(z)))) = s(elem!1))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[2168, 3794])).
% 3.04/3.25 tff(3796,plain,
% 3.04/3.25 (s(elem!1) = s(s(s(s(elem!1))))),
% 3.04/3.25 inference(monotonicity,[status(thm)],[3793])).
% 3.04/3.25 tff(3797,plain,
% 3.04/3.25 (s(s(s(s(elem!1)))) = s(elem!1)),
% 3.04/3.25 inference(symmetry,[status(thm)],[3796])).
% 3.04/3.25 tff(3798,plain,
% 3.04/3.25 (b(s(s(s(s(z)))), s(s(s(s(elem!1))))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 3.04/3.25 inference(monotonicity,[status(thm)],[3797])).
% 3.04/3.25 tff(3799,plain,
% 3.04/3.25 ((~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) <=> (~b(s(s(s(s(z)))), s(elem!1)))),
% 3.04/3.25 inference(monotonicity,[status(thm)],[3798])).
% 3.04/3.25 tff(3800,plain,
% 3.04/3.25 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 3.04/3.25 inference(monotonicity,[status(thm)],[3796])).
% 3.04/3.25 tff(3801,plain,
% 3.04/3.25 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.04/3.25 inference(monotonicity,[status(thm)],[3793])).
% 3.04/3.25 tff(3802,plain,
% 3.04/3.25 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.04/3.25 inference(modus_ponens,[status(thm)],[3771, 3801])).
% 3.04/3.25 tff(3803,plain,
% 3.04/3.25 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.04/3.25 inference(monotonicity,[status(thm)],[2855])).
% 3.04/3.25 tff(3804,plain,
% 3.04/3.25 (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))))),
% 3.04/3.25 inference(symmetry,[status(thm)],[3803])).
% 3.04/3.25 tff(3805,plain,
% 3.04/3.25 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[2859, 3306, 1527])).
% 3.04/3.25 tff(3806,plain,
% 3.04/3.25 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[703, 3805])).
% 3.04/3.25 tff(3807,plain,
% 3.04/3.25 (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))))),
% 3.04/3.25 inference(monotonicity,[status(thm)],[1527])).
% 3.04/3.25 tff(3808,plain,
% 3.04/3.25 (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)),
% 3.04/3.25 inference(symmetry,[status(thm)],[3807])).
% 3.04/3.25 tff(3809,plain,
% 3.04/3.25 ((~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))),
% 3.04/3.25 inference(monotonicity,[status(thm)],[3808])).
% 3.04/3.25 tff(3810,plain,
% 3.04/3.25 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.25 inference(monotonicity,[status(thm)],[1527])).
% 3.04/3.25 tff(3811,plain,
% 3.04/3.25 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.25 inference(rewrite,[status(thm)],[])).
% 3.04/3.25 tff(3812,plain,
% 3.04/3.25 (((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.25 inference(rewrite,[status(thm)],[])).
% 3.04/3.25 tff(3813,plain,
% 3.04/3.25 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.04/3.25 inference(monotonicity,[status(thm)],[3812])).
% 3.04/3.25 tff(3814,plain,
% 3.04/3.25 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.25 inference(transitivity,[status(thm)],[3813, 3811])).
% 3.04/3.25 tff(3815,plain,
% 3.04/3.25 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)))),
% 3.04/3.25 inference(quant_inst,[status(thm)],[])).
% 3.04/3.25 tff(3816,plain,
% 3.04/3.25 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.04/3.25 inference(modus_ponens,[status(thm)],[3815, 3814])).
% 3.04/3.25 tff(3817,plain,
% 3.04/3.25 ($false),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[3816, 118, 521, 1265, 203])).
% 3.04/3.25 tff(3818,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.25 tff(3819,plain,
% 3.04/3.25 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[3818, 203, 521])).
% 3.04/3.25 tff(3820,plain,
% 3.04/3.25 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[691, 3819, 3805])).
% 3.04/3.25 tff(3821,plain,
% 3.04/3.25 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.25 inference(modus_ponens,[status(thm)],[3820, 3810])).
% 3.04/3.25 tff(3822,plain,
% 3.04/3.25 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[3259, 557, 145])).
% 3.04/3.25 tff(3823,plain,
% 3.04/3.25 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.04/3.25 inference(rewrite,[status(thm)],[])).
% 3.04/3.25 tff(3824,plain,
% 3.04/3.25 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.04/3.25 inference(quant_inst,[status(thm)],[])).
% 3.04/3.25 tff(3825,plain,
% 3.04/3.25 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.04/3.25 inference(modus_ponens,[status(thm)],[3824, 3823])).
% 3.04/3.25 tff(3826,plain,
% 3.04/3.25 ((s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[3825, 41, 3822])).
% 3.04/3.25 tff(3827,plain,
% 3.04/3.25 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[3826, 3306])).
% 3.04/3.25 tff(3828,assumption,(b(s(s(s(s(z)))), s(s(s(elem!1))))), introduced(assumption)).
% 3.04/3.25 tff(3829,assumption,(b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))), introduced(assumption)).
% 3.04/3.25 tff(3830,assumption,(b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 3.04/3.25 tff(3831,assumption,(b(s(s(s(elem!1))), s(s(s(s(z)))))), introduced(assumption)).
% 3.04/3.25 tff(3832,plain,
% 3.04/3.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(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(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(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(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.04/3.25 inference(rewrite,[status(thm)],[])).
% 3.04/3.25 tff(3833,plain,
% 3.04/3.25 (((~b(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))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~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(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~b(s(s(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(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.04/3.25 inference(rewrite,[status(thm)],[])).
% 3.04/3.25 tff(3834,plain,
% 3.04/3.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(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(s(s(z)))), s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(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(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))))),
% 3.04/3.25 inference(monotonicity,[status(thm)],[3833])).
% 3.04/3.25 tff(3835,plain,
% 3.04/3.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(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(s(s(z)))), s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(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(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.04/3.25 inference(transitivity,[status(thm)],[3834, 3832])).
% 3.04/3.25 tff(3836,plain,
% 3.04/3.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(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(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.04/3.25 inference(quant_inst,[status(thm)],[])).
% 3.04/3.25 tff(3837,plain,
% 3.04/3.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 3.04/3.25 inference(modus_ponens,[status(thm)],[3836, 3835])).
% 3.04/3.25 tff(3838,plain,
% 3.04/3.25 ($false),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[3837, 178, 251, 3828, 3831, 3830, 3829])).
% 3.04/3.25 tff(3839,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(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(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.25 tff(3840,plain,
% 3.04/3.25 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[3839, 223, 3828, 3827, 3821])).
% 3.04/3.25 tff(3841,plain,
% 3.04/3.25 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.04/3.25 inference(modus_ponens,[status(thm)],[3840, 3809])).
% 3.04/3.25 tff(3842,plain,
% 3.04/3.25 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[3444, 3841, 3806])).
% 3.04/3.25 tff(3843,plain,
% 3.04/3.25 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.04/3.25 inference(modus_ponens,[status(thm)],[3842, 3804])).
% 3.04/3.25 tff(3844,plain,
% 3.04/3.25 ($false),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[3531, 118, 557, 203, 3843])).
% 3.04/3.25 tff(3845,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(elem!1))))) | (~(elem!1 = s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.25 tff(3846,plain,
% 3.04/3.25 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[3845, 3793, 557, 3802, 521, 145])).
% 3.04/3.25 tff(3847,plain,
% 3.04/3.25 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[271, 3846])).
% 3.04/3.25 tff(3848,plain,
% 3.04/3.25 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.25 inference(monotonicity,[status(thm)],[3793])).
% 3.04/3.25 tff(3849,plain,
% 3.04/3.25 ((s(elem!1) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(z)))),
% 3.04/3.25 inference(monotonicity,[status(thm)],[3796])).
% 3.04/3.25 tff(3850,plain,
% 3.04/3.25 ((s(elem!1) = s(s(z))) <=> (s(s(z)) = s(s(s(s(elem!1)))))),
% 3.04/3.25 inference(transitivity,[status(thm)],[3849, 2129])).
% 3.04/3.25 tff(3851,plain,
% 3.04/3.25 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(elem!1) = s(s(z)))),
% 3.04/3.25 inference(symmetry,[status(thm)],[3850])).
% 3.04/3.25 tff(3852,plain,
% 3.04/3.25 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(s(elem!1) = s(s(z))))),
% 3.04/3.25 inference(monotonicity,[status(thm)],[3851])).
% 3.04/3.25 tff(3853,plain,
% 3.04/3.25 (~(s(elem!1) = s(s(z)))),
% 3.04/3.25 inference(modus_ponens,[status(thm)],[2131, 3852])).
% 3.04/3.25 tff(3854,plain,
% 3.04/3.25 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[2840, 3853])).
% 3.04/3.25 tff(3855,plain,
% 3.04/3.25 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[2859, 3854, 3793])).
% 3.04/3.25 tff(3856,plain,
% 3.04/3.25 (r(elem!1, s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 3.04/3.25 inference(monotonicity,[status(thm)],[3793])).
% 3.04/3.25 tff(3857,plain,
% 3.04/3.25 (r(s(s(s(elem!1))), s(s(z)))),
% 3.04/3.25 inference(modus_ponens,[status(thm)],[450, 3856])).
% 3.04/3.25 tff(3858,plain,
% 3.04/3.25 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.04/3.25 inference(modus_ponens,[status(thm)],[3771, 3290])).
% 3.04/3.25 tff(3859,assumption,(r(s(s(s(elem!1))), s(s(z)))), introduced(assumption)).
% 3.04/3.25 tff(3860,plain,
% 3.04/3.25 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[3845, 1527, 557, 3858, 521, 145])).
% 3.04/3.25 tff(3861,plain,
% 3.04/3.25 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[271, 3860])).
% 3.04/3.25 tff(3862,plain,
% 3.04/3.25 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(s(elem!1))))),
% 3.04/3.25 inference(monotonicity,[status(thm)],[1527])).
% 3.04/3.25 tff(3863,plain,
% 3.04/3.25 (r(s(s(z)), s(s(s(elem!1))))),
% 3.04/3.25 inference(modus_ponens,[status(thm)],[438, 3862])).
% 3.04/3.25 tff(3864,plain,
% 3.04/3.25 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[2803, 1265, 438])).
% 3.04/3.25 tff(3865,plain,
% 3.04/3.25 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[249, 3864])).
% 3.04/3.25 tff(3866,plain,
% 3.04/3.25 (b(elem!1, s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 3.04/3.25 inference(monotonicity,[status(thm)],[1527])).
% 3.04/3.25 tff(3867,plain,
% 3.04/3.25 (b(s(s(s(elem!1))), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 3.04/3.25 inference(symmetry,[status(thm)],[3866])).
% 3.04/3.25 tff(3868,plain,
% 3.04/3.25 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.04/3.25 inference(monotonicity,[status(thm)],[3300])).
% 3.04/3.25 tff(3869,plain,
% 3.04/3.25 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 3.04/3.25 inference(symmetry,[status(thm)],[3868])).
% 3.04/3.25 tff(3870,plain,
% 3.04/3.25 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(elem!1, s(elem!1))),
% 3.04/3.25 inference(transitivity,[status(thm)],[3869, 3867])).
% 3.04/3.25 tff(3871,plain,
% 3.04/3.25 ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) <=> (~b(elem!1, s(elem!1)))),
% 3.04/3.25 inference(monotonicity,[status(thm)],[3870])).
% 3.04/3.25 tff(3872,plain,
% 3.04/3.25 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 3.04/3.25 inference(monotonicity,[status(thm)],[3300])).
% 3.04/3.25 tff(3873,plain,
% 3.04/3.25 (~(elem!1 = z)),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[3276, 273, 461])).
% 3.04/3.25 tff(3874,plain,
% 3.04/3.25 (~(z = elem!1)),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[317, 3873])).
% 3.04/3.25 tff(3875,plain,
% 3.04/3.25 (~(s(s(elem!1)) = s(s(z)))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[2386, 3874])).
% 3.04/3.25 tff(3876,plain,
% 3.04/3.25 (~(s(elem!1) = s(s(s(s(z)))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[2498, 1527, 3875])).
% 3.04/3.25 tff(3877,plain,
% 3.04/3.25 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.04/3.25 inference(monotonicity,[status(thm)],[1527])).
% 3.04/3.25 tff(3878,plain,
% 3.04/3.25 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 3.04/3.25 inference(symmetry,[status(thm)],[3877])).
% 3.04/3.25 tff(3879,plain,
% 3.04/3.25 (b(elem!1, s(s(s(s(z)))))),
% 3.04/3.25 inference(modus_ponens,[status(thm)],[3831, 3878])).
% 3.04/3.25 tff(3880,plain,
% 3.04/3.25 ((s(elem!1) = elem!1) <=> (elem!1 = s(elem!1))),
% 3.04/3.25 inference(symmetry,[status(thm)],[3190])).
% 3.04/3.25 tff(3881,plain,
% 3.04/3.25 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 3.04/3.25 inference(commutativity,[status(thm)],[])).
% 3.04/3.25 tff(3882,plain,
% 3.04/3.25 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(s(elem!1))))),
% 3.04/3.25 inference(monotonicity,[status(thm)],[1527])).
% 3.04/3.25 tff(3883,plain,
% 3.04/3.25 ((s(elem!1) = elem!1) <=> (s(s(s(elem!1))) = s(elem!1))),
% 3.04/3.25 inference(transitivity,[status(thm)],[3882, 3881])).
% 3.04/3.25 tff(3884,plain,
% 3.04/3.25 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = elem!1)),
% 3.04/3.25 inference(symmetry,[status(thm)],[3883])).
% 3.04/3.25 tff(3885,plain,
% 3.04/3.25 ((s(s(s(elem!1))) = s(elem!1)) <=> (elem!1 = s(elem!1))),
% 3.04/3.25 inference(transitivity,[status(thm)],[3884, 3880])).
% 3.04/3.25 tff(3886,plain,
% 3.04/3.25 (elem!1 = s(elem!1)),
% 3.04/3.25 inference(modus_ponens,[status(thm)],[340, 3885])).
% 3.04/3.25 tff(3887,plain,
% 3.04/3.25 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 3.04/3.25 inference(rewrite,[status(thm)],[])).
% 3.04/3.25 tff(3888,plain,
% 3.04/3.25 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(s(s(s(z))))))), s(s(s(s(z)))))))),
% 3.04/3.25 inference(quant_inst,[status(thm)],[])).
% 3.04/3.25 tff(3889,plain,
% 3.04/3.25 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 3.04/3.25 inference(modus_ponens,[status(thm)],[3888, 3887])).
% 3.04/3.25 tff(3890,plain,
% 3.04/3.25 ($false),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[3889, 118, 1130, 193, 107])).
% 3.04/3.25 tff(3891,plain,((~r(s(s(s(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(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.25 tff(3892,plain,
% 3.04/3.25 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[3891, 107, 193])).
% 3.04/3.25 tff(3893,plain,
% 3.04/3.25 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[84, 3892])).
% 3.04/3.25 tff(3894,plain,
% 3.04/3.25 (s(s(s(elem!1))) = elem!1),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[1530, 1527])).
% 3.04/3.25 tff(3895,plain,
% 3.04/3.25 (elem!1 = s(s(s(s(elem!1))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[1509, 340])).
% 3.04/3.25 tff(3896,plain,
% 3.04/3.25 (s(s(s(s(elem!1)))) = elem!1),
% 3.04/3.25 inference(symmetry,[status(thm)],[1414])).
% 3.04/3.25 tff(3897,plain,
% 3.04/3.25 (b(s(s(s(s(elem!1)))), s(s(z))) <=> b(elem!1, s(s(z)))),
% 3.04/3.25 inference(monotonicity,[status(thm)],[3896])).
% 3.04/3.25 tff(3898,assumption,(b(s(s(s(s(elem!1)))), s(s(z)))), introduced(assumption)).
% 3.04/3.25 tff(3899,plain,
% 3.04/3.25 (b(elem!1, s(s(z)))),
% 3.04/3.25 inference(modus_ponens,[status(thm)],[3898, 3897])).
% 3.04/3.25 tff(3900,plain,
% 3.04/3.25 ($false),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[461, 3899])).
% 3.04/3.25 tff(3901,plain,((~b(s(s(s(s(elem!1)))), s(s(z)))) | b(elem!1, s(s(z))) | (~(elem!1 = s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.25 tff(3902,plain,
% 3.04/3.25 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[3901, 3895, 461])).
% 3.04/3.25 tff(3903,plain,
% 3.04/3.25 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[1170, 3902])).
% 3.04/3.25 tff(3904,plain,
% 3.04/3.25 (r(s(s(s(s(elem!1)))), s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 3.04/3.25 inference(monotonicity,[status(thm)],[1520])).
% 3.04/3.25 tff(3905,plain,
% 3.04/3.25 (r(s(elem!1), s(s(z)))),
% 3.04/3.25 inference(modus_ponens,[status(thm)],[3636, 3904])).
% 3.04/3.25 tff(3906,plain,
% 3.04/3.25 ($false),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[927, 3905])).
% 3.04/3.25 tff(3907,plain,((~r(s(s(s(s(elem!1)))), s(s(z)))) | r(s(elem!1), s(s(z))) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.25 tff(3908,plain,
% 3.04/3.25 (r(s(elem!1), s(s(z)))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[3907, 3903, 3894])).
% 3.04/3.25 tff(3909,plain,
% 3.04/3.25 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.04/3.25 inference(monotonicity,[status(thm)],[745])).
% 3.04/3.25 tff(3910,plain,
% 3.04/3.25 (r(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.04/3.25 inference(symmetry,[status(thm)],[3909])).
% 3.04/3.25 tff(3911,plain,
% 3.04/3.25 ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) <=> (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 3.04/3.25 inference(monotonicity,[status(thm)],[3910])).
% 3.04/3.25 tff(3912,plain,
% 3.04/3.25 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[802, 118, 363, 107])).
% 3.04/3.25 tff(3913,plain,
% 3.04/3.25 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.04/3.25 inference(modus_ponens,[status(thm)],[3912, 3911])).
% 3.04/3.25 tff(3914,assumption,(~(s(s(s(s(s(s(s(z))))))) = elem!1)), introduced(assumption)).
% 3.04/3.25 tff(3915,plain,
% 3.04/3.25 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(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)))))),
% 3.04/3.25 inference(rewrite,[status(thm)],[])).
% 3.04/3.25 tff(3916,plain,
% 3.04/3.25 (((~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(z)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(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)))))),
% 3.04/3.25 inference(rewrite,[status(thm)],[])).
% 3.04/3.25 tff(3917,plain,
% 3.04/3.25 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(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))))))),
% 3.04/3.25 inference(monotonicity,[status(thm)],[3916])).
% 3.04/3.25 tff(3918,plain,
% 3.04/3.25 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(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)))))),
% 3.04/3.25 inference(transitivity,[status(thm)],[3917, 3915])).
% 3.04/3.25 tff(3919,plain,
% 3.04/3.25 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.25 inference(quant_inst,[status(thm)],[])).
% 3.04/3.25 tff(3920,plain,
% 3.04/3.25 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 3.04/3.25 inference(modus_ponens,[status(thm)],[3919, 3918])).
% 3.04/3.25 tff(3921,plain,
% 3.04/3.25 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[3920, 118, 193, 107])).
% 3.04/3.25 tff(3922,plain,
% 3.04/3.25 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[222, 3921])).
% 3.04/3.25 tff(3923,plain,
% 3.04/3.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.25 inference(rewrite,[status(thm)],[])).
% 3.04/3.25 tff(3924,plain,
% 3.04/3.25 (((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(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(s(s(s(s(z)))), s(s(s(s(s(s(s(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)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.25 inference(rewrite,[status(thm)],[])).
% 3.04/3.25 tff(3925,plain,
% 3.04/3.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(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(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 3.04/3.25 inference(monotonicity,[status(thm)],[3924])).
% 3.04/3.25 tff(3926,plain,
% 3.04/3.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(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(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.25 inference(transitivity,[status(thm)],[3925, 3923])).
% 3.04/3.25 tff(3927,plain,
% 3.04/3.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(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(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.25 inference(quant_inst,[status(thm)],[])).
% 3.04/3.25 tff(3928,plain,
% 3.04/3.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 3.04/3.25 inference(modus_ponens,[status(thm)],[3927, 3926])).
% 3.04/3.25 tff(3929,plain,
% 3.04/3.25 ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[3928, 178, 104, 3771, 1301])).
% 3.04/3.25 tff(3930,plain,
% 3.04/3.25 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[3929, 3922])).
% 3.04/3.25 tff(3931,plain,
% 3.04/3.25 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[3444, 3930, 3914])).
% 3.04/3.25 tff(3932,plain,
% 3.04/3.25 ($false),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[3931, 3913])).
% 3.04/3.25 tff(3933,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~(elem!1 = s(elem!1))) | (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(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(elem!1), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.25 tff(3934,plain,
% 3.04/3.25 (~(elem!1 = s(elem!1))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[3933, 3908, 3771, 107, 3806, 1301, 193, 3893])).
% 3.04/3.25 tff(3935,plain,
% 3.04/3.25 ($false),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[3934, 3886])).
% 3.04/3.25 tff(3936,plain,((~(s(s(s(elem!1))) = s(elem!1))) | (~(elem!1 = s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | b(elem!1, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.25 tff(3937,plain,
% 3.04/3.25 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[3936, 107, 3771, 1527, 3879, 193, 461])).
% 3.04/3.26 tff(3938,plain,
% 3.04/3.26 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[1649, 3937])).
% 3.04/3.26 tff(3939,plain,
% 3.04/3.26 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[1657, 3938])).
% 3.04/3.26 tff(3940,plain,
% 3.04/3.26 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[3644, 3636, 1823])).
% 3.04/3.26 tff(3941,plain,
% 3.04/3.26 (r(s(elem!1), s(s(z)))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[3907, 3636, 3894])).
% 3.04/3.26 tff(3942,plain,
% 3.04/3.26 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 3.04/3.26 inference(rewrite,[status(thm)],[])).
% 3.04/3.26 tff(3943,plain,
% 3.04/3.26 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(s(s(s(z))))))) <=> ((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 3.04/3.26 inference(rewrite,[status(thm)],[])).
% 3.04/3.26 tff(3944,plain,
% 3.04/3.26 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 3.04/3.26 inference(monotonicity,[status(thm)],[3943])).
% 3.04/3.26 tff(3945,plain,
% 3.04/3.26 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 3.04/3.26 inference(transitivity,[status(thm)],[3944, 3942])).
% 3.04/3.26 tff(3946,plain,
% 3.04/3.26 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 3.04/3.26 inference(quant_inst,[status(thm)],[])).
% 3.04/3.26 tff(3947,plain,
% 3.04/3.26 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 3.04/3.26 inference(modus_ponens,[status(thm)],[3946, 3945])).
% 3.04/3.26 tff(3948,plain,
% 3.04/3.26 ($false),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[3947, 118, 363, 908, 193])).
% 3.04/3.26 tff(3949,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.26 tff(3950,plain,
% 3.04/3.26 (~r(s(elem!1), s(s(s(s(z)))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[3949, 3941, 193])).
% 3.04/3.26 tff(3951,plain,
% 3.04/3.26 (b(s(elem!1), s(s(s(s(z)))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[1084, 3950, 1369])).
% 3.04/3.26 tff(3952,plain,
% 3.04/3.26 (b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 3.04/3.26 inference(modus_ponens,[status(thm)],[3951, 3872])).
% 3.04/3.26 tff(3953,plain,
% 3.04/3.26 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 3.04/3.26 inference(rewrite,[status(thm)],[])).
% 3.04/3.26 tff(3954,plain,
% 3.04/3.26 (((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 3.04/3.26 inference(rewrite,[status(thm)],[])).
% 3.04/3.26 tff(3955,plain,
% 3.04/3.26 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 3.04/3.26 inference(monotonicity,[status(thm)],[3954])).
% 3.04/3.26 tff(3956,plain,
% 3.04/3.26 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 3.04/3.26 inference(transitivity,[status(thm)],[3955, 3953])).
% 3.04/3.26 tff(3957,plain,
% 3.04/3.26 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 3.04/3.26 inference(quant_inst,[status(thm)],[])).
% 3.04/3.26 tff(3958,plain,
% 3.04/3.26 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 3.04/3.26 inference(modus_ponens,[status(thm)],[3957, 3956])).
% 3.04/3.26 tff(3959,plain,
% 3.04/3.26 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[3958, 118, 3636, 3859])).
% 3.04/3.26 tff(3960,assumption,(b(s(s(s(s(elem!1)))), s(s(s(s(z)))))), introduced(assumption)).
% 3.04/3.26 tff(3961,assumption,(~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 3.04/3.26 tff(3962,plain,
% 3.04/3.26 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[1988, 1693, 3961])).
% 3.04/3.26 tff(3963,assumption,(~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 3.04/3.26 tff(3964,plain,
% 3.04/3.26 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[1695, 1693])).
% 3.04/3.26 tff(3965,plain,
% 3.04/3.26 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[1750, 3964, 3963])).
% 3.04/3.26 tff(3966,plain,
% 3.04/3.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(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)))))))),
% 3.04/3.26 inference(rewrite,[status(thm)],[])).
% 3.04/3.26 tff(3967,plain,
% 3.04/3.26 (((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(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(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(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)))))))),
% 3.04/3.26 inference(rewrite,[status(thm)],[])).
% 3.04/3.26 tff(3968,plain,
% 3.04/3.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(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(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(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))))))))),
% 3.04/3.26 inference(monotonicity,[status(thm)],[3967])).
% 3.04/3.26 tff(3969,plain,
% 3.04/3.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(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(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(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)))))))),
% 3.04/3.26 inference(transitivity,[status(thm)],[3968, 3966])).
% 3.04/3.26 tff(3970,plain,
% 3.04/3.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(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(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 3.04/3.26 inference(quant_inst,[status(thm)],[])).
% 3.04/3.26 tff(3971,plain,
% 3.04/3.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.04/3.26 inference(modus_ponens,[status(thm)],[3970, 3969])).
% 3.04/3.26 tff(3972,plain,
% 3.04/3.26 ($false),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[3971, 178, 3965, 3962, 3828, 3831, 3960])).
% 3.04/3.26 tff(3973,plain,((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.26 tff(3974,plain,
% 3.04/3.26 ($false),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[3973, 3959, 3952, 1693, 3831, 3940, 3828])).
% 3.04/3.26 tff(3975,plain,((~r(s(s(s(s(elem!1)))), s(s(z)))) | (s(s(s(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(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~(elem!1 = s(s(s(elem!1))))) | (s(elem!1) = s(s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.26 tff(3976,plain,
% 3.04/3.26 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[3975, 3939, 3831, 3858, 3859, 1527, 3876, 193, 1823])).
% 3.04/3.26 tff(3977,plain,
% 3.04/3.26 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[1170, 3976])).
% 3.04/3.26 tff(3978,plain,
% 3.04/3.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.26 inference(rewrite,[status(thm)],[])).
% 3.04/3.26 tff(3979,plain,
% 3.04/3.26 (((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.26 inference(rewrite,[status(thm)],[])).
% 3.04/3.26 tff(3980,plain,
% 3.04/3.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 3.04/3.26 inference(monotonicity,[status(thm)],[3979])).
% 3.04/3.26 tff(3981,plain,
% 3.04/3.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.26 inference(transitivity,[status(thm)],[3980, 3978])).
% 3.04/3.26 tff(3982,plain,
% 3.04/3.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 3.04/3.26 inference(quant_inst,[status(thm)],[])).
% 3.04/3.26 tff(3983,plain,
% 3.04/3.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 3.04/3.26 inference(modus_ponens,[status(thm)],[3982, 3981])).
% 3.04/3.26 tff(3984,plain,
% 3.04/3.26 (~b(s(s(s(s(elem!1)))), z)),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[3983, 178, 273, 3977, 166, 595])).
% 3.04/3.26 tff(3985,plain,
% 3.04/3.26 (r(s(s(s(s(elem!1)))), z)),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[1716, 3984])).
% 3.04/3.26 tff(3986,plain,
% 3.04/3.26 (r(s(elem!1), z) <=> r(s(s(s(s(elem!1)))), z)),
% 3.04/3.26 inference(monotonicity,[status(thm)],[3300])).
% 3.04/3.26 tff(3987,plain,
% 3.04/3.26 (r(s(s(s(s(elem!1)))), z) <=> r(s(elem!1), z)),
% 3.04/3.26 inference(symmetry,[status(thm)],[3986])).
% 3.04/3.26 tff(3988,assumption,(r(s(s(s(s(elem!1)))), z)), introduced(assumption)).
% 3.04/3.26 tff(3989,plain,
% 3.04/3.26 (r(s(elem!1), z)),
% 3.04/3.26 inference(modus_ponens,[status(thm)],[3988, 3987])).
% 3.04/3.26 tff(3990,plain,
% 3.04/3.26 ($false),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[767, 3989])).
% 3.04/3.26 tff(3991,plain,((~r(s(s(s(s(elem!1)))), z)) | r(s(elem!1), z) | (~(elem!1 = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.26 tff(3992,plain,
% 3.04/3.26 (r(s(elem!1), z)),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[3991, 3985, 1527])).
% 3.04/3.26 tff(3993,plain,
% 3.04/3.26 (~r(s(elem!1), s(s(s(s(z)))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[916, 3992, 194])).
% 3.04/3.26 tff(3994,plain,
% 3.04/3.26 (b(s(elem!1), s(s(s(s(z)))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[1084, 3993, 3876])).
% 3.04/3.26 tff(3995,plain,
% 3.04/3.26 (b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 3.04/3.26 inference(modus_ponens,[status(thm)],[3994, 3872])).
% 3.04/3.26 tff(3996,plain,
% 3.04/3.26 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.04/3.26 inference(monotonicity,[status(thm)],[3300])).
% 3.04/3.26 tff(3997,plain,
% 3.04/3.26 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(elem!1))))),
% 3.04/3.26 inference(monotonicity,[status(thm)],[1527])).
% 3.04/3.26 tff(3998,plain,
% 3.04/3.26 (b(s(elem!1), elem!1) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.04/3.26 inference(transitivity,[status(thm)],[3997, 3996])).
% 3.04/3.26 tff(3999,plain,
% 3.04/3.26 (~(elem!1 = s(s(elem!1)))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[1539, 3937])).
% 3.04/3.26 tff(4000,plain,
% 3.04/3.26 (~(s(s(elem!1)) = elem!1)),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[1546, 3999])).
% 3.04/3.26 tff(4001,plain,
% 3.04/3.26 (~(s(elem!1) = elem!1)),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[672, 4000])).
% 3.04/3.26 tff(4002,plain,
% 3.04/3.26 (~r(s(elem!1), elem!1)),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[1284, 3992, 521])).
% 3.04/3.26 tff(4003,plain,
% 3.04/3.26 (b(s(elem!1), elem!1)),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[677, 4002, 4001])).
% 3.04/3.26 tff(4004,plain,
% 3.04/3.26 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.04/3.26 inference(modus_ponens,[status(thm)],[4003, 3998])).
% 3.04/3.26 tff(4005,plain,
% 3.04/3.26 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[3971, 178, 4004, 3858, 3831, 3995])).
% 3.04/3.26 tff(4006,plain,
% 3.04/3.26 (~b(elem!1, s(elem!1))),
% 3.04/3.26 inference(modus_ponens,[status(thm)],[4005, 3871])).
% 3.04/3.26 tff(4007,plain,
% 3.04/3.26 (~(elem!1 = s(elem!1))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[748, 4001])).
% 3.04/3.26 tff(4008,plain,
% 3.04/3.26 (~(s(s(s(s(z)))) = s(elem!1))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[2168, 3876])).
% 3.04/3.26 tff(4009,plain,
% 3.04/3.26 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 3.04/3.26 inference(transitivity,[status(thm)],[609, 658, 304, 1527])).
% 3.04/3.26 tff(4010,plain,
% 3.04/3.26 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(s(elem!1))))),
% 3.04/3.26 inference(monotonicity,[status(thm)],[4009])).
% 3.04/3.26 tff(4011,plain,
% 3.04/3.26 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 3.04/3.26 inference(transitivity,[status(thm)],[239, 4010, 343])).
% 3.04/3.26 tff(4012,plain,
% 3.04/3.26 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(elem!1)))),
% 3.04/3.26 inference(monotonicity,[status(thm)],[4011])).
% 3.04/3.26 tff(4013,plain,
% 3.04/3.26 (s(s(s(s(z)))) = s(elem!1)),
% 3.04/3.26 inference(transitivity,[status(thm)],[663, 4012, 328])).
% 3.04/3.26 tff(4014,plain,
% 3.04/3.26 ($false),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[2508, 4013])).
% 3.04/3.26 tff(4015,plain,((~(elem!1 = s(s(s(elem!1))))) | (s(s(s(s(z)))) = s(elem!1)) | (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.26 tff(4016,plain,
% 3.04/3.26 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[4015, 4008, 1527])).
% 3.04/3.26 tff(4017,assumption,(~(s(s(s(s(s(s(s(z))))))) = s(elem!1))), introduced(assumption)).
% 3.04/3.26 tff(4018,plain,
% 3.04/3.26 ($false),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[4017, 656])).
% 3.04/3.26 tff(4019,plain,((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.26 tff(4020,plain,
% 3.04/3.26 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[4019, 4016])).
% 3.04/3.26 tff(4021,plain,
% 3.04/3.26 (s(s(s(s(elem!1)))) = s(elem!1)),
% 3.04/3.26 inference(symmetry,[status(thm)],[3300])).
% 3.04/3.26 tff(4022,plain,
% 3.04/3.26 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 3.04/3.26 inference(monotonicity,[status(thm)],[4021])).
% 3.04/3.26 tff(4023,plain,
% 3.04/3.26 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.04/3.26 inference(symmetry,[status(thm)],[4022])).
% 3.04/3.26 tff(4024,plain,
% 3.04/3.26 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(s(elem!1))))),
% 3.04/3.26 inference(monotonicity,[status(thm)],[1527])).
% 3.04/3.26 tff(4025,plain,
% 3.04/3.26 (r(s(elem!1), elem!1) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.04/3.26 inference(transitivity,[status(thm)],[4024, 4023])).
% 3.04/3.26 tff(4026,plain,
% 3.04/3.26 ((~r(s(elem!1), elem!1)) <=> (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 3.04/3.26 inference(monotonicity,[status(thm)],[4025])).
% 3.04/3.26 tff(4027,plain,
% 3.04/3.26 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.04/3.26 inference(modus_ponens,[status(thm)],[4002, 4026])).
% 3.04/3.26 tff(4028,plain,
% 3.04/3.26 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[3973, 3995, 3939, 3831, 4027, 3858])).
% 3.04/3.26 tff(4029,plain,
% 3.04/3.26 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 3.04/3.26 inference(rewrite,[status(thm)],[])).
% 3.04/3.26 tff(4030,plain,
% 3.04/3.26 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1)))))) <=> ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 3.04/3.26 inference(rewrite,[status(thm)],[])).
% 3.04/3.26 tff(4031,plain,
% 3.04/3.26 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1))))))))),
% 3.04/3.26 inference(monotonicity,[status(thm)],[4030])).
% 3.04/3.26 tff(4032,plain,
% 3.04/3.26 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 3.04/3.26 inference(transitivity,[status(thm)],[4031, 4029])).
% 3.04/3.26 tff(4033,plain,
% 3.04/3.26 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 3.04/3.26 inference(quant_inst,[status(thm)],[])).
% 3.04/3.26 tff(4034,plain,
% 3.04/3.26 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1))))))),
% 3.04/3.26 inference(modus_ponens,[status(thm)],[4033, 4032])).
% 3.04/3.26 tff(4035,plain,
% 3.04/3.26 ($false),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[4034, 118, 1403, 1823, 1876])).
% 3.04/3.26 tff(4036,plain,((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.26 tff(4037,plain,
% 3.04/3.26 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[4036, 4028, 1823])).
% 3.04/3.26 tff(4038,plain,
% 3.04/3.26 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[2136, 4037])).
% 3.04/3.26 tff(4039,plain,
% 3.04/3.26 (b(s(s(z)), s(elem!1))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[1524, 4038, 3894])).
% 3.04/3.26 tff(4040,plain,
% 3.04/3.26 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[2529, 4039, 3893, 3994, 166])).
% 3.04/3.26 tff(4041,plain,
% 3.04/3.26 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[395, 4040, 4020])).
% 3.04/3.26 tff(4042,plain,
% 3.04/3.26 (~r(elem!1, s(elem!1))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[2935, 4041, 1265])).
% 3.04/3.26 tff(4043,plain,
% 3.04/3.26 (b(elem!1, s(elem!1))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[756, 4042, 4007])).
% 3.04/3.26 tff(4044,plain,
% 3.04/3.26 ($false),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[4043, 4006])).
% 3.04/3.26 tff(4045,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~(elem!1 = s(s(s(elem!1))))) | (~r(elem!1, 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(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | b(elem!1, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.26 tff(4046,plain,
% 3.04/3.26 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[4045, 1265, 1527, 3865, 3863, 3827, 521, 194, 3549, 3861, 3859, 193, 3771, 461])).
% 3.04/3.26 tff(4047,plain,
% 3.04/3.26 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[3578, 4046])).
% 3.04/3.26 tff(4048,plain,
% 3.04/3.26 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[3569, 4047, 145, 193, 3549, 3425])).
% 3.04/3.26 tff(4049,plain,
% 3.04/3.27 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[222, 4048])).
% 3.04/3.27 tff(4050,plain,
% 3.04/3.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), 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))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), 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))))))), z)))),
% 3.04/3.27 inference(rewrite,[status(thm)],[])).
% 3.04/3.27 tff(4051,plain,
% 3.04/3.27 (((~b(z, 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(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), 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))))))), z)))),
% 3.04/3.27 inference(rewrite,[status(thm)],[])).
% 3.04/3.27 tff(4052,plain,
% 3.04/3.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), 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))))))), z))))),
% 3.04/3.27 inference(monotonicity,[status(thm)],[4051])).
% 3.04/3.27 tff(4053,plain,
% 3.04/3.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), 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))))))), z)))),
% 3.04/3.27 inference(transitivity,[status(thm)],[4052, 4050])).
% 3.04/3.27 tff(4054,plain,
% 3.04/3.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.27 inference(quant_inst,[status(thm)],[])).
% 3.04/3.27 tff(4055,plain,
% 3.04/3.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 3.04/3.27 inference(modus_ponens,[status(thm)],[4054, 4053])).
% 3.04/3.27 tff(4056,plain,
% 3.04/3.27 ($false),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[4055, 178, 3461, 273, 166, 146, 1146])).
% 3.04/3.27 tff(4057,plain,((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.27 tff(4058,plain,
% 3.04/3.27 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[4057, 4047, 3425, 3549, 3865])).
% 3.04/3.27 tff(4059,plain,
% 3.04/3.27 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[133, 4058])).
% 3.04/3.27 tff(4060,plain,
% 3.04/3.27 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[1138, 4059, 145])).
% 3.04/3.27 tff(4061,plain,
% 3.04/3.27 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[84, 4060])).
% 3.04/3.27 tff(4062,plain,
% 3.04/3.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(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(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(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(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.04/3.27 inference(rewrite,[status(thm)],[])).
% 3.04/3.27 tff(4063,plain,
% 3.04/3.27 (((~b(s(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(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(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)))))) | (~b(s(s(s(s(z)))), s(s(s(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(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.04/3.27 inference(rewrite,[status(thm)],[])).
% 3.04/3.27 tff(4064,plain,
% 3.04/3.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(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(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))))),
% 3.04/3.27 inference(monotonicity,[status(thm)],[4063])).
% 3.04/3.27 tff(4065,plain,
% 3.04/3.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(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(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.04/3.27 inference(transitivity,[status(thm)],[4064, 4062])).
% 3.04/3.27 tff(4066,plain,
% 3.04/3.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.27 inference(quant_inst,[status(thm)],[])).
% 3.04/3.27 tff(4067,plain,
% 3.04/3.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(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(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 3.04/3.27 inference(modus_ponens,[status(thm)],[4066, 4065])).
% 3.04/3.27 tff(4068,plain,
% 3.04/3.27 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[4067, 178, 4061, 4049, 3858, 3827])).
% 3.04/3.27 tff(4069,plain,
% 3.04/3.27 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.04/3.27 inference(modus_ponens,[status(thm)],[4068, 3809])).
% 3.04/3.27 tff(4070,plain,
% 3.04/3.27 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[3444, 4069, 3806])).
% 3.04/3.27 tff(4071,plain,
% 3.04/3.27 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.04/3.27 inference(modus_ponens,[status(thm)],[4070, 3804])).
% 3.04/3.27 tff(4072,plain,
% 3.04/3.27 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.04/3.27 inference(rewrite,[status(thm)],[])).
% 3.04/3.27 tff(4073,plain,
% 3.04/3.27 (((~r(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))))))), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.04/3.27 inference(rewrite,[status(thm)],[])).
% 3.04/3.27 tff(4074,plain,
% 3.04/3.27 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))))),
% 3.04/3.27 inference(monotonicity,[status(thm)],[4073])).
% 3.04/3.27 tff(4075,plain,
% 3.04/3.27 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.04/3.27 inference(transitivity,[status(thm)],[4074, 4072])).
% 3.04/3.27 tff(4076,plain,
% 3.04/3.27 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))))))), z)))),
% 3.04/3.27 inference(quant_inst,[status(thm)],[])).
% 3.04/3.27 tff(4077,plain,
% 3.04/3.27 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 3.04/3.27 inference(modus_ponens,[status(thm)],[4076, 4075])).
% 3.04/3.27 tff(4078,plain,
% 3.04/3.27 ($false),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[4077, 118, 557, 4059, 4071])).
% 3.04/3.27 tff(4079,plain,((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(elem!1))))) | (~(elem!1 = s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | b(elem!1, s(s(z))) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.27 tff(4080,plain,
% 3.04/3.27 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[4079, 3793, 557, 145, 193, 521, 194, 3857, 3771, 461, 438])).
% 3.04/3.27 tff(4081,plain,
% 3.04/3.27 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[691, 4080, 3855])).
% 3.04/3.27 tff(4082,plain,
% 3.04/3.27 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.27 inference(modus_ponens,[status(thm)],[4081, 3848])).
% 3.04/3.27 tff(4083,plain,
% 3.04/3.27 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[3826, 3854])).
% 3.04/3.27 tff(4084,plain,
% 3.04/3.27 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[3891, 1130, 193])).
% 3.04/3.27 tff(4085,plain,
% 3.04/3.27 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[3578, 4084])).
% 3.04/3.27 tff(4086,plain,
% 3.04/3.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, 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))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, 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))))))), z)))),
% 3.04/3.27 inference(rewrite,[status(thm)],[])).
% 3.04/3.27 tff(4087,plain,
% 3.04/3.27 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(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(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, 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))))))), z)))),
% 3.04/3.27 inference(rewrite,[status(thm)],[])).
% 3.04/3.27 tff(4088,plain,
% 3.04/3.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(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(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, 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))))))), z))))),
% 3.04/3.27 inference(monotonicity,[status(thm)],[4087])).
% 3.04/3.27 tff(4089,plain,
% 3.04/3.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(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(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, 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))))))), z)))),
% 3.04/3.27 inference(transitivity,[status(thm)],[4088, 4086])).
% 3.04/3.27 tff(4090,plain,
% 3.04/3.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(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(z, s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.27 inference(quant_inst,[status(thm)],[])).
% 3.04/3.27 tff(4091,plain,
% 3.04/3.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 3.04/3.27 inference(modus_ponens,[status(thm)],[4090, 4089])).
% 3.04/3.27 tff(4092,plain,
% 3.04/3.27 ($false),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[4091, 178, 3461, 3549, 595, 1140, 4085])).
% 3.04/3.27 tff(4093,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.27 tff(4094,plain,
% 3.04/3.27 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[4093, 3847, 3425, 193, 145])).
% 3.04/3.27 tff(4095,plain,
% 3.04/3.27 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[84, 4094])).
% 3.04/3.27 tff(4096,plain,
% 3.04/3.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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))))))))) | (~b(s(s(s(s(z)))), s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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))))))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.04/3.27 inference(rewrite,[status(thm)],[])).
% 3.04/3.27 tff(4097,plain,
% 3.04/3.27 (((~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(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(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(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(s(s(s(s(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(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.04/3.27 inference(rewrite,[status(thm)],[])).
% 3.04/3.27 tff(4098,plain,
% 3.04/3.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(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(z)))))) | (~b(s(s(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(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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))))))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 3.04/3.27 inference(monotonicity,[status(thm)],[4097])).
% 3.04/3.27 tff(4099,plain,
% 3.04/3.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(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(z)))))) | (~b(s(s(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(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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))))))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.04/3.27 inference(transitivity,[status(thm)],[4098, 4096])).
% 3.04/3.27 tff(4100,plain,
% 3.04/3.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(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(z)))))) | (~b(s(s(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(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.04/3.27 inference(quant_inst,[status(thm)],[])).
% 3.04/3.27 tff(4101,plain,
% 3.04/3.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.04/3.27 inference(modus_ponens,[status(thm)],[4100, 4099])).
% 3.04/3.27 tff(4102,plain,
% 3.04/3.27 ($false),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[4101, 178, 104, 251, 3828, 3831, 3830])).
% 3.04/3.27 tff(4103,plain,((~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(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.27 tff(4104,plain,
% 3.04/3.27 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[4103, 4095, 3802, 4083, 4082])).
% 3.04/3.27 tff(4105,plain,
% 3.04/3.27 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[222, 4104])).
% 3.04/3.27 tff(4106,plain,
% 3.04/3.27 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[3559, 4105, 193])).
% 3.04/3.27 tff(4107,plain,
% 3.04/3.27 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[249, 4106])).
% 3.04/3.27 tff(4108,plain,
% 3.04/3.27 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(s(elem!1))))),
% 3.04/3.27 inference(monotonicity,[status(thm)],[3793])).
% 3.04/3.27 tff(4109,plain,
% 3.04/3.27 (r(s(s(z)), s(s(s(elem!1))))),
% 3.04/3.27 inference(modus_ponens,[status(thm)],[438, 4108])).
% 3.04/3.27 tff(4110,plain,
% 3.04/3.27 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.04/3.27 inference(monotonicity,[status(thm)],[3793])).
% 3.04/3.27 tff(4111,plain,
% 3.04/3.27 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 3.04/3.27 inference(symmetry,[status(thm)],[4110])).
% 3.04/3.27 tff(4112,plain,
% 3.04/3.27 (b(elem!1, s(s(s(s(z)))))),
% 3.04/3.27 inference(modus_ponens,[status(thm)],[4083, 4111])).
% 3.04/3.27 tff(4113,plain,
% 3.04/3.27 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[3569, 4105, 145, 193, 3549, 3425])).
% 3.04/3.27 tff(4114,plain,
% 3.04/3.27 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[3578, 4113])).
% 3.04/3.27 tff(4115,plain,
% 3.04/3.27 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[3936, 4114, 3771, 3793, 4112, 193, 461])).
% 3.04/3.27 tff(4116,plain,
% 3.04/3.27 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[1649, 4115])).
% 3.04/3.27 tff(4117,plain,
% 3.04/3.27 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[1657, 4116])).
% 3.04/3.27 tff(4118,plain,
% 3.04/3.27 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[3975, 4117, 4083, 3802, 3857, 3793, 3794, 193, 4109])).
% 3.04/3.27 tff(4119,plain,
% 3.04/3.27 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[1170, 4118])).
% 3.04/3.27 tff(4120,plain,
% 3.04/3.27 (~b(s(s(s(s(elem!1)))), z)),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[3983, 178, 3549, 4119, 4107, 3847])).
% 3.04/3.27 tff(4121,plain,
% 3.04/3.27 (r(s(s(s(s(elem!1)))), z)),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[1716, 4120])).
% 3.04/3.27 tff(4122,plain,
% 3.04/3.27 (r(s(elem!1), z)),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[3991, 4121, 3793])).
% 3.04/3.27 tff(4123,plain,
% 3.04/3.27 (~r(s(elem!1), s(s(s(s(z)))))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[916, 4122, 194])).
% 3.04/3.27 tff(4124,plain,
% 3.04/3.27 (b(s(elem!1), s(s(s(s(z)))))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[1084, 4123, 3794])).
% 3.04/3.27 tff(4125,plain,
% 3.04/3.27 (b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 3.04/3.27 inference(modus_ponens,[status(thm)],[4124, 3800])).
% 3.04/3.27 tff(4126,plain,
% 3.04/3.27 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.04/3.27 inference(monotonicity,[status(thm)],[3796])).
% 3.04/3.27 tff(4127,plain,
% 3.04/3.27 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(elem!1))))),
% 3.04/3.27 inference(monotonicity,[status(thm)],[3793])).
% 3.04/3.27 tff(4128,plain,
% 3.04/3.27 (b(s(elem!1), elem!1) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.04/3.27 inference(transitivity,[status(thm)],[4127, 4126])).
% 3.04/3.27 tff(4129,plain,
% 3.04/3.27 (~(elem!1 = s(s(elem!1)))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[1539, 4115])).
% 3.04/3.27 tff(4130,plain,
% 3.04/3.27 (~(s(s(elem!1)) = elem!1)),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[1546, 4129])).
% 3.04/3.27 tff(4131,plain,
% 3.04/3.27 (~(s(elem!1) = elem!1)),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[672, 4130])).
% 3.04/3.27 tff(4132,plain,
% 3.04/3.27 (~r(s(elem!1), elem!1)),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[1284, 4122, 521])).
% 3.04/3.28 tff(4133,plain,
% 3.04/3.28 (b(s(elem!1), elem!1)),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[677, 4132, 4131])).
% 3.04/3.28 tff(4134,plain,
% 3.04/3.28 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.04/3.28 inference(modus_ponens,[status(thm)],[4133, 4128])).
% 3.04/3.28 tff(4135,plain,
% 3.04/3.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(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)))))))),
% 3.04/3.28 inference(rewrite,[status(thm)],[])).
% 3.04/3.28 tff(4136,plain,
% 3.04/3.28 (((~b(s(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(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(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)))))))),
% 3.04/3.28 inference(rewrite,[status(thm)],[])).
% 3.04/3.28 tff(4137,plain,
% 3.04/3.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(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))))))))),
% 3.04/3.28 inference(monotonicity,[status(thm)],[4136])).
% 3.04/3.28 tff(4138,plain,
% 3.04/3.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(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)))))))),
% 3.04/3.28 inference(transitivity,[status(thm)],[4137, 4135])).
% 3.04/3.28 tff(4139,plain,
% 3.04/3.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 3.04/3.28 inference(quant_inst,[status(thm)],[])).
% 3.04/3.28 tff(4140,plain,
% 3.04/3.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(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))))))),
% 3.04/3.28 inference(modus_ponens,[status(thm)],[4139, 4138])).
% 3.04/3.28 tff(4141,plain,
% 3.04/3.28 (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[4140, 178, 4134, 3802, 4083, 4125])).
% 3.04/3.28 tff(4142,plain,
% 3.04/3.28 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.04/3.28 inference(modus_ponens,[status(thm)],[4141, 3799])).
% 3.04/3.28 tff(4143,plain,
% 3.04/3.28 (r(s(s(s(s(z)))), s(s(s(s(elem!1))))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 3.04/3.28 inference(monotonicity,[status(thm)],[3797])).
% 3.04/3.28 tff(4144,plain,
% 3.04/3.28 ((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) <=> (~r(s(s(s(s(z)))), s(elem!1)))),
% 3.04/3.28 inference(monotonicity,[status(thm)],[4143])).
% 3.04/3.28 tff(4145,plain,
% 3.04/3.28 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 3.04/3.28 inference(rewrite,[status(thm)],[])).
% 3.04/3.28 tff(4146,plain,
% 3.04/3.28 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 3.04/3.28 inference(quant_inst,[status(thm)],[])).
% 3.04/3.28 tff(4147,plain,
% 3.04/3.28 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))),
% 3.04/3.28 inference(modus_ponens,[status(thm)],[4146, 4145])).
% 3.04/3.28 tff(4148,plain,
% 3.04/3.28 (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[4147, 118, 4121, 194])).
% 3.04/3.28 tff(4149,plain,
% 3.04/3.28 (~r(s(s(s(s(z)))), s(elem!1))),
% 3.04/3.28 inference(modus_ponens,[status(thm)],[4148, 4144])).
% 3.04/3.28 tff(4150,plain,
% 3.04/3.28 ($false),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[2173, 4149, 4142, 3795])).
% 3.04/3.28 tff(4151,plain,((~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | b(elem!1, s(s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | b(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.28 tff(4152,plain,
% 3.04/3.28 (~r(z, elem!1)),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[4151, 103, 194, 3768, 461, 47, 3243, 3788, 3777, 3240])).
% 3.04/3.28 tff(4153,plain,
% 3.04/3.28 (b(z, elem!1)),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[585, 4152, 3787])).
% 3.04/3.28 tff(4154,plain,
% 3.04/3.28 (~(elem!1 = s(s(s(s(z)))))),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[1846, 4153, 1])).
% 3.04/3.28 tff(4155,plain,
% 3.04/3.28 (b(elem!1, s(s(s(s(z)))))),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[483, 4154, 3786])).
% 3.04/3.28 tff(4156,assumption,(s(s(s(s(z)))) = s(s(s(elem!1)))), introduced(assumption)).
% 3.04/3.28 tff(4157,plain,
% 3.04/3.28 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(s(elem!1))))),
% 3.04/3.28 inference(monotonicity,[status(thm)],[4156])).
% 3.04/3.28 tff(4158,plain,
% 3.04/3.28 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(s(z)))))),
% 3.04/3.28 inference(symmetry,[status(thm)],[4157])).
% 3.04/3.28 tff(4159,plain,
% 3.04/3.28 ((~b(elem!1, s(s(s(elem!1))))) <=> (~b(elem!1, s(s(s(s(z))))))),
% 3.04/3.28 inference(monotonicity,[status(thm)],[4158])).
% 3.04/3.28 tff(4160,plain,
% 3.04/3.28 (~b(elem!1, s(s(s(s(z)))))),
% 3.04/3.28 inference(modus_ponens,[status(thm)],[3240, 4159])).
% 3.04/3.28 tff(4161,plain,
% 3.04/3.28 ($false),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[1301, 4160])).
% 3.04/3.28 tff(4162,plain,((~(s(s(s(s(z)))) = s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))) | b(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.28 tff(4163,plain,
% 3.04/3.28 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[4162, 4155, 3240])).
% 3.04/3.28 tff(4164,plain,
% 3.04/3.28 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 3.04/3.28 inference(symmetry,[status(thm)],[3289])).
% 3.04/3.28 tff(4165,plain,
% 3.04/3.28 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 3.04/3.28 inference(modus_ponens,[status(thm)],[2834, 4164])).
% 3.04/3.28 tff(4166,assumption,(~(s(s(s(s(z)))) = s(s(s(elem!1))))), introduced(assumption)).
% 3.04/3.28 tff(4167,plain,
% 3.04/3.28 ($false),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[4166, 4165])).
% 3.04/3.28 tff(4168,plain,((~(s(s(s(elem!1))) = s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.28 tff(4169,plain,
% 3.04/3.28 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[4168, 4163])).
% 3.04/3.28 tff(4170,assumption,(~b(s(s(s(elem!1))), s(s(s(s(z)))))), introduced(assumption)).
% 3.04/3.28 tff(4171,assumption,(~r(s(s(s(elem!1))), s(s(s(s(z)))))), introduced(assumption)).
% 3.04/3.28 tff(4172,plain,
% 3.04/3.28 ($false),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[3825, 41, 2857, 4171, 4170])).
% 3.04/3.28 tff(4173,plain,(b(s(s(s(elem!1))), s(s(s(s(z))))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.28 tff(4174,plain,
% 3.04/3.28 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[4173, 4169, 3260])).
% 3.04/3.28 tff(4175,plain,
% 3.04/3.28 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[3287, 3243, 194])).
% 3.04/3.28 tff(4176,plain,
% 3.04/3.28 ((s(s(s(s(z)))) = s(s(s(elem!1)))) | b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[3296, 41, 4175])).
% 3.04/3.28 tff(4177,plain,
% 3.04/3.28 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[4176, 4163])).
% 3.04/3.28 tff(4178,assumption,(s(s(s(elem!1))) = s(s(z))), introduced(assumption)).
% 3.04/3.28 tff(4179,plain,
% 3.04/3.28 (s(s(z)) = s(s(s(elem!1)))),
% 3.04/3.28 inference(symmetry,[status(thm)],[4178])).
% 3.04/3.28 tff(4180,plain,
% 3.04/3.28 ($false),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[1683, 4179])).
% 3.04/3.28 tff(4181,plain,(~(s(s(s(elem!1))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.28 tff(4182,plain,
% 3.04/3.28 (b(z, elem!1) <=> b(z, s(s(s(elem!1))))),
% 3.04/3.28 inference(monotonicity,[status(thm)],[1527])).
% 3.04/3.28 tff(4183,plain,
% 3.04/3.28 (b(z, s(s(s(elem!1)))) <=> b(z, elem!1)),
% 3.04/3.28 inference(symmetry,[status(thm)],[4182])).
% 3.04/3.28 tff(4184,plain,
% 3.04/3.28 ((~b(z, s(s(s(elem!1))))) <=> (~b(z, elem!1))),
% 3.04/3.28 inference(monotonicity,[status(thm)],[4183])).
% 3.04/3.28 tff(4185,plain,
% 3.04/3.28 (~b(z, elem!1)),
% 3.04/3.28 inference(modus_ponens,[status(thm)],[3242, 4184])).
% 3.04/3.28 tff(4186,plain,
% 3.04/3.28 ($false),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[818, 4185])).
% 3.04/3.28 tff(4187,plain,((~(elem!1 = s(s(s(elem!1))))) | (~b(z, elem!1)) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.28 tff(4188,plain,
% 3.04/3.28 (~(elem!1 = s(s(s(elem!1))))),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[4187, 4153, 3242])).
% 3.04/3.28 tff(4189,plain,
% 3.04/3.28 (~(s(s(s(elem!1))) = elem!1)),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[2489, 4188])).
% 3.04/3.28 tff(4190,plain,
% 3.04/3.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.04/3.28 inference(rewrite,[status(thm)],[])).
% 3.04/3.28 tff(4191,plain,
% 3.04/3.28 (((~b(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(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(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(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.04/3.28 inference(rewrite,[status(thm)],[])).
% 3.04/3.28 tff(4192,plain,
% 3.04/3.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(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(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 3.04/3.28 inference(monotonicity,[status(thm)],[4191])).
% 3.04/3.28 tff(4193,plain,
% 3.04/3.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(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(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.04/3.28 inference(transitivity,[status(thm)],[4192, 4190])).
% 3.04/3.28 tff(4194,plain,
% 3.04/3.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(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(s(s(z)))), s(s(s(elem!1))))))),
% 3.04/3.28 inference(quant_inst,[status(thm)],[])).
% 3.04/3.28 tff(4195,plain,
% 3.04/3.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.04/3.28 inference(modus_ponens,[status(thm)],[4194, 4193])).
% 3.04/3.28 tff(4196,plain,
% 3.04/3.28 (~b(s(s(s(elem!1))), elem!1)),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[4195, 178, 3768, 4155, 4177, 4174])).
% 3.04/3.28 tff(4197,plain,
% 3.04/3.28 (r(s(s(s(elem!1))), elem!1)),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[570, 4196, 4189])).
% 3.04/3.28 tff(4198,plain,
% 3.04/3.28 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 3.04/3.28 inference(rewrite,[status(thm)],[])).
% 3.04/3.28 tff(4199,plain,
% 3.04/3.28 (((~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 3.04/3.28 inference(rewrite,[status(thm)],[])).
% 3.04/3.28 tff(4200,plain,
% 3.04/3.28 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 3.04/3.28 inference(monotonicity,[status(thm)],[4199])).
% 3.04/3.28 tff(4201,plain,
% 3.04/3.28 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 3.04/3.28 inference(transitivity,[status(thm)],[4200, 4198])).
% 3.04/3.28 tff(4202,plain,
% 3.04/3.28 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 3.04/3.28 inference(quant_inst,[status(thm)],[])).
% 3.04/3.28 tff(4203,plain,
% 3.04/3.28 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 3.04/3.28 inference(modus_ponens,[status(thm)],[4202, 4201])).
% 3.04/3.28 tff(4204,plain,
% 3.04/3.28 ($false),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[4203, 118, 556, 450, 3859])).
% 3.04/3.28 tff(4205,plain,((~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.28 tff(4206,plain,
% 3.04/3.28 (~r(s(s(s(elem!1))), s(s(z)))),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[4205, 4197, 3777])).
% 3.04/3.28 tff(4207,plain,
% 3.04/3.28 (((~![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))))),
% 3.04/3.28 inference(rewrite,[status(thm)],[])).
% 3.04/3.28 tff(4208,plain,
% 3.04/3.28 ((~![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))))),
% 3.04/3.28 inference(quant_inst,[status(thm)],[])).
% 3.04/3.28 tff(4209,plain,
% 3.04/3.28 ((~![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)))),
% 3.04/3.28 inference(modus_ponens,[status(thm)],[4208, 4207])).
% 3.04/3.28 tff(4210,plain,
% 3.04/3.28 (b(s(s(s(elem!1))), s(s(z)))),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[4209, 41, 4206, 4181])).
% 3.04/3.28 tff(4211,plain,
% 3.04/3.28 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)))),
% 3.04/3.28 inference(rewrite,[status(thm)],[])).
% 3.04/3.28 tff(4212,plain,
% 3.04/3.28 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(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)))),
% 3.04/3.28 inference(rewrite,[status(thm)],[])).
% 3.04/3.28 tff(4213,plain,
% 3.04/3.28 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1))))),
% 3.04/3.28 inference(monotonicity,[status(thm)],[4212])).
% 3.04/3.28 tff(4214,plain,
% 3.04/3.28 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)))),
% 3.04/3.28 inference(transitivity,[status(thm)],[4213, 4211])).
% 3.04/3.28 tff(4215,plain,
% 3.04/3.28 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 3.04/3.28 inference(quant_inst,[status(thm)],[])).
% 3.04/3.28 tff(4216,plain,
% 3.04/3.28 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1))),
% 3.04/3.28 inference(modus_ponens,[status(thm)],[4215, 4214])).
% 3.04/3.28 tff(4217,plain,
% 3.04/3.28 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[4216, 118, 4197, 3788])).
% 3.04/3.28 tff(4218,assumption,(~b(s(s(z)), s(s(s(elem!1))))), introduced(assumption)).
% 3.04/3.28 tff(4219,plain,
% 3.04/3.28 (((~![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)))))),
% 3.04/3.28 inference(rewrite,[status(thm)],[])).
% 3.04/3.28 tff(4220,plain,
% 3.04/3.28 ((~![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)))))),
% 3.04/3.28 inference(quant_inst,[status(thm)],[])).
% 3.04/3.28 tff(4221,plain,
% 3.04/3.28 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1))))),
% 3.04/3.28 inference(modus_ponens,[status(thm)],[4220, 4219])).
% 3.04/3.28 tff(4222,plain,
% 3.04/3.28 ($false),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[4221, 41, 1683, 1836, 4218])).
% 3.04/3.28 tff(4223,plain,(b(s(s(z)), s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.28 tff(4224,plain,
% 3.04/3.28 (b(s(s(z)), s(s(s(elem!1))))),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[4223, 4217])).
% 3.04/3.28 tff(4225,plain,
% 3.04/3.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.04/3.28 inference(rewrite,[status(thm)],[])).
% 3.04/3.28 tff(4226,plain,
% 3.04/3.28 (((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.04/3.28 inference(rewrite,[status(thm)],[])).
% 3.04/3.28 tff(4227,plain,
% 3.04/3.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 3.04/3.28 inference(monotonicity,[status(thm)],[4226])).
% 3.04/3.28 tff(4228,plain,
% 3.04/3.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.04/3.28 inference(transitivity,[status(thm)],[4227, 4225])).
% 3.04/3.28 tff(4229,plain,
% 3.04/3.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 3.04/3.28 inference(quant_inst,[status(thm)],[])).
% 3.04/3.28 tff(4230,plain,
% 3.04/3.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.04/3.29 inference(modus_ponens,[status(thm)],[4229, 4228])).
% 3.04/3.29 tff(4231,plain,
% 3.04/3.29 (~b(s(s(z)), s(s(s(s(z)))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[4230, 178, 4224, 4210, 4177, 4174])).
% 3.04/3.29 tff(4232,plain,
% 3.04/3.29 (r(s(s(z)), s(s(s(s(z)))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[164, 4231])).
% 3.04/3.29 tff(4233,plain,
% 3.04/3.29 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[3488, 4232, 47, 3250])).
% 3.04/3.29 tff(4234,plain,
% 3.04/3.29 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[84, 4233])).
% 3.04/3.29 tff(4235,assumption,(~b(z, s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 3.04/3.29 tff(4236,plain,
% 3.04/3.29 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[271, 4235])).
% 3.04/3.29 tff(4237,plain,
% 3.04/3.29 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[212, 4236, 145])).
% 3.04/3.29 tff(4238,plain,
% 3.04/3.29 (b(z, elem!1) <=> b(z, s(s(s(s(s(s(s(z))))))))),
% 3.04/3.29 inference(monotonicity,[status(thm)],[679])).
% 3.04/3.29 tff(4239,plain,
% 3.04/3.29 (b(z, s(s(s(s(s(s(s(z)))))))) <=> b(z, elem!1)),
% 3.04/3.29 inference(symmetry,[status(thm)],[4238])).
% 3.04/3.29 tff(4240,plain,
% 3.04/3.29 ((~b(z, s(s(s(s(s(s(s(z))))))))) <=> (~b(z, elem!1))),
% 3.04/3.29 inference(monotonicity,[status(thm)],[4239])).
% 3.04/3.29 tff(4241,plain,
% 3.04/3.29 (~b(z, elem!1)),
% 3.04/3.29 inference(modus_ponens,[status(thm)],[4235, 4240])).
% 3.04/3.29 tff(4242,plain,
% 3.04/3.29 ($false),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[818, 4241])).
% 3.04/3.29 tff(4243,plain,((~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | b(z, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.29 tff(4244,plain,
% 3.04/3.29 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[4243, 4235, 818])).
% 3.04/3.29 tff(4245,plain,
% 3.04/3.29 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[703, 701])).
% 3.04/3.29 tff(4246,plain,
% 3.04/3.29 (~r(elem!1, s(s(s(s(z)))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[3785, 1042, 193])).
% 3.04/3.29 tff(4247,plain,
% 3.04/3.29 (b(elem!1, s(s(s(s(z)))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[483, 4246, 469])).
% 3.04/3.29 tff(4248,plain,
% 3.04/3.29 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[3928, 178, 104, 3771, 4247, 251])).
% 3.04/3.29 tff(4249,plain,
% 3.04/3.29 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[3444, 4248, 4245])).
% 3.04/3.29 tff(4250,plain,
% 3.04/3.29 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), 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))))))),
% 3.04/3.29 inference(rewrite,[status(thm)],[])).
% 3.04/3.29 tff(4251,plain,
% 3.04/3.29 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.04/3.29 inference(quant_inst,[status(thm)],[])).
% 3.04/3.29 tff(4252,plain,
% 3.04/3.29 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 3.04/3.29 inference(modus_ponens,[status(thm)],[4251, 4250])).
% 3.04/3.29 tff(4253,plain,
% 3.04/3.29 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[4252, 118, 556, 4249])).
% 3.04/3.29 tff(4254,plain,
% 3.04/3.29 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[3502, 551])).
% 3.04/3.29 tff(4255,plain,
% 3.04/3.29 (b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[3524, 41, 4254, 4253])).
% 3.04/3.29 tff(4256,plain,
% 3.04/3.29 (r(s(s(z)), elem!1)),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[448, 12, 3241])).
% 3.04/3.29 tff(4257,plain,
% 3.04/3.29 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[2956, 118, 4256, 4249])).
% 3.04/3.29 tff(4258,plain,
% 3.04/3.29 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[3578, 4257])).
% 3.04/3.29 tff(4259,plain,
% 3.04/3.29 (~r(s(s(s(elem!1))), s(s(z)))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[4205, 1042, 556])).
% 3.04/3.29 tff(4260,plain,
% 3.04/3.29 (b(s(s(s(elem!1))), s(s(z)))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[4209, 41, 4259, 4181])).
% 3.04/3.29 tff(4261,plain,
% 3.04/3.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.29 inference(rewrite,[status(thm)],[])).
% 3.04/3.29 tff(4262,plain,
% 3.04/3.29 (((~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(elem!1, s(s(s(s(z)))))) | (~b(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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.29 inference(rewrite,[status(thm)],[])).
% 3.04/3.29 tff(4263,plain,
% 3.04/3.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.04/3.29 inference(monotonicity,[status(thm)],[4262])).
% 3.04/3.29 tff(4264,plain,
% 3.04/3.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.29 inference(transitivity,[status(thm)],[4263, 4261])).
% 3.04/3.29 tff(4265,plain,
% 3.04/3.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 3.04/3.29 inference(quant_inst,[status(thm)],[])).
% 3.04/3.29 tff(4266,plain,
% 3.04/3.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.04/3.29 inference(modus_ponens,[status(thm)],[4265, 4264])).
% 3.04/3.29 tff(4267,plain,
% 3.04/3.29 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[4266, 178, 104, 3771, 4247, 251])).
% 3.04/3.29 tff(4268,plain,
% 3.04/3.29 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[691, 4267, 701])).
% 3.04/3.29 tff(4269,plain,
% 3.04/3.29 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[2803, 4268, 4256])).
% 3.04/3.29 tff(4270,plain,
% 3.04/3.29 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[249, 4269])).
% 3.04/3.29 tff(4271,plain,
% 3.04/3.29 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[4216, 118, 556, 4256])).
% 3.04/3.29 tff(4272,plain,
% 3.04/3.29 (b(s(s(z)), s(s(s(elem!1))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[4223, 4271])).
% 3.04/3.29 tff(4273,plain,
% 3.04/3.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(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(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(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(elem!1))))))),
% 3.04/3.29 inference(rewrite,[status(thm)],[])).
% 3.04/3.29 tff(4274,plain,
% 3.04/3.29 (((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), 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(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(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(elem!1))))))),
% 3.04/3.29 inference(rewrite,[status(thm)],[])).
% 3.04/3.29 tff(4275,plain,
% 3.04/3.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(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(elem!1)))))))),
% 3.04/3.29 inference(monotonicity,[status(thm)],[4274])).
% 3.04/3.29 tff(4276,plain,
% 3.04/3.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(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(elem!1))))))),
% 3.04/3.29 inference(transitivity,[status(thm)],[4275, 4273])).
% 3.04/3.29 tff(4277,plain,
% 3.04/3.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.29 inference(quant_inst,[status(thm)],[])).
% 3.04/3.29 tff(4278,plain,
% 3.04/3.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 3.04/3.29 inference(modus_ponens,[status(thm)],[4277, 4276])).
% 3.04/3.29 tff(4279,plain,
% 3.04/3.29 ($false),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[4278, 178, 4272, 4270, 4260, 4258, 4255])).
% 3.04/3.29 tff(4280,plain,((s(s(z)) = elem!1) | (~r(s(s(s(elem!1))), elem!1)) | (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)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | b(elem!1, s(s(z))) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.04/3.29 tff(4281,plain,
% 3.04/3.29 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[4280, 4244, 12, 556, 3771, 104, 469, 193, 461, 3241])).
% 3.04/3.29 tff(4282,plain,
% 3.04/3.29 ($false),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[222, 4281, 4237])).
% 3.04/3.29 tff(4283,plain,(b(z, s(s(s(s(s(s(s(z)))))))) | (s(s(z)) = elem!1) | (~r(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (elem!1 = s(s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | b(elem!1, s(s(z))) | b(s(s(z)), elem!1) | (~r(z, s(s(s(s(z)))))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.29 tff(4284,plain,
% 3.04/3.29 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[4283, 3775, 4197, 3768, 4234, 4154, 103, 461, 3241, 47, 4153])).
% 3.04/3.29 tff(4285,plain,
% 3.04/3.29 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[1309, 4284, 4153, 4155, 4234])).
% 3.04/3.29 tff(4286,plain,
% 3.04/3.29 (~(s(s(s(s(z)))) = elem!1)),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[504, 4154])).
% 3.04/3.29 tff(4287,plain,
% 3.04/3.29 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[3502, 4286])).
% 3.04/3.29 tff(4288,plain,
% 3.04/3.29 (r(elem!1, s(s(s(elem!1))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[2054, 4188, 3240])).
% 3.04/3.29 tff(4289,assumption,(~b(elem!1, s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 3.04/3.29 tff(4290,plain,
% 3.04/3.29 (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 3.04/3.29 inference(modus_ponens,[status(thm)],[3521, 3541])).
% 3.04/3.29 tff(4291,assumption,(b(s(s(z)), s(s(s(elem!1))))), introduced(assumption)).
% 3.04/3.29 tff(4292,plain,
% 3.04/3.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.04/3.29 inference(rewrite,[status(thm)],[])).
% 3.04/3.29 tff(4293,plain,
% 3.04/3.29 (((~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(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(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(z)), s(s(s(elem!1)))))) <=> ((~b(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(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.04/3.29 inference(rewrite,[status(thm)],[])).
% 3.04/3.29 tff(4294,plain,
% 3.04/3.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(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(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(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(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 3.04/3.29 inference(monotonicity,[status(thm)],[4293])).
% 3.04/3.29 tff(4295,plain,
% 3.04/3.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(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(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(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(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.04/3.29 inference(transitivity,[status(thm)],[4294, 4292])).
% 3.04/3.29 tff(4296,plain,
% 3.04/3.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(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(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(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(z)), s(s(s(elem!1))))))),
% 3.04/3.29 inference(quant_inst,[status(thm)],[])).
% 3.04/3.29 tff(4297,plain,
% 3.04/3.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.04/3.29 inference(modus_ponens,[status(thm)],[4296, 4295])).
% 3.04/3.29 tff(4298,plain,
% 3.04/3.29 (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[4297, 178, 4291, 104, 166, 3831])).
% 3.04/3.29 tff(4299,plain,
% 3.04/3.29 ((s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))) | r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[3612, 41, 4298])).
% 3.04/3.29 tff(4300,plain,
% 3.04/3.29 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[4299, 4290])).
% 3.04/3.29 tff(4301,plain,
% 3.04/3.29 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[3623, 4300, 3311])).
% 3.04/3.29 tff(4302,plain,
% 3.04/3.29 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[691, 4301, 4289])).
% 3.04/3.29 tff(4303,plain,
% 3.04/3.29 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.29 inference(monotonicity,[status(thm)],[4302])).
% 3.04/3.29 tff(4304,plain,
% 3.04/3.29 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(z)), elem!1)),
% 3.04/3.29 inference(symmetry,[status(thm)],[4303])).
% 3.04/3.29 tff(4305,plain,
% 3.04/3.29 (b(s(s(z)), elem!1)),
% 3.04/3.29 inference(modus_ponens,[status(thm)],[166, 4304])).
% 3.04/3.29 tff(4306,plain,
% 3.04/3.29 ($false),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[3241, 4305])).
% 3.04/3.29 tff(4307,plain,((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | b(s(s(z)), elem!1) | b(elem!1, s(s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(elem!1))))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.29 tff(4308,plain,
% 3.04/3.29 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[4307, 4285, 3241, 4288, 4287, 4224, 4234, 4174])).
% 3.04/3.29 tff(4309,plain,
% 3.04/3.29 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[249, 4308])).
% 3.04/3.29 tff(4310,plain,
% 3.04/3.29 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[2803, 4309, 3788])).
% 3.04/3.29 tff(4311,plain,
% 3.04/3.29 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[691, 4310, 4285])).
% 3.04/3.29 tff(4312,plain,
% 3.04/3.29 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 3.04/3.29 inference(monotonicity,[status(thm)],[4311])).
% 3.04/3.29 tff(4313,plain,
% 3.04/3.29 (s(s(elem!1)) = s(s(s(s(s(s(s(s(s(z)))))))))),
% 3.04/3.29 inference(monotonicity,[status(thm)],[4312])).
% 3.04/3.29 tff(4314,plain,
% 3.04/3.29 (s(s(s(elem!1))) = s(s(s(s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.29 inference(monotonicity,[status(thm)],[4313])).
% 3.04/3.29 tff(4315,plain,
% 3.04/3.29 ((s(s(s(s(z)))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(s(z)))))),
% 3.04/3.29 inference(commutativity,[status(thm)],[])).
% 3.04/3.29 tff(4316,plain,
% 3.04/3.29 ((s(s(s(s(elem!1)))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(s(elem!1)))))),
% 3.04/3.29 inference(symmetry,[status(thm)],[4315])).
% 3.04/3.29 tff(4317,plain,
% 3.04/3.29 ((~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(s(s(elem!1))))))),
% 3.04/3.29 inference(monotonicity,[status(thm)],[4316])).
% 3.04/3.29 tff(4318,plain,
% 3.04/3.29 ((s(s(elem!1)) = s(s(z))) <=> (s(s(s(s(s(s(s(s(s(z))))))))) = s(s(z)))),
% 3.04/3.29 inference(monotonicity,[status(thm)],[4313])).
% 3.04/3.29 tff(4319,plain,
% 3.04/3.29 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(s(s(s(s(s(s(s(z))))))))) = s(s(z))))),
% 3.04/3.29 inference(monotonicity,[status(thm)],[4318])).
% 3.04/3.29 tff(4320,plain,
% 3.04/3.29 (~(s(s(elem!1)) = s(s(z)))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[2386, 3787])).
% 3.04/3.29 tff(4321,plain,
% 3.04/3.29 (~(s(s(s(s(s(s(s(s(s(z))))))))) = s(s(z)))),
% 3.04/3.29 inference(modus_ponens,[status(thm)],[4320, 4319])).
% 3.04/3.29 tff(4322,assumption,(s(s(s(s(elem!1)))) = s(s(s(s(z))))), introduced(assumption)).
% 3.04/3.29 tff(4323,plain,
% 3.04/3.29 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 3.04/3.29 inference(symmetry,[status(thm)],[4322])).
% 3.04/3.29 tff(4324,plain,
% 3.04/3.29 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(elem!1)))))),
% 3.04/3.29 inference(monotonicity,[status(thm)],[4323])).
% 3.04/3.29 tff(4325,plain,
% 3.04/3.29 (s(s(s(z))) = s(s(s(s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.29 inference(transitivity,[status(thm)],[61, 4324, 946, 2847])).
% 3.04/3.29 tff(4326,plain,
% 3.04/3.29 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 3.04/3.29 inference(monotonicity,[status(thm)],[4325])).
% 3.04/3.29 tff(4327,plain,
% 3.04/3.29 (inj_0(s(s(s(s(s(s(s(s(s(s(z))))))))))) = inj_0(s(s(s(z))))),
% 3.04/3.29 inference(symmetry,[status(thm)],[4326])).
% 3.04/3.29 tff(4328,plain,
% 3.04/3.29 (s(s(s(s(s(s(s(s(s(z))))))))) = inj_0(s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 3.04/3.29 inference(symmetry,[status(thm)],[2845])).
% 3.04/3.29 tff(4329,plain,
% 3.04/3.29 (s(s(s(s(s(s(s(s(s(z))))))))) = s(s(z))),
% 3.04/3.29 inference(transitivity,[status(thm)],[4328, 4327, 65])).
% 3.04/3.29 tff(4330,assumption,(~(s(s(s(s(s(s(s(s(s(z))))))))) = s(s(z)))), introduced(assumption)).
% 3.04/3.29 tff(4331,plain,
% 3.04/3.29 ($false),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[4330, 4329])).
% 3.04/3.29 tff(4332,plain,((~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))) | (s(s(s(s(s(s(s(s(s(z))))))))) = s(s(z))) | (~(elem!1 = s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.29 tff(4333,plain,
% 3.04/3.29 (~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[4332, 4321, 4311])).
% 3.04/3.29 tff(4334,plain,
% 3.04/3.29 (~(s(s(s(s(z)))) = s(s(s(s(elem!1)))))),
% 3.04/3.29 inference(modus_ponens,[status(thm)],[4333, 4317])).
% 3.04/3.29 tff(4335,plain,
% 3.04/3.29 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[951, 4189])).
% 3.04/3.29 tff(4336,plain,
% 3.04/3.29 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[1695, 1691])).
% 3.04/3.29 tff(4337,plain,
% 3.04/3.29 (s(s(elem!1)) = s(s(s(elem!1)))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[1657, 4336])).
% 3.04/3.29 tff(4338,plain,
% 3.04/3.29 (s(s(s(elem!1))) = s(elem!1)),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[1649, 4337])).
% 3.04/3.29 tff(4339,plain,
% 3.04/3.29 (s(elem!1) = s(s(s(elem!1)))),
% 3.04/3.29 inference(symmetry,[status(thm)],[4338])).
% 3.04/3.29 tff(4340,plain,
% 3.04/3.29 (s(elem!1) = s(s(s(s(elem!1))))),
% 3.04/3.29 inference(transitivity,[status(thm)],[4339, 1691])).
% 3.04/3.29 tff(4341,assumption,(~(s(elem!1) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 3.04/3.29 tff(4342,plain,
% 3.04/3.29 ($false),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[4341, 4340])).
% 3.04/3.29 tff(4343,plain,((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) | (s(elem!1) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.29 tff(4344,plain,
% 3.04/3.29 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[4343, 4335])).
% 3.04/3.29 tff(4345,plain,
% 3.04/3.29 (s(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(s(elem!1)))),
% 3.04/3.29 inference(symmetry,[status(thm)],[2847])).
% 3.04/3.29 tff(4346,plain,
% 3.04/3.29 (r(z, s(s(s(s(s(s(s(s(s(s(z))))))))))) <=> r(z, s(s(s(elem!1))))),
% 3.04/3.29 inference(monotonicity,[status(thm)],[4345])).
% 3.04/3.29 tff(4347,plain,
% 3.04/3.29 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 3.04/3.29 inference(symmetry,[status(thm)],[4346])).
% 3.04/3.29 tff(4348,plain,
% 3.04/3.29 (r(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 3.04/3.29 inference(modus_ponens,[status(thm)],[557, 4347])).
% 3.04/3.29 tff(4349,plain,
% 3.04/3.29 (r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.04/3.29 inference(monotonicity,[status(thm)],[4345])).
% 3.04/3.29 tff(4350,plain,
% 3.04/3.29 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(elem!1)))))),
% 3.04/3.29 inference(symmetry,[status(thm)],[4349])).
% 3.04/3.29 tff(4351,assumption,(b(s(s(s(elem!1))), s(s(z)))), introduced(assumption)).
% 3.04/3.29 tff(4352,plain,
% 3.04/3.29 (~(elem!1 = s(s(s(s(elem!1)))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[3901, 3898, 461])).
% 3.04/3.29 tff(4353,plain,
% 3.04/3.29 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[1509, 4352])).
% 3.04/3.29 tff(4354,plain,
% 3.04/3.29 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[1649, 4353])).
% 3.04/3.29 tff(4355,plain,
% 3.04/3.29 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[1657, 4354])).
% 3.04/3.29 tff(4356,plain,
% 3.04/3.29 (b(elem!1, z) <=> b(s(s(s(s(s(s(s(z))))))), z)),
% 3.04/3.29 inference(monotonicity,[status(thm)],[679])).
% 3.04/3.29 tff(4357,plain,
% 3.04/3.29 (~r(elem!1, z)),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[3421, 3311, 557])).
% 3.04/3.29 tff(4358,plain,
% 3.04/3.29 (b(elem!1, z)),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[498, 4357, 3873])).
% 3.04/3.29 tff(4359,plain,
% 3.04/3.29 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.04/3.29 inference(modus_ponens,[status(thm)],[4358, 4356])).
% 3.04/3.29 tff(4360,plain,
% 3.04/3.29 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 3.04/3.29 inference(monotonicity,[status(thm)],[680])).
% 3.04/3.29 tff(4361,plain,
% 3.04/3.29 ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) <=> (~r(elem!1, s(s(s(s(elem!1))))))),
% 3.04/3.29 inference(monotonicity,[status(thm)],[4360])).
% 3.04/3.29 tff(4362,plain,
% 3.04/3.29 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z))))))))))) <=> r(elem!1, s(s(s(elem!1))))),
% 3.04/3.29 inference(monotonicity,[status(thm)],[680, 4345])).
% 3.04/3.29 tff(4363,plain,
% 3.04/3.29 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 3.04/3.29 inference(symmetry,[status(thm)],[4362])).
% 3.04/3.29 tff(4364,plain,
% 3.04/3.29 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 3.04/3.29 inference(modus_ponens,[status(thm)],[3311, 4363])).
% 3.04/3.29 tff(4365,plain,
% 3.04/3.29 (r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(s(s(z))))))))))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.04/3.29 inference(monotonicity,[status(thm)],[4345])).
% 3.04/3.29 tff(4366,plain,
% 3.04/3.29 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 3.04/3.29 inference(symmetry,[status(thm)],[4365])).
% 3.04/3.29 tff(4367,plain,
% 3.04/3.29 (r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 3.04/3.29 inference(modus_ponens,[status(thm)],[3630, 4366])).
% 3.04/3.29 tff(4368,plain,
% 3.04/3.29 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 3.04/3.30 inference(rewrite,[status(thm)],[])).
% 3.04/3.30 tff(4369,plain,
% 3.04/3.30 (((~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 3.04/3.30 inference(rewrite,[status(thm)],[])).
% 3.04/3.30 tff(4370,plain,
% 3.04/3.30 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(s(s(z))))))))))))))),
% 3.14/3.30 inference(monotonicity,[status(thm)],[4369])).
% 3.14/3.30 tff(4371,plain,
% 3.14/3.30 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 3.14/3.30 inference(transitivity,[status(thm)],[4370, 4368])).
% 3.14/3.30 tff(4372,plain,
% 3.14/3.30 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))),
% 3.14/3.30 inference(quant_inst,[status(thm)],[])).
% 3.14/3.30 tff(4373,plain,
% 3.14/3.30 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(s(s(z))))))))))))),
% 3.14/3.30 inference(modus_ponens,[status(thm)],[4372, 4371])).
% 3.14/3.30 tff(4374,plain,
% 3.14/3.30 ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(s(s(z))))))))))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[4373, 118])).
% 3.14/3.30 tff(4375,plain,
% 3.14/3.30 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[4374, 4367, 4364])).
% 3.14/3.30 tff(4376,plain,
% 3.14/3.30 (~r(elem!1, s(s(s(s(elem!1)))))),
% 3.14/3.30 inference(modus_ponens,[status(thm)],[4375, 4361])).
% 3.14/3.30 tff(4377,plain,
% 3.14/3.30 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 3.14/3.30 inference(monotonicity,[status(thm)],[680])).
% 3.14/3.30 tff(4378,plain,
% 3.14/3.30 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) <=> (~b(elem!1, s(s(s(s(elem!1))))))),
% 3.14/3.30 inference(monotonicity,[status(thm)],[4377])).
% 3.14/3.30 tff(4379,plain,
% 3.14/3.30 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 3.14/3.30 inference(rewrite,[status(thm)],[])).
% 3.14/3.30 tff(4380,plain,
% 3.14/3.30 (((~r(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(elem!1)))), z))) <=> ((~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 3.14/3.30 inference(rewrite,[status(thm)],[])).
% 3.14/3.30 tff(4381,plain,
% 3.14/3.30 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(s(s(z))))))))))))))),
% 3.14/3.30 inference(monotonicity,[status(thm)],[4380])).
% 3.14/3.30 tff(4382,plain,
% 3.14/3.30 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 3.14/3.30 inference(transitivity,[status(thm)],[4381, 4379])).
% 3.14/3.30 tff(4383,plain,
% 3.14/3.30 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 3.14/3.30 inference(quant_inst,[status(thm)],[])).
% 3.14/3.30 tff(4384,plain,
% 3.14/3.30 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(s(s(z))))))))))))),
% 3.14/3.30 inference(modus_ponens,[status(thm)],[4383, 4382])).
% 3.14/3.30 tff(4385,plain,
% 3.14/3.30 ((~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(s(s(z))))))))))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[4384, 118])).
% 3.14/3.30 tff(4386,plain,
% 3.14/3.30 (~r(s(s(s(s(elem!1)))), z)),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[4385, 4367, 4348])).
% 3.14/3.30 tff(4387,plain,
% 3.14/3.30 (b(s(s(s(s(elem!1)))), z)),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[1716, 4386])).
% 3.14/3.30 tff(4388,plain,
% 3.14/3.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.14/3.30 inference(rewrite,[status(thm)],[])).
% 3.14/3.30 tff(4389,plain,
% 3.14/3.30 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.14/3.30 inference(rewrite,[status(thm)],[])).
% 3.14/3.30 tff(4390,plain,
% 3.14/3.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 3.14/3.30 inference(monotonicity,[status(thm)],[4389])).
% 3.14/3.30 tff(4391,plain,
% 3.14/3.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.14/3.30 inference(transitivity,[status(thm)],[4390, 4388])).
% 3.14/3.30 tff(4392,plain,
% 3.14/3.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))),
% 3.14/3.30 inference(quant_inst,[status(thm)],[])).
% 3.14/3.30 tff(4393,plain,
% 3.14/3.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 3.14/3.30 inference(modus_ponens,[status(thm)],[4392, 4391])).
% 3.14/3.30 tff(4394,plain,
% 3.14/3.30 ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1))))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[4393, 178, 273, 3898, 146])).
% 3.14/3.30 tff(4395,plain,
% 3.14/3.30 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[4394, 4387])).
% 3.14/3.30 tff(4396,plain,
% 3.14/3.30 (~b(elem!1, s(s(s(s(elem!1)))))),
% 3.14/3.30 inference(modus_ponens,[status(thm)],[4395, 4378])).
% 3.14/3.30 tff(4397,plain,
% 3.14/3.30 ($false),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[1465, 4396, 4376, 1507])).
% 3.14/3.30 tff(4398,plain,((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (elem!1 = s(s(s(s(elem!1))))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.30 tff(4399,plain,
% 3.14/3.30 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[4398, 4352, 679, 273, 3898, 4359, 557, 3311])).
% 3.14/3.30 tff(4400,plain,
% 3.14/3.30 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[1988, 4399, 4355])).
% 3.14/3.30 tff(4401,assumption,(b(s(s(s(elem!1))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 3.14/3.30 tff(4402,plain,
% 3.14/3.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 3.14/3.30 inference(rewrite,[status(thm)],[])).
% 3.14/3.30 tff(4403,plain,
% 3.14/3.30 (((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 3.14/3.30 inference(rewrite,[status(thm)],[])).
% 3.14/3.30 tff(4404,plain,
% 3.14/3.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z))))))),
% 3.14/3.30 inference(monotonicity,[status(thm)],[4403])).
% 3.14/3.30 tff(4405,plain,
% 3.14/3.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 3.14/3.30 inference(transitivity,[status(thm)],[4404, 4402])).
% 3.14/3.30 tff(4406,plain,
% 3.14/3.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 3.14/3.30 inference(quant_inst,[status(thm)],[])).
% 3.14/3.30 tff(4407,plain,
% 3.14/3.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 3.14/3.30 inference(modus_ponens,[status(thm)],[4406, 4405])).
% 3.14/3.30 tff(4408,plain,
% 3.14/3.30 ($false),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[4407, 178, 3898, 4291, 4401, 3709, 4351])).
% 3.14/3.30 tff(4409,plain,((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.30 tff(4410,plain,
% 3.14/3.30 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[4409, 4400, 4291, 4351, 3898])).
% 3.14/3.30 tff(4411,plain,
% 3.14/3.30 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[1750, 4410, 1858])).
% 3.14/3.30 tff(4412,plain,
% 3.14/3.30 (r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(elem!1)))))),
% 3.14/3.30 inference(modus_ponens,[status(thm)],[4411, 4350])).
% 3.14/3.30 tff(4413,plain,
% 3.14/3.30 ((z = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = z)),
% 3.14/3.30 inference(commutativity,[status(thm)],[])).
% 3.14/3.30 tff(4414,plain,
% 3.14/3.30 ((s(s(s(s(elem!1)))) = z) <=> (z = s(s(s(s(elem!1)))))),
% 3.14/3.30 inference(symmetry,[status(thm)],[4413])).
% 3.14/3.30 tff(4415,plain,
% 3.14/3.30 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(z = s(s(s(s(elem!1))))))),
% 3.14/3.30 inference(monotonicity,[status(thm)],[4414])).
% 3.14/3.30 tff(4416,plain,
% 3.14/3.30 (~(z = s(s(s(s(elem!1)))))),
% 3.14/3.30 inference(modus_ponens,[status(thm)],[1712, 4415])).
% 3.14/3.30 tff(4417,plain,
% 3.14/3.30 (b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z))))))))))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 3.14/3.30 inference(monotonicity,[status(thm)],[4345])).
% 3.14/3.30 tff(4418,plain,
% 3.14/3.30 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 3.14/3.30 inference(symmetry,[status(thm)],[4417])).
% 3.14/3.30 tff(4419,plain,
% 3.14/3.30 (b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 3.14/3.30 inference(modus_ponens,[status(thm)],[4291, 4418])).
% 3.14/3.30 tff(4420,plain,
% 3.14/3.30 (b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(s(s(z))))))))))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.14/3.30 inference(monotonicity,[status(thm)],[4345])).
% 3.14/3.30 tff(4421,plain,
% 3.14/3.30 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 3.14/3.30 inference(symmetry,[status(thm)],[4420])).
% 3.14/3.30 tff(4422,plain,
% 3.14/3.30 (b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 3.14/3.30 inference(modus_ponens,[status(thm)],[4400, 4421])).
% 3.14/3.30 tff(4423,plain,
% 3.14/3.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 3.14/3.30 inference(rewrite,[status(thm)],[])).
% 3.14/3.30 tff(4424,plain,
% 3.14/3.30 (((~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 3.14/3.30 inference(rewrite,[status(thm)],[])).
% 3.14/3.30 tff(4425,plain,
% 3.14/3.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(s(s(z))))))))))))))),
% 3.14/3.30 inference(monotonicity,[status(thm)],[4424])).
% 3.14/3.30 tff(4426,plain,
% 3.14/3.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 3.14/3.30 inference(transitivity,[status(thm)],[4425, 4423])).
% 3.14/3.30 tff(4427,plain,
% 3.14/3.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))))),
% 3.14/3.31 inference(quant_inst,[status(thm)],[])).
% 3.14/3.31 tff(4428,plain,
% 3.14/3.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(s(s(z))))))))))))),
% 3.14/3.31 inference(modus_ponens,[status(thm)],[4427, 4426])).
% 3.14/3.31 tff(4429,plain,
% 3.14/3.31 (~b(z, s(s(s(s(elem!1)))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[4428, 178, 273, 3898, 4422, 4419])).
% 3.14/3.31 tff(4430,plain,
% 3.14/3.31 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1))))))),
% 3.14/3.31 inference(rewrite,[status(thm)],[])).
% 3.14/3.31 tff(4431,plain,
% 3.14/3.31 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1))))))),
% 3.14/3.31 inference(quant_inst,[status(thm)],[])).
% 3.14/3.31 tff(4432,plain,
% 3.14/3.31 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1)))))),
% 3.14/3.31 inference(modus_ponens,[status(thm)],[4431, 4430])).
% 3.14/3.31 tff(4433,plain,
% 3.14/3.31 ((z = s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1)))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[4432, 41, 4429])).
% 3.14/3.31 tff(4434,plain,
% 3.14/3.31 (r(z, s(s(s(s(elem!1)))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[4433, 4416])).
% 3.14/3.31 tff(4435,plain,
% 3.14/3.31 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(elem!1)))))))),
% 3.14/3.31 inference(rewrite,[status(thm)],[])).
% 3.14/3.31 tff(4436,plain,
% 3.14/3.31 (((~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(s(s(s(s(s(z))))))))))))) <=> ((~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(elem!1)))))))),
% 3.14/3.31 inference(rewrite,[status(thm)],[])).
% 3.14/3.31 tff(4437,plain,
% 3.14/3.31 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(elem!1))))))))),
% 3.14/3.31 inference(monotonicity,[status(thm)],[4436])).
% 3.14/3.31 tff(4438,plain,
% 3.14/3.31 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(elem!1)))))))),
% 3.14/3.31 inference(transitivity,[status(thm)],[4437, 4435])).
% 3.14/3.31 tff(4439,plain,
% 3.14/3.31 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 3.14/3.31 inference(quant_inst,[status(thm)],[])).
% 3.14/3.31 tff(4440,plain,
% 3.14/3.31 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(elem!1))))))),
% 3.14/3.31 inference(modus_ponens,[status(thm)],[4439, 4438])).
% 3.14/3.31 tff(4441,plain,
% 3.14/3.31 ((~r(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(elem!1))))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[4440, 118, 4434])).
% 3.14/3.31 tff(4442,plain,
% 3.14/3.31 ($false),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[4441, 4412, 4348])).
% 3.14/3.31 tff(4443,plain,((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~r(elem!1, s(s(s(elem!1))))) | b(elem!1, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.31 tff(4444,plain,
% 3.14/3.31 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[4443, 4311, 3243, 3271, 4344, 4224, 4210, 4288, 461])).
% 3.14/3.31 tff(4445,plain,
% 3.14/3.31 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[1170, 4444])).
% 3.14/3.31 tff(4446,plain,
% 3.14/3.31 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 3.14/3.31 inference(rewrite,[status(thm)],[])).
% 3.14/3.31 tff(4447,plain,
% 3.14/3.31 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 3.14/3.31 inference(quant_inst,[status(thm)],[])).
% 3.14/3.31 tff(4448,plain,
% 3.14/3.31 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))),
% 3.14/3.31 inference(modus_ponens,[status(thm)],[4447, 4446])).
% 3.14/3.31 tff(4449,plain,
% 3.14/3.31 (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[4448, 118, 4445, 103])).
% 3.14/3.31 tff(4450,plain,
% 3.14/3.31 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(elem!1))))) | b(s(s(s(s(z)))), s(s(s(s(elem!1))))) | r(s(s(s(s(z)))), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(elem!1))))) | b(s(s(s(s(z)))), s(s(s(s(elem!1))))) | r(s(s(s(s(z)))), s(s(s(s(elem!1))))))),
% 3.14/3.31 inference(rewrite,[status(thm)],[])).
% 3.14/3.31 tff(4451,plain,
% 3.14/3.31 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(elem!1))))) | b(s(s(s(s(z)))), s(s(s(s(elem!1))))) | r(s(s(s(s(z)))), s(s(s(s(elem!1))))))),
% 3.14/3.31 inference(quant_inst,[status(thm)],[])).
% 3.14/3.31 tff(4452,plain,
% 3.14/3.31 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(elem!1))))) | b(s(s(s(s(z)))), s(s(s(s(elem!1))))) | r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 3.14/3.31 inference(modus_ponens,[status(thm)],[4451, 4450])).
% 3.14/3.31 tff(4453,plain,
% 3.14/3.31 ((s(s(s(s(z)))) = s(s(s(s(elem!1))))) | b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[4452, 41, 4449])).
% 3.14/3.31 tff(4454,plain,
% 3.14/3.31 (b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[4453, 4334])).
% 3.14/3.31 tff(4455,plain,
% 3.14/3.31 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 3.14/3.31 inference(rewrite,[status(thm)],[])).
% 3.14/3.31 tff(4456,plain,
% 3.14/3.31 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 3.14/3.31 inference(rewrite,[status(thm)],[])).
% 3.14/3.31 tff(4457,plain,
% 3.14/3.31 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))))),
% 3.14/3.31 inference(monotonicity,[status(thm)],[4456])).
% 3.14/3.31 tff(4458,plain,
% 3.14/3.31 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 3.14/3.31 inference(transitivity,[status(thm)],[4457, 4455])).
% 3.14/3.31 tff(4459,plain,
% 3.14/3.31 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 3.14/3.31 inference(quant_inst,[status(thm)],[])).
% 3.14/3.31 tff(4460,plain,
% 3.14/3.31 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 3.14/3.31 inference(modus_ponens,[status(thm)],[4459, 4458])).
% 3.14/3.31 tff(4461,plain,
% 3.14/3.31 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[4460, 118, 4445, 103])).
% 3.14/3.31 tff(4462,plain,
% 3.14/3.31 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(s(z))))) | b(s(s(s(s(elem!1)))), s(s(s(s(z))))) | r(s(s(s(s(elem!1)))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(s(z))))) | b(s(s(s(s(elem!1)))), s(s(s(s(z))))) | r(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 3.14/3.31 inference(rewrite,[status(thm)],[])).
% 3.14/3.31 tff(4463,plain,
% 3.14/3.31 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(s(z))))) | b(s(s(s(s(elem!1)))), s(s(s(s(z))))) | r(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 3.14/3.31 inference(quant_inst,[status(thm)],[])).
% 3.14/3.31 tff(4464,plain,
% 3.14/3.31 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(s(z))))) | b(s(s(s(s(elem!1)))), s(s(s(s(z))))) | r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 3.14/3.31 inference(modus_ponens,[status(thm)],[4463, 4462])).
% 3.14/3.31 tff(4465,plain,
% 3.14/3.31 ((s(s(s(s(elem!1)))) = s(s(s(s(z))))) | b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[4464, 41, 4461])).
% 3.14/3.31 tff(4466,plain,
% 3.14/3.31 (b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[4465, 4333])).
% 3.14/3.31 tff(4467,plain,
% 3.14/3.31 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[3559, 4309, 103])).
% 3.14/3.31 tff(4468,plain,
% 3.14/3.31 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[222, 4467])).
% 3.14/3.31 tff(4469,plain,
% 3.14/3.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 3.14/3.31 inference(rewrite,[status(thm)],[])).
% 3.14/3.31 tff(4470,plain,
% 3.14/3.31 (((~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(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(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(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 3.14/3.31 inference(rewrite,[status(thm)],[])).
% 3.14/3.31 tff(4471,plain,
% 3.14/3.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))))),
% 3.14/3.31 inference(monotonicity,[status(thm)],[4470])).
% 3.14/3.31 tff(4472,plain,
% 3.14/3.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 3.14/3.31 inference(transitivity,[status(thm)],[4471, 4469])).
% 3.14/3.31 tff(4473,plain,
% 3.14/3.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 3.14/3.31 inference(quant_inst,[status(thm)],[])).
% 3.14/3.31 tff(4474,plain,
% 3.14/3.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 3.14/3.31 inference(modus_ponens,[status(thm)],[4473, 4472])).
% 3.14/3.31 tff(4475,plain,
% 3.14/3.31 ((~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[4474, 178, 4234, 4468, 4466])).
% 3.14/3.31 tff(4476,plain,
% 3.14/3.31 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[4475, 4454])).
% 3.14/3.31 tff(4477,plain,
% 3.14/3.31 (r(elem!1, s(s(z))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.14/3.31 inference(monotonicity,[status(thm)],[4311])).
% 3.14/3.31 tff(4478,plain,
% 3.14/3.31 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.14/3.31 inference(modus_ponens,[status(thm)],[3777, 4477])).
% 3.14/3.31 tff(4479,plain,
% 3.14/3.31 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 3.14/3.31 inference(rewrite,[status(thm)],[])).
% 3.14/3.31 tff(4480,plain,
% 3.14/3.31 (((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 3.14/3.31 inference(rewrite,[status(thm)],[])).
% 3.14/3.31 tff(4481,plain,
% 3.14/3.31 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))))),
% 3.14/3.31 inference(monotonicity,[status(thm)],[4480])).
% 3.14/3.31 tff(4482,plain,
% 3.14/3.31 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 3.14/3.31 inference(transitivity,[status(thm)],[4481, 4479])).
% 3.14/3.31 tff(4483,plain,
% 3.14/3.31 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 3.14/3.31 inference(quant_inst,[status(thm)],[])).
% 3.14/3.31 tff(4484,plain,
% 3.14/3.31 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))),
% 3.14/3.31 inference(modus_ponens,[status(thm)],[4483, 4482])).
% 3.14/3.31 tff(4485,plain,
% 3.14/3.31 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[4484, 118, 4445, 4478])).
% 3.14/3.31 tff(4486,plain,
% 3.14/3.31 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))) | r(s(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(s(elem!1)))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))),
% 3.14/3.31 inference(rewrite,[status(thm)],[])).
% 3.14/3.31 tff(4487,plain,
% 3.14/3.31 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))),
% 3.14/3.31 inference(quant_inst,[status(thm)],[])).
% 3.14/3.31 tff(4488,plain,
% 3.14/3.31 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))),
% 3.14/3.31 inference(modus_ponens,[status(thm)],[4487, 4486])).
% 3.14/3.31 tff(4489,plain,
% 3.14/3.31 ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[4488, 41, 4485])).
% 3.14/3.31 tff(4490,plain,
% 3.14/3.31 (s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(z)))))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[4489, 4476])).
% 3.14/3.31 tff(4491,plain,
% 3.14/3.31 (s(s(s(s(s(s(s(z))))))) = s(s(s(s(elem!1))))),
% 3.14/3.31 inference(symmetry,[status(thm)],[4490])).
% 3.14/3.31 tff(4492,plain,
% 3.14/3.31 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(s(s(elem!1)))))),
% 3.14/3.31 inference(monotonicity,[status(thm)],[4491])).
% 3.14/3.31 tff(4493,plain,
% 3.14/3.31 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(s(s(s(s(z))))))))))),
% 3.14/3.31 inference(transitivity,[status(thm)],[609, 4492, 946, 4314])).
% 3.14/3.31 tff(4494,plain,
% 3.14/3.31 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 3.14/3.31 inference(monotonicity,[status(thm)],[4493])).
% 3.14/3.31 tff(4495,plain,
% 3.14/3.31 (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(s(s(z)))))))))),
% 3.14/3.31 inference(transitivity,[status(thm)],[239, 4494, 2845])).
% 3.14/3.31 tff(4496,plain,
% 3.14/3.31 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(s(s(s(s(s(z))))))))))),
% 3.14/3.31 inference(monotonicity,[status(thm)],[4495])).
% 3.14/3.31 tff(4497,plain,
% 3.14/3.31 (s(s(s(s(z)))) = s(s(s(s(s(s(s(s(z))))))))),
% 3.14/3.31 inference(transitivity,[status(thm)],[663, 4496, 2843])).
% 3.14/3.31 tff(4498,plain,
% 3.14/3.31 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(s(s(z)))))))))),
% 3.14/3.31 inference(monotonicity,[status(thm)],[4497])).
% 3.14/3.31 tff(4499,plain,
% 3.14/3.31 (inj_0(s(s(s(s(s(s(s(s(z))))))))) = inj_0(s(s(s(s(z)))))),
% 3.14/3.31 inference(symmetry,[status(thm)],[4498])).
% 3.14/3.31 tff(4500,plain,
% 3.14/3.31 (s(s(s(s(s(s(s(z))))))) = s(s(s(z)))),
% 3.14/3.31 inference(transitivity,[status(thm)],[2829, 4499, 11])).
% 3.14/3.31 tff(4501,plain,
% 3.14/3.31 ($false),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[1104, 4500])).
% 3.14/3.31 tff(4502,plain,(b(s(s(s(s(z)))), s(s(z))) | b(elem!1, s(s(z))) | b(s(s(z)), elem!1) | b(elem!1, s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | b(z, s(s(s(s(z))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.31 tff(4503,plain,
% 3.14/3.31 (b(s(s(s(s(z)))), s(s(z)))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[4502, 3242, 3241, 3240, 461, 1, 3244])).
% 3.14/3.31 tff(4504,plain,
% 3.14/3.31 (b(s(s(s(s(z)))), s(s(z))) <=> b(elem!1, s(s(z)))),
% 3.14/3.31 inference(monotonicity,[status(thm)],[331])).
% 3.14/3.31 tff(4505,plain,
% 3.14/3.31 (b(elem!1, s(s(z))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 3.14/3.31 inference(symmetry,[status(thm)],[4504])).
% 3.14/3.31 tff(4506,plain,
% 3.14/3.31 ((~b(elem!1, s(s(z)))) <=> (~b(s(s(s(s(z)))), s(s(z))))),
% 3.14/3.31 inference(monotonicity,[status(thm)],[4505])).
% 3.14/3.31 tff(4507,plain,
% 3.14/3.31 (~b(s(s(s(s(z)))), s(s(z)))),
% 3.14/3.31 inference(modus_ponens,[status(thm)],[461, 4506])).
% 3.14/3.31 tff(4508,plain,
% 3.14/3.31 ($false),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[202, 4507])).
% 3.14/3.31 tff(4509,plain,((~(s(s(s(s(z)))) = elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | b(elem!1, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.31 tff(4510,plain,
% 3.14/3.31 (~(s(s(s(s(z)))) = elem!1)),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[4509, 202, 461])).
% 3.14/3.31 tff(4511,plain,
% 3.14/3.31 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[3502, 4510])).
% 3.14/3.31 tff(4512,assumption,(~r(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 3.14/3.31 tff(4513,plain,
% 3.14/3.31 (elem!1 = s(s(s(elem!1)))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[2054, 4512, 3240])).
% 3.14/3.31 tff(4514,plain,
% 3.14/3.31 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(elem!1))))),
% 3.14/3.31 inference(monotonicity,[status(thm)],[4513])).
% 3.14/3.31 tff(4515,plain,
% 3.14/3.31 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 3.14/3.31 inference(symmetry,[status(thm)],[4514])).
% 3.14/3.31 tff(4516,plain,
% 3.14/3.31 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(z)) = elem!1))),
% 3.14/3.31 inference(monotonicity,[status(thm)],[4515])).
% 3.14/3.31 tff(4517,plain,
% 3.14/3.31 (~(s(s(z)) = elem!1)),
% 3.14/3.31 inference(modus_ponens,[status(thm)],[1683, 4516])).
% 3.14/3.31 tff(4518,plain,
% 3.14/3.31 (r(s(s(z)), elem!1)),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[448, 4517, 3241])).
% 3.14/3.31 tff(4519,plain,
% 3.14/3.31 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[3259, 3243, 145])).
% 3.14/3.31 tff(4520,plain,
% 3.14/3.31 (~(elem!1 = s(s(s(s(z)))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[325, 4510])).
% 3.14/3.31 tff(4521,plain,
% 3.14/3.31 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[4168, 2834])).
% 3.14/3.31 tff(4522,plain,
% 3.14/3.31 (~b(elem!1, s(s(s(s(z)))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[4162, 4521, 3240])).
% 3.14/3.31 tff(4523,plain,
% 3.14/3.31 (r(elem!1, s(s(s(s(z)))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[483, 4522, 4520])).
% 3.14/3.31 tff(4524,plain,
% 3.14/3.31 (~r(elem!1, z)),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[478, 4523, 145])).
% 3.14/3.31 tff(4525,plain,
% 3.14/3.31 (s(elem!1) = s(s(z))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[2840, 2834])).
% 3.14/3.31 tff(4526,plain,
% 3.14/3.31 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 3.14/3.31 inference(monotonicity,[status(thm)],[4525])).
% 3.14/3.31 tff(4527,plain,
% 3.14/3.31 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 3.14/3.31 inference(symmetry,[status(thm)],[4526])).
% 3.14/3.31 tff(4528,plain,
% 3.14/3.31 (s(z) = elem!1),
% 3.14/3.31 inference(transitivity,[status(thm)],[71, 4527, 304])).
% 3.14/3.31 tff(4529,plain,
% 3.14/3.31 ((s(z) = z) <=> (elem!1 = z)),
% 3.14/3.31 inference(monotonicity,[status(thm)],[4528])).
% 3.14/3.31 tff(4530,plain,
% 3.14/3.31 ((s(z) = z) <=> (z = elem!1)),
% 3.14/3.31 inference(transitivity,[status(thm)],[4529, 313])).
% 3.14/3.31 tff(4531,plain,
% 3.14/3.31 ((s(z) = z) <=> (elem!1 = z)),
% 3.14/3.31 inference(transitivity,[status(thm)],[4530, 314])).
% 3.14/3.31 tff(4532,plain,
% 3.14/3.31 ((~(s(z) = z)) <=> (~(elem!1 = z))),
% 3.14/3.31 inference(monotonicity,[status(thm)],[4531])).
% 3.14/3.31 tff(4533,plain,
% 3.14/3.31 (~(elem!1 = z)),
% 3.14/3.31 inference(modus_ponens,[status(thm)],[1476, 4532])).
% 3.14/3.31 tff(4534,plain,
% 3.14/3.31 (b(elem!1, z)),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[498, 4533, 4524])).
% 3.14/3.31 tff(4535,plain,
% 3.14/3.31 (elem!1 = s(z)),
% 3.14/3.31 inference(transitivity,[status(thm)],[517, 4526, 70])).
% 3.14/3.31 tff(4536,plain,
% 3.14/3.31 (r(elem!1, z) <=> r(s(z), z)),
% 3.14/3.31 inference(monotonicity,[status(thm)],[4535])).
% 3.14/3.31 tff(4537,plain,
% 3.14/3.31 ((~r(elem!1, z)) <=> (~r(s(z), z))),
% 3.14/3.31 inference(monotonicity,[status(thm)],[4536])).
% 3.14/3.31 tff(4538,plain,
% 3.14/3.31 (~r(s(z), z)),
% 3.14/3.31 inference(modus_ponens,[status(thm)],[4524, 4537])).
% 3.14/3.31 tff(4539,plain,
% 3.14/3.31 (((~![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))),
% 3.14/3.31 inference(rewrite,[status(thm)],[])).
% 3.14/3.31 tff(4540,plain,
% 3.14/3.31 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))),
% 3.14/3.31 inference(quant_inst,[status(thm)],[])).
% 3.14/3.31 tff(4541,plain,
% 3.14/3.31 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z)),
% 3.14/3.31 inference(modus_ponens,[status(thm)],[4540, 4539])).
% 3.14/3.31 tff(4542,plain,
% 3.14/3.31 (b(s(z), z)),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[4541, 41, 1476, 4538])).
% 3.14/3.31 tff(4543,plain,
% 3.14/3.31 (r(s(z), s(s(s(s(z))))) <=> r(elem!1, s(s(s(elem!1))))),
% 3.14/3.31 inference(monotonicity,[status(thm)],[4528, 4521])).
% 3.14/3.31 tff(4544,plain,
% 3.14/3.31 (r(elem!1, s(s(s(elem!1)))) <=> r(s(z), s(s(s(s(z)))))),
% 3.14/3.31 inference(symmetry,[status(thm)],[4543])).
% 3.14/3.31 tff(4545,plain,
% 3.14/3.31 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(s(s(elem!1))))),
% 3.14/3.31 inference(monotonicity,[status(thm)],[4521])).
% 3.14/3.31 tff(4546,plain,
% 3.14/3.31 (r(elem!1, s(s(s(elem!1))))),
% 3.14/3.31 inference(modus_ponens,[status(thm)],[4523, 4545])).
% 3.14/3.31 tff(4547,plain,
% 3.14/3.31 (r(s(z), s(s(s(s(z)))))),
% 3.14/3.31 inference(modus_ponens,[status(thm)],[4546, 4544])).
% 3.14/3.31 tff(4548,plain,
% 3.14/3.31 (b(z, elem!1) <=> b(z, s(z))),
% 3.14/3.31 inference(monotonicity,[status(thm)],[4535])).
% 3.14/3.32 tff(4549,plain,
% 3.14/3.32 (~r(z, elem!1)),
% 3.14/3.32 inference(unit_resolution,[status(thm)],[529, 4523, 145])).
% 3.14/3.32 tff(4550,plain,
% 3.14/3.32 ((~(s(z) = z)) <=> (~(z = elem!1))),
% 3.14/3.32 inference(monotonicity,[status(thm)],[4530])).
% 3.14/3.32 tff(4551,plain,
% 3.14/3.32 (~(z = elem!1)),
% 3.14/3.32 inference(modus_ponens,[status(thm)],[1476, 4550])).
% 3.14/3.32 tff(4552,plain,
% 3.14/3.32 (b(z, elem!1)),
% 3.14/3.32 inference(unit_resolution,[status(thm)],[585, 4551, 4549])).
% 3.14/3.32 tff(4553,plain,
% 3.14/3.32 (b(z, s(z))),
% 3.14/3.32 inference(modus_ponens,[status(thm)],[4552, 4548])).
% 3.14/3.32 tff(4554,assumption,(r(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 3.14/3.32 tff(4555,plain,
% 3.14/3.32 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 3.14/3.32 inference(rewrite,[status(thm)],[])).
% 3.14/3.32 tff(4556,plain,
% 3.14/3.32 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 3.14/3.32 inference(rewrite,[status(thm)],[])).
% 3.14/3.32 tff(4557,plain,
% 3.14/3.32 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))))),
% 3.14/3.32 inference(monotonicity,[status(thm)],[4556])).
% 3.14/3.32 tff(4558,plain,
% 3.14/3.32 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 3.14/3.32 inference(transitivity,[status(thm)],[4557, 4555])).
% 3.14/3.32 tff(4559,plain,
% 3.14/3.32 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.14/3.32 inference(quant_inst,[status(thm)],[])).
% 3.14/3.32 tff(4560,plain,
% 3.14/3.32 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))),
% 3.14/3.32 inference(modus_ponens,[status(thm)],[4559, 4558])).
% 3.14/3.32 tff(4561,plain,
% 3.14/3.32 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.14/3.32 inference(unit_resolution,[status(thm)],[4560, 118, 1130, 4554])).
% 3.14/3.32 tff(4562,plain,
% 3.14/3.32 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.14/3.32 inference(unit_resolution,[status(thm)],[615, 41, 612, 4561])).
% 3.14/3.32 tff(4563,plain,
% 3.14/3.32 ($false),
% 3.14/3.32 inference(unit_resolution,[status(thm)],[601, 178, 1145, 1791, 1790, 3462, 4562])).
% 3.14/3.32 tff(4564,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.32 tff(4565,plain,
% 3.14/3.32 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.14/3.32 inference(unit_resolution,[status(thm)],[4564, 4553, 145, 4547, 4542])).
% 3.14/3.32 tff(4566,plain,
% 3.14/3.32 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.14/3.32 inference(unit_resolution,[status(thm)],[84, 4565])).
% 3.14/3.32 tff(4567,plain,
% 3.14/3.32 ((s(elem!1) = elem!1) <=> (s(s(z)) = elem!1)),
% 3.14/3.32 inference(monotonicity,[status(thm)],[4525])).
% 3.14/3.32 tff(4568,plain,
% 3.14/3.32 ((~(s(elem!1) = elem!1)) <=> (~(s(s(z)) = elem!1))),
% 3.14/3.32 inference(monotonicity,[status(thm)],[4567])).
% 3.14/3.32 tff(4569,plain,
% 3.14/3.32 (~(elem!1 = s(s(s(s(elem!1)))))),
% 3.14/3.32 inference(unit_resolution,[status(thm)],[1422, 4525])).
% 3.14/3.32 tff(4570,plain,
% 3.14/3.32 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.14/3.32 inference(unit_resolution,[status(thm)],[1509, 4569])).
% 3.14/3.32 tff(4571,plain,
% 3.14/3.32 (~(elem!1 = s(s(elem!1)))),
% 3.14/3.32 inference(unit_resolution,[status(thm)],[1539, 4570])).
% 3.14/3.32 tff(4572,plain,
% 3.14/3.32 (~(s(s(elem!1)) = elem!1)),
% 3.14/3.32 inference(unit_resolution,[status(thm)],[1546, 4571])).
% 3.14/3.32 tff(4573,plain,
% 3.14/3.32 (~(s(elem!1) = elem!1)),
% 3.14/3.32 inference(unit_resolution,[status(thm)],[672, 4572])).
% 3.14/3.32 tff(4574,plain,
% 3.14/3.32 (~(s(s(z)) = elem!1)),
% 3.14/3.32 inference(modus_ponens,[status(thm)],[4573, 4568])).
% 3.14/3.32 tff(4575,plain,
% 3.14/3.32 (r(s(s(z)), elem!1)),
% 3.14/3.32 inference(unit_resolution,[status(thm)],[448, 4574, 3241])).
% 3.14/3.32 tff(4576,plain,
% 3.14/3.32 ((s(z) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 3.14/3.32 inference(monotonicity,[status(thm)],[4528])).
% 3.14/3.32 tff(4577,plain,
% 3.14/3.32 ((s(z) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 3.14/3.32 inference(transitivity,[status(thm)],[4576, 1611])).
% 3.14/3.32 tff(4578,plain,
% 3.14/3.32 ((s(s(z)) = elem!1) <=> (s(z) = s(s(z)))),
% 3.14/3.32 inference(symmetry,[status(thm)],[4577])).
% 3.14/3.32 tff(4579,plain,
% 3.14/3.32 ((~(s(s(z)) = elem!1)) <=> (~(s(z) = s(s(z))))),
% 3.14/3.32 inference(monotonicity,[status(thm)],[4578])).
% 3.14/3.32 tff(4580,plain,
% 3.14/3.32 (~(s(z) = s(s(z)))),
% 3.14/3.32 inference(modus_ponens,[status(thm)],[4574, 4579])).
% 3.14/3.32 tff(4581,plain,
% 3.14/3.32 (b(s(z), s(s(z))) <=> b(elem!1, s(s(z)))),
% 3.14/3.32 inference(monotonicity,[status(thm)],[4528])).
% 3.14/3.32 tff(4582,plain,
% 3.14/3.32 (b(elem!1, s(s(z))) <=> b(s(z), s(s(z)))),
% 3.14/3.32 inference(symmetry,[status(thm)],[4581])).
% 3.14/3.32 tff(4583,plain,
% 3.14/3.32 ((~b(elem!1, s(s(z)))) <=> (~b(s(z), s(s(z))))),
% 3.14/3.32 inference(monotonicity,[status(thm)],[4582])).
% 3.14/3.32 tff(4584,plain,
% 3.14/3.32 (~b(s(z), s(s(z)))),
% 3.14/3.32 inference(modus_ponens,[status(thm)],[461, 4583])).
% 3.14/3.32 tff(4585,plain,
% 3.14/3.32 (r(s(z), s(s(z)))),
% 3.14/3.32 inference(unit_resolution,[status(thm)],[1619, 41, 4584, 4580])).
% 3.14/3.32 tff(4586,plain,
% 3.14/3.32 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.14/3.32 inference(rewrite,[status(thm)],[])).
% 3.14/3.32 tff(4587,plain,
% 3.14/3.32 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.14/3.32 inference(rewrite,[status(thm)],[])).
% 3.14/3.32 tff(4588,plain,
% 3.14/3.32 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 3.14/3.32 inference(monotonicity,[status(thm)],[4587])).
% 3.14/3.32 tff(4589,plain,
% 3.14/3.32 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.14/3.32 inference(transitivity,[status(thm)],[4588, 4586])).
% 3.14/3.32 tff(4590,plain,
% 3.14/3.32 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))),
% 3.14/3.32 inference(quant_inst,[status(thm)],[])).
% 3.14/3.32 tff(4591,plain,
% 3.14/3.32 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 3.14/3.32 inference(modus_ponens,[status(thm)],[4590, 4589])).
% 3.14/3.32 tff(4592,plain,
% 3.14/3.32 ($false),
% 3.14/3.32 inference(unit_resolution,[status(thm)],[4591, 118, 147, 2624, 4554])).
% 3.14/3.32 tff(4593,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.32 tff(4594,plain,
% 3.14/3.32 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.14/3.32 inference(unit_resolution,[status(thm)],[4593, 4585, 4547])).
% 3.14/3.32 tff(4595,plain,
% 3.14/3.32 (b(s(s(z)), s(s(s(s(z)))))),
% 3.14/3.32 inference(unit_resolution,[status(thm)],[164, 4594])).
% 3.14/3.32 tff(4596,plain,
% 3.14/3.32 (b(s(elem!1), elem!1) <=> b(s(s(z)), elem!1)),
% 3.14/3.32 inference(monotonicity,[status(thm)],[4525])).
% 3.14/3.32 tff(4597,plain,
% 3.14/3.32 (b(s(s(z)), elem!1) <=> b(s(elem!1), elem!1)),
% 3.14/3.32 inference(symmetry,[status(thm)],[4596])).
% 3.14/3.32 tff(4598,plain,
% 3.14/3.32 ((~b(s(s(z)), elem!1)) <=> (~b(s(elem!1), elem!1))),
% 3.14/3.32 inference(monotonicity,[status(thm)],[4597])).
% 3.14/3.32 tff(4599,plain,
% 3.14/3.32 (~b(s(elem!1), elem!1)),
% 3.14/3.32 inference(modus_ponens,[status(thm)],[3241, 4598])).
% 3.14/3.32 tff(4600,plain,
% 3.14/3.32 (r(s(elem!1), elem!1)),
% 3.14/3.32 inference(unit_resolution,[status(thm)],[677, 4599, 4573])).
% 3.14/3.32 tff(4601,plain,
% 3.14/3.32 (r(s(s(s(s(z)))), z) <=> r(s(s(s(elem!1))), z)),
% 3.14/3.32 inference(monotonicity,[status(thm)],[4521])).
% 3.14/3.32 tff(4602,plain,
% 3.14/3.32 (r(s(s(s(elem!1))), z)),
% 3.14/3.32 inference(modus_ponens,[status(thm)],[194, 4601])).
% 3.14/3.32 tff(4603,plain,
% 3.14/3.32 (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))))))))),
% 3.14/3.32 inference(monotonicity,[status(thm)],[4156])).
% 3.14/3.32 tff(4604,plain,
% 3.14/3.32 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.14/3.32 inference(modus_ponens,[status(thm)],[223, 4603])).
% 3.14/3.32 tff(4605,plain,
% 3.14/3.32 (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(elem!1))))),
% 3.14/3.32 inference(monotonicity,[status(thm)],[4156])).
% 3.14/3.32 tff(4606,plain,
% 3.14/3.32 (b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.14/3.32 inference(modus_ponens,[status(thm)],[104, 4605])).
% 3.14/3.32 tff(4607,plain,
% 3.14/3.32 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 3.14/3.32 inference(monotonicity,[status(thm)],[4156])).
% 3.14/3.32 tff(4608,plain,
% 3.14/3.32 (b(s(s(s(elem!1))), s(s(z)))),
% 3.14/3.32 inference(modus_ponens,[status(thm)],[202, 4607])).
% 3.14/3.32 tff(4609,plain,
% 3.14/3.32 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 3.14/3.32 inference(monotonicity,[status(thm)],[4156])).
% 3.14/3.32 tff(4610,plain,
% 3.14/3.32 (b(s(s(z)), s(s(s(elem!1))))),
% 3.14/3.32 inference(modus_ponens,[status(thm)],[167, 4609])).
% 3.14/3.32 tff(4611,plain,
% 3.14/3.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(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))))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(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))))))), s(s(s(elem!1))))))),
% 3.14/3.32 inference(rewrite,[status(thm)],[])).
% 3.14/3.32 tff(4612,plain,
% 3.14/3.32 (((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), 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))))))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(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))))))), s(s(s(elem!1))))))),
% 3.14/3.32 inference(rewrite,[status(thm)],[])).
% 3.14/3.32 tff(4613,plain,
% 3.14/3.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(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))))))), s(s(s(elem!1)))))))),
% 3.14/3.32 inference(monotonicity,[status(thm)],[4612])).
% 3.14/3.32 tff(4614,plain,
% 3.14/3.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(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))))))), s(s(s(elem!1))))))),
% 3.14/3.32 inference(transitivity,[status(thm)],[4613, 4611])).
% 3.14/3.32 tff(4615,plain,
% 3.14/3.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 3.14/3.32 inference(quant_inst,[status(thm)],[])).
% 3.14/3.32 tff(4616,plain,
% 3.14/3.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(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))))))), s(s(s(elem!1)))))),
% 3.14/3.32 inference(modus_ponens,[status(thm)],[4615, 4614])).
% 3.14/3.32 tff(4617,plain,
% 3.14/3.32 ((~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(z))))),
% 3.14/3.32 inference(unit_resolution,[status(thm)],[4616, 178, 4610, 4608, 4606])).
% 3.14/3.32 tff(4618,plain,
% 3.14/3.32 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.14/3.32 inference(unit_resolution,[status(thm)],[4617, 4604])).
% 3.14/3.32 tff(4619,plain,
% 3.14/3.32 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.14/3.32 inference(unit_resolution,[status(thm)],[3578, 4618])).
% 3.14/3.32 tff(4620,plain,
% 3.14/3.32 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.14/3.32 inference(unit_resolution,[status(thm)],[259, 223, 202, 167, 104])).
% 3.14/3.32 tff(4621,plain,
% 3.14/3.32 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.14/3.32 inference(unit_resolution,[status(thm)],[249, 4620])).
% 3.14/3.32 tff(4622,plain,
% 3.14/3.32 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.14/3.32 inference(unit_resolution,[status(thm)],[2803, 4621, 438])).
% 3.14/3.32 tff(4623,plain,
% 3.14/3.32 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.14/3.32 inference(unit_resolution,[status(thm)],[691, 4622, 701])).
% 3.14/3.32 tff(4624,plain,
% 3.14/3.32 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.14/3.32 inference(modus_ponens,[status(thm)],[4623, 2617])).
% 3.14/3.32 tff(4625,plain,
% 3.14/3.32 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 3.14/3.32 inference(commutativity,[status(thm)],[])).
% 3.14/3.32 tff(4626,plain,
% 3.14/3.32 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 3.14/3.32 inference(monotonicity,[status(thm)],[4156])).
% 3.14/3.32 tff(4627,plain,
% 3.14/3.32 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 3.14/3.32 inference(symmetry,[status(thm)],[4626])).
% 3.14/3.32 tff(4628,plain,
% 3.14/3.32 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))),
% 3.14/3.32 inference(monotonicity,[status(thm)],[4627])).
% 3.14/3.32 tff(4629,plain,
% 3.14/3.32 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 3.14/3.32 inference(transitivity,[status(thm)],[4628, 4625])).
% 3.14/3.32 tff(4630,plain,
% 3.14/3.32 ((s(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(elem!1)))))),
% 3.14/3.32 inference(symmetry,[status(thm)],[4629])).
% 3.14/3.32 tff(4631,plain,
% 3.14/3.32 ((~(s(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(elem!1))))))),
% 3.14/3.32 inference(monotonicity,[status(thm)],[4630])).
% 3.14/3.32 tff(4632,plain,
% 3.14/3.32 ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 3.14/3.32 inference(monotonicity,[status(thm)],[4627])).
% 3.14/3.32 tff(4633,plain,
% 3.14/3.32 ((~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))))),
% 3.14/3.32 inference(monotonicity,[status(thm)],[4632])).
% 3.14/3.32 tff(4634,assumption,(s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 3.14/3.32 tff(4635,plain,
% 3.14/3.32 (s(s(s(s(s(s(s(z))))))) = s(s(s(s(elem!1))))),
% 3.14/3.32 inference(symmetry,[status(thm)],[4634])).
% 3.14/3.32 tff(4636,plain,
% 3.14/3.32 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(s(s(elem!1)))))),
% 3.14/3.32 inference(monotonicity,[status(thm)],[4635])).
% 3.14/3.32 tff(4637,plain,
% 3.14/3.32 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 3.14/3.32 inference(symmetry,[status(thm)],[4636])).
% 3.14/3.32 tff(4638,plain,
% 3.14/3.32 (s(s(s(s(z)))) = s(s(s(s(s(s(z))))))),
% 3.14/3.32 inference(transitivity,[status(thm)],[4156, 947, 4637, 57])).
% 3.14/3.32 tff(4639,plain,
% 3.14/3.32 ($false),
% 3.14/3.32 inference(unit_resolution,[status(thm)],[3698, 4638])).
% 3.14/3.32 tff(4640,plain,((~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(z))))))))) | (~(s(s(s(s(z)))) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.32 tff(4641,plain,
% 3.14/3.32 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(z))))))))),
% 3.14/3.32 inference(unit_resolution,[status(thm)],[4640, 4156])).
% 3.14/3.32 tff(4642,plain,
% 3.14/3.32 (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 3.14/3.32 inference(modus_ponens,[status(thm)],[4641, 4633])).
% 3.14/3.32 tff(4643,plain,
% 3.14/3.32 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(elem!1)))))),
% 3.14/3.32 inference(modus_ponens,[status(thm)],[4642, 4631])).
% 3.14/3.32 tff(4644,plain,
% 3.14/3.32 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), 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(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), 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(s(s(s(elem!1)))))))),
% 3.14/3.32 inference(rewrite,[status(thm)],[])).
% 3.14/3.32 tff(4645,plain,
% 3.14/3.32 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), 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(s(s(s(elem!1)))))))),
% 3.14/3.32 inference(quant_inst,[status(thm)],[])).
% 3.14/3.32 tff(4646,plain,
% 3.14/3.32 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), 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(s(s(s(elem!1))))))),
% 3.14/3.32 inference(modus_ponens,[status(thm)],[4645, 4644])).
% 3.14/3.32 tff(4647,plain,
% 3.14/3.32 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))),
% 3.14/3.32 inference(unit_resolution,[status(thm)],[4646, 118, 3636, 107])).
% 3.14/3.32 tff(4648,plain,
% 3.14/3.32 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))),
% 3.14/3.32 inference(unit_resolution,[status(thm)],[3758, 41, 4647])).
% 3.14/3.32 tff(4649,plain,
% 3.14/3.32 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))),
% 3.14/3.32 inference(unit_resolution,[status(thm)],[4648, 4643])).
% 3.14/3.32 tff(4650,plain,
% 3.14/3.32 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 3.14/3.32 inference(monotonicity,[status(thm)],[534])).
% 3.14/3.32 tff(4651,plain,
% 3.14/3.32 ((s(s(s(s(elem!1)))) = s(z)) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 3.14/3.32 inference(transitivity,[status(thm)],[4650, 1409])).
% 3.14/3.32 tff(4652,plain,
% 3.14/3.32 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(z))),
% 3.14/3.32 inference(symmetry,[status(thm)],[4651])).
% 3.14/3.32 tff(4653,plain,
% 3.14/3.32 ((~(elem!1 = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(z)))),
% 3.14/3.32 inference(monotonicity,[status(thm)],[4652])).
% 3.14/3.32 tff(4654,plain,
% 3.14/3.32 (~(s(s(s(s(elem!1)))) = s(z))),
% 3.14/3.32 inference(modus_ponens,[status(thm)],[1423, 4653])).
% 3.14/3.32 tff(4655,plain,
% 3.14/3.32 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(z)))))),
% 3.14/3.32 inference(rewrite,[status(thm)],[])).
% 3.14/3.32 tff(4656,plain,
% 3.14/3.32 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z)))) <=> ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(z)))))),
% 3.14/3.32 inference(rewrite,[status(thm)],[])).
% 3.14/3.32 tff(4657,plain,
% 3.14/3.32 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(z))))))),
% 3.14/3.32 inference(monotonicity,[status(thm)],[4656])).
% 3.14/3.32 tff(4658,plain,
% 3.14/3.32 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(z)))))),
% 3.14/3.32 inference(transitivity,[status(thm)],[4657, 4655])).
% 3.14/3.32 tff(4659,plain,
% 3.14/3.32 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 3.14/3.32 inference(quant_inst,[status(thm)],[])).
% 3.14/3.32 tff(4660,plain,
% 3.14/3.32 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(z))))),
% 3.14/3.32 inference(modus_ponens,[status(thm)],[4659, 4658])).
% 3.14/3.32 tff(4661,plain,
% 3.14/3.32 (~r(s(s(s(s(elem!1)))), s(z))),
% 3.14/3.32 inference(unit_resolution,[status(thm)],[4660, 118, 3636, 2624])).
% 3.14/3.32 tff(4662,plain,
% 3.14/3.32 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z)))),
% 3.14/3.32 inference(rewrite,[status(thm)],[])).
% 3.14/3.32 tff(4663,plain,
% 3.14/3.32 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z)))),
% 3.14/3.32 inference(quant_inst,[status(thm)],[])).
% 3.14/3.32 tff(4664,plain,
% 3.14/3.32 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z))),
% 3.14/3.32 inference(modus_ponens,[status(thm)],[4663, 4662])).
% 3.14/3.32 tff(4665,plain,
% 3.14/3.32 ((s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z))),
% 3.14/3.32 inference(unit_resolution,[status(thm)],[4664, 41, 4661])).
% 3.14/3.32 tff(4666,plain,
% 3.14/3.32 (b(s(s(s(s(elem!1)))), s(z))),
% 3.14/3.32 inference(unit_resolution,[status(thm)],[4665, 4654])).
% 3.14/3.32 tff(4667,plain,
% 3.14/3.32 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))),
% 3.14/3.32 inference(unit_resolution,[status(thm)],[4484, 118, 3636, 107])).
% 3.14/3.32 tff(4668,plain,
% 3.14/3.32 (b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))),
% 3.14/3.32 inference(unit_resolution,[status(thm)],[4488, 41, 4641, 4667])).
% 3.14/3.32 tff(4669,assumption,(b(s(z), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 3.14/3.32 tff(4670,plain,
% 3.14/3.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.14/3.32 inference(rewrite,[status(thm)],[])).
% 3.14/3.32 tff(4671,plain,
% 3.14/3.32 (((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.14/3.32 inference(rewrite,[status(thm)],[])).
% 3.14/3.32 tff(4672,plain,
% 3.14/3.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.14/3.32 inference(monotonicity,[status(thm)],[4671])).
% 3.14/3.32 tff(4673,plain,
% 3.14/3.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.14/3.32 inference(transitivity,[status(thm)],[4672, 4670])).
% 3.14/3.32 tff(4674,plain,
% 3.14/3.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))),
% 3.14/3.33 inference(quant_inst,[status(thm)],[])).
% 3.14/3.33 tff(4675,plain,
% 3.14/3.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.14/3.33 inference(modus_ponens,[status(thm)],[4674, 4673])).
% 3.14/3.33 tff(4676,plain,
% 3.14/3.33 ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1))))))),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[4675, 178, 2642, 4669, 4668])).
% 3.14/3.33 tff(4677,plain,
% 3.14/3.33 ($false),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[4676, 4666, 4649])).
% 3.14/3.33 tff(4678,plain,((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~(s(elem!1) = s(s(z)))) | (~(s(s(s(s(z)))) = s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.33 tff(4679,plain,
% 3.14/3.33 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[4678, 4624, 515, 4156, 4619, 2624])).
% 3.14/3.33 tff(4680,plain,
% 3.14/3.33 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[1170, 4679])).
% 3.14/3.33 tff(4681,plain,
% 3.14/3.33 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[1649, 1510])).
% 3.14/3.33 tff(4682,plain,
% 3.14/3.33 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[1657, 4681])).
% 3.14/3.33 tff(4683,plain,
% 3.14/3.33 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.14/3.33 inference(rewrite,[status(thm)],[])).
% 3.14/3.33 tff(4684,plain,
% 3.14/3.33 (((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.14/3.33 inference(rewrite,[status(thm)],[])).
% 3.14/3.33 tff(4685,plain,
% 3.14/3.33 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 3.14/3.33 inference(monotonicity,[status(thm)],[4684])).
% 3.14/3.33 tff(4686,plain,
% 3.14/3.33 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.14/3.33 inference(transitivity,[status(thm)],[4685, 4683])).
% 3.14/3.33 tff(4687,plain,
% 3.14/3.33 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))))),
% 3.14/3.33 inference(quant_inst,[status(thm)],[])).
% 3.14/3.33 tff(4688,plain,
% 3.14/3.33 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 3.14/3.33 inference(modus_ponens,[status(thm)],[4687, 4686])).
% 3.14/3.33 tff(4689,plain,
% 3.14/3.33 ($false),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[4688, 118, 3261, 224, 203])).
% 3.14/3.33 tff(4690,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.33 tff(4691,plain,
% 3.14/3.33 (~r(z, s(s(z)))),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[4690, 4621, 203])).
% 3.14/3.33 tff(4692,plain,
% 3.14/3.33 (b(z, s(s(z)))),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[143, 4691])).
% 3.14/3.33 tff(4693,plain,
% 3.14/3.33 (~r(s(s(z)), z)),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[232, 4621, 203])).
% 3.14/3.33 tff(4694,plain,
% 3.14/3.33 (b(s(s(z)), z)),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[3249, 4693])).
% 3.14/3.33 tff(4695,plain,
% 3.14/3.33 (b(s(s(s(s(s(z))))), s(s(z)))),
% 3.14/3.33 inference(modus_ponens,[status(thm)],[3898, 1685])).
% 3.14/3.33 tff(4696,assumption,(~b(s(s(s(s(s(z))))), s(s(z)))), introduced(assumption)).
% 3.14/3.33 tff(4697,plain,
% 3.14/3.33 ($false),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[4696, 4695])).
% 3.14/3.33 tff(4698,plain,((~b(s(s(s(s(elem!1)))), s(s(z)))) | b(s(s(s(s(s(z))))), s(s(z))) | (~(s(elem!1) = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.33 tff(4699,plain,
% 3.14/3.33 (b(s(s(s(s(s(z))))), s(s(z)))),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[4698, 4680, 515])).
% 3.14/3.33 tff(4700,plain,
% 3.14/3.33 ((~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(s(z)))))))),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[1817, 178, 167, 202])).
% 3.14/3.33 tff(4701,plain,
% 3.14/3.33 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[4700, 1663, 1851])).
% 3.14/3.33 tff(4702,plain,
% 3.14/3.33 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.14/3.33 inference(modus_ponens,[status(thm)],[4701, 1660])).
% 3.14/3.33 tff(4703,plain,
% 3.14/3.33 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[1988, 4702, 1693])).
% 3.14/3.33 tff(4704,plain,
% 3.14/3.33 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.14/3.33 inference(modus_ponens,[status(thm)],[4703, 1639])).
% 3.14/3.33 tff(4705,plain,
% 3.14/3.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 3.14/3.33 inference(rewrite,[status(thm)],[])).
% 3.14/3.33 tff(4706,plain,
% 3.14/3.33 (((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 3.14/3.33 inference(rewrite,[status(thm)],[])).
% 3.14/3.33 tff(4707,plain,
% 3.14/3.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 3.14/3.33 inference(monotonicity,[status(thm)],[4706])).
% 3.14/3.33 tff(4708,plain,
% 3.14/3.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 3.14/3.33 inference(transitivity,[status(thm)],[4707, 4705])).
% 3.14/3.33 tff(4709,plain,
% 3.14/3.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)))),
% 3.14/3.33 inference(quant_inst,[status(thm)],[])).
% 3.14/3.33 tff(4710,plain,
% 3.14/3.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 3.14/3.33 inference(modus_ponens,[status(thm)],[4709, 4708])).
% 3.14/3.33 tff(4711,plain,
% 3.14/3.33 ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[4710, 178, 3461, 273])).
% 3.14/3.33 tff(4712,plain,
% 3.14/3.33 (~b(z, s(s(s(s(s(z))))))),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[4711, 1663, 1851])).
% 3.14/3.33 tff(4713,plain,
% 3.14/3.33 ((z = s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z))))))),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[1490, 41, 4712])).
% 3.14/3.33 tff(4714,plain,
% 3.14/3.33 (r(z, s(s(s(s(s(z))))))),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[4713, 1408])).
% 3.14/3.33 tff(4715,plain,
% 3.14/3.33 ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z)))))))),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[1997, 118, 145])).
% 3.14/3.33 tff(4716,plain,
% 3.14/3.33 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[4715, 4714])).
% 3.14/3.33 tff(4717,plain,
% 3.14/3.33 ($false),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[4716, 4704])).
% 3.14/3.33 tff(4718,plain,((~b(s(s(s(s(s(z))))), s(s(z)))) | (~(s(elem!1) = s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(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(z)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.33 tff(4719,plain,
% 3.14/3.33 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[4718, 4699, 202, 4694, 4692, 4682, 167, 145, 515])).
% 3.14/3.33 tff(4720,plain,
% 3.14/3.33 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[2136, 4719])).
% 3.14/3.33 tff(4721,plain,
% 3.14/3.33 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 3.14/3.33 inference(modus_ponens,[status(thm)],[4720, 1449])).
% 3.14/3.33 tff(4722,plain,
% 3.14/3.33 (~r(elem!1, s(s(s(s(elem!1)))))),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[1460, 4721, 1426])).
% 3.14/3.33 tff(4723,plain,
% 3.14/3.33 (b(elem!1, s(s(s(s(elem!1)))))),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[1465, 4722, 1423])).
% 3.14/3.33 tff(4724,plain,
% 3.14/3.33 (b(s(z), s(s(s(s(elem!1)))))),
% 3.14/3.33 inference(modus_ponens,[status(thm)],[4723, 1446])).
% 3.14/3.33 tff(4725,plain,
% 3.14/3.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), z)))),
% 3.14/3.33 inference(rewrite,[status(thm)],[])).
% 3.14/3.33 tff(4726,plain,
% 3.14/3.33 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1))))))) <=> ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), z)))),
% 3.14/3.33 inference(rewrite,[status(thm)],[])).
% 3.14/3.33 tff(4727,plain,
% 3.14/3.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), z))))),
% 3.14/3.33 inference(monotonicity,[status(thm)],[4726])).
% 3.14/3.33 tff(4728,plain,
% 3.14/3.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), z)))),
% 3.14/3.33 inference(transitivity,[status(thm)],[4727, 4725])).
% 3.14/3.33 tff(4729,plain,
% 3.14/3.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 3.14/3.33 inference(quant_inst,[status(thm)],[])).
% 3.14/3.33 tff(4730,plain,
% 3.14/3.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), z))),
% 3.14/3.33 inference(modus_ponens,[status(thm)],[4729, 4728])).
% 3.14/3.33 tff(4731,plain,
% 3.14/3.33 ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[4730, 178, 4692, 4680, 1791])).
% 3.14/3.33 tff(4732,plain,
% 3.14/3.33 (~b(s(s(s(s(elem!1)))), z)),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[4731, 4724])).
% 3.14/3.33 tff(4733,plain,
% 3.14/3.33 (r(s(s(s(s(elem!1)))), z)),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[1716, 4732])).
% 3.14/3.33 tff(4734,plain,
% 3.14/3.33 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 3.14/3.33 inference(rewrite,[status(thm)],[])).
% 3.14/3.33 tff(4735,plain,
% 3.14/3.33 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 3.14/3.33 inference(quant_inst,[status(thm)],[])).
% 3.14/3.33 tff(4736,plain,
% 3.14/3.33 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 3.14/3.33 inference(modus_ponens,[status(thm)],[4735, 4734])).
% 3.14/3.33 tff(4737,plain,
% 3.14/3.33 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[4736, 118, 1552, 4733])).
% 3.14/3.33 tff(4738,plain,
% 3.14/3.33 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[1988, 4737, 4682])).
% 3.14/3.33 tff(4739,plain,
% 3.14/3.33 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[1695, 4682])).
% 3.14/3.33 tff(4740,plain,
% 3.14/3.33 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 3.14/3.33 inference(rewrite,[status(thm)],[])).
% 3.14/3.33 tff(4741,plain,
% 3.14/3.33 (((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 3.14/3.33 inference(rewrite,[status(thm)],[])).
% 3.14/3.33 tff(4742,plain,
% 3.14/3.33 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))))),
% 3.14/3.33 inference(monotonicity,[status(thm)],[4741])).
% 3.14/3.33 tff(4743,plain,
% 3.14/3.33 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 3.14/3.33 inference(transitivity,[status(thm)],[4742, 4740])).
% 3.14/3.33 tff(4744,plain,
% 3.14/3.33 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 3.14/3.33 inference(quant_inst,[status(thm)],[])).
% 3.14/3.33 tff(4745,plain,
% 3.14/3.33 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))),
% 3.14/3.33 inference(modus_ponens,[status(thm)],[4744, 4743])).
% 3.14/3.33 tff(4746,plain,
% 3.14/3.33 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[4745, 118, 1552, 4733])).
% 3.14/3.33 tff(4747,plain,
% 3.14/3.33 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[1750, 4746, 4739])).
% 3.14/3.33 tff(4748,plain,
% 3.14/3.33 ($false),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[4409, 4747, 4738, 4610, 4608, 4680])).
% 3.14/3.33 tff(4749,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~(s(elem!1) = s(s(z)))) | (~r(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~(s(s(s(s(z)))) = s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.33 tff(4750,plain,
% 3.14/3.33 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[4749, 4602, 4542, 4525, 4600, 202, 4595, 145, 4521, 4585, 701, 4575, 4566])).
% 3.14/3.33 tff(4751,plain,
% 3.14/3.33 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[271, 4750])).
% 3.14/3.33 tff(4752,plain,
% 3.14/3.33 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.14/3.33 inference(monotonicity,[status(thm)],[4535])).
% 3.14/3.33 tff(4753,plain,
% 3.14/3.33 (r(s(s(s(s(s(s(s(z))))))), s(z)) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.14/3.33 inference(symmetry,[status(thm)],[4752])).
% 3.14/3.33 tff(4754,plain,
% 3.14/3.33 ((~r(s(s(s(s(s(s(s(z))))))), s(z))) <=> (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 3.14/3.33 inference(monotonicity,[status(thm)],[4753])).
% 3.14/3.33 tff(4755,plain,
% 3.14/3.33 (r(s(s(z)), s(z)) <=> r(s(s(z)), elem!1)),
% 3.14/3.33 inference(monotonicity,[status(thm)],[4528])).
% 3.14/3.33 tff(4756,plain,
% 3.14/3.33 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(z))),
% 3.14/3.33 inference(symmetry,[status(thm)],[4755])).
% 3.14/3.33 tff(4757,plain,
% 3.14/3.33 (r(s(s(z)), s(z))),
% 3.14/3.33 inference(modus_ponens,[status(thm)],[4575, 4756])).
% 3.14/3.33 tff(4758,plain,
% 3.14/3.33 (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(elem!1))))),
% 3.14/3.33 inference(monotonicity,[status(thm)],[4521])).
% 3.14/3.33 tff(4759,plain,
% 3.14/3.33 (b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.14/3.33 inference(modus_ponens,[status(thm)],[4566, 4758])).
% 3.14/3.33 tff(4760,plain,
% 3.14/3.33 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 3.14/3.33 inference(monotonicity,[status(thm)],[4521])).
% 3.14/3.33 tff(4761,plain,
% 3.14/3.33 (b(s(s(s(elem!1))), s(s(z)))),
% 3.14/3.33 inference(modus_ponens,[status(thm)],[202, 4760])).
% 3.14/3.33 tff(4762,plain,
% 3.14/3.33 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 3.14/3.33 inference(monotonicity,[status(thm)],[4521])).
% 3.14/3.33 tff(4763,plain,
% 3.14/3.33 (b(s(s(z)), s(s(s(elem!1))))),
% 3.14/3.33 inference(modus_ponens,[status(thm)],[4595, 4762])).
% 3.14/3.33 tff(4764,assumption,(r(s(s(z)), s(z))), introduced(assumption)).
% 3.14/3.33 tff(4765,plain,
% 3.14/3.33 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.14/3.33 inference(monotonicity,[status(thm)],[4156])).
% 3.14/3.33 tff(4766,plain,
% 3.14/3.33 (b(s(s(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))))))))),
% 3.14/3.33 inference(symmetry,[status(thm)],[4603])).
% 3.14/3.33 tff(4767,plain,
% 3.14/3.33 ((~b(s(s(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)))))))))),
% 3.14/3.33 inference(monotonicity,[status(thm)],[4766])).
% 3.14/3.33 tff(4768,plain,
% 3.14/3.33 ((~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(z))))),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[4616, 178, 4291, 4351, 3829])).
% 3.14/3.33 tff(4769,plain,
% 3.14/3.33 (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[4768, 1146])).
% 3.14/3.33 tff(4770,plain,
% 3.14/3.33 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.14/3.33 inference(modus_ponens,[status(thm)],[4769, 4767])).
% 3.14/3.33 tff(4771,plain,
% 3.14/3.33 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[222, 4770])).
% 3.14/3.33 tff(4772,plain,
% 3.14/3.33 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.14/3.33 inference(modus_ponens,[status(thm)],[4771, 4765])).
% 3.14/3.33 tff(4773,plain,
% 3.14/3.33 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[3623, 4772, 3311])).
% 3.14/3.33 tff(4774,plain,
% 3.14/3.33 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[691, 4773, 701])).
% 3.14/3.33 tff(4775,plain,
% 3.14/3.33 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[3672, 4774, 818, 595, 506])).
% 3.14/3.33 tff(4776,plain,
% 3.14/3.33 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[3444, 4775, 4245])).
% 3.14/3.33 tff(4777,plain,
% 3.14/3.33 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.14/3.33 inference(modus_ponens,[status(thm)],[4776, 603])).
% 3.14/3.33 tff(4778,plain,
% 3.14/3.33 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.14/3.33 inference(rewrite,[status(thm)],[])).
% 3.14/3.33 tff(4779,plain,
% 3.14/3.33 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.14/3.33 inference(quant_inst,[status(thm)],[])).
% 3.14/3.33 tff(4780,plain,
% 3.14/3.33 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 3.14/3.33 inference(modus_ponens,[status(thm)],[4779, 4778])).
% 3.14/3.33 tff(4781,plain,
% 3.14/3.33 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[4780, 118, 4777, 4764])).
% 3.14/3.33 tff(4782,plain,
% 3.14/3.33 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[249, 4781])).
% 3.14/3.33 tff(4783,plain,
% 3.14/3.33 ($false),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[4278, 178, 4291, 4782, 4351, 1146, 3829])).
% 3.14/3.33 tff(4784,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~(s(elem!1) = s(s(z)))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(elem!1))))) | (~(s(s(s(s(z)))) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.33 tff(4785,plain,
% 3.14/3.33 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[4784, 4763, 4761, 4759, 4757, 4525, 4552, 4751, 4534, 701, 4546, 4521])).
% 3.14/3.33 tff(4786,plain,
% 3.14/3.33 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[3578, 4785])).
% 3.14/3.33 tff(4787,plain,
% 3.14/3.33 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[2640, 118, 4585, 4786])).
% 3.14/3.33 tff(4788,plain,
% 3.14/3.33 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.14/3.33 inference(modus_ponens,[status(thm)],[4787, 4754])).
% 3.14/3.33 tff(4789,plain,
% 3.14/3.33 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.14/3.33 inference(unit_resolution,[status(thm)],[3444, 4788, 4245])).
% 3.14/3.34 tff(4790,plain,
% 3.14/3.34 (r(s(z), s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.14/3.34 inference(monotonicity,[status(thm)],[4528])).
% 3.14/3.34 tff(4791,plain,
% 3.14/3.34 ((~r(s(z), s(s(s(s(s(s(s(z))))))))) <=> (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.14/3.34 inference(monotonicity,[status(thm)],[4790])).
% 3.14/3.34 tff(4792,plain,
% 3.14/3.34 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[2630, 118, 4585, 4786])).
% 3.14/3.34 tff(4793,plain,
% 3.14/3.34 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.14/3.34 inference(modus_ponens,[status(thm)],[4792, 4791])).
% 3.14/3.34 tff(4794,plain,
% 3.14/3.34 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[691, 4793, 701])).
% 3.14/3.34 tff(4795,plain,
% 3.14/3.34 ($false),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[3672, 4794, 4789, 4552, 4751, 4534])).
% 3.14/3.34 tff(4796,plain,((~(s(s(s(elem!1))) = s(s(s(s(z)))))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))) | b(s(s(z)), elem!1) | b(elem!1, s(s(z))) | (~r(s(s(s(s(z)))), z)) | b(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.34 tff(4797,plain,
% 3.14/3.34 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[4796, 701, 202, 145, 3241, 461, 194, 3240])).
% 3.14/3.34 tff(4798,plain,
% 3.14/3.34 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[4173, 4797, 4519])).
% 3.14/3.34 tff(4799,plain,
% 3.14/3.34 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(s(elem!1)))))),
% 3.14/3.34 inference(monotonicity,[status(thm)],[4164])).
% 3.14/3.34 tff(4800,plain,
% 3.14/3.34 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 3.14/3.34 inference(modus_ponens,[status(thm)],[4797, 4799])).
% 3.14/3.34 tff(4801,plain,
% 3.14/3.34 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[4176, 4800])).
% 3.14/3.34 tff(4802,plain,
% 3.14/3.34 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[3478, 3261, 145])).
% 3.14/3.34 tff(4803,plain,
% 3.14/3.34 (b(s(s(z)), s(s(s(s(z)))))),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[164, 4802])).
% 3.14/3.34 tff(4804,plain,
% 3.14/3.34 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))))),
% 3.14/3.34 inference(rewrite,[status(thm)],[])).
% 3.14/3.34 tff(4805,plain,
% 3.14/3.34 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))))),
% 3.14/3.34 inference(quant_inst,[status(thm)],[])).
% 3.14/3.34 tff(4806,plain,
% 3.14/3.34 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z))))),
% 3.14/3.34 inference(modus_ponens,[status(thm)],[4805, 4804])).
% 3.14/3.34 tff(4807,plain,
% 3.14/3.34 ($false),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[4806, 118, 557, 3261, 1823])).
% 3.14/3.34 tff(4808,plain,((~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.34 tff(4809,plain,
% 3.14/3.34 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[4808, 3261, 557])).
% 3.14/3.34 tff(4810,plain,
% 3.14/3.34 (b(s(s(z)), s(s(s(elem!1))))),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[4223, 4809])).
% 3.14/3.34 tff(4811,plain,
% 3.14/3.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.14/3.34 inference(rewrite,[status(thm)],[])).
% 3.14/3.34 tff(4812,plain,
% 3.14/3.34 (((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.14/3.34 inference(rewrite,[status(thm)],[])).
% 3.14/3.34 tff(4813,plain,
% 3.14/3.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 3.14/3.34 inference(monotonicity,[status(thm)],[4812])).
% 3.14/3.34 tff(4814,plain,
% 3.14/3.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.14/3.34 inference(transitivity,[status(thm)],[4813, 4811])).
% 3.14/3.34 tff(4815,plain,
% 3.14/3.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 3.14/3.34 inference(quant_inst,[status(thm)],[])).
% 3.14/3.34 tff(4816,plain,
% 3.14/3.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.14/3.34 inference(modus_ponens,[status(thm)],[4815, 4814])).
% 3.14/3.34 tff(4817,plain,
% 3.14/3.34 ($false),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[4816, 178, 4810, 4803, 202, 3828, 3831])).
% 3.14/3.34 tff(4818,plain,((~r(z, s(s(z)))) | (~b(s(s(s(s(z)))), 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)))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.34 tff(4819,plain,
% 3.14/3.34 (~r(z, s(s(z)))),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[4818, 4801, 202, 4798, 3243, 145])).
% 3.14/3.34 tff(4820,plain,
% 3.14/3.34 (b(z, s(s(z)))),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[143, 4819])).
% 3.14/3.34 tff(4821,plain,
% 3.14/3.34 (~(elem!1 = z)),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[3276, 4820, 461])).
% 3.14/3.34 tff(4822,plain,
% 3.14/3.34 (~(z = elem!1)),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[317, 4821])).
% 3.14/3.34 tff(4823,plain,
% 3.14/3.34 (~(s(s(elem!1)) = s(s(z)))),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[2386, 4822])).
% 3.14/3.34 tff(4824,assumption,(s(s(s(z))) = elem!1), introduced(assumption)).
% 3.14/3.34 tff(4825,plain,
% 3.14/3.34 (s(s(s(z))) = s(s(s(elem!1)))),
% 3.14/3.34 inference(transitivity,[status(thm)],[4824, 1527])).
% 3.14/3.34 tff(4826,plain,
% 3.14/3.34 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 3.14/3.34 inference(monotonicity,[status(thm)],[4825])).
% 3.14/3.34 tff(4827,plain,
% 3.14/3.34 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 3.14/3.34 inference(symmetry,[status(thm)],[4826])).
% 3.14/3.34 tff(4828,plain,
% 3.14/3.34 (s(s(elem!1)) = s(s(z))),
% 3.14/3.34 inference(transitivity,[status(thm)],[344, 4827, 65])).
% 3.14/3.34 tff(4829,plain,
% 3.14/3.34 ($false),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[2484, 4828])).
% 3.14/3.34 tff(4830,plain,((~(s(s(s(z))) = elem!1)) | (s(s(elem!1)) = s(s(z))) | (~(elem!1 = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.34 tff(4831,plain,
% 3.14/3.34 (~(s(s(s(z))) = elem!1)),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[4830, 4513, 4823])).
% 3.14/3.34 tff(4832,plain,
% 3.14/3.34 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(elem!1))))),
% 3.14/3.34 inference(monotonicity,[status(thm)],[4513])).
% 3.14/3.34 tff(4833,plain,
% 3.14/3.34 ((~b(s(s(z)), elem!1)) <=> (~b(s(s(z)), s(s(s(elem!1)))))),
% 3.14/3.34 inference(monotonicity,[status(thm)],[4832])).
% 3.14/3.34 tff(4834,plain,
% 3.14/3.34 (~b(s(s(z)), s(s(s(elem!1))))),
% 3.14/3.34 inference(modus_ponens,[status(thm)],[3241, 4833])).
% 3.14/3.34 tff(4835,plain,
% 3.14/3.34 (r(s(s(z)), s(s(s(elem!1))))),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[4221, 41, 1683, 4834])).
% 3.14/3.34 tff(4836,plain,
% 3.14/3.34 (~r(s(s(z)), z)),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[1831, 4835, 3243])).
% 3.14/3.34 tff(4837,plain,
% 3.14/3.34 (b(s(s(z)), z)),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[3249, 4836])).
% 3.14/3.34 tff(4838,plain,
% 3.14/3.34 (b(elem!1, s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 3.14/3.34 inference(monotonicity,[status(thm)],[4513])).
% 3.14/3.34 tff(4839,plain,
% 3.14/3.34 ((~b(elem!1, s(s(z)))) <=> (~b(s(s(s(elem!1))), s(s(z))))),
% 3.14/3.34 inference(monotonicity,[status(thm)],[4838])).
% 3.14/3.34 tff(4840,plain,
% 3.14/3.34 (~b(s(s(s(elem!1))), s(s(z)))),
% 3.14/3.34 inference(modus_ponens,[status(thm)],[461, 4839])).
% 3.14/3.34 tff(4841,plain,
% 3.14/3.34 (r(s(s(s(elem!1))), s(s(z)))),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[4209, 41, 4840, 4181])).
% 3.14/3.34 tff(4842,plain,
% 3.14/3.34 ($false),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[1143, 118, 1130, 145, 203])).
% 3.14/3.34 tff(4843,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.34 tff(4844,plain,
% 3.14/3.34 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[4843, 1130, 145])).
% 3.14/3.34 tff(4845,plain,
% 3.14/3.34 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[271, 4844])).
% 3.14/3.34 tff(4846,plain,
% 3.14/3.34 (r(elem!1, s(s(s(elem!1)))) <=> r(z, s(s(s(elem!1))))),
% 3.14/3.34 inference(monotonicity,[status(thm)],[928])).
% 3.14/3.34 tff(4847,plain,
% 3.14/3.34 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 3.14/3.34 inference(symmetry,[status(thm)],[4846])).
% 3.14/3.34 tff(4848,plain,
% 3.14/3.34 (r(elem!1, s(s(s(elem!1))))),
% 3.14/3.34 inference(modus_ponens,[status(thm)],[557, 4847])).
% 3.14/3.34 tff(4849,plain,
% 3.14/3.34 ($false),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[4512, 4848])).
% 3.14/3.34 tff(4850,plain,((~(elem!1 = z)) | r(elem!1, s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.34 tff(4851,plain,
% 3.14/3.34 (~(elem!1 = z)),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[4850, 4512, 3243])).
% 3.14/3.34 tff(4852,plain,
% 3.14/3.34 (~(z = elem!1)),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[317, 4851])).
% 3.14/3.34 tff(4853,plain,
% 3.14/3.34 (~b(z, elem!1)),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[4187, 1527, 3242])).
% 3.14/3.34 tff(4854,plain,
% 3.14/3.34 (r(z, elem!1)),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[585, 4853, 507])).
% 3.14/3.34 tff(4855,plain,
% 3.14/3.34 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(z)))))),
% 3.14/3.34 inference(rewrite,[status(thm)],[])).
% 3.14/3.34 tff(4856,plain,
% 3.14/3.34 (((~r(elem!1, s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(z)))))),
% 3.14/3.34 inference(rewrite,[status(thm)],[])).
% 3.14/3.34 tff(4857,plain,
% 3.14/3.34 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(z))))))),
% 3.14/3.34 inference(monotonicity,[status(thm)],[4856])).
% 3.14/3.34 tff(4858,plain,
% 3.14/3.34 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(z)))))),
% 3.14/3.34 inference(transitivity,[status(thm)],[4857, 4855])).
% 3.14/3.34 tff(4859,plain,
% 3.14/3.34 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, elem!1)))),
% 3.14/3.34 inference(quant_inst,[status(thm)],[])).
% 3.14/3.34 tff(4860,plain,
% 3.14/3.34 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(z))))),
% 3.14/3.34 inference(modus_ponens,[status(thm)],[4859, 4858])).
% 3.14/3.34 tff(4861,plain,
% 3.14/3.34 ($false),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[4860, 118, 521, 3261, 450])).
% 3.14/3.34 tff(4862,plain,((~r(z, s(s(z)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.34 tff(4863,plain,
% 3.14/3.34 (~r(elem!1, s(s(z)))),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[4862, 4854, 3261])).
% 3.14/3.34 tff(4864,plain,
% 3.14/3.34 (elem!1 = s(s(z))),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[467, 4863, 461])).
% 3.14/3.34 tff(4865,plain,
% 3.14/3.34 (s(s(z)) = elem!1),
% 3.14/3.34 inference(symmetry,[status(thm)],[4864])).
% 3.14/3.34 tff(4866,plain,
% 3.14/3.34 (s(s(z)) = s(s(s(elem!1)))),
% 3.14/3.34 inference(transitivity,[status(thm)],[4865, 1527])).
% 3.14/3.34 tff(4867,plain,
% 3.14/3.34 ($false),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[1683, 4866])).
% 3.14/3.34 tff(4868,plain,((~(elem!1 = s(s(s(elem!1))))) | b(elem!1, s(s(z))) | (~r(z, s(s(z)))) | (z = elem!1) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.34 tff(4869,plain,
% 3.14/3.34 (~r(z, s(s(z)))),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[4868, 4852, 461, 3242, 4513])).
% 3.14/3.34 tff(4870,plain,
% 3.14/3.34 (b(z, s(s(z)))),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[143, 4869])).
% 3.14/3.34 tff(4871,plain,
% 3.14/3.34 ($false),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[4091, 178, 4837, 4870, 595, 146, 1146])).
% 3.14/3.34 tff(4872,plain,(r(elem!1, s(s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | b(s(s(z)), elem!1) | b(elem!1, s(s(z))) | b(z, s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.34 tff(4873,plain,
% 3.14/3.34 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[4872, 4512, 1140, 4845, 3241, 461, 3242, 3240])).
% 3.14/3.34 tff(4874,plain,
% 3.14/3.34 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[3578, 4873])).
% 3.14/3.34 tff(4875,plain,
% 3.14/3.34 (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))))),
% 3.14/3.34 inference(monotonicity,[status(thm)],[4513])).
% 3.14/3.34 tff(4876,plain,
% 3.14/3.34 (s(s(s(elem!1))) = elem!1),
% 3.14/3.34 inference(symmetry,[status(thm)],[4513])).
% 3.14/3.34 tff(4877,plain,
% 3.14/3.34 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.14/3.34 inference(monotonicity,[status(thm)],[4876])).
% 3.14/3.34 tff(4878,plain,
% 3.14/3.34 ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 3.14/3.34 inference(monotonicity,[status(thm)],[4877])).
% 3.14/3.34 tff(4879,plain,
% 3.14/3.34 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), 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(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.14/3.34 inference(rewrite,[status(thm)],[])).
% 3.14/3.34 tff(4880,plain,
% 3.14/3.34 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), 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(s(s(elem!1))))))),
% 3.14/3.34 inference(quant_inst,[status(thm)],[])).
% 3.14/3.34 tff(4881,plain,
% 3.14/3.34 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 3.14/3.34 inference(modus_ponens,[status(thm)],[4880, 4879])).
% 3.14/3.34 tff(4882,plain,
% 3.14/3.34 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[4881, 118, 4841, 4874])).
% 3.14/3.34 tff(4883,plain,
% 3.14/3.34 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.14/3.34 inference(modus_ponens,[status(thm)],[4882, 4878])).
% 3.14/3.34 tff(4884,plain,
% 3.14/3.34 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[3444, 4883, 3914])).
% 3.14/3.34 tff(4885,plain,
% 3.14/3.34 (b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.14/3.34 inference(modus_ponens,[status(thm)],[4884, 4875])).
% 3.14/3.34 tff(4886,assumption,(s(s(s(z))) = s(s(s(s(z))))), introduced(assumption)).
% 3.14/3.34 tff(4887,plain,
% 3.14/3.34 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(z)))))),
% 3.14/3.34 inference(monotonicity,[status(thm)],[4886])).
% 3.14/3.34 tff(4888,plain,
% 3.14/3.34 (s(s(z)) = s(s(s(s(z))))),
% 3.14/3.34 inference(transitivity,[status(thm)],[66, 4887, 11, 4886])).
% 3.14/3.34 tff(4889,plain,
% 3.14/3.34 ($false),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[159, 4888])).
% 3.14/3.34 tff(4890,plain,(~(s(s(s(z))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.34 tff(4891,assumption,(r(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 3.14/3.34 tff(4892,plain,
% 3.14/3.34 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[3043, 118, 1130, 4891])).
% 3.14/3.34 tff(4893,plain,
% 3.14/3.34 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 4892])).
% 3.14/3.34 tff(4894,plain,
% 3.14/3.34 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 3.14/3.34 inference(rewrite,[status(thm)],[])).
% 3.14/3.34 tff(4895,plain,
% 3.14/3.34 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 3.14/3.34 inference(rewrite,[status(thm)],[])).
% 3.14/3.34 tff(4896,plain,
% 3.14/3.34 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 3.14/3.34 inference(monotonicity,[status(thm)],[4895])).
% 3.14/3.34 tff(4897,plain,
% 3.14/3.34 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 3.14/3.34 inference(transitivity,[status(thm)],[4896, 4894])).
% 3.14/3.34 tff(4898,plain,
% 3.14/3.34 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 3.14/3.34 inference(quant_inst,[status(thm)],[])).
% 3.14/3.34 tff(4899,plain,
% 3.14/3.34 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 3.14/3.34 inference(modus_ponens,[status(thm)],[4898, 4897])).
% 3.14/3.34 tff(4900,plain,
% 3.14/3.34 (~r(s(s(s(z))), z)),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[4899, 118, 145, 4891])).
% 3.14/3.34 tff(4901,plain,
% 3.14/3.34 (((~![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))),
% 3.14/3.34 inference(rewrite,[status(thm)],[])).
% 3.14/3.34 tff(4902,plain,
% 3.14/3.34 ((~![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))),
% 3.14/3.34 inference(quant_inst,[status(thm)],[])).
% 3.14/3.34 tff(4903,plain,
% 3.14/3.34 ((~![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)),
% 3.14/3.34 inference(modus_ponens,[status(thm)],[4902, 4901])).
% 3.14/3.34 tff(4904,plain,
% 3.14/3.34 (b(s(s(s(z))), z)),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[4903, 41, 77, 4900])).
% 3.14/3.34 tff(4905,plain,
% 3.14/3.34 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 3.14/3.34 inference(rewrite,[status(thm)],[])).
% 3.14/3.34 tff(4906,plain,
% 3.14/3.34 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 3.14/3.34 inference(rewrite,[status(thm)],[])).
% 3.14/3.34 tff(4907,plain,
% 3.14/3.34 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 3.14/3.34 inference(monotonicity,[status(thm)],[4906])).
% 3.14/3.34 tff(4908,plain,
% 3.14/3.34 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 3.14/3.34 inference(transitivity,[status(thm)],[4907, 4905])).
% 3.14/3.34 tff(4909,plain,
% 3.14/3.34 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))),
% 3.14/3.34 inference(quant_inst,[status(thm)],[])).
% 3.14/3.34 tff(4910,plain,
% 3.14/3.34 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 3.14/3.34 inference(modus_ponens,[status(thm)],[4909, 4908])).
% 3.14/3.34 tff(4911,plain,
% 3.14/3.34 (~r(z, s(s(s(z))))),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[4910, 118, 145, 4891])).
% 3.14/3.34 tff(4912,plain,
% 3.14/3.34 ((z = s(s(s(z)))) <=> (s(s(s(z))) = z)),
% 3.14/3.34 inference(commutativity,[status(thm)],[])).
% 3.14/3.34 tff(4913,plain,
% 3.14/3.34 ((s(s(s(z))) = z) <=> (z = s(s(s(z))))),
% 3.14/3.34 inference(symmetry,[status(thm)],[4912])).
% 3.14/3.34 tff(4914,plain,
% 3.14/3.34 ((~(s(s(s(z))) = z)) <=> (~(z = s(s(s(z)))))),
% 3.14/3.34 inference(monotonicity,[status(thm)],[4913])).
% 3.14/3.34 tff(4915,plain,
% 3.14/3.34 (~(z = s(s(s(z))))),
% 3.14/3.34 inference(modus_ponens,[status(thm)],[77, 4914])).
% 3.14/3.34 tff(4916,plain,
% 3.14/3.34 (((~![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)))))),
% 3.14/3.34 inference(rewrite,[status(thm)],[])).
% 3.14/3.34 tff(4917,plain,
% 3.14/3.34 ((~![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)))))),
% 3.14/3.34 inference(quant_inst,[status(thm)],[])).
% 3.14/3.34 tff(4918,plain,
% 3.14/3.34 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 3.14/3.34 inference(modus_ponens,[status(thm)],[4917, 4916])).
% 3.14/3.34 tff(4919,plain,
% 3.14/3.34 ((z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[4918, 41])).
% 3.14/3.34 tff(4920,plain,
% 3.14/3.34 (b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[4919, 4915])).
% 3.14/3.34 tff(4921,plain,
% 3.14/3.34 (b(z, s(s(s(z))))),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[4920, 4911])).
% 3.14/3.34 tff(4922,plain,
% 3.14/3.34 ($false),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[2944, 178, 1145, 1140, 4921, 4904, 4893])).
% 3.14/3.34 tff(4923,plain,((~r(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))))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.34 tff(4924,plain,
% 3.14/3.34 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 3.14/3.34 inference(unit_resolution,[status(thm)],[4923, 1130, 145])).
% 3.14/3.34 tff(4925,plain,
% 3.14/3.34 (((~![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))))))),
% 3.14/3.35 inference(rewrite,[status(thm)],[])).
% 3.14/3.35 tff(4926,plain,
% 3.14/3.35 ((~![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))))))),
% 3.14/3.35 inference(quant_inst,[status(thm)],[])).
% 3.14/3.35 tff(4927,plain,
% 3.14/3.35 ((~![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)))))),
% 3.14/3.35 inference(modus_ponens,[status(thm)],[4926, 4925])).
% 3.14/3.35 tff(4928,plain,
% 3.14/3.35 ((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)))))),
% 3.14/3.35 inference(unit_resolution,[status(thm)],[4927, 41])).
% 3.14/3.35 tff(4929,plain,
% 3.14/3.35 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.14/3.35 inference(unit_resolution,[status(thm)],[4928, 4924, 4890])).
% 3.14/3.35 tff(4930,plain,
% 3.14/3.35 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.14/3.35 inference(unit_resolution,[status(thm)],[3488, 4837, 145, 1130])).
% 3.14/3.35 tff(4931,plain,
% 3.14/3.35 (b(s(s(z)), s(s(s(s(z)))))),
% 3.14/3.35 inference(unit_resolution,[status(thm)],[164, 4930])).
% 3.14/3.35 tff(4932,assumption,(b(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 3.14/3.35 tff(4933,plain,
% 3.14/3.35 ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 3.14/3.35 inference(unit_resolution,[status(thm)],[2213, 178, 273, 167, 1126])).
% 3.14/3.35 tff(4934,plain,
% 3.14/3.35 (~b(z, s(s(s(z))))),
% 3.14/3.35 inference(unit_resolution,[status(thm)],[4933, 4932])).
% 3.14/3.35 tff(4935,plain,
% 3.14/3.35 (r(z, s(s(s(z))))),
% 3.14/3.35 inference(unit_resolution,[status(thm)],[4920, 4934])).
% 3.14/3.35 tff(4936,plain,
% 3.14/3.35 ((s(s(s(z))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 3.14/3.35 inference(commutativity,[status(thm)],[])).
% 3.14/3.35 tff(4937,plain,
% 3.14/3.35 ((~(s(s(s(z))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(s(z)))))),
% 3.14/3.35 inference(monotonicity,[status(thm)],[4936])).
% 3.14/3.35 tff(4938,plain,
% 3.14/3.35 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 3.14/3.35 inference(modus_ponens,[status(thm)],[4890, 4937])).
% 3.14/3.35 tff(4939,plain,
% 3.14/3.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 3.14/3.35 inference(rewrite,[status(thm)],[])).
% 3.14/3.35 tff(4940,plain,
% 3.14/3.35 (((~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(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 3.14/3.35 inference(rewrite,[status(thm)],[])).
% 3.14/3.35 tff(4941,plain,
% 3.14/3.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z))))))),
% 3.14/3.35 inference(monotonicity,[status(thm)],[4940])).
% 3.14/3.35 tff(4942,plain,
% 3.14/3.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 3.14/3.35 inference(transitivity,[status(thm)],[4941, 4939])).
% 3.14/3.35 tff(4943,plain,
% 3.14/3.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.14/3.35 inference(quant_inst,[status(thm)],[])).
% 3.14/3.35 tff(4944,plain,
% 3.14/3.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z))))),
% 3.14/3.35 inference(modus_ponens,[status(thm)],[4943, 4942])).
% 3.14/3.35 tff(4945,plain,
% 3.14/3.35 ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 3.14/3.35 inference(unit_resolution,[status(thm)],[4944, 178, 167, 202, 1126])).
% 3.14/3.35 tff(4946,plain,
% 3.14/3.35 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.14/3.35 inference(unit_resolution,[status(thm)],[4945, 4932])).
% 3.14/3.35 tff(4947,plain,
% 3.14/3.35 (((~![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)))))),
% 3.14/3.35 inference(rewrite,[status(thm)],[])).
% 3.14/3.35 tff(4948,plain,
% 3.14/3.35 ((~![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)))))),
% 3.14/3.35 inference(quant_inst,[status(thm)],[])).
% 3.14/3.35 tff(4949,plain,
% 3.14/3.35 ((~![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))))),
% 3.14/3.35 inference(modus_ponens,[status(thm)],[4948, 4947])).
% 3.14/3.35 tff(4950,plain,
% 3.14/3.35 ((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))))),
% 3.14/3.35 inference(unit_resolution,[status(thm)],[4949, 41])).
% 3.14/3.35 tff(4951,plain,
% 3.14/3.35 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.14/3.35 inference(unit_resolution,[status(thm)],[4950, 4946, 4938])).
% 3.14/3.35 tff(4952,assumption,(r(z, s(s(s(z))))), introduced(assumption)).
% 3.14/3.35 tff(4953,assumption,(r(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 3.14/3.35 tff(4954,plain,
% 3.14/3.35 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 3.14/3.35 inference(rewrite,[status(thm)],[])).
% 3.14/3.35 tff(4955,plain,
% 3.14/3.35 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 3.14/3.35 inference(rewrite,[status(thm)],[])).
% 3.14/3.35 tff(4956,plain,
% 3.14/3.35 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z)))))))),
% 3.14/3.35 inference(monotonicity,[status(thm)],[4955])).
% 3.14/3.35 tff(4957,plain,
% 3.14/3.35 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 3.14/3.35 inference(transitivity,[status(thm)],[4956, 4954])).
% 3.14/3.35 tff(4958,plain,
% 3.14/3.35 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 3.14/3.35 inference(quant_inst,[status(thm)],[])).
% 3.14/3.35 tff(4959,plain,
% 3.14/3.35 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z)))))),
% 3.14/3.35 inference(modus_ponens,[status(thm)],[4958, 4957])).
% 3.14/3.35 tff(4960,plain,
% 3.14/3.35 ($false),
% 3.14/3.35 inference(unit_resolution,[status(thm)],[4959, 118, 194, 4953, 4952])).
% 3.14/3.35 tff(4961,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.35 tff(4962,plain,
% 3.14/3.35 ($false),
% 3.14/3.35 inference(unit_resolution,[status(thm)],[4961, 4951, 4935, 194])).
% 3.14/3.35 tff(4963,plain,((~b(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), 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(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.35 tff(4964,plain,
% 3.14/3.35 (~b(s(s(s(z))), s(s(z)))),
% 3.14/3.35 inference(unit_resolution,[status(thm)],[4963, 4931, 194, 202, 4929, 4870])).
% 3.14/3.35 tff(4965,plain,
% 3.14/3.35 ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 3.14/3.35 inference(unit_resolution,[status(thm)],[3018, 41])).
% 3.14/3.35 tff(4966,plain,
% 3.14/3.35 (b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 3.14/3.35 inference(unit_resolution,[status(thm)],[4965, 3204])).
% 3.14/3.35 tff(4967,plain,
% 3.14/3.35 (r(s(s(s(z))), s(s(z)))),
% 3.14/3.35 inference(unit_resolution,[status(thm)],[4966, 4964])).
% 3.14/3.35 tff(4968,plain,
% 3.14/3.35 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(s(z))), elem!1)),
% 3.14/3.35 inference(monotonicity,[status(thm)],[2855])).
% 3.14/3.35 tff(4969,plain,
% 3.14/3.35 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 3.14/3.35 inference(symmetry,[status(thm)],[4968])).
% 3.14/3.35 tff(4970,assumption,(~(s(s(s(z))) = elem!1)), introduced(assumption)).
% 3.14/3.35 tff(4971,plain,
% 3.14/3.35 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), elem!1)),
% 3.14/3.35 inference(monotonicity,[status(thm)],[2855])).
% 3.14/3.35 tff(4972,plain,
% 3.14/3.35 ((~r(s(s(s(z))), s(s(s(elem!1))))) <=> (~r(s(s(s(z))), elem!1))),
% 3.14/3.35 inference(monotonicity,[status(thm)],[4971])).
% 3.14/3.35 tff(4973,plain,
% 3.14/3.35 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 3.14/3.35 inference(rewrite,[status(thm)],[])).
% 3.14/3.35 tff(4974,plain,
% 3.14/3.35 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 3.14/3.35 inference(quant_inst,[status(thm)],[])).
% 3.14/3.35 tff(4975,plain,
% 3.14/3.35 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 3.14/3.35 inference(modus_ponens,[status(thm)],[4974, 4973])).
% 3.14/3.35 tff(4976,plain,
% 3.14/3.35 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 3.14/3.35 inference(unit_resolution,[status(thm)],[4975, 118, 3859, 1125])).
% 3.14/3.35 tff(4977,plain,
% 3.14/3.35 (~r(s(s(s(z))), elem!1)),
% 3.14/3.35 inference(modus_ponens,[status(thm)],[4976, 4972])).
% 3.14/3.35 tff(4978,plain,
% 3.14/3.35 (((~![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))),
% 3.14/3.35 inference(rewrite,[status(thm)],[])).
% 3.14/3.35 tff(4979,plain,
% 3.14/3.35 ((~![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))),
% 3.14/3.35 inference(quant_inst,[status(thm)],[])).
% 3.14/3.35 tff(4980,plain,
% 3.14/3.35 ((~![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)),
% 3.14/3.35 inference(modus_ponens,[status(thm)],[4979, 4978])).
% 3.14/3.35 tff(4981,plain,
% 3.14/3.35 ((s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1)),
% 3.14/3.35 inference(unit_resolution,[status(thm)],[4980, 41])).
% 3.14/3.35 tff(4982,plain,
% 3.14/3.35 (b(s(s(s(z))), elem!1)),
% 3.14/3.35 inference(unit_resolution,[status(thm)],[4981, 4977, 4970])).
% 3.14/3.35 tff(4983,plain,
% 3.14/3.35 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.14/3.35 inference(modus_ponens,[status(thm)],[4982, 4969])).
% 3.14/3.35 tff(4984,plain,
% 3.14/3.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), 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(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), 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(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 3.14/3.35 inference(rewrite,[status(thm)],[])).
% 3.14/3.35 tff(4985,plain,
% 3.14/3.35 (((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(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(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~b(s(s(s(elem!1))), 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(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 3.14/3.35 inference(rewrite,[status(thm)],[])).
% 3.14/3.35 tff(4986,plain,
% 3.14/3.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(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(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), 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(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 3.14/3.35 inference(monotonicity,[status(thm)],[4985])).
% 3.14/3.35 tff(4987,plain,
% 3.14/3.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(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(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), 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(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 3.14/3.35 inference(transitivity,[status(thm)],[4986, 4984])).
% 3.14/3.35 tff(4988,plain,
% 3.14/3.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(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(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 3.14/3.35 inference(quant_inst,[status(thm)],[])).
% 3.14/3.35 tff(4989,plain,
% 3.14/3.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 3.14/3.35 inference(modus_ponens,[status(thm)],[4988, 4987])).
% 3.14/3.35 tff(4990,plain,
% 3.14/3.35 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 3.14/3.35 inference(unit_resolution,[status(thm)],[4989, 178, 1126, 3831, 3829])).
% 3.14/3.35 tff(4991,plain,
% 3.14/3.35 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 3.14/3.35 inference(unit_resolution,[status(thm)],[4990, 1217])).
% 3.14/3.35 tff(4992,plain,
% 3.14/3.35 ($false),
% 3.14/3.35 inference(unit_resolution,[status(thm)],[4991, 4983])).
% 3.14/3.35 tff(4993,plain,((~r(s(s(s(z))), s(s(z)))) | (~(elem!1 = s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (s(s(s(z))) = elem!1) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.35 tff(4994,plain,
% 3.14/3.35 (s(s(s(z))) = elem!1),
% 3.14/3.35 inference(unit_resolution,[status(thm)],[4993, 4967, 4929, 3831, 4885, 4513, 4874, 4841])).
% 3.14/3.35 tff(4995,plain,
% 3.14/3.35 (s(s(s(z))) = s(s(s(elem!1)))),
% 3.14/3.35 inference(transitivity,[status(thm)],[4994, 4513])).
% 3.14/3.35 tff(4996,plain,
% 3.14/3.35 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 3.14/3.35 inference(monotonicity,[status(thm)],[4995])).
% 3.14/3.35 tff(4997,plain,
% 3.14/3.35 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 3.14/3.35 inference(symmetry,[status(thm)],[4996])).
% 3.14/3.35 tff(4998,plain,
% 3.14/3.35 (s(s(elem!1)) = s(s(z))),
% 3.14/3.35 inference(transitivity,[status(thm)],[344, 4997, 65])).
% 3.14/3.35 tff(4999,plain,
% 3.14/3.35 (~(s(s(elem!1)) = s(s(z)))),
% 3.14/3.35 inference(unit_resolution,[status(thm)],[2386, 4852])).
% 3.14/3.35 tff(5000,plain,
% 3.14/3.35 ($false),
% 3.14/3.35 inference(unit_resolution,[status(thm)],[4999, 4998])).
% 3.14/3.35 tff(5001,plain,(r(elem!1, s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | b(elem!1, s(s(z))) | b(s(s(z)), elem!1) | b(z, s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.35 tff(5002,plain,
% 3.14/3.35 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.14/3.35 inference(unit_resolution,[status(thm)],[5001, 4512, 194, 202, 4245, 145, 4798, 461, 3241, 3242, 3240])).
% 3.14/3.35 tff(5003,plain,
% 3.14/3.35 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.14/3.35 inference(unit_resolution,[status(thm)],[84, 5002])).
% 3.14/3.35 tff(5004,plain,
% 3.14/3.35 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.14/3.35 inference(monotonicity,[status(thm)],[1527])).
% 3.14/3.35 tff(5005,plain,
% 3.14/3.35 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.14/3.35 inference(symmetry,[status(thm)],[3810])).
% 3.14/3.35 tff(5006,plain,
% 3.14/3.35 ((~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) <=> (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.14/3.35 inference(monotonicity,[status(thm)],[5005])).
% 3.14/3.35 tff(5007,plain,
% 3.14/3.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.14/3.35 inference(rewrite,[status(thm)],[])).
% 3.14/3.35 tff(5008,plain,
% 3.14/3.35 (((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(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(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(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(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.14/3.35 inference(rewrite,[status(thm)],[])).
% 3.14/3.35 tff(5009,plain,
% 3.14/3.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(s(z)))))) | (~b(s(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(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))))),
% 3.14/3.35 inference(monotonicity,[status(thm)],[5008])).
% 3.14/3.35 tff(5010,plain,
% 3.14/3.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(s(z)))))) | (~b(s(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(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.14/3.35 inference(transitivity,[status(thm)],[5009, 5007])).
% 3.14/3.35 tff(5011,plain,
% 3.14/3.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(s(z)))))) | (~b(s(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(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 3.14/3.35 inference(quant_inst,[status(thm)],[])).
% 3.14/3.35 tff(5012,plain,
% 3.14/3.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 3.14/3.35 inference(modus_ponens,[status(thm)],[5011, 5010])).
% 3.14/3.35 tff(5013,plain,
% 3.14/3.35 (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.14/3.35 inference(unit_resolution,[status(thm)],[5012, 178, 104, 3828, 3831, 3829])).
% 3.14/3.35 tff(5014,plain,
% 3.14/3.35 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.14/3.35 inference(modus_ponens,[status(thm)],[5013, 5006])).
% 3.14/3.35 tff(5015,plain,
% 3.14/3.35 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.14/3.35 inference(unit_resolution,[status(thm)],[691, 5014, 701])).
% 3.14/3.35 tff(5016,plain,
% 3.14/3.35 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.14/3.35 inference(modus_ponens,[status(thm)],[5015, 5004])).
% 3.14/3.35 tff(5017,plain,
% 3.14/3.35 ((~b(s(s(s(z))), s(s(s(elem!1))))) <=> (~b(s(s(s(z))), elem!1))),
% 3.14/3.35 inference(monotonicity,[status(thm)],[4968])).
% 3.14/3.35 tff(5018,plain,
% 3.14/3.35 ((s(s(s(z))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(z))))),
% 3.14/3.35 inference(commutativity,[status(thm)],[])).
% 3.14/3.35 tff(5019,plain,
% 3.14/3.35 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(s(s(z))))))))),
% 3.14/3.35 inference(symmetry,[status(thm)],[5018])).
% 3.14/3.35 tff(5020,plain,
% 3.14/3.35 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(s(s(s(s(s(z)))))))))),
% 3.14/3.36 inference(monotonicity,[status(thm)],[5019])).
% 3.14/3.36 tff(5021,plain,
% 3.14/3.36 (~(s(s(s(z))) = s(s(s(s(s(s(s(z))))))))),
% 3.14/3.36 inference(modus_ponens,[status(thm)],[1104, 5020])).
% 3.14/3.36 tff(5022,plain,
% 3.14/3.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.14/3.36 inference(rewrite,[status(thm)],[])).
% 3.14/3.36 tff(5023,plain,
% 3.14/3.36 (((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.14/3.36 inference(rewrite,[status(thm)],[])).
% 3.14/3.36 tff(5024,plain,
% 3.14/3.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(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(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))))),
% 3.14/3.36 inference(monotonicity,[status(thm)],[5023])).
% 3.14/3.36 tff(5025,plain,
% 3.14/3.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(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(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.14/3.36 inference(transitivity,[status(thm)],[5024, 5022])).
% 3.14/3.36 tff(5026,plain,
% 3.14/3.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(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(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.14/3.36 inference(quant_inst,[status(thm)],[])).
% 3.14/3.36 tff(5027,plain,
% 3.14/3.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 3.14/3.36 inference(modus_ponens,[status(thm)],[5026, 5025])).
% 3.14/3.36 tff(5028,plain,
% 3.14/3.36 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.14/3.36 inference(unit_resolution,[status(thm)],[5027, 178, 104, 1126, 3828, 3829])).
% 3.14/3.36 tff(5029,plain,
% 3.14/3.36 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.14/3.36 inference(rewrite,[status(thm)],[])).
% 3.14/3.36 tff(5030,plain,
% 3.14/3.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.14/3.36 inference(quant_inst,[status(thm)],[])).
% 3.14/3.36 tff(5031,plain,
% 3.14/3.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.14/3.36 inference(modus_ponens,[status(thm)],[5030, 5029])).
% 3.14/3.36 tff(5032,plain,
% 3.14/3.36 ((s(s(s(z))) = s(s(s(s(s(s(s(z)))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.14/3.36 inference(unit_resolution,[status(thm)],[5031, 41, 5028])).
% 3.14/3.36 tff(5033,plain,
% 3.14/3.36 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.14/3.36 inference(unit_resolution,[status(thm)],[5032, 5021])).
% 3.14/3.36 tff(5034,plain,
% 3.14/3.36 ((~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(elem!1)))))),
% 3.14/3.36 inference(unit_resolution,[status(thm)],[4067, 178, 104, 3828, 3831])).
% 3.14/3.36 tff(5035,plain,
% 3.14/3.36 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.14/3.36 inference(unit_resolution,[status(thm)],[5034, 3829])).
% 3.14/3.36 tff(5036,plain,
% 3.14/3.36 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.14/3.36 inference(unit_resolution,[status(thm)],[222, 5035])).
% 3.14/3.36 tff(5037,plain,
% 3.14/3.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 3.14/3.36 inference(rewrite,[status(thm)],[])).
% 3.14/3.36 tff(5038,plain,
% 3.14/3.36 (((~r(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))))))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 3.14/3.36 inference(rewrite,[status(thm)],[])).
% 3.14/3.36 tff(5039,plain,
% 3.14/3.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 3.14/3.36 inference(monotonicity,[status(thm)],[5038])).
% 3.14/3.36 tff(5040,plain,
% 3.14/3.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 3.14/3.36 inference(transitivity,[status(thm)],[5039, 5037])).
% 3.14/3.36 tff(5041,plain,
% 3.14/3.36 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 3.14/3.36 inference(quant_inst,[status(thm)],[])).
% 3.14/3.36 tff(5042,plain,
% 3.14/3.36 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 3.14/3.36 inference(modus_ponens,[status(thm)],[5041, 5040])).
% 3.14/3.36 tff(5043,plain,
% 3.14/3.36 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.14/3.36 inference(unit_resolution,[status(thm)],[5042, 118, 5036, 5033])).
% 3.14/3.36 tff(5044,plain,
% 3.14/3.36 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.14/3.36 inference(unit_resolution,[status(thm)],[4950, 5043, 4938])).
% 3.14/3.36 tff(5045,plain,
% 3.14/3.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(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(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(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(s(elem!1))))))),
% 3.14/3.36 inference(rewrite,[status(thm)],[])).
% 3.14/3.36 tff(5046,plain,
% 3.14/3.36 (((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(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(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(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(s(elem!1))))))),
% 3.14/3.36 inference(rewrite,[status(thm)],[])).
% 3.14/3.36 tff(5047,plain,
% 3.14/3.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(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(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(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(s(elem!1)))))))),
% 3.14/3.36 inference(monotonicity,[status(thm)],[5046])).
% 3.14/3.36 tff(5048,plain,
% 3.14/3.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(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(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(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(s(elem!1))))))),
% 3.14/3.36 inference(transitivity,[status(thm)],[5047, 5045])).
% 3.14/3.36 tff(5049,plain,
% 3.14/3.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(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(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.14/3.36 inference(quant_inst,[status(thm)],[])).
% 3.14/3.36 tff(5050,plain,
% 3.14/3.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(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(s(elem!1)))))),
% 3.14/3.36 inference(modus_ponens,[status(thm)],[5049, 5048])).
% 3.14/3.36 tff(5051,plain,
% 3.14/3.36 ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 3.14/3.36 inference(unit_resolution,[status(thm)],[5050, 178, 1126, 3828, 3831])).
% 3.14/3.36 tff(5052,plain,
% 3.14/3.36 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 3.14/3.36 inference(unit_resolution,[status(thm)],[5051, 5044])).
% 3.14/3.36 tff(5053,plain,
% 3.14/3.36 (~b(s(s(s(z))), elem!1)),
% 3.14/3.36 inference(modus_ponens,[status(thm)],[5052, 5017])).
% 3.14/3.36 tff(5054,plain,
% 3.14/3.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(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(s(s(z))), s(s(s(elem!1))))))),
% 3.14/3.36 inference(rewrite,[status(thm)],[])).
% 3.14/3.36 tff(5055,plain,
% 3.14/3.36 (((~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(elem!1)))))) <=> ((~r(s(s(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(s(s(z))), s(s(s(elem!1))))))),
% 3.14/3.36 inference(rewrite,[status(thm)],[])).
% 3.14/3.36 tff(5056,plain,
% 3.14/3.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(elem!1)))))))),
% 3.14/3.36 inference(monotonicity,[status(thm)],[5055])).
% 3.14/3.36 tff(5057,plain,
% 3.14/3.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 3.14/3.36 inference(transitivity,[status(thm)],[5056, 5054])).
% 3.14/3.36 tff(5058,plain,
% 3.14/3.36 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 3.14/3.36 inference(quant_inst,[status(thm)],[])).
% 3.14/3.36 tff(5059,plain,
% 3.14/3.36 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 3.14/3.36 inference(modus_ponens,[status(thm)],[5058, 5057])).
% 3.14/3.36 tff(5060,plain,
% 3.14/3.36 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 3.14/3.36 inference(unit_resolution,[status(thm)],[5059, 118, 5033, 3615])).
% 3.14/3.36 tff(5061,plain,
% 3.14/3.36 (~r(s(s(s(z))), elem!1)),
% 3.14/3.36 inference(modus_ponens,[status(thm)],[5060, 4972])).
% 3.14/3.36 tff(5062,plain,
% 3.14/3.36 ($false),
% 3.14/3.36 inference(unit_resolution,[status(thm)],[4981, 5061, 5053, 4970])).
% 3.14/3.36 tff(5063,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (s(s(s(z))) = elem!1) | (~(elem!1 = s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(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(s(s(s(z))))))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.36 tff(5064,plain,
% 3.14/3.36 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 3.14/3.36 inference(unit_resolution,[status(thm)],[5063, 5016, 1527, 3828, 3831, 4970, 104, 3829])).
% 3.14/3.36 tff(5065,plain,
% 3.14/3.36 (r(s(s(s(z))), s(s(s(s(z)))))),
% 3.14/3.36 inference(unit_resolution,[status(thm)],[4928, 5064, 4890])).
% 3.14/3.36 tff(5066,plain,
% 3.14/3.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 3.14/3.36 inference(rewrite,[status(thm)],[])).
% 3.14/3.36 tff(5067,plain,
% 3.14/3.36 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 3.14/3.36 inference(rewrite,[status(thm)],[])).
% 3.14/3.36 tff(5068,plain,
% 3.14/3.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 3.14/3.36 inference(monotonicity,[status(thm)],[5067])).
% 3.14/3.36 tff(5069,plain,
% 3.14/3.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 3.14/3.36 inference(transitivity,[status(thm)],[5068, 5066])).
% 3.14/3.36 tff(5070,plain,
% 3.14/3.36 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))),
% 3.14/3.36 inference(quant_inst,[status(thm)],[])).
% 3.14/3.36 tff(5071,plain,
% 3.14/3.36 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 3.14/3.36 inference(modus_ponens,[status(thm)],[5070, 5069])).
% 3.14/3.36 tff(5072,plain,
% 3.14/3.36 (~r(s(s(s(z))), s(s(z)))),
% 3.14/3.36 inference(unit_resolution,[status(thm)],[5071, 118, 147, 4891])).
% 3.14/3.36 tff(5073,plain,
% 3.14/3.36 (b(s(s(s(z))), s(s(z)))),
% 3.14/3.36 inference(unit_resolution,[status(thm)],[4966, 5072])).
% 3.14/3.36 tff(5074,plain,
% 3.14/3.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 3.14/3.36 inference(rewrite,[status(thm)],[])).
% 3.14/3.36 tff(5075,plain,
% 3.14/3.36 (((~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)))))) <=> ((~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)))))))),
% 3.14/3.36 inference(rewrite,[status(thm)],[])).
% 3.14/3.36 tff(5076,plain,
% 3.14/3.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 3.14/3.36 inference(monotonicity,[status(thm)],[5075])).
% 3.14/3.36 tff(5077,plain,
% 3.14/3.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 3.14/3.36 inference(transitivity,[status(thm)],[5076, 5074])).
% 3.14/3.36 tff(5078,plain,
% 3.14/3.36 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 3.14/3.36 inference(quant_inst,[status(thm)],[])).
% 3.14/3.36 tff(5079,plain,
% 3.14/3.36 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 3.14/3.36 inference(modus_ponens,[status(thm)],[5078, 5077])).
% 3.14/3.36 tff(5080,plain,
% 3.14/3.36 (~r(s(s(z)), s(s(s(z))))),
% 3.14/3.36 inference(unit_resolution,[status(thm)],[5079, 118, 147, 4891])).
% 3.14/3.36 tff(5081,assumption,(~r(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 3.14/3.36 tff(5082,assumption,(~b(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 3.14/3.36 tff(5083,plain,
% 3.14/3.36 (((~![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)))))),
% 3.14/3.36 inference(rewrite,[status(thm)],[])).
% 3.14/3.36 tff(5084,plain,
% 3.14/3.36 ((~![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)))))),
% 3.14/3.36 inference(quant_inst,[status(thm)],[])).
% 3.14/3.36 tff(5085,plain,
% 3.14/3.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 3.14/3.36 inference(modus_ponens,[status(thm)],[5084, 5083])).
% 3.14/3.36 tff(5086,plain,
% 3.14/3.36 ($false),
% 3.14/3.36 inference(unit_resolution,[status(thm)],[5085, 41, 5082, 5081, 3006])).
% 3.14/3.36 tff(5087,plain,(b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z)))) | (s(s(z)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.37 tff(5088,plain,
% 3.14/3.37 (b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[5087, 3205])).
% 3.14/3.37 tff(5089,plain,
% 3.14/3.37 (b(s(s(z)), s(s(s(z))))),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[5088, 5080])).
% 3.14/3.37 tff(5090,assumption,(b(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 3.14/3.37 tff(5091,plain,
% 3.14/3.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 3.14/3.37 inference(rewrite,[status(thm)],[])).
% 3.14/3.37 tff(5092,plain,
% 3.14/3.37 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 3.14/3.37 inference(rewrite,[status(thm)],[])).
% 3.14/3.37 tff(5093,plain,
% 3.14/3.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))))),
% 3.14/3.37 inference(monotonicity,[status(thm)],[5092])).
% 3.14/3.37 tff(5094,plain,
% 3.14/3.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 3.14/3.37 inference(transitivity,[status(thm)],[5093, 5091])).
% 3.14/3.37 tff(5095,plain,
% 3.14/3.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 3.14/3.37 inference(quant_inst,[status(thm)],[])).
% 3.14/3.37 tff(5096,plain,
% 3.14/3.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))),
% 3.14/3.37 inference(modus_ponens,[status(thm)],[5095, 5094])).
% 3.14/3.37 tff(5097,plain,
% 3.14/3.37 ($false),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[5096, 178, 3461, 3008, 5090, 4932, 1127])).
% 3.14/3.37 tff(5098,plain,((~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.37 tff(5099,plain,
% 3.14/3.37 (~b(s(s(s(z))), z)),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[5098, 5089, 5073, 4921, 3461])).
% 3.14/3.37 tff(5100,plain,
% 3.14/3.37 ($false),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[4903, 41, 77, 5099, 4900])).
% 3.14/3.37 tff(5101,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.37 tff(5102,plain,
% 3.14/3.37 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[5101, 5065, 3461, 145])).
% 3.14/3.37 tff(5103,plain,
% 3.14/3.37 (b(s(s(z)), s(s(s(s(z)))))),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[164, 5102])).
% 3.14/3.37 tff(5104,plain,
% 3.14/3.37 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[2803, 5015, 438])).
% 3.14/3.37 tff(5105,plain,
% 3.14/3.37 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[249, 5104])).
% 3.14/3.37 tff(5106,plain,
% 3.14/3.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.14/3.37 inference(rewrite,[status(thm)],[])).
% 3.14/3.37 tff(5107,plain,
% 3.14/3.37 (((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(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(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(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(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.14/3.37 inference(rewrite,[status(thm)],[])).
% 3.14/3.37 tff(5108,plain,
% 3.14/3.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(s(z)))))) | (~b(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(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))))),
% 3.14/3.37 inference(monotonicity,[status(thm)],[5107])).
% 3.14/3.37 tff(5109,plain,
% 3.14/3.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(s(z)))))) | (~b(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(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.14/3.37 inference(transitivity,[status(thm)],[5108, 5106])).
% 3.14/3.37 tff(5110,plain,
% 3.14/3.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(s(z)))))) | (~b(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(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.14/3.37 inference(quant_inst,[status(thm)],[])).
% 3.14/3.37 tff(5111,plain,
% 3.14/3.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 3.14/3.37 inference(modus_ponens,[status(thm)],[5110, 5109])).
% 3.14/3.37 tff(5112,plain,
% 3.14/3.37 ($false),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[5111, 178, 104, 5105, 5103, 3828, 3829])).
% 3.14/3.37 tff(5113,plain,((~b(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(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~(elem!1 = s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (s(s(s(z))) = elem!1) | (~r(s(s(z)), elem!1)) | (elem!1 = s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.37 tff(5114,plain,
% 3.14/3.37 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[5113, 5003, 4801, 4837, 145, 4513, 4798, 4831, 4518, 701])).
% 3.14/3.37 tff(5115,assumption,(~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))), introduced(assumption)).
% 3.14/3.37 tff(5116,assumption,(~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))), introduced(assumption)).
% 3.14/3.37 tff(5117,plain,
% 3.14/3.37 ($false),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[3524, 41, 3521, 5116, 5115])).
% 3.14/3.37 tff(5118,plain,(b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.37 tff(5119,plain,
% 3.14/3.37 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[5118, 5114, 4511])).
% 3.14/3.37 tff(5120,plain,
% 3.14/3.37 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[4843, 203, 145])).
% 3.14/3.37 tff(5121,plain,
% 3.14/3.37 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[84, 5120])).
% 3.14/3.37 tff(5122,plain,
% 3.14/3.37 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[4067, 178, 5121, 223, 3828, 3831])).
% 3.14/3.37 tff(5123,plain,
% 3.14/3.37 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[3524, 41, 3521, 5122])).
% 3.14/3.37 tff(5124,plain,
% 3.14/3.37 ($false),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[3531, 118, 557, 203, 5123])).
% 3.14/3.37 tff(5125,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(elem!1))))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.37 tff(5126,plain,
% 3.14/3.37 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[5125, 4801, 4511, 3243, 4798, 145])).
% 3.14/3.37 tff(5127,plain,
% 3.14/3.37 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[271, 5126])).
% 3.14/3.37 tff(5128,assumption,(r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))), introduced(assumption)).
% 3.14/3.37 tff(5129,plain,
% 3.14/3.37 ($false),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[4077, 118, 557, 108, 5128])).
% 3.14/3.37 tff(5130,plain,((~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))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.37 tff(5131,plain,
% 3.14/3.37 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[5130, 5119, 3243])).
% 3.14/3.37 tff(5132,plain,
% 3.14/3.37 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[133, 5131])).
% 3.14/3.37 tff(5133,plain,
% 3.14/3.37 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[4872, 5132, 4512, 5127, 3241, 461, 3242, 3240])).
% 3.14/3.37 tff(5134,plain,
% 3.14/3.37 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[3578, 5133])).
% 3.14/3.37 tff(5135,plain,
% 3.14/3.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.14/3.37 inference(rewrite,[status(thm)],[])).
% 3.14/3.37 tff(5136,plain,
% 3.14/3.37 (((~r(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(s(z))))) <=> ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.14/3.37 inference(rewrite,[status(thm)],[])).
% 3.14/3.37 tff(5137,plain,
% 3.14/3.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))))),
% 3.14/3.37 inference(monotonicity,[status(thm)],[5136])).
% 3.14/3.37 tff(5138,plain,
% 3.14/3.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.14/3.37 inference(transitivity,[status(thm)],[5137, 5135])).
% 3.14/3.37 tff(5139,plain,
% 3.14/3.37 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(s(z)))))),
% 3.14/3.37 inference(quant_inst,[status(thm)],[])).
% 3.14/3.37 tff(5140,plain,
% 3.14/3.37 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 3.14/3.37 inference(modus_ponens,[status(thm)],[5139, 5138])).
% 3.14/3.37 tff(5141,plain,
% 3.14/3.37 ($false),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[5140, 118, 4835, 5134, 5119])).
% 3.14/3.37 tff(5142,plain,(r(elem!1, s(s(s(elem!1)))) | b(s(s(z)), elem!1) | b(elem!1, s(s(z))) | b(z, s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | (~r(z, s(s(s(s(z)))))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.37 tff(5143,plain,
% 3.14/3.37 (r(elem!1, s(s(s(elem!1))))),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[5142, 701, 461, 3242, 3240, 47, 3241, 3244, 4503])).
% 3.14/3.37 tff(5144,plain,
% 3.14/3.37 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[4796, 701, 4503, 47, 3241, 461, 3244, 3240])).
% 3.14/3.37 tff(5145,plain,
% 3.14/3.37 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[4173, 5144, 3260])).
% 3.14/3.37 tff(5146,plain,
% 3.14/3.37 (~(s(s(s(s(z)))) = elem!1)),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[4509, 4503, 461])).
% 3.14/3.37 tff(5147,plain,
% 3.14/3.37 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[3502, 5146])).
% 3.14/3.37 tff(5148,plain,
% 3.14/3.37 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 3.14/3.37 inference(modus_ponens,[status(thm)],[5144, 4799])).
% 3.14/3.37 tff(5149,plain,
% 3.14/3.37 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[3287, 3243, 3244])).
% 3.14/3.37 tff(5150,plain,
% 3.14/3.37 ((s(s(s(s(z)))) = s(s(s(elem!1)))) | b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[3296, 41, 5149])).
% 3.14/3.37 tff(5151,plain,
% 3.14/3.37 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[5150, 5148])).
% 3.14/3.37 tff(5152,plain,
% 3.14/3.37 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[5125, 5151, 5147, 3243, 5145, 47])).
% 3.14/3.37 tff(5153,plain,
% 3.14/3.37 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[271, 5152])).
% 3.14/3.37 tff(5154,plain,
% 3.14/3.37 (~r(z, s(s(z)))),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[4818, 5151, 4503, 5145, 3243, 47])).
% 3.14/3.37 tff(5155,plain,
% 3.14/3.37 (b(z, s(s(z)))),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[143, 5154])).
% 3.14/3.37 tff(5156,plain,
% 3.14/3.37 (~(elem!1 = z)),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[3276, 5155, 461])).
% 3.14/3.37 tff(5157,plain,
% 3.14/3.37 (~(z = elem!1)),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[317, 5156])).
% 3.14/3.37 tff(5158,plain,
% 3.14/3.37 (~r(z, elem!1)),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[3319, 5143, 3243])).
% 3.14/3.37 tff(5159,plain,
% 3.14/3.37 (b(z, elem!1)),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[585, 5158, 5157])).
% 3.14/3.37 tff(5160,plain,
% 3.14/3.37 (~(elem!1 = s(s(s(elem!1))))),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[4187, 5159, 3242])).
% 3.14/3.37 tff(5161,plain,
% 3.14/3.37 (~(s(s(s(elem!1))) = elem!1)),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[2489, 5160])).
% 3.14/3.37 tff(5162,plain,
% 3.14/3.37 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[3287, 557, 3244])).
% 3.14/3.37 tff(5163,plain,
% 3.14/3.37 ((s(s(s(s(z)))) = s(s(s(elem!1)))) | b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[3296, 41, 5162])).
% 3.14/3.37 tff(5164,plain,
% 3.14/3.37 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[5163, 4166])).
% 3.14/3.37 tff(5165,plain,
% 3.14/3.37 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[5125, 5164, 4511, 557, 3831, 47])).
% 3.14/3.37 tff(5166,plain,
% 3.14/3.37 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[271, 5165])).
% 3.14/3.37 tff(5167,plain,
% 3.14/3.37 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[1138, 1130, 47])).
% 3.14/3.37 tff(5168,plain,
% 3.14/3.37 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[133, 5167])).
% 3.14/3.37 tff(5169,plain,
% 3.14/3.37 (~r(z, elem!1)),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[3319, 3311, 557])).
% 3.14/3.37 tff(5170,plain,
% 3.14/3.37 (z = elem!1),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[2820, 4357, 595, 146, 869, 5169])).
% 3.14/3.37 tff(5171,plain,
% 3.14/3.37 (elem!1 = z),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[317, 5170])).
% 3.14/3.37 tff(5172,plain,
% 3.14/3.37 (~b(z, s(s(z)))),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[3276, 5171, 461])).
% 3.14/3.37 tff(5173,plain,
% 3.14/3.37 (r(z, s(s(z)))),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[143, 5172])).
% 3.14/3.37 tff(5174,plain,
% 3.14/3.37 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 3.14/3.37 inference(monotonicity,[status(thm)],[17])).
% 3.14/3.37 tff(5175,plain,
% 3.14/3.37 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 3.14/3.37 inference(symmetry,[status(thm)],[5174])).
% 3.14/3.37 tff(5176,plain,
% 3.14/3.37 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 3.14/3.37 inference(monotonicity,[status(thm)],[13])).
% 3.14/3.37 tff(5177,assumption,(b(s(s(s(s(elem!1)))), z)), introduced(assumption)).
% 3.14/3.37 tff(5178,plain,
% 3.14/3.37 (b(s(s(s(s(elem!1)))), elem!1)),
% 3.14/3.37 inference(modus_ponens,[status(thm)],[5177, 5176])).
% 3.14/3.37 tff(5179,plain,
% 3.14/3.37 (b(s(s(s(s(z)))), elem!1)),
% 3.14/3.37 inference(modus_ponens,[status(thm)],[5178, 5175])).
% 3.14/3.37 tff(5180,plain,
% 3.14/3.37 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(z)))), elem!1)),
% 3.14/3.37 inference(monotonicity,[status(thm)],[13])).
% 3.14/3.37 tff(5181,plain,
% 3.14/3.37 ((~b(s(s(s(s(z)))), z)) <=> (~b(s(s(s(s(z)))), elem!1))),
% 3.14/3.37 inference(monotonicity,[status(thm)],[5180])).
% 3.14/3.37 tff(5182,plain,
% 3.14/3.37 (~b(s(s(s(s(z)))), elem!1)),
% 3.14/3.37 inference(modus_ponens,[status(thm)],[3170, 5181])).
% 3.14/3.37 tff(5183,plain,
% 3.14/3.37 ($false),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[5182, 5179])).
% 3.14/3.37 tff(5184,plain,((~(z = elem!1)) | b(s(s(s(s(z)))), z) | (~b(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.37 tff(5185,plain,
% 3.14/3.37 (~b(s(s(s(s(elem!1)))), z)),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[5184, 13, 3170])).
% 3.14/3.37 tff(5186,plain,
% 3.14/3.37 (r(s(s(s(s(elem!1)))), z)),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[1716, 5185])).
% 3.14/3.37 tff(5187,plain,
% 3.14/3.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), z)))),
% 3.14/3.37 inference(rewrite,[status(thm)],[])).
% 3.14/3.37 tff(5188,plain,
% 3.14/3.37 (((~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), z))) <=> ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), z)))),
% 3.14/3.37 inference(rewrite,[status(thm)],[])).
% 3.14/3.37 tff(5189,plain,
% 3.14/3.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), z))))),
% 3.14/3.37 inference(monotonicity,[status(thm)],[5188])).
% 3.14/3.37 tff(5190,plain,
% 3.14/3.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), z)))),
% 3.14/3.37 inference(transitivity,[status(thm)],[5189, 5187])).
% 3.14/3.37 tff(5191,plain,
% 3.14/3.37 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), z)))),
% 3.14/3.37 inference(quant_inst,[status(thm)],[])).
% 3.14/3.37 tff(5192,plain,
% 3.14/3.37 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), z))),
% 3.14/3.37 inference(modus_ponens,[status(thm)],[5191, 5190])).
% 3.14/3.37 tff(5193,plain,
% 3.14/3.37 ($false),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[5192, 118, 3261, 3988, 3636])).
% 3.14/3.37 tff(5194,plain,((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.37 tff(5195,plain,
% 3.14/3.37 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[5194, 5186, 3261])).
% 3.14/3.37 tff(5196,plain,
% 3.14/3.37 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[1170, 5195])).
% 3.14/3.37 tff(5197,plain,
% 3.14/3.37 (~(elem!1 = s(s(s(s(elem!1)))))),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[3901, 5196, 461])).
% 3.14/3.37 tff(5198,plain,
% 3.14/3.37 (elem!1 = z),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[317, 13])).
% 3.14/3.37 tff(5199,plain,
% 3.14/3.37 (b(elem!1, s(s(s(s(z))))) <=> b(z, s(s(s(s(z)))))),
% 3.14/3.37 inference(monotonicity,[status(thm)],[928])).
% 3.14/3.37 tff(5200,plain,
% 3.14/3.37 (b(z, s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 3.14/3.37 inference(symmetry,[status(thm)],[5199])).
% 3.14/3.37 tff(5201,plain,
% 3.14/3.37 ((~b(z, s(s(s(s(z)))))) <=> (~b(elem!1, s(s(s(s(z))))))),
% 3.14/3.37 inference(monotonicity,[status(thm)],[5200])).
% 3.14/3.37 tff(5202,plain,
% 3.14/3.37 (~b(elem!1, s(s(s(s(z)))))),
% 3.14/3.37 inference(modus_ponens,[status(thm)],[1, 5201])).
% 3.14/3.37 tff(5203,plain,
% 3.14/3.37 ($false),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[1301, 5202])).
% 3.14/3.37 tff(5204,plain,((~(elem!1 = z)) | (~b(elem!1, s(s(s(s(z)))))) | b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.37 tff(5205,plain,
% 3.14/3.37 (~b(elem!1, s(s(s(s(z)))))),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[5204, 5198, 1])).
% 3.14/3.37 tff(5206,plain,
% 3.14/3.37 (r(elem!1, s(s(s(s(z)))))),
% 3.14/3.37 inference(unit_resolution,[status(thm)],[483, 5205, 4520])).
% 3.14/3.37 tff(5207,plain,
% 3.14/3.37 (s(s(s(z))) = s(s(s(elem!1)))),
% 3.14/3.37 inference(symmetry,[status(thm)],[931])).
% 3.14/3.37 tff(5208,plain,
% 3.14/3.37 (r(z, s(s(s(z)))) <=> r(z, s(s(s(elem!1))))),
% 3.14/3.37 inference(monotonicity,[status(thm)],[5207])).
% 3.14/3.37 tff(5209,plain,
% 3.14/3.37 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(z))))),
% 3.14/3.37 inference(symmetry,[status(thm)],[5208])).
% 3.14/3.37 tff(5210,plain,
% 3.14/3.37 (r(z, s(s(s(elem!1))))),
% 3.14/3.37 inference(modus_ponens,[status(thm)],[3311, 4846])).
% 3.14/3.37 tff(5211,plain,
% 3.14/3.37 (r(z, s(s(s(z))))),
% 3.14/3.37 inference(modus_ponens,[status(thm)],[5210, 5209])).
% 3.14/3.37 tff(5212,plain,
% 3.14/3.37 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.14/3.37 inference(monotonicity,[status(thm)],[5207])).
% 3.14/3.37 tff(5213,plain,
% 3.14/3.37 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 3.14/3.37 inference(symmetry,[status(thm)],[5212])).
% 3.14/3.37 tff(5214,plain,
% 3.14/3.37 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.14/3.37 inference(monotonicity,[status(thm)],[932])).
% 3.14/3.37 tff(5215,plain,
% 3.14/3.37 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 3.14/3.37 inference(monotonicity,[status(thm)],[931, 932])).
% 3.14/3.37 tff(5216,plain,
% 3.14/3.37 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.14/3.37 inference(symmetry,[status(thm)],[5215])).
% 3.14/3.37 tff(5217,plain,
% 3.14/3.37 ((~b(s(s(s(z))), s(s(s(s(z)))))) <=> (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 3.14/3.37 inference(monotonicity,[status(thm)],[5216])).
% 3.14/3.37 tff(5218,plain,
% 3.14/3.37 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 3.14/3.37 inference(monotonicity,[status(thm)],[5207])).
% 3.14/3.37 tff(5219,plain,
% 3.14/3.37 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(z))), s(s(z)))),
% 3.14/3.37 inference(symmetry,[status(thm)],[5218])).
% 3.14/3.37 tff(5220,plain,
% 3.14/3.37 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 3.14/3.37 inference(monotonicity,[status(thm)],[930])).
% 3.14/3.37 tff(5221,plain,
% 3.14/3.37 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(z)))),
% 3.14/3.37 inference(transitivity,[status(thm)],[5220, 5219])).
% 3.14/3.37 tff(5222,assumption,(~(s(s(s(elem!1))) = s(s(elem!1)))), introduced(assumption)).
% 3.14/3.37 tff(5223,plain,
% 3.14/3.37 (r(z, s(s(elem!1))) <=> r(z, s(s(z)))),
% 3.14/3.37 inference(monotonicity,[status(thm)],[930])).
% 3.14/3.37 tff(5224,plain,
% 3.14/3.37 (r(z, s(s(z))) <=> r(z, s(s(elem!1)))),
% 3.14/3.37 inference(symmetry,[status(thm)],[5223])).
% 3.14/3.37 tff(5225,plain,
% 3.14/3.37 (r(z, s(s(elem!1)))),
% 3.14/3.37 inference(modus_ponens,[status(thm)],[3261, 5224])).
% 3.14/3.37 tff(5226,assumption,(r(z, s(s(elem!1)))), introduced(assumption)).
% 3.14/3.37 tff(5227,assumption,(r(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 3.14/3.37 tff(5228,plain,
% 3.14/3.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.14/3.37 inference(rewrite,[status(thm)],[])).
% 3.14/3.37 tff(5229,plain,
% 3.14/3.37 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.14/3.37 inference(rewrite,[status(thm)],[])).
% 3.14/3.37 tff(5230,plain,
% 3.14/3.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))))),
% 3.14/3.37 inference(monotonicity,[status(thm)],[5229])).
% 3.14/3.37 tff(5231,plain,
% 3.14/3.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.14/3.37 inference(transitivity,[status(thm)],[5230, 5228])).
% 3.14/3.37 tff(5232,plain,
% 3.14/3.37 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))),
% 3.14/3.37 inference(quant_inst,[status(thm)],[])).
% 3.14/3.37 tff(5233,plain,
% 3.14/3.37 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 3.14/3.38 inference(modus_ponens,[status(thm)],[5232, 5231])).
% 3.14/3.38 tff(5234,plain,
% 3.14/3.38 ($false),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[5233, 118, 557, 5227, 5226])).
% 3.14/3.38 tff(5235,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.38 tff(5236,plain,
% 3.14/3.38 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[5235, 5225, 5210])).
% 3.14/3.38 tff(5237,plain,
% 3.14/3.38 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[3409, 5236, 5222])).
% 3.14/3.38 tff(5238,plain,
% 3.14/3.38 (b(s(s(s(z))), s(s(z)))),
% 3.14/3.38 inference(modus_ponens,[status(thm)],[5237, 5221])).
% 3.14/3.38 tff(5239,plain,
% 3.14/3.38 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 3.14/3.38 inference(monotonicity,[status(thm)],[5207])).
% 3.14/3.38 tff(5240,plain,
% 3.14/3.38 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(z))))),
% 3.14/3.38 inference(symmetry,[status(thm)],[5239])).
% 3.14/3.38 tff(5241,plain,
% 3.14/3.38 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[4808, 5210, 3261])).
% 3.14/3.38 tff(5242,plain,
% 3.14/3.38 (b(s(s(z)), s(s(s(elem!1))))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[4223, 5241])).
% 3.14/3.38 tff(5243,plain,
% 3.14/3.38 (b(s(s(z)), s(s(s(z))))),
% 3.14/3.38 inference(modus_ponens,[status(thm)],[5242, 5240])).
% 3.14/3.38 tff(5244,plain,
% 3.14/3.38 (r(elem!1, s(s(s(s(z))))) <=> r(z, s(s(s(s(z)))))),
% 3.14/3.38 inference(monotonicity,[status(thm)],[928])).
% 3.14/3.38 tff(5245,plain,
% 3.14/3.38 (r(z, s(s(s(s(z)))))),
% 3.14/3.38 inference(modus_ponens,[status(thm)],[470, 5244])).
% 3.14/3.38 tff(5246,plain,
% 3.14/3.38 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[3478, 5245, 3261])).
% 3.14/3.38 tff(5247,plain,
% 3.14/3.38 (b(s(s(z)), s(s(s(s(z)))))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[164, 5246])).
% 3.14/3.38 tff(5248,plain,
% 3.14/3.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 3.14/3.38 inference(rewrite,[status(thm)],[])).
% 3.14/3.38 tff(5249,plain,
% 3.14/3.38 (((~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(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(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(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 3.14/3.38 inference(rewrite,[status(thm)],[])).
% 3.14/3.38 tff(5250,plain,
% 3.14/3.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(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(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))))),
% 3.14/3.38 inference(monotonicity,[status(thm)],[5249])).
% 3.14/3.38 tff(5251,plain,
% 3.14/3.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(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(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 3.14/3.38 inference(transitivity,[status(thm)],[5250, 5248])).
% 3.14/3.38 tff(5252,plain,
% 3.14/3.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(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(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 3.14/3.38 inference(quant_inst,[status(thm)],[])).
% 3.14/3.38 tff(5253,plain,
% 3.14/3.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 3.14/3.38 inference(modus_ponens,[status(thm)],[5252, 5251])).
% 3.14/3.38 tff(5254,plain,
% 3.14/3.38 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[5253, 178, 5247, 202, 5243, 5238])).
% 3.14/3.38 tff(5255,plain,
% 3.14/3.38 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.14/3.38 inference(modus_ponens,[status(thm)],[5254, 5217])).
% 3.14/3.38 tff(5256,plain,
% 3.14/3.38 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[1750, 5255, 1858])).
% 3.14/3.38 tff(5257,plain,
% 3.14/3.38 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.14/3.38 inference(modus_ponens,[status(thm)],[5256, 5214])).
% 3.14/3.38 tff(5258,plain,
% 3.14/3.38 (r(s(s(s(z))), s(s(s(s(z)))))),
% 3.14/3.38 inference(modus_ponens,[status(thm)],[5257, 5213])).
% 3.14/3.38 tff(5259,plain,
% 3.14/3.38 (~r(z, s(s(s(z))))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[4910, 118, 5245, 5258])).
% 3.14/3.38 tff(5260,plain,
% 3.14/3.38 ($false),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[5259, 5211])).
% 3.14/3.38 tff(5261,plain,((~(elem!1 = z)) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(z, s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.38 tff(5262,plain,
% 3.14/3.38 (s(s(s(elem!1))) = s(s(elem!1))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[5261, 5206, 3311, 202, 5198, 3261, 1858])).
% 3.14/3.38 tff(5263,plain,
% 3.14/3.38 (s(s(elem!1)) = s(s(s(elem!1)))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[3404, 5262])).
% 3.14/3.38 tff(5264,plain,
% 3.14/3.38 (s(s(s(elem!1))) = s(elem!1)),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[1649, 5263])).
% 3.14/3.38 tff(5265,plain,
% 3.14/3.38 ($false),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[1509, 5264, 5197])).
% 3.14/3.38 tff(5266,plain,((~(z = elem!1)) | b(elem!1, s(s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(z, s(s(s(s(z))))) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 3.14/3.38 tff(5267,plain,
% 3.14/3.38 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[5266, 5173, 3311, 202, 5170, 461, 1, 3170])).
% 3.14/3.38 tff(5268,plain,
% 3.14/3.38 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[1695, 5267])).
% 3.14/3.38 tff(5269,plain,
% 3.14/3.38 (s(s(elem!1)) = s(s(s(elem!1)))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[1657, 5268])).
% 3.14/3.38 tff(5270,plain,
% 3.14/3.38 (~b(s(s(s(s(elem!1)))), z)),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[5184, 5170, 3170])).
% 3.14/3.38 tff(5271,plain,
% 3.14/3.38 (r(s(s(s(s(elem!1)))), z)),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[1716, 5270])).
% 3.14/3.38 tff(5272,plain,
% 3.14/3.38 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[5194, 5271, 5173])).
% 3.14/3.38 tff(5273,plain,
% 3.14/3.38 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[1170, 5272])).
% 3.14/3.38 tff(5274,plain,
% 3.14/3.38 (~(elem!1 = s(s(s(s(elem!1)))))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[3901, 5273, 461])).
% 3.14/3.38 tff(5275,plain,
% 3.14/3.38 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[1509, 5274])).
% 3.14/3.38 tff(5276,plain,
% 3.14/3.38 ($false),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[1649, 5275, 5269])).
% 3.14/3.38 tff(5277,plain,((~r(elem!1, s(s(s(elem!1))))) | b(elem!1, s(s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | b(z, s(s(s(s(z))))) | b(s(s(s(s(z)))), z) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.38 tff(5278,plain,
% 3.14/3.38 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[5277, 5168, 202, 1, 3170, 5166, 3311, 461, 557])).
% 3.14/3.38 tff(5279,plain,
% 3.14/3.38 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[691, 5278, 701])).
% 3.14/3.38 tff(5280,plain,
% 3.14/3.38 (~r(z, s(s(z)))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[4818, 5164, 202, 3831, 557, 47])).
% 3.14/3.38 tff(5281,plain,
% 3.14/3.38 (b(z, s(s(z)))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[143, 5280])).
% 3.14/3.38 tff(5282,plain,
% 3.14/3.38 (~(elem!1 = z)),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[3276, 5281, 461])).
% 3.14/3.38 tff(5283,plain,
% 3.14/3.38 (~(s(elem!1) = elem!1)),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[2150, 949])).
% 3.14/3.38 tff(5284,plain,
% 3.14/3.38 (b(elem!1, z)),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[498, 1342, 290])).
% 3.14/3.38 tff(5285,plain,
% 3.14/3.38 (~(s(s(z)) = elem!1)),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[1345, 106, 1342])).
% 3.14/3.38 tff(5286,plain,
% 3.14/3.38 (r(s(s(z)), elem!1)),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[448, 5285, 3241])).
% 3.14/3.38 tff(5287,plain,
% 3.14/3.38 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[2803, 5286, 1265])).
% 3.14/3.38 tff(5288,plain,
% 3.14/3.38 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[249, 5287])).
% 3.14/3.38 tff(5289,plain,
% 3.14/3.38 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[1154, 5288, 273, 595, 146])).
% 3.14/3.38 tff(5290,plain,
% 3.14/3.38 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[3578, 5289])).
% 3.14/3.38 tff(5291,plain,
% 3.14/3.38 (b(s(elem!1), s(s(z)))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[2660, 5290, 273, 106, 194, 145, 165, 290, 5285])).
% 3.14/3.38 tff(5292,plain,
% 3.14/3.38 ($false),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[3089, 5291, 5290, 145, 469, 194, 273, 725, 106, 5285, 5284, 318, 165])).
% 3.14/3.38 tff(5293,plain,((~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (elem!1 = s(s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (s(elem!1) = elem!1) | (elem!1 = z) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | b(s(s(z)), elem!1) | r(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 3.14/3.38 tff(5294,plain,
% 3.14/3.38 (~r(s(s(z)), z)),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[5293, 5168, 4520, 3244, 5281, 5283, 5282, 5166, 47, 5279, 3241, 4357])).
% 3.14/3.38 tff(5295,plain,
% 3.14/3.38 (b(s(s(z)), z)),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[3249, 5294])).
% 3.14/3.38 tff(5296,plain,
% 3.14/3.38 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[3486, 178, 5295, 5281, 5166, 5168])).
% 3.14/3.38 tff(5297,plain,
% 3.14/3.38 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[249, 5296])).
% 3.14/3.38 tff(5298,plain,
% 3.14/3.38 (~r(s(s(z)), elem!1)),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[2803, 5297, 5279])).
% 3.14/3.38 tff(5299,plain,
% 3.14/3.38 (s(s(z)) = elem!1),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[448, 5298, 3241])).
% 3.14/3.38 tff(5300,plain,
% 3.14/3.38 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(elem!1))), elem!1)),
% 3.14/3.38 inference(monotonicity,[status(thm)],[5299])).
% 3.14/3.38 tff(5301,plain,
% 3.14/3.38 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(z)))),
% 3.14/3.38 inference(symmetry,[status(thm)],[5300])).
% 3.14/3.38 tff(5302,plain,
% 3.14/3.38 (b(elem!1, z)),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[498, 4357, 5282])).
% 3.14/3.38 tff(5303,plain,
% 3.14/3.38 (~(z = elem!1)),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[317, 5282])).
% 3.14/3.38 tff(5304,plain,
% 3.14/3.38 (b(z, elem!1)),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[585, 5169, 5303])).
% 3.14/3.38 tff(5305,plain,
% 3.14/3.38 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[3455, 178, 5304, 5302, 5166, 5168])).
% 3.14/3.38 tff(5306,plain,
% 3.14/3.38 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[3444, 5305, 4245])).
% 3.14/3.38 tff(5307,plain,
% 3.14/3.38 (~r(s(s(s(s(z)))), elem!1)),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[3442, 5306, 1130])).
% 3.14/3.38 tff(5308,assumption,(~b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 3.14/3.38 tff(5309,plain,
% 3.14/3.38 (r(s(s(s(elem!1))), elem!1)),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[570, 949, 5308])).
% 3.14/3.38 tff(5310,plain,
% 3.14/3.38 (~r(z, elem!1)),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[565, 5309, 557])).
% 3.14/3.38 tff(5311,plain,
% 3.14/3.38 (b(z, elem!1)),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[585, 5310, 318])).
% 3.14/3.38 tff(5312,plain,
% 3.14/3.38 ((~b(z, elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[2818, 178, 506, 1145, 1140])).
% 3.14/3.38 tff(5313,plain,
% 3.14/3.38 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[5312, 5311])).
% 3.14/3.38 tff(5314,plain,
% 3.14/3.38 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[691, 5313, 701])).
% 3.14/3.38 tff(5315,plain,
% 3.14/3.38 (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)))))),
% 3.14/3.38 inference(monotonicity,[status(thm)],[3494])).
% 3.14/3.38 tff(5316,plain,
% 3.14/3.38 (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)))))),
% 3.14/3.38 inference(symmetry,[status(thm)],[5315])).
% 3.14/3.38 tff(5317,plain,
% 3.14/3.38 ((~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))))))),
% 3.14/3.38 inference(monotonicity,[status(thm)],[5316])).
% 3.14/3.38 tff(5318,plain,
% 3.14/3.38 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.14/3.38 inference(modus_ponens,[status(thm)],[4171, 5317])).
% 3.14/3.38 tff(5319,plain,
% 3.14/3.38 ($false),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[1130, 5318])).
% 3.14/3.38 tff(5320,plain,((~(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(s(z)))))) | r(s(s(s(elem!1))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.38 tff(5321,plain,
% 3.14/3.38 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[5320, 1130, 3822])).
% 3.14/3.38 tff(5322,plain,
% 3.14/3.38 (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 3.14/3.38 inference(modus_ponens,[status(thm)],[5321, 3541])).
% 3.14/3.38 tff(5323,plain,
% 3.14/3.38 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[3455, 178, 5311, 506, 1145, 1140])).
% 3.14/3.38 tff(5324,plain,
% 3.14/3.38 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[3444, 5323, 4245])).
% 3.14/3.38 tff(5325,plain,
% 3.14/3.38 (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[3680, 118, 5309, 5324])).
% 3.14/3.38 tff(5326,plain,
% 3.14/3.38 ((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))))))))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[3612, 41, 5325])).
% 3.14/3.38 tff(5327,plain,
% 3.14/3.38 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[5326, 5322])).
% 3.14/3.38 tff(5328,plain,
% 3.14/3.38 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[4252, 118, 5309, 5324])).
% 3.14/3.38 tff(5329,plain,
% 3.14/3.38 (b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[3524, 41, 5321, 5328])).
% 3.14/3.38 tff(5330,plain,
% 3.14/3.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(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))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(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))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.14/3.38 inference(rewrite,[status(thm)],[])).
% 3.14/3.38 tff(5331,plain,
% 3.14/3.38 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(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(s(elem!1))), z)) | (~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(s(s(s(elem!1))), z)) | (~b(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(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.14/3.38 inference(rewrite,[status(thm)],[])).
% 3.14/3.38 tff(5332,plain,
% 3.14/3.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), 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(elem!1))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(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))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))))),
% 3.14/3.38 inference(monotonicity,[status(thm)],[5331])).
% 3.14/3.38 tff(5333,plain,
% 3.14/3.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), 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(elem!1))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(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))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.14/3.38 inference(transitivity,[status(thm)],[5332, 5330])).
% 3.14/3.38 tff(5334,plain,
% 3.14/3.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), 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(elem!1))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.14/3.38 inference(quant_inst,[status(thm)],[])).
% 3.14/3.38 tff(5335,plain,
% 3.14/3.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(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))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 3.14/3.38 inference(modus_ponens,[status(thm)],[5334, 5333])).
% 3.14/3.38 tff(5336,plain,
% 3.14/3.38 (~b(s(s(s(elem!1))), z)),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[5335, 178, 1145, 1140, 5329, 5327])).
% 3.14/3.38 tff(5337,plain,
% 3.14/3.38 (r(s(s(s(elem!1))), z)),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[1565, 5336])).
% 3.14/3.38 tff(5338,plain,
% 3.14/3.38 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.14/3.38 inference(rewrite,[status(thm)],[])).
% 3.14/3.38 tff(5339,plain,
% 3.14/3.38 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.14/3.38 inference(quant_inst,[status(thm)],[])).
% 3.14/3.38 tff(5340,plain,
% 3.14/3.38 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 3.14/3.38 inference(modus_ponens,[status(thm)],[5339, 5338])).
% 3.14/3.38 tff(5341,plain,
% 3.14/3.38 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[5340, 118, 5337, 194])).
% 3.14/3.38 tff(5342,plain,
% 3.14/3.38 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[3296, 41, 5341, 4166])).
% 3.14/3.38 tff(5343,plain,
% 3.14/3.38 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[4216, 118, 556, 438])).
% 3.14/3.38 tff(5344,plain,
% 3.14/3.38 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[2803, 438, 1265])).
% 3.14/3.38 tff(5345,plain,
% 3.14/3.38 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.14/3.38 inference(unit_resolution,[status(thm)],[249, 5344])).
% 3.14/3.38 tff(5346,plain,
% 3.14/3.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.14/3.38 inference(rewrite,[status(thm)],[])).
% 3.14/3.38 tff(5347,plain,
% 3.14/3.38 (((~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(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.14/3.38 inference(rewrite,[status(thm)],[])).
% 3.14/3.38 tff(5348,plain,
% 3.14/3.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 3.14/3.38 inference(monotonicity,[status(thm)],[5347])).
% 3.14/3.38 tff(5349,plain,
% 3.14/3.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.14/3.38 inference(transitivity,[status(thm)],[5348, 5346])).
% 3.14/3.38 tff(5350,plain,
% 3.14/3.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 3.14/3.38 inference(quant_inst,[status(thm)],[])).
% 3.14/3.38 tff(5351,plain,
% 3.14/3.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 3.14/3.39 inference(modus_ponens,[status(thm)],[5350, 5349])).
% 3.14/3.39 tff(5352,plain,
% 3.14/3.39 (~b(s(s(z)), s(s(s(elem!1))))),
% 3.14/3.39 inference(unit_resolution,[status(thm)],[5351, 178, 5345, 202, 3828, 3830])).
% 3.14/3.39 tff(5353,plain,
% 3.14/3.39 ($false),
% 3.14/3.39 inference(unit_resolution,[status(thm)],[4223, 5352, 5343])).
% 3.14/3.39 tff(5354,plain,((~r(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.39 tff(5355,plain,
% 3.14/3.39 (~r(s(s(z)), elem!1)),
% 3.14/3.39 inference(unit_resolution,[status(thm)],[5354, 5342, 202, 5327, 5309, 5314])).
% 3.14/3.39 tff(5356,plain,
% 3.14/3.39 (s(s(z)) = elem!1),
% 3.14/3.39 inference(unit_resolution,[status(thm)],[448, 5355, 3241])).
% 3.14/3.39 tff(5357,plain,
% 3.14/3.39 (s(s(z)) = s(s(s(s(s(s(z))))))),
% 3.14/3.39 inference(transitivity,[status(thm)],[1324, 517, 646, 57])).
% 3.14/3.39 tff(5358,plain,
% 3.14/3.39 (s(s(s(z))) = s(s(s(s(s(s(s(z)))))))),
% 3.14/3.39 inference(monotonicity,[status(thm)],[5357])).
% 3.14/3.39 tff(5359,plain,
% 3.14/3.39 (s(s(s(s(s(s(s(z))))))) = s(s(s(z)))),
% 3.14/3.39 inference(symmetry,[status(thm)],[5358])).
% 3.14/3.39 tff(5360,plain,
% 3.14/3.39 ($false),
% 3.14/3.39 inference(unit_resolution,[status(thm)],[1104, 5359])).
% 3.14/3.39 tff(5361,plain,((~(s(s(z)) = elem!1)) | (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.39 tff(5362,plain,
% 3.14/3.39 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.14/3.39 inference(unit_resolution,[status(thm)],[5361, 5356])).
% 3.14/3.39 tff(5363,plain,
% 3.14/3.39 (s(s(s(z))) = s(elem!1)),
% 3.14/3.39 inference(monotonicity,[status(thm)],[5356])).
% 3.14/3.39 tff(5364,plain,
% 3.14/3.39 (s(s(s(s(z)))) = s(s(elem!1))),
% 3.14/3.39 inference(monotonicity,[status(thm)],[5363])).
% 3.14/3.39 tff(5365,plain,
% 3.14/3.39 (s(s(elem!1)) = s(s(s(s(z))))),
% 3.14/3.39 inference(symmetry,[status(thm)],[5364])).
% 3.14/3.39 tff(5366,plain,
% 3.14/3.39 (r(s(elem!1), s(s(elem!1))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 3.14/3.39 inference(monotonicity,[status(thm)],[5365])).
% 3.14/3.39 tff(5367,plain,
% 3.14/3.39 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 3.14/3.39 inference(monotonicity,[status(thm)],[5364])).
% 3.14/3.39 tff(5368,plain,
% 3.14/3.39 ((~r(s(s(s(s(z)))), elem!1)) <=> (~r(s(s(elem!1)), elem!1))),
% 3.14/3.39 inference(monotonicity,[status(thm)],[5367])).
% 3.14/3.39 tff(5369,assumption,(~r(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 3.14/3.39 tff(5370,plain,
% 3.14/3.39 (~r(s(s(elem!1)), elem!1)),
% 3.14/3.39 inference(modus_ponens,[status(thm)],[5369, 5368])).
% 3.14/3.39 tff(5371,plain,
% 3.14/3.39 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.14/3.39 inference(monotonicity,[status(thm)],[5364])).
% 3.14/3.39 tff(5372,plain,
% 3.14/3.39 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.14/3.39 inference(modus_ponens,[status(thm)],[5342, 5371])).
% 3.14/3.39 tff(5373,plain,
% 3.14/3.39 (elem!1 = s(s(z))),
% 3.14/3.39 inference(symmetry,[status(thm)],[5356])).
% 3.14/3.39 tff(5374,plain,
% 3.14/3.39 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(z)) = s(s(s(s(elem!1)))))),
% 3.14/3.39 inference(monotonicity,[status(thm)],[5373])).
% 3.14/3.39 tff(5375,plain,
% 3.14/3.39 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 3.14/3.39 inference(symmetry,[status(thm)],[5374])).
% 3.14/3.39 tff(5376,plain,
% 3.14/3.39 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 3.14/3.39 inference(monotonicity,[status(thm)],[5375])).
% 3.14/3.39 tff(5377,plain,
% 3.14/3.39 (~(elem!1 = s(s(s(s(elem!1)))))),
% 3.14/3.39 inference(modus_ponens,[status(thm)],[2131, 5376])).
% 3.14/3.39 tff(5378,plain,
% 3.14/3.39 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.14/3.39 inference(unit_resolution,[status(thm)],[1509, 5377])).
% 3.14/3.39 tff(5379,plain,
% 3.14/3.39 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.14/3.39 inference(monotonicity,[status(thm)],[5364])).
% 3.14/3.39 tff(5380,plain,
% 3.14/3.39 ((~(s(s(s(s(z)))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(z))))))),
% 3.14/3.39 inference(monotonicity,[status(thm)],[3289])).
% 3.14/3.39 tff(5381,plain,
% 3.14/3.39 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.14/3.39 inference(modus_ponens,[status(thm)],[4166, 5380])).
% 3.14/3.39 tff(5382,plain,
% 3.14/3.39 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.14/3.39 inference(unit_resolution,[status(thm)],[3825, 41, 5381, 3822])).
% 3.14/3.39 tff(5383,plain,
% 3.14/3.39 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.14/3.39 inference(modus_ponens,[status(thm)],[5382, 5379])).
% 3.14/3.39 tff(5384,assumption,(~r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 3.14/3.39 tff(5385,plain,
% 3.14/3.39 (b(s(s(elem!1)), elem!1)),
% 3.14/3.39 inference(unit_resolution,[status(thm)],[3362, 1547, 5384])).
% 3.14/3.39 tff(5386,plain,
% 3.14/3.39 ((~(elem!1 = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 3.14/3.39 inference(monotonicity,[status(thm)],[1526])).
% 3.14/3.39 tff(5387,plain,
% 3.14/3.39 (~(s(s(s(elem!1))) = elem!1)),
% 3.14/3.39 inference(modus_ponens,[status(thm)],[1586, 5386])).
% 3.14/3.39 tff(5388,assumption,(~r(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 3.14/3.39 tff(5389,plain,
% 3.14/3.39 (~(s(elem!1) = s(s(elem!1)))),
% 3.14/3.39 inference(unit_resolution,[status(thm)],[979, 1547])).
% 3.14/3.39 tff(5390,plain,
% 3.14/3.39 (b(s(elem!1), s(s(elem!1)))),
% 3.14/3.39 inference(unit_resolution,[status(thm)],[1028, 5389, 5388])).
% 3.14/3.39 tff(5391,assumption,(b(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 3.14/3.39 tff(5392,assumption,(s(elem!1) = s(s(s(elem!1)))), introduced(assumption)).
% 3.14/3.39 tff(5393,plain,
% 3.14/3.39 (s(s(s(elem!1))) = s(elem!1)),
% 3.14/3.39 inference(modus_ponens,[status(thm)],[5392, 3881])).
% 3.14/3.39 tff(5394,plain,
% 3.14/3.39 ($false),
% 3.14/3.39 inference(unit_resolution,[status(thm)],[356, 5393])).
% 3.14/3.39 tff(5395,plain,((~(s(elem!1) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.39 tff(5396,plain,
% 3.14/3.39 (~(s(elem!1) = s(s(s(elem!1))))),
% 3.14/3.39 inference(unit_resolution,[status(thm)],[5395, 356])).
% 3.14/3.39 tff(5397,plain,
% 3.14/3.39 (b(elem!1, z)),
% 3.14/3.39 inference(unit_resolution,[status(thm)],[498, 4357, 290])).
% 3.14/3.39 tff(5398,plain,
% 3.14/3.39 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)))),
% 3.14/3.39 inference(rewrite,[status(thm)],[])).
% 3.14/3.39 tff(5399,plain,
% 3.14/3.39 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)))),
% 3.14/3.39 inference(rewrite,[status(thm)],[])).
% 3.14/3.39 tff(5400,plain,
% 3.14/3.39 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1))))),
% 3.14/3.39 inference(monotonicity,[status(thm)],[5399])).
% 3.14/3.39 tff(5401,plain,
% 3.14/3.39 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)))),
% 3.14/3.39 inference(transitivity,[status(thm)],[5400, 5398])).
% 3.14/3.39 tff(5402,plain,
% 3.14/3.39 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)))),
% 3.14/3.39 inference(quant_inst,[status(thm)],[])).
% 3.14/3.39 tff(5403,plain,
% 3.14/3.39 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1))),
% 3.14/3.39 inference(modus_ponens,[status(thm)],[5402, 5401])).
% 3.14/3.39 tff(5404,plain,
% 3.14/3.39 (~r(s(elem!1), elem!1)),
% 3.14/3.39 inference(unit_resolution,[status(thm)],[5403, 118, 3311, 2102])).
% 3.14/3.39 tff(5405,plain,
% 3.14/3.39 (b(s(elem!1), elem!1)),
% 3.14/3.39 inference(unit_resolution,[status(thm)],[677, 5404, 725])).
% 3.14/3.39 tff(5406,plain,
% 3.14/3.39 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))))),
% 3.14/3.39 inference(rewrite,[status(thm)],[])).
% 3.14/3.39 tff(5407,plain,
% 3.14/3.39 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))))),
% 3.14/3.39 inference(rewrite,[status(thm)],[])).
% 3.14/3.39 tff(5408,plain,
% 3.14/3.39 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1)))))))),
% 3.14/3.39 inference(monotonicity,[status(thm)],[5407])).
% 3.14/3.39 tff(5409,plain,
% 3.14/3.39 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))))),
% 3.14/3.39 inference(transitivity,[status(thm)],[5408, 5406])).
% 3.14/3.39 tff(5410,plain,
% 3.14/3.39 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(elem!1))))),
% 3.14/3.39 inference(quant_inst,[status(thm)],[])).
% 3.14/3.39 tff(5411,plain,
% 3.14/3.39 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1)))))),
% 3.14/3.39 inference(modus_ponens,[status(thm)],[5410, 5409])).
% 3.14/3.39 tff(5412,plain,
% 3.14/3.39 (~r(z, s(elem!1))),
% 3.14/3.39 inference(unit_resolution,[status(thm)],[5411, 118, 557, 2102])).
% 3.14/3.39 tff(5413,plain,
% 3.14/3.39 (b(z, s(elem!1))),
% 3.14/3.39 inference(unit_resolution,[status(thm)],[2351, 5412])).
% 3.14/3.39 tff(5414,plain,
% 3.14/3.39 (~b(elem!1, s(elem!1))),
% 3.14/3.39 inference(unit_resolution,[status(thm)],[1396, 5413, 818, 506, 5405])).
% 3.14/3.39 tff(5415,plain,
% 3.14/3.39 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))),
% 3.14/3.39 inference(rewrite,[status(thm)],[])).
% 3.14/3.39 tff(5416,plain,
% 3.14/3.39 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))),
% 3.14/3.39 inference(rewrite,[status(thm)],[])).
% 3.14/3.39 tff(5417,plain,
% 3.14/3.39 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1)))))))),
% 3.14/3.39 inference(monotonicity,[status(thm)],[5416])).
% 3.14/3.39 tff(5418,plain,
% 3.14/3.39 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))),
% 3.14/3.39 inference(transitivity,[status(thm)],[5417, 5415])).
% 3.14/3.39 tff(5419,plain,
% 3.14/3.39 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))))),
% 3.14/3.39 inference(quant_inst,[status(thm)],[])).
% 3.14/3.39 tff(5420,plain,
% 3.14/3.39 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1)))))),
% 3.14/3.39 inference(modus_ponens,[status(thm)],[5419, 5418])).
% 3.14/3.39 tff(5421,plain,
% 3.14/3.39 (~r(elem!1, s(elem!1))),
% 3.14/3.39 inference(unit_resolution,[status(thm)],[5420, 118, 3311, 2102])).
% 3.14/3.39 tff(5422,plain,
% 3.14/3.39 ($false),
% 3.14/3.39 inference(unit_resolution,[status(thm)],[754, 41, 5421, 5414, 749])).
% 3.14/3.39 tff(5423,plain,((~r(s(elem!1), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(elem!1) = elem!1) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.39 tff(5424,plain,
% 3.14/3.39 (~r(s(elem!1), s(s(s(elem!1))))),
% 3.14/3.39 inference(unit_resolution,[status(thm)],[5423, 5397, 818, 5283, 557, 3311])).
% 3.14/3.39 tff(5425,assumption,(~(s(elem!1) = s(s(s(elem!1))))), introduced(assumption)).
% 3.14/3.39 tff(5426,assumption,(~r(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 3.14/3.39 tff(5427,assumption,(~b(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 3.14/3.39 tff(5428,plain,
% 3.14/3.39 (((~![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)))))),
% 3.14/3.39 inference(rewrite,[status(thm)],[])).
% 3.14/3.39 tff(5429,plain,
% 3.14/3.39 ((~![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)))))),
% 3.14/3.39 inference(quant_inst,[status(thm)],[])).
% 3.14/3.39 tff(5430,plain,
% 3.14/3.39 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1))))),
% 3.14/3.39 inference(modus_ponens,[status(thm)],[5429, 5428])).
% 3.14/3.39 tff(5431,plain,
% 3.14/3.39 ($false),
% 3.14/3.39 inference(unit_resolution,[status(thm)],[5430, 41, 5427, 5426, 5425])).
% 3.14/3.39 tff(5432,plain,(b(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1)))) | (s(elem!1) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.39 tff(5433,plain,
% 3.14/3.39 (b(s(elem!1), s(s(s(elem!1))))),
% 3.14/3.39 inference(unit_resolution,[status(thm)],[5432, 5424, 5396])).
% 3.14/3.39 tff(5434,assumption,(b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 3.14/3.39 tff(5435,plain,
% 3.14/3.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 3.14/3.39 inference(rewrite,[status(thm)],[])).
% 3.14/3.39 tff(5436,plain,
% 3.14/3.39 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 3.14/3.39 inference(rewrite,[status(thm)],[])).
% 3.14/3.39 tff(5437,plain,
% 3.14/3.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 3.14/3.39 inference(monotonicity,[status(thm)],[5436])).
% 3.14/3.39 tff(5438,plain,
% 3.14/3.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 3.14/3.39 inference(transitivity,[status(thm)],[5437, 5435])).
% 3.14/3.39 tff(5439,plain,
% 3.14/3.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 3.14/3.39 inference(quant_inst,[status(thm)],[])).
% 3.14/3.39 tff(5440,plain,
% 3.14/3.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 3.14/3.39 inference(modus_ponens,[status(thm)],[5439, 5438])).
% 3.14/3.39 tff(5441,plain,
% 3.14/3.39 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.14/3.39 inference(unit_resolution,[status(thm)],[5440, 178, 5433, 3512, 5391, 3511])).
% 3.14/3.39 tff(5442,plain,
% 3.14/3.39 (r(s(s(s(elem!1))), s(elem!1))),
% 3.14/3.39 inference(unit_resolution,[status(thm)],[373, 5441, 356])).
% 3.14/3.39 tff(5443,plain,
% 3.14/3.39 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))))),
% 3.14/3.39 inference(rewrite,[status(thm)],[])).
% 3.14/3.39 tff(5444,plain,
% 3.14/3.39 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))))),
% 3.14/3.39 inference(quant_inst,[status(thm)],[])).
% 3.14/3.39 tff(5445,plain,
% 3.14/3.39 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1)))))),
% 3.14/3.39 inference(modus_ponens,[status(thm)],[5444, 5443])).
% 3.14/3.39 tff(5446,plain,
% 3.14/3.39 ($false),
% 3.14/3.39 inference(unit_resolution,[status(thm)],[5445, 118, 1551, 2333, 557])).
% 3.14/3.39 tff(5447,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.39 tff(5448,plain,
% 3.14/3.39 (~r(z, s(elem!1))),
% 3.14/3.39 inference(unit_resolution,[status(thm)],[5447, 5442, 557])).
% 3.14/3.39 tff(5449,plain,
% 3.14/3.39 (b(z, s(elem!1))),
% 3.14/3.39 inference(unit_resolution,[status(thm)],[2351, 5448])).
% 3.14/3.39 tff(5450,plain,
% 3.14/3.39 (~(elem!1 = s(elem!1))),
% 3.14/3.39 inference(unit_resolution,[status(thm)],[748, 5283])).
% 3.14/3.39 tff(5451,plain,
% 3.14/3.39 (~r(elem!1, s(elem!1))),
% 3.14/3.39 inference(unit_resolution,[status(thm)],[1591, 5442, 3311])).
% 3.14/3.39 tff(5452,plain,
% 3.14/3.39 (b(elem!1, s(elem!1))),
% 3.14/3.39 inference(unit_resolution,[status(thm)],[754, 41, 5451, 5450])).
% 3.14/3.39 tff(5453,plain,
% 3.14/3.39 (~b(s(elem!1), elem!1)),
% 3.14/3.39 inference(unit_resolution,[status(thm)],[1396, 5452, 818, 5397, 5449])).
% 3.14/3.39 tff(5454,plain,
% 3.14/3.39 (r(s(elem!1), elem!1)),
% 3.14/3.39 inference(unit_resolution,[status(thm)],[677, 5453, 5283])).
% 3.14/3.39 tff(5455,plain,
% 3.14/3.39 (~r(s(s(s(elem!1))), elem!1)),
% 3.14/3.39 inference(unit_resolution,[status(thm)],[1576, 5454, 5442])).
% 3.14/3.39 tff(5456,plain,
% 3.14/3.39 (b(s(s(s(elem!1))), elem!1)),
% 3.14/3.39 inference(unit_resolution,[status(thm)],[570, 5455, 949])).
% 3.14/3.39 tff(5457,plain,
% 3.14/3.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.14/3.39 inference(rewrite,[status(thm)],[])).
% 3.14/3.39 tff(5458,plain,
% 3.14/3.39 (((~b(s(s(elem!1)), 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(elem!1), 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(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.14/3.39 inference(rewrite,[status(thm)],[])).
% 3.14/3.39 tff(5459,plain,
% 3.14/3.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 3.14/3.39 inference(monotonicity,[status(thm)],[5458])).
% 3.14/3.39 tff(5460,plain,
% 3.14/3.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.14/3.39 inference(transitivity,[status(thm)],[5459, 5457])).
% 3.14/3.39 tff(5461,plain,
% 3.14/3.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 3.14/3.39 inference(quant_inst,[status(thm)],[])).
% 3.14/3.39 tff(5462,plain,
% 3.14/3.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 3.14/3.39 inference(modus_ponens,[status(thm)],[5461, 5460])).
% 3.14/3.39 tff(5463,plain,
% 3.14/3.39 ($false),
% 3.14/3.39 inference(unit_resolution,[status(thm)],[5462, 178, 5456, 5434, 5433, 3512, 5391])).
% 3.14/3.39 tff(5464,plain,((~r(elem!1, s(s(s(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(elem!1)))) | (s(s(s(elem!1))) = elem!1) | (~b(z, elem!1)) | (~r(z, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 3.14/3.39 tff(5465,plain,
% 3.14/3.39 (~r(elem!1, s(s(s(elem!1))))),
% 3.14/3.39 inference(unit_resolution,[status(thm)],[5464, 5385, 3512, 5390, 5387, 818, 557, 356, 3511, 290])).
% 3.14/3.39 tff(5466,plain,
% 3.14/3.39 (b(elem!1, s(s(s(elem!1))))),
% 3.14/3.39 inference(unit_resolution,[status(thm)],[2054, 5465, 1586])).
% 3.14/3.39 tff(5467,assumption,(~r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 3.14/3.39 tff(5468,plain,
% 3.14/3.39 (((~![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))))),
% 3.14/3.40 inference(rewrite,[status(thm)],[])).
% 3.14/3.40 tff(5469,plain,
% 3.14/3.40 ((~![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))))),
% 3.14/3.40 inference(quant_inst,[status(thm)],[])).
% 3.14/3.40 tff(5470,plain,
% 3.14/3.40 ((~![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)))),
% 3.14/3.40 inference(modus_ponens,[status(thm)],[5469, 5468])).
% 3.14/3.40 tff(5471,plain,
% 3.14/3.40 (b(elem!1, s(s(elem!1)))),
% 3.14/3.40 inference(unit_resolution,[status(thm)],[5470, 41, 1544, 5467])).
% 3.14/3.40 tff(5472,plain,
% 3.14/3.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 3.14/3.40 inference(rewrite,[status(thm)],[])).
% 3.14/3.40 tff(5473,plain,
% 3.14/3.40 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 3.14/3.40 inference(rewrite,[status(thm)],[])).
% 3.14/3.40 tff(5474,plain,
% 3.14/3.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 3.14/3.40 inference(monotonicity,[status(thm)],[5473])).
% 3.14/3.40 tff(5475,plain,
% 3.14/3.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 3.14/3.40 inference(transitivity,[status(thm)],[5474, 5472])).
% 3.14/3.40 tff(5476,plain,
% 3.14/3.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))),
% 3.14/3.40 inference(quant_inst,[status(thm)],[])).
% 3.14/3.40 tff(5477,plain,
% 3.14/3.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 3.24/3.40 inference(modus_ponens,[status(thm)],[5476, 5475])).
% 3.24/3.40 tff(5478,plain,
% 3.24/3.40 ($false),
% 3.24/3.40 inference(unit_resolution,[status(thm)],[5477, 178, 5434, 2042, 3512, 3511, 5471])).
% 3.24/3.40 tff(5479,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (elem!1 = s(s(elem!1))) | r(elem!1, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.40 tff(5480,plain,
% 3.24/3.40 (r(elem!1, s(s(elem!1)))),
% 3.24/3.40 inference(unit_resolution,[status(thm)],[5479, 5466, 3511, 3512, 1540, 5385])).
% 3.24/3.40 tff(5481,plain,
% 3.24/3.40 (~(s(s(elem!1)) = s(elem!1))),
% 3.24/3.40 inference(unit_resolution,[status(thm)],[986, 5389])).
% 3.24/3.40 tff(5482,plain,
% 3.24/3.40 (~(s(elem!1) = elem!1)),
% 3.24/3.40 inference(unit_resolution,[status(thm)],[2150, 5387])).
% 3.24/3.40 tff(5483,plain,
% 3.24/3.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 3.24/3.40 inference(rewrite,[status(thm)],[])).
% 3.24/3.40 tff(5484,plain,
% 3.24/3.40 (((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(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), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 3.24/3.40 inference(rewrite,[status(thm)],[])).
% 3.24/3.40 tff(5485,plain,
% 3.24/3.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(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(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 3.24/3.40 inference(monotonicity,[status(thm)],[5484])).
% 3.24/3.40 tff(5486,plain,
% 3.24/3.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(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(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 3.24/3.40 inference(transitivity,[status(thm)],[5485, 5483])).
% 3.24/3.40 tff(5487,plain,
% 3.24/3.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(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(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 3.24/3.40 inference(quant_inst,[status(thm)],[])).
% 3.24/3.40 tff(5488,plain,
% 3.24/3.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 3.24/3.40 inference(modus_ponens,[status(thm)],[5487, 5486])).
% 3.24/3.40 tff(5489,plain,
% 3.24/3.40 ($false),
% 3.24/3.40 inference(unit_resolution,[status(thm)],[5488, 178, 683, 5434, 2042, 5391, 3511])).
% 3.24/3.40 tff(5490,plain,((~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), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.40 tff(5491,plain,
% 3.24/3.40 (~b(s(elem!1), elem!1)),
% 3.24/3.40 inference(unit_resolution,[status(thm)],[5490, 5385, 5466, 5390, 3511])).
% 3.24/3.40 tff(5492,plain,
% 3.24/3.40 (r(s(elem!1), elem!1)),
% 3.24/3.40 inference(unit_resolution,[status(thm)],[677, 5491, 5482])).
% 3.24/3.40 tff(5493,plain,
% 3.24/3.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 3.24/3.40 inference(rewrite,[status(thm)],[])).
% 3.24/3.40 tff(5494,plain,
% 3.24/3.40 (((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(s(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))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 3.24/3.40 inference(rewrite,[status(thm)],[])).
% 3.24/3.40 tff(5495,plain,
% 3.24/3.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(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(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 3.24/3.40 inference(monotonicity,[status(thm)],[5494])).
% 3.24/3.40 tff(5496,plain,
% 3.24/3.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(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(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 3.24/3.40 inference(transitivity,[status(thm)],[5495, 5493])).
% 3.24/3.40 tff(5497,plain,
% 3.24/3.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(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(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.24/3.40 inference(quant_inst,[status(thm)],[])).
% 3.24/3.40 tff(5498,plain,
% 3.24/3.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 3.24/3.40 inference(modus_ponens,[status(thm)],[5497, 5496])).
% 3.24/3.40 tff(5499,plain,
% 3.24/3.40 ($false),
% 3.24/3.40 inference(unit_resolution,[status(thm)],[5498, 178, 1597, 5434, 2042, 3512, 3511])).
% 3.24/3.40 tff(5500,plain,((~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))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.40 tff(5501,plain,
% 3.24/3.40 (~b(s(s(s(elem!1))), elem!1)),
% 3.24/3.40 inference(unit_resolution,[status(thm)],[5500, 5385, 5466, 3512, 3511])).
% 3.24/3.40 tff(5502,plain,
% 3.24/3.40 (r(s(s(s(elem!1))), elem!1)),
% 3.24/3.40 inference(unit_resolution,[status(thm)],[570, 5501, 5387])).
% 3.24/3.40 tff(5503,plain,
% 3.24/3.40 (~r(s(elem!1), s(s(s(elem!1))))),
% 3.24/3.40 inference(unit_resolution,[status(thm)],[2110, 5502, 5492])).
% 3.24/3.40 tff(5504,plain,
% 3.24/3.40 (b(s(elem!1), s(s(s(elem!1))))),
% 3.24/3.40 inference(unit_resolution,[status(thm)],[5432, 5503, 5396])).
% 3.24/3.40 tff(5505,plain,
% 3.24/3.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 3.24/3.40 inference(rewrite,[status(thm)],[])).
% 3.24/3.40 tff(5506,plain,
% 3.24/3.40 (((~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(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 3.24/3.40 inference(rewrite,[status(thm)],[])).
% 3.24/3.40 tff(5507,plain,
% 3.24/3.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(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(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 3.24/3.40 inference(monotonicity,[status(thm)],[5506])).
% 3.24/3.40 tff(5508,plain,
% 3.24/3.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(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(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 3.24/3.40 inference(transitivity,[status(thm)],[5507, 5505])).
% 3.24/3.40 tff(5509,plain,
% 3.24/3.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(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(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 3.24/3.40 inference(quant_inst,[status(thm)],[])).
% 3.24/3.40 tff(5510,plain,
% 3.24/3.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 3.24/3.40 inference(modus_ponens,[status(thm)],[5509, 5508])).
% 3.24/3.40 tff(5511,plain,
% 3.24/3.40 ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 3.24/3.40 inference(unit_resolution,[status(thm)],[5510, 178, 3512, 5390, 3511])).
% 3.24/3.40 tff(5512,plain,
% 3.24/3.40 (~b(s(s(elem!1)), s(elem!1))),
% 3.24/3.40 inference(unit_resolution,[status(thm)],[5511, 5504])).
% 3.24/3.40 tff(5513,plain,
% 3.24/3.40 (r(s(s(elem!1)), s(elem!1))),
% 3.24/3.40 inference(unit_resolution,[status(thm)],[1006, 5512, 5481])).
% 3.24/3.40 tff(5514,plain,
% 3.24/3.40 (~(elem!1 = s(elem!1))),
% 3.24/3.40 inference(unit_resolution,[status(thm)],[748, 5482])).
% 3.24/3.40 tff(5515,plain,
% 3.24/3.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.24/3.40 inference(rewrite,[status(thm)],[])).
% 3.24/3.40 tff(5516,plain,
% 3.24/3.40 (((~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(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(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.24/3.40 inference(rewrite,[status(thm)],[])).
% 3.24/3.40 tff(5517,plain,
% 3.24/3.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 3.24/3.40 inference(monotonicity,[status(thm)],[5516])).
% 3.24/3.40 tff(5518,plain,
% 3.24/3.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.24/3.40 inference(transitivity,[status(thm)],[5517, 5515])).
% 3.24/3.40 tff(5519,plain,
% 3.24/3.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))),
% 3.24/3.40 inference(quant_inst,[status(thm)],[])).
% 3.24/3.40 tff(5520,plain,
% 3.24/3.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 3.24/3.40 inference(modus_ponens,[status(thm)],[5519, 5518])).
% 3.24/3.40 tff(5521,plain,
% 3.24/3.40 ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 3.24/3.40 inference(unit_resolution,[status(thm)],[5520, 178, 5466, 3512, 5390])).
% 3.24/3.40 tff(5522,plain,
% 3.24/3.40 (~b(elem!1, s(elem!1))),
% 3.24/3.40 inference(unit_resolution,[status(thm)],[5521, 5504])).
% 3.24/3.40 tff(5523,plain,
% 3.24/3.40 (r(elem!1, s(elem!1))),
% 3.24/3.40 inference(unit_resolution,[status(thm)],[754, 41, 5522, 5514])).
% 3.24/3.40 tff(5524,plain,
% 3.24/3.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))))),
% 3.24/3.40 inference(rewrite,[status(thm)],[])).
% 3.24/3.40 tff(5525,plain,
% 3.24/3.40 (((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))))),
% 3.24/3.40 inference(rewrite,[status(thm)],[])).
% 3.24/3.40 tff(5526,plain,
% 3.24/3.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1))))))),
% 3.24/3.40 inference(monotonicity,[status(thm)],[5525])).
% 3.24/3.40 tff(5527,plain,
% 3.24/3.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))))),
% 3.24/3.40 inference(transitivity,[status(thm)],[5526, 5524])).
% 3.24/3.40 tff(5528,plain,
% 3.24/3.40 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))))),
% 3.24/3.40 inference(quant_inst,[status(thm)],[])).
% 3.24/3.40 tff(5529,plain,
% 3.24/3.40 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1))))),
% 3.24/3.40 inference(modus_ponens,[status(thm)],[5528, 5527])).
% 3.24/3.40 tff(5530,plain,
% 3.24/3.40 ($false),
% 3.24/3.40 inference(unit_resolution,[status(thm)],[5529, 118, 5523, 5513, 5480])).
% 3.24/3.40 tff(5531,plain,((s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (elem!1 = s(s(s(elem!1)))) | (~b(z, elem!1)) | (~r(z, s(s(s(elem!1))))) | (elem!1 = z) | r(s(elem!1), s(s(elem!1))) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.24/3.40 tff(5532,plain,
% 3.24/3.40 (r(s(elem!1), s(s(elem!1)))),
% 3.24/3.40 inference(unit_resolution,[status(thm)],[5531, 5383, 5311, 5378, 1585, 557, 290, 5372, 5370])).
% 3.24/3.40 tff(5533,plain,
% 3.24/3.40 (r(s(elem!1), s(s(s(s(z)))))),
% 3.24/3.40 inference(modus_ponens,[status(thm)],[5532, 5366])).
% 3.24/3.40 tff(5534,plain,
% 3.24/3.40 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.24/3.40 inference(modus_ponens,[status(thm)],[5362, 2561])).
% 3.24/3.40 tff(5535,plain,
% 3.24/3.40 (r(z, s(s(s(s(z))))) <=> r(z, s(s(elem!1)))),
% 3.24/3.41 inference(monotonicity,[status(thm)],[5364])).
% 3.24/3.41 tff(5536,plain,
% 3.24/3.41 (r(z, s(s(elem!1)))),
% 3.24/3.41 inference(modus_ponens,[status(thm)],[145, 5535])).
% 3.24/3.41 tff(5537,plain,
% 3.24/3.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 3.24/3.41 inference(rewrite,[status(thm)],[])).
% 3.24/3.41 tff(5538,plain,
% 3.24/3.41 (((~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 3.24/3.41 inference(rewrite,[status(thm)],[])).
% 3.24/3.41 tff(5539,plain,
% 3.24/3.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))))),
% 3.24/3.41 inference(monotonicity,[status(thm)],[5538])).
% 3.24/3.41 tff(5540,plain,
% 3.24/3.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 3.24/3.41 inference(transitivity,[status(thm)],[5539, 5537])).
% 3.24/3.41 tff(5541,plain,
% 3.24/3.41 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)))),
% 3.24/3.41 inference(quant_inst,[status(thm)],[])).
% 3.24/3.41 tff(5542,plain,
% 3.24/3.41 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))),
% 3.24/3.41 inference(modus_ponens,[status(thm)],[5541, 5540])).
% 3.24/3.41 tff(5543,plain,
% 3.24/3.41 (~r(s(elem!1), z)),
% 3.24/3.41 inference(unit_resolution,[status(thm)],[5542, 118, 5532, 5536])).
% 3.24/3.41 tff(5544,plain,
% 3.24/3.41 (b(s(elem!1), z)),
% 3.24/3.41 inference(unit_resolution,[status(thm)],[774, 5543])).
% 3.24/3.41 tff(5545,plain,
% 3.24/3.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 3.24/3.41 inference(rewrite,[status(thm)],[])).
% 3.24/3.41 tff(5546,plain,
% 3.24/3.41 (((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 3.24/3.41 inference(rewrite,[status(thm)],[])).
% 3.24/3.41 tff(5547,plain,
% 3.24/3.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))))),
% 3.24/3.41 inference(monotonicity,[status(thm)],[5546])).
% 3.24/3.41 tff(5548,plain,
% 3.24/3.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 3.24/3.41 inference(transitivity,[status(thm)],[5547, 5545])).
% 3.24/3.41 tff(5549,plain,
% 3.24/3.41 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))),
% 3.24/3.41 inference(quant_inst,[status(thm)],[])).
% 3.24/3.41 tff(5550,plain,
% 3.24/3.41 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))),
% 3.24/3.41 inference(modus_ponens,[status(thm)],[5549, 5548])).
% 3.24/3.41 tff(5551,plain,
% 3.24/3.41 (~r(z, s(elem!1))),
% 3.24/3.41 inference(unit_resolution,[status(thm)],[5550, 118, 5532, 5536])).
% 3.24/3.41 tff(5552,plain,
% 3.24/3.41 (b(z, s(elem!1))),
% 3.24/3.41 inference(unit_resolution,[status(thm)],[2351, 5551])).
% 3.24/3.41 tff(5553,plain,
% 3.24/3.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 3.24/3.41 inference(rewrite,[status(thm)],[])).
% 3.24/3.41 tff(5554,plain,
% 3.24/3.41 (((~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(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 3.24/3.41 inference(rewrite,[status(thm)],[])).
% 3.24/3.41 tff(5555,plain,
% 3.24/3.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 3.24/3.41 inference(monotonicity,[status(thm)],[5554])).
% 3.24/3.41 tff(5556,plain,
% 3.24/3.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 3.24/3.41 inference(transitivity,[status(thm)],[5555, 5553])).
% 3.24/3.41 tff(5557,plain,
% 3.24/3.41 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 3.24/3.41 inference(quant_inst,[status(thm)],[])).
% 3.24/3.41 tff(5558,plain,
% 3.24/3.41 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 3.24/3.41 inference(modus_ponens,[status(thm)],[5557, 5556])).
% 3.24/3.41 tff(5559,plain,
% 3.24/3.41 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.24/3.41 inference(unit_resolution,[status(thm)],[5558, 118, 1130, 908])).
% 3.24/3.41 tff(5560,plain,
% 3.24/3.41 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.24/3.41 inference(unit_resolution,[status(thm)],[806, 41, 5559, 4017])).
% 3.24/3.41 tff(5561,plain,
% 3.24/3.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(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)))))))),
% 3.24/3.41 inference(rewrite,[status(thm)],[])).
% 3.24/3.41 tff(5562,plain,
% 3.24/3.41 (((~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)))))))))) <=> ((~r(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)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 3.24/3.41 inference(rewrite,[status(thm)],[])).
% 3.24/3.41 tff(5563,plain,
% 3.24/3.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(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))))))))),
% 3.24/3.41 inference(monotonicity,[status(thm)],[5562])).
% 3.24/3.41 tff(5564,plain,
% 3.24/3.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(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)))))))),
% 3.24/3.41 inference(transitivity,[status(thm)],[5563, 5561])).
% 3.24/3.41 tff(5565,plain,
% 3.24/3.41 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 3.24/3.41 inference(quant_inst,[status(thm)],[])).
% 3.24/3.41 tff(5566,plain,
% 3.24/3.41 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 3.24/3.41 inference(modus_ponens,[status(thm)],[5565, 5564])).
% 3.24/3.41 tff(5567,plain,
% 3.24/3.41 ($false),
% 3.24/3.41 inference(unit_resolution,[status(thm)],[5566, 118, 1130, 908, 382])).
% 3.24/3.41 tff(5568,plain,((~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)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.41 tff(5569,plain,
% 3.24/3.41 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.24/3.41 inference(unit_resolution,[status(thm)],[5568, 1130, 908])).
% 3.24/3.41 tff(5570,plain,
% 3.24/3.41 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.24/3.41 inference(unit_resolution,[status(thm)],[395, 5569, 2286])).
% 3.24/3.41 tff(5571,plain,
% 3.24/3.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 3.24/3.41 inference(rewrite,[status(thm)],[])).
% 3.24/3.41 tff(5572,plain,
% 3.24/3.41 (((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 3.24/3.41 inference(rewrite,[status(thm)],[])).
% 3.24/3.41 tff(5573,plain,
% 3.24/3.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 3.24/3.41 inference(monotonicity,[status(thm)],[5572])).
% 3.24/3.41 tff(5574,plain,
% 3.24/3.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 3.24/3.41 inference(transitivity,[status(thm)],[5573, 5571])).
% 3.24/3.41 tff(5575,plain,
% 3.24/3.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 3.24/3.41 inference(quant_inst,[status(thm)],[])).
% 3.24/3.41 tff(5576,plain,
% 3.24/3.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 3.24/3.41 inference(modus_ponens,[status(thm)],[5575, 5574])).
% 3.24/3.41 tff(5577,plain,
% 3.24/3.41 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.24/3.41 inference(unit_resolution,[status(thm)],[5576, 178, 855, 853, 5570, 5560])).
% 3.24/3.41 tff(5578,plain,
% 3.24/3.41 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.24/3.41 inference(unit_resolution,[status(thm)],[133, 5577])).
% 3.24/3.41 tff(5579,plain,
% 3.24/3.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 3.24/3.41 inference(rewrite,[status(thm)],[])).
% 3.24/3.41 tff(5580,plain,
% 3.24/3.41 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 3.24/3.41 inference(quant_inst,[status(thm)],[])).
% 3.24/3.41 tff(5581,plain,
% 3.24/3.41 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 3.24/3.41 inference(modus_ponens,[status(thm)],[5580, 5579])).
% 3.24/3.41 tff(5582,plain,
% 3.24/3.41 ($false),
% 3.24/3.41 inference(unit_resolution,[status(thm)],[5581, 118, 1130, 194, 5578])).
% 3.24/3.41 tff(5583,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (s(elem!1) = s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.41 tff(5584,plain,
% 3.24/3.41 ($false),
% 3.24/3.41 inference(unit_resolution,[status(thm)],[5583, 5552, 5544, 194, 1130, 5534, 5533, 5362])).
% 3.24/3.41 tff(5585,plain,((s(s(s(elem!1))) = elem!1) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (elem!1 = z) | (~r(z, s(s(s(s(z)))))) | r(s(s(s(s(z)))), elem!1) | b(s(s(z)), elem!1) | (~b(s(s(s(s(z)))), s(s(z)))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~b(elem!1, z)) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.24/3.41 tff(5586,plain,
% 3.24/3.41 (b(s(s(s(elem!1))), elem!1)),
% 3.24/3.41 inference(unit_resolution,[status(thm)],[5585, 5307, 202, 557, 949, 47, 5282, 3241, 1130, 4166, 5302, 701, 3244])).
% 3.24/3.41 tff(5587,plain,
% 3.24/3.41 (b(s(s(s(elem!1))), s(s(z)))),
% 3.24/3.41 inference(modus_ponens,[status(thm)],[5586, 5301])).
% 3.24/3.41 tff(5588,plain,
% 3.24/3.41 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.24/3.41 inference(unit_resolution,[status(thm)],[3488, 5295, 47, 1130])).
% 3.24/3.41 tff(5589,plain,
% 3.24/3.41 (b(s(s(z)), s(s(s(s(z)))))),
% 3.24/3.41 inference(unit_resolution,[status(thm)],[164, 5588])).
% 3.24/3.41 tff(5590,plain,
% 3.24/3.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.24/3.41 inference(rewrite,[status(thm)],[])).
% 3.24/3.41 tff(5591,plain,
% 3.24/3.41 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.24/3.41 inference(rewrite,[status(thm)],[])).
% 3.24/3.41 tff(5592,plain,
% 3.24/3.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 3.24/3.41 inference(monotonicity,[status(thm)],[5591])).
% 3.24/3.41 tff(5593,plain,
% 3.24/3.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.24/3.41 inference(transitivity,[status(thm)],[5592, 5590])).
% 3.24/3.41 tff(5594,plain,
% 3.24/3.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.24/3.41 inference(quant_inst,[status(thm)],[])).
% 3.24/3.41 tff(5595,plain,
% 3.24/3.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.24/3.41 inference(modus_ponens,[status(thm)],[5594, 5593])).
% 3.24/3.41 tff(5596,plain,
% 3.24/3.41 (~b(s(s(s(elem!1))), s(s(z)))),
% 3.24/3.41 inference(unit_resolution,[status(thm)],[5595, 178, 5589, 202, 5164, 3831])).
% 3.24/3.41 tff(5597,plain,
% 3.24/3.41 ($false),
% 3.24/3.41 inference(unit_resolution,[status(thm)],[5596, 5587])).
% 3.24/3.41 tff(5598,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | b(s(s(z)), elem!1) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | b(z, s(s(s(s(z))))) | b(s(s(s(s(z)))), z) | (~r(elem!1, s(s(s(elem!1))))) | b(elem!1, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.41 tff(5599,plain,
% 3.24/3.41 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.24/3.41 inference(unit_resolution,[status(thm)],[5598, 5145, 4503, 3241, 3243, 5161, 5148, 701, 1, 3170, 5143, 461])).
% 3.24/3.41 tff(5600,plain,
% 3.24/3.41 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.24/3.41 inference(unit_resolution,[status(thm)],[84, 5599])).
% 3.24/3.41 tff(5601,plain,
% 3.24/3.41 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.24/3.41 inference(unit_resolution,[status(thm)],[5130, 5128, 557])).
% 3.24/3.41 tff(5602,plain,
% 3.24/3.41 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.24/3.41 inference(unit_resolution,[status(thm)],[133, 5601])).
% 3.24/3.41 tff(5603,plain,
% 3.24/3.41 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.24/3.41 inference(unit_resolution,[status(thm)],[5277, 5602, 202, 1, 3170, 595, 3311, 461, 557])).
% 3.24/3.41 tff(5604,plain,
% 3.24/3.41 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.24/3.41 inference(unit_resolution,[status(thm)],[691, 5603, 701])).
% 3.24/3.41 tff(5605,plain,
% 3.24/3.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.24/3.41 inference(rewrite,[status(thm)],[])).
% 3.24/3.41 tff(5606,plain,
% 3.24/3.41 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.24/3.41 inference(rewrite,[status(thm)],[])).
% 3.24/3.41 tff(5607,plain,
% 3.24/3.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))))),
% 3.24/3.41 inference(monotonicity,[status(thm)],[5606])).
% 3.24/3.41 tff(5608,plain,
% 3.24/3.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.24/3.41 inference(transitivity,[status(thm)],[5607, 5605])).
% 3.24/3.41 tff(5609,plain,
% 3.24/3.41 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.24/3.41 inference(quant_inst,[status(thm)],[])).
% 3.24/3.41 tff(5610,plain,
% 3.24/3.41 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 3.24/3.41 inference(modus_ponens,[status(thm)],[5609, 5608])).
% 3.24/3.41 tff(5611,plain,
% 3.24/3.41 ($false),
% 3.24/3.41 inference(unit_resolution,[status(thm)],[5610, 118, 3311, 5604, 5128])).
% 3.24/3.41 tff(5612,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | b(z, s(s(s(s(z))))) | b(s(s(s(s(z)))), z) | (~b(z, s(s(s(s(s(s(s(z))))))))) | b(elem!1, s(s(z))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.41 tff(5613,plain,
% 3.24/3.41 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.24/3.41 inference(unit_resolution,[status(thm)],[5612, 5143, 701, 4503, 1, 3170, 5153, 461, 3243])).
% 3.24/3.41 tff(5614,plain,
% 3.24/3.41 (b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.24/3.41 inference(unit_resolution,[status(thm)],[5118, 5613, 5147])).
% 3.24/3.41 tff(5615,plain,
% 3.24/3.41 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.24/3.41 inference(unit_resolution,[status(thm)],[4067, 178, 5600, 5151, 5145, 5614])).
% 3.24/3.41 tff(5616,plain,
% 3.24/3.41 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.24/3.41 inference(unit_resolution,[status(thm)],[222, 5615])).
% 3.24/3.41 tff(5617,plain,
% 3.24/3.41 (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 3.24/3.41 inference(modus_ponens,[status(thm)],[4511, 3541])).
% 3.24/3.41 tff(5618,assumption,(~r(s(s(z)), z)), introduced(assumption)).
% 3.24/3.41 tff(5619,plain,
% 3.24/3.41 (b(s(s(z)), z)),
% 3.24/3.41 inference(unit_resolution,[status(thm)],[3249, 5618])).
% 3.24/3.41 tff(5620,plain,
% 3.24/3.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.24/3.42 inference(rewrite,[status(thm)],[])).
% 3.24/3.42 tff(5621,plain,
% 3.24/3.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.24/3.42 inference(quant_inst,[status(thm)],[])).
% 3.24/3.42 tff(5622,plain,
% 3.24/3.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 3.24/3.42 inference(modus_ponens,[status(thm)],[5621, 5620])).
% 3.24/3.42 tff(5623,plain,
% 3.24/3.42 ($false),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[5622, 118, 224, 147, 204])).
% 3.24/3.42 tff(5624,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.42 tff(5625,plain,
% 3.24/3.42 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[5624, 147, 204])).
% 3.24/3.42 tff(5626,plain,
% 3.24/3.42 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[249, 5625])).
% 3.24/3.42 tff(5627,plain,
% 3.24/3.42 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[5125, 3828, 4511, 557, 3831, 145])).
% 3.24/3.42 tff(5628,plain,
% 3.24/3.42 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[271, 5627])).
% 3.24/3.42 tff(5629,plain,
% 3.24/3.42 (~r(z, s(s(z)))),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[4818, 3828, 202, 3831, 557, 145])).
% 3.24/3.42 tff(5630,plain,
% 3.24/3.42 (b(z, s(s(z)))),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[143, 5629])).
% 3.24/3.42 tff(5631,plain,
% 3.24/3.42 (~(elem!1 = z)),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[3276, 5630, 461])).
% 3.24/3.42 tff(5632,plain,
% 3.24/3.42 (~(z = elem!1)),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[317, 5631])).
% 3.24/3.42 tff(5633,plain,
% 3.24/3.42 (b(z, elem!1)),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[585, 5169, 5632])).
% 3.24/3.42 tff(5634,plain,
% 3.24/3.42 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[5101, 147, 3461, 145])).
% 3.24/3.42 tff(5635,plain,
% 3.24/3.42 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[4928, 5634, 4890])).
% 3.24/3.42 tff(5636,plain,
% 3.24/3.42 (s(elem!1) = s(s(s(z)))),
% 3.24/3.42 inference(monotonicity,[status(thm)],[308])).
% 3.24/3.42 tff(5637,plain,
% 3.24/3.42 (s(s(elem!1)) = s(s(s(s(z))))),
% 3.24/3.42 inference(monotonicity,[status(thm)],[5636])).
% 3.24/3.42 tff(5638,plain,
% 3.24/3.42 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.24/3.42 inference(monotonicity,[status(thm)],[5637])).
% 3.24/3.42 tff(5639,plain,
% 3.24/3.42 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.24/3.42 inference(symmetry,[status(thm)],[5638])).
% 3.24/3.42 tff(5640,plain,
% 3.24/3.42 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.24/3.42 inference(modus_ponens,[status(thm)],[3831, 5639])).
% 3.24/3.42 tff(5641,plain,
% 3.24/3.42 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(z)) = s(s(s(s(elem!1)))))),
% 3.24/3.42 inference(monotonicity,[status(thm)],[308])).
% 3.24/3.42 tff(5642,plain,
% 3.24/3.42 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 3.24/3.42 inference(symmetry,[status(thm)],[5641])).
% 3.24/3.42 tff(5643,plain,
% 3.24/3.42 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 3.24/3.42 inference(monotonicity,[status(thm)],[5642])).
% 3.24/3.42 tff(5644,plain,
% 3.24/3.42 (~(elem!1 = s(s(s(s(elem!1)))))),
% 3.24/3.42 inference(modus_ponens,[status(thm)],[2131, 5643])).
% 3.24/3.42 tff(5645,plain,
% 3.24/3.42 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[1509, 5644])).
% 3.24/3.42 tff(5646,plain,
% 3.24/3.42 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.24/3.42 inference(monotonicity,[status(thm)],[5637])).
% 3.24/3.42 tff(5647,plain,
% 3.24/3.42 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.24/3.42 inference(symmetry,[status(thm)],[5646])).
% 3.24/3.42 tff(5648,plain,
% 3.24/3.42 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.24/3.42 inference(modus_ponens,[status(thm)],[3828, 5647])).
% 3.24/3.42 tff(5649,plain,
% 3.24/3.42 (b(z, elem!1)),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[585, 5169, 318])).
% 3.24/3.42 tff(5650,plain,
% 3.24/3.42 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(z)))),
% 3.24/3.42 inference(monotonicity,[status(thm)],[308])).
% 3.24/3.42 tff(5651,plain,
% 3.24/3.42 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(elem!1)), elem!1)),
% 3.24/3.42 inference(symmetry,[status(thm)],[5650])).
% 3.24/3.42 tff(5652,plain,
% 3.24/3.42 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 3.24/3.42 inference(monotonicity,[status(thm)],[5637])).
% 3.24/3.42 tff(5653,plain,
% 3.24/3.42 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 3.24/3.42 inference(symmetry,[status(thm)],[5652])).
% 3.24/3.42 tff(5654,plain,
% 3.24/3.42 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(elem!1)), elem!1)),
% 3.24/3.42 inference(transitivity,[status(thm)],[5653, 5651])).
% 3.24/3.42 tff(5655,plain,
% 3.24/3.42 (b(s(s(elem!1)), elem!1)),
% 3.24/3.42 inference(modus_ponens,[status(thm)],[202, 5654])).
% 3.24/3.42 tff(5656,plain,
% 3.24/3.42 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 3.24/3.42 inference(monotonicity,[status(thm)],[5636, 5637])).
% 3.24/3.42 tff(5657,plain,
% 3.24/3.42 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(elem!1)))),
% 3.24/3.42 inference(symmetry,[status(thm)],[5656])).
% 3.24/3.42 tff(5658,plain,
% 3.24/3.42 (b(s(elem!1), s(s(elem!1)))),
% 3.24/3.42 inference(modus_ponens,[status(thm)],[1126, 5657])).
% 3.24/3.42 tff(5659,plain,
% 3.24/3.42 ($false),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[5464, 5658, 5655, 5649, 3311, 949, 5648, 557, 5645, 5640, 290])).
% 3.24/3.42 tff(5660,plain,((~(elem!1 = s(s(z)))) | (~r(elem!1, s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1) | (~r(z, s(s(s(elem!1))))) | (elem!1 = z) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.42 tff(5661,plain,
% 3.24/3.42 (~(elem!1 = s(s(z)))),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[5660, 5635, 949, 557, 5631, 3828, 3311, 3831, 202])).
% 3.24/3.42 tff(5662,plain,
% 3.24/3.42 (r(elem!1, s(s(z)))),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[467, 5661, 461])).
% 3.24/3.42 tff(5663,plain,
% 3.24/3.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.24/3.42 inference(rewrite,[status(thm)],[])).
% 3.24/3.42 tff(5664,plain,
% 3.24/3.42 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(z))))) <=> ((~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.24/3.42 inference(rewrite,[status(thm)],[])).
% 3.24/3.42 tff(5665,plain,
% 3.24/3.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 3.24/3.42 inference(monotonicity,[status(thm)],[5664])).
% 3.24/3.42 tff(5666,plain,
% 3.24/3.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.24/3.42 inference(transitivity,[status(thm)],[5665, 5663])).
% 3.24/3.42 tff(5667,plain,
% 3.24/3.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))),
% 3.24/3.42 inference(quant_inst,[status(thm)],[])).
% 3.24/3.42 tff(5668,plain,
% 3.24/3.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 3.24/3.42 inference(modus_ponens,[status(thm)],[5667, 5666])).
% 3.24/3.42 tff(5669,plain,
% 3.24/3.42 ($false),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[5668, 118, 450, 470, 147])).
% 3.24/3.42 tff(5670,plain,((~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.42 tff(5671,plain,
% 3.24/3.42 (~r(elem!1, s(s(s(s(z)))))),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[5670, 5662, 147])).
% 3.24/3.42 tff(5672,plain,
% 3.24/3.42 (b(elem!1, s(s(s(s(z)))))),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[483, 5671, 4520])).
% 3.24/3.42 tff(5673,plain,
% 3.24/3.42 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[1309, 5672, 5633, 5628, 104])).
% 3.24/3.42 tff(5674,plain,
% 3.24/3.42 (~b(s(s(z)), s(s(s(elem!1))))),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[4307, 5673, 3241, 3311, 4511, 104, 5626, 3831])).
% 3.24/3.42 tff(5675,plain,
% 3.24/3.42 (r(s(s(z)), s(s(s(elem!1))))),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[4223, 5674])).
% 3.24/3.42 tff(5676,plain,
% 3.24/3.42 ((~(elem!1 = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 3.24/3.42 inference(monotonicity,[status(thm)],[1611])).
% 3.24/3.42 tff(5677,plain,
% 3.24/3.42 (~(s(s(z)) = elem!1)),
% 3.24/3.42 inference(modus_ponens,[status(thm)],[5661, 5676])).
% 3.24/3.42 tff(5678,plain,
% 3.24/3.42 (r(s(s(z)), elem!1)),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[448, 5677, 3241])).
% 3.24/3.42 tff(5679,plain,
% 3.24/3.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(z)), elem!1)))),
% 3.24/3.42 inference(rewrite,[status(thm)],[])).
% 3.24/3.42 tff(5680,plain,
% 3.24/3.42 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), elem!1))) <=> ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(z)), elem!1)))),
% 3.24/3.42 inference(rewrite,[status(thm)],[])).
% 3.24/3.42 tff(5681,plain,
% 3.24/3.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(z)), elem!1))))),
% 3.24/3.42 inference(monotonicity,[status(thm)],[5680])).
% 3.24/3.42 tff(5682,plain,
% 3.24/3.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(z)), elem!1)))),
% 3.24/3.42 inference(transitivity,[status(thm)],[5681, 5679])).
% 3.24/3.42 tff(5683,plain,
% 3.24/3.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), elem!1)))),
% 3.24/3.42 inference(quant_inst,[status(thm)],[])).
% 3.24/3.42 tff(5684,plain,
% 3.24/3.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(z)), elem!1))),
% 3.24/3.42 inference(modus_ponens,[status(thm)],[5683, 5682])).
% 3.24/3.42 tff(5685,plain,
% 3.24/3.42 ($false),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[5684, 118, 3311, 5678, 5675])).
% 3.24/3.42 tff(5686,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(elem!1))))) | b(s(s(z)), elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | b(elem!1, s(s(z))) | (s(s(s(elem!1))) = elem!1) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.42 tff(5687,plain,
% 3.24/3.42 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[5686, 5619, 3241, 104, 3831, 461, 949, 557, 3828, 202, 3311, 145, 204])).
% 3.24/3.42 tff(5688,plain,
% 3.24/3.42 (b(s(s(z)), s(s(s(s(z)))))),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[164, 5687])).
% 3.24/3.42 tff(5689,plain,
% 3.24/3.42 (~b(s(s(z)), s(s(s(elem!1))))),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[4816, 178, 5688, 202, 3828, 3831])).
% 3.24/3.42 tff(5690,plain,
% 3.24/3.42 (r(s(s(z)), s(s(s(elem!1))))),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[4223, 5689])).
% 3.24/3.42 tff(5691,plain,
% 3.24/3.42 (~r(s(s(z)), elem!1)),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[5684, 118, 3311, 5690])).
% 3.24/3.42 tff(5692,plain,
% 3.24/3.42 (s(s(z)) = elem!1),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[448, 5691, 3241])).
% 3.24/3.42 tff(5693,plain,
% 3.24/3.42 (s(s(s(z))) = s(elem!1)),
% 3.24/3.42 inference(monotonicity,[status(thm)],[5692])).
% 3.24/3.42 tff(5694,plain,
% 3.24/3.42 (s(s(s(s(z)))) = s(s(elem!1))),
% 3.24/3.42 inference(monotonicity,[status(thm)],[5693])).
% 3.24/3.42 tff(5695,plain,
% 3.24/3.42 (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)))),
% 3.24/3.42 inference(monotonicity,[status(thm)],[5694])).
% 3.24/3.42 tff(5696,plain,
% 3.24/3.42 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.24/3.42 inference(modus_ponens,[status(thm)],[104, 5695])).
% 3.24/3.42 tff(5697,plain,
% 3.24/3.42 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[5361, 5692])).
% 3.24/3.42 tff(5698,plain,
% 3.24/3.42 (r(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.24/3.42 inference(monotonicity,[status(thm)],[5692])).
% 3.24/3.42 tff(5699,plain,
% 3.24/3.42 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[279, 178, 5630, 104, 5688, 5628])).
% 3.24/3.42 tff(5700,plain,
% 3.24/3.42 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[249, 5699])).
% 3.24/3.42 tff(5701,plain,
% 3.24/3.42 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.24/3.42 inference(modus_ponens,[status(thm)],[5700, 5698])).
% 3.24/3.42 tff(5702,plain,
% 3.24/3.42 (elem!1 = s(s(z))),
% 3.24/3.42 inference(symmetry,[status(thm)],[5692])).
% 3.24/3.42 tff(5703,plain,
% 3.24/3.42 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(z)) = s(s(s(s(elem!1)))))),
% 3.24/3.42 inference(monotonicity,[status(thm)],[5702])).
% 3.24/3.42 tff(5704,plain,
% 3.24/3.42 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 3.24/3.42 inference(symmetry,[status(thm)],[5703])).
% 3.24/3.42 tff(5705,plain,
% 3.24/3.42 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 3.24/3.42 inference(monotonicity,[status(thm)],[5704])).
% 3.24/3.42 tff(5706,plain,
% 3.24/3.42 (~(elem!1 = s(s(s(s(elem!1)))))),
% 3.24/3.42 inference(modus_ponens,[status(thm)],[2131, 5705])).
% 3.24/3.42 tff(5707,plain,
% 3.24/3.42 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[1509, 5706])).
% 3.24/3.42 tff(5708,plain,
% 3.24/3.42 (r(s(s(z)), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 3.24/3.42 inference(monotonicity,[status(thm)],[5692])).
% 3.24/3.42 tff(5709,plain,
% 3.24/3.42 ((~r(s(s(z)), s(s(s(s(z)))))) <=> (~r(elem!1, s(s(s(s(z))))))),
% 3.24/3.42 inference(monotonicity,[status(thm)],[5708])).
% 3.24/3.42 tff(5710,plain,
% 3.24/3.42 (~r(elem!1, s(s(s(s(z)))))),
% 3.24/3.42 inference(modus_ponens,[status(thm)],[5687, 5709])).
% 3.24/3.42 tff(5711,plain,
% 3.24/3.42 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 3.24/3.42 inference(monotonicity,[status(thm)],[5693])).
% 3.24/3.42 tff(5712,plain,
% 3.24/3.42 ((~b(s(s(s(z))), s(s(s(s(z)))))) <=> (~b(s(elem!1), s(s(s(s(z))))))),
% 3.24/3.42 inference(monotonicity,[status(thm)],[5711])).
% 3.24/3.42 tff(5713,plain,
% 3.24/3.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(z)))))),
% 3.24/3.42 inference(rewrite,[status(thm)],[])).
% 3.24/3.42 tff(5714,plain,
% 3.24/3.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(z)))))),
% 3.24/3.42 inference(quant_inst,[status(thm)],[])).
% 3.24/3.42 tff(5715,plain,
% 3.24/3.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(z))))),
% 3.24/3.42 inference(modus_ponens,[status(thm)],[5714, 5713])).
% 3.24/3.42 tff(5716,plain,
% 3.24/3.42 (~r(elem!1, s(s(z)))),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[5715, 118, 3311, 5690])).
% 3.24/3.42 tff(5717,plain,
% 3.24/3.42 (elem!1 = s(s(z))),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[467, 5716, 461])).
% 3.24/3.42 tff(5718,plain,
% 3.24/3.42 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[5660, 5717, 949, 557, 5631, 3828, 3311, 3831, 202])).
% 3.24/3.42 tff(5719,plain,
% 3.24/3.42 (~b(s(elem!1), s(s(s(s(z)))))),
% 3.24/3.42 inference(modus_ponens,[status(thm)],[5718, 5712])).
% 3.24/3.42 tff(5720,assumption,(~b(s(elem!1), s(s(s(s(z)))))), introduced(assumption)).
% 3.24/3.42 tff(5721,assumption,(~r(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 3.24/3.42 tff(5722,plain,
% 3.24/3.42 (b(elem!1, s(s(s(s(z)))))),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[483, 4520, 5721])).
% 3.24/3.42 tff(5723,assumption,(~b(elem!1, z)), introduced(assumption)).
% 3.24/3.42 tff(5724,plain,
% 3.24/3.42 (~(elem!1 = s(elem!1))),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[748, 1548])).
% 3.24/3.42 tff(5725,plain,
% 3.24/3.42 (b(elem!1, s(elem!1))),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[756, 5724, 744])).
% 3.24/3.42 tff(5726,plain,
% 3.24/3.42 (~(s(s(z)) = elem!1)),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[1337, 1061, 1548, 744])).
% 3.24/3.42 tff(5727,plain,
% 3.24/3.42 (~(elem!1 = s(s(z)))),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[311, 5726])).
% 3.24/3.42 tff(5728,plain,
% 3.24/3.42 (r(elem!1, s(s(z)))),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[467, 5727, 461])).
% 3.24/3.42 tff(5729,plain,
% 3.24/3.42 (~(s(elem!1) = s(s(z)))),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[1047, 5728, 744])).
% 3.24/3.42 tff(5730,plain,
% 3.24/3.42 (~(s(s(z)) = s(elem!1))),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[1058, 5729])).
% 3.24/3.42 tff(5731,plain,
% 3.24/3.42 (r(s(s(z)), s(elem!1))),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[1067, 5730, 1061])).
% 3.24/3.42 tff(5732,plain,
% 3.24/3.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(z)))))),
% 3.24/3.42 inference(rewrite,[status(thm)],[])).
% 3.24/3.42 tff(5733,plain,
% 3.24/3.42 (((~r(z, s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(z)))))),
% 3.24/3.42 inference(rewrite,[status(thm)],[])).
% 3.24/3.42 tff(5734,plain,
% 3.24/3.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(z))))))),
% 3.24/3.42 inference(monotonicity,[status(thm)],[5733])).
% 3.24/3.42 tff(5735,plain,
% 3.24/3.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(z)))))),
% 3.24/3.42 inference(transitivity,[status(thm)],[5734, 5732])).
% 3.24/3.42 tff(5736,plain,
% 3.24/3.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, z)))),
% 3.24/3.42 inference(quant_inst,[status(thm)],[])).
% 3.24/3.42 tff(5737,plain,
% 3.24/3.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(z))))),
% 3.24/3.42 inference(modus_ponens,[status(thm)],[5736, 5735])).
% 3.24/3.42 tff(5738,plain,
% 3.24/3.42 (~r(elem!1, z)),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[5737, 118, 3261, 450])).
% 3.24/3.42 tff(5739,plain,
% 3.24/3.42 (elem!1 = z),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[498, 5738, 5723])).
% 3.24/3.42 tff(5740,plain,
% 3.24/3.42 (s(elem!1) = s(z)),
% 3.24/3.42 inference(monotonicity,[status(thm)],[5739])).
% 3.24/3.42 tff(5741,plain,
% 3.24/3.42 (s(s(elem!1)) = s(s(z))),
% 3.24/3.42 inference(monotonicity,[status(thm)],[5740])).
% 3.24/3.42 tff(5742,plain,
% 3.24/3.42 (b(s(elem!1), s(s(elem!1))) <=> b(s(z), s(s(z)))),
% 3.24/3.42 inference(monotonicity,[status(thm)],[5740, 5741])).
% 3.24/3.42 tff(5743,plain,
% 3.24/3.42 (b(s(z), s(s(z))) <=> b(s(elem!1), s(s(elem!1)))),
% 3.24/3.42 inference(symmetry,[status(thm)],[5742])).
% 3.24/3.42 tff(5744,plain,
% 3.24/3.42 ((~b(s(z), s(s(z)))) <=> (~b(s(elem!1), s(s(elem!1))))),
% 3.24/3.42 inference(monotonicity,[status(thm)],[5743])).
% 3.24/3.42 tff(5745,plain,
% 3.24/3.42 (s(z) = s(elem!1)),
% 3.24/3.42 inference(symmetry,[status(thm)],[5740])).
% 3.24/3.42 tff(5746,plain,
% 3.24/3.42 (b(s(z), z) <=> b(s(elem!1), z)),
% 3.24/3.42 inference(monotonicity,[status(thm)],[5745])).
% 3.24/3.42 tff(5747,plain,
% 3.24/3.42 (b(s(elem!1), z) <=> b(s(z), z)),
% 3.24/3.42 inference(symmetry,[status(thm)],[5746])).
% 3.24/3.42 tff(5748,plain,
% 3.24/3.42 (~r(s(elem!1), z)),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[916, 908, 3244])).
% 3.24/3.42 tff(5749,plain,
% 3.24/3.42 (b(s(elem!1), z)),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[774, 5748])).
% 3.24/3.42 tff(5750,plain,
% 3.24/3.42 (b(s(z), z)),
% 3.24/3.42 inference(modus_ponens,[status(thm)],[5749, 5747])).
% 3.24/3.42 tff(5751,plain,
% 3.24/3.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 3.24/3.42 inference(rewrite,[status(thm)],[])).
% 3.24/3.42 tff(5752,plain,
% 3.24/3.42 (((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(elem!1)))) <=> ((~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 3.24/3.42 inference(rewrite,[status(thm)],[])).
% 3.24/3.42 tff(5753,plain,
% 3.24/3.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 3.24/3.42 inference(monotonicity,[status(thm)],[5752])).
% 3.24/3.42 tff(5754,plain,
% 3.24/3.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 3.24/3.42 inference(transitivity,[status(thm)],[5753, 5751])).
% 3.24/3.42 tff(5755,plain,
% 3.24/3.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(elem!1))))),
% 3.24/3.42 inference(quant_inst,[status(thm)],[])).
% 3.24/3.42 tff(5756,plain,
% 3.24/3.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 3.24/3.42 inference(modus_ponens,[status(thm)],[5755, 5754])).
% 3.24/3.42 tff(5757,plain,
% 3.24/3.42 ($false),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[5756, 118, 1329, 908, 147])).
% 3.24/3.42 tff(5758,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.42 tff(5759,plain,
% 3.24/3.42 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[5758, 908, 1329])).
% 3.24/3.42 tff(5760,plain,
% 3.24/3.42 (b(s(s(z)), s(s(s(s(z)))))),
% 3.24/3.42 inference(unit_resolution,[status(thm)],[164, 5759])).
% 3.24/3.42 tff(5761,plain,
% 3.24/3.42 (b(elem!1, s(s(s(s(z))))) <=> b(z, s(s(s(s(z)))))),
% 3.24/3.42 inference(monotonicity,[status(thm)],[5739])).
% 3.24/3.42 tff(5762,plain,
% 3.24/3.42 (b(z, s(s(s(s(z)))))),
% 3.24/3.42 inference(modus_ponens,[status(thm)],[1301, 5761])).
% 3.24/3.42 tff(5763,plain,
% 3.24/3.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))))),
% 3.24/3.42 inference(rewrite,[status(thm)],[])).
% 3.24/3.42 tff(5764,plain,
% 3.24/3.42 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))))),
% 3.24/3.42 inference(rewrite,[status(thm)],[])).
% 3.24/3.42 tff(5765,plain,
% 3.24/3.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z))))))))),
% 3.24/3.43 inference(monotonicity,[status(thm)],[5764])).
% 3.24/3.43 tff(5766,plain,
% 3.24/3.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))))),
% 3.24/3.43 inference(transitivity,[status(thm)],[5765, 5763])).
% 3.24/3.43 tff(5767,plain,
% 3.24/3.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 3.24/3.43 inference(quant_inst,[status(thm)],[])).
% 3.24/3.43 tff(5768,plain,
% 3.24/3.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z))))))),
% 3.24/3.43 inference(modus_ponens,[status(thm)],[5767, 5766])).
% 3.24/3.43 tff(5769,plain,
% 3.24/3.43 (~b(s(z), s(s(z)))),
% 3.24/3.43 inference(unit_resolution,[status(thm)],[5768, 178, 3461, 5762, 5760, 5750])).
% 3.24/3.43 tff(5770,plain,
% 3.24/3.43 (~b(s(elem!1), s(s(elem!1)))),
% 3.24/3.43 inference(modus_ponens,[status(thm)],[5769, 5744])).
% 3.24/3.43 tff(5771,plain,
% 3.24/3.43 (r(s(elem!1), s(s(elem!1)))),
% 3.24/3.43 inference(unit_resolution,[status(thm)],[1028, 5770, 5389])).
% 3.24/3.43 tff(5772,plain,
% 3.24/3.43 (z = elem!1),
% 3.24/3.43 inference(unit_resolution,[status(thm)],[2808, 5739])).
% 3.24/3.43 tff(5773,plain,
% 3.24/3.43 (~b(s(s(s(s(elem!1)))), z)),
% 3.24/3.43 inference(unit_resolution,[status(thm)],[5184, 5772, 3170])).
% 3.24/3.43 tff(5774,plain,
% 3.24/3.43 (r(s(s(s(s(elem!1)))), z)),
% 3.24/3.43 inference(unit_resolution,[status(thm)],[1716, 5773])).
% 3.24/3.43 tff(5775,plain,
% 3.24/3.43 (~(elem!1 = s(s(s(elem!1))))),
% 3.24/3.43 inference(unit_resolution,[status(thm)],[3991, 5774, 5748])).
% 3.24/3.43 tff(5776,plain,
% 3.24/3.43 (~(s(s(s(elem!1))) = elem!1)),
% 3.24/3.43 inference(unit_resolution,[status(thm)],[2489, 5775])).
% 3.24/3.43 tff(5777,plain,
% 3.24/3.43 (b(z, elem!1) <=> b(z, z)),
% 3.24/3.43 inference(monotonicity,[status(thm)],[5739])).
% 3.24/3.43 tff(5778,plain,
% 3.24/3.43 (b(z, z) <=> b(z, elem!1)),
% 3.24/3.43 inference(symmetry,[status(thm)],[5777])).
% 3.24/3.43 tff(5779,plain,
% 3.24/3.43 ((~b(z, z)) <=> (~b(z, elem!1))),
% 3.24/3.43 inference(monotonicity,[status(thm)],[5778])).
% 3.24/3.43 tff(5780,plain,
% 3.24/3.43 ((~![X: $i] : (~b(X, X))) | (~b(z, z))),
% 3.24/3.43 inference(quant_inst,[status(thm)],[])).
% 3.24/3.43 tff(5781,plain,
% 3.24/3.43 (~b(z, z)),
% 3.24/3.43 inference(unit_resolution,[status(thm)],[5780, 3218])).
% 3.24/3.43 tff(5782,plain,
% 3.24/3.43 (~b(z, elem!1)),
% 3.24/3.43 inference(modus_ponens,[status(thm)],[5781, 5779])).
% 3.24/3.43 tff(5783,plain,
% 3.24/3.43 (b(s(elem!1), elem!1) <=> b(s(elem!1), z)),
% 3.24/3.43 inference(monotonicity,[status(thm)],[5739])).
% 3.24/3.43 tff(5784,plain,
% 3.24/3.43 (b(s(elem!1), z) <=> b(s(elem!1), elem!1)),
% 3.24/3.43 inference(symmetry,[status(thm)],[5783])).
% 3.24/3.43 tff(5785,plain,
% 3.24/3.43 (b(s(elem!1), elem!1)),
% 3.24/3.43 inference(modus_ponens,[status(thm)],[5749, 5784])).
% 3.24/3.43 tff(5786,assumption,(~b(z, elem!1)), introduced(assumption)).
% 3.24/3.43 tff(5787,plain,
% 3.24/3.43 (~r(z, elem!1)),
% 3.24/3.43 inference(unit_resolution,[status(thm)],[4862, 3261, 450])).
% 3.24/3.43 tff(5788,plain,
% 3.24/3.43 (z = elem!1),
% 3.24/3.43 inference(unit_resolution,[status(thm)],[585, 5787, 5786])).
% 3.24/3.43 tff(5789,plain,
% 3.24/3.43 (elem!1 = z),
% 3.24/3.43 inference(symmetry,[status(thm)],[5788])).
% 3.24/3.43 tff(5790,plain,
% 3.24/3.43 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(elem!1)))), z)),
% 3.24/3.43 inference(monotonicity,[status(thm)],[5789])).
% 3.24/3.43 tff(5791,plain,
% 3.24/3.43 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 3.24/3.43 inference(symmetry,[status(thm)],[5790])).
% 3.24/3.43 tff(5792,plain,
% 3.24/3.43 (~b(s(s(s(s(elem!1)))), z)),
% 3.24/3.43 inference(unit_resolution,[status(thm)],[5184, 5788, 3170])).
% 3.24/3.43 tff(5793,plain,
% 3.24/3.43 (r(s(s(s(s(elem!1)))), z)),
% 3.24/3.43 inference(unit_resolution,[status(thm)],[1716, 5792])).
% 3.24/3.43 tff(5794,plain,
% 3.24/3.43 (r(s(s(s(s(elem!1)))), elem!1)),
% 3.24/3.43 inference(modus_ponens,[status(thm)],[5793, 5791])).
% 3.24/3.43 tff(5795,plain,
% 3.24/3.43 (s(z) = s(elem!1)),
% 3.24/3.43 inference(monotonicity,[status(thm)],[5788])).
% 3.24/3.43 tff(5796,plain,
% 3.24/3.43 (s(s(z)) = s(s(elem!1))),
% 3.24/3.43 inference(monotonicity,[status(thm)],[5795])).
% 3.24/3.43 tff(5797,plain,
% 3.24/3.43 (s(s(s(z))) = s(s(s(elem!1)))),
% 3.24/3.43 inference(monotonicity,[status(thm)],[5796])).
% 3.24/3.43 tff(5798,plain,
% 3.24/3.43 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 3.24/3.43 inference(monotonicity,[status(thm)],[5797])).
% 3.24/3.43 tff(5799,plain,
% 3.24/3.43 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 3.24/3.43 inference(monotonicity,[status(thm)],[5798])).
% 3.24/3.43 tff(5800,plain,
% 3.24/3.43 (b(elem!1, s(s(s(s(elem!1)))))),
% 3.24/3.43 inference(modus_ponens,[status(thm)],[1301, 5799])).
% 3.24/3.43 tff(5801,plain,
% 3.24/3.43 (b(s(s(s(s(elem!1)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.24/3.43 inference(monotonicity,[status(thm)],[5796])).
% 3.24/3.43 tff(5802,plain,
% 3.24/3.43 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 3.24/3.43 inference(unit_resolution,[status(thm)],[5194, 5793, 3261])).
% 3.24/3.43 tff(5803,plain,
% 3.24/3.43 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 3.24/3.43 inference(unit_resolution,[status(thm)],[1170, 5802])).
% 3.24/3.43 tff(5804,plain,
% 3.24/3.43 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.24/3.43 inference(modus_ponens,[status(thm)],[5803, 5801])).
% 3.24/3.43 tff(5805,plain,
% 3.24/3.43 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 3.24/3.43 inference(monotonicity,[status(thm)],[5796, 5798])).
% 3.24/3.43 tff(5806,plain,
% 3.24/3.43 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 3.24/3.43 inference(modus_ponens,[status(thm)],[167, 5805])).
% 3.24/3.43 tff(5807,plain,
% 3.24/3.43 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 3.24/3.43 inference(unit_resolution,[status(thm)],[3404, 1650])).
% 3.24/3.43 tff(5808,plain,
% 3.24/3.43 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.24/3.43 inference(monotonicity,[status(thm)],[5796])).
% 3.24/3.43 tff(5809,plain,
% 3.24/3.43 ((~r(s(s(s(elem!1))), s(s(z)))) <=> (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 3.24/3.43 inference(monotonicity,[status(thm)],[5808])).
% 3.24/3.43 tff(5810,assumption,(~r(s(s(s(elem!1))), s(s(z)))), introduced(assumption)).
% 3.24/3.43 tff(5811,plain,
% 3.24/3.43 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.24/3.43 inference(modus_ponens,[status(thm)],[5810, 5809])).
% 3.24/3.43 tff(5812,plain,
% 3.24/3.43 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.24/3.43 inference(unit_resolution,[status(thm)],[3409, 5811, 5807])).
% 3.24/3.43 tff(5813,plain,
% 3.24/3.43 (~(elem!1 = s(s(s(elem!1))))),
% 3.24/3.43 inference(unit_resolution,[status(thm)],[3991, 5793, 5748])).
% 3.24/3.43 tff(5814,plain,
% 3.24/3.43 (r(elem!1, s(s(z))) <=> r(elem!1, s(s(elem!1)))),
% 3.24/3.43 inference(monotonicity,[status(thm)],[5796])).
% 3.24/3.43 tff(5815,plain,
% 3.24/3.43 (r(elem!1, s(s(elem!1)))),
% 3.24/3.43 inference(modus_ponens,[status(thm)],[450, 5814])).
% 3.24/3.43 tff(5816,assumption,(r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 3.24/3.43 tff(5817,assumption,(b(s(s(s(s(elem!1)))), s(s(elem!1)))), introduced(assumption)).
% 3.24/3.43 tff(5818,assumption,(b(elem!1, s(s(s(s(elem!1)))))), introduced(assumption)).
% 3.24/3.43 tff(5819,plain,
% 3.24/3.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 3.24/3.43 inference(rewrite,[status(thm)],[])).
% 3.24/3.43 tff(5820,plain,
% 3.24/3.43 (((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 3.24/3.43 inference(rewrite,[status(thm)],[])).
% 3.24/3.43 tff(5821,plain,
% 3.24/3.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 3.24/3.43 inference(monotonicity,[status(thm)],[5820])).
% 3.24/3.43 tff(5822,plain,
% 3.24/3.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 3.24/3.43 inference(transitivity,[status(thm)],[5821, 5819])).
% 3.24/3.43 tff(5823,plain,
% 3.24/3.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 3.24/3.43 inference(quant_inst,[status(thm)],[])).
% 3.24/3.43 tff(5824,plain,
% 3.24/3.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 3.24/3.43 inference(modus_ponens,[status(thm)],[5823, 5822])).
% 3.24/3.43 tff(5825,plain,
% 3.24/3.43 ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1)))))),
% 3.24/3.43 inference(unit_resolution,[status(thm)],[5824, 178, 5818, 3512, 5817])).
% 3.24/3.43 tff(5826,plain,
% 3.24/3.43 (~b(elem!1, s(s(s(elem!1))))),
% 3.24/3.43 inference(unit_resolution,[status(thm)],[5825, 4401])).
% 3.24/3.43 tff(5827,plain,
% 3.24/3.43 (r(elem!1, s(s(s(elem!1))))),
% 3.24/3.43 inference(unit_resolution,[status(thm)],[2054, 5826, 1586])).
% 3.24/3.43 tff(5828,assumption,(b(s(s(elem!1)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 3.24/3.43 tff(5829,plain,
% 3.24/3.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 3.24/3.43 inference(rewrite,[status(thm)],[])).
% 3.24/3.43 tff(5830,plain,
% 3.24/3.43 (((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 3.24/3.43 inference(rewrite,[status(thm)],[])).
% 3.24/3.43 tff(5831,plain,
% 3.24/3.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 3.24/3.43 inference(monotonicity,[status(thm)],[5830])).
% 3.24/3.43 tff(5832,plain,
% 3.24/3.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 3.24/3.43 inference(transitivity,[status(thm)],[5831, 5829])).
% 3.24/3.43 tff(5833,plain,
% 3.24/3.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 3.24/3.43 inference(quant_inst,[status(thm)],[])).
% 3.24/3.43 tff(5834,plain,
% 3.24/3.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 3.24/3.43 inference(modus_ponens,[status(thm)],[5833, 5832])).
% 3.24/3.43 tff(5835,plain,
% 3.24/3.43 ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 3.24/3.43 inference(unit_resolution,[status(thm)],[5834, 178, 3512, 5828, 5817])).
% 3.24/3.43 tff(5836,plain,
% 3.24/3.43 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.24/3.43 inference(unit_resolution,[status(thm)],[5835, 4401])).
% 3.24/3.43 tff(5837,plain,
% 3.24/3.43 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.24/3.43 inference(unit_resolution,[status(thm)],[3375, 5836, 1655])).
% 3.24/3.43 tff(5838,plain,
% 3.24/3.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))),
% 3.24/3.43 inference(rewrite,[status(thm)],[])).
% 3.24/3.43 tff(5839,plain,
% 3.24/3.43 (((~r(s(s(elem!1)), s(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(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))),
% 3.24/3.43 inference(rewrite,[status(thm)],[])).
% 3.24/3.43 tff(5840,plain,
% 3.24/3.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1))))))),
% 3.24/3.43 inference(monotonicity,[status(thm)],[5839])).
% 3.24/3.43 tff(5841,plain,
% 3.24/3.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))),
% 3.24/3.43 inference(transitivity,[status(thm)],[5840, 5838])).
% 3.24/3.43 tff(5842,plain,
% 3.24/3.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))),
% 3.24/3.43 inference(quant_inst,[status(thm)],[])).
% 3.24/3.43 tff(5843,plain,
% 3.24/3.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1))))),
% 3.24/3.43 inference(modus_ponens,[status(thm)],[5842, 5841])).
% 3.24/3.43 tff(5844,plain,
% 3.24/3.43 ($false),
% 3.24/3.43 inference(unit_resolution,[status(thm)],[5843, 118, 3311, 3364, 5816])).
% 3.24/3.43 tff(5845,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.43 tff(5846,plain,
% 3.24/3.43 ($false),
% 3.24/3.43 inference(unit_resolution,[status(thm)],[5845, 5837, 5827, 5816])).
% 3.24/3.43 tff(5847,plain,((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (elem!1 = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.43 tff(5848,plain,
% 3.24/3.43 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.24/3.43 inference(unit_resolution,[status(thm)],[5847, 5815, 1650, 5813, 5812, 5806, 5804, 5800])).
% 3.24/3.43 tff(5849,plain,
% 3.24/3.43 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.24/3.43 inference(unit_resolution,[status(thm)],[1750, 5848, 1696])).
% 3.24/3.43 tff(5850,plain,
% 3.24/3.43 (~(s(s(s(elem!1))) = elem!1)),
% 3.24/3.43 inference(unit_resolution,[status(thm)],[2489, 5813])).
% 3.24/3.43 tff(5851,plain,
% 3.24/3.43 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(elem!1)))))),
% 3.24/3.43 inference(monotonicity,[status(thm)],[5798])).
% 3.24/3.43 tff(5852,plain,
% 3.24/3.43 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 3.24/3.43 inference(modus_ponens,[status(thm)],[908, 5851])).
% 3.24/3.43 tff(5853,plain,
% 3.24/3.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 3.24/3.43 inference(rewrite,[status(thm)],[])).
% 3.24/3.43 tff(5854,plain,
% 3.24/3.43 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 3.24/3.43 inference(rewrite,[status(thm)],[])).
% 3.24/3.43 tff(5855,plain,
% 3.24/3.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1))))))))),
% 3.24/3.43 inference(monotonicity,[status(thm)],[5854])).
% 3.24/3.43 tff(5856,plain,
% 3.24/3.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 3.24/3.43 inference(transitivity,[status(thm)],[5855, 5853])).
% 3.24/3.43 tff(5857,plain,
% 3.24/3.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 3.24/3.43 inference(quant_inst,[status(thm)],[])).
% 3.24/3.43 tff(5858,plain,
% 3.24/3.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1))))))),
% 3.24/3.43 inference(modus_ponens,[status(thm)],[5857, 5856])).
% 3.24/3.43 tff(5859,plain,
% 3.24/3.43 (~r(s(elem!1), s(s(s(elem!1))))),
% 3.24/3.43 inference(unit_resolution,[status(thm)],[5858, 118, 5849, 5852])).
% 3.24/3.43 tff(5860,plain,
% 3.24/3.43 (b(s(elem!1), s(s(s(elem!1))))),
% 3.24/3.43 inference(unit_resolution,[status(thm)],[5432, 5859, 5396])).
% 3.24/3.43 tff(5861,plain,
% 3.24/3.43 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 3.24/3.43 inference(monotonicity,[status(thm)],[13])).
% 3.24/3.43 tff(5862,plain,
% 3.24/3.43 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), z)),
% 3.24/3.43 inference(symmetry,[status(thm)],[5861])).
% 3.24/3.43 tff(5863,plain,
% 3.24/3.43 ((~b(s(s(elem!1)), elem!1)) <=> (~b(s(s(elem!1)), z))),
% 3.24/3.43 inference(monotonicity,[status(thm)],[5862])).
% 3.24/3.43 tff(5864,plain,
% 3.24/3.43 (~b(s(s(elem!1)), z)),
% 3.24/3.43 inference(modus_ponens,[status(thm)],[3358, 5863])).
% 3.24/3.43 tff(5865,plain,
% 3.24/3.43 (b(s(s(z)), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 3.24/3.43 inference(monotonicity,[status(thm)],[15])).
% 3.24/3.43 tff(5866,plain,
% 3.24/3.43 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), elem!1)),
% 3.24/3.43 inference(symmetry,[status(thm)],[5865])).
% 3.24/3.43 tff(5867,plain,
% 3.24/3.43 ((~b(s(s(elem!1)), elem!1)) <=> (~b(s(s(z)), elem!1))),
% 3.24/3.43 inference(monotonicity,[status(thm)],[5866])).
% 3.24/3.43 tff(5868,plain,
% 3.24/3.43 ((~b(s(s(elem!1)), z)) <=> (~b(s(s(elem!1)), elem!1))),
% 3.24/3.43 inference(monotonicity,[status(thm)],[5861])).
% 3.24/3.43 tff(5869,assumption,(~b(s(s(elem!1)), z)), introduced(assumption)).
% 3.24/3.43 tff(5870,plain,
% 3.24/3.43 (~b(s(s(elem!1)), elem!1)),
% 3.24/3.43 inference(modus_ponens,[status(thm)],[5869, 5868])).
% 3.24/3.43 tff(5871,plain,
% 3.24/3.43 (~b(s(s(z)), elem!1)),
% 3.24/3.43 inference(modus_ponens,[status(thm)],[5870, 5867])).
% 3.24/3.43 tff(5872,plain,
% 3.24/3.43 (b(s(s(z)), z) <=> b(s(s(z)), elem!1)),
% 3.24/3.43 inference(monotonicity,[status(thm)],[13])).
% 3.24/3.43 tff(5873,plain,
% 3.24/3.43 (b(s(s(z)), elem!1)),
% 3.24/3.43 inference(modus_ponens,[status(thm)],[3461, 5872])).
% 3.24/3.43 tff(5874,plain,
% 3.24/3.43 ($false),
% 3.24/3.43 inference(unit_resolution,[status(thm)],[5873, 5871])).
% 3.24/3.43 tff(5875,plain,((~(z = elem!1)) | b(s(s(elem!1)), z) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.43 tff(5876,plain,
% 3.24/3.43 (b(s(s(elem!1)), z)),
% 3.24/3.43 inference(unit_resolution,[status(thm)],[5875, 13, 3461])).
% 3.24/3.43 tff(5877,plain,
% 3.24/3.43 ($false),
% 3.24/3.43 inference(unit_resolution,[status(thm)],[5876, 5864])).
% 3.24/3.43 tff(5878,plain,((~(z = elem!1)) | b(s(s(elem!1)), elem!1) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.43 tff(5879,plain,
% 3.24/3.43 (b(s(s(elem!1)), elem!1)),
% 3.24/3.43 inference(unit_resolution,[status(thm)],[5878, 5788, 3461])).
% 3.24/3.43 tff(5880,plain,
% 3.24/3.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 3.24/3.43 inference(rewrite,[status(thm)],[])).
% 3.24/3.43 tff(5881,plain,
% 3.24/3.43 (((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 3.24/3.43 inference(rewrite,[status(thm)],[])).
% 3.24/3.43 tff(5882,plain,
% 3.24/3.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1))))))))),
% 3.24/3.43 inference(monotonicity,[status(thm)],[5881])).
% 3.24/3.43 tff(5883,plain,
% 3.24/3.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 3.24/3.43 inference(transitivity,[status(thm)],[5882, 5880])).
% 3.24/3.43 tff(5884,plain,
% 3.24/3.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 3.24/3.43 inference(quant_inst,[status(thm)],[])).
% 3.24/3.43 tff(5885,plain,
% 3.24/3.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1))))))),
% 3.24/3.43 inference(modus_ponens,[status(thm)],[5884, 5883])).
% 3.24/3.43 tff(5886,plain,
% 3.24/3.43 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.24/3.43 inference(unit_resolution,[status(thm)],[5885, 118, 5849, 5852])).
% 3.24/3.43 tff(5887,plain,
% 3.24/3.43 (b(s(s(s(elem!1))), s(elem!1))),
% 3.24/3.43 inference(unit_resolution,[status(thm)],[373, 5886, 356])).
% 3.24/3.43 tff(5888,assumption,(b(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 3.24/3.43 tff(5889,plain,
% 3.24/3.43 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 3.24/3.43 inference(unit_resolution,[status(thm)],[3356, 984])).
% 3.24/3.43 tff(5890,plain,
% 3.24/3.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 3.24/3.43 inference(rewrite,[status(thm)],[])).
% 3.24/3.43 tff(5891,plain,
% 3.24/3.43 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 3.24/3.43 inference(rewrite,[status(thm)],[])).
% 3.24/3.43 tff(5892,plain,
% 3.24/3.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 3.24/3.43 inference(monotonicity,[status(thm)],[5891])).
% 3.24/3.43 tff(5893,plain,
% 3.24/3.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 3.24/3.44 inference(transitivity,[status(thm)],[5892, 5890])).
% 3.24/3.44 tff(5894,plain,
% 3.24/3.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1))), 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))))))),
% 3.24/3.44 inference(quant_inst,[status(thm)],[])).
% 3.24/3.44 tff(5895,plain,
% 3.24/3.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 3.24/3.44 inference(modus_ponens,[status(thm)],[5894, 5893])).
% 3.24/3.44 tff(5896,plain,
% 3.24/3.44 ($false),
% 3.24/3.44 inference(unit_resolution,[status(thm)],[5895, 178, 2044, 1597, 854, 5434, 3511])).
% 3.24/3.44 tff(5897,plain,((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.44 tff(5898,plain,
% 3.24/3.44 (~b(elem!1, s(elem!1))),
% 3.24/3.44 inference(unit_resolution,[status(thm)],[5897, 3511, 5434, 2044, 1597])).
% 3.24/3.44 tff(5899,plain,
% 3.24/3.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 3.24/3.44 inference(rewrite,[status(thm)],[])).
% 3.24/3.44 tff(5900,plain,
% 3.24/3.44 (((~b(s(s(s(elem!1))), 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(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 3.24/3.44 inference(rewrite,[status(thm)],[])).
% 3.24/3.44 tff(5901,plain,
% 3.24/3.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(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(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 3.24/3.44 inference(monotonicity,[status(thm)],[5900])).
% 3.24/3.44 tff(5902,plain,
% 3.24/3.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(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(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 3.24/3.44 inference(transitivity,[status(thm)],[5901, 5899])).
% 3.24/3.44 tff(5903,plain,
% 3.24/3.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(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(elem!1), s(s(elem!1)))))),
% 3.24/3.44 inference(quant_inst,[status(thm)],[])).
% 3.24/3.44 tff(5904,plain,
% 3.24/3.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 3.24/3.44 inference(modus_ponens,[status(thm)],[5903, 5902])).
% 3.24/3.44 tff(5905,plain,
% 3.24/3.44 ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 3.24/3.44 inference(unit_resolution,[status(thm)],[5904, 178, 1597, 5434, 5888])).
% 3.24/3.44 tff(5906,plain,
% 3.24/3.44 (~b(s(elem!1), s(s(elem!1)))),
% 3.24/3.44 inference(unit_resolution,[status(thm)],[5905, 3511])).
% 3.24/3.44 tff(5907,plain,
% 3.24/3.44 (r(s(elem!1), s(s(elem!1)))),
% 3.24/3.44 inference(unit_resolution,[status(thm)],[1028, 5906, 984])).
% 3.24/3.44 tff(5908,plain,
% 3.24/3.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 3.24/3.44 inference(rewrite,[status(thm)],[])).
% 3.24/3.44 tff(5909,plain,
% 3.24/3.44 (((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 3.24/3.44 inference(rewrite,[status(thm)],[])).
% 3.24/3.44 tff(5910,plain,
% 3.24/3.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))))),
% 3.24/3.44 inference(monotonicity,[status(thm)],[5909])).
% 3.24/3.44 tff(5911,plain,
% 3.24/3.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 3.24/3.44 inference(transitivity,[status(thm)],[5910, 5908])).
% 3.24/3.44 tff(5912,plain,
% 3.24/3.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))))),
% 3.24/3.44 inference(quant_inst,[status(thm)],[])).
% 3.24/3.44 tff(5913,plain,
% 3.24/3.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))),
% 3.24/3.44 inference(modus_ponens,[status(thm)],[5912, 5911])).
% 3.24/3.44 tff(5914,plain,
% 3.24/3.44 (~r(elem!1, s(elem!1))),
% 3.24/3.44 inference(unit_resolution,[status(thm)],[5913, 118, 5907, 5816])).
% 3.24/3.44 tff(5915,plain,
% 3.24/3.44 ($false),
% 3.24/3.44 inference(unit_resolution,[status(thm)],[754, 41, 5914, 5898, 750])).
% 3.24/3.44 tff(5916,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (elem!1 = s(elem!1)) | (~r(elem!1, s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.44 tff(5917,plain,
% 3.24/3.44 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.24/3.44 inference(unit_resolution,[status(thm)],[5916, 1597, 5816, 984, 750, 5434, 5888, 2044])).
% 3.24/3.44 tff(5918,plain,
% 3.24/3.44 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.24/3.44 inference(unit_resolution,[status(thm)],[3375, 5917, 5889])).
% 3.24/3.44 tff(5919,plain,
% 3.24/3.44 (~r(elem!1, s(s(s(elem!1))))),
% 3.24/3.44 inference(unit_resolution,[status(thm)],[5845, 5918, 5816])).
% 3.24/3.44 tff(5920,plain,
% 3.24/3.44 (b(elem!1, s(s(s(elem!1))))),
% 3.24/3.44 inference(unit_resolution,[status(thm)],[2054, 5919, 1586])).
% 3.24/3.44 tff(5921,plain,
% 3.24/3.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), 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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), 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))))))),
% 3.24/3.44 inference(rewrite,[status(thm)],[])).
% 3.24/3.44 tff(5922,plain,
% 3.24/3.44 (((~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(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), 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))))))),
% 3.24/3.44 inference(rewrite,[status(thm)],[])).
% 3.24/3.44 tff(5923,plain,
% 3.24/3.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), 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)))))))),
% 3.24/3.44 inference(monotonicity,[status(thm)],[5922])).
% 3.24/3.44 tff(5924,plain,
% 3.24/3.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), 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))))))),
% 3.24/3.44 inference(transitivity,[status(thm)],[5923, 5921])).
% 3.24/3.44 tff(5925,plain,
% 3.24/3.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 3.24/3.44 inference(quant_inst,[status(thm)],[])).
% 3.24/3.44 tff(5926,plain,
% 3.24/3.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))),
% 3.24/3.44 inference(modus_ponens,[status(thm)],[5925, 5924])).
% 3.24/3.44 tff(5927,plain,
% 3.24/3.44 ($false),
% 3.24/3.44 inference(unit_resolution,[status(thm)],[5926, 178, 2044, 683, 1597, 5920, 5888])).
% 3.24/3.44 tff(5928,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (elem!1 = s(s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (elem!1 = s(elem!1)) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.44 tff(5929,plain,
% 3.24/3.44 (~b(s(s(s(elem!1))), elem!1)),
% 3.24/3.44 inference(unit_resolution,[status(thm)],[5928, 5887, 5879, 5815, 5813, 683, 5389, 5724, 5860])).
% 3.24/3.44 tff(5930,plain,
% 3.24/3.44 (r(s(s(s(elem!1))), elem!1)),
% 3.24/3.44 inference(unit_resolution,[status(thm)],[570, 5929, 5850])).
% 3.24/3.44 tff(5931,plain,
% 3.24/3.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 3.24/3.44 inference(rewrite,[status(thm)],[])).
% 3.24/3.44 tff(5932,plain,
% 3.24/3.44 (((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 3.24/3.44 inference(rewrite,[status(thm)],[])).
% 3.24/3.44 tff(5933,plain,
% 3.24/3.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))))),
% 3.24/3.44 inference(monotonicity,[status(thm)],[5932])).
% 3.24/3.44 tff(5934,plain,
% 3.24/3.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 3.24/3.44 inference(transitivity,[status(thm)],[5933, 5931])).
% 3.24/3.44 tff(5935,plain,
% 3.24/3.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 3.24/3.44 inference(quant_inst,[status(thm)],[])).
% 3.24/3.44 tff(5936,plain,
% 3.24/3.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 3.24/3.44 inference(modus_ponens,[status(thm)],[5935, 5934])).
% 3.24/3.44 tff(5937,plain,
% 3.24/3.44 (~r(s(s(s(s(elem!1)))), elem!1)),
% 3.24/3.44 inference(unit_resolution,[status(thm)],[5936, 118, 5930, 5849])).
% 3.24/3.44 tff(5938,plain,
% 3.24/3.44 ($false),
% 3.24/3.44 inference(unit_resolution,[status(thm)],[5937, 5794])).
% 3.24/3.44 tff(5939,plain,((~r(z, s(s(z)))) | (~b(s(elem!1), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | r(s(s(s(elem!1))), s(s(z))) | (~r(elem!1, s(s(z)))) | b(s(s(s(s(z)))), z) | (~b(s(s(z)), z)) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.24/3.44 tff(5940,plain,
% 3.24/3.44 (r(s(s(s(elem!1))), s(s(z)))),
% 3.24/3.44 inference(unit_resolution,[status(thm)],[5939, 5785, 356, 3261, 908, 1301, 5760, 450, 3170, 3461, 5782])).
% 3.24/3.44 tff(5941,plain,
% 3.24/3.44 (~r(s(s(s(elem!1))), elem!1)),
% 3.24/3.44 inference(unit_resolution,[status(thm)],[4205, 5940, 450])).
% 3.24/3.44 tff(5942,plain,
% 3.24/3.44 (b(s(s(s(elem!1))), elem!1)),
% 3.24/3.44 inference(unit_resolution,[status(thm)],[570, 5941, 5776])).
% 3.24/3.44 tff(5943,plain,
% 3.24/3.44 (r(elem!1, s(s(elem!1))) <=> r(z, s(s(elem!1)))),
% 3.24/3.44 inference(monotonicity,[status(thm)],[5739])).
% 3.24/3.44 tff(5944,plain,
% 3.24/3.44 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 3.24/3.44 inference(symmetry,[status(thm)],[5943])).
% 3.24/3.44 tff(5945,plain,
% 3.24/3.44 (r(z, s(s(elem!1))) <=> r(z, s(s(z)))),
% 3.24/3.44 inference(monotonicity,[status(thm)],[5741])).
% 3.24/3.44 tff(5946,plain,
% 3.24/3.44 (r(z, s(s(z))) <=> r(z, s(s(elem!1)))),
% 3.24/3.44 inference(symmetry,[status(thm)],[5945])).
% 3.24/3.44 tff(5947,plain,
% 3.24/3.44 (r(z, s(s(z))) <=> r(elem!1, s(s(elem!1)))),
% 3.24/3.44 inference(transitivity,[status(thm)],[5946, 5944])).
% 3.24/3.44 tff(5948,plain,
% 3.24/3.44 (r(elem!1, s(s(elem!1)))),
% 3.24/3.44 inference(modus_ponens,[status(thm)],[3261, 5947])).
% 3.24/3.44 tff(5949,plain,
% 3.24/3.44 (b(s(s(elem!1)), elem!1)),
% 3.24/3.44 inference(unit_resolution,[status(thm)],[5878, 5772, 3461])).
% 3.24/3.44 tff(5950,plain,
% 3.24/3.44 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 3.24/3.44 inference(monotonicity,[status(thm)],[5741])).
% 3.24/3.44 tff(5951,plain,
% 3.24/3.44 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.24/3.44 inference(symmetry,[status(thm)],[5950])).
% 3.24/3.44 tff(5952,plain,
% 3.24/3.44 (s(s(s(elem!1))) = s(s(s(z)))),
% 3.24/3.44 inference(monotonicity,[status(thm)],[5741])).
% 3.24/3.44 tff(5953,plain,
% 3.24/3.44 (s(s(s(z))) = s(s(s(elem!1)))),
% 3.24/3.44 inference(symmetry,[status(thm)],[5952])).
% 3.24/3.44 tff(5954,plain,
% 3.24/3.44 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 3.24/3.44 inference(monotonicity,[status(thm)],[5953])).
% 3.24/3.44 tff(5955,plain,
% 3.24/3.44 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.24/3.44 inference(transitivity,[status(thm)],[5954, 5951])).
% 3.24/3.44 tff(5956,plain,
% 3.24/3.44 ((~b(s(s(s(z))), s(s(z)))) <=> (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 3.24/3.44 inference(monotonicity,[status(thm)],[5955])).
% 3.24/3.44 tff(5957,plain,
% 3.24/3.44 (b(s(s(s(z))), z) <=> b(s(s(s(elem!1))), z)),
% 3.24/3.44 inference(monotonicity,[status(thm)],[5953])).
% 3.24/3.44 tff(5958,plain,
% 3.24/3.44 (b(s(s(s(elem!1))), z) <=> b(s(s(s(z))), z)),
% 3.24/3.44 inference(symmetry,[status(thm)],[5957])).
% 3.24/3.44 tff(5959,plain,
% 3.24/3.44 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), z)),
% 3.24/3.44 inference(monotonicity,[status(thm)],[5739])).
% 3.24/3.44 tff(5960,plain,
% 3.24/3.44 (b(s(s(s(elem!1))), z)),
% 3.24/3.44 inference(modus_ponens,[status(thm)],[5942, 5959])).
% 3.24/3.44 tff(5961,plain,
% 3.24/3.44 (b(s(s(s(z))), z)),
% 3.24/3.44 inference(modus_ponens,[status(thm)],[5960, 5958])).
% 3.24/3.44 tff(5962,plain,
% 3.24/3.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 3.24/3.44 inference(rewrite,[status(thm)],[])).
% 3.24/3.44 tff(5963,plain,
% 3.24/3.44 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 3.24/3.44 inference(rewrite,[status(thm)],[])).
% 3.24/3.44 tff(5964,plain,
% 3.24/3.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))))),
% 3.24/3.44 inference(monotonicity,[status(thm)],[5963])).
% 3.24/3.44 tff(5965,plain,
% 3.24/3.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 3.24/3.44 inference(transitivity,[status(thm)],[5964, 5962])).
% 3.24/3.44 tff(5966,plain,
% 3.24/3.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 3.24/3.44 inference(quant_inst,[status(thm)],[])).
% 3.24/3.44 tff(5967,plain,
% 3.24/3.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))),
% 3.24/3.44 inference(modus_ponens,[status(thm)],[5966, 5965])).
% 3.24/3.44 tff(5968,plain,
% 3.24/3.44 ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))),
% 3.24/3.44 inference(unit_resolution,[status(thm)],[5967, 178, 3461, 5762, 5760])).
% 3.24/3.44 tff(5969,plain,
% 3.24/3.44 (~b(s(s(s(z))), s(s(z)))),
% 3.24/3.44 inference(unit_resolution,[status(thm)],[5968, 5961])).
% 3.24/3.44 tff(5970,plain,
% 3.24/3.44 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.24/3.44 inference(modus_ponens,[status(thm)],[5969, 5956])).
% 3.24/3.44 tff(5971,plain,
% 3.24/3.44 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.24/3.44 inference(unit_resolution,[status(thm)],[3409, 5970, 5807])).
% 3.24/3.44 tff(5972,assumption,(r(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 3.24/3.44 tff(5973,plain,
% 3.24/3.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.24/3.44 inference(rewrite,[status(thm)],[])).
% 3.24/3.44 tff(5974,plain,
% 3.24/3.44 (((~r(s(elem!1), s(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(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.24/3.44 inference(rewrite,[status(thm)],[])).
% 3.24/3.44 tff(5975,plain,
% 3.24/3.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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))))))),
% 3.24/3.44 inference(monotonicity,[status(thm)],[5974])).
% 3.24/3.44 tff(5976,plain,
% 3.24/3.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(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)))))),
% 3.24/3.44 inference(transitivity,[status(thm)],[5975, 5973])).
% 3.24/3.44 tff(5977,plain,
% 3.24/3.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 3.24/3.44 inference(quant_inst,[status(thm)],[])).
% 3.24/3.44 tff(5978,plain,
% 3.24/3.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 3.24/3.44 inference(modus_ponens,[status(thm)],[5977, 5976])).
% 3.24/3.44 tff(5979,plain,
% 3.24/3.44 ($false),
% 3.24/3.44 inference(unit_resolution,[status(thm)],[5978, 118, 1551, 5227, 5972])).
% 3.24/3.44 tff(5980,plain,((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.44 tff(5981,plain,
% 3.24/3.44 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.24/3.45 inference(unit_resolution,[status(thm)],[5980, 5971, 5771])).
% 3.24/3.45 tff(5982,plain,
% 3.24/3.45 (b(s(s(s(elem!1))), s(elem!1))),
% 3.24/3.45 inference(unit_resolution,[status(thm)],[373, 5981, 356])).
% 3.24/3.45 tff(5983,plain,
% 3.24/3.45 (~b(s(elem!1), s(s(s(elem!1))))),
% 3.24/3.45 inference(unit_resolution,[status(thm)],[5928, 5982, 5949, 5948, 5775, 5785, 5389, 5724, 5942])).
% 3.24/3.45 tff(5984,plain,
% 3.24/3.45 (r(s(elem!1), s(s(s(elem!1))))),
% 3.24/3.45 inference(unit_resolution,[status(thm)],[5432, 5983, 5396])).
% 3.24/3.45 tff(5985,plain,
% 3.24/3.45 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.24/3.45 inference(unit_resolution,[status(thm)],[5897, 5982, 854, 5949, 5942])).
% 3.24/3.45 tff(5986,plain,
% 3.24/3.45 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.24/3.45 inference(unit_resolution,[status(thm)],[3375, 5985, 1650])).
% 3.24/3.45 tff(5987,plain,
% 3.24/3.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 3.24/3.45 inference(rewrite,[status(thm)],[])).
% 3.24/3.45 tff(5988,plain,
% 3.24/3.45 (((~r(s(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(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 3.24/3.45 inference(rewrite,[status(thm)],[])).
% 3.24/3.45 tff(5989,plain,
% 3.24/3.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1))))))),
% 3.24/3.45 inference(monotonicity,[status(thm)],[5988])).
% 3.24/3.45 tff(5990,plain,
% 3.24/3.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 3.24/3.45 inference(transitivity,[status(thm)],[5989, 5987])).
% 3.24/3.45 tff(5991,plain,
% 3.24/3.45 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 3.24/3.45 inference(quant_inst,[status(thm)],[])).
% 3.24/3.45 tff(5992,plain,
% 3.24/3.45 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1))))),
% 3.24/3.45 inference(modus_ponens,[status(thm)],[5991, 5990])).
% 3.24/3.45 tff(5993,plain,
% 3.24/3.45 ($false),
% 3.24/3.45 inference(unit_resolution,[status(thm)],[5992, 118, 2102, 5972, 3364])).
% 3.24/3.45 tff(5994,plain,((~r(s(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))))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.45 tff(5995,plain,
% 3.24/3.45 ($false),
% 3.24/3.45 inference(unit_resolution,[status(thm)],[5994, 5986, 5984, 5771])).
% 3.24/3.45 tff(5996,plain,((~r(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(z)), z)) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | b(s(s(s(s(z)))), z) | b(elem!1, z) | (~r(s(s(z)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.45 tff(5997,plain,
% 3.24/3.45 (~r(s(elem!1), s(s(s(s(z)))))),
% 3.24/3.45 inference(unit_resolution,[status(thm)],[5996, 3261, 356, 3461, 450, 854, 1301, 3170, 5723, 1329])).
% 3.24/3.45 tff(5998,plain,
% 3.24/3.45 (s(elem!1) = s(s(s(s(z))))),
% 3.24/3.45 inference(unit_resolution,[status(thm)],[1084, 5997, 5720])).
% 3.24/3.45 tff(5999,plain,
% 3.24/3.45 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 3.24/3.45 inference(monotonicity,[status(thm)],[5998])).
% 3.24/3.45 tff(6000,plain,
% 3.24/3.45 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 3.24/3.45 inference(symmetry,[status(thm)],[5999])).
% 3.24/3.45 tff(6001,plain,
% 3.24/3.45 (s(s(s(z))) = elem!1),
% 3.24/3.45 inference(transitivity,[status(thm)],[61, 6000, 304])).
% 3.24/3.45 tff(6002,plain,
% 3.24/3.45 (r(s(s(s(z))), z) <=> r(elem!1, z)),
% 3.24/3.45 inference(monotonicity,[status(thm)],[6001])).
% 3.24/3.45 tff(6003,plain,
% 3.24/3.45 (r(elem!1, z) <=> r(s(s(s(z))), z)),
% 3.24/3.45 inference(symmetry,[status(thm)],[6002])).
% 3.24/3.45 tff(6004,plain,
% 3.24/3.45 ((s(s(s(z))) = z) <=> (elem!1 = z)),
% 3.24/3.45 inference(monotonicity,[status(thm)],[6001])).
% 3.24/3.45 tff(6005,plain,
% 3.24/3.45 ((s(s(s(z))) = z) <=> (z = elem!1)),
% 3.24/3.45 inference(transitivity,[status(thm)],[6004, 313])).
% 3.24/3.45 tff(6006,plain,
% 3.24/3.45 ((s(s(s(z))) = z) <=> (elem!1 = z)),
% 3.24/3.45 inference(transitivity,[status(thm)],[6005, 314])).
% 3.24/3.45 tff(6007,plain,
% 3.24/3.45 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = z))),
% 3.24/3.45 inference(monotonicity,[status(thm)],[6006])).
% 3.24/3.45 tff(6008,plain,
% 3.24/3.45 (~(elem!1 = z)),
% 3.24/3.45 inference(modus_ponens,[status(thm)],[77, 6007])).
% 3.24/3.45 tff(6009,plain,
% 3.24/3.45 (r(elem!1, z)),
% 3.24/3.45 inference(unit_resolution,[status(thm)],[498, 6008, 5723])).
% 3.24/3.45 tff(6010,plain,
% 3.24/3.45 (r(s(s(s(z))), z)),
% 3.24/3.45 inference(modus_ponens,[status(thm)],[6009, 6003])).
% 3.24/3.45 tff(6011,plain,
% 3.24/3.45 (r(s(s(s(z))), s(s(z))) <=> r(elem!1, s(s(z)))),
% 3.24/3.45 inference(monotonicity,[status(thm)],[6001])).
% 3.24/3.45 tff(6012,plain,
% 3.24/3.45 (r(elem!1, s(s(z))) <=> r(s(s(s(z))), s(s(z)))),
% 3.24/3.45 inference(symmetry,[status(thm)],[6011])).
% 3.24/3.45 tff(6013,plain,
% 3.24/3.45 (r(s(s(s(z))), s(s(z)))),
% 3.24/3.45 inference(modus_ponens,[status(thm)],[450, 6012])).
% 3.24/3.45 tff(6014,plain,
% 3.24/3.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 3.24/3.45 inference(rewrite,[status(thm)],[])).
% 3.24/3.45 tff(6015,plain,
% 3.24/3.45 (((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 3.24/3.45 inference(rewrite,[status(thm)],[])).
% 3.24/3.45 tff(6016,plain,
% 3.24/3.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z))))))),
% 3.24/3.45 inference(monotonicity,[status(thm)],[6015])).
% 3.24/3.45 tff(6017,plain,
% 3.24/3.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 3.24/3.45 inference(transitivity,[status(thm)],[6016, 6014])).
% 3.24/3.45 tff(6018,plain,
% 3.24/3.45 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))),
% 3.24/3.45 inference(quant_inst,[status(thm)],[])).
% 3.24/3.45 tff(6019,plain,
% 3.24/3.45 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z))))),
% 3.24/3.45 inference(modus_ponens,[status(thm)],[6018, 6017])).
% 3.24/3.45 tff(6020,plain,
% 3.24/3.45 ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z))))),
% 3.24/3.45 inference(unit_resolution,[status(thm)],[6019, 118, 3261])).
% 3.24/3.45 tff(6021,plain,
% 3.24/3.45 ($false),
% 3.24/3.45 inference(unit_resolution,[status(thm)],[6020, 6013, 6010])).
% 3.24/3.45 tff(6022,plain,((~r(z, s(s(z)))) | (~r(elem!1, s(s(z)))) | b(elem!1, z) | b(s(elem!1), s(s(s(s(z))))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | b(s(s(s(s(z)))), z) | (~r(s(s(z)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.45 tff(6023,plain,
% 3.24/3.45 (~r(z, s(s(z)))),
% 3.24/3.45 inference(unit_resolution,[status(thm)],[6022, 5728, 5723, 5720, 356, 5619, 5725, 1301, 3170, 5731])).
% 3.24/3.45 tff(6024,plain,
% 3.24/3.45 (b(z, s(s(z)))),
% 3.24/3.45 inference(unit_resolution,[status(thm)],[143, 6023])).
% 3.24/3.45 tff(6025,plain,
% 3.24/3.45 (~(elem!1 = z)),
% 3.24/3.45 inference(unit_resolution,[status(thm)],[3276, 6024, 461])).
% 3.24/3.45 tff(6026,plain,
% 3.24/3.45 (r(elem!1, z)),
% 3.24/3.45 inference(unit_resolution,[status(thm)],[498, 6025, 5723])).
% 3.24/3.45 tff(6027,plain,
% 3.24/3.45 (~(z = elem!1)),
% 3.24/3.45 inference(unit_resolution,[status(thm)],[317, 6025])).
% 3.24/3.45 tff(6028,plain,
% 3.24/3.45 (~(s(s(elem!1)) = s(s(z)))),
% 3.24/3.45 inference(unit_resolution,[status(thm)],[2386, 6027])).
% 3.24/3.45 tff(6029,plain,
% 3.24/3.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.24/3.45 inference(rewrite,[status(thm)],[])).
% 3.24/3.45 tff(6030,plain,
% 3.24/3.45 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.24/3.45 inference(quant_inst,[status(thm)],[])).
% 3.24/3.45 tff(6031,plain,
% 3.24/3.45 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1))),
% 3.24/3.45 inference(modus_ponens,[status(thm)],[6030, 6029])).
% 3.24/3.45 tff(6032,plain,
% 3.24/3.45 ($false),
% 3.24/3.45 inference(unit_resolution,[status(thm)],[6031, 118, 437, 3132, 194])).
% 3.24/3.45 tff(6033,plain,((~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.45 tff(6034,plain,
% 3.24/3.45 (~r(s(s(s(s(z)))), elem!1)),
% 3.24/3.45 inference(unit_resolution,[status(thm)],[6033, 6026, 3244])).
% 3.24/3.45 tff(6035,plain,
% 3.24/3.45 (b(s(s(s(s(z)))), elem!1)),
% 3.24/3.45 inference(unit_resolution,[status(thm)],[3142, 6034, 4510])).
% 3.24/3.45 tff(6036,plain,
% 3.24/3.45 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 3.24/3.45 inference(symmetry,[status(thm)],[1119])).
% 3.24/3.45 tff(6037,plain,
% 3.24/3.45 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 3.24/3.45 inference(monotonicity,[status(thm)],[6036, 2491])).
% 3.24/3.45 tff(6038,plain,
% 3.24/3.45 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 3.24/3.45 inference(symmetry,[status(thm)],[6037])).
% 3.24/3.45 tff(6039,plain,
% 3.24/3.45 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 3.24/3.45 inference(monotonicity,[status(thm)],[1119, 1117])).
% 3.24/3.45 tff(6040,plain,
% 3.24/3.45 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 3.24/3.45 inference(symmetry,[status(thm)],[6039])).
% 3.24/3.45 tff(6041,plain,
% 3.24/3.45 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 3.24/3.45 inference(monotonicity,[status(thm)],[6040])).
% 3.24/3.45 tff(6042,plain,
% 3.24/3.45 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.24/3.45 inference(modus_ponens,[status(thm)],[3771, 1278])).
% 3.24/3.45 tff(6043,plain,
% 3.24/3.45 (~(elem!1 = s(s(s(elem!1))))),
% 3.24/3.45 inference(unit_resolution,[status(thm)],[2498, 1117, 2484])).
% 3.24/3.45 tff(6044,plain,
% 3.24/3.45 (~(s(s(s(elem!1))) = elem!1)),
% 3.24/3.45 inference(unit_resolution,[status(thm)],[2489, 6043])).
% 3.24/3.45 tff(6045,plain,
% 3.24/3.45 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 3.24/3.45 inference(monotonicity,[status(thm)],[1183])).
% 3.24/3.45 tff(6046,plain,
% 3.24/3.45 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 3.24/3.45 inference(symmetry,[status(thm)],[6045])).
% 3.24/3.45 tff(6047,plain,
% 3.24/3.45 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.24/3.45 inference(modus_ponens,[status(thm)],[1301, 6046])).
% 3.24/3.45 tff(6048,plain,
% 3.24/3.45 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 3.24/3.45 inference(monotonicity,[status(thm)],[1218, 1119])).
% 3.24/3.45 tff(6049,plain,
% 3.24/3.45 (r(s(s(s(z))), s(s(s(s(s(s(z))))))) <=> r(elem!1, s(s(s(elem!1))))),
% 3.24/3.45 inference(monotonicity,[status(thm)],[1183, 6036])).
% 3.24/3.45 tff(6050,plain,
% 3.24/3.45 ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) <=> (~r(elem!1, s(s(s(elem!1)))))),
% 3.24/3.45 inference(monotonicity,[status(thm)],[6049])).
% 3.24/3.45 tff(6051,plain,
% 3.24/3.45 (r(s(s(s(z))), s(s(z))) <=> r(elem!1, s(s(z)))),
% 3.24/3.45 inference(monotonicity,[status(thm)],[1183])).
% 3.24/3.45 tff(6052,plain,
% 3.24/3.45 (r(elem!1, s(s(z))) <=> r(s(s(s(z))), s(s(z)))),
% 3.24/3.45 inference(symmetry,[status(thm)],[6051])).
% 3.24/3.45 tff(6053,plain,
% 3.24/3.45 (r(s(s(s(z))), s(s(z)))),
% 3.24/3.45 inference(modus_ponens,[status(thm)],[450, 6052])).
% 3.24/3.45 tff(6054,assumption,(s(s(s(s(s(s(z)))))) = s(s(z))), introduced(assumption)).
% 3.24/3.45 tff(6055,plain,
% 3.24/3.45 (s(s(z)) = s(s(s(s(s(s(z))))))),
% 3.24/3.45 inference(symmetry,[status(thm)],[6054])).
% 3.24/3.45 tff(6056,plain,
% 3.24/3.45 (s(s(z)) = s(s(s(elem!1)))),
% 3.24/3.45 inference(transitivity,[status(thm)],[6055, 6036])).
% 3.24/3.45 tff(6057,plain,
% 3.24/3.45 ($false),
% 3.24/3.45 inference(unit_resolution,[status(thm)],[1683, 6056])).
% 3.24/3.45 tff(6058,plain,((~(s(s(s(s(s(s(z)))))) = s(s(z)))) | (~(s(elem!1) = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.45 tff(6059,plain,
% 3.24/3.45 (~(s(s(s(s(s(s(z)))))) = s(s(z)))),
% 3.24/3.45 inference(unit_resolution,[status(thm)],[6058, 1117])).
% 3.24/3.45 tff(6060,plain,
% 3.24/3.45 (r(s(elem!1), z) <=> r(s(s(s(s(z)))), z)),
% 3.24/3.45 inference(monotonicity,[status(thm)],[1117])).
% 3.24/3.45 tff(6061,plain,
% 3.24/3.45 (r(s(s(s(s(z)))), z) <=> r(s(elem!1), z)),
% 3.24/3.45 inference(symmetry,[status(thm)],[6060])).
% 3.24/3.45 tff(6062,plain,
% 3.24/3.45 (r(s(elem!1), z)),
% 3.24/3.45 inference(modus_ponens,[status(thm)],[194, 6061])).
% 3.24/3.45 tff(6063,plain,
% 3.24/3.45 (b(s(s(z)), s(s(s(s(s(s(z))))))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 3.24/3.45 inference(monotonicity,[status(thm)],[6036])).
% 3.24/3.45 tff(6064,plain,
% 3.24/3.45 ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) <=> (~b(s(s(z)), s(s(s(elem!1)))))),
% 3.24/3.45 inference(monotonicity,[status(thm)],[6063])).
% 3.24/3.45 tff(6065,plain,
% 3.24/3.45 (b(s(s(s(s(s(s(z)))))), z) <=> b(s(s(s(elem!1))), z)),
% 3.24/3.45 inference(monotonicity,[status(thm)],[6036])).
% 3.24/3.45 tff(6066,plain,
% 3.24/3.45 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(s(s(z)))))), z)),
% 3.24/3.45 inference(symmetry,[status(thm)],[6065])).
% 3.24/3.45 tff(6067,assumption,(b(s(s(s(s(s(s(z)))))), s(s(z)))), introduced(assumption)).
% 3.24/3.45 tff(6068,plain,
% 3.24/3.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))),
% 3.24/3.45 inference(rewrite,[status(thm)],[])).
% 3.24/3.45 tff(6069,plain,
% 3.24/3.45 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))),
% 3.24/3.45 inference(quant_inst,[status(thm)],[])).
% 3.24/3.45 tff(6070,plain,
% 3.24/3.45 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1)))))),
% 3.24/3.45 inference(modus_ponens,[status(thm)],[6069, 6068])).
% 3.24/3.45 tff(6071,plain,
% 3.24/3.45 ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1)))))),
% 3.24/3.45 inference(unit_resolution,[status(thm)],[6070, 118])).
% 3.24/3.45 tff(6072,plain,
% 3.24/3.45 (~r(s(s(s(elem!1))), z)),
% 3.24/3.45 inference(unit_resolution,[status(thm)],[6071, 3311, 437])).
% 3.24/3.45 tff(6073,plain,
% 3.24/3.45 (b(s(s(s(elem!1))), z)),
% 3.24/3.45 inference(unit_resolution,[status(thm)],[1565, 6072])).
% 3.24/3.45 tff(6074,plain,
% 3.24/3.45 (b(s(s(s(s(s(s(z)))))), z)),
% 3.24/3.45 inference(modus_ponens,[status(thm)],[6073, 6066])).
% 3.24/3.45 tff(6075,plain,
% 3.24/3.45 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(s(s(s(z)))))))),
% 3.24/3.45 inference(monotonicity,[status(thm)],[1119])).
% 3.24/3.45 tff(6076,plain,
% 3.24/3.45 (~r(z, s(s(s(elem!1))))),
% 3.24/3.45 inference(unit_resolution,[status(thm)],[3421, 3311, 437])).
% 3.24/3.45 tff(6077,plain,
% 3.24/3.45 (b(z, s(s(s(elem!1))))),
% 3.24/3.45 inference(unit_resolution,[status(thm)],[2095, 6076])).
% 3.24/3.45 tff(6078,plain,
% 3.24/3.45 (b(z, s(s(s(s(s(s(z)))))))),
% 3.24/3.45 inference(modus_ponens,[status(thm)],[6077, 6075])).
% 3.24/3.45 tff(6079,plain,
% 3.24/3.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 3.24/3.45 inference(rewrite,[status(thm)],[])).
% 3.24/3.45 tff(6080,plain,
% 3.24/3.45 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(z))))))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 3.24/3.45 inference(rewrite,[status(thm)],[])).
% 3.24/3.45 tff(6081,plain,
% 3.24/3.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 3.24/3.45 inference(monotonicity,[status(thm)],[6080])).
% 3.24/3.45 tff(6082,plain,
% 3.24/3.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 3.24/3.45 inference(transitivity,[status(thm)],[6081, 6079])).
% 3.24/3.45 tff(6083,plain,
% 3.24/3.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 3.24/3.45 inference(quant_inst,[status(thm)],[])).
% 3.24/3.45 tff(6084,plain,
% 3.24/3.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))),
% 3.24/3.45 inference(modus_ponens,[status(thm)],[6083, 6082])).
% 3.24/3.45 tff(6085,plain,
% 3.24/3.45 ($false),
% 3.24/3.45 inference(unit_resolution,[status(thm)],[6084, 178, 3461, 273, 6078, 6067, 6074])).
% 3.24/3.45 tff(6086,plain,((~r(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~(s(elem!1) = s(s(s(s(z)))))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.45 tff(6087,plain,
% 3.24/3.45 (~r(elem!1, s(s(s(elem!1))))),
% 3.24/3.45 inference(unit_resolution,[status(thm)],[6086, 6067, 273, 3461, 1117, 437])).
% 3.24/3.45 tff(6088,plain,
% 3.24/3.45 (b(elem!1, s(s(s(elem!1))))),
% 3.24/3.45 inference(unit_resolution,[status(thm)],[2054, 6087, 1586])).
% 3.24/3.45 tff(6089,plain,
% 3.24/3.45 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 3.24/3.45 inference(modus_ponens,[status(thm)],[6088, 6048])).
% 3.24/3.45 tff(6090,plain,
% 3.24/3.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), 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(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), 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(z)))))),
% 3.24/3.45 inference(rewrite,[status(thm)],[])).
% 3.24/3.45 tff(6091,plain,
% 3.24/3.45 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(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(s(s(z))))))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), 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(z)))))),
% 3.24/3.45 inference(rewrite,[status(thm)],[])).
% 3.24/3.45 tff(6092,plain,
% 3.24/3.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(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(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), 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(z))))))),
% 3.24/3.45 inference(monotonicity,[status(thm)],[6091])).
% 3.24/3.45 tff(6093,plain,
% 3.24/3.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(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(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), 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(z)))))),
% 3.24/3.45 inference(transitivity,[status(thm)],[6092, 6090])).
% 3.24/3.45 tff(6094,plain,
% 3.24/3.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(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(s(s(z)))))))))),
% 3.24/3.45 inference(quant_inst,[status(thm)],[])).
% 3.24/3.45 tff(6095,plain,
% 3.24/3.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), 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(z))))),
% 3.24/3.45 inference(modus_ponens,[status(thm)],[6094, 6093])).
% 3.24/3.45 tff(6096,plain,
% 3.24/3.45 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 3.24/3.45 inference(unit_resolution,[status(thm)],[6095, 178, 202, 1126, 6067, 6089])).
% 3.24/3.45 tff(6097,plain,
% 3.24/3.45 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.24/3.45 inference(modus_ponens,[status(thm)],[6096, 6041])).
% 3.24/3.45 tff(6098,plain,
% 3.24/3.45 (r(s(s(s(elem!1))), s(elem!1))),
% 3.24/3.45 inference(unit_resolution,[status(thm)],[373, 6097, 356])).
% 3.24/3.45 tff(6099,plain,
% 3.24/3.45 (~r(s(s(s(elem!1))), z)),
% 3.24/3.45 inference(unit_resolution,[status(thm)],[1557, 6098, 844])).
% 3.24/3.45 tff(6100,plain,
% 3.24/3.45 (b(s(s(s(elem!1))), z)),
% 3.24/3.45 inference(unit_resolution,[status(thm)],[1565, 6099])).
% 3.24/3.45 tff(6101,plain,
% 3.24/3.45 (b(s(s(s(s(s(s(z)))))), z)),
% 3.24/3.45 inference(modus_ponens,[status(thm)],[6100, 6066])).
% 3.24/3.45 tff(6102,plain,
% 3.24/3.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 3.24/3.45 inference(rewrite,[status(thm)],[])).
% 3.24/3.45 tff(6103,plain,
% 3.24/3.45 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 3.24/3.45 inference(rewrite,[status(thm)],[])).
% 3.24/3.45 tff(6104,plain,
% 3.24/3.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 3.24/3.45 inference(monotonicity,[status(thm)],[6103])).
% 3.24/3.45 tff(6105,plain,
% 3.24/3.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 3.24/3.45 inference(transitivity,[status(thm)],[6104, 6102])).
% 3.24/3.45 tff(6106,plain,
% 3.24/3.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 3.24/3.45 inference(quant_inst,[status(thm)],[])).
% 3.24/3.45 tff(6107,plain,
% 3.24/3.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))),
% 3.24/3.45 inference(modus_ponens,[status(thm)],[6106, 6105])).
% 3.24/3.45 tff(6108,plain,
% 3.24/3.45 ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 3.24/3.45 inference(unit_resolution,[status(thm)],[6107, 178, 3461, 273, 6067])).
% 3.24/3.45 tff(6109,plain,
% 3.24/3.45 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 3.24/3.45 inference(unit_resolution,[status(thm)],[6108, 6101])).
% 3.24/3.45 tff(6110,plain,
% 3.24/3.45 (~b(s(s(z)), s(s(s(elem!1))))),
% 3.24/3.45 inference(modus_ponens,[status(thm)],[6109, 6064])).
% 3.24/3.45 tff(6111,plain,
% 3.24/3.45 (b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 3.24/3.45 inference(monotonicity,[status(thm)],[2491, 6036])).
% 3.24/3.45 tff(6112,plain,
% 3.24/3.46 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) <=> (~b(s(elem!1), s(s(s(elem!1)))))),
% 3.24/3.46 inference(monotonicity,[status(thm)],[6111])).
% 3.24/3.46 tff(6113,plain,
% 3.24/3.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(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(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(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(z)))))),
% 3.24/3.46 inference(rewrite,[status(thm)],[])).
% 3.24/3.46 tff(6114,plain,
% 3.24/3.46 (((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), 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(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(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(z)))))),
% 3.24/3.46 inference(rewrite,[status(thm)],[])).
% 3.24/3.46 tff(6115,plain,
% 3.24/3.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), 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(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(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(z))))))),
% 3.24/3.46 inference(monotonicity,[status(thm)],[6114])).
% 3.24/3.46 tff(6116,plain,
% 3.24/3.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), 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(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(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(z)))))),
% 3.24/3.46 inference(transitivity,[status(thm)],[6115, 6113])).
% 3.24/3.46 tff(6117,plain,
% 3.24/3.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), 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(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 3.24/3.46 inference(quant_inst,[status(thm)],[])).
% 3.24/3.46 tff(6118,plain,
% 3.24/3.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(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(z))))),
% 3.24/3.46 inference(modus_ponens,[status(thm)],[6117, 6116])).
% 3.24/3.46 tff(6119,plain,
% 3.24/3.46 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 3.24/3.46 inference(unit_resolution,[status(thm)],[6118, 178, 202, 1126, 6067, 6089])).
% 3.24/3.46 tff(6120,plain,
% 3.24/3.46 (~b(s(elem!1), s(s(s(elem!1))))),
% 3.24/3.46 inference(modus_ponens,[status(thm)],[6119, 6112])).
% 3.24/3.46 tff(6121,plain,
% 3.24/3.46 (r(s(elem!1), s(s(s(elem!1))))),
% 3.24/3.46 inference(unit_resolution,[status(thm)],[5430, 41, 5427, 5425])).
% 3.24/3.46 tff(6122,plain,
% 3.24/3.46 (r(s(s(z)), s(s(s(elem!1))))),
% 3.24/3.46 inference(unit_resolution,[status(thm)],[4221, 41, 1683, 4218])).
% 3.24/3.46 tff(6123,plain,
% 3.24/3.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(elem!1))))),
% 3.24/3.46 inference(rewrite,[status(thm)],[])).
% 3.24/3.46 tff(6124,plain,
% 3.24/3.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(elem!1))))),
% 3.24/3.46 inference(quant_inst,[status(thm)],[])).
% 3.24/3.46 tff(6125,plain,
% 3.24/3.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(elem!1)))),
% 3.24/3.46 inference(modus_ponens,[status(thm)],[6124, 6123])).
% 3.24/3.46 tff(6126,plain,
% 3.24/3.46 ($false),
% 3.24/3.46 inference(unit_resolution,[status(thm)],[6125, 118, 1329, 6122, 6121])).
% 3.24/3.46 tff(6127,plain,(b(s(s(z)), s(s(s(elem!1)))) | (~r(s(s(z)), s(elem!1))) | b(s(elem!1), s(s(s(elem!1)))) | (s(elem!1) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.46 tff(6128,plain,
% 3.24/3.46 (b(s(s(z)), s(s(s(elem!1))))),
% 3.24/3.46 inference(unit_resolution,[status(thm)],[6127, 6120, 5396, 1329])).
% 3.24/3.46 tff(6129,plain,
% 3.24/3.46 ($false),
% 3.24/3.46 inference(unit_resolution,[status(thm)],[6128, 6110])).
% 3.24/3.46 tff(6130,plain,((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~(s(elem!1) = s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(s(elem!1), z)) | (~r(s(s(z)), s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (elem!1 = s(s(s(elem!1)))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.46 tff(6131,plain,
% 3.24/3.46 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 3.24/3.46 inference(unit_resolution,[status(thm)],[6130, 1117, 3461, 273, 6062, 1329, 356, 202, 6047, 6043, 437])).
% 3.24/3.46 tff(6132,assumption,(~r(s(s(s(s(s(s(z)))))), s(s(z)))), introduced(assumption)).
% 3.24/3.46 tff(6133,assumption,(~b(s(s(s(s(s(s(z)))))), s(s(z)))), introduced(assumption)).
% 3.24/3.46 tff(6134,assumption,(~(s(s(s(s(s(s(z)))))) = s(s(z)))), introduced(assumption)).
% 3.24/3.46 tff(6135,plain,
% 3.24/3.46 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 3.24/3.46 inference(rewrite,[status(thm)],[])).
% 3.24/3.46 tff(6136,plain,
% 3.24/3.46 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 3.24/3.46 inference(quant_inst,[status(thm)],[])).
% 3.24/3.46 tff(6137,plain,
% 3.24/3.46 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 3.24/3.46 inference(modus_ponens,[status(thm)],[6136, 6135])).
% 3.24/3.46 tff(6138,plain,
% 3.24/3.46 ($false),
% 3.24/3.46 inference(unit_resolution,[status(thm)],[6137, 41, 6134, 6133, 6132])).
% 3.24/3.46 tff(6139,plain,(r(s(s(s(s(s(s(z)))))), s(s(z))) | (s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.46 tff(6140,plain,
% 3.24/3.46 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 3.24/3.46 inference(unit_resolution,[status(thm)],[6139, 6131, 6059])).
% 3.24/3.46 tff(6141,plain,
% 3.24/3.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(z)))))),
% 3.24/3.46 inference(rewrite,[status(thm)],[])).
% 3.24/3.46 tff(6142,plain,
% 3.24/3.46 (((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(z)))))),
% 3.24/3.46 inference(rewrite,[status(thm)],[])).
% 3.24/3.46 tff(6143,plain,
% 3.24/3.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(z))))))),
% 3.24/3.46 inference(monotonicity,[status(thm)],[6142])).
% 3.24/3.46 tff(6144,plain,
% 3.24/3.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(z)))))),
% 3.24/3.46 inference(transitivity,[status(thm)],[6143, 6141])).
% 3.24/3.46 tff(6145,plain,
% 3.24/3.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 3.24/3.46 inference(quant_inst,[status(thm)],[])).
% 3.24/3.46 tff(6146,plain,
% 3.24/3.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(z))))),
% 3.24/3.46 inference(modus_ponens,[status(thm)],[6145, 6144])).
% 3.24/3.46 tff(6147,plain,
% 3.24/3.46 ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(z))))),
% 3.24/3.46 inference(unit_resolution,[status(thm)],[6146, 118, 6140])).
% 3.24/3.46 tff(6148,plain,
% 3.24/3.46 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 3.24/3.46 inference(unit_resolution,[status(thm)],[6147, 6053])).
% 3.24/3.46 tff(6149,plain,
% 3.24/3.46 (~r(elem!1, s(s(s(elem!1))))),
% 3.24/3.46 inference(modus_ponens,[status(thm)],[6148, 6050])).
% 3.24/3.46 tff(6150,plain,
% 3.24/3.46 (b(elem!1, s(s(s(elem!1))))),
% 3.24/3.46 inference(unit_resolution,[status(thm)],[2054, 6149, 6043])).
% 3.24/3.46 tff(6151,plain,
% 3.24/3.46 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 3.24/3.46 inference(modus_ponens,[status(thm)],[6150, 6048])).
% 3.24/3.46 tff(6152,plain,
% 3.24/3.46 (b(s(s(s(s(s(s(z)))))), s(s(s(z)))) <=> b(s(s(s(elem!1))), elem!1)),
% 3.24/3.46 inference(monotonicity,[status(thm)],[6036, 1183])).
% 3.24/3.46 tff(6153,plain,
% 3.24/3.46 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 3.24/3.46 inference(symmetry,[status(thm)],[6152])).
% 3.24/3.46 tff(6154,assumption,(b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))), introduced(assumption)).
% 3.24/3.46 tff(6155,assumption,(b(s(s(s(z))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 3.24/3.46 tff(6156,plain,
% 3.24/3.46 ($false),
% 3.24/3.46 inference(unit_resolution,[status(thm)],[6095, 178, 202, 6154, 1126, 6155, 6067])).
% 3.24/3.46 tff(6157,plain,((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.46 tff(6158,plain,
% 3.24/3.46 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 3.24/3.46 inference(unit_resolution,[status(thm)],[6157, 6155, 6154, 1126, 202])).
% 3.24/3.46 tff(6159,plain,
% 3.24/3.46 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 3.24/3.46 inference(unit_resolution,[status(thm)],[6139, 6158, 6059])).
% 3.24/3.46 tff(6160,plain,
% 3.24/3.46 (r(s(s(s(s(s(s(z)))))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 3.24/3.46 inference(monotonicity,[status(thm)],[6036])).
% 3.24/3.46 tff(6161,plain,
% 3.24/3.46 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 3.24/3.46 inference(symmetry,[status(thm)],[6160])).
% 3.24/3.46 tff(6162,plain,
% 3.24/3.46 ((~r(s(s(s(elem!1))), s(s(z)))) <=> (~r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 3.24/3.46 inference(monotonicity,[status(thm)],[6161])).
% 3.24/3.46 tff(6163,plain,
% 3.24/3.46 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 3.24/3.46 inference(modus_ponens,[status(thm)],[5810, 6162])).
% 3.24/3.46 tff(6164,plain,
% 3.24/3.46 ($false),
% 3.24/3.46 inference(unit_resolution,[status(thm)],[2405, 6163])).
% 3.24/3.46 tff(6165,plain,((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | r(s(s(s(elem!1))), s(s(z))) | (~(s(elem!1) = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.46 tff(6166,plain,
% 3.24/3.46 (r(s(s(s(elem!1))), s(s(z)))),
% 3.24/3.46 inference(unit_resolution,[status(thm)],[6165, 6159, 1117])).
% 3.24/3.46 tff(6167,plain,
% 3.24/3.46 (~r(s(s(s(elem!1))), elem!1)),
% 3.24/3.46 inference(unit_resolution,[status(thm)],[4205, 6166, 450])).
% 3.24/3.46 tff(6168,plain,
% 3.24/3.46 (b(s(s(s(elem!1))), elem!1)),
% 3.24/3.46 inference(unit_resolution,[status(thm)],[570, 6167, 949])).
% 3.24/3.46 tff(6169,plain,
% 3.24/3.46 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 3.24/3.46 inference(modus_ponens,[status(thm)],[6168, 6153])).
% 3.24/3.46 tff(6170,assumption,(b(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 3.24/3.46 tff(6171,plain,
% 3.24/3.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 3.24/3.46 inference(rewrite,[status(thm)],[])).
% 3.24/3.46 tff(6172,plain,
% 3.24/3.46 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 3.24/3.46 inference(rewrite,[status(thm)],[])).
% 3.24/3.46 tff(6173,plain,
% 3.24/3.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 3.24/3.46 inference(monotonicity,[status(thm)],[6172])).
% 3.24/3.46 tff(6174,plain,
% 3.24/3.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 3.24/3.46 inference(transitivity,[status(thm)],[6173, 6171])).
% 3.24/3.46 tff(6175,plain,
% 3.24/3.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 3.24/3.46 inference(quant_inst,[status(thm)],[])).
% 3.24/3.46 tff(6176,plain,
% 3.24/3.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 3.24/3.46 inference(modus_ponens,[status(thm)],[6175, 6174])).
% 3.24/3.46 tff(6177,plain,
% 3.24/3.46 ($false),
% 3.24/3.46 inference(unit_resolution,[status(thm)],[6176, 178, 6154, 1126, 6155, 6170, 6169])).
% 3.24/3.46 tff(6178,plain,((~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)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~(s(elem!1) = s(s(s(s(z)))))) | (s(s(s(elem!1))) = elem!1) | (~r(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.46 tff(6179,plain,
% 3.24/3.46 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 3.24/3.46 inference(unit_resolution,[status(thm)],[6178, 6151, 450, 6047, 1117, 6044, 6042, 202])).
% 3.24/3.46 tff(6180,plain,
% 3.24/3.46 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.24/3.46 inference(modus_ponens,[status(thm)],[6179, 6041])).
% 3.24/3.46 tff(6181,plain,
% 3.24/3.46 (r(s(s(s(elem!1))), s(elem!1))),
% 3.24/3.46 inference(unit_resolution,[status(thm)],[373, 6180, 356])).
% 3.24/3.46 tff(6182,plain,
% 3.24/3.46 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 3.24/3.46 inference(modus_ponens,[status(thm)],[6181, 6038])).
% 3.24/3.46 tff(6183,plain,
% 3.24/3.46 (r(s(s(z)), s(elem!1)) <=> r(s(s(z)), s(s(s(s(z)))))),
% 3.24/3.46 inference(monotonicity,[status(thm)],[1117])).
% 3.24/3.46 tff(6184,plain,
% 3.24/3.46 (r(s(s(z)), s(s(s(s(z)))))),
% 3.24/3.46 inference(modus_ponens,[status(thm)],[1329, 6183])).
% 3.24/3.46 tff(6185,plain,
% 3.24/3.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 3.24/3.46 inference(rewrite,[status(thm)],[])).
% 3.24/3.46 tff(6186,plain,
% 3.24/3.46 (((~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))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 3.24/3.46 inference(rewrite,[status(thm)],[])).
% 3.24/3.46 tff(6187,plain,
% 3.24/3.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 3.24/3.46 inference(monotonicity,[status(thm)],[6186])).
% 3.24/3.46 tff(6188,plain,
% 3.24/3.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 3.24/3.46 inference(transitivity,[status(thm)],[6187, 6185])).
% 3.24/3.46 tff(6189,plain,
% 3.24/3.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 3.24/3.46 inference(quant_inst,[status(thm)],[])).
% 3.24/3.46 tff(6190,plain,
% 3.24/3.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 3.24/3.46 inference(modus_ponens,[status(thm)],[6189, 6188])).
% 3.24/3.46 tff(6191,plain,
% 3.24/3.46 ($false),
% 3.24/3.46 inference(unit_resolution,[status(thm)],[6190, 118, 6184, 6140, 6182])).
% 3.24/3.46 tff(6192,plain,((~(s(elem!1) = s(s(s(s(z)))))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(s(s(z)), s(elem!1))) | (~r(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z)) | (s(s(elem!1)) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.46 tff(6193,plain,
% 3.24/3.46 (~(s(elem!1) = s(s(s(s(z)))))),
% 3.24/3.46 inference(unit_resolution,[status(thm)],[6192, 5728, 356, 202, 5619, 6024, 5731, 6026, 1301, 6035, 3244, 6028])).
% 3.24/3.46 tff(6194,plain,
% 3.24/3.46 (r(s(elem!1), s(s(s(s(z)))))),
% 3.24/3.46 inference(unit_resolution,[status(thm)],[1084, 6193, 5720])).
% 3.24/3.46 tff(6195,plain,
% 3.24/3.46 (~r(s(elem!1), z)),
% 3.24/3.46 inference(unit_resolution,[status(thm)],[916, 6194, 3244])).
% 3.24/3.46 tff(6196,plain,
% 3.24/3.46 (b(s(elem!1), z)),
% 3.24/3.46 inference(unit_resolution,[status(thm)],[774, 6195])).
% 3.24/3.46 tff(6197,plain,
% 3.24/3.46 (r(elem!1, s(elem!1)) <=> r(z, s(elem!1))),
% 3.24/3.46 inference(monotonicity,[status(thm)],[928])).
% 3.24/3.46 tff(6198,plain,
% 3.24/3.46 (r(z, s(elem!1)) <=> r(elem!1, s(elem!1))),
% 3.24/3.46 inference(symmetry,[status(thm)],[6197])).
% 3.24/3.46 tff(6199,plain,
% 3.24/3.46 (r(elem!1, s(elem!1))),
% 3.24/3.46 inference(modus_ponens,[status(thm)],[2333, 6198])).
% 3.24/3.46 tff(6200,plain,
% 3.24/3.46 ($false),
% 3.24/3.46 inference(unit_resolution,[status(thm)],[744, 6199])).
% 3.24/3.46 tff(6201,plain,((~(elem!1 = z)) | r(elem!1, s(elem!1)) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.46 tff(6202,plain,
% 3.24/3.46 (~(elem!1 = z)),
% 3.24/3.46 inference(unit_resolution,[status(thm)],[6201, 2333, 744])).
% 3.24/3.46 tff(6203,plain,
% 3.24/3.46 (r(elem!1, z)),
% 3.24/3.46 inference(unit_resolution,[status(thm)],[498, 6202, 5723])).
% 3.24/3.46 tff(6204,plain,
% 3.24/3.46 (r(s(s(z)), z)),
% 3.24/3.46 inference(modus_ponens,[status(thm)],[437, 1340])).
% 3.24/3.46 tff(6205,plain,
% 3.24/3.46 ($false),
% 3.24/3.46 inference(unit_resolution,[status(thm)],[5618, 6204])).
% 3.24/3.46 tff(6206,plain,((~(s(s(z)) = elem!1)) | r(s(s(z)), z) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.46 tff(6207,plain,
% 3.24/3.46 (~(s(s(z)) = elem!1)),
% 3.24/3.46 inference(unit_resolution,[status(thm)],[6206, 6203, 5618])).
% 3.24/3.46 tff(6208,plain,
% 3.24/3.46 (~(elem!1 = s(s(z)))),
% 3.24/3.46 inference(unit_resolution,[status(thm)],[311, 6207])).
% 3.24/3.46 tff(6209,plain,
% 3.24/3.46 (r(elem!1, s(s(z)))),
% 3.24/3.46 inference(unit_resolution,[status(thm)],[467, 6208, 461])).
% 3.24/3.46 tff(6210,plain,
% 3.24/3.46 (~(s(elem!1) = s(s(z)))),
% 3.24/3.46 inference(unit_resolution,[status(thm)],[1047, 6209, 744])).
% 3.24/3.46 tff(6211,plain,
% 3.24/3.46 (~(s(s(z)) = s(elem!1))),
% 3.24/3.46 inference(unit_resolution,[status(thm)],[1058, 6210])).
% 3.24/3.46 tff(6212,plain,
% 3.24/3.46 (r(s(s(z)), s(elem!1))),
% 3.24/3.46 inference(unit_resolution,[status(thm)],[1067, 6211, 1061])).
% 3.24/3.46 tff(6213,plain,
% 3.24/3.46 (~r(z, s(s(s(s(z)))))),
% 3.24/3.46 inference(unit_resolution,[status(thm)],[2766, 908, 2333])).
% 3.24/3.46 tff(6214,plain,
% 3.24/3.46 (b(z, s(s(s(s(z)))))),
% 3.24/3.46 inference(unit_resolution,[status(thm)],[46, 6213])).
% 3.24/3.46 tff(6215,plain,
% 3.24/3.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(elem!1))))),
% 3.24/3.46 inference(rewrite,[status(thm)],[])).
% 3.24/3.46 tff(6216,plain,
% 3.24/3.46 (((~r(s(s(z)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(z))))) <=> ((~r(z, s(elem!1))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(elem!1))))),
% 3.24/3.46 inference(rewrite,[status(thm)],[])).
% 3.24/3.46 tff(6217,plain,
% 3.24/3.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(elem!1)))))),
% 3.24/3.46 inference(monotonicity,[status(thm)],[6216])).
% 3.24/3.46 tff(6218,plain,
% 3.24/3.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(elem!1))))),
% 3.24/3.46 inference(transitivity,[status(thm)],[6217, 6215])).
% 3.24/3.46 tff(6219,plain,
% 3.24/3.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(z)))))),
% 3.24/3.46 inference(quant_inst,[status(thm)],[])).
% 3.24/3.46 tff(6220,plain,
% 3.24/3.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(elem!1)))),
% 3.24/3.46 inference(modus_ponens,[status(thm)],[6219, 6218])).
% 3.24/3.46 tff(6221,plain,
% 3.24/3.46 (~r(z, s(s(z)))),
% 3.24/3.46 inference(unit_resolution,[status(thm)],[6220, 118, 2333, 1329])).
% 3.24/3.46 tff(6222,plain,
% 3.24/3.46 (b(z, s(s(z)))),
% 3.24/3.46 inference(unit_resolution,[status(thm)],[143, 6221])).
% 3.24/3.46 tff(6223,plain,
% 3.24/3.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 3.24/3.47 inference(rewrite,[status(thm)],[])).
% 3.24/3.47 tff(6224,plain,
% 3.24/3.47 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), 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)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 3.24/3.47 inference(rewrite,[status(thm)],[])).
% 3.24/3.47 tff(6225,plain,
% 3.24/3.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))))),
% 3.24/3.47 inference(monotonicity,[status(thm)],[6224])).
% 3.24/3.47 tff(6226,plain,
% 3.24/3.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 3.24/3.47 inference(transitivity,[status(thm)],[6225, 6223])).
% 3.24/3.47 tff(6227,plain,
% 3.24/3.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 3.24/3.47 inference(quant_inst,[status(thm)],[])).
% 3.24/3.47 tff(6228,plain,
% 3.24/3.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))),
% 3.24/3.47 inference(modus_ponens,[status(thm)],[6227, 6226])).
% 3.24/3.47 tff(6229,plain,
% 3.24/3.47 ($false),
% 3.24/3.47 inference(unit_resolution,[status(thm)],[6228, 178, 3461, 6222, 6214, 5760, 202])).
% 3.24/3.47 tff(6230,plain,((~r(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(elem!1))) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.47 tff(6231,plain,
% 3.24/3.47 (~r(s(elem!1), s(s(s(s(z)))))),
% 3.24/3.47 inference(unit_resolution,[status(thm)],[6230, 6212, 202, 5619, 2333])).
% 3.24/3.47 tff(6232,plain,
% 3.24/3.47 (s(elem!1) = s(s(s(s(z))))),
% 3.24/3.47 inference(unit_resolution,[status(thm)],[1084, 6231, 5720])).
% 3.24/3.47 tff(6233,plain,
% 3.24/3.47 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 3.24/3.47 inference(monotonicity,[status(thm)],[6232])).
% 3.24/3.47 tff(6234,plain,
% 3.24/3.47 (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))),
% 3.24/3.47 inference(monotonicity,[status(thm)],[6233])).
% 3.24/3.47 tff(6235,plain,
% 3.24/3.47 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 3.24/3.47 inference(symmetry,[status(thm)],[6234])).
% 3.24/3.47 tff(6236,plain,
% 3.24/3.47 (s(s(s(s(z)))) = s(elem!1)),
% 3.24/3.47 inference(symmetry,[status(thm)],[6232])).
% 3.24/3.47 tff(6237,plain,
% 3.24/3.47 (b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 3.24/3.47 inference(monotonicity,[status(thm)],[6236, 6235])).
% 3.24/3.47 tff(6238,plain,
% 3.24/3.47 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) <=> (~b(s(elem!1), s(s(s(elem!1)))))),
% 3.24/3.47 inference(monotonicity,[status(thm)],[6237])).
% 3.24/3.47 tff(6239,plain,
% 3.24/3.47 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 3.24/3.47 inference(monotonicity,[status(thm)],[6232])).
% 3.24/3.47 tff(6240,plain,
% 3.24/3.47 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 3.24/3.47 inference(symmetry,[status(thm)],[6239])).
% 3.24/3.47 tff(6241,plain,
% 3.24/3.47 (s(s(s(z))) = elem!1),
% 3.24/3.47 inference(transitivity,[status(thm)],[61, 6240, 304])).
% 3.24/3.47 tff(6242,plain,
% 3.24/3.47 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), elem!1)),
% 3.24/3.47 inference(monotonicity,[status(thm)],[6241])).
% 3.24/3.47 tff(6243,plain,
% 3.24/3.47 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 3.24/3.47 inference(symmetry,[status(thm)],[6242])).
% 3.24/3.47 tff(6244,plain,
% 3.24/3.47 (~r(s(s(s(s(z)))), elem!1)),
% 3.24/3.47 inference(unit_resolution,[status(thm)],[6033, 6203, 194])).
% 3.24/3.47 tff(6245,plain,
% 3.24/3.47 (b(s(s(s(s(z)))), elem!1)),
% 3.24/3.47 inference(unit_resolution,[status(thm)],[3142, 6244, 4510])).
% 3.24/3.47 tff(6246,plain,
% 3.24/3.47 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.24/3.47 inference(modus_ponens,[status(thm)],[6245, 6243])).
% 3.24/3.47 tff(6247,plain,
% 3.24/3.47 (b(s(s(s(s(s(s(z)))))), s(s(s(z)))) <=> b(s(s(s(elem!1))), elem!1)),
% 3.24/3.47 inference(monotonicity,[status(thm)],[6235, 6241])).
% 3.24/3.47 tff(6248,plain,
% 3.24/3.47 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 3.24/3.47 inference(symmetry,[status(thm)],[6247])).
% 3.24/3.47 tff(6249,plain,
% 3.24/3.47 (~(z = elem!1)),
% 3.24/3.47 inference(unit_resolution,[status(thm)],[317, 6202])).
% 3.24/3.47 tff(6250,plain,
% 3.24/3.47 (~(s(s(elem!1)) = s(s(z)))),
% 3.24/3.47 inference(unit_resolution,[status(thm)],[2386, 6249])).
% 3.24/3.47 tff(6251,plain,
% 3.24/3.47 (~(elem!1 = s(s(s(elem!1))))),
% 3.24/3.47 inference(unit_resolution,[status(thm)],[2498, 6232, 6250])).
% 3.24/3.47 tff(6252,plain,
% 3.24/3.47 (~(s(s(s(elem!1))) = elem!1)),
% 3.24/3.47 inference(unit_resolution,[status(thm)],[2489, 6251])).
% 3.24/3.47 tff(6253,plain,
% 3.24/3.47 (~(s(s(s(s(s(s(z)))))) = s(s(z)))),
% 3.24/3.47 inference(unit_resolution,[status(thm)],[6058, 6232])).
% 3.24/3.47 tff(6254,plain,
% 3.24/3.47 (b(s(s(s(s(s(s(z)))))), z) <=> b(s(s(s(elem!1))), z)),
% 3.24/3.47 inference(monotonicity,[status(thm)],[6235])).
% 3.24/3.47 tff(6255,plain,
% 3.24/3.47 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(s(s(z)))))), z)),
% 3.24/3.47 inference(symmetry,[status(thm)],[6254])).
% 3.24/3.47 tff(6256,plain,
% 3.24/3.47 (elem!1 = s(s(s(z)))),
% 3.24/3.47 inference(transitivity,[status(thm)],[517, 6239, 11])).
% 3.24/3.47 tff(6257,plain,
% 3.24/3.47 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 3.24/3.47 inference(monotonicity,[status(thm)],[6256, 6234])).
% 3.24/3.47 tff(6258,plain,
% 3.24/3.47 (b(s(s(s(z))), s(s(s(s(s(s(z))))))) <=> b(elem!1, s(s(s(elem!1))))),
% 3.24/3.47 inference(symmetry,[status(thm)],[6257])).
% 3.24/3.47 tff(6259,plain,
% 3.24/3.47 ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) <=> (~b(elem!1, s(s(s(elem!1)))))),
% 3.24/3.47 inference(monotonicity,[status(thm)],[6258])).
% 3.24/3.47 tff(6260,plain,
% 3.24/3.47 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 3.24/3.47 inference(monotonicity,[status(thm)],[6241])).
% 3.24/3.47 tff(6261,plain,
% 3.24/3.47 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 3.24/3.47 inference(symmetry,[status(thm)],[6260])).
% 3.24/3.47 tff(6262,plain,
% 3.24/3.47 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.24/3.47 inference(modus_ponens,[status(thm)],[1301, 6261])).
% 3.24/3.47 tff(6263,plain,
% 3.24/3.47 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 3.24/3.47 inference(monotonicity,[status(thm)],[6234, 6232])).
% 3.24/3.47 tff(6264,plain,
% 3.24/3.47 (r(s(s(z)), s(elem!1)) <=> r(s(s(z)), s(s(s(s(z)))))),
% 3.24/3.47 inference(monotonicity,[status(thm)],[6232])).
% 3.24/3.47 tff(6265,plain,
% 3.24/3.47 (r(s(s(z)), s(s(s(s(z)))))),
% 3.24/3.47 inference(modus_ponens,[status(thm)],[6212, 6264])).
% 3.24/3.47 tff(6266,plain,
% 3.24/3.47 (r(z, s(elem!1)) <=> r(z, s(s(s(s(z)))))),
% 3.24/3.47 inference(monotonicity,[status(thm)],[6232])).
% 3.24/3.47 tff(6267,plain,
% 3.24/3.47 (r(z, s(s(s(s(z)))))),
% 3.24/3.47 inference(modus_ponens,[status(thm)],[2333, 6266])).
% 3.24/3.47 tff(6268,plain,
% 3.24/3.47 (~r(z, s(s(z)))),
% 3.24/3.47 inference(unit_resolution,[status(thm)],[3476, 118, 6267, 6265])).
% 3.24/3.47 tff(6269,plain,
% 3.24/3.47 (b(z, s(s(z)))),
% 3.24/3.47 inference(unit_resolution,[status(thm)],[143, 6268])).
% 3.24/3.47 tff(6270,plain,
% 3.24/3.47 (~r(z, s(s(s(elem!1))))),
% 3.24/3.47 inference(unit_resolution,[status(thm)],[5447, 1551, 2333])).
% 3.24/3.47 tff(6271,plain,
% 3.24/3.47 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(elem!1))))),
% 3.24/3.47 inference(rewrite,[status(thm)],[])).
% 3.24/3.47 tff(6272,plain,
% 3.24/3.47 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(elem!1))))),
% 3.24/3.47 inference(rewrite,[status(thm)],[])).
% 3.24/3.47 tff(6273,plain,
% 3.24/3.47 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(elem!1)))))),
% 3.24/3.47 inference(monotonicity,[status(thm)],[6272])).
% 3.24/3.47 tff(6274,plain,
% 3.24/3.47 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(elem!1))))),
% 3.24/3.47 inference(transitivity,[status(thm)],[6273, 6271])).
% 3.24/3.47 tff(6275,plain,
% 3.24/3.47 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 3.24/3.47 inference(quant_inst,[status(thm)],[])).
% 3.24/3.47 tff(6276,plain,
% 3.24/3.47 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(elem!1)))),
% 3.24/3.47 inference(modus_ponens,[status(thm)],[6275, 6274])).
% 3.24/3.47 tff(6277,plain,
% 3.24/3.47 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.24/3.47 inference(unit_resolution,[status(thm)],[6276, 118, 1551, 1329])).
% 3.24/3.47 tff(6278,plain,
% 3.24/3.47 (b(s(s(z)), s(s(s(elem!1))))),
% 3.24/3.47 inference(unit_resolution,[status(thm)],[4221, 41, 1683, 6277])).
% 3.24/3.47 tff(6279,plain,
% 3.24/3.47 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))))),
% 3.24/3.47 inference(rewrite,[status(thm)],[])).
% 3.24/3.47 tff(6280,plain,
% 3.24/3.47 (((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))))),
% 3.24/3.47 inference(rewrite,[status(thm)],[])).
% 3.24/3.47 tff(6281,plain,
% 3.24/3.47 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1)))))),
% 3.24/3.47 inference(monotonicity,[status(thm)],[6280])).
% 3.24/3.47 tff(6282,plain,
% 3.24/3.47 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))))),
% 3.24/3.47 inference(transitivity,[status(thm)],[6281, 6279])).
% 3.24/3.47 tff(6283,plain,
% 3.24/3.47 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)))),
% 3.24/3.47 inference(quant_inst,[status(thm)],[])).
% 3.24/3.47 tff(6284,plain,
% 3.24/3.47 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1)))),
% 3.24/3.47 inference(modus_ponens,[status(thm)],[6283, 6282])).
% 3.24/3.47 tff(6285,plain,
% 3.24/3.47 (~r(s(s(s(elem!1))), z)),
% 3.24/3.47 inference(unit_resolution,[status(thm)],[6284, 118, 1551, 2333])).
% 3.24/3.47 tff(6286,plain,
% 3.24/3.47 (b(s(s(s(elem!1))), z)),
% 3.24/3.47 inference(unit_resolution,[status(thm)],[1565, 6285])).
% 3.24/3.47 tff(6287,plain,
% 3.24/3.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)))),
% 3.24/3.47 inference(rewrite,[status(thm)],[])).
% 3.24/3.47 tff(6288,plain,
% 3.24/3.47 (((~b(s(s(s(elem!1))), 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(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(z))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)))),
% 3.24/3.47 inference(rewrite,[status(thm)],[])).
% 3.24/3.47 tff(6289,plain,
% 3.24/3.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z))))),
% 3.24/3.47 inference(monotonicity,[status(thm)],[6288])).
% 3.24/3.47 tff(6290,plain,
% 3.24/3.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)))),
% 3.24/3.47 inference(transitivity,[status(thm)],[6289, 6287])).
% 3.24/3.47 tff(6291,plain,
% 3.24/3.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(z)))))),
% 3.24/3.47 inference(quant_inst,[status(thm)],[])).
% 3.24/3.47 tff(6292,plain,
% 3.24/3.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z))),
% 3.24/3.47 inference(modus_ponens,[status(thm)],[6291, 6290])).
% 3.24/3.47 tff(6293,plain,
% 3.24/3.47 ($false),
% 3.24/3.47 inference(unit_resolution,[status(thm)],[6292, 178, 2043, 6286, 3461, 273, 6278])).
% 3.24/3.47 tff(6294,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(s(s(z)), s(elem!1))) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.47 tff(6295,plain,
% 3.24/3.47 (~b(z, s(s(s(elem!1))))),
% 3.24/3.47 inference(unit_resolution,[status(thm)],[6294, 1551, 3461, 273, 1329, 2333])).
% 3.24/3.47 tff(6296,plain,
% 3.24/3.47 ($false),
% 3.24/3.47 inference(unit_resolution,[status(thm)],[2095, 6295, 6270])).
% 3.24/3.47 tff(6297,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(s(s(z)), s(elem!1))) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.47 tff(6298,plain,
% 3.24/3.47 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.24/3.47 inference(unit_resolution,[status(thm)],[6297, 6269, 5619, 6212, 2333])).
% 3.24/3.47 tff(6299,plain,
% 3.24/3.47 (b(s(s(s(elem!1))), s(elem!1))),
% 3.24/3.47 inference(unit_resolution,[status(thm)],[373, 6298, 356])).
% 3.24/3.47 tff(6300,plain,
% 3.24/3.47 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 3.24/3.47 inference(modus_ponens,[status(thm)],[6299, 6263])).
% 3.24/3.47 tff(6301,plain,
% 3.24/3.47 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 3.24/3.47 inference(unit_resolution,[status(thm)],[6178, 6300, 6262, 6246, 6232, 6252, 6209, 202])).
% 3.24/3.47 tff(6302,plain,
% 3.24/3.47 (~b(elem!1, s(s(s(elem!1))))),
% 3.24/3.47 inference(modus_ponens,[status(thm)],[6301, 6259])).
% 3.24/3.47 tff(6303,plain,
% 3.24/3.47 (r(elem!1, s(s(s(elem!1))))),
% 3.24/3.47 inference(unit_resolution,[status(thm)],[2054, 6302, 6251])).
% 3.24/3.47 tff(6304,plain,
% 3.24/3.47 (~r(s(s(s(elem!1))), z)),
% 3.24/3.47 inference(unit_resolution,[status(thm)],[6071, 6303, 6203])).
% 3.24/3.47 tff(6305,plain,
% 3.24/3.47 (b(s(s(s(elem!1))), z)),
% 3.24/3.47 inference(unit_resolution,[status(thm)],[1565, 6304])).
% 3.24/3.47 tff(6306,plain,
% 3.24/3.47 (b(s(s(s(s(s(s(z)))))), z)),
% 3.24/3.47 inference(modus_ponens,[status(thm)],[6305, 6255])).
% 3.24/3.47 tff(6307,plain,
% 3.24/3.47 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(s(s(s(z)))))))),
% 3.24/3.47 inference(monotonicity,[status(thm)],[6234])).
% 3.24/3.47 tff(6308,plain,
% 3.24/3.47 (~r(z, s(s(s(elem!1))))),
% 3.24/3.47 inference(unit_resolution,[status(thm)],[3421, 6303, 6203])).
% 3.24/3.47 tff(6309,plain,
% 3.24/3.47 (b(z, s(s(s(elem!1))))),
% 3.24/3.47 inference(unit_resolution,[status(thm)],[2095, 6308])).
% 3.24/3.47 tff(6310,plain,
% 3.24/3.47 (b(z, s(s(s(s(s(s(z)))))))),
% 3.24/3.47 inference(modus_ponens,[status(thm)],[6309, 6307])).
% 3.24/3.47 tff(6311,plain,
% 3.24/3.47 ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))),
% 3.24/3.47 inference(unit_resolution,[status(thm)],[6084, 178, 5619, 6269, 6310])).
% 3.24/3.47 tff(6312,plain,
% 3.24/3.47 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 3.24/3.47 inference(unit_resolution,[status(thm)],[6311, 6306])).
% 3.24/3.47 tff(6313,plain,
% 3.24/3.47 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 3.24/3.47 inference(unit_resolution,[status(thm)],[6139, 6312, 6253])).
% 3.24/3.47 tff(6314,plain,
% 3.24/3.47 (r(s(s(s(elem!1))), s(s(z)))),
% 3.24/3.47 inference(unit_resolution,[status(thm)],[6165, 6313, 6232])).
% 3.24/3.47 tff(6315,plain,
% 3.24/3.47 (~r(s(s(s(elem!1))), elem!1)),
% 3.24/3.47 inference(unit_resolution,[status(thm)],[4205, 6314, 6209])).
% 3.24/3.47 tff(6316,plain,
% 3.24/3.47 (b(s(s(s(elem!1))), elem!1)),
% 3.24/3.47 inference(unit_resolution,[status(thm)],[570, 6315, 6252])).
% 3.24/3.47 tff(6317,plain,
% 3.24/3.47 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 3.24/3.47 inference(modus_ponens,[status(thm)],[6316, 6248])).
% 3.24/3.47 tff(6318,plain,
% 3.24/3.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 3.24/3.47 inference(rewrite,[status(thm)],[])).
% 3.24/3.47 tff(6319,plain,
% 3.24/3.47 (((~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(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 3.24/3.47 inference(rewrite,[status(thm)],[])).
% 3.24/3.47 tff(6320,plain,
% 3.24/3.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 3.24/3.47 inference(monotonicity,[status(thm)],[6319])).
% 3.24/3.47 tff(6321,plain,
% 3.24/3.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 3.24/3.47 inference(transitivity,[status(thm)],[6320, 6318])).
% 3.24/3.47 tff(6322,plain,
% 3.24/3.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 3.24/3.47 inference(quant_inst,[status(thm)],[])).
% 3.24/3.47 tff(6323,plain,
% 3.24/3.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 3.24/3.47 inference(modus_ponens,[status(thm)],[6322, 6321])).
% 3.24/3.47 tff(6324,plain,
% 3.24/3.47 ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 3.24/3.47 inference(unit_resolution,[status(thm)],[6323, 178, 6300, 6262])).
% 3.24/3.47 tff(6325,plain,
% 3.24/3.47 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 3.24/3.47 inference(unit_resolution,[status(thm)],[6324, 6317, 6246])).
% 3.24/3.47 tff(6326,plain,
% 3.24/3.47 (~b(s(elem!1), s(s(s(elem!1))))),
% 3.24/3.47 inference(modus_ponens,[status(thm)],[6325, 6238])).
% 3.24/3.47 tff(6327,plain,
% 3.24/3.47 (b(s(s(z)), s(s(s(s(s(s(z))))))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 3.24/3.47 inference(monotonicity,[status(thm)],[6235])).
% 3.24/3.47 tff(6328,plain,
% 3.24/3.47 ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) <=> (~b(s(s(z)), s(s(s(elem!1)))))),
% 3.24/3.47 inference(monotonicity,[status(thm)],[6327])).
% 3.24/3.47 tff(6329,plain,
% 3.24/3.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 3.24/3.47 inference(rewrite,[status(thm)],[])).
% 3.24/3.47 tff(6330,plain,
% 3.24/3.47 (((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 3.24/3.47 inference(rewrite,[status(thm)],[])).
% 3.24/3.47 tff(6331,plain,
% 3.24/3.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 3.24/3.48 inference(monotonicity,[status(thm)],[6330])).
% 3.24/3.48 tff(6332,plain,
% 3.24/3.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 3.24/3.48 inference(transitivity,[status(thm)],[6331, 6329])).
% 3.24/3.48 tff(6333,plain,
% 3.24/3.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(z)))))),
% 3.24/3.48 inference(quant_inst,[status(thm)],[])).
% 3.24/3.48 tff(6334,plain,
% 3.24/3.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 3.24/3.48 inference(modus_ponens,[status(thm)],[6333, 6332])).
% 3.24/3.48 tff(6335,plain,
% 3.24/3.48 ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 3.24/3.48 inference(unit_resolution,[status(thm)],[6334, 178, 5619, 6269, 6310])).
% 3.24/3.48 tff(6336,plain,
% 3.24/3.48 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 3.24/3.48 inference(unit_resolution,[status(thm)],[6335, 6306])).
% 3.24/3.48 tff(6337,plain,
% 3.24/3.48 (~b(s(s(z)), s(s(s(elem!1))))),
% 3.24/3.48 inference(modus_ponens,[status(thm)],[6336, 6328])).
% 3.24/3.48 tff(6338,plain,
% 3.24/3.48 (b(s(elem!1), s(s(s(elem!1))))),
% 3.24/3.48 inference(unit_resolution,[status(thm)],[6127, 6337, 5396, 6212])).
% 3.24/3.48 tff(6339,plain,
% 3.24/3.48 ($false),
% 3.24/3.48 inference(unit_resolution,[status(thm)],[6338, 6326])).
% 3.24/3.48 tff(6340,plain,((~r(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(s(z)))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | b(s(elem!1), s(s(s(s(z))))) | b(s(s(z)), s(elem!1)) | r(elem!1, s(elem!1)) | b(elem!1, s(s(z))) | (~r(s(s(s(s(z)))), z)) | r(s(s(z)), z) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 3.24/3.48 tff(6341,plain,
% 3.24/3.48 (~r(z, s(elem!1))),
% 3.24/3.48 inference(unit_resolution,[status(thm)],[6340, 1061, 356, 1301, 5720, 202, 744, 461, 3244, 5618, 5723])).
% 3.24/3.48 tff(6342,plain,
% 3.24/3.48 (b(z, s(elem!1))),
% 3.24/3.48 inference(unit_resolution,[status(thm)],[2351, 6341])).
% 3.24/3.48 tff(6343,plain,
% 3.24/3.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 3.24/3.48 inference(rewrite,[status(thm)],[])).
% 3.24/3.48 tff(6344,plain,
% 3.24/3.48 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1)))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 3.24/3.48 inference(rewrite,[status(thm)],[])).
% 3.24/3.48 tff(6345,plain,
% 3.24/3.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 3.24/3.48 inference(monotonicity,[status(thm)],[6344])).
% 3.24/3.48 tff(6346,plain,
% 3.24/3.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 3.24/3.48 inference(transitivity,[status(thm)],[6345, 6343])).
% 3.24/3.48 tff(6347,plain,
% 3.24/3.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))))),
% 3.24/3.48 inference(quant_inst,[status(thm)],[])).
% 3.24/3.48 tff(6348,plain,
% 3.24/3.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 3.24/3.48 inference(modus_ponens,[status(thm)],[6347, 6346])).
% 3.24/3.48 tff(6349,plain,
% 3.24/3.48 (~b(s(elem!1), s(s(s(elem!1))))),
% 3.24/3.48 inference(unit_resolution,[status(thm)],[6348, 178, 855, 6077, 6073, 853])).
% 3.24/3.48 tff(6350,plain,
% 3.24/3.48 (~b(s(s(z)), s(s(s(elem!1))))),
% 3.24/3.48 inference(unit_resolution,[status(thm)],[6292, 178, 6077, 6073, 3461, 273])).
% 3.24/3.48 tff(6351,plain,
% 3.24/3.48 ($false),
% 3.24/3.48 inference(unit_resolution,[status(thm)],[6127, 6350, 6349, 5425, 1329])).
% 3.24/3.48 tff(6352,plain,((~r(elem!1, s(s(s(elem!1))))) | (s(elem!1) = s(s(s(elem!1)))) | (~r(s(s(z)), s(elem!1))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.48 tff(6353,plain,
% 3.24/3.48 (~r(elem!1, s(s(s(elem!1))))),
% 3.24/3.48 inference(unit_resolution,[status(thm)],[6352, 5731, 5396, 5619, 6024, 6342, 6196, 6026])).
% 3.24/3.48 tff(6354,plain,
% 3.24/3.48 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.24/3.48 inference(unit_resolution,[status(thm)],[5758, 6194, 5731])).
% 3.24/3.48 tff(6355,plain,
% 3.24/3.48 (b(s(s(z)), s(s(s(s(z)))))),
% 3.24/3.48 inference(unit_resolution,[status(thm)],[164, 6354])).
% 3.24/3.48 tff(6356,plain,
% 3.24/3.48 (~b(s(s(z)), elem!1)),
% 3.24/3.48 inference(unit_resolution,[status(thm)],[3149, 178, 6035, 1301, 6355, 202])).
% 3.24/3.48 tff(6357,plain,
% 3.24/3.48 (r(s(s(z)), elem!1)),
% 3.24/3.48 inference(unit_resolution,[status(thm)],[448, 6356, 5726])).
% 3.24/3.48 tff(6358,plain,
% 3.24/3.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)))),
% 3.24/3.48 inference(rewrite,[status(thm)],[])).
% 3.24/3.48 tff(6359,plain,
% 3.24/3.48 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)))),
% 3.24/3.48 inference(rewrite,[status(thm)],[])).
% 3.24/3.48 tff(6360,plain,
% 3.24/3.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z))))),
% 3.24/3.48 inference(monotonicity,[status(thm)],[6359])).
% 3.24/3.48 tff(6361,plain,
% 3.24/3.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)))),
% 3.24/3.48 inference(transitivity,[status(thm)],[6360, 6358])).
% 3.24/3.48 tff(6362,plain,
% 3.24/3.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))))),
% 3.24/3.48 inference(quant_inst,[status(thm)],[])).
% 3.24/3.48 tff(6363,plain,
% 3.24/3.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z))),
% 3.24/3.48 inference(modus_ponens,[status(thm)],[6362, 6361])).
% 3.24/3.48 tff(6364,plain,
% 3.24/3.48 (~b(s(elem!1), s(s(z)))),
% 3.24/3.48 inference(unit_resolution,[status(thm)],[6363, 178, 6342, 6196, 5619, 6024])).
% 3.24/3.48 tff(6365,plain,
% 3.24/3.48 (r(s(elem!1), s(s(z)))),
% 3.24/3.48 inference(unit_resolution,[status(thm)],[421, 6364, 5729])).
% 3.24/3.48 tff(6366,plain,
% 3.24/3.48 (~r(s(elem!1), elem!1)),
% 3.24/3.48 inference(unit_resolution,[status(thm)],[625, 118, 5728, 6365])).
% 3.24/3.48 tff(6367,plain,
% 3.24/3.48 (b(s(elem!1), elem!1)),
% 3.24/3.48 inference(unit_resolution,[status(thm)],[677, 6366, 1548])).
% 3.24/3.48 tff(6368,plain,
% 3.24/3.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))),
% 3.24/3.48 inference(rewrite,[status(thm)],[])).
% 3.24/3.48 tff(6369,plain,
% 3.24/3.48 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z))) <=> ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))),
% 3.24/3.48 inference(rewrite,[status(thm)],[])).
% 3.24/3.48 tff(6370,plain,
% 3.24/3.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z))))),
% 3.24/3.48 inference(monotonicity,[status(thm)],[6369])).
% 3.24/3.48 tff(6371,plain,
% 3.24/3.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))),
% 3.24/3.48 inference(transitivity,[status(thm)],[6370, 6368])).
% 3.24/3.48 tff(6372,plain,
% 3.24/3.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)))),
% 3.24/3.48 inference(quant_inst,[status(thm)],[])).
% 3.24/3.48 tff(6373,plain,
% 3.24/3.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z))),
% 3.24/3.48 inference(modus_ponens,[status(thm)],[6372, 6371])).
% 3.24/3.48 tff(6374,plain,
% 3.24/3.48 (~b(z, elem!1)),
% 3.24/3.48 inference(unit_resolution,[status(thm)],[6373, 178, 6342, 6367, 5725, 6196])).
% 3.24/3.48 tff(6375,plain,
% 3.24/3.48 (r(z, elem!1)),
% 3.24/3.48 inference(unit_resolution,[status(thm)],[585, 6374, 6027])).
% 3.24/3.48 tff(6376,plain,
% 3.24/3.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 3.24/3.48 inference(rewrite,[status(thm)],[])).
% 3.24/3.48 tff(6377,plain,
% 3.24/3.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 3.24/3.48 inference(quant_inst,[status(thm)],[])).
% 3.24/3.48 tff(6378,plain,
% 3.24/3.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z))),
% 3.24/3.48 inference(modus_ponens,[status(thm)],[6377, 6376])).
% 3.24/3.48 tff(6379,plain,
% 3.24/3.48 (~r(s(s(s(elem!1))), z)),
% 3.24/3.48 inference(unit_resolution,[status(thm)],[6378, 118, 521, 556])).
% 3.24/3.48 tff(6380,plain,
% 3.24/3.48 (b(s(s(s(elem!1))), z)),
% 3.24/3.48 inference(unit_resolution,[status(thm)],[1565, 6379])).
% 3.24/3.48 tff(6381,plain,
% 3.24/3.48 (~r(z, s(s(s(elem!1))))),
% 3.24/3.48 inference(unit_resolution,[status(thm)],[565, 556, 521])).
% 3.24/3.48 tff(6382,plain,
% 3.24/3.48 (b(z, s(s(s(elem!1))))),
% 3.24/3.48 inference(unit_resolution,[status(thm)],[2095, 6381])).
% 3.24/3.48 tff(6383,plain,
% 3.24/3.48 ($false),
% 3.24/3.48 inference(unit_resolution,[status(thm)],[6292, 178, 6382, 6380, 3461, 273, 4291])).
% 3.24/3.48 tff(6384,plain,((~r(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.48 tff(6385,plain,
% 3.24/3.48 (~b(s(s(z)), s(s(s(elem!1))))),
% 3.24/3.48 inference(unit_resolution,[status(thm)],[6384, 556, 3461, 521, 273])).
% 3.24/3.48 tff(6386,plain,
% 3.24/3.48 (r(s(s(z)), s(s(s(elem!1))))),
% 3.24/3.48 inference(unit_resolution,[status(thm)],[4223, 6385])).
% 3.24/3.48 tff(6387,plain,
% 3.24/3.48 ($false),
% 3.24/3.48 inference(unit_resolution,[status(thm)],[4216, 118, 556, 438, 6386])).
% 3.24/3.48 tff(6388,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~r(z, elem!1)) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.48 tff(6389,plain,
% 3.24/3.48 (~r(s(s(s(elem!1))), elem!1)),
% 3.24/3.48 inference(unit_resolution,[status(thm)],[6388, 6375, 5619, 6357, 6024])).
% 3.24/3.48 tff(6390,plain,
% 3.24/3.48 (~(s(s(s(s(z)))) = s(elem!1))),
% 3.24/3.48 inference(unit_resolution,[status(thm)],[2168, 6193])).
% 3.24/3.48 tff(6391,plain,
% 3.24/3.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(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(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(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(s(z)))), s(elem!1))))),
% 3.24/3.48 inference(rewrite,[status(thm)],[])).
% 3.24/3.48 tff(6392,plain,
% 3.24/3.48 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(elem!1, s(elem!1))) | (~b(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(s(z)))), s(elem!1))))),
% 3.24/3.48 inference(rewrite,[status(thm)],[])).
% 3.24/3.48 tff(6393,plain,
% 3.24/3.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(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(s(z)))), s(elem!1)))))),
% 3.24/3.48 inference(monotonicity,[status(thm)],[6392])).
% 3.24/3.48 tff(6394,plain,
% 3.24/3.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(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(s(z)))), s(elem!1))))),
% 3.24/3.48 inference(transitivity,[status(thm)],[6393, 6391])).
% 3.24/3.48 tff(6395,plain,
% 3.24/3.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))))),
% 3.24/3.48 inference(quant_inst,[status(thm)],[])).
% 3.24/3.48 tff(6396,plain,
% 3.24/3.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(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(s(z)))), s(elem!1)))),
% 3.24/3.48 inference(modus_ponens,[status(thm)],[6395, 6394])).
% 3.24/3.48 tff(6397,plain,
% 3.24/3.48 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.24/3.48 inference(unit_resolution,[status(thm)],[6396, 178, 6367, 5725, 6035, 1301])).
% 3.24/3.48 tff(6398,plain,
% 3.24/3.48 (r(s(s(s(s(z)))), s(elem!1))),
% 3.24/3.48 inference(unit_resolution,[status(thm)],[2173, 6397, 6390])).
% 3.24/3.48 tff(6399,plain,
% 3.24/3.48 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.24/3.48 inference(unit_resolution,[status(thm)],[2840, 5729])).
% 3.24/3.48 tff(6400,assumption,(r(s(s(s(s(z)))), s(elem!1))), introduced(assumption)).
% 3.24/3.48 tff(6401,plain,
% 3.24/3.48 (b(elem!1, s(s(s(elem!1))))),
% 3.24/3.48 inference(unit_resolution,[status(thm)],[2054, 1586, 4512])).
% 3.24/3.48 tff(6402,assumption,(~r(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 3.24/3.48 tff(6403,plain,
% 3.24/3.48 (~(s(s(s(elem!1))) = elem!1)),
% 3.24/3.48 inference(unit_resolution,[status(thm)],[2489, 1586])).
% 3.24/3.48 tff(6404,plain,
% 3.24/3.48 (b(s(s(s(elem!1))), elem!1)),
% 3.24/3.48 inference(unit_resolution,[status(thm)],[570, 6403, 6402])).
% 3.24/3.48 tff(6405,plain,
% 3.24/3.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~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)))))))),
% 3.24/3.48 inference(rewrite,[status(thm)],[])).
% 3.24/3.48 tff(6406,plain,
% 3.24/3.48 (((~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(s(s(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(elem!1, s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~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)))))))),
% 3.24/3.48 inference(rewrite,[status(thm)],[])).
% 3.24/3.48 tff(6407,plain,
% 3.24/3.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(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(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~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))))))))),
% 3.24/3.48 inference(monotonicity,[status(thm)],[6406])).
% 3.24/3.48 tff(6408,plain,
% 3.24/3.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(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(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~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)))))))),
% 3.24/3.48 inference(transitivity,[status(thm)],[6407, 6405])).
% 3.24/3.48 tff(6409,plain,
% 3.24/3.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(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(elem!1))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 3.24/3.48 inference(quant_inst,[status(thm)],[])).
% 3.24/3.48 tff(6410,plain,
% 3.24/3.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~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))))))),
% 3.24/3.48 inference(modus_ponens,[status(thm)],[6409, 6408])).
% 3.24/3.48 tff(6411,plain,
% 3.24/3.48 ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.24/3.48 inference(unit_resolution,[status(thm)],[6410, 178, 1597, 3771, 1301])).
% 3.24/3.48 tff(6412,plain,
% 3.24/3.48 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.24/3.48 inference(unit_resolution,[status(thm)],[6411, 2042])).
% 3.24/3.48 tff(6413,plain,
% 3.24/3.48 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.24/3.48 inference(unit_resolution,[status(thm)],[3825, 41, 2857, 6412])).
% 3.24/3.49 tff(6414,plain,
% 3.24/3.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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))))))),
% 3.24/3.49 inference(rewrite,[status(thm)],[])).
% 3.24/3.49 tff(6415,plain,
% 3.24/3.49 (((~b(s(elem!1), 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(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 3.24/3.49 inference(rewrite,[status(thm)],[])).
% 3.24/3.49 tff(6416,plain,
% 3.24/3.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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)))))))),
% 3.24/3.49 inference(monotonicity,[status(thm)],[6415])).
% 3.24/3.49 tff(6417,plain,
% 3.24/3.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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))))))),
% 3.24/3.49 inference(transitivity,[status(thm)],[6416, 6414])).
% 3.24/3.49 tff(6418,plain,
% 3.24/3.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 3.24/3.49 inference(quant_inst,[status(thm)],[])).
% 3.24/3.49 tff(6419,plain,
% 3.24/3.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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)))))),
% 3.24/3.49 inference(modus_ponens,[status(thm)],[6418, 6417])).
% 3.24/3.49 tff(6420,plain,
% 3.24/3.49 ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))),
% 3.24/3.49 inference(unit_resolution,[status(thm)],[6419, 178, 683, 1597, 854])).
% 3.24/3.49 tff(6421,plain,
% 3.24/3.49 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.24/3.49 inference(unit_resolution,[status(thm)],[6420, 2042])).
% 3.24/3.49 tff(6422,plain,
% 3.24/3.49 (r(s(s(s(elem!1))), s(elem!1))),
% 3.24/3.49 inference(unit_resolution,[status(thm)],[373, 6421, 356])).
% 3.24/3.49 tff(6423,plain,
% 3.24/3.49 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.24/3.49 inference(rewrite,[status(thm)],[])).
% 3.24/3.49 tff(6424,plain,
% 3.24/3.49 (((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.24/3.49 inference(rewrite,[status(thm)],[])).
% 3.24/3.49 tff(6425,plain,
% 3.24/3.49 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 3.24/3.49 inference(monotonicity,[status(thm)],[6424])).
% 3.24/3.49 tff(6426,plain,
% 3.24/3.49 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.24/3.49 inference(transitivity,[status(thm)],[6425, 6423])).
% 3.24/3.49 tff(6427,plain,
% 3.24/3.49 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.24/3.49 inference(quant_inst,[status(thm)],[])).
% 3.24/3.49 tff(6428,plain,
% 3.24/3.49 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.24/3.49 inference(modus_ponens,[status(thm)],[6427, 6426])).
% 3.24/3.49 tff(6429,plain,
% 3.24/3.49 ($false),
% 3.24/3.49 inference(unit_resolution,[status(thm)],[6428, 118, 6422, 6400, 6413])).
% 3.24/3.49 tff(6430,plain,((~b(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.49 tff(6431,plain,
% 3.24/3.49 ($false),
% 3.24/3.49 inference(unit_resolution,[status(thm)],[6430, 6404, 6401, 2857, 356, 6400, 3771, 1301, 683, 854])).
% 3.24/3.49 tff(6432,plain,((elem!1 = s(s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | r(s(s(s(elem!1))), elem!1) | r(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.49 tff(6433,plain,
% 3.24/3.49 (elem!1 = s(s(s(elem!1)))),
% 3.24/3.49 inference(unit_resolution,[status(thm)],[6432, 6399, 356, 6398, 6035, 1301, 6367, 5725, 6389, 6353])).
% 3.24/3.49 tff(6434,plain,
% 3.24/3.49 (s(s(s(elem!1))) = elem!1),
% 3.24/3.49 inference(unit_resolution,[status(thm)],[1530, 6433])).
% 3.24/3.49 tff(6435,assumption,(s(s(s(s(elem!1)))) = s(s(elem!1))), introduced(assumption)).
% 3.24/3.49 tff(6436,plain,
% 3.24/3.49 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(elem!1)))),
% 3.24/3.49 inference(monotonicity,[status(thm)],[6435])).
% 3.24/3.49 tff(6437,plain,
% 3.24/3.49 (s(s(s(elem!1))) = s(elem!1)),
% 3.24/3.49 inference(transitivity,[status(thm)],[947, 6436, 328])).
% 3.24/3.49 tff(6438,plain,
% 3.24/3.49 ($false),
% 3.24/3.49 inference(unit_resolution,[status(thm)],[356, 6437])).
% 3.24/3.49 tff(6439,plain,((~(s(s(s(s(elem!1)))) = s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.49 tff(6440,plain,
% 3.24/3.49 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 3.24/3.49 inference(unit_resolution,[status(thm)],[6439, 356])).
% 3.24/3.49 tff(6441,plain,
% 3.24/3.49 (b(s(elem!1), s(s(s(elem!1))))),
% 3.24/3.49 inference(modus_ponens,[status(thm)],[683, 3997])).
% 3.24/3.49 tff(6442,plain,
% 3.24/3.49 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.24/3.49 inference(modus_ponens,[status(thm)],[6441, 3996])).
% 3.24/3.49 tff(6443,plain,
% 3.24/3.49 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.24/3.49 inference(modus_ponens,[status(thm)],[2044, 3868])).
% 3.24/3.49 tff(6444,plain,
% 3.24/3.49 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 3.24/3.49 inference(unit_resolution,[status(thm)],[3404, 1655])).
% 3.24/3.49 tff(6445,plain,
% 3.24/3.49 (r(z, elem!1) <=> r(z, s(s(s(elem!1))))),
% 3.24/3.49 inference(monotonicity,[status(thm)],[1527])).
% 3.24/3.49 tff(6446,plain,
% 3.24/3.49 (r(z, s(s(s(elem!1))))),
% 3.24/3.49 inference(modus_ponens,[status(thm)],[521, 6445])).
% 3.24/3.49 tff(6447,plain,
% 3.24/3.49 (r(elem!1, s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 3.24/3.49 inference(monotonicity,[status(thm)],[1527])).
% 3.24/3.49 tff(6448,plain,
% 3.24/3.49 (r(s(s(s(elem!1))), s(s(z)))),
% 3.24/3.49 inference(modus_ponens,[status(thm)],[450, 6447])).
% 3.24/3.49 tff(6449,assumption,(r(s(s(z)), s(s(elem!1)))), introduced(assumption)).
% 3.24/3.49 tff(6450,plain,
% 3.24/3.49 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 3.24/3.49 inference(rewrite,[status(thm)],[])).
% 3.24/3.49 tff(6451,plain,
% 3.24/3.49 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 3.24/3.49 inference(quant_inst,[status(thm)],[])).
% 3.24/3.49 tff(6452,plain,
% 3.24/3.49 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 3.24/3.49 inference(modus_ponens,[status(thm)],[6451, 6450])).
% 3.24/3.49 tff(6453,plain,
% 3.24/3.49 ($false),
% 3.24/3.49 inference(unit_resolution,[status(thm)],[6452, 118, 3859, 5227, 6449])).
% 3.24/3.49 tff(6454,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.49 tff(6455,plain,
% 3.24/3.49 (~r(s(s(z)), s(s(elem!1)))),
% 3.24/3.49 inference(unit_resolution,[status(thm)],[6454, 5227, 3859])).
% 3.24/3.49 tff(6456,plain,
% 3.24/3.49 ((s(s(z)) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(z)))),
% 3.24/3.49 inference(commutativity,[status(thm)],[])).
% 3.24/3.49 tff(6457,assumption,(s(s(z)) = s(s(elem!1))), introduced(assumption)).
% 3.24/3.49 tff(6458,plain,
% 3.24/3.49 (s(s(elem!1)) = s(s(z))),
% 3.24/3.49 inference(modus_ponens,[status(thm)],[6457, 6456])).
% 3.24/3.49 tff(6459,plain,
% 3.24/3.49 ($false),
% 3.24/3.49 inference(unit_resolution,[status(thm)],[2484, 6458])).
% 3.24/3.49 tff(6460,plain,((~(s(s(z)) = s(s(elem!1)))) | (s(s(elem!1)) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.49 tff(6461,plain,
% 3.24/3.49 (~(s(s(z)) = s(s(elem!1)))),
% 3.24/3.49 inference(unit_resolution,[status(thm)],[6460, 2484])).
% 3.24/3.49 tff(6462,plain,
% 3.24/3.49 (~r(z, s(s(elem!1)))),
% 3.24/3.49 inference(unit_resolution,[status(thm)],[5235, 5227, 557])).
% 3.24/3.49 tff(6463,assumption,(z = s(s(elem!1))), introduced(assumption)).
% 3.24/3.49 tff(6464,plain,
% 3.24/3.49 (s(s(elem!1)) = z),
% 3.24/3.49 inference(symmetry,[status(thm)],[6463])).
% 3.24/3.49 tff(6465,plain,
% 3.24/3.49 ($false),
% 3.24/3.49 inference(unit_resolution,[status(thm)],[970, 6464])).
% 3.24/3.49 tff(6466,plain,(~(z = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.49 tff(6467,plain,
% 3.24/3.49 (((~![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))))),
% 3.24/3.49 inference(rewrite,[status(thm)],[])).
% 3.24/3.49 tff(6468,plain,
% 3.24/3.49 ((~![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))))),
% 3.24/3.49 inference(quant_inst,[status(thm)],[])).
% 3.24/3.49 tff(6469,plain,
% 3.24/3.49 ((~![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)))),
% 3.24/3.49 inference(modus_ponens,[status(thm)],[6468, 6467])).
% 3.24/3.49 tff(6470,plain,
% 3.24/3.49 (b(z, s(s(elem!1)))),
% 3.24/3.49 inference(unit_resolution,[status(thm)],[6469, 41, 6466, 6462])).
% 3.24/3.49 tff(6471,assumption,(~r(s(s(z)), s(s(elem!1)))), introduced(assumption)).
% 3.24/3.49 tff(6472,assumption,(~(s(s(z)) = s(s(elem!1)))), introduced(assumption)).
% 3.24/3.49 tff(6473,plain,
% 3.24/3.49 (((~![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))))),
% 3.24/3.49 inference(rewrite,[status(thm)],[])).
% 3.24/3.49 tff(6474,plain,
% 3.24/3.49 ((~![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))))),
% 3.24/3.49 inference(quant_inst,[status(thm)],[])).
% 3.24/3.49 tff(6475,plain,
% 3.24/3.49 ((~![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)))),
% 3.24/3.49 inference(modus_ponens,[status(thm)],[6474, 6473])).
% 3.24/3.49 tff(6476,plain,
% 3.24/3.49 (b(s(s(z)), s(s(elem!1)))),
% 3.24/3.49 inference(unit_resolution,[status(thm)],[6475, 41, 6472, 6471])).
% 3.24/3.49 tff(6477,assumption,(b(z, s(s(elem!1)))), introduced(assumption)).
% 3.24/3.49 tff(6478,assumption,(b(s(s(elem!1)), s(s(z)))), introduced(assumption)).
% 3.24/3.49 tff(6479,plain,
% 3.24/3.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 3.24/3.49 inference(rewrite,[status(thm)],[])).
% 3.24/3.49 tff(6480,plain,
% 3.24/3.49 (((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 3.24/3.49 inference(rewrite,[status(thm)],[])).
% 3.24/3.49 tff(6481,plain,
% 3.24/3.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z))))))),
% 3.24/3.49 inference(monotonicity,[status(thm)],[6480])).
% 3.24/3.49 tff(6482,plain,
% 3.24/3.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 3.24/3.49 inference(transitivity,[status(thm)],[6481, 6479])).
% 3.24/3.49 tff(6483,plain,
% 3.24/3.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)))),
% 3.24/3.49 inference(quant_inst,[status(thm)],[])).
% 3.24/3.49 tff(6484,plain,
% 3.24/3.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z))))),
% 3.24/3.49 inference(modus_ponens,[status(thm)],[6483, 6482])).
% 3.24/3.49 tff(6485,plain,
% 3.24/3.49 ($false),
% 3.24/3.49 inference(unit_resolution,[status(thm)],[6484, 178, 3461, 273, 6478, 6477, 6476])).
% 3.24/3.49 tff(6486,plain,((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | r(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.49 tff(6487,plain,
% 3.24/3.49 (~b(s(s(elem!1)), s(s(z)))),
% 3.24/3.49 inference(unit_resolution,[status(thm)],[6486, 6470, 273, 3461, 6461, 6455])).
% 3.24/3.49 tff(6488,assumption,(~r(s(s(elem!1)), s(s(z)))), introduced(assumption)).
% 3.24/3.49 tff(6489,assumption,(~b(s(s(elem!1)), s(s(z)))), introduced(assumption)).
% 3.24/3.49 tff(6490,plain,
% 3.24/3.49 (((~![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))))),
% 3.24/3.49 inference(rewrite,[status(thm)],[])).
% 3.24/3.49 tff(6491,plain,
% 3.24/3.49 ((~![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))))),
% 3.24/3.49 inference(quant_inst,[status(thm)],[])).
% 3.24/3.49 tff(6492,plain,
% 3.24/3.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z))) | r(s(s(elem!1)), s(s(z)))),
% 3.24/3.49 inference(modus_ponens,[status(thm)],[6491, 6490])).
% 3.24/3.49 tff(6493,plain,
% 3.24/3.49 ($false),
% 3.24/3.49 inference(unit_resolution,[status(thm)],[6492, 41, 6489, 2484, 6488])).
% 3.24/3.49 tff(6494,plain,(b(s(s(elem!1)), s(s(z))) | (s(s(elem!1)) = s(s(z))) | r(s(s(elem!1)), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.49 tff(6495,plain,
% 3.24/3.49 (r(s(s(elem!1)), s(s(z)))),
% 3.24/3.49 inference(unit_resolution,[status(thm)],[6494, 6487, 2484])).
% 3.24/3.49 tff(6496,plain,
% 3.24/3.49 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 3.24/3.49 inference(rewrite,[status(thm)],[])).
% 3.24/3.49 tff(6497,plain,
% 3.24/3.49 (((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 3.24/3.49 inference(rewrite,[status(thm)],[])).
% 3.24/3.49 tff(6498,plain,
% 3.24/3.49 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z))))))),
% 3.24/3.49 inference(monotonicity,[status(thm)],[6497])).
% 3.24/3.49 tff(6499,plain,
% 3.24/3.49 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 3.24/3.49 inference(transitivity,[status(thm)],[6498, 6496])).
% 3.24/3.49 tff(6500,plain,
% 3.24/3.49 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.24/3.49 inference(quant_inst,[status(thm)],[])).
% 3.24/3.49 tff(6501,plain,
% 3.24/3.49 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z))))),
% 3.24/3.49 inference(modus_ponens,[status(thm)],[6500, 6499])).
% 3.24/3.49 tff(6502,plain,
% 3.24/3.49 ($false),
% 3.24/3.49 inference(unit_resolution,[status(thm)],[6501, 118, 3859, 5227, 6495])).
% 3.24/3.49 tff(6503,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (s(s(elem!1)) = s(s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.49 tff(6504,plain,
% 3.24/3.49 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.24/3.49 inference(unit_resolution,[status(thm)],[6503, 6448, 2484, 273, 3461, 6446])).
% 3.24/3.50 tff(6505,plain,
% 3.24/3.50 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.24/3.50 inference(unit_resolution,[status(thm)],[3409, 6504, 6444])).
% 3.24/3.50 tff(6506,plain,
% 3.24/3.50 (r(s(s(s(s(elem!1)))), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 3.24/3.50 inference(monotonicity,[status(thm)],[4021])).
% 3.24/3.50 tff(6507,plain,
% 3.24/3.50 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 3.24/3.50 inference(symmetry,[status(thm)],[6506])).
% 3.24/3.50 tff(6508,plain,
% 3.24/3.50 (r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 3.24/3.50 inference(modus_ponens,[status(thm)],[908, 6507])).
% 3.24/3.50 tff(6509,assumption,(~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))), introduced(assumption)).
% 3.24/3.50 tff(6510,plain,
% 3.24/3.50 ($false),
% 3.24/3.50 inference(unit_resolution,[status(thm)],[6509, 6508])).
% 3.24/3.50 tff(6511,plain,(r(s(s(s(s(elem!1)))), s(s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~(elem!1 = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.24/3.50 tff(6512,plain,
% 3.24/3.50 (r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 3.24/3.50 inference(unit_resolution,[status(thm)],[6511, 1527, 908])).
% 3.24/3.50 tff(6513,plain,
% 3.24/3.50 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 3.24/3.50 inference(monotonicity,[status(thm)],[2855])).
% 3.24/3.50 tff(6514,plain,
% 3.24/3.50 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.24/3.50 inference(symmetry,[status(thm)],[6513])).
% 3.24/3.50 tff(6515,plain,
% 3.24/3.50 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.24/3.50 inference(modus_ponens,[status(thm)],[1301, 6514])).
% 3.24/3.50 tff(6516,plain,
% 3.24/3.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 3.24/3.50 inference(rewrite,[status(thm)],[])).
% 3.24/3.50 tff(6517,plain,
% 3.24/3.50 (((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 3.24/3.50 inference(rewrite,[status(thm)],[])).
% 3.24/3.50 tff(6518,plain,
% 3.24/3.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 3.24/3.50 inference(monotonicity,[status(thm)],[6517])).
% 3.24/3.50 tff(6519,plain,
% 3.24/3.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 3.34/3.50 inference(transitivity,[status(thm)],[6518, 6516])).
% 3.34/3.50 tff(6520,plain,
% 3.34/3.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.34/3.50 inference(quant_inst,[status(thm)],[])).
% 3.34/3.50 tff(6521,plain,
% 3.34/3.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 3.34/3.50 inference(modus_ponens,[status(thm)],[6520, 6519])).
% 3.34/3.50 tff(6522,plain,
% 3.34/3.50 ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 3.34/3.50 inference(unit_resolution,[status(thm)],[6521, 178, 3512, 3511, 3828])).
% 3.34/3.50 tff(6523,plain,
% 3.34/3.50 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 3.34/3.50 inference(unit_resolution,[status(thm)],[6522, 6515])).
% 3.34/3.50 tff(6524,assumption,(s(s(elem!1)) = s(s(s(s(z))))), introduced(assumption)).
% 3.34/3.50 tff(6525,plain,
% 3.34/3.50 (s(s(s(s(z)))) = s(s(elem!1))),
% 3.34/3.50 inference(symmetry,[status(thm)],[6524])).
% 3.34/3.50 tff(6526,plain,
% 3.34/3.50 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 3.34/3.50 inference(monotonicity,[status(thm)],[6525])).
% 3.34/3.50 tff(6527,plain,
% 3.34/3.50 (s(s(s(z))) = s(s(s(s(elem!1))))),
% 3.34/3.50 inference(transitivity,[status(thm)],[61, 6526, 328, 3300])).
% 3.34/3.50 tff(6528,plain,
% 3.34/3.50 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(elem!1)))))),
% 3.34/3.50 inference(monotonicity,[status(thm)],[6527])).
% 3.34/3.50 tff(6529,plain,
% 3.34/3.50 (s(s(z)) = s(s(s(elem!1)))),
% 3.34/3.50 inference(transitivity,[status(thm)],[66, 6528, 946])).
% 3.34/3.50 tff(6530,plain,
% 3.34/3.50 ($false),
% 3.34/3.50 inference(unit_resolution,[status(thm)],[1683, 6529])).
% 3.34/3.50 tff(6531,plain,((~(s(s(elem!1)) = s(s(s(s(z)))))) | (~(elem!1 = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.50 tff(6532,plain,
% 3.34/3.50 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 3.34/3.50 inference(unit_resolution,[status(thm)],[6531, 1527])).
% 3.34/3.50 tff(6533,plain,
% 3.34/3.50 (((~![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))))))),
% 3.34/3.50 inference(rewrite,[status(thm)],[])).
% 3.34/3.50 tff(6534,plain,
% 3.34/3.50 ((~![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))))))),
% 3.34/3.50 inference(quant_inst,[status(thm)],[])).
% 3.34/3.50 tff(6535,plain,
% 3.34/3.50 ((~![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)))))),
% 3.34/3.50 inference(modus_ponens,[status(thm)],[6534, 6533])).
% 3.34/3.50 tff(6536,plain,
% 3.34/3.50 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 3.34/3.50 inference(unit_resolution,[status(thm)],[6535, 41, 6532, 6523])).
% 3.34/3.50 tff(6537,assumption,(r(s(s(s(s(elem!1)))), s(s(s(s(z)))))), introduced(assumption)).
% 3.34/3.50 tff(6538,plain,
% 3.34/3.50 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 3.34/3.50 inference(symmetry,[status(thm)],[3685])).
% 3.34/3.50 tff(6539,plain,
% 3.34/3.50 ((~(s(s(s(s(elem!1)))) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 3.34/3.50 inference(monotonicity,[status(thm)],[6538])).
% 3.34/3.50 tff(6540,plain,
% 3.34/3.50 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 3.34/3.50 inference(modus_ponens,[status(thm)],[3702, 6539])).
% 3.34/3.50 tff(6541,plain,
% 3.34/3.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 3.34/3.50 inference(rewrite,[status(thm)],[])).
% 3.34/3.50 tff(6542,plain,
% 3.34/3.50 (((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 3.34/3.50 inference(rewrite,[status(thm)],[])).
% 3.34/3.50 tff(6543,plain,
% 3.34/3.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 3.34/3.50 inference(monotonicity,[status(thm)],[6542])).
% 3.34/3.50 tff(6544,plain,
% 3.34/3.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 3.34/3.50 inference(transitivity,[status(thm)],[6543, 6541])).
% 3.34/3.50 tff(6545,plain,
% 3.34/3.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.34/3.50 inference(quant_inst,[status(thm)],[])).
% 3.34/3.50 tff(6546,plain,
% 3.34/3.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 3.34/3.50 inference(modus_ponens,[status(thm)],[6545, 6544])).
% 3.34/3.50 tff(6547,plain,
% 3.34/3.50 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 3.34/3.50 inference(unit_resolution,[status(thm)],[6546, 178, 3512, 4401, 3511, 3709])).
% 3.34/3.50 tff(6548,plain,
% 3.34/3.50 ((s(s(elem!1)) = s(s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 3.34/3.50 inference(unit_resolution,[status(thm)],[3720, 41, 6547])).
% 3.34/3.50 tff(6549,plain,
% 3.34/3.50 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 3.34/3.50 inference(unit_resolution,[status(thm)],[6548, 6540])).
% 3.34/3.50 tff(6550,plain,
% 3.34/3.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 3.34/3.50 inference(rewrite,[status(thm)],[])).
% 3.34/3.50 tff(6551,plain,
% 3.34/3.50 (((~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 3.34/3.50 inference(rewrite,[status(thm)],[])).
% 3.34/3.50 tff(6552,plain,
% 3.34/3.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))))),
% 3.34/3.50 inference(monotonicity,[status(thm)],[6551])).
% 3.34/3.50 tff(6553,plain,
% 3.34/3.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 3.34/3.50 inference(transitivity,[status(thm)],[6552, 6550])).
% 3.34/3.50 tff(6554,plain,
% 3.34/3.50 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 3.34/3.50 inference(quant_inst,[status(thm)],[])).
% 3.34/3.50 tff(6555,plain,
% 3.34/3.50 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 3.34/3.50 inference(modus_ponens,[status(thm)],[6554, 6553])).
% 3.34/3.50 tff(6556,plain,
% 3.34/3.50 ($false),
% 3.34/3.50 inference(unit_resolution,[status(thm)],[6555, 118, 6549, 6537, 6536])).
% 3.34/3.50 tff(6557,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))) | (~(elem!1 = s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.50 tff(6558,plain,
% 3.34/3.50 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.34/3.50 inference(unit_resolution,[status(thm)],[6557, 6512, 3702, 6505, 3858, 1301, 1527, 6443, 6442])).
% 3.34/3.50 tff(6559,plain,
% 3.34/3.50 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.34/3.50 inference(unit_resolution,[status(thm)],[3375, 6558, 1655])).
% 3.34/3.50 tff(6560,plain,
% 3.34/3.50 (b(elem!1, s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.34/3.50 inference(monotonicity,[status(thm)],[1527])).
% 3.34/3.50 tff(6561,plain,
% 3.34/3.50 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 3.34/3.50 inference(symmetry,[status(thm)],[6560])).
% 3.34/3.50 tff(6562,plain,
% 3.34/3.50 (b(elem!1, s(s(elem!1)))),
% 3.34/3.50 inference(modus_ponens,[status(thm)],[6505, 6561])).
% 3.34/3.50 tff(6563,plain,
% 3.34/3.50 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.34/3.50 inference(monotonicity,[status(thm)],[1527])).
% 3.34/3.50 tff(6564,plain,
% 3.34/3.50 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), elem!1)),
% 3.34/3.50 inference(symmetry,[status(thm)],[6563])).
% 3.34/3.50 tff(6565,plain,
% 3.34/3.50 ((~b(s(s(elem!1)), s(s(s(elem!1))))) <=> (~b(s(s(elem!1)), elem!1))),
% 3.34/3.50 inference(monotonicity,[status(thm)],[6564])).
% 3.34/3.50 tff(6566,plain,
% 3.34/3.50 (~b(s(s(elem!1)), elem!1)),
% 3.34/3.50 inference(modus_ponens,[status(thm)],[3347, 6565])).
% 3.34/3.50 tff(6567,plain,
% 3.34/3.50 ($false),
% 3.34/3.50 inference(unit_resolution,[status(thm)],[5434, 6566])).
% 3.34/3.50 tff(6568,plain,((~(elem!1 = s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | b(s(s(elem!1)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.50 tff(6569,plain,
% 3.34/3.50 (~b(s(s(elem!1)), elem!1)),
% 3.34/3.50 inference(unit_resolution,[status(thm)],[6568, 6558, 1527])).
% 3.34/3.50 tff(6570,plain,
% 3.34/3.50 (r(s(s(elem!1)), elem!1)),
% 3.34/3.50 inference(unit_resolution,[status(thm)],[3362, 6569, 346])).
% 3.34/3.50 tff(6571,plain,
% 3.34/3.50 (r(z, s(s(elem!1)))),
% 3.34/3.50 inference(unit_resolution,[status(thm)],[6469, 41, 3394, 6466])).
% 3.34/3.50 tff(6572,assumption,(b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 3.34/3.50 tff(6573,plain,
% 3.34/3.50 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 3.34/3.50 inference(monotonicity,[status(thm)],[13])).
% 3.34/3.50 tff(6574,plain,
% 3.34/3.50 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(elem!1)))),
% 3.34/3.50 inference(symmetry,[status(thm)],[6573])).
% 3.34/3.50 tff(6575,plain,
% 3.34/3.50 (b(z, s(s(elem!1)))),
% 3.34/3.50 inference(modus_ponens,[status(thm)],[6572, 6574])).
% 3.34/3.50 tff(6576,plain,
% 3.34/3.50 ($false),
% 3.34/3.50 inference(unit_resolution,[status(thm)],[3394, 6575])).
% 3.34/3.50 tff(6577,plain,((~(z = elem!1)) | b(z, s(s(elem!1))) | (~b(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.50 tff(6578,plain,
% 3.34/3.50 (~(z = elem!1)),
% 3.34/3.50 inference(unit_resolution,[status(thm)],[6577, 3394, 6572])).
% 3.34/3.50 tff(6579,plain,
% 3.34/3.50 (r(z, elem!1)),
% 3.34/3.50 inference(unit_resolution,[status(thm)],[585, 6578, 5786])).
% 3.34/3.50 tff(6580,plain,
% 3.34/3.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 3.34/3.50 inference(rewrite,[status(thm)],[])).
% 3.34/3.50 tff(6581,plain,
% 3.34/3.50 (((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1))))) <=> ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 3.34/3.50 inference(rewrite,[status(thm)],[])).
% 3.34/3.50 tff(6582,plain,
% 3.34/3.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1))))))),
% 3.34/3.50 inference(monotonicity,[status(thm)],[6581])).
% 3.34/3.50 tff(6583,plain,
% 3.34/3.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 3.34/3.50 inference(transitivity,[status(thm)],[6582, 6580])).
% 3.34/3.50 tff(6584,plain,
% 3.34/3.50 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))),
% 3.34/3.50 inference(quant_inst,[status(thm)],[])).
% 3.34/3.50 tff(6585,plain,
% 3.34/3.50 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1))))),
% 3.34/3.50 inference(modus_ponens,[status(thm)],[6584, 6583])).
% 3.34/3.50 tff(6586,plain,
% 3.34/3.50 ($false),
% 3.34/3.50 inference(unit_resolution,[status(thm)],[6585, 118, 6579, 3365, 6571])).
% 3.34/3.50 tff(6587,plain,(b(z, s(s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | b(z, elem!1) | (~b(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.50 tff(6588,plain,
% 3.34/3.50 (b(z, s(s(elem!1)))),
% 3.34/3.50 inference(unit_resolution,[status(thm)],[6587, 6570, 6562, 5786])).
% 3.34/3.50 tff(6589,plain,
% 3.34/3.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))),
% 3.34/3.50 inference(rewrite,[status(thm)],[])).
% 3.34/3.50 tff(6590,plain,
% 3.34/3.50 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))),
% 3.34/3.50 inference(quant_inst,[status(thm)],[])).
% 3.34/3.50 tff(6591,plain,
% 3.34/3.50 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z))),
% 3.34/3.50 inference(modus_ponens,[status(thm)],[6590, 6589])).
% 3.34/3.50 tff(6592,plain,
% 3.34/3.50 ($false),
% 3.34/3.50 inference(unit_resolution,[status(thm)],[6591, 118, 521, 3365, 991])).
% 3.34/3.50 tff(6593,plain,((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.50 tff(6594,plain,
% 3.34/3.50 (~r(s(s(elem!1)), z)),
% 3.34/3.50 inference(unit_resolution,[status(thm)],[6593, 6570, 521])).
% 3.34/3.50 tff(6595,assumption,(~r(s(s(elem!1)), z)), introduced(assumption)).
% 3.34/3.50 tff(6596,plain,
% 3.34/3.50 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z))),
% 3.34/3.50 inference(rewrite,[status(thm)],[])).
% 3.34/3.50 tff(6597,plain,
% 3.34/3.50 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z))),
% 3.34/3.50 inference(quant_inst,[status(thm)],[])).
% 3.34/3.50 tff(6598,plain,
% 3.34/3.50 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z)),
% 3.34/3.50 inference(modus_ponens,[status(thm)],[6597, 6596])).
% 3.34/3.50 tff(6599,plain,
% 3.34/3.50 ($false),
% 3.34/3.50 inference(unit_resolution,[status(thm)],[6598, 41, 970, 5869, 6595])).
% 3.34/3.50 tff(6600,plain,(r(s(s(elem!1)), z) | b(s(s(elem!1)), z)), inference(lemma,lemma(discharge,[]))).
% 3.34/3.50 tff(6601,plain,
% 3.34/3.50 (b(s(s(elem!1)), z)),
% 3.34/3.50 inference(unit_resolution,[status(thm)],[6600, 6594])).
% 3.34/3.50 tff(6602,plain,
% 3.34/3.50 (~r(z, s(s(z)))),
% 3.34/3.50 inference(unit_resolution,[status(thm)],[4808, 1823, 557])).
% 3.34/3.50 tff(6603,plain,
% 3.34/3.50 (b(z, s(s(z)))),
% 3.34/3.50 inference(unit_resolution,[status(thm)],[143, 6602])).
% 3.34/3.50 tff(6604,assumption,(b(s(s(elem!1)), z)), introduced(assumption)).
% 3.34/3.50 tff(6605,plain,
% 3.34/3.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))),
% 3.34/3.50 inference(rewrite,[status(thm)],[])).
% 3.34/3.50 tff(6606,plain,
% 3.34/3.50 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))),
% 3.34/3.50 inference(rewrite,[status(thm)],[])).
% 3.34/3.50 tff(6607,plain,
% 3.34/3.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1))))))),
% 3.34/3.50 inference(monotonicity,[status(thm)],[6606])).
% 3.34/3.50 tff(6608,plain,
% 3.34/3.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))),
% 3.34/3.51 inference(transitivity,[status(thm)],[6607, 6605])).
% 3.34/3.51 tff(6609,plain,
% 3.34/3.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))))),
% 3.34/3.51 inference(quant_inst,[status(thm)],[])).
% 3.34/3.51 tff(6610,plain,
% 3.34/3.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1))))),
% 3.34/3.51 inference(modus_ponens,[status(thm)],[6609, 6608])).
% 3.34/3.51 tff(6611,plain,
% 3.34/3.51 ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[6610, 178, 3461, 6604, 6477])).
% 3.34/3.51 tff(6612,plain,
% 3.34/3.51 (~b(s(s(z)), s(s(elem!1)))),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[6611, 6603])).
% 3.34/3.51 tff(6613,plain,
% 3.34/3.51 (r(s(s(z)), s(s(elem!1)))),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[6475, 41, 6612, 6472])).
% 3.34/3.51 tff(6614,plain,
% 3.34/3.51 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))))),
% 3.34/3.51 inference(rewrite,[status(thm)],[])).
% 3.34/3.51 tff(6615,plain,
% 3.34/3.51 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1))))) <=> ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))))),
% 3.34/3.51 inference(rewrite,[status(thm)],[])).
% 3.34/3.51 tff(6616,plain,
% 3.34/3.51 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1))))))),
% 3.34/3.51 inference(monotonicity,[status(thm)],[6615])).
% 3.34/3.51 tff(6617,plain,
% 3.34/3.51 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))))),
% 3.34/3.51 inference(transitivity,[status(thm)],[6616, 6614])).
% 3.34/3.51 tff(6618,plain,
% 3.34/3.51 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))))),
% 3.34/3.51 inference(quant_inst,[status(thm)],[])).
% 3.34/3.51 tff(6619,plain,
% 3.34/3.51 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1))))),
% 3.34/3.51 inference(modus_ponens,[status(thm)],[6618, 6617])).
% 3.34/3.51 tff(6620,plain,
% 3.34/3.51 ($false),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[6619, 118, 1823, 3364, 6613])).
% 3.34/3.51 tff(6621,plain,((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(z)) = s(s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.51 tff(6622,plain,
% 3.34/3.51 ($false),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[6621, 6601, 6588, 3461, 6446, 6461, 3863, 6559])).
% 3.34/3.51 tff(6623,plain,((~(elem!1 = s(s(s(elem!1))))) | (~b(s(s(z)), z)) | b(z, elem!1) | (~r(z, elem!1)) | (s(s(elem!1)) = elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.51 tff(6624,plain,
% 3.34/3.51 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[6623, 6433, 6374, 6375, 1547, 1650, 6440, 1301, 6194, 6028, 6024, 5619, 6035, 5728, 6357, 6367])).
% 3.34/3.51 tff(6625,plain,
% 3.34/3.51 (b(s(s(s(elem!1))), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 3.34/3.51 inference(monotonicity,[status(thm)],[1519])).
% 3.34/3.51 tff(6626,plain,
% 3.34/3.51 (b(elem!1, s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 3.34/3.51 inference(symmetry,[status(thm)],[6625])).
% 3.34/3.51 tff(6627,plain,
% 3.34/3.51 (b(s(s(s(elem!1))), s(elem!1))),
% 3.34/3.51 inference(modus_ponens,[status(thm)],[854, 6626])).
% 3.34/3.51 tff(6628,assumption,(~b(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 3.34/3.51 tff(6629,plain,
% 3.34/3.51 ($false),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[6628, 6627])).
% 3.34/3.51 tff(6630,plain,((~(s(s(s(elem!1))) = elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.51 tff(6631,plain,
% 3.34/3.51 ($false),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[6630, 6624, 6434, 5725])).
% 3.34/3.51 tff(6632,plain,(b(s(s(z)), s(elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | b(s(elem!1), s(s(s(s(z))))) | b(elem!1, z) | b(elem!1, s(s(z))) | b(s(s(s(s(z)))), z) | r(elem!1, s(elem!1)) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 3.34/3.51 tff(6633,plain,
% 3.34/3.51 (b(s(s(z)), s(elem!1))),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[6632, 5723, 356, 202, 5720, 1301, 461, 3170, 744, 5618])).
% 3.34/3.51 tff(6634,plain,
% 3.34/3.51 (s(s(z)) = elem!1),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[311, 308])).
% 3.34/3.51 tff(6635,plain,
% 3.34/3.51 (~r(elem!1, z)),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[6206, 6634, 5618])).
% 3.34/3.51 tff(6636,plain,
% 3.34/3.51 (elem!1 = z),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[498, 6635, 5723])).
% 3.34/3.51 tff(6637,plain,
% 3.34/3.51 (z = elem!1),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[2808, 6636])).
% 3.34/3.51 tff(6638,plain,
% 3.34/3.51 (elem!1 = z),
% 3.34/3.51 inference(symmetry,[status(thm)],[6637])).
% 3.34/3.51 tff(6639,plain,
% 3.34/3.51 (s(s(z)) = z),
% 3.34/3.51 inference(transitivity,[status(thm)],[309, 6638])).
% 3.34/3.51 tff(6640,plain,
% 3.34/3.51 ($false),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[95, 6639])).
% 3.34/3.51 tff(6641,plain,((~(elem!1 = s(s(z)))) | b(elem!1, z) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 3.34/3.51 tff(6642,plain,
% 3.34/3.51 (~(elem!1 = s(s(z)))),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[6641, 5723, 5618])).
% 3.34/3.51 tff(6643,plain,
% 3.34/3.51 (r(elem!1, s(s(z)))),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[467, 6642, 461])).
% 3.34/3.51 tff(6644,plain,
% 3.34/3.51 (b(s(s(z)), s(z)) <=> b(s(s(z)), s(elem!1))),
% 3.34/3.51 inference(monotonicity,[status(thm)],[5745])).
% 3.34/3.51 tff(6645,plain,
% 3.34/3.51 (b(s(s(z)), s(elem!1)) <=> b(s(s(z)), s(z))),
% 3.34/3.51 inference(symmetry,[status(thm)],[6644])).
% 3.34/3.51 tff(6646,plain,
% 3.34/3.51 (b(s(s(z)), s(z))),
% 3.34/3.51 inference(modus_ponens,[status(thm)],[1071, 6645])).
% 3.34/3.51 tff(6647,plain,
% 3.34/3.51 (b(z, s(z)) <=> b(z, s(elem!1))),
% 3.34/3.51 inference(monotonicity,[status(thm)],[5745])).
% 3.34/3.51 tff(6648,plain,
% 3.34/3.51 (b(z, s(elem!1)) <=> b(z, s(z))),
% 3.34/3.51 inference(symmetry,[status(thm)],[6647])).
% 3.34/3.51 tff(6649,plain,
% 3.34/3.51 (~r(z, s(elem!1))),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[6201, 5739, 744])).
% 3.34/3.51 tff(6650,plain,
% 3.34/3.51 (b(z, s(elem!1))),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[2351, 6649])).
% 3.34/3.51 tff(6651,plain,
% 3.34/3.51 (b(z, s(z))),
% 3.34/3.51 inference(modus_ponens,[status(thm)],[6650, 6648])).
% 3.34/3.51 tff(6652,plain,
% 3.34/3.51 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 3.34/3.51 inference(monotonicity,[status(thm)],[5952])).
% 3.34/3.51 tff(6653,plain,
% 3.34/3.51 (r(s(elem!1), s(s(s(s(elem!1))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 3.34/3.51 inference(monotonicity,[status(thm)],[6652])).
% 3.34/3.51 tff(6654,plain,
% 3.34/3.51 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = z)),
% 3.34/3.51 inference(monotonicity,[status(thm)],[5739])).
% 3.34/3.51 tff(6655,plain,
% 3.34/3.51 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 3.34/3.51 inference(symmetry,[status(thm)],[6654])).
% 3.34/3.51 tff(6656,plain,
% 3.34/3.51 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 3.34/3.51 inference(monotonicity,[status(thm)],[6655])).
% 3.34/3.51 tff(6657,plain,
% 3.34/3.51 (~(s(s(s(elem!1))) = elem!1)),
% 3.34/3.51 inference(modus_ponens,[status(thm)],[940, 6656])).
% 3.34/3.51 tff(6658,plain,
% 3.34/3.51 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[951, 6657])).
% 3.34/3.51 tff(6659,plain,
% 3.34/3.51 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 3.34/3.51 inference(monotonicity,[status(thm)],[5740])).
% 3.34/3.51 tff(6660,plain,
% 3.34/3.51 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 3.34/3.51 inference(symmetry,[status(thm)],[6659])).
% 3.34/3.51 tff(6661,plain,
% 3.34/3.51 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 3.34/3.51 inference(symmetry,[status(thm)],[6652])).
% 3.34/3.51 tff(6662,plain,
% 3.34/3.51 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 3.34/3.51 inference(monotonicity,[status(thm)],[5740, 6661])).
% 3.34/3.51 tff(6663,plain,
% 3.34/3.51 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 3.34/3.51 inference(transitivity,[status(thm)],[6662, 6660])).
% 3.34/3.51 tff(6664,plain,
% 3.34/3.51 ((~b(s(elem!1), s(s(s(s(z)))))) <=> (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 3.34/3.51 inference(monotonicity,[status(thm)],[6663])).
% 3.34/3.51 tff(6665,plain,
% 3.34/3.51 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 3.34/3.51 inference(modus_ponens,[status(thm)],[5720, 6664])).
% 3.34/3.51 tff(6666,plain,
% 3.34/3.51 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[963, 6665, 6658])).
% 3.34/3.51 tff(6667,plain,
% 3.34/3.51 (r(s(elem!1), s(s(s(s(z)))))),
% 3.34/3.51 inference(modus_ponens,[status(thm)],[6666, 6653])).
% 3.34/3.51 tff(6668,plain,
% 3.34/3.51 (~r(s(elem!1), z)),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[916, 6667, 3244])).
% 3.34/3.51 tff(6669,plain,
% 3.34/3.51 (b(s(elem!1), z)),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[774, 6668])).
% 3.34/3.51 tff(6670,plain,
% 3.34/3.51 (b(s(z), z)),
% 3.34/3.51 inference(modus_ponens,[status(thm)],[6669, 5747])).
% 3.34/3.51 tff(6671,plain,
% 3.34/3.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(z))))),
% 3.34/3.51 inference(rewrite,[status(thm)],[])).
% 3.34/3.51 tff(6672,plain,
% 3.34/3.51 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(z))))),
% 3.34/3.51 inference(rewrite,[status(thm)],[])).
% 3.34/3.51 tff(6673,plain,
% 3.34/3.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(z)))))),
% 3.34/3.51 inference(monotonicity,[status(thm)],[6672])).
% 3.34/3.51 tff(6674,plain,
% 3.34/3.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(z))))),
% 3.34/3.51 inference(transitivity,[status(thm)],[6673, 6671])).
% 3.34/3.51 tff(6675,plain,
% 3.34/3.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 3.34/3.51 inference(quant_inst,[status(thm)],[])).
% 3.34/3.51 tff(6676,plain,
% 3.34/3.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(z)))),
% 3.34/3.51 inference(modus_ponens,[status(thm)],[6675, 6674])).
% 3.34/3.51 tff(6677,plain,
% 3.34/3.51 ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[6676, 178, 3461, 6670, 6651])).
% 3.34/3.51 tff(6678,plain,
% 3.34/3.51 (~b(s(z), s(s(z)))),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[6677, 6646])).
% 3.34/3.51 tff(6679,plain,
% 3.34/3.51 (~b(s(elem!1), s(s(elem!1)))),
% 3.34/3.51 inference(modus_ponens,[status(thm)],[6678, 5744])).
% 3.34/3.51 tff(6680,plain,
% 3.34/3.51 (r(s(elem!1), s(s(elem!1)))),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[1028, 6679, 5389])).
% 3.34/3.51 tff(6681,plain,
% 3.34/3.51 (r(z, s(s(elem!1)))),
% 3.34/3.51 inference(modus_ponens,[status(thm)],[3261, 5946])).
% 3.34/3.51 tff(6682,plain,
% 3.34/3.51 (~(s(elem!1) = s(s(z)))),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[1047, 450, 744])).
% 3.34/3.51 tff(6683,plain,
% 3.34/3.51 (s(z) = s(elem!1)),
% 3.34/3.51 inference(symmetry,[status(thm)],[929])).
% 3.34/3.51 tff(6684,plain,
% 3.34/3.51 (r(s(z), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 3.34/3.51 inference(monotonicity,[status(thm)],[6683])).
% 3.34/3.51 tff(6685,plain,
% 3.34/3.51 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(z), s(s(s(s(z)))))),
% 3.34/3.51 inference(symmetry,[status(thm)],[6684])).
% 3.34/3.51 tff(6686,plain,
% 3.34/3.51 (r(s(z), s(s(s(s(z)))))),
% 3.34/3.51 inference(modus_ponens,[status(thm)],[908, 6685])).
% 3.34/3.51 tff(6687,assumption,(~r(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 3.34/3.51 tff(6688,plain,
% 3.34/3.51 ($false),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[6687, 6686])).
% 3.34/3.51 tff(6689,plain,(r(s(z), s(s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.51 tff(6690,plain,
% 3.34/3.51 (r(s(z), s(s(s(s(z)))))),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[6689, 6667, 5739])).
% 3.34/3.51 tff(6691,plain,
% 3.34/3.51 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 3.34/3.51 inference(monotonicity,[status(thm)],[5745])).
% 3.34/3.51 tff(6692,plain,
% 3.34/3.51 (r(s(elem!1), s(s(z))) <=> r(s(z), s(s(z)))),
% 3.34/3.51 inference(symmetry,[status(thm)],[6691])).
% 3.34/3.51 tff(6693,plain,
% 3.34/3.51 (b(s(elem!1), s(s(z))) <=> b(s(z), s(s(z)))),
% 3.34/3.51 inference(monotonicity,[status(thm)],[5740])).
% 3.34/3.51 tff(6694,plain,
% 3.34/3.51 (b(s(z), s(s(z))) <=> b(s(elem!1), s(s(z)))),
% 3.34/3.51 inference(symmetry,[status(thm)],[6693])).
% 3.34/3.51 tff(6695,plain,
% 3.34/3.51 ((~b(s(z), s(s(z)))) <=> (~b(s(elem!1), s(s(z))))),
% 3.34/3.51 inference(monotonicity,[status(thm)],[6694])).
% 3.34/3.51 tff(6696,plain,
% 3.34/3.51 (~b(s(elem!1), s(s(z)))),
% 3.34/3.51 inference(modus_ponens,[status(thm)],[6678, 6695])).
% 3.34/3.51 tff(6697,plain,
% 3.34/3.51 (r(s(elem!1), s(s(z)))),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[421, 6696, 6682])).
% 3.34/3.51 tff(6698,plain,
% 3.34/3.51 (r(s(z), s(s(z)))),
% 3.34/3.51 inference(modus_ponens,[status(thm)],[6697, 6692])).
% 3.34/3.51 tff(6699,plain,
% 3.34/3.51 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[4593, 6698, 6690])).
% 3.34/3.51 tff(6700,plain,
% 3.34/3.51 (b(s(s(z)), s(s(s(s(z)))))),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[164, 6699])).
% 3.34/3.51 tff(6701,plain,
% 3.34/3.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 3.34/3.51 inference(rewrite,[status(thm)],[])).
% 3.34/3.51 tff(6702,plain,
% 3.34/3.51 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z))))) <=> ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 3.34/3.51 inference(rewrite,[status(thm)],[])).
% 3.34/3.51 tff(6703,plain,
% 3.34/3.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 3.34/3.51 inference(monotonicity,[status(thm)],[6702])).
% 3.34/3.51 tff(6704,plain,
% 3.34/3.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 3.34/3.51 inference(transitivity,[status(thm)],[6703, 6701])).
% 3.34/3.51 tff(6705,plain,
% 3.34/3.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))))),
% 3.34/3.51 inference(quant_inst,[status(thm)],[])).
% 3.34/3.51 tff(6706,plain,
% 3.34/3.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 3.34/3.51 inference(modus_ponens,[status(thm)],[6705, 6704])).
% 3.34/3.51 tff(6707,plain,
% 3.34/3.51 (~b(s(elem!1), s(s(z)))),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[6706, 178, 5749, 3461, 1687, 167])).
% 3.34/3.51 tff(6708,plain,
% 3.34/3.51 (r(s(elem!1), s(s(z)))),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[421, 6707, 1056])).
% 3.34/3.51 tff(6709,plain,
% 3.34/3.51 (~r(s(elem!1), elem!1)),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[625, 118, 450, 6708])).
% 3.34/3.51 tff(6710,plain,
% 3.34/3.51 (b(s(elem!1), elem!1)),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[677, 6709, 1548])).
% 3.34/3.51 tff(6711,plain,
% 3.34/3.51 (~b(z, elem!1)),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[6373, 178, 855, 6710, 854, 5749])).
% 3.34/3.51 tff(6712,plain,
% 3.34/3.51 (~r(z, s(s(z)))),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[5939, 6710, 356, 167, 908, 1301, 5810, 450, 3170, 3461, 6711])).
% 3.34/3.51 tff(6713,plain,
% 3.34/3.51 (b(z, s(s(z)))),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[143, 6712])).
% 3.34/3.51 tff(6714,plain,
% 3.34/3.51 ($false),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[6228, 178, 3461, 6713, 1687, 167, 202])).
% 3.34/3.51 tff(6715,plain,((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | r(s(s(s(elem!1))), s(s(z))) | (~r(elem!1, s(s(z)))) | b(s(s(s(s(z)))), z) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (s(elem!1) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.51 tff(6716,plain,
% 3.34/3.51 (r(s(s(s(elem!1))), s(s(z)))),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[6715, 6700, 5762, 202, 356, 6667, 1301, 3461, 450, 3170, 6650, 5725, 6682])).
% 3.34/3.51 tff(6717,plain,
% 3.34/3.51 (~r(s(s(s(elem!1))), elem!1)),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[4205, 6716, 450])).
% 3.34/3.51 tff(6718,plain,
% 3.34/3.51 (b(s(s(s(elem!1))), elem!1)),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[570, 6717, 6657])).
% 3.34/3.51 tff(6719,plain,
% 3.34/3.51 (b(s(s(s(elem!1))), z)),
% 3.34/3.51 inference(modus_ponens,[status(thm)],[6718, 5959])).
% 3.34/3.51 tff(6720,plain,
% 3.34/3.51 (b(s(s(s(z))), z)),
% 3.34/3.51 inference(modus_ponens,[status(thm)],[6719, 5958])).
% 3.34/3.51 tff(6721,plain,
% 3.34/3.51 ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[5967, 178, 3461, 5762, 6700])).
% 3.34/3.51 tff(6722,plain,
% 3.34/3.51 (~b(s(s(s(z))), s(s(z)))),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[6721, 6720])).
% 3.34/3.51 tff(6723,plain,
% 3.34/3.51 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.34/3.51 inference(modus_ponens,[status(thm)],[6722, 5956])).
% 3.34/3.51 tff(6724,plain,
% 3.34/3.51 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[3409, 6723, 5807])).
% 3.34/3.51 tff(6725,plain,
% 3.34/3.51 (~r(z, s(s(s(elem!1))))),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[5235, 6724, 6681])).
% 3.34/3.51 tff(6726,plain,
% 3.34/3.51 (b(z, s(s(s(elem!1))))),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[2095, 6725])).
% 3.34/3.51 tff(6727,plain,
% 3.34/3.51 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[5980, 6724, 6680])).
% 3.34/3.51 tff(6728,plain,
% 3.34/3.51 (b(s(s(s(elem!1))), s(elem!1))),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[373, 6727, 356])).
% 3.34/3.51 tff(6729,plain,
% 3.34/3.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 3.34/3.51 inference(rewrite,[status(thm)],[])).
% 3.34/3.51 tff(6730,plain,
% 3.34/3.51 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 3.34/3.51 inference(rewrite,[status(thm)],[])).
% 3.34/3.51 tff(6731,plain,
% 3.34/3.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 3.34/3.51 inference(monotonicity,[status(thm)],[6730])).
% 3.34/3.51 tff(6732,plain,
% 3.34/3.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 3.34/3.51 inference(transitivity,[status(thm)],[6731, 6729])).
% 3.34/3.51 tff(6733,plain,
% 3.34/3.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 3.34/3.51 inference(quant_inst,[status(thm)],[])).
% 3.34/3.51 tff(6734,plain,
% 3.34/3.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 3.34/3.51 inference(modus_ponens,[status(thm)],[6733, 6732])).
% 3.34/3.51 tff(6735,plain,
% 3.34/3.51 ($false),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[6734, 178, 2044, 855, 2043, 853, 5888])).
% 3.34/3.51 tff(6736,plain,((~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))))) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.51 tff(6737,plain,
% 3.34/3.51 (~b(s(elem!1), s(s(s(elem!1))))),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[6736, 6728, 6650, 6669, 6726])).
% 3.34/3.51 tff(6738,plain,
% 3.34/3.51 (r(s(elem!1), s(s(s(elem!1))))),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[5432, 6737, 5396])).
% 3.34/3.51 tff(6739,plain,
% 3.34/3.51 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[5897, 6728, 5725, 5949, 6718])).
% 3.34/3.51 tff(6740,plain,
% 3.34/3.51 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[3375, 6739, 1650])).
% 3.34/3.51 tff(6741,plain,
% 3.34/3.51 ($false),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[5994, 6740, 6738, 6680])).
% 3.34/3.51 tff(6742,plain,((~r(z, s(s(z)))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(z)), z)) | (~r(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | b(s(s(s(s(z)))), z) | (~b(s(s(z)), s(elem!1))) | b(s(elem!1), s(s(s(s(z))))) | r(elem!1, s(elem!1)) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 3.34/3.51 tff(6743,plain,
% 3.34/3.51 (~r(z, s(s(z)))),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[6742, 6643, 5619, 356, 202, 1301, 3170, 6633, 5720, 744, 5723])).
% 3.34/3.51 tff(6744,plain,
% 3.34/3.51 (b(z, s(s(z)))),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[143, 6743])).
% 3.34/3.51 tff(6745,plain,
% 3.34/3.51 (~(elem!1 = z)),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[3276, 6744, 461])).
% 3.34/3.51 tff(6746,plain,
% 3.34/3.51 (r(elem!1, z)),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[498, 6745, 5723])).
% 3.34/3.51 tff(6747,plain,
% 3.34/3.51 (~r(s(s(s(s(z)))), elem!1)),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[6033, 6746, 3244])).
% 3.34/3.51 tff(6748,plain,
% 3.34/3.51 (b(s(s(s(s(z)))), elem!1)),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[3142, 6747, 4510])).
% 3.34/3.51 tff(6749,plain,
% 3.34/3.51 (~(z = elem!1)),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[317, 6745])).
% 3.34/3.51 tff(6750,plain,
% 3.34/3.51 (~(s(elem!1) = s(s(z)))),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[1047, 6643, 744])).
% 3.34/3.51 tff(6751,plain,
% 3.34/3.51 (~r(s(elem!1), z)),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[916, 908, 194])).
% 3.34/3.51 tff(6752,plain,
% 3.34/3.51 (b(s(elem!1), z)),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[774, 6751])).
% 3.34/3.51 tff(6753,plain,
% 3.34/3.51 (~r(s(s(z)), s(elem!1))),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[5758, 147, 908])).
% 3.34/3.51 tff(6754,plain,
% 3.34/3.51 ((s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z)))),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[420, 41, 927])).
% 3.34/3.51 tff(6755,plain,
% 3.34/3.51 (b(s(elem!1), s(s(z)))),
% 3.34/3.51 inference(unit_resolution,[status(thm)],[6754, 1056])).
% 3.34/3.51 tff(6756,plain,
% 3.34/3.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)))),
% 3.34/3.51 inference(rewrite,[status(thm)],[])).
% 3.34/3.51 tff(6757,plain,
% 3.34/3.51 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)))),
% 3.34/3.51 inference(rewrite,[status(thm)],[])).
% 3.34/3.51 tff(6758,plain,
% 3.34/3.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z))))),
% 3.34/3.52 inference(monotonicity,[status(thm)],[6757])).
% 3.34/3.52 tff(6759,plain,
% 3.34/3.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)))),
% 3.34/3.52 inference(transitivity,[status(thm)],[6758, 6756])).
% 3.34/3.52 tff(6760,plain,
% 3.34/3.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), s(elem!1))))),
% 3.34/3.52 inference(quant_inst,[status(thm)],[])).
% 3.34/3.52 tff(6761,plain,
% 3.34/3.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z))),
% 3.34/3.52 inference(modus_ponens,[status(thm)],[6760, 6759])).
% 3.34/3.52 tff(6762,plain,
% 3.34/3.52 (~b(s(s(z)), s(elem!1))),
% 3.34/3.52 inference(unit_resolution,[status(thm)],[6761, 178, 853, 3461, 273, 6755])).
% 3.34/3.52 tff(6763,plain,
% 3.34/3.52 ((s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1))),
% 3.34/3.52 inference(unit_resolution,[status(thm)],[1065, 41, 1062])).
% 3.34/3.52 tff(6764,plain,
% 3.34/3.52 (s(s(z)) = s(elem!1)),
% 3.34/3.52 inference(unit_resolution,[status(thm)],[6763, 6762])).
% 3.34/3.52 tff(6765,plain,
% 3.34/3.52 (s(elem!1) = s(s(z))),
% 3.34/3.52 inference(modus_ponens,[status(thm)],[6764, 1358])).
% 3.34/3.52 tff(6766,plain,
% 3.34/3.52 ($false),
% 3.34/3.52 inference(unit_resolution,[status(thm)],[1056, 6765])).
% 3.34/3.52 tff(6767,plain,((s(elem!1) = s(s(z))) | r(s(s(z)), s(elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | r(s(elem!1), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.52 tff(6768,plain,
% 3.34/3.52 (r(s(elem!1), s(s(z)))),
% 3.34/3.52 inference(unit_resolution,[status(thm)],[6767, 6753, 3461, 1056, 273, 853])).
% 3.34/3.52 tff(6769,plain,
% 3.34/3.52 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 3.34/3.52 inference(rewrite,[status(thm)],[])).
% 3.34/3.52 tff(6770,plain,
% 3.34/3.52 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(z))))) <=> ((~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 3.34/3.52 inference(rewrite,[status(thm)],[])).
% 3.34/3.52 tff(6771,plain,
% 3.34/3.52 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 3.34/3.52 inference(monotonicity,[status(thm)],[6770])).
% 3.34/3.52 tff(6772,plain,
% 3.34/3.52 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 3.34/3.52 inference(transitivity,[status(thm)],[6771, 6769])).
% 3.34/3.52 tff(6773,plain,
% 3.34/3.52 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(z)))))),
% 3.34/3.52 inference(quant_inst,[status(thm)],[])).
% 3.34/3.52 tff(6774,plain,
% 3.34/3.52 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 3.34/3.52 inference(modus_ponens,[status(thm)],[6773, 6772])).
% 3.34/3.52 tff(6775,plain,
% 3.34/3.52 ($false),
% 3.34/3.52 inference(unit_resolution,[status(thm)],[6774, 118, 6768, 908, 147])).
% 3.34/3.52 tff(6776,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (s(elem!1) = s(s(z))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.52 tff(6777,plain,
% 3.34/3.52 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.34/3.52 inference(unit_resolution,[status(thm)],[6776, 908, 3461, 1056, 273, 6752])).
% 3.34/3.52 tff(6778,plain,
% 3.34/3.52 (b(s(s(z)), s(s(s(s(z)))))),
% 3.34/3.52 inference(unit_resolution,[status(thm)],[164, 6777])).
% 3.34/3.52 tff(6779,plain,
% 3.34/3.52 (~b(z, s(s(s(s(z)))))),
% 3.34/3.52 inference(unit_resolution,[status(thm)],[6228, 178, 3461, 273, 6778, 202])).
% 3.34/3.52 tff(6780,plain,
% 3.34/3.52 (r(z, s(s(s(s(z)))))),
% 3.34/3.52 inference(unit_resolution,[status(thm)],[46, 6779])).
% 3.34/3.52 tff(6781,plain,
% 3.34/3.52 (~r(z, s(elem!1))),
% 3.34/3.52 inference(unit_resolution,[status(thm)],[2766, 6780, 908])).
% 3.34/3.52 tff(6782,plain,
% 3.34/3.52 (b(z, s(elem!1))),
% 3.34/3.52 inference(unit_resolution,[status(thm)],[2351, 6781])).
% 3.34/3.52 tff(6783,plain,
% 3.34/3.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 3.34/3.52 inference(rewrite,[status(thm)],[])).
% 3.34/3.52 tff(6784,plain,
% 3.34/3.52 (((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(s(z))))) <=> ((~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 3.34/3.52 inference(rewrite,[status(thm)],[])).
% 3.34/3.52 tff(6785,plain,
% 3.34/3.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))))),
% 3.34/3.52 inference(monotonicity,[status(thm)],[6784])).
% 3.34/3.52 tff(6786,plain,
% 3.34/3.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 3.34/3.52 inference(transitivity,[status(thm)],[6785, 6783])).
% 3.34/3.52 tff(6787,plain,
% 3.34/3.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(s(z)))))),
% 3.34/3.52 inference(quant_inst,[status(thm)],[])).
% 3.34/3.52 tff(6788,plain,
% 3.34/3.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))),
% 3.34/3.52 inference(modus_ponens,[status(thm)],[6787, 6786])).
% 3.34/3.52 tff(6789,plain,
% 3.34/3.52 ($false),
% 3.34/3.52 inference(unit_resolution,[status(thm)],[6788, 178, 6782, 6752, 3461, 273, 1071])).
% 3.34/3.52 tff(6790,plain,((~r(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(z)))) | (s(elem!1) = s(s(z))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.52 tff(6791,plain,
% 3.34/3.52 (~r(s(elem!1), s(s(s(s(z)))))),
% 3.34/3.52 inference(unit_resolution,[status(thm)],[6790, 6744, 5619, 6633, 202, 6750, 3244])).
% 3.34/3.52 tff(6792,plain,
% 3.34/3.52 (s(elem!1) = s(s(s(s(z))))),
% 3.34/3.52 inference(unit_resolution,[status(thm)],[1084, 6791, 5720])).
% 3.34/3.52 tff(6793,plain,
% 3.34/3.52 (~(s(s(elem!1)) = s(s(z)))),
% 3.34/3.52 inference(unit_resolution,[status(thm)],[2386, 6749])).
% 3.34/3.52 tff(6794,plain,
% 3.34/3.52 (~(elem!1 = s(s(s(elem!1))))),
% 3.34/3.52 inference(unit_resolution,[status(thm)],[2498, 6792, 6793])).
% 3.34/3.52 tff(6795,plain,
% 3.34/3.52 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 3.34/3.52 inference(symmetry,[status(thm)],[6049])).
% 3.34/3.52 tff(6796,plain,
% 3.34/3.52 (b(s(s(s(s(z)))), elem!1) <=> b(s(elem!1), elem!1)),
% 3.34/3.52 inference(symmetry,[status(thm)],[1279])).
% 3.34/3.52 tff(6797,plain,
% 3.34/3.52 (b(s(elem!1), elem!1)),
% 3.34/3.52 inference(modus_ponens,[status(thm)],[3771, 6796])).
% 3.34/3.52 tff(6798,plain,
% 3.34/3.52 (b(s(s(z)), s(elem!1)) <=> b(s(s(z)), s(s(s(s(z)))))),
% 3.34/3.52 inference(monotonicity,[status(thm)],[1117])).
% 3.34/3.52 tff(6799,plain,
% 3.34/3.52 (b(s(s(z)), s(s(s(s(z)))))),
% 3.34/3.52 inference(modus_ponens,[status(thm)],[1071, 6798])).
% 3.34/3.52 tff(6800,plain,
% 3.34/3.52 (b(s(s(elem!1)), z) <=> b(s(s(s(s(s(z))))), z)),
% 3.34/3.52 inference(monotonicity,[status(thm)],[1118])).
% 3.34/3.52 tff(6801,plain,
% 3.34/3.52 (b(s(s(s(s(s(z))))), z) <=> b(s(s(elem!1)), z)),
% 3.34/3.52 inference(symmetry,[status(thm)],[6800])).
% 3.34/3.52 tff(6802,plain,
% 3.34/3.52 ((~b(s(s(s(s(s(z))))), z)) <=> (~b(s(s(elem!1)), z))),
% 3.34/3.52 inference(monotonicity,[status(thm)],[6801])).
% 3.34/3.52 tff(6803,plain,
% 3.34/3.52 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 3.34/3.52 inference(symmetry,[status(thm)],[1118])).
% 3.34/3.52 tff(6804,plain,
% 3.34/3.52 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.34/3.52 inference(monotonicity,[status(thm)],[6036, 6803])).
% 3.34/3.52 tff(6805,plain,
% 3.34/3.52 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 3.34/3.52 inference(symmetry,[status(thm)],[6804])).
% 3.34/3.52 tff(6806,plain,
% 3.34/3.52 (b(s(s(s(s(s(s(z)))))), z)),
% 3.34/3.52 inference(modus_ponens,[status(thm)],[1566, 6066])).
% 3.34/3.52 tff(6807,plain,
% 3.34/3.52 (r(z, s(elem!1)) <=> r(z, s(s(s(s(z)))))),
% 3.34/3.52 inference(monotonicity,[status(thm)],[1117])).
% 3.34/3.52 tff(6808,plain,
% 3.34/3.52 (r(z, s(s(s(s(z))))) <=> r(z, s(elem!1))),
% 3.34/3.52 inference(symmetry,[status(thm)],[6807])).
% 3.34/3.52 tff(6809,plain,
% 3.34/3.52 (~b(z, s(s(s(s(z)))))),
% 3.34/3.52 inference(unit_resolution,[status(thm)],[6228, 178, 3461, 273, 167, 202])).
% 3.34/3.52 tff(6810,plain,
% 3.34/3.52 (r(z, s(s(s(s(z)))))),
% 3.34/3.52 inference(unit_resolution,[status(thm)],[46, 6809])).
% 3.34/3.52 tff(6811,plain,
% 3.34/3.52 (r(z, s(elem!1))),
% 3.34/3.52 inference(modus_ponens,[status(thm)],[6810, 6808])).
% 3.34/3.52 tff(6812,plain,
% 3.34/3.52 (~r(z, s(s(s(elem!1))))),
% 3.34/3.52 inference(unit_resolution,[status(thm)],[5447, 1551, 6811])).
% 3.34/3.52 tff(6813,plain,
% 3.34/3.52 (b(z, s(s(s(elem!1))))),
% 3.34/3.52 inference(unit_resolution,[status(thm)],[2095, 6812])).
% 3.34/3.52 tff(6814,plain,
% 3.34/3.52 (b(z, s(s(s(s(s(s(z)))))))),
% 3.34/3.52 inference(modus_ponens,[status(thm)],[6813, 6075])).
% 3.34/3.52 tff(6815,plain,
% 3.34/3.52 ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))),
% 3.34/3.52 inference(unit_resolution,[status(thm)],[6084, 178, 3461, 273, 6814])).
% 3.34/3.52 tff(6816,plain,
% 3.34/3.52 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 3.34/3.52 inference(unit_resolution,[status(thm)],[6815, 6806])).
% 3.34/3.52 tff(6817,plain,
% 3.34/3.52 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 3.34/3.52 inference(unit_resolution,[status(thm)],[6139, 6816, 6059])).
% 3.34/3.52 tff(6818,plain,
% 3.34/3.52 (r(s(s(s(elem!1))), s(s(z)))),
% 3.34/3.52 inference(unit_resolution,[status(thm)],[6165, 6817, 1117])).
% 3.34/3.52 tff(6819,plain,
% 3.34/3.52 (r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 3.34/3.52 inference(monotonicity,[status(thm)],[2491, 6036])).
% 3.34/3.52 tff(6820,plain,
% 3.34/3.52 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 3.34/3.52 inference(symmetry,[status(thm)],[6819])).
% 3.34/3.52 tff(6821,plain,
% 3.34/3.52 (~r(s(s(s(elem!1))), elem!1)),
% 3.34/3.52 inference(unit_resolution,[status(thm)],[4205, 6818, 450])).
% 3.34/3.52 tff(6822,plain,
% 3.34/3.52 (b(s(s(s(elem!1))), elem!1)),
% 3.34/3.52 inference(unit_resolution,[status(thm)],[570, 6821, 6403])).
% 3.34/3.52 tff(6823,plain,
% 3.34/3.52 ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(z))))),
% 3.34/3.52 inference(unit_resolution,[status(thm)],[6146, 118, 6817])).
% 3.34/3.52 tff(6824,plain,
% 3.34/3.52 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 3.34/3.52 inference(unit_resolution,[status(thm)],[6823, 6053])).
% 3.34/3.52 tff(6825,plain,
% 3.34/3.52 (~r(elem!1, s(s(s(elem!1))))),
% 3.34/3.52 inference(modus_ponens,[status(thm)],[6824, 6050])).
% 3.34/3.52 tff(6826,plain,
% 3.34/3.52 (b(elem!1, s(s(s(elem!1))))),
% 3.34/3.52 inference(unit_resolution,[status(thm)],[2054, 6825, 1586])).
% 3.34/3.52 tff(6827,plain,
% 3.34/3.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), 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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), 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))))))),
% 3.34/3.52 inference(rewrite,[status(thm)],[])).
% 3.34/3.52 tff(6828,plain,
% 3.34/3.52 (((~b(s(s(s(elem!1))), 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(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), 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))))))),
% 3.34/3.52 inference(rewrite,[status(thm)],[])).
% 3.34/3.52 tff(6829,plain,
% 3.34/3.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(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(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), 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)))))))),
% 3.34/3.52 inference(monotonicity,[status(thm)],[6828])).
% 3.34/3.52 tff(6830,plain,
% 3.34/3.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(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(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), 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))))))),
% 3.34/3.52 inference(transitivity,[status(thm)],[6829, 6827])).
% 3.34/3.52 tff(6831,plain,
% 3.34/3.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(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(elem!1, s(elem!1))))),
% 3.34/3.52 inference(quant_inst,[status(thm)],[])).
% 3.34/3.52 tff(6832,plain,
% 3.34/3.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))),
% 3.34/3.52 inference(modus_ponens,[status(thm)],[6831, 6830])).
% 3.34/3.52 tff(6833,plain,
% 3.34/3.52 ($false),
% 3.34/3.52 inference(unit_resolution,[status(thm)],[6832, 178, 683, 1597, 854, 2042, 5888])).
% 3.34/3.52 tff(6834,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), 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)))))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.52 tff(6835,plain,
% 3.34/3.52 (~b(s(elem!1), s(s(s(elem!1))))),
% 3.34/3.52 inference(unit_resolution,[status(thm)],[6834, 6826, 854, 683, 6822])).
% 3.34/3.52 tff(6836,plain,
% 3.34/3.52 (r(s(elem!1), s(s(s(elem!1))))),
% 3.34/3.52 inference(unit_resolution,[status(thm)],[5432, 6835, 5425])).
% 3.34/3.52 tff(6837,plain,
% 3.34/3.52 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 3.34/3.52 inference(modus_ponens,[status(thm)],[6836, 6820])).
% 3.34/3.52 tff(6838,plain,
% 3.34/3.52 (b(z, s(s(s(z)))) <=> b(z, elem!1)),
% 3.34/3.52 inference(symmetry,[status(thm)],[1234])).
% 3.34/3.52 tff(6839,plain,
% 3.34/3.52 ((~b(z, s(s(s(z))))) <=> (~b(z, elem!1))),
% 3.34/3.52 inference(monotonicity,[status(thm)],[6838])).
% 3.34/3.52 tff(6840,plain,
% 3.34/3.52 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 3.34/3.52 inference(modus_ponens,[status(thm)],[6822, 6153])).
% 3.34/3.52 tff(6841,plain,
% 3.34/3.52 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 3.34/3.52 inference(modus_ponens,[status(thm)],[6826, 6048])).
% 3.34/3.52 tff(6842,plain,
% 3.34/3.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 3.34/3.52 inference(rewrite,[status(thm)],[])).
% 3.34/3.52 tff(6843,plain,
% 3.34/3.52 (((~b(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(s(s(z)))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z))) <=> ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 3.34/3.52 inference(rewrite,[status(thm)],[])).
% 3.34/3.52 tff(6844,plain,
% 3.34/3.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(s(s(z)))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 3.34/3.52 inference(monotonicity,[status(thm)],[6843])).
% 3.34/3.52 tff(6845,plain,
% 3.34/3.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(s(s(z)))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 3.34/3.52 inference(transitivity,[status(thm)],[6844, 6842])).
% 3.34/3.52 tff(6846,plain,
% 3.34/3.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(s(s(z)))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 3.34/3.52 inference(quant_inst,[status(thm)],[])).
% 3.34/3.52 tff(6847,plain,
% 3.34/3.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 3.34/3.52 inference(modus_ponens,[status(thm)],[6846, 6845])).
% 3.34/3.52 tff(6848,plain,
% 3.34/3.52 (~b(z, s(s(s(z))))),
% 3.34/3.52 inference(unit_resolution,[status(thm)],[6847, 178, 6814, 6841, 6806, 6840])).
% 3.34/3.52 tff(6849,plain,
% 3.34/3.52 (~b(z, elem!1)),
% 3.34/3.52 inference(modus_ponens,[status(thm)],[6848, 6839])).
% 3.34/3.52 tff(6850,plain,
% 3.34/3.52 (r(z, elem!1)),
% 3.34/3.52 inference(unit_resolution,[status(thm)],[585, 6849, 507])).
% 3.34/3.52 tff(6851,plain,
% 3.34/3.52 (r(s(s(z)), s(s(s(s(s(z)))))) <=> r(s(s(z)), s(s(elem!1)))),
% 3.34/3.52 inference(monotonicity,[status(thm)],[6803])).
% 3.34/3.52 tff(6852,plain,
% 3.34/3.52 (r(s(s(z)), s(s(elem!1))) <=> r(s(s(z)), s(s(s(s(s(z))))))),
% 3.34/3.52 inference(symmetry,[status(thm)],[6851])).
% 3.34/3.52 tff(6853,plain,
% 3.34/3.52 ((~r(s(s(z)), s(s(elem!1)))) <=> (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 3.34/3.52 inference(monotonicity,[status(thm)],[6852])).
% 3.34/3.52 tff(6854,plain,
% 3.34/3.52 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 3.34/3.52 inference(modus_ponens,[status(thm)],[6455, 6853])).
% 3.34/3.52 tff(6855,plain,
% 3.34/3.52 ((s(s(z)) = s(s(s(s(s(z)))))) <=> (s(s(z)) = s(s(elem!1)))),
% 3.34/3.52 inference(monotonicity,[status(thm)],[6803])).
% 3.34/3.52 tff(6856,plain,
% 3.34/3.52 ((s(s(z)) = s(s(s(s(s(z)))))) <=> (s(s(elem!1)) = s(s(z)))),
% 3.34/3.52 inference(transitivity,[status(thm)],[6855, 6456])).
% 3.34/3.52 tff(6857,plain,
% 3.34/3.52 ((s(s(elem!1)) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(z))))))),
% 3.34/3.52 inference(symmetry,[status(thm)],[6856])).
% 3.34/3.52 tff(6858,plain,
% 3.34/3.52 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(s(z)))))))),
% 3.34/3.52 inference(monotonicity,[status(thm)],[6857])).
% 3.34/3.52 tff(6859,plain,
% 3.34/3.52 (~(s(s(z)) = s(s(s(s(s(z))))))),
% 3.34/3.52 inference(modus_ponens,[status(thm)],[2484, 6858])).
% 3.34/3.52 tff(6860,plain,
% 3.34/3.52 ((s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z))))))),
% 3.34/3.52 inference(unit_resolution,[status(thm)],[2781, 41])).
% 3.34/3.52 tff(6861,plain,
% 3.34/3.52 (b(s(s(z)), s(s(s(s(s(z))))))),
% 3.34/3.52 inference(unit_resolution,[status(thm)],[6860, 6859, 6854])).
% 3.34/3.52 tff(6862,plain,
% 3.34/3.52 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.34/3.52 inference(monotonicity,[status(thm)],[6803, 6036])).
% 3.34/3.52 tff(6863,plain,
% 3.34/3.52 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 3.34/3.52 inference(symmetry,[status(thm)],[6862])).
% 3.34/3.52 tff(6864,plain,
% 3.34/3.52 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.34/3.52 inference(monotonicity,[status(thm)],[6803, 6036])).
% 3.34/3.52 tff(6865,plain,
% 3.34/3.52 ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) <=> (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 3.34/3.52 inference(monotonicity,[status(thm)],[6864])).
% 3.34/3.52 tff(6866,assumption,(r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 3.34/3.52 tff(6867,plain,
% 3.34/3.52 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(elem!1))),
% 3.34/3.52 inference(monotonicity,[status(thm)],[2491])).
% 3.34/3.52 tff(6868,plain,
% 3.34/3.52 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(elem!1)))),
% 3.34/3.52 inference(transitivity,[status(thm)],[6867, 981])).
% 3.34/3.52 tff(6869,plain,
% 3.34/3.52 ((s(elem!1) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 3.34/3.52 inference(symmetry,[status(thm)],[6868])).
% 3.34/3.52 tff(6870,plain,
% 3.34/3.52 ((~(s(elem!1) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(s(s(s(z))))))),
% 3.34/3.52 inference(monotonicity,[status(thm)],[6869])).
% 3.34/3.52 tff(6871,plain,
% 3.34/3.52 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 3.34/3.52 inference(modus_ponens,[status(thm)],[3348, 6870])).
% 3.34/3.52 tff(6872,plain,
% 3.34/3.52 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.34/3.52 inference(monotonicity,[status(thm)],[1117, 1118])).
% 3.34/3.53 tff(6873,plain,
% 3.34/3.53 (~r(s(elem!1), s(s(elem!1)))),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[5980, 5227, 1551])).
% 3.34/3.53 tff(6874,plain,
% 3.34/3.53 (b(s(elem!1), s(s(elem!1)))),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[1028, 6873, 3348])).
% 3.34/3.53 tff(6875,plain,
% 3.34/3.53 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.34/3.53 inference(modus_ponens,[status(thm)],[6874, 6872])).
% 3.34/3.53 tff(6876,plain,
% 3.34/3.53 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 3.34/3.53 inference(modus_ponens,[status(thm)],[6471, 6853])).
% 3.34/3.53 tff(6877,plain,
% 3.34/3.53 ((s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z))))))),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[2781, 41, 6876])).
% 3.34/3.53 tff(6878,plain,
% 3.34/3.53 (b(s(s(z)), s(s(s(s(s(z))))))),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[6877, 6859])).
% 3.34/3.53 tff(6879,plain,
% 3.34/3.53 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 3.34/3.53 inference(monotonicity,[status(thm)],[6803])).
% 3.34/3.53 tff(6880,plain,
% 3.34/3.53 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 3.34/3.53 inference(symmetry,[status(thm)],[6879])).
% 3.34/3.53 tff(6881,plain,
% 3.34/3.53 ((~(s(s(elem!1)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(s(z))))) = s(s(s(s(z))))))),
% 3.34/3.53 inference(monotonicity,[status(thm)],[6880])).
% 3.34/3.53 tff(6882,assumption,(~(s(s(elem!1)) = s(s(s(s(z)))))), introduced(assumption)).
% 3.34/3.53 tff(6883,plain,
% 3.34/3.53 (~(s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 3.34/3.53 inference(modus_ponens,[status(thm)],[6882, 6881])).
% 3.34/3.53 tff(6884,assumption,(r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 3.34/3.53 tff(6885,plain,
% 3.34/3.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 3.34/3.53 inference(rewrite,[status(thm)],[])).
% 3.34/3.53 tff(6886,plain,
% 3.34/3.53 (((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 3.34/3.53 inference(rewrite,[status(thm)],[])).
% 3.34/3.53 tff(6887,plain,
% 3.34/3.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))))),
% 3.34/3.53 inference(monotonicity,[status(thm)],[6886])).
% 3.34/3.53 tff(6888,plain,
% 3.34/3.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 3.34/3.53 inference(transitivity,[status(thm)],[6887, 6885])).
% 3.34/3.53 tff(6889,plain,
% 3.34/3.53 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.34/3.53 inference(quant_inst,[status(thm)],[])).
% 3.34/3.53 tff(6890,plain,
% 3.34/3.53 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 3.34/3.53 inference(modus_ponens,[status(thm)],[6889, 6888])).
% 3.34/3.53 tff(6891,plain,
% 3.34/3.53 ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[6890, 118, 6866])).
% 3.34/3.53 tff(6892,plain,
% 3.34/3.53 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[6891, 6884])).
% 3.34/3.53 tff(6893,plain,
% 3.34/3.53 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 3.34/3.53 inference(rewrite,[status(thm)],[])).
% 3.34/3.53 tff(6894,plain,
% 3.34/3.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 3.34/3.53 inference(quant_inst,[status(thm)],[])).
% 3.34/3.53 tff(6895,plain,
% 3.34/3.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.34/3.53 inference(modus_ponens,[status(thm)],[6894, 6893])).
% 3.34/3.53 tff(6896,plain,
% 3.34/3.53 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[6895, 41, 6892])).
% 3.34/3.53 tff(6897,plain,
% 3.34/3.53 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[6896, 6883])).
% 3.34/3.53 tff(6898,plain,
% 3.34/3.53 ($false),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[1868, 6897, 6878, 202, 1860, 167])).
% 3.34/3.53 tff(6899,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(s(s(z))))) | (~(s(elem!1) = s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | r(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.53 tff(6900,plain,
% 3.34/3.53 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[6899, 6875, 202, 167, 6871, 1117, 2484, 6866, 6455])).
% 3.34/3.53 tff(6901,plain,
% 3.34/3.53 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.34/3.53 inference(modus_ponens,[status(thm)],[6900, 6865])).
% 3.34/3.53 tff(6902,plain,
% 3.34/3.53 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[3375, 6901, 1655])).
% 3.34/3.53 tff(6903,plain,
% 3.34/3.53 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 3.34/3.53 inference(modus_ponens,[status(thm)],[6902, 6863])).
% 3.34/3.53 tff(6904,assumption,(b(z, s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 3.34/3.53 tff(6905,plain,
% 3.34/3.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 3.34/3.53 inference(rewrite,[status(thm)],[])).
% 3.34/3.53 tff(6906,plain,
% 3.34/3.53 (((~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 3.34/3.53 inference(rewrite,[status(thm)],[])).
% 3.34/3.53 tff(6907,plain,
% 3.34/3.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))))),
% 3.34/3.53 inference(monotonicity,[status(thm)],[6906])).
% 3.34/3.53 tff(6908,plain,
% 3.34/3.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 3.34/3.53 inference(transitivity,[status(thm)],[6907, 6905])).
% 3.34/3.53 tff(6909,plain,
% 3.34/3.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 3.34/3.53 inference(quant_inst,[status(thm)],[])).
% 3.34/3.53 tff(6910,plain,
% 3.34/3.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 3.34/3.53 inference(modus_ponens,[status(thm)],[6909, 6908])).
% 3.34/3.53 tff(6911,plain,
% 3.34/3.53 ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[6910, 178, 3461, 6904])).
% 3.34/3.53 tff(6912,plain,
% 3.34/3.53 (~b(s(s(s(s(s(z))))), z)),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[6911, 6903, 6861])).
% 3.34/3.53 tff(6913,plain,
% 3.34/3.53 (~b(s(s(elem!1)), z)),
% 3.34/3.53 inference(modus_ponens,[status(thm)],[6912, 6802])).
% 3.34/3.53 tff(6914,plain,
% 3.34/3.53 (~b(s(s(elem!1)), elem!1)),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[5490, 6902, 2042, 683, 6874])).
% 3.34/3.53 tff(6915,plain,
% 3.34/3.53 (r(s(s(elem!1)), elem!1)),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[3362, 6914, 346])).
% 3.34/3.53 tff(6916,plain,
% 3.34/3.53 (~r(s(s(elem!1)), z)),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[6593, 6915, 521])).
% 3.34/3.53 tff(6917,plain,
% 3.34/3.53 (b(s(s(elem!1)), z)),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[6600, 6916])).
% 3.34/3.53 tff(6918,plain,
% 3.34/3.53 ($false),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[6917, 6913])).
% 3.34/3.53 tff(6919,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~(s(elem!1) = s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (s(s(elem!1)) = s(s(z))) | (~r(z, elem!1)) | (s(s(elem!1)) = elem!1) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.53 tff(6920,plain,
% 3.34/3.53 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[6919, 6814, 3461, 1117, 2387, 6850, 346, 6826, 683, 1655, 202, 167, 6837, 1551, 6818])).
% 3.34/3.53 tff(6921,plain,
% 3.34/3.53 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[3409, 6920, 6444])).
% 3.34/3.53 tff(6922,plain,
% 3.34/3.53 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 3.34/3.53 inference(modus_ponens,[status(thm)],[6921, 6805])).
% 3.34/3.53 tff(6923,plain,
% 3.34/3.53 (r(s(s(z)), s(s(s(s(s(s(z))))))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 3.34/3.53 inference(monotonicity,[status(thm)],[6036])).
% 3.34/3.53 tff(6924,plain,
% 3.34/3.53 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 3.34/3.53 inference(symmetry,[status(thm)],[6923])).
% 3.34/3.53 tff(6925,plain,
% 3.34/3.53 ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[6334, 178, 3461, 273, 6814])).
% 3.34/3.53 tff(6926,plain,
% 3.34/3.53 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[6925, 6806])).
% 3.34/3.53 tff(6927,plain,
% 3.34/3.53 (~b(s(s(z)), s(s(s(elem!1))))),
% 3.34/3.53 inference(modus_ponens,[status(thm)],[6926, 6064])).
% 3.34/3.53 tff(6928,plain,
% 3.34/3.53 (r(s(s(z)), s(s(s(elem!1))))),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[4223, 6927])).
% 3.34/3.53 tff(6929,plain,
% 3.34/3.53 (r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 3.34/3.53 inference(modus_ponens,[status(thm)],[6928, 6924])).
% 3.34/3.53 tff(6930,plain,
% 3.34/3.53 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 3.34/3.53 inference(modus_ponens,[status(thm)],[2102, 6820])).
% 3.34/3.53 tff(6931,plain,
% 3.34/3.53 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 3.34/3.53 inference(modus_ponens,[status(thm)],[984, 6870])).
% 3.34/3.53 tff(6932,plain,
% 3.34/3.53 (~r(s(elem!1), s(s(elem!1)))),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[5994, 3364, 2102])).
% 3.34/3.53 tff(6933,plain,
% 3.34/3.53 (b(s(elem!1), s(s(elem!1)))),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[1028, 6932, 984])).
% 3.34/3.53 tff(6934,plain,
% 3.34/3.53 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.34/3.53 inference(modus_ponens,[status(thm)],[6933, 6872])).
% 3.34/3.53 tff(6935,plain,
% 3.34/3.53 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 3.34/3.53 inference(symmetry,[status(thm)],[6864])).
% 3.34/3.53 tff(6936,plain,
% 3.34/3.53 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 3.34/3.53 inference(modus_ponens,[status(thm)],[3364, 6935])).
% 3.34/3.53 tff(6937,plain,
% 3.34/3.53 (r(s(s(z)), s(s(elem!1)))),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[6899, 6936, 6934, 167, 6931, 1117, 2484, 6930, 202])).
% 3.34/3.53 tff(6938,plain,
% 3.34/3.53 (r(s(s(z)), s(s(s(s(s(z))))))),
% 3.34/3.53 inference(modus_ponens,[status(thm)],[6937, 6852])).
% 3.34/3.53 tff(6939,assumption,(r(s(s(z)), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 3.34/3.53 tff(6940,plain,
% 3.34/3.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 3.34/3.53 inference(rewrite,[status(thm)],[])).
% 3.34/3.53 tff(6941,plain,
% 3.34/3.53 (((~r(s(s(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(z)), s(s(s(s(s(z)))))))) <=> ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 3.34/3.53 inference(rewrite,[status(thm)],[])).
% 3.34/3.53 tff(6942,plain,
% 3.34/3.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))))),
% 3.34/3.53 inference(monotonicity,[status(thm)],[6941])).
% 3.34/3.53 tff(6943,plain,
% 3.34/3.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 3.34/3.53 inference(transitivity,[status(thm)],[6942, 6940])).
% 3.34/3.53 tff(6944,plain,
% 3.34/3.53 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 3.34/3.53 inference(quant_inst,[status(thm)],[])).
% 3.34/3.53 tff(6945,plain,
% 3.34/3.53 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 3.34/3.53 inference(modus_ponens,[status(thm)],[6944, 6943])).
% 3.34/3.53 tff(6946,plain,
% 3.34/3.53 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[6945, 118, 6939, 6936])).
% 3.34/3.53 tff(6947,plain,
% 3.34/3.53 ($false),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[6946, 6938])).
% 3.34/3.53 tff(6948,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~(s(elem!1) = 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)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.53 tff(6949,plain,
% 3.34/3.53 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[6948, 6929, 167, 2387, 202, 1117, 3348, 6836])).
% 3.34/3.53 tff(6950,plain,
% 3.34/3.53 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[3375, 6949, 1655])).
% 3.34/3.53 tff(6951,plain,
% 3.34/3.53 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 3.34/3.53 inference(modus_ponens,[status(thm)],[6950, 6863])).
% 3.34/3.53 tff(6952,plain,
% 3.34/3.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 3.34/3.53 inference(rewrite,[status(thm)],[])).
% 3.34/3.53 tff(6953,plain,
% 3.34/3.53 (((~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 3.34/3.53 inference(rewrite,[status(thm)],[])).
% 3.34/3.53 tff(6954,plain,
% 3.34/3.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))))),
% 3.34/3.53 inference(monotonicity,[status(thm)],[6953])).
% 3.34/3.53 tff(6955,plain,
% 3.34/3.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 3.34/3.53 inference(transitivity,[status(thm)],[6954, 6952])).
% 3.34/3.53 tff(6956,plain,
% 3.34/3.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 3.34/3.53 inference(quant_inst,[status(thm)],[])).
% 3.34/3.53 tff(6957,plain,
% 3.34/3.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))),
% 3.34/3.53 inference(modus_ponens,[status(thm)],[6956, 6955])).
% 3.34/3.53 tff(6958,plain,
% 3.34/3.53 ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[6957, 178, 6814, 6806])).
% 3.34/3.53 tff(6959,plain,
% 3.34/3.53 (~b(s(s(s(s(s(z))))), z)),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[6958, 6951, 6922])).
% 3.34/3.53 tff(6960,plain,
% 3.34/3.53 (~b(s(s(elem!1)), z)),
% 3.34/3.53 inference(modus_ponens,[status(thm)],[6959, 6802])).
% 3.34/3.53 tff(6961,plain,
% 3.34/3.53 (~b(s(s(elem!1)), elem!1)),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[5500, 6950, 6826, 6822, 6921])).
% 3.34/3.53 tff(6962,plain,
% 3.34/3.53 (r(s(s(elem!1)), elem!1)),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[3362, 6961, 346])).
% 3.34/3.53 tff(6963,plain,
% 3.34/3.53 (~r(s(s(elem!1)), z)),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[6593, 6962, 6850])).
% 3.34/3.53 tff(6964,plain,
% 3.34/3.53 (b(s(s(elem!1)), z)),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[6600, 6963])).
% 3.34/3.53 tff(6965,plain,
% 3.34/3.53 ($false),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[6964, 6960])).
% 3.34/3.53 tff(6966,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~(s(elem!1) = s(s(s(s(z)))))) | (s(s(elem!1)) = elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(elem!1), elem!1)) | (z = elem!1) | (s(elem!1) = s(s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (elem!1 = s(s(s(elem!1)))) | (~r(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.53 tff(6967,plain,
% 3.34/3.53 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[6966, 1117, 1547, 1650, 6799, 202, 3461, 6797, 507, 5396, 854, 1586, 450, 273, 6062])).
% 3.34/3.53 tff(6968,plain,
% 3.34/3.53 (b(s(s(s(elem!1))), s(elem!1))),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[373, 6967, 356])).
% 3.34/3.53 tff(6969,plain,
% 3.34/3.53 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 3.34/3.53 inference(modus_ponens,[status(thm)],[6968, 6039])).
% 3.34/3.53 tff(6970,plain,
% 3.34/3.53 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[6178, 6969, 450, 6042, 1117, 6403, 6047, 202])).
% 3.34/3.53 tff(6971,plain,
% 3.34/3.53 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 3.34/3.53 inference(modus_ponens,[status(thm)],[2042, 6048])).
% 3.34/3.53 tff(6972,assumption,(~b(s(s(s(z))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 3.34/3.53 tff(6973,plain,
% 3.34/3.53 ($false),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[6972, 6971])).
% 3.34/3.53 tff(6974,plain,((~b(elem!1, s(s(s(elem!1))))) | b(s(s(s(z))), s(s(s(s(s(s(z))))))) | (~(s(elem!1) = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.53 tff(6975,plain,
% 3.34/3.53 (~b(elem!1, s(s(s(elem!1))))),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[6974, 6970, 1117])).
% 3.34/3.53 tff(6976,plain,
% 3.34/3.53 (r(elem!1, s(s(s(elem!1))))),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[2054, 6975, 1586])).
% 3.34/3.53 tff(6977,plain,
% 3.34/3.53 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 3.34/3.53 inference(modus_ponens,[status(thm)],[6976, 6795])).
% 3.34/3.53 tff(6978,plain,
% 3.34/3.53 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[6086, 6976, 273, 437, 1117, 3461])).
% 3.34/3.53 tff(6979,plain,
% 3.34/3.53 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[6139, 6978, 6059])).
% 3.34/3.53 tff(6980,plain,
% 3.34/3.53 ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(z))))),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[6146, 118, 6979])).
% 3.34/3.53 tff(6981,plain,
% 3.34/3.53 ($false),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[6980, 6977, 6053])).
% 3.34/3.53 tff(6982,plain,((~(s(elem!1) = s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~r(elem!1, z)) | (~b(s(s(z)), z)) | (elem!1 = s(s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (s(s(s(elem!1))) = s(elem!1)) | (z = elem!1) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.53 tff(6983,plain,
% 3.34/3.53 ($false),
% 3.34/3.53 inference(unit_resolution,[status(thm)],[6982, 6794, 6792, 6744, 6746, 5619, 6643, 202, 356, 6749, 5725, 1301, 6748, 6633, 3244])).
% 3.34/3.54 tff(6984,plain,(b(elem!1, z) | (~b(s(s(s(s(z)))), s(s(z)))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | b(s(elem!1), s(s(s(s(z))))) | b(elem!1, s(s(z))) | b(s(s(s(s(z)))), z) | r(elem!1, s(elem!1)) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 3.34/3.54 tff(6985,plain,
% 3.34/3.54 (b(elem!1, z)),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[6984, 202, 356, 5722, 5720, 461, 3170, 744, 5618])).
% 3.34/3.54 tff(6986,plain,
% 3.34/3.54 (b(elem!1, z) <=> b(elem!1, elem!1)),
% 3.34/3.54 inference(monotonicity,[status(thm)],[13])).
% 3.34/3.54 tff(6987,plain,
% 3.34/3.54 (b(elem!1, elem!1) <=> b(elem!1, z)),
% 3.34/3.54 inference(symmetry,[status(thm)],[6986])).
% 3.34/3.54 tff(6988,plain,
% 3.34/3.54 ((~b(elem!1, elem!1)) <=> (~b(elem!1, z))),
% 3.34/3.54 inference(monotonicity,[status(thm)],[6987])).
% 3.34/3.54 tff(6989,plain,
% 3.34/3.54 (~b(elem!1, z)),
% 3.34/3.54 inference(modus_ponens,[status(thm)],[3220, 6988])).
% 3.34/3.54 tff(6990,plain,
% 3.34/3.54 ($false),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[506, 6989])).
% 3.34/3.54 tff(6991,plain,((~(z = elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.54 tff(6992,plain,
% 3.34/3.54 (~(z = elem!1)),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[6991, 506])).
% 3.34/3.54 tff(6993,plain,
% 3.34/3.54 (~r(z, s(s(s(s(z)))))),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[3478, 147, 3261])).
% 3.34/3.54 tff(6994,plain,
% 3.34/3.54 (b(z, s(s(s(s(z)))))),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[46, 6993])).
% 3.34/3.54 tff(6995,plain,
% 3.34/3.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 3.34/3.54 inference(rewrite,[status(thm)],[])).
% 3.34/3.54 tff(6996,plain,
% 3.34/3.54 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 3.34/3.54 inference(rewrite,[status(thm)],[])).
% 3.34/3.54 tff(6997,plain,
% 3.34/3.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 3.34/3.54 inference(monotonicity,[status(thm)],[6996])).
% 3.34/3.54 tff(6998,plain,
% 3.34/3.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 3.34/3.54 inference(transitivity,[status(thm)],[6997, 6995])).
% 3.34/3.54 tff(6999,plain,
% 3.34/3.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)))),
% 3.34/3.54 inference(quant_inst,[status(thm)],[])).
% 3.34/3.54 tff(7000,plain,
% 3.34/3.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 3.34/3.54 inference(modus_ponens,[status(thm)],[6999, 6998])).
% 3.34/3.54 tff(7001,plain,
% 3.34/3.54 (~b(s(elem!1), elem!1)),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[7000, 178, 506, 853, 6994, 1301])).
% 3.34/3.54 tff(7002,plain,
% 3.34/3.54 (r(s(elem!1), elem!1)),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[677, 7001, 725])).
% 3.34/3.54 tff(7003,plain,
% 3.34/3.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.34/3.54 inference(rewrite,[status(thm)],[])).
% 3.34/3.54 tff(7004,plain,
% 3.34/3.54 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z))))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.34/3.54 inference(rewrite,[status(thm)],[])).
% 3.34/3.54 tff(7005,plain,
% 3.34/3.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))))),
% 3.34/3.54 inference(monotonicity,[status(thm)],[7004])).
% 3.34/3.54 tff(7006,plain,
% 3.34/3.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.34/3.54 inference(transitivity,[status(thm)],[7005, 7003])).
% 3.34/3.54 tff(7007,plain,
% 3.34/3.54 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 3.34/3.54 inference(quant_inst,[status(thm)],[])).
% 3.34/3.54 tff(7008,plain,
% 3.34/3.54 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))),
% 3.34/3.54 inference(modus_ponens,[status(thm)],[7007, 7006])).
% 3.34/3.54 tff(7009,plain,
% 3.34/3.54 ($false),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[7008, 118, 1426, 3132, 908])).
% 3.34/3.54 tff(7010,plain,((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.54 tff(7011,plain,
% 3.34/3.54 (~r(s(s(s(s(z)))), elem!1)),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[7010, 7002, 908])).
% 3.34/3.54 tff(7012,plain,
% 3.34/3.54 (b(s(s(s(s(z)))), elem!1)),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[3142, 7011, 323])).
% 3.34/3.54 tff(7013,plain,
% 3.34/3.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 3.34/3.54 inference(rewrite,[status(thm)],[])).
% 3.34/3.54 tff(7014,plain,
% 3.34/3.54 (((~b(s(s(s(s(z)))), elem!1)) | (~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(z, s(s(s(s(z)))))) | (~b(elem!1, z))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 3.34/3.54 inference(rewrite,[status(thm)],[])).
% 3.34/3.54 tff(7015,plain,
% 3.34/3.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z))))))))),
% 3.34/3.54 inference(monotonicity,[status(thm)],[7014])).
% 3.34/3.54 tff(7016,plain,
% 3.34/3.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 3.34/3.54 inference(transitivity,[status(thm)],[7015, 7013])).
% 3.34/3.54 tff(7017,plain,
% 3.34/3.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, z)))),
% 3.34/3.54 inference(quant_inst,[status(thm)],[])).
% 3.34/3.54 tff(7018,plain,
% 3.34/3.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z))))))),
% 3.34/3.54 inference(modus_ponens,[status(thm)],[7017, 7016])).
% 3.34/3.54 tff(7019,plain,
% 3.34/3.54 ($false),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[7018, 178, 818, 506, 3771, 1687, 1301])).
% 3.34/3.54 tff(7020,plain,((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.54 tff(7021,plain,
% 3.34/3.54 (~b(z, elem!1)),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[7020, 7012, 506, 6994, 1301])).
% 3.34/3.54 tff(7022,plain,
% 3.34/3.54 (~r(s(elem!1), s(s(z)))),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[6774, 118, 908, 147])).
% 3.34/3.54 tff(7023,plain,
% 3.34/3.54 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(z)))),
% 3.34/3.54 inference(monotonicity,[status(thm)],[308])).
% 3.34/3.54 tff(7024,plain,
% 3.34/3.54 (r(s(elem!1), s(s(z))) <=> r(s(elem!1), elem!1)),
% 3.34/3.54 inference(symmetry,[status(thm)],[7023])).
% 3.34/3.54 tff(7025,plain,
% 3.34/3.54 ((~r(s(elem!1), s(s(z)))) <=> (~r(s(elem!1), elem!1))),
% 3.34/3.54 inference(monotonicity,[status(thm)],[7024])).
% 3.34/3.54 tff(7026,plain,
% 3.34/3.54 (~r(s(elem!1), elem!1)),
% 3.34/3.54 inference(modus_ponens,[status(thm)],[927, 7025])).
% 3.34/3.54 tff(7027,plain,
% 3.34/3.54 ($false),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[1426, 7026])).
% 3.34/3.54 tff(7028,plain,((~(elem!1 = s(s(z)))) | (~r(s(elem!1), elem!1)) | r(s(elem!1), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.54 tff(7029,plain,
% 3.34/3.54 (~(elem!1 = s(s(z)))),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[7028, 7002, 7022])).
% 3.34/3.54 tff(7030,plain,
% 3.34/3.54 (r(elem!1, s(s(z)))),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[467, 7029, 461])).
% 3.34/3.54 tff(7031,plain,
% 3.34/3.54 (~r(z, elem!1)),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[4862, 7030, 3261])).
% 3.34/3.54 tff(7032,plain,
% 3.34/3.54 ($false),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[585, 7031, 7021, 6992])).
% 3.34/3.54 tff(7033,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | b(elem!1, s(s(z))) | (s(s(s(s(z)))) = elem!1) | (~r(s(elem!1), s(s(s(s(z)))))) | (s(elem!1) = elem!1) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.54 tff(7034,plain,
% 3.34/3.54 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[7033, 908, 506, 1301, 461, 4510, 3261, 1548, 6752])).
% 3.34/3.54 tff(7035,plain,
% 3.34/3.54 (b(s(s(z)), s(s(s(s(z)))))),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[164, 7034])).
% 3.34/3.54 tff(7036,plain,
% 3.34/3.54 (s(s(s(z))) = s(elem!1)),
% 3.34/3.54 inference(symmetry,[status(thm)],[5636])).
% 3.34/3.54 tff(7037,plain,
% 3.34/3.54 (b(s(s(s(z))), z) <=> b(s(elem!1), z)),
% 3.34/3.54 inference(monotonicity,[status(thm)],[7036])).
% 3.34/3.54 tff(7038,plain,
% 3.34/3.54 (b(s(elem!1), z) <=> b(s(s(s(z))), z)),
% 3.34/3.54 inference(symmetry,[status(thm)],[7037])).
% 3.34/3.54 tff(7039,plain,
% 3.34/3.54 (b(s(s(s(z))), z)),
% 3.34/3.54 inference(modus_ponens,[status(thm)],[853, 7038])).
% 3.34/3.54 tff(7040,assumption,(~b(s(s(s(z))), z)), introduced(assumption)).
% 3.34/3.54 tff(7041,plain,
% 3.34/3.54 ($false),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[7040, 7039])).
% 3.34/3.54 tff(7042,plain,(b(s(s(s(z))), z) | (~b(s(elem!1), z)) | (~(elem!1 = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.54 tff(7043,plain,
% 3.34/3.54 (b(s(s(s(z))), z)),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[7042, 308, 6752])).
% 3.34/3.54 tff(7044,plain,
% 3.34/3.54 (b(s(s(s(z))), s(s(z))) <=> b(s(elem!1), s(s(z)))),
% 3.34/3.54 inference(monotonicity,[status(thm)],[7036])).
% 3.34/3.54 tff(7045,plain,
% 3.34/3.54 (b(s(elem!1), s(s(z))) <=> b(s(s(s(z))), s(s(z)))),
% 3.34/3.54 inference(symmetry,[status(thm)],[7044])).
% 3.34/3.54 tff(7046,plain,
% 3.34/3.54 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(z)))),
% 3.34/3.54 inference(monotonicity,[status(thm)],[308])).
% 3.34/3.54 tff(7047,plain,
% 3.34/3.54 (b(s(s(z)), s(elem!1))),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[1337, 6634, 1548, 744])).
% 3.34/3.54 tff(7048,plain,
% 3.34/3.54 (r(z, s(s(z))) <=> r(z, elem!1)),
% 3.34/3.54 inference(monotonicity,[status(thm)],[1324])).
% 3.34/3.54 tff(7049,plain,
% 3.34/3.54 (r(z, elem!1) <=> r(z, s(s(z)))),
% 3.34/3.54 inference(symmetry,[status(thm)],[7048])).
% 3.34/3.54 tff(7050,plain,
% 3.34/3.54 ((~r(z, elem!1)) <=> (~r(z, s(s(z))))),
% 3.34/3.54 inference(monotonicity,[status(thm)],[7049])).
% 3.34/3.54 tff(7051,plain,
% 3.34/3.54 (~r(z, s(s(z)))),
% 3.34/3.54 inference(modus_ponens,[status(thm)],[2811, 7050])).
% 3.34/3.54 tff(7052,plain,
% 3.34/3.54 ($false),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[3261, 7051])).
% 3.34/3.54 tff(7053,plain,((~(s(s(z)) = elem!1)) | (~r(z, s(s(z)))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.34/3.54 tff(7054,plain,
% 3.34/3.54 (r(z, elem!1)),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[7053, 6634, 3261])).
% 3.34/3.54 tff(7055,plain,
% 3.34/3.54 (r(s(elem!1), s(s(elem!1))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 3.34/3.54 inference(monotonicity,[status(thm)],[5637])).
% 3.34/3.54 tff(7056,plain,
% 3.34/3.54 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(elem!1), s(s(elem!1)))),
% 3.34/3.54 inference(symmetry,[status(thm)],[7055])).
% 3.34/3.54 tff(7057,plain,
% 3.34/3.54 (r(s(elem!1), s(s(elem!1)))),
% 3.34/3.54 inference(modus_ponens,[status(thm)],[908, 7056])).
% 3.34/3.54 tff(7058,plain,
% 3.34/3.54 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), s(elem!1))),
% 3.34/3.54 inference(monotonicity,[status(thm)],[7036])).
% 3.34/3.54 tff(7059,plain,
% 3.34/3.54 (b(s(s(z)), s(elem!1)) <=> b(s(s(z)), s(s(s(z))))),
% 3.34/3.54 inference(symmetry,[status(thm)],[7058])).
% 3.34/3.54 tff(7060,plain,
% 3.34/3.54 (b(s(s(z)), s(s(s(z))))),
% 3.34/3.54 inference(modus_ponens,[status(thm)],[1071, 7059])).
% 3.34/3.54 tff(7061,plain,
% 3.34/3.54 (b(z, s(elem!1)) <=> b(z, s(s(s(z))))),
% 3.34/3.54 inference(monotonicity,[status(thm)],[5636])).
% 3.34/3.54 tff(7062,plain,
% 3.34/3.54 (r(s(elem!1), elem!1)),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[677, 2141, 1548])).
% 3.34/3.54 tff(7063,plain,
% 3.34/3.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)))),
% 3.34/3.54 inference(rewrite,[status(thm)],[])).
% 3.34/3.54 tff(7064,plain,
% 3.34/3.54 (((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1)))) <=> ((~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)))),
% 3.34/3.54 inference(rewrite,[status(thm)],[])).
% 3.34/3.54 tff(7065,plain,
% 3.34/3.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1))))),
% 3.34/3.54 inference(monotonicity,[status(thm)],[7064])).
% 3.34/3.54 tff(7066,plain,
% 3.34/3.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)))),
% 3.34/3.54 inference(transitivity,[status(thm)],[7065, 7063])).
% 3.34/3.54 tff(7067,plain,
% 3.34/3.54 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 3.34/3.54 inference(quant_inst,[status(thm)],[])).
% 3.34/3.54 tff(7068,plain,
% 3.34/3.54 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1))),
% 3.34/3.54 inference(modus_ponens,[status(thm)],[7067, 7066])).
% 3.34/3.54 tff(7069,plain,
% 3.34/3.54 ($false),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[7068, 118, 521, 2333, 1426])).
% 3.34/3.54 tff(7070,plain,((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.54 tff(7071,plain,
% 3.34/3.54 (~r(z, s(elem!1))),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[7070, 7062, 521])).
% 3.34/3.54 tff(7072,plain,
% 3.34/3.54 (b(z, s(elem!1))),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[2351, 7071])).
% 3.34/3.54 tff(7073,plain,
% 3.34/3.54 (b(z, s(s(s(z))))),
% 3.34/3.54 inference(modus_ponens,[status(thm)],[7072, 7061])).
% 3.34/3.54 tff(7074,plain,
% 3.34/3.54 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 3.34/3.54 inference(monotonicity,[status(thm)],[5637])).
% 3.34/3.54 tff(7075,plain,
% 3.34/3.54 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(s(z))))), z)),
% 3.34/3.54 inference(monotonicity,[status(thm)],[7074])).
% 3.34/3.54 tff(7076,plain,
% 3.34/3.54 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.34/3.54 inference(monotonicity,[status(thm)],[5637, 7074])).
% 3.34/3.54 tff(7077,plain,
% 3.34/3.54 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 3.34/3.54 inference(symmetry,[status(thm)],[7074])).
% 3.34/3.54 tff(7078,plain,
% 3.34/3.54 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.34/3.54 inference(monotonicity,[status(thm)],[7077])).
% 3.34/3.54 tff(7079,plain,
% 3.34/3.54 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.34/3.54 inference(transitivity,[status(thm)],[7078, 5647])).
% 3.34/3.54 tff(7080,plain,
% 3.34/3.54 ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) <=> (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 3.34/3.54 inference(monotonicity,[status(thm)],[7079])).
% 3.34/3.54 tff(7081,plain,
% 3.34/3.54 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.34/3.54 inference(monotonicity,[status(thm)],[7074, 5637])).
% 3.34/3.54 tff(7082,plain,
% 3.34/3.54 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(z)))),
% 3.34/3.54 inference(monotonicity,[status(thm)],[308])).
% 3.34/3.54 tff(7083,plain,
% 3.34/3.54 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(elem!1))), elem!1)),
% 3.34/3.54 inference(symmetry,[status(thm)],[7082])).
% 3.34/3.54 tff(7084,plain,
% 3.34/3.54 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 3.34/3.54 inference(monotonicity,[status(thm)],[7077])).
% 3.34/3.54 tff(7085,plain,
% 3.34/3.54 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(elem!1))), elem!1)),
% 3.34/3.54 inference(transitivity,[status(thm)],[7084, 7083])).
% 3.34/3.54 tff(7086,plain,
% 3.34/3.54 ((~b(s(s(s(s(s(z))))), s(s(z)))) <=> (~b(s(s(s(elem!1))), elem!1))),
% 3.34/3.54 inference(monotonicity,[status(thm)],[7085])).
% 3.34/3.54 tff(7087,plain,
% 3.34/3.54 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 3.34/3.54 inference(monotonicity,[status(thm)],[7077, 7036])).
% 3.34/3.54 tff(7088,plain,
% 3.34/3.54 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.34/3.54 inference(symmetry,[status(thm)],[7087])).
% 3.34/3.54 tff(7089,plain,
% 3.34/3.54 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.34/3.54 inference(modus_ponens,[status(thm)],[2044, 7088])).
% 3.34/3.54 tff(7090,plain,
% 3.34/3.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.34/3.54 inference(rewrite,[status(thm)],[])).
% 3.34/3.54 tff(7091,plain,
% 3.34/3.54 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.34/3.54 inference(rewrite,[status(thm)],[])).
% 3.34/3.54 tff(7092,plain,
% 3.34/3.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 3.34/3.54 inference(monotonicity,[status(thm)],[7091])).
% 3.34/3.54 tff(7093,plain,
% 3.34/3.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.34/3.54 inference(transitivity,[status(thm)],[7092, 7090])).
% 3.34/3.54 tff(7094,plain,
% 3.34/3.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 3.34/3.54 inference(quant_inst,[status(thm)],[])).
% 3.34/3.54 tff(7095,plain,
% 3.34/3.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 3.34/3.54 inference(modus_ponens,[status(thm)],[7094, 7093])).
% 3.34/3.54 tff(7096,plain,
% 3.34/3.54 ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[7095, 178, 3461, 5090, 7039])).
% 3.34/3.54 tff(7097,plain,
% 3.34/3.54 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[7096, 7089])).
% 3.34/3.54 tff(7098,plain,
% 3.34/3.54 (~b(s(s(s(elem!1))), elem!1)),
% 3.34/3.54 inference(modus_ponens,[status(thm)],[7097, 7086])).
% 3.34/3.54 tff(7099,plain,
% 3.34/3.54 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 3.34/3.54 inference(monotonicity,[status(thm)],[309])).
% 3.34/3.54 tff(7100,plain,
% 3.34/3.54 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 3.34/3.54 inference(transitivity,[status(thm)],[7099, 1526])).
% 3.34/3.54 tff(7101,plain,
% 3.34/3.54 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 3.34/3.54 inference(monotonicity,[status(thm)],[7100])).
% 3.34/3.54 tff(7102,plain,
% 3.34/3.54 (~(s(s(s(elem!1))) = elem!1)),
% 3.34/3.54 inference(modus_ponens,[status(thm)],[1683, 7101])).
% 3.34/3.54 tff(7103,plain,
% 3.34/3.54 (r(s(s(s(elem!1))), elem!1)),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[570, 7098, 7102])).
% 3.34/3.54 tff(7104,plain,
% 3.34/3.54 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(elem!1))))),
% 3.34/3.54 inference(symmetry,[status(thm)],[3881])).
% 3.34/3.54 tff(7105,plain,
% 3.34/3.54 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 3.34/3.54 inference(monotonicity,[status(thm)],[7104])).
% 3.34/3.54 tff(7106,plain,
% 3.34/3.54 (~(s(elem!1) = s(s(s(elem!1))))),
% 3.34/3.54 inference(modus_ponens,[status(thm)],[356, 7105])).
% 3.34/3.54 tff(7107,plain,
% 3.34/3.54 (~b(s(elem!1), s(s(s(elem!1))))),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[6736, 2044, 855, 2043, 853])).
% 3.34/3.54 tff(7108,plain,
% 3.34/3.54 ((s(elem!1) = s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1))))),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[5430, 41, 7107])).
% 3.34/3.54 tff(7109,plain,
% 3.34/3.54 (r(s(elem!1), s(s(s(elem!1))))),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[7108, 7106])).
% 3.34/3.54 tff(7110,plain,
% 3.34/3.54 (~r(s(elem!1), elem!1)),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[2110, 7109, 556])).
% 3.34/3.54 tff(7111,plain,
% 3.34/3.54 (s(elem!1) = elem!1),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[677, 7110, 2141])).
% 3.34/3.54 tff(7112,plain,
% 3.34/3.54 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), elem!1)),
% 3.34/3.54 inference(monotonicity,[status(thm)],[7111])).
% 3.34/3.54 tff(7113,plain,
% 3.34/3.54 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(elem!1))),
% 3.34/3.54 inference(symmetry,[status(thm)],[7112])).
% 3.34/3.54 tff(7114,plain,
% 3.34/3.54 ((~b(s(s(s(elem!1))), elem!1)) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 3.34/3.54 inference(monotonicity,[status(thm)],[7113])).
% 3.34/3.54 tff(7115,plain,
% 3.34/3.54 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.34/3.54 inference(modus_ponens,[status(thm)],[5308, 7114])).
% 3.34/3.54 tff(7116,plain,
% 3.34/3.54 ($false),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[2044, 7115])).
% 3.34/3.54 tff(7117,plain,((~b(s(s(s(elem!1))), s(elem!1))) | b(s(s(s(elem!1))), elem!1) | b(s(elem!1), elem!1) | (~r(s(s(s(elem!1))), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.54 tff(7118,plain,
% 3.34/3.54 (~b(z, s(s(s(elem!1))))),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[7117, 7103, 356, 853, 2141, 7072, 7098, 2044])).
% 3.34/3.54 tff(7119,plain,
% 3.34/3.54 (~r(z, s(s(s(elem!1))))),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[565, 7103, 521])).
% 3.34/3.54 tff(7120,plain,
% 3.34/3.54 ($false),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[2095, 7119, 7118])).
% 3.34/3.54 tff(7121,plain,((~b(s(s(s(elem!1))), s(elem!1))) | (~r(z, elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(elem!1), z)) | b(s(elem!1), elem!1) | (~(elem!1 = s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.54 tff(7122,plain,
% 3.34/3.54 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[7121, 2141, 356, 853, 521, 308, 3461, 7060])).
% 3.34/3.54 tff(7123,plain,
% 3.34/3.54 (r(s(s(s(elem!1))), s(elem!1))),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[373, 7122, 356])).
% 3.34/3.54 tff(7124,plain,
% 3.34/3.54 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[5980, 7123, 5972])).
% 3.34/3.54 tff(7125,plain,
% 3.34/3.54 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[3409, 7124, 5807])).
% 3.34/3.54 tff(7126,plain,
% 3.34/3.54 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.34/3.54 inference(modus_ponens,[status(thm)],[7125, 7081])).
% 3.34/3.54 tff(7127,plain,
% 3.34/3.54 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 3.34/3.54 inference(symmetry,[status(thm)],[7084])).
% 3.34/3.54 tff(7128,plain,
% 3.34/3.54 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 3.34/3.54 inference(transitivity,[status(thm)],[7082, 7127])).
% 3.34/3.54 tff(7129,plain,
% 3.34/3.54 (~r(s(s(s(elem!1))), elem!1)),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[1576, 7123, 7062])).
% 3.34/3.54 tff(7130,plain,
% 3.34/3.54 (b(s(s(s(elem!1))), elem!1)),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[570, 7129, 7102])).
% 3.34/3.54 tff(7131,plain,
% 3.34/3.54 (b(s(s(s(s(s(z))))), s(s(z)))),
% 3.34/3.54 inference(modus_ponens,[status(thm)],[7130, 7128])).
% 3.34/3.54 tff(7132,plain,
% 3.34/3.54 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[2702, 178, 167, 202, 7131, 7126])).
% 3.34/3.54 tff(7133,plain,
% 3.34/3.54 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.34/3.54 inference(modus_ponens,[status(thm)],[7132, 7080])).
% 3.34/3.54 tff(7134,plain,
% 3.34/3.54 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[3375, 7133, 1650])).
% 3.34/3.54 tff(7135,plain,
% 3.34/3.54 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.34/3.54 inference(modus_ponens,[status(thm)],[7134, 7076])).
% 3.34/3.54 tff(7136,plain,
% 3.34/3.54 (r(s(s(s(s(s(z))))), z) <=> r(s(s(s(elem!1))), z)),
% 3.34/3.54 inference(monotonicity,[status(thm)],[7077])).
% 3.34/3.54 tff(7137,plain,
% 3.34/3.54 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(s(z))))), z)),
% 3.34/3.54 inference(symmetry,[status(thm)],[7136])).
% 3.34/3.54 tff(7138,plain,
% 3.34/3.54 (r(s(s(s(s(s(z))))), z)),
% 3.34/3.54 inference(modus_ponens,[status(thm)],[1552, 7137])).
% 3.34/3.54 tff(7139,assumption,(r(s(s(s(s(z)))), s(s(s(s(s(z))))))), introduced(assumption)).
% 3.34/3.54 tff(7140,plain,
% 3.34/3.54 (~r(s(s(s(s(s(z))))), z)),
% 3.34/3.54 inference(unit_resolution,[status(thm)],[1744, 118, 194, 7139])).
% 3.34/3.55 tff(7141,plain,
% 3.34/3.55 ($false),
% 3.34/3.55 inference(unit_resolution,[status(thm)],[7140, 7138])).
% 3.34/3.55 tff(7142,plain,((~r(s(s(s(elem!1))), z)) | (~(elem!1 = s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.55 tff(7143,plain,
% 3.34/3.55 (~r(s(s(s(elem!1))), z)),
% 3.34/3.55 inference(unit_resolution,[status(thm)],[7142, 7135, 194, 308])).
% 3.34/3.55 tff(7144,plain,
% 3.34/3.55 (b(s(s(s(elem!1))), z)),
% 3.34/3.55 inference(unit_resolution,[status(thm)],[1565, 7143])).
% 3.34/3.55 tff(7145,plain,
% 3.34/3.55 (b(s(s(s(s(s(z))))), z)),
% 3.34/3.55 inference(modus_ponens,[status(thm)],[7144, 7075])).
% 3.34/3.55 tff(7146,plain,
% 3.34/3.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 3.34/3.55 inference(rewrite,[status(thm)],[])).
% 3.34/3.55 tff(7147,plain,
% 3.34/3.55 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 3.34/3.55 inference(rewrite,[status(thm)],[])).
% 3.34/3.55 tff(7148,plain,
% 3.34/3.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 3.34/3.55 inference(monotonicity,[status(thm)],[7147])).
% 3.34/3.55 tff(7149,plain,
% 3.34/3.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 3.34/3.55 inference(transitivity,[status(thm)],[7148, 7146])).
% 3.34/3.55 tff(7150,plain,
% 3.34/3.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 3.34/3.55 inference(quant_inst,[status(thm)],[])).
% 3.34/3.55 tff(7151,plain,
% 3.34/3.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 3.34/3.55 inference(modus_ponens,[status(thm)],[7150, 7149])).
% 3.34/3.55 tff(7152,plain,
% 3.34/3.55 ($false),
% 3.34/3.55 inference(unit_resolution,[status(thm)],[7151, 178, 3461, 7131, 7145, 7073, 7060])).
% 3.34/3.55 tff(7153,plain,(b(s(elem!1), elem!1) | (~b(s(s(z)), z)) | (~(elem!1 = s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(elem!1), s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(elem!1), z)) | (~r(z, elem!1)) | (~b(s(s(z)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.55 tff(7154,plain,
% 3.34/3.55 (b(s(elem!1), elem!1)),
% 3.34/3.55 inference(unit_resolution,[status(thm)],[7153, 308, 3461, 194, 167, 202, 7057, 356, 6752, 7054, 7047])).
% 3.34/3.55 tff(7155,plain,
% 3.34/3.55 (b(s(elem!1), s(s(z)))),
% 3.34/3.55 inference(modus_ponens,[status(thm)],[7154, 7046])).
% 3.34/3.55 tff(7156,plain,
% 3.34/3.55 (b(s(s(s(z))), s(s(z)))),
% 3.34/3.55 inference(modus_ponens,[status(thm)],[7155, 7045])).
% 3.34/3.55 tff(7157,plain,
% 3.34/3.55 (b(z, s(s(s(z)))) <=> b(z, s(elem!1))),
% 3.34/3.55 inference(symmetry,[status(thm)],[7061])).
% 3.34/3.55 tff(7158,plain,
% 3.34/3.55 ((~b(z, s(s(s(z))))) <=> (~b(z, s(elem!1)))),
% 3.34/3.55 inference(monotonicity,[status(thm)],[7157])).
% 3.34/3.55 tff(7159,plain,
% 3.34/3.55 (b(s(s(z)), s(s(s(z))))),
% 3.34/3.55 inference(modus_ponens,[status(thm)],[7047, 7059])).
% 3.34/3.55 tff(7160,plain,
% 3.34/3.55 (~b(z, s(s(s(z))))),
% 3.34/3.55 inference(unit_resolution,[status(thm)],[5098, 7159, 3461, 7156, 7043])).
% 3.34/3.55 tff(7161,plain,
% 3.34/3.55 (~b(z, s(elem!1))),
% 3.34/3.55 inference(modus_ponens,[status(thm)],[7160, 7158])).
% 3.34/3.55 tff(7162,plain,
% 3.34/3.55 (r(z, s(elem!1))),
% 3.34/3.55 inference(unit_resolution,[status(thm)],[2351, 7161])).
% 3.34/3.55 tff(7163,plain,
% 3.34/3.55 (~r(z, s(s(s(s(z)))))),
% 3.34/3.55 inference(unit_resolution,[status(thm)],[2766, 7162, 908])).
% 3.34/3.55 tff(7164,plain,
% 3.34/3.55 (b(z, s(s(s(s(z)))))),
% 3.34/3.55 inference(unit_resolution,[status(thm)],[46, 7163])).
% 3.34/3.55 tff(7165,plain,
% 3.34/3.55 ($false),
% 3.34/3.55 inference(unit_resolution,[status(thm)],[5967, 178, 3461, 7164, 167, 7156, 7043])).
% 3.34/3.55 tff(7166,plain,((~(elem!1 = s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(z, s(s(z)))) | r(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.55 tff(7167,plain,
% 3.34/3.55 (~(elem!1 = s(s(z)))),
% 3.34/3.55 inference(unit_resolution,[status(thm)],[7166, 7035, 3461, 908, 194, 202, 356, 3261, 744])).
% 3.34/3.55 tff(7168,plain,
% 3.34/3.55 (r(elem!1, s(s(z)))),
% 3.34/3.55 inference(unit_resolution,[status(thm)],[467, 7167, 461])).
% 3.34/3.55 tff(7169,plain,
% 3.34/3.55 (~r(z, elem!1)),
% 3.34/3.55 inference(unit_resolution,[status(thm)],[4862, 7168, 3261])).
% 3.34/3.55 tff(7170,plain,
% 3.34/3.55 (b(z, elem!1)),
% 3.34/3.55 inference(unit_resolution,[status(thm)],[585, 7169, 6992])).
% 3.34/3.55 tff(7171,plain,
% 3.34/3.55 (~b(z, s(elem!1))),
% 3.34/3.55 inference(unit_resolution,[status(thm)],[863, 7170, 506, 5725, 6752])).
% 3.34/3.55 tff(7172,plain,
% 3.34/3.55 (r(z, s(elem!1))),
% 3.34/3.55 inference(unit_resolution,[status(thm)],[2351, 7171])).
% 3.34/3.55 tff(7173,plain,
% 3.34/3.55 (~r(z, s(s(s(s(z)))))),
% 3.34/3.55 inference(unit_resolution,[status(thm)],[2766, 7172, 908])).
% 3.34/3.55 tff(7174,plain,
% 3.34/3.55 (b(z, s(s(s(s(z)))))),
% 3.34/3.55 inference(unit_resolution,[status(thm)],[46, 7173])).
% 3.34/3.55 tff(7175,plain,
% 3.34/3.55 (~b(s(s(s(s(z)))), elem!1)),
% 3.34/3.55 inference(unit_resolution,[status(thm)],[7020, 7174, 506, 7170, 1301])).
% 3.34/3.55 tff(7176,plain,
% 3.34/3.55 (r(s(s(s(s(z)))), elem!1)),
% 3.34/3.55 inference(unit_resolution,[status(thm)],[3142, 7175, 4510])).
% 3.34/3.55 tff(7177,plain,
% 3.34/3.55 (~r(s(elem!1), elem!1)),
% 3.34/3.55 inference(unit_resolution,[status(thm)],[7010, 7176, 908])).
% 3.34/3.55 tff(7178,plain,
% 3.34/3.55 (b(s(elem!1), elem!1)),
% 3.34/3.55 inference(unit_resolution,[status(thm)],[677, 7177, 1548])).
% 3.34/3.55 tff(7179,plain,
% 3.34/3.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 3.34/3.55 inference(rewrite,[status(thm)],[])).
% 3.34/3.55 tff(7180,plain,
% 3.34/3.55 (((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, 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(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 3.34/3.55 inference(rewrite,[status(thm)],[])).
% 3.34/3.55 tff(7181,plain,
% 3.34/3.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 3.34/3.55 inference(monotonicity,[status(thm)],[7180])).
% 3.34/3.55 tff(7182,plain,
% 3.34/3.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 3.34/3.55 inference(transitivity,[status(thm)],[7181, 7179])).
% 3.34/3.55 tff(7183,plain,
% 3.34/3.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)))),
% 3.34/3.55 inference(quant_inst,[status(thm)],[])).
% 3.34/3.55 tff(7184,plain,
% 3.34/3.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 3.34/3.55 inference(modus_ponens,[status(thm)],[7183, 7182])).
% 3.34/3.55 tff(7185,plain,
% 3.34/3.55 ($false),
% 3.34/3.55 inference(unit_resolution,[status(thm)],[7184, 178, 7170, 7178, 6752, 7174, 1301])).
% 3.34/3.55 tff(7186,plain,((~r(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~r(z, s(s(z)))) | b(elem!1, s(s(z))) | (~b(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (s(s(s(elem!1))) = s(elem!1)) | r(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.55 tff(7187,plain,
% 3.34/3.55 (~r(s(elem!1), s(s(s(s(z)))))),
% 3.34/3.55 inference(unit_resolution,[status(thm)],[7186, 3261, 506, 1301, 461, 3461, 194, 202, 356, 744])).
% 3.34/3.55 tff(7188,plain,
% 3.34/3.55 (s(elem!1) = s(s(s(s(z))))),
% 3.34/3.55 inference(unit_resolution,[status(thm)],[1084, 7187, 5720])).
% 3.34/3.55 tff(7189,plain,
% 3.34/3.55 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 3.34/3.55 inference(monotonicity,[status(thm)],[7188])).
% 3.34/3.55 tff(7190,plain,
% 3.34/3.55 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 3.34/3.55 inference(symmetry,[status(thm)],[7189])).
% 3.34/3.55 tff(7191,plain,
% 3.34/3.55 (s(s(s(z))) = elem!1),
% 3.34/3.55 inference(transitivity,[status(thm)],[61, 7190, 304])).
% 3.34/3.55 tff(7192,plain,
% 3.34/3.55 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 3.34/3.55 inference(monotonicity,[status(thm)],[7191])).
% 3.34/3.55 tff(7193,plain,
% 3.34/3.55 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 3.34/3.55 inference(symmetry,[status(thm)],[7192])).
% 3.34/3.55 tff(7194,plain,
% 3.34/3.55 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.34/3.55 inference(modus_ponens,[status(thm)],[1301, 7193])).
% 3.34/3.55 tff(7195,plain,
% 3.34/3.55 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 3.34/3.55 inference(monotonicity,[status(thm)],[1119])).
% 3.34/3.55 tff(7196,plain,
% 3.34/3.55 (r(s(s(z)), s(s(s(s(s(s(z))))))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 3.34/3.55 inference(symmetry,[status(thm)],[7195])).
% 3.34/3.55 tff(7197,plain,
% 3.34/3.55 ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) <=> (~r(s(s(z)), s(s(s(elem!1)))))),
% 3.34/3.55 inference(monotonicity,[status(thm)],[7196])).
% 3.34/3.55 tff(7198,plain,
% 3.34/3.55 (r(s(s(s(s(s(s(z)))))), s(s(s(z)))) <=> r(s(s(s(elem!1))), elem!1)),
% 3.34/3.55 inference(monotonicity,[status(thm)],[6036, 1183])).
% 3.34/3.55 tff(7199,plain,
% 3.34/3.55 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 3.34/3.55 inference(symmetry,[status(thm)],[7198])).
% 3.34/3.55 tff(7200,plain,
% 3.34/3.55 (~(s(s(elem!1)) = s(s(z)))),
% 3.34/3.55 inference(unit_resolution,[status(thm)],[2386, 6992])).
% 3.34/3.55 tff(7201,plain,
% 3.34/3.55 (~(elem!1 = s(s(s(elem!1))))),
% 3.34/3.55 inference(unit_resolution,[status(thm)],[2498, 1117, 7200])).
% 3.34/3.55 tff(7202,plain,
% 3.34/3.55 (~(s(s(s(elem!1))) = elem!1)),
% 3.34/3.55 inference(unit_resolution,[status(thm)],[2489, 7201])).
% 3.34/3.55 tff(7203,plain,
% 3.34/3.55 (~r(z, elem!1)),
% 3.34/3.55 inference(unit_resolution,[status(thm)],[4862, 450, 3261])).
% 3.34/3.55 tff(7204,plain,
% 3.34/3.55 (b(z, elem!1)),
% 3.34/3.55 inference(unit_resolution,[status(thm)],[585, 7203, 6992])).
% 3.34/3.55 tff(7205,plain,
% 3.34/3.55 (b(elem!1, z) <=> b(s(s(s(z))), z)),
% 3.34/3.55 inference(monotonicity,[status(thm)],[1218])).
% 3.34/3.55 tff(7206,plain,
% 3.34/3.55 (b(s(s(s(z))), z)),
% 3.34/3.55 inference(modus_ponens,[status(thm)],[506, 7205])).
% 3.34/3.55 tff(7207,plain,
% 3.34/3.55 (b(z, s(s(s(z))))),
% 3.34/3.55 inference(modus_ponens,[status(thm)],[7204, 1234])).
% 3.34/3.55 tff(7208,plain,
% 3.34/3.55 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 3.34/3.55 inference(monotonicity,[status(thm)],[2491])).
% 3.34/3.55 tff(7209,plain,
% 3.34/3.55 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.34/3.55 inference(symmetry,[status(thm)],[7208])).
% 3.34/3.55 tff(7210,plain,
% 3.34/3.55 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(s(s(elem!1))) = s(s(s(s(z))))))),
% 3.34/3.55 inference(monotonicity,[status(thm)],[7209])).
% 3.34/3.55 tff(7211,plain,
% 3.34/3.55 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.34/3.55 inference(modus_ponens,[status(thm)],[356, 7210])).
% 3.34/3.55 tff(7212,plain,
% 3.34/3.55 (~(s(s(z)) = elem!1)),
% 3.34/3.55 inference(unit_resolution,[status(thm)],[7053, 7203, 3261])).
% 3.34/3.55 tff(7213,plain,
% 3.34/3.55 (r(s(elem!1), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 3.34/3.55 inference(monotonicity,[status(thm)],[1117])).
% 3.34/3.55 tff(7214,plain,
% 3.34/3.55 (r(s(s(s(s(z)))), elem!1)),
% 3.34/3.55 inference(modus_ponens,[status(thm)],[1426, 7213])).
% 3.34/3.55 tff(7215,plain,
% 3.34/3.55 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), elem!1)),
% 3.34/3.55 inference(monotonicity,[status(thm)],[1183])).
% 3.34/3.55 tff(7216,plain,
% 3.34/3.55 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 3.34/3.55 inference(symmetry,[status(thm)],[7215])).
% 3.34/3.55 tff(7217,plain,
% 3.34/3.55 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.34/3.55 inference(modus_ponens,[status(thm)],[3132, 7216])).
% 3.34/3.55 tff(7218,assumption,(~r(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 3.34/3.55 tff(7219,plain,
% 3.34/3.55 ($false),
% 3.34/3.55 inference(unit_resolution,[status(thm)],[7218, 7217])).
% 3.34/3.55 tff(7220,plain,(r(s(s(s(s(z)))), s(s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~(s(elem!1) = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.55 tff(7221,plain,
% 3.34/3.55 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.34/3.55 inference(unit_resolution,[status(thm)],[7220, 7214, 1117])).
% 3.34/3.55 tff(7222,plain,
% 3.34/3.55 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(z)), elem!1)),
% 3.34/3.55 inference(monotonicity,[status(thm)],[1183])).
% 3.34/3.55 tff(7223,plain,
% 3.34/3.55 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(s(z))))),
% 3.34/3.55 inference(symmetry,[status(thm)],[7222])).
% 3.34/3.55 tff(7224,plain,
% 3.34/3.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 3.34/3.55 inference(rewrite,[status(thm)],[])).
% 3.34/3.55 tff(7225,plain,
% 3.34/3.55 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 3.34/3.55 inference(rewrite,[status(thm)],[])).
% 3.34/3.55 tff(7226,plain,
% 3.34/3.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 3.34/3.55 inference(monotonicity,[status(thm)],[7225])).
% 3.34/3.55 tff(7227,plain,
% 3.34/3.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 3.34/3.55 inference(transitivity,[status(thm)],[7226, 7224])).
% 3.34/3.55 tff(7228,plain,
% 3.34/3.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 3.34/3.55 inference(quant_inst,[status(thm)],[])).
% 3.34/3.55 tff(7229,plain,
% 3.34/3.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 3.34/3.55 inference(modus_ponens,[status(thm)],[7228, 7227])).
% 3.34/3.55 tff(7230,plain,
% 3.34/3.55 (~b(s(s(z)), s(s(s(z))))),
% 3.34/3.55 inference(unit_resolution,[status(thm)],[7229, 178, 3461, 6994, 1126, 1127])).
% 3.34/3.55 tff(7231,plain,
% 3.34/3.55 (~b(s(s(z)), elem!1)),
% 3.34/3.55 inference(modus_ponens,[status(thm)],[7230, 1221])).
% 3.34/3.55 tff(7232,plain,
% 3.34/3.55 (r(s(s(z)), elem!1)),
% 3.34/3.55 inference(unit_resolution,[status(thm)],[448, 7231, 12])).
% 3.34/3.55 tff(7233,plain,
% 3.34/3.55 (r(s(s(z)), s(s(s(z))))),
% 3.34/3.55 inference(modus_ponens,[status(thm)],[7232, 7223])).
% 3.34/3.55 tff(7234,plain,
% 3.34/3.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 3.34/3.55 inference(rewrite,[status(thm)],[])).
% 3.34/3.55 tff(7235,plain,
% 3.34/3.55 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 3.34/3.55 inference(rewrite,[status(thm)],[])).
% 3.34/3.55 tff(7236,plain,
% 3.34/3.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 3.34/3.55 inference(monotonicity,[status(thm)],[7235])).
% 3.34/3.55 tff(7237,plain,
% 3.34/3.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 3.34/3.55 inference(transitivity,[status(thm)],[7236, 7234])).
% 3.34/3.55 tff(7238,plain,
% 3.34/3.55 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.34/3.55 inference(quant_inst,[status(thm)],[])).
% 3.34/3.55 tff(7239,plain,
% 3.34/3.55 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 3.34/3.55 inference(modus_ponens,[status(thm)],[7238, 7237])).
% 3.34/3.55 tff(7240,plain,
% 3.34/3.55 ($false),
% 3.34/3.55 inference(unit_resolution,[status(thm)],[7239, 118, 147, 4953, 7233])).
% 3.34/3.55 tff(7241,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~(s(elem!1) = s(s(s(s(z)))))) | (s(s(z)) = elem!1) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.55 tff(7242,plain,
% 3.34/3.55 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.34/3.55 inference(unit_resolution,[status(thm)],[7241, 7221, 1117, 7212, 3461, 1126, 1127, 3261])).
% 3.34/3.55 tff(7243,plain,
% 3.34/3.55 (b(s(s(z)), s(s(s(s(z)))))),
% 3.34/3.55 inference(unit_resolution,[status(thm)],[164, 7242])).
% 3.34/3.55 tff(7244,plain,
% 3.34/3.55 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.34/3.55 inference(monotonicity,[status(thm)],[1117])).
% 3.34/3.55 tff(7245,plain,
% 3.34/3.55 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 3.34/3.55 inference(symmetry,[status(thm)],[7244])).
% 3.34/3.55 tff(7246,plain,
% 3.34/3.55 (b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.34/3.55 inference(monotonicity,[status(thm)],[6036])).
% 3.34/3.55 tff(7247,plain,
% 3.34/3.55 (b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 3.34/3.55 inference(transitivity,[status(thm)],[7246, 7245])).
% 3.34/3.55 tff(7248,plain,
% 3.34/3.55 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) <=> (~b(s(elem!1), s(s(s(elem!1)))))),
% 3.34/3.55 inference(monotonicity,[status(thm)],[7247])).
% 3.34/3.55 tff(7249,plain,
% 3.34/3.55 ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) <=> (~b(s(s(s(elem!1))), elem!1))),
% 3.34/3.55 inference(monotonicity,[status(thm)],[6152])).
% 3.34/3.55 tff(7250,plain,
% 3.34/3.55 (b(z, s(s(s(s(s(s(z))))))) <=> b(z, s(s(s(elem!1))))),
% 3.34/3.55 inference(symmetry,[status(thm)],[6075])).
% 3.34/3.55 tff(7251,plain,
% 3.34/3.55 ((~b(z, s(s(s(s(s(s(z)))))))) <=> (~b(z, s(s(s(elem!1)))))),
% 3.34/3.55 inference(monotonicity,[status(thm)],[7250])).
% 3.34/3.55 tff(7252,assumption,(b(s(s(s(s(s(s(z)))))), s(s(s(z))))), introduced(assumption)).
% 3.34/3.55 tff(7253,plain,
% 3.34/3.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 3.34/3.55 inference(rewrite,[status(thm)],[])).
% 3.34/3.55 tff(7254,plain,
% 3.34/3.55 (((~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(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(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(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 3.34/3.55 inference(rewrite,[status(thm)],[])).
% 3.34/3.55 tff(7255,plain,
% 3.34/3.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 3.34/3.55 inference(monotonicity,[status(thm)],[7254])).
% 3.34/3.56 tff(7256,plain,
% 3.34/3.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 3.34/3.56 inference(transitivity,[status(thm)],[7255, 7253])).
% 3.34/3.56 tff(7257,plain,
% 3.34/3.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 3.34/3.56 inference(quant_inst,[status(thm)],[])).
% 3.34/3.56 tff(7258,plain,
% 3.34/3.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 3.34/3.56 inference(modus_ponens,[status(thm)],[7257, 7256])).
% 3.34/3.56 tff(7259,plain,
% 3.34/3.56 ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 3.34/3.56 inference(unit_resolution,[status(thm)],[7258, 178, 6154, 1126, 3008])).
% 3.34/3.56 tff(7260,plain,
% 3.34/3.56 (~b(z, s(s(s(s(s(s(z)))))))),
% 3.34/3.56 inference(unit_resolution,[status(thm)],[7259, 7252])).
% 3.34/3.56 tff(7261,plain,
% 3.34/3.56 (~b(z, s(s(s(elem!1))))),
% 3.34/3.56 inference(modus_ponens,[status(thm)],[7260, 7251])).
% 3.34/3.56 tff(7262,plain,
% 3.34/3.56 (r(z, s(s(s(elem!1))))),
% 3.34/3.56 inference(unit_resolution,[status(thm)],[2095, 7261])).
% 3.34/3.56 tff(7263,plain,
% 3.34/3.56 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.34/3.56 inference(unit_resolution,[status(thm)],[4808, 7262, 3261])).
% 3.34/3.56 tff(7264,plain,
% 3.34/3.56 (b(s(s(z)), s(s(s(elem!1))))),
% 3.34/3.56 inference(unit_resolution,[status(thm)],[4223, 7263])).
% 3.34/3.56 tff(7265,assumption,(~b(s(s(z)), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 3.34/3.56 tff(7266,plain,
% 3.34/3.56 (~b(s(s(z)), s(s(s(elem!1))))),
% 3.34/3.56 inference(modus_ponens,[status(thm)],[7265, 6064])).
% 3.34/3.56 tff(7267,plain,
% 3.34/3.56 ($false),
% 3.34/3.56 inference(unit_resolution,[status(thm)],[4291, 7266])).
% 3.34/3.56 tff(7268,plain,(b(s(s(z)), s(s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~(s(elem!1) = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.56 tff(7269,plain,
% 3.34/3.56 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 3.34/3.56 inference(unit_resolution,[status(thm)],[7268, 7264, 1117])).
% 3.34/3.56 tff(7270,plain,
% 3.34/3.56 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 3.34/3.56 inference(monotonicity,[status(thm)],[6036])).
% 3.34/3.56 tff(7271,plain,
% 3.34/3.56 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.34/3.56 inference(transitivity,[status(thm)],[7270, 3289])).
% 3.34/3.56 tff(7272,plain,
% 3.34/3.56 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))),
% 3.34/3.56 inference(symmetry,[status(thm)],[7271])).
% 3.34/3.56 tff(7273,plain,
% 3.34/3.56 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(s(s(s(s(z))))))))),
% 3.34/3.56 inference(monotonicity,[status(thm)],[7272])).
% 3.34/3.56 tff(7274,plain,
% 3.34/3.56 (~(s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))),
% 3.34/3.56 inference(modus_ponens,[status(thm)],[2857, 7273])).
% 3.34/3.56 tff(7275,plain,
% 3.34/3.56 (r(s(s(s(s(s(s(z)))))), z) <=> r(s(s(s(elem!1))), z)),
% 3.34/3.56 inference(monotonicity,[status(thm)],[6036])).
% 3.34/3.56 tff(7276,plain,
% 3.34/3.56 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(s(s(z)))))), z)),
% 3.34/3.56 inference(symmetry,[status(thm)],[7275])).
% 3.34/3.56 tff(7277,plain,
% 3.34/3.56 ((~b(s(s(s(s(s(s(z)))))), z)) <=> (~b(s(s(s(elem!1))), z))),
% 3.34/3.56 inference(monotonicity,[status(thm)],[6065])).
% 3.34/3.56 tff(7278,plain,
% 3.34/3.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 3.34/3.56 inference(rewrite,[status(thm)],[])).
% 3.34/3.56 tff(7279,plain,
% 3.34/3.56 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 3.34/3.56 inference(rewrite,[status(thm)],[])).
% 3.34/3.56 tff(7280,plain,
% 3.34/3.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 3.34/3.56 inference(monotonicity,[status(thm)],[7279])).
% 3.34/3.56 tff(7281,plain,
% 3.34/3.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 3.34/3.56 inference(transitivity,[status(thm)],[7280, 7278])).
% 3.34/3.56 tff(7282,plain,
% 3.34/3.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 3.34/3.56 inference(quant_inst,[status(thm)],[])).
% 3.34/3.56 tff(7283,plain,
% 3.34/3.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 3.34/3.56 inference(modus_ponens,[status(thm)],[7282, 7281])).
% 3.34/3.56 tff(7284,plain,
% 3.34/3.56 ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 3.34/3.56 inference(unit_resolution,[status(thm)],[7283, 178, 3461, 3008, 7252])).
% 3.34/3.56 tff(7285,plain,
% 3.34/3.56 (~b(s(s(s(s(s(s(z)))))), z)),
% 3.34/3.56 inference(unit_resolution,[status(thm)],[7284, 7269])).
% 3.34/3.56 tff(7286,plain,
% 3.34/3.56 (~b(s(s(s(elem!1))), z)),
% 3.34/3.56 inference(modus_ponens,[status(thm)],[7285, 7277])).
% 3.34/3.56 tff(7287,plain,
% 3.34/3.56 (r(s(s(s(elem!1))), z)),
% 3.34/3.56 inference(unit_resolution,[status(thm)],[1565, 7286])).
% 3.34/3.56 tff(7288,plain,
% 3.34/3.56 (r(s(s(s(s(s(s(z)))))), z)),
% 3.34/3.56 inference(modus_ponens,[status(thm)],[7287, 7276])).
% 3.34/3.56 tff(7289,plain,
% 3.34/3.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 3.34/3.56 inference(rewrite,[status(thm)],[])).
% 3.34/3.56 tff(7290,plain,
% 3.34/3.56 (((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 3.34/3.56 inference(rewrite,[status(thm)],[])).
% 3.34/3.56 tff(7291,plain,
% 3.34/3.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 3.34/3.56 inference(monotonicity,[status(thm)],[7290])).
% 3.34/3.56 tff(7292,plain,
% 3.34/3.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 3.34/3.56 inference(transitivity,[status(thm)],[7291, 7289])).
% 3.34/3.56 tff(7293,plain,
% 3.34/3.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 3.34/3.56 inference(quant_inst,[status(thm)],[])).
% 3.34/3.56 tff(7294,plain,
% 3.34/3.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 3.34/3.56 inference(modus_ponens,[status(thm)],[7293, 7292])).
% 3.34/3.56 tff(7295,plain,
% 3.34/3.56 ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 3.34/3.56 inference(unit_resolution,[status(thm)],[7294, 118, 194])).
% 3.34/3.56 tff(7296,plain,
% 3.34/3.56 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 3.34/3.56 inference(unit_resolution,[status(thm)],[7295, 7288])).
% 3.34/3.56 tff(7297,plain,
% 3.34/3.56 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 3.34/3.56 inference(rewrite,[status(thm)],[])).
% 3.34/3.56 tff(7298,plain,
% 3.34/3.56 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 3.34/3.56 inference(quant_inst,[status(thm)],[])).
% 3.34/3.56 tff(7299,plain,
% 3.34/3.56 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 3.34/3.56 inference(modus_ponens,[status(thm)],[7298, 7297])).
% 3.34/3.56 tff(7300,plain,
% 3.34/3.56 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 3.34/3.56 inference(unit_resolution,[status(thm)],[7299, 41, 7296])).
% 3.34/3.56 tff(7301,plain,
% 3.34/3.56 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 3.34/3.56 inference(unit_resolution,[status(thm)],[7300, 7274])).
% 3.34/3.56 tff(7302,plain,
% 3.34/3.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 3.34/3.56 inference(rewrite,[status(thm)],[])).
% 3.34/3.56 tff(7303,plain,
% 3.34/3.56 (((~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(z)), s(s(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(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 3.34/3.56 inference(rewrite,[status(thm)],[])).
% 3.34/3.56 tff(7304,plain,
% 3.34/3.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), s(s(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(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 3.34/3.56 inference(monotonicity,[status(thm)],[7303])).
% 3.34/3.56 tff(7305,plain,
% 3.34/3.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), s(s(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(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 3.34/3.56 inference(transitivity,[status(thm)],[7304, 7302])).
% 3.34/3.56 tff(7306,plain,
% 3.34/3.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), s(s(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(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 3.34/3.56 inference(quant_inst,[status(thm)],[])).
% 3.34/3.56 tff(7307,plain,
% 3.34/3.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 3.34/3.56 inference(modus_ponens,[status(thm)],[7306, 7305])).
% 3.34/3.56 tff(7308,plain,
% 3.34/3.56 ($false),
% 3.34/3.56 inference(unit_resolution,[status(thm)],[7307, 178, 167, 202, 6154, 7301, 7269])).
% 3.34/3.56 tff(7309,plain,((~b(s(s(s(s(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(s(s(s(s(z)))))), s(s(s(s(z)))))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~(s(elem!1) = s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~r(z, s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.56 tff(7310,plain,
% 3.34/3.56 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 3.34/3.56 inference(unit_resolution,[status(thm)],[7309, 6154, 202, 167, 2857, 1117, 194, 3461, 3008, 3261, 1126])).
% 3.34/3.56 tff(7311,plain,
% 3.34/3.56 (~b(s(s(s(elem!1))), elem!1)),
% 3.34/3.56 inference(modus_ponens,[status(thm)],[7310, 7249])).
% 3.34/3.56 tff(7312,plain,
% 3.34/3.56 (r(s(s(s(elem!1))), elem!1)),
% 3.34/3.56 inference(unit_resolution,[status(thm)],[570, 7311, 949])).
% 3.34/3.56 tff(7313,plain,
% 3.34/3.56 (~r(s(s(s(elem!1))), s(s(z)))),
% 3.34/3.56 inference(unit_resolution,[status(thm)],[4205, 7312, 450])).
% 3.34/3.56 tff(7314,plain,
% 3.34/3.56 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 3.34/3.56 inference(unit_resolution,[status(thm)],[6165, 7313, 1117])).
% 3.34/3.56 tff(7315,plain,
% 3.34/3.56 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 3.34/3.56 inference(unit_resolution,[status(thm)],[6139, 7314, 6059])).
% 3.34/3.56 tff(7316,plain,
% 3.34/3.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 3.34/3.56 inference(rewrite,[status(thm)],[])).
% 3.34/3.56 tff(7317,plain,
% 3.34/3.56 (((~b(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(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(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(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(s(s(s(s(z)))))), s(s(z)))))),
% 3.34/3.56 inference(rewrite,[status(thm)],[])).
% 3.34/3.56 tff(7318,plain,
% 3.34/3.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(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(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 3.34/3.56 inference(monotonicity,[status(thm)],[7317])).
% 3.34/3.56 tff(7319,plain,
% 3.34/3.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(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(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 3.34/3.56 inference(transitivity,[status(thm)],[7318, 7316])).
% 3.34/3.56 tff(7320,plain,
% 3.34/3.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(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(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 3.34/3.56 inference(quant_inst,[status(thm)],[])).
% 3.34/3.56 tff(7321,plain,
% 3.34/3.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))),
% 3.34/3.56 inference(modus_ponens,[status(thm)],[7320, 7319])).
% 3.34/3.57 tff(7322,plain,
% 3.34/3.57 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[7321, 178, 167, 202, 6154])).
% 3.34/3.57 tff(7323,plain,
% 3.34/3.57 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[7322, 7315])).
% 3.34/3.57 tff(7324,plain,
% 3.34/3.57 (~b(s(elem!1), s(s(s(elem!1))))),
% 3.34/3.57 inference(modus_ponens,[status(thm)],[7323, 7248])).
% 3.34/3.57 tff(7325,plain,
% 3.34/3.57 (~r(s(elem!1), s(s(s(elem!1))))),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[2110, 7312, 1426])).
% 3.34/3.57 tff(7326,plain,
% 3.34/3.57 (b(s(elem!1), s(s(s(elem!1))))),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[5432, 7325, 5425])).
% 3.34/3.57 tff(7327,plain,
% 3.34/3.57 ($false),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[7326, 7324])).
% 3.34/3.57 tff(7328,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~(s(elem!1) = s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (s(elem!1) = s(s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(z)))) | (s(s(s(elem!1))) = elem!1) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~r(z, s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.57 tff(7329,plain,
% 3.34/3.57 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[7328, 7243, 1117, 202, 5396, 1426, 450, 949, 7211, 194, 3461, 3008, 3261, 1126])).
% 3.34/3.57 tff(7330,plain,
% 3.34/3.57 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.34/3.57 inference(modus_ponens,[status(thm)],[7329, 6041])).
% 3.34/3.57 tff(7331,plain,
% 3.34/3.57 (r(s(s(s(elem!1))), s(elem!1))),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[373, 7330, 356])).
% 3.34/3.57 tff(7332,plain,
% 3.34/3.57 (~r(s(s(s(elem!1))), z)),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[1557, 7331, 6062])).
% 3.34/3.57 tff(7333,plain,
% 3.34/3.57 (b(s(s(s(elem!1))), z)),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[1565, 7332])).
% 3.34/3.57 tff(7334,plain,
% 3.34/3.57 (b(s(s(s(s(s(s(z)))))), z)),
% 3.34/3.57 inference(modus_ponens,[status(thm)],[7333, 6066])).
% 3.34/3.57 tff(7335,plain,
% 3.34/3.57 (~r(s(s(s(elem!1))), elem!1)),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[1576, 7331, 1426])).
% 3.34/3.57 tff(7336,plain,
% 3.34/3.57 (b(s(s(s(elem!1))), elem!1)),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[570, 7335, 949])).
% 3.34/3.57 tff(7337,plain,
% 3.34/3.57 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 3.34/3.57 inference(modus_ponens,[status(thm)],[7336, 6153])).
% 3.34/3.57 tff(7338,plain,
% 3.34/3.57 (b(z, s(elem!1)) <=> b(z, s(s(s(s(z)))))),
% 3.34/3.57 inference(monotonicity,[status(thm)],[1117])).
% 3.34/3.57 tff(7339,plain,
% 3.34/3.57 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 3.34/3.57 inference(modus_ponens,[status(thm)],[1578, 6153])).
% 3.34/3.57 tff(7340,plain,
% 3.34/3.57 (b(z, s(s(s(elem!1))))),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[2095, 6270])).
% 3.34/3.57 tff(7341,plain,
% 3.34/3.57 (b(z, s(s(s(s(s(s(z)))))))),
% 3.34/3.57 inference(modus_ponens,[status(thm)],[7340, 6075])).
% 3.34/3.57 tff(7342,plain,
% 3.34/3.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 3.34/3.57 inference(rewrite,[status(thm)],[])).
% 3.34/3.57 tff(7343,plain,
% 3.34/3.57 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(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)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 3.34/3.57 inference(rewrite,[status(thm)],[])).
% 3.34/3.57 tff(7344,plain,
% 3.34/3.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 3.34/3.57 inference(monotonicity,[status(thm)],[7343])).
% 3.34/3.57 tff(7345,plain,
% 3.34/3.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 3.34/3.57 inference(transitivity,[status(thm)],[7344, 7342])).
% 3.34/3.57 tff(7346,plain,
% 3.34/3.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 3.34/3.57 inference(quant_inst,[status(thm)],[])).
% 3.34/3.57 tff(7347,plain,
% 3.34/3.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 3.34/3.57 inference(modus_ponens,[status(thm)],[7346, 7345])).
% 3.34/3.57 tff(7348,plain,
% 3.34/3.57 ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[7347, 178, 7341, 3008, 1127])).
% 3.34/3.57 tff(7349,plain,
% 3.34/3.57 ($false),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[7348, 7339, 6806])).
% 3.34/3.57 tff(7350,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~(s(elem!1) = s(s(s(s(z)))))) | (s(s(s(elem!1))) = elem!1) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.57 tff(7351,plain,
% 3.34/3.57 (~r(z, s(elem!1))),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[7350, 7331, 1127, 1117, 949, 6062, 1426, 3008])).
% 3.34/3.57 tff(7352,plain,
% 3.34/3.57 (b(z, s(elem!1))),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[2351, 7351])).
% 3.34/3.57 tff(7353,plain,
% 3.34/3.57 (b(z, s(s(s(s(z)))))),
% 3.34/3.57 inference(modus_ponens,[status(thm)],[7352, 7338])).
% 3.34/3.57 tff(7354,plain,
% 3.34/3.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 3.34/3.57 inference(rewrite,[status(thm)],[])).
% 3.34/3.57 tff(7355,plain,
% 3.34/3.57 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 3.34/3.57 inference(rewrite,[status(thm)],[])).
% 3.34/3.57 tff(7356,plain,
% 3.34/3.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 3.34/3.57 inference(monotonicity,[status(thm)],[7355])).
% 3.34/3.57 tff(7357,plain,
% 3.34/3.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 3.34/3.57 inference(transitivity,[status(thm)],[7356, 7354])).
% 3.34/3.57 tff(7358,plain,
% 3.34/3.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 3.34/3.57 inference(quant_inst,[status(thm)],[])).
% 3.34/3.57 tff(7359,plain,
% 3.34/3.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 3.34/3.57 inference(modus_ponens,[status(thm)],[7358, 7357])).
% 3.34/3.57 tff(7360,plain,
% 3.34/3.57 (~b(s(s(s(s(s(s(z)))))), z)),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[7359, 178, 7353, 1126, 3008, 7337])).
% 3.34/3.57 tff(7361,plain,
% 3.34/3.57 ($false),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[7360, 7334])).
% 3.34/3.57 tff(7362,plain,((~r(s(elem!1), elem!1)) | (~(s(elem!1) = s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (s(s(s(elem!1))) = elem!1) | (~b(s(s(s(z))), z)) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.57 tff(7363,plain,
% 3.34/3.57 (~r(s(elem!1), elem!1)),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[7362, 7207, 1126, 1117, 7202, 7206, 356, 202, 450, 194, 3461, 3261])).
% 3.34/3.57 tff(7364,plain,
% 3.34/3.57 (b(s(elem!1), elem!1)),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[677, 7363, 1548])).
% 3.34/3.57 tff(7365,plain,
% 3.34/3.57 (~b(z, s(elem!1))),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[1396, 7364, 854, 506, 7204])).
% 3.34/3.57 tff(7366,plain,
% 3.34/3.57 (r(z, s(elem!1))),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[2351, 7365])).
% 3.34/3.57 tff(7367,plain,
% 3.34/3.57 (r(z, s(s(s(s(z)))))),
% 3.34/3.57 inference(modus_ponens,[status(thm)],[2333, 6807])).
% 3.34/3.57 tff(7368,plain,
% 3.34/3.57 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[3478, 7367, 3261])).
% 3.34/3.57 tff(7369,plain,
% 3.34/3.57 (b(s(s(z)), s(s(s(s(z)))))),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[164, 7368])).
% 3.34/3.57 tff(7370,plain,
% 3.34/3.57 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 3.34/3.57 inference(modus_ponens,[status(thm)],[1597, 6153])).
% 3.34/3.57 tff(7371,plain,
% 3.34/3.57 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[7309, 7370, 202, 7369, 7211, 1117, 194, 3461, 3008, 3261, 1126])).
% 3.34/3.57 tff(7372,plain,
% 3.34/3.57 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.34/3.57 inference(modus_ponens,[status(thm)],[7371, 6041])).
% 3.34/3.57 tff(7373,plain,
% 3.34/3.57 (r(s(s(s(elem!1))), s(elem!1))),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[373, 7372, 356])).
% 3.34/3.57 tff(7374,plain,
% 3.34/3.57 (~r(s(s(s(elem!1))), z)),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[1557, 7373, 6062])).
% 3.34/3.57 tff(7375,plain,
% 3.34/3.57 (b(s(s(s(elem!1))), z)),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[1565, 7374])).
% 3.34/3.57 tff(7376,plain,
% 3.34/3.57 (b(s(s(s(s(s(s(z)))))), z)),
% 3.34/3.57 inference(modus_ponens,[status(thm)],[7375, 6066])).
% 3.34/3.57 tff(7377,plain,
% 3.34/3.57 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[5447, 557, 2333])).
% 3.34/3.57 tff(7378,plain,
% 3.34/3.57 (b(s(s(s(elem!1))), s(elem!1))),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[373, 7377, 356])).
% 3.34/3.57 tff(7379,plain,
% 3.34/3.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 3.34/3.57 inference(rewrite,[status(thm)],[])).
% 3.34/3.57 tff(7380,plain,
% 3.34/3.57 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 3.34/3.57 inference(rewrite,[status(thm)],[])).
% 3.34/3.57 tff(7381,plain,
% 3.34/3.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))))),
% 3.34/3.57 inference(monotonicity,[status(thm)],[7380])).
% 3.34/3.57 tff(7382,plain,
% 3.34/3.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 3.34/3.57 inference(transitivity,[status(thm)],[7381, 7379])).
% 3.34/3.57 tff(7383,plain,
% 3.34/3.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 3.34/3.57 inference(quant_inst,[status(thm)],[])).
% 3.34/3.57 tff(7384,plain,
% 3.34/3.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))),
% 3.34/3.57 inference(modus_ponens,[status(thm)],[7383, 7382])).
% 3.34/3.57 tff(7385,plain,
% 3.34/3.57 (~b(s(elem!1), s(s(s(elem!1))))),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[7384, 178, 7378, 683, 1597, 854])).
% 3.34/3.57 tff(7386,plain,
% 3.34/3.57 ((s(elem!1) = s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1))))),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[5430, 41, 7385])).
% 3.34/3.57 tff(7387,plain,
% 3.34/3.57 (r(s(elem!1), s(s(s(elem!1))))),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[7386, 7106])).
% 3.34/3.57 tff(7388,plain,
% 3.34/3.57 ($false),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[5411, 118, 2333, 557, 7387])).
% 3.34/3.57 tff(7389,plain,((~r(z, s(s(s(elem!1))))) | (~r(z, s(elem!1))) | (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(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.57 tff(7390,plain,
% 3.34/3.57 (~r(z, s(s(s(elem!1))))),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[7389, 1597, 854, 683, 356, 2333])).
% 3.34/3.57 tff(7391,plain,
% 3.34/3.57 (b(z, s(s(s(elem!1))))),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[2095, 7390])).
% 3.34/3.57 tff(7392,plain,
% 3.34/3.57 (b(z, s(s(s(s(s(s(z)))))))),
% 3.34/3.57 inference(modus_ponens,[status(thm)],[7391, 6075])).
% 3.34/3.57 tff(7393,plain,
% 3.34/3.57 ($false),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[7347, 178, 7392, 3008, 1127, 7370, 7376])).
% 3.34/3.57 tff(7394,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~(s(elem!1) = s(s(s(s(z)))))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~r(z, s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.57 tff(7395,plain,
% 3.34/3.57 (~b(s(s(s(elem!1))), elem!1)),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[7394, 7207, 7206, 1117, 356, 202, 194, 3461, 3261, 1126, 854, 7364, 7366])).
% 3.34/3.57 tff(7396,plain,
% 3.34/3.57 (r(s(s(s(elem!1))), elem!1)),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[570, 7395, 7202])).
% 3.34/3.57 tff(7397,plain,
% 3.34/3.57 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 3.34/3.57 inference(modus_ponens,[status(thm)],[7396, 7199])).
% 3.34/3.57 tff(7398,plain,
% 3.34/3.57 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.34/3.57 inference(modus_ponens,[status(thm)],[7364, 1280])).
% 3.34/3.57 tff(7399,plain,
% 3.34/3.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 3.34/3.57 inference(rewrite,[status(thm)],[])).
% 3.34/3.57 tff(7400,plain,
% 3.34/3.57 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 3.34/3.57 inference(rewrite,[status(thm)],[])).
% 3.34/3.57 tff(7401,plain,
% 3.34/3.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 3.34/3.57 inference(monotonicity,[status(thm)],[7400])).
% 3.34/3.57 tff(7402,plain,
% 3.34/3.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 3.34/3.57 inference(transitivity,[status(thm)],[7401, 7399])).
% 3.34/3.57 tff(7403,plain,
% 3.34/3.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 3.34/3.57 inference(quant_inst,[status(thm)],[])).
% 3.34/3.57 tff(7404,plain,
% 3.34/3.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 3.34/3.57 inference(modus_ponens,[status(thm)],[7403, 7402])).
% 3.34/3.57 tff(7405,plain,
% 3.34/3.57 (~b(s(s(z)), s(s(s(z))))),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[7404, 178, 3461, 202, 7398, 7206])).
% 3.34/3.57 tff(7406,plain,
% 3.34/3.57 (~b(s(s(z)), elem!1)),
% 3.34/3.57 inference(modus_ponens,[status(thm)],[7405, 1221])).
% 3.34/3.57 tff(7407,plain,
% 3.34/3.57 (r(s(s(z)), elem!1)),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[448, 7406, 7212])).
% 3.34/3.57 tff(7408,plain,
% 3.34/3.57 (r(s(s(z)), s(s(s(z))))),
% 3.34/3.57 inference(modus_ponens,[status(thm)],[7407, 7223])).
% 3.34/3.57 tff(7409,plain,
% 3.34/3.57 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 3.34/3.57 inference(rewrite,[status(thm)],[])).
% 3.34/3.57 tff(7410,plain,
% 3.34/3.57 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 3.34/3.57 inference(quant_inst,[status(thm)],[])).
% 3.34/3.57 tff(7411,plain,
% 3.34/3.57 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 3.34/3.57 inference(modus_ponens,[status(thm)],[7410, 7409])).
% 3.34/3.57 tff(7412,plain,
% 3.34/3.57 ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[7411, 118, 7408])).
% 3.34/3.57 tff(7413,plain,
% 3.34/3.57 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[7412, 7397])).
% 3.34/3.57 tff(7414,plain,
% 3.34/3.57 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.34/3.57 inference(modus_ponens,[status(thm)],[7413, 7197])).
% 3.34/3.57 tff(7415,plain,
% 3.34/3.57 (b(s(s(z)), s(s(s(elem!1))))),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[4223, 7414])).
% 3.34/3.57 tff(7416,plain,
% 3.34/3.57 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[7268, 7415, 1117])).
% 3.34/3.57 tff(7417,plain,
% 3.34/3.57 (~r(s(s(s(elem!1))), s(s(z)))),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[4205, 7396, 450])).
% 3.34/3.57 tff(7418,plain,
% 3.34/3.57 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[6165, 7417, 1117])).
% 3.34/3.57 tff(7419,plain,
% 3.34/3.57 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[6139, 7418, 6059])).
% 3.34/3.57 tff(7420,plain,
% 3.34/3.57 (r(z, s(s(s(s(z)))))),
% 3.34/3.57 inference(modus_ponens,[status(thm)],[7366, 6807])).
% 3.34/3.57 tff(7421,plain,
% 3.34/3.57 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[3478, 7420, 3261])).
% 3.34/3.57 tff(7422,plain,
% 3.34/3.57 (b(s(s(z)), s(s(s(s(z)))))),
% 3.34/3.57 inference(unit_resolution,[status(thm)],[164, 7421])).
% 3.34/3.57 tff(7423,plain,
% 3.34/3.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 3.34/3.58 inference(rewrite,[status(thm)],[])).
% 3.34/3.58 tff(7424,plain,
% 3.34/3.58 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 3.34/3.58 inference(rewrite,[status(thm)],[])).
% 3.34/3.58 tff(7425,plain,
% 3.34/3.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 3.34/3.58 inference(monotonicity,[status(thm)],[7424])).
% 3.34/3.58 tff(7426,plain,
% 3.34/3.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 3.34/3.58 inference(transitivity,[status(thm)],[7425, 7423])).
% 3.34/3.58 tff(7427,plain,
% 3.34/3.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 3.34/3.58 inference(quant_inst,[status(thm)],[])).
% 3.34/3.58 tff(7428,plain,
% 3.34/3.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))),
% 3.34/3.58 inference(modus_ponens,[status(thm)],[7427, 7426])).
% 3.34/3.58 tff(7429,plain,
% 3.34/3.58 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[7428, 178, 7422, 202, 7419])).
% 3.34/3.58 tff(7430,plain,
% 3.34/3.58 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[7429, 7416])).
% 3.34/3.58 tff(7431,plain,
% 3.34/3.58 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.34/3.58 inference(modus_ponens,[status(thm)],[7430, 6041])).
% 3.34/3.58 tff(7432,plain,
% 3.34/3.58 (r(s(s(s(elem!1))), s(elem!1))),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[373, 7431, 356])).
% 3.34/3.58 tff(7433,plain,
% 3.34/3.58 (~r(s(s(s(elem!1))), z)),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[1557, 7432, 6062])).
% 3.34/3.58 tff(7434,plain,
% 3.34/3.58 (b(s(s(s(elem!1))), z)),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[1565, 7433])).
% 3.34/3.58 tff(7435,plain,
% 3.34/3.58 (b(s(s(s(s(s(s(z)))))), z)),
% 3.34/3.58 inference(modus_ponens,[status(thm)],[7434, 6066])).
% 3.34/3.58 tff(7436,plain,
% 3.34/3.58 (~r(z, s(s(s(elem!1))))),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[5447, 7432, 7366])).
% 3.34/3.58 tff(7437,plain,
% 3.34/3.58 (b(z, s(s(s(elem!1))))),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[2095, 7436])).
% 3.34/3.58 tff(7438,plain,
% 3.34/3.58 (b(z, s(s(s(s(s(s(z)))))))),
% 3.34/3.58 inference(modus_ponens,[status(thm)],[7437, 6075])).
% 3.34/3.58 tff(7439,plain,
% 3.34/3.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 3.34/3.58 inference(rewrite,[status(thm)],[])).
% 3.34/3.58 tff(7440,plain,
% 3.34/3.58 (((~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 3.34/3.58 inference(rewrite,[status(thm)],[])).
% 3.34/3.58 tff(7441,plain,
% 3.34/3.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 3.34/3.58 inference(monotonicity,[status(thm)],[7440])).
% 3.34/3.58 tff(7442,plain,
% 3.34/3.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 3.34/3.58 inference(transitivity,[status(thm)],[7441, 7439])).
% 3.34/3.58 tff(7443,plain,
% 3.34/3.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 3.34/3.58 inference(quant_inst,[status(thm)],[])).
% 3.34/3.58 tff(7444,plain,
% 3.34/3.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))),
% 3.34/3.58 inference(modus_ponens,[status(thm)],[7443, 7442])).
% 3.34/3.58 tff(7445,plain,
% 3.34/3.58 (~b(s(s(s(s(s(s(z)))))), z)),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[7444, 178, 3461, 7438, 7419, 7416])).
% 3.34/3.58 tff(7446,plain,
% 3.34/3.58 ($false),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[7445, 7435])).
% 3.34/3.58 tff(7447,plain,((~r(elem!1, s(s(z)))) | (~(s(elem!1) = s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.58 tff(7448,plain,
% 3.34/3.58 (~r(elem!1, s(s(z)))),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[7447, 7188, 3461, 356, 202, 194, 3261, 7194, 5725, 506])).
% 3.34/3.58 tff(7449,plain,
% 3.34/3.58 (elem!1 = s(s(z))),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[467, 7448, 461])).
% 3.34/3.58 tff(7450,plain,
% 3.34/3.58 (s(s(s(z))) = s(s(z))),
% 3.34/3.58 inference(transitivity,[status(thm)],[61, 7190, 304, 7449])).
% 3.34/3.58 tff(7451,plain,
% 3.34/3.58 (s(s(s(s(z)))) = s(s(s(z)))),
% 3.34/3.58 inference(monotonicity,[status(thm)],[7450])).
% 3.34/3.58 tff(7452,plain,
% 3.34/3.58 (s(s(s(s(z)))) = elem!1),
% 3.34/3.58 inference(transitivity,[status(thm)],[7451, 61, 7190, 304])).
% 3.34/3.58 tff(7453,plain,
% 3.34/3.58 ($false),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[4510, 7452])).
% 3.34/3.58 tff(7454,plain,((~r(z, s(s(z)))) | b(elem!1, s(s(z))) | (~b(s(s(z)), z)) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | b(s(elem!1), s(s(s(s(z))))) | r(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.58 tff(7455,plain,
% 3.34/3.58 (~r(z, s(s(z)))),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[7454, 202, 5619, 356, 461, 3244, 6985, 5722, 5720, 744])).
% 3.34/3.58 tff(7456,plain,
% 3.34/3.58 (b(z, s(s(z)))),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[143, 7455])).
% 3.34/3.58 tff(7457,plain,
% 3.34/3.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 3.34/3.58 inference(rewrite,[status(thm)],[])).
% 3.34/3.58 tff(7458,plain,
% 3.34/3.58 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, z))) <=> ((~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 3.34/3.58 inference(rewrite,[status(thm)],[])).
% 3.34/3.58 tff(7459,plain,
% 3.34/3.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))))),
% 3.34/3.58 inference(monotonicity,[status(thm)],[7458])).
% 3.34/3.58 tff(7460,plain,
% 3.34/3.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 3.34/3.58 inference(transitivity,[status(thm)],[7459, 7457])).
% 3.34/3.58 tff(7461,plain,
% 3.34/3.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, z)))),
% 3.34/3.58 inference(quant_inst,[status(thm)],[])).
% 3.34/3.58 tff(7462,plain,
% 3.34/3.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))),
% 3.34/3.58 inference(modus_ponens,[status(thm)],[7461, 7460])).
% 3.34/3.58 tff(7463,plain,
% 3.34/3.58 (~b(z, s(s(s(s(z)))))),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[7462, 178, 6985, 7456, 5722, 202])).
% 3.34/3.58 tff(7464,plain,
% 3.34/3.58 (r(z, s(s(s(s(z)))))),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[46, 7463])).
% 3.34/3.58 tff(7465,plain,
% 3.34/3.58 (~r(z, s(elem!1))),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[2766, 908, 145])).
% 3.34/3.58 tff(7466,plain,
% 3.34/3.58 (b(z, s(elem!1))),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[2351, 7465])).
% 3.34/3.58 tff(7467,plain,
% 3.34/3.58 (~b(s(elem!1), s(s(z)))),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[6363, 178, 7466, 6752, 3461, 273])).
% 3.34/3.58 tff(7468,plain,
% 3.34/3.58 (~b(s(s(z)), s(elem!1))),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[6788, 178, 7466, 6752, 3461, 273])).
% 3.34/3.58 tff(7469,plain,
% 3.34/3.58 (~(s(s(z)) = elem!1)),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[1337, 7468, 725, 744])).
% 3.34/3.58 tff(7470,plain,
% 3.34/3.58 (~(elem!1 = s(s(z)))),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[311, 7469])).
% 3.34/3.58 tff(7471,plain,
% 3.34/3.58 (r(elem!1, s(s(z)))),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[467, 7470, 461])).
% 3.34/3.58 tff(7472,plain,
% 3.34/3.58 (~(s(elem!1) = s(s(z)))),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[1047, 7471, 744])).
% 3.34/3.58 tff(7473,plain,
% 3.34/3.58 (r(s(elem!1), s(s(z)))),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[421, 7472, 7467])).
% 3.34/3.58 tff(7474,plain,
% 3.34/3.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 3.34/3.58 inference(rewrite,[status(thm)],[])).
% 3.34/3.58 tff(7475,plain,
% 3.34/3.58 (((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 3.34/3.58 inference(rewrite,[status(thm)],[])).
% 3.34/3.58 tff(7476,plain,
% 3.34/3.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))))),
% 3.34/3.58 inference(monotonicity,[status(thm)],[7475])).
% 3.34/3.58 tff(7477,plain,
% 3.34/3.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 3.34/3.58 inference(transitivity,[status(thm)],[7476, 7474])).
% 3.34/3.58 tff(7478,plain,
% 3.34/3.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)))),
% 3.34/3.58 inference(quant_inst,[status(thm)],[])).
% 3.34/3.58 tff(7479,plain,
% 3.34/3.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))),
% 3.34/3.58 inference(modus_ponens,[status(thm)],[7478, 7477])).
% 3.34/3.58 tff(7480,plain,
% 3.34/3.58 (~b(s(s(z)), elem!1)),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[7479, 178, 506, 7466, 757, 3461])).
% 3.34/3.58 tff(7481,plain,
% 3.34/3.58 (r(s(s(z)), elem!1)),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[448, 7469, 7480])).
% 3.34/3.58 tff(7482,plain,
% 3.34/3.58 (~b(s(elem!1), elem!1)),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[2479, 178, 506, 7466, 757, 6752])).
% 3.34/3.58 tff(7483,plain,
% 3.34/3.58 (r(s(elem!1), elem!1)),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[677, 7482, 725])).
% 3.34/3.58 tff(7484,plain,
% 3.34/3.58 ($false),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[2247, 118, 7483, 7481, 7473])).
% 3.34/3.58 tff(7485,plain,((~r(s(elem!1), s(s(s(s(z)))))) | r(elem!1, s(elem!1)) | b(elem!1, s(s(z))) | (s(elem!1) = elem!1) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.58 tff(7486,plain,
% 3.34/3.58 (~r(s(elem!1), s(s(s(s(z)))))),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[7485, 7456, 461, 1548, 5619, 744, 6985, 7464, 3244])).
% 3.34/3.58 tff(7487,plain,
% 3.34/3.58 (s(elem!1) = s(s(s(s(z))))),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[1084, 7486, 5720])).
% 3.34/3.58 tff(7488,plain,
% 3.34/3.58 (r(s(elem!1), z) <=> r(s(s(s(s(z)))), z)),
% 3.34/3.58 inference(monotonicity,[status(thm)],[7487])).
% 3.34/3.58 tff(7489,plain,
% 3.34/3.58 (r(s(s(s(s(z)))), z) <=> r(s(elem!1), z)),
% 3.34/3.58 inference(symmetry,[status(thm)],[7488])).
% 3.34/3.58 tff(7490,plain,
% 3.34/3.58 (r(s(elem!1), z)),
% 3.34/3.58 inference(modus_ponens,[status(thm)],[3244, 7489])).
% 3.34/3.58 tff(7491,plain,
% 3.34/3.58 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 3.34/3.58 inference(monotonicity,[status(thm)],[7487])).
% 3.34/3.58 tff(7492,plain,
% 3.34/3.58 (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))),
% 3.34/3.58 inference(monotonicity,[status(thm)],[7491])).
% 3.34/3.58 tff(7493,plain,
% 3.34/3.58 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 3.34/3.58 inference(monotonicity,[status(thm)],[7492, 7487])).
% 3.34/3.58 tff(7494,plain,
% 3.34/3.58 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 3.34/3.58 inference(symmetry,[status(thm)],[7493])).
% 3.34/3.58 tff(7495,plain,
% 3.34/3.58 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 3.34/3.58 inference(monotonicity,[status(thm)],[7494])).
% 3.34/3.58 tff(7496,plain,
% 3.34/3.58 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 3.34/3.58 inference(monotonicity,[status(thm)],[7492])).
% 3.34/3.58 tff(7497,plain,
% 3.34/3.58 (r(s(s(z)), s(s(s(s(s(s(z))))))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 3.34/3.58 inference(symmetry,[status(thm)],[7496])).
% 3.34/3.58 tff(7498,plain,
% 3.34/3.58 ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) <=> (~r(s(s(z)), s(s(s(elem!1)))))),
% 3.34/3.58 inference(monotonicity,[status(thm)],[7497])).
% 3.34/3.58 tff(7499,plain,
% 3.34/3.58 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 3.34/3.58 inference(monotonicity,[status(thm)],[7487])).
% 3.34/3.58 tff(7500,plain,
% 3.34/3.58 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 3.34/3.58 inference(symmetry,[status(thm)],[7499])).
% 3.34/3.58 tff(7501,plain,
% 3.34/3.58 (s(s(s(z))) = elem!1),
% 3.34/3.58 inference(transitivity,[status(thm)],[61, 7500, 304])).
% 3.34/3.58 tff(7502,plain,
% 3.34/3.58 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 3.34/3.58 inference(symmetry,[status(thm)],[7492])).
% 3.34/3.58 tff(7503,plain,
% 3.34/3.58 (r(s(s(s(s(s(s(z)))))), s(s(s(z)))) <=> r(s(s(s(elem!1))), elem!1)),
% 3.34/3.58 inference(monotonicity,[status(thm)],[7502, 7501])).
% 3.34/3.58 tff(7504,plain,
% 3.34/3.58 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 3.34/3.58 inference(symmetry,[status(thm)],[7503])).
% 3.34/3.58 tff(7505,plain,
% 3.34/3.58 (~(z = elem!1)),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[6991, 6985])).
% 3.34/3.58 tff(7506,plain,
% 3.34/3.58 (~(s(s(elem!1)) = s(s(z)))),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[2386, 7505])).
% 3.34/3.58 tff(7507,plain,
% 3.34/3.58 (~(elem!1 = s(s(s(elem!1))))),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[2498, 7487, 7506])).
% 3.34/3.58 tff(7508,plain,
% 3.34/3.58 (~(s(s(s(elem!1))) = elem!1)),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[2489, 7507])).
% 3.34/3.58 tff(7509,plain,
% 3.34/3.58 (~(elem!1 = s(s(z)))),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[1353, 4510, 7487])).
% 3.34/3.58 tff(7510,plain,
% 3.34/3.58 (r(elem!1, s(s(z)))),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[467, 7509, 461])).
% 3.34/3.58 tff(7511,plain,
% 3.34/3.58 (r(z, s(elem!1)) <=> r(z, s(s(s(s(z)))))),
% 3.34/3.58 inference(monotonicity,[status(thm)],[7487])).
% 3.34/3.58 tff(7512,plain,
% 3.34/3.58 (r(z, s(s(s(s(z))))) <=> r(z, s(elem!1))),
% 3.34/3.58 inference(symmetry,[status(thm)],[7511])).
% 3.34/3.58 tff(7513,plain,
% 3.34/3.58 (r(z, s(elem!1))),
% 3.34/3.58 inference(modus_ponens,[status(thm)],[7464, 7512])).
% 3.34/3.58 tff(7514,plain,
% 3.34/3.58 (elem!1 = s(s(s(z)))),
% 3.34/3.58 inference(transitivity,[status(thm)],[517, 7499, 11])).
% 3.34/3.58 tff(7515,plain,
% 3.34/3.58 (b(elem!1, z) <=> b(s(s(s(z))), z)),
% 3.34/3.58 inference(monotonicity,[status(thm)],[7514])).
% 3.34/3.58 tff(7516,plain,
% 3.34/3.58 (b(s(s(s(z))), z)),
% 3.34/3.58 inference(modus_ponens,[status(thm)],[6985, 7515])).
% 3.34/3.58 tff(7517,plain,
% 3.34/3.58 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 3.34/3.58 inference(monotonicity,[status(thm)],[7501])).
% 3.34/3.58 tff(7518,plain,
% 3.34/3.58 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 3.34/3.58 inference(symmetry,[status(thm)],[7517])).
% 3.34/3.58 tff(7519,plain,
% 3.34/3.58 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.34/3.58 inference(modus_ponens,[status(thm)],[5722, 7518])).
% 3.34/3.58 tff(7520,plain,
% 3.34/3.58 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(z)), elem!1)),
% 3.34/3.58 inference(monotonicity,[status(thm)],[7501])).
% 3.34/3.58 tff(7521,plain,
% 3.34/3.58 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(s(z))))),
% 3.34/3.58 inference(symmetry,[status(thm)],[7520])).
% 3.34/3.58 tff(7522,plain,
% 3.34/3.58 (~(s(s(z)) = elem!1)),
% 3.34/3.58 inference(modus_ponens,[status(thm)],[7509, 5676])).
% 3.34/3.58 tff(7523,plain,
% 3.34/3.58 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(z))))),
% 3.34/3.58 inference(monotonicity,[status(thm)],[7514])).
% 3.34/3.58 tff(7524,plain,
% 3.34/3.58 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), elem!1)),
% 3.34/3.58 inference(symmetry,[status(thm)],[7523])).
% 3.34/3.58 tff(7525,plain,
% 3.34/3.58 ((~b(s(s(z)), s(s(s(z))))) <=> (~b(s(s(z)), elem!1))),
% 3.34/3.58 inference(monotonicity,[status(thm)],[7524])).
% 3.34/3.58 tff(7526,plain,
% 3.34/3.58 (~(elem!1 = s(s(s(elem!1))))),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[2498, 1117, 2387])).
% 3.34/3.58 tff(7527,plain,
% 3.34/3.58 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 3.34/3.58 inference(monotonicity,[status(thm)],[1119, 1218])).
% 3.34/3.58 tff(7528,plain,
% 3.34/3.58 (~(s(s(s(elem!1))) = elem!1)),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[2489, 7526])).
% 3.34/3.58 tff(7529,plain,
% 3.34/3.58 (r(z, s(elem!1))),
% 3.34/3.58 inference(modus_ponens,[status(thm)],[145, 6808])).
% 3.34/3.58 tff(7530,plain,
% 3.34/3.58 (~r(s(elem!1), elem!1)),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[7070, 521, 7529])).
% 3.34/3.58 tff(7531,plain,
% 3.34/3.58 (b(s(elem!1), elem!1)),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[677, 7530, 1548])).
% 3.34/3.58 tff(7532,plain,
% 3.34/3.58 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.34/3.58 inference(modus_ponens,[status(thm)],[7531, 1280])).
% 3.34/3.58 tff(7533,plain,
% 3.34/3.58 (~b(s(s(z)), s(s(s(z))))),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[7404, 178, 3461, 202, 7532, 1127])).
% 3.34/3.58 tff(7534,plain,
% 3.34/3.58 (~b(s(s(z)), elem!1)),
% 3.34/3.58 inference(modus_ponens,[status(thm)],[7533, 1221])).
% 3.34/3.58 tff(7535,plain,
% 3.34/3.58 (r(s(s(z)), elem!1)),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[448, 7534, 12])).
% 3.34/3.58 tff(7536,plain,
% 3.34/3.58 (~r(s(s(s(elem!1))), elem!1)),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[6388, 7535, 3461, 521, 273])).
% 3.34/3.58 tff(7537,plain,
% 3.34/3.58 (b(s(s(s(elem!1))), elem!1)),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[570, 7536, 7528])).
% 3.34/3.58 tff(7538,plain,
% 3.34/3.58 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 3.34/3.58 inference(modus_ponens,[status(thm)],[7537, 7527])).
% 3.34/3.58 tff(7539,plain,
% 3.34/3.58 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(z)), s(elem!1))),
% 3.34/3.58 inference(symmetry,[status(thm)],[6183])).
% 3.34/3.58 tff(7540,plain,
% 3.34/3.58 (r(s(s(z)), s(elem!1))),
% 3.34/3.58 inference(modus_ponens,[status(thm)],[147, 7539])).
% 3.34/3.58 tff(7541,plain,
% 3.34/3.58 (~(s(s(z)) = elem!1)),
% 3.34/3.58 inference(unit_resolution,[status(thm)],[1331, 7540, 744])).
% 3.34/3.59 tff(7542,plain,
% 3.34/3.59 (r(s(s(z)), elem!1)),
% 3.34/3.59 inference(unit_resolution,[status(thm)],[448, 7541, 3241])).
% 3.34/3.59 tff(7543,plain,
% 3.34/3.59 (~r(s(s(s(elem!1))), elem!1)),
% 3.34/3.59 inference(unit_resolution,[status(thm)],[6388, 7542, 3461, 521, 273])).
% 3.34/3.59 tff(7544,plain,
% 3.34/3.59 (b(s(s(s(elem!1))), elem!1)),
% 3.34/3.59 inference(unit_resolution,[status(thm)],[570, 7543, 6403])).
% 3.34/3.59 tff(7545,plain,
% 3.34/3.59 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 3.34/3.59 inference(modus_ponens,[status(thm)],[7544, 7527])).
% 3.34/3.59 tff(7546,plain,
% 3.34/3.59 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.34/3.59 inference(unit_resolution,[status(thm)],[6297, 7540, 3461, 273, 7529])).
% 3.34/3.59 tff(7547,plain,
% 3.34/3.59 (b(s(s(s(elem!1))), s(elem!1))),
% 3.34/3.59 inference(unit_resolution,[status(thm)],[373, 7546, 356])).
% 3.34/3.59 tff(7548,plain,
% 3.34/3.59 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 3.34/3.59 inference(modus_ponens,[status(thm)],[7547, 6039])).
% 3.34/3.59 tff(7549,plain,
% 3.34/3.59 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 3.34/3.59 inference(unit_resolution,[status(thm)],[6176, 178, 7548, 1126, 7532, 7545])).
% 3.34/3.59 tff(7550,plain,
% 3.34/3.59 (~b(elem!1, s(s(s(elem!1))))),
% 3.34/3.59 inference(unit_resolution,[status(thm)],[6974, 7549, 1117])).
% 3.34/3.59 tff(7551,plain,
% 3.34/3.59 (r(elem!1, s(s(s(elem!1))))),
% 3.34/3.59 inference(unit_resolution,[status(thm)],[2054, 7550, 1586])).
% 3.34/3.59 tff(7552,plain,
% 3.34/3.59 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 3.34/3.59 inference(modus_ponens,[status(thm)],[7551, 6795])).
% 3.34/3.59 tff(7553,plain,
% 3.34/3.59 (s(s(s(s(s(s(s(z))))))) = s(s(s(s(elem!1))))),
% 3.34/3.59 inference(symmetry,[status(thm)],[1120])).
% 3.34/3.59 tff(7554,plain,
% 3.34/3.59 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.34/3.59 inference(monotonicity,[status(thm)],[7553, 6036])).
% 3.34/3.59 tff(7555,plain,
% 3.34/3.59 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 3.34/3.59 inference(symmetry,[status(thm)],[7554])).
% 3.34/3.59 tff(7556,plain,
% 3.34/3.59 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 3.34/3.59 inference(monotonicity,[status(thm)],[1120, 1119])).
% 3.34/3.59 tff(7557,plain,
% 3.34/3.59 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.34/3.59 inference(symmetry,[status(thm)],[7556])).
% 3.34/3.59 tff(7558,plain,
% 3.34/3.59 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) <=> (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 3.34/3.59 inference(monotonicity,[status(thm)],[7557])).
% 3.34/3.59 tff(7559,plain,
% 3.34/3.59 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.34/3.59 inference(unit_resolution,[status(thm)],[3488, 147, 3461, 145])).
% 3.34/3.59 tff(7560,plain,
% 3.34/3.59 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.34/3.59 inference(unit_resolution,[status(thm)],[84, 7559])).
% 3.34/3.59 tff(7561,plain,
% 3.34/3.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))),
% 3.34/3.59 inference(rewrite,[status(thm)],[])).
% 3.34/3.59 tff(7562,plain,
% 3.34/3.59 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(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(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), 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(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))),
% 3.34/3.59 inference(rewrite,[status(thm)],[])).
% 3.34/3.59 tff(7563,plain,
% 3.34/3.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(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(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))))))),
% 3.34/3.59 inference(monotonicity,[status(thm)],[7562])).
% 3.34/3.59 tff(7564,plain,
% 3.34/3.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(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(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))),
% 3.34/3.59 inference(transitivity,[status(thm)],[7563, 7561])).
% 3.34/3.59 tff(7565,plain,
% 3.34/3.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(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(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))),
% 3.34/3.59 inference(quant_inst,[status(thm)],[])).
% 3.34/3.59 tff(7566,plain,
% 3.34/3.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))))),
% 3.34/3.59 inference(modus_ponens,[status(thm)],[7565, 7564])).
% 3.34/3.59 tff(7567,plain,
% 3.34/3.59 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 3.34/3.59 inference(unit_resolution,[status(thm)],[7566, 178, 7560, 7548, 7532, 7545])).
% 3.34/3.59 tff(7568,plain,
% 3.34/3.59 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.34/3.59 inference(modus_ponens,[status(thm)],[7567, 7558])).
% 3.34/3.59 tff(7569,plain,
% 3.34/3.59 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.34/3.59 inference(unit_resolution,[status(thm)],[1988, 7568, 1658])).
% 3.34/3.59 tff(7570,plain,
% 3.34/3.59 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 3.34/3.59 inference(modus_ponens,[status(thm)],[7569, 7555])).
% 3.34/3.59 tff(7571,plain,
% 3.34/3.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 3.34/3.59 inference(rewrite,[status(thm)],[])).
% 3.34/3.59 tff(7572,plain,
% 3.34/3.59 (((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 3.34/3.59 inference(rewrite,[status(thm)],[])).
% 3.34/3.59 tff(7573,plain,
% 3.34/3.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))))),
% 3.34/3.59 inference(monotonicity,[status(thm)],[7572])).
% 3.34/3.59 tff(7574,plain,
% 3.34/3.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 3.34/3.59 inference(transitivity,[status(thm)],[7573, 7571])).
% 3.34/3.59 tff(7575,plain,
% 3.34/3.59 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 3.34/3.59 inference(quant_inst,[status(thm)],[])).
% 3.34/3.59 tff(7576,plain,
% 3.34/3.59 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 3.34/3.59 inference(modus_ponens,[status(thm)],[7575, 7574])).
% 3.34/3.59 tff(7577,plain,
% 3.34/3.59 ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 3.34/3.59 inference(unit_resolution,[status(thm)],[7576, 118, 7570])).
% 3.34/3.59 tff(7578,plain,
% 3.34/3.59 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.34/3.59 inference(unit_resolution,[status(thm)],[7577, 7552])).
% 3.34/3.59 tff(7579,plain,
% 3.34/3.59 (~(s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))),
% 3.34/3.59 inference(modus_ponens,[status(thm)],[7211, 7273])).
% 3.34/3.59 tff(7580,plain,
% 3.34/3.59 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 3.34/3.59 inference(unit_resolution,[status(thm)],[6323, 178, 7548, 1126, 7532, 7545])).
% 3.34/3.59 tff(7581,plain,
% 3.34/3.59 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 3.34/3.59 inference(unit_resolution,[status(thm)],[7299, 41, 7580])).
% 3.34/3.59 tff(7582,plain,
% 3.34/3.59 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 3.34/3.59 inference(unit_resolution,[status(thm)],[7581, 7579])).
% 3.34/3.59 tff(7583,plain,
% 3.34/3.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 3.34/3.59 inference(rewrite,[status(thm)],[])).
% 3.34/3.59 tff(7584,plain,
% 3.34/3.59 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(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))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 3.34/3.59 inference(rewrite,[status(thm)],[])).
% 3.34/3.59 tff(7585,plain,
% 3.34/3.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 3.34/3.59 inference(monotonicity,[status(thm)],[7584])).
% 3.34/3.59 tff(7586,plain,
% 3.34/3.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 3.34/3.59 inference(transitivity,[status(thm)],[7585, 7583])).
% 3.34/3.59 tff(7587,plain,
% 3.34/3.59 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.34/3.59 inference(quant_inst,[status(thm)],[])).
% 3.34/3.59 tff(7588,plain,
% 3.34/3.59 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 3.34/3.59 inference(modus_ponens,[status(thm)],[7587, 7586])).
% 3.34/3.59 tff(7589,plain,
% 3.34/3.59 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.34/3.59 inference(unit_resolution,[status(thm)],[7588, 118, 7582, 7570])).
% 3.34/3.59 tff(7590,plain,
% 3.34/3.59 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.34/3.59 inference(unit_resolution,[status(thm)],[222, 7589])).
% 3.34/3.59 tff(7591,plain,
% 3.34/3.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(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(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(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(z))))))),
% 3.34/3.59 inference(rewrite,[status(thm)],[])).
% 3.34/3.59 tff(7592,plain,
% 3.34/3.59 (((~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(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), 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(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(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(z))))))),
% 3.34/3.59 inference(rewrite,[status(thm)],[])).
% 3.34/3.59 tff(7593,plain,
% 3.34/3.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(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(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(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(z)))))))),
% 3.34/3.59 inference(monotonicity,[status(thm)],[7592])).
% 3.34/3.59 tff(7594,plain,
% 3.34/3.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(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(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(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(z))))))),
% 3.34/3.59 inference(transitivity,[status(thm)],[7593, 7591])).
% 3.34/3.59 tff(7595,plain,
% 3.34/3.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(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(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.34/3.59 inference(quant_inst,[status(thm)],[])).
% 3.34/3.59 tff(7596,plain,
% 3.34/3.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 3.34/3.59 inference(modus_ponens,[status(thm)],[7595, 7594])).
% 3.34/3.59 tff(7597,plain,
% 3.34/3.59 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 3.34/3.59 inference(unit_resolution,[status(thm)],[7596, 178, 7560, 1126, 7532])).
% 3.34/3.59 tff(7598,plain,
% 3.34/3.59 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.34/3.59 inference(unit_resolution,[status(thm)],[7597, 7590])).
% 3.34/3.59 tff(7599,plain,
% 3.34/3.59 (s(s(s(z))) = s(s(s(s(s(s(s(z)))))))),
% 3.34/3.59 inference(symmetry,[status(thm)],[1094])).
% 3.34/3.59 tff(7600,plain,
% 3.34/3.59 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 3.34/3.59 inference(monotonicity,[status(thm)],[7599])).
% 3.34/3.59 tff(7601,plain,
% 3.34/3.59 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(s(z))))),
% 3.34/3.59 inference(symmetry,[status(thm)],[7600])).
% 3.34/3.59 tff(7602,plain,
% 3.34/3.59 (s(s(s(s(s(s(z)))))) = s(s(z))),
% 3.34/3.59 inference(transitivity,[status(thm)],[609, 7601, 65])).
% 3.34/3.59 tff(7603,plain,
% 3.34/3.59 ($false),
% 3.34/3.59 inference(unit_resolution,[status(thm)],[6134, 7602])).
% 3.34/3.59 tff(7604,plain,((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) | (s(s(s(s(s(s(z)))))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.59 tff(7605,plain,
% 3.34/3.59 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))),
% 3.34/3.59 inference(unit_resolution,[status(thm)],[7604, 6059])).
% 3.34/3.59 tff(7606,plain,
% 3.34/3.59 ($false),
% 3.34/3.59 inference(unit_resolution,[status(thm)],[1179, 41, 7605, 7598, 7578])).
% 3.34/3.59 tff(7607,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~(s(elem!1) = s(s(s(s(z)))))) | (elem!1 = s(s(s(elem!1)))) | (~b(s(s(z)), z)) | (~r(z, elem!1)) | (~b(z, s(s(z)))) | (s(s(s(elem!1))) = s(elem!1)) | b(s(s(z)), elem!1) | r(elem!1, s(elem!1)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.59 tff(7608,plain,
% 3.34/3.59 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.34/3.59 inference(unit_resolution,[status(thm)],[7607, 7534, 1117, 7526, 3461, 1126, 273, 356, 521, 744, 145])).
% 3.34/3.59 tff(7609,plain,
% 3.34/3.59 (b(s(s(z)), s(s(s(s(z)))))),
% 3.34/3.59 inference(unit_resolution,[status(thm)],[164, 7608])).
% 3.34/3.59 tff(7610,plain,
% 3.34/3.59 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.34/3.59 inference(unit_resolution,[status(thm)],[6966, 7609, 1547, 1650, 273, 202, 3461, 1117, 507, 5396, 5725, 7526, 450, 7531, 844])).
% 3.34/3.59 tff(7611,plain,
% 3.34/3.59 (b(s(s(s(elem!1))), s(elem!1))),
% 3.34/3.59 inference(unit_resolution,[status(thm)],[373, 7610, 356])).
% 3.34/3.59 tff(7612,plain,
% 3.34/3.59 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 3.34/3.59 inference(modus_ponens,[status(thm)],[7611, 6039])).
% 3.34/3.59 tff(7613,plain,
% 3.34/3.59 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 3.34/3.59 inference(unit_resolution,[status(thm)],[6176, 178, 7612, 1126, 7532, 7538])).
% 3.34/3.59 tff(7614,plain,
% 3.34/3.59 (~b(elem!1, s(s(s(elem!1))))),
% 3.34/3.59 inference(unit_resolution,[status(thm)],[6974, 7613, 1117])).
% 3.34/3.59 tff(7615,plain,
% 3.34/3.59 (r(elem!1, s(s(s(elem!1))))),
% 3.34/3.59 inference(unit_resolution,[status(thm)],[2054, 7614, 7526])).
% 3.34/3.59 tff(7616,plain,
% 3.34/3.59 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 3.34/3.59 inference(modus_ponens,[status(thm)],[7615, 6795])).
% 3.34/3.59 tff(7617,plain,
% 3.34/3.59 (~r(z, s(s(s(elem!1))))),
% 3.34/3.59 inference(unit_resolution,[status(thm)],[7389, 7537, 5725, 7531, 356, 7529])).
% 3.34/3.59 tff(7618,plain,
% 3.34/3.59 (b(z, s(s(s(elem!1))))),
% 3.34/3.59 inference(unit_resolution,[status(thm)],[2095, 7617])).
% 3.34/3.59 tff(7619,plain,
% 3.34/3.59 (b(z, s(s(s(s(s(s(z)))))))),
% 3.34/3.59 inference(modus_ponens,[status(thm)],[7618, 6075])).
% 3.34/3.59 tff(7620,plain,
% 3.34/3.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, 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(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, 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(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 3.34/3.59 inference(rewrite,[status(thm)],[])).
% 3.34/3.59 tff(7621,plain,
% 3.34/3.59 (((~b(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(s(s(z)))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(z))))))))) <=> ((~b(z, 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(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 3.34/3.59 inference(rewrite,[status(thm)],[])).
% 3.34/3.59 tff(7622,plain,
% 3.34/3.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(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(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, 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(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 3.34/3.59 inference(monotonicity,[status(thm)],[7621])).
% 3.34/3.59 tff(7623,plain,
% 3.34/3.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(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(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, 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(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 3.34/3.59 inference(transitivity,[status(thm)],[7622, 7620])).
% 3.34/3.59 tff(7624,plain,
% 3.34/3.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(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(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 3.34/3.59 inference(quant_inst,[status(thm)],[])).
% 3.34/3.59 tff(7625,plain,
% 3.34/3.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))),
% 3.34/3.59 inference(modus_ponens,[status(thm)],[7624, 7623])).
% 3.34/3.59 tff(7626,plain,
% 3.34/3.59 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 3.34/3.59 inference(unit_resolution,[status(thm)],[7625, 178, 273, 7609, 7619, 7612])).
% 3.34/3.59 tff(7627,plain,
% 3.34/3.59 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 3.34/3.59 inference(unit_resolution,[status(thm)],[6139, 7626, 6059])).
% 3.34/3.59 tff(7628,plain,
% 3.34/3.59 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 3.34/3.59 inference(unit_resolution,[status(thm)],[6146, 118, 7627, 6053])).
% 3.34/3.59 tff(7629,plain,
% 3.34/3.59 ($false),
% 3.34/3.59 inference(unit_resolution,[status(thm)],[7628, 7616])).
% 3.34/3.59 tff(7630,plain,((~r(z, elem!1)) | (~(s(elem!1) = s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (z = elem!1) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), z)) | r(elem!1, s(elem!1)) | (~r(z, s(s(s(s(z)))))) | (s(s(z)) = elem!1) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 3.34/3.60 tff(7631,plain,
% 3.34/3.60 (~r(z, elem!1)),
% 3.34/3.60 inference(unit_resolution,[status(thm)],[7630, 7487, 7519, 7456, 356, 202, 5619, 7505, 7510, 7490, 744, 7464, 7522, 7516])).
% 3.34/3.60 tff(7632,plain,
% 3.34/3.60 (b(z, elem!1)),
% 3.34/3.60 inference(unit_resolution,[status(thm)],[585, 7631, 7505])).
% 3.34/3.60 tff(7633,plain,
% 3.34/3.60 (b(z, s(s(s(z))))),
% 3.34/3.60 inference(unit_resolution,[status(thm)],[1238, 7632, 7487])).
% 3.34/3.60 tff(7634,plain,
% 3.34/3.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 3.34/3.60 inference(rewrite,[status(thm)],[])).
% 3.34/3.60 tff(7635,plain,
% 3.34/3.60 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 3.34/3.60 inference(rewrite,[status(thm)],[])).
% 3.34/3.60 tff(7636,plain,
% 3.34/3.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 3.34/3.60 inference(monotonicity,[status(thm)],[7635])).
% 3.34/3.60 tff(7637,plain,
% 3.34/3.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 3.34/3.60 inference(transitivity,[status(thm)],[7636, 7634])).
% 3.34/3.60 tff(7638,plain,
% 3.34/3.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))),
% 3.34/3.60 inference(quant_inst,[status(thm)],[])).
% 3.34/3.60 tff(7639,plain,
% 3.34/3.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 3.34/3.60 inference(modus_ponens,[status(thm)],[7638, 7637])).
% 3.34/3.60 tff(7640,plain,
% 3.34/3.60 (~b(s(s(z)), s(s(s(z))))),
% 3.34/3.60 inference(unit_resolution,[status(thm)],[7639, 178, 5619, 7456, 7633, 7516])).
% 3.34/3.60 tff(7641,plain,
% 3.34/3.60 (~b(s(s(z)), elem!1)),
% 3.34/3.60 inference(modus_ponens,[status(thm)],[7640, 7525])).
% 3.34/3.60 tff(7642,plain,
% 3.34/3.60 (r(s(s(z)), elem!1)),
% 3.34/3.60 inference(unit_resolution,[status(thm)],[448, 7641, 7522])).
% 3.34/3.60 tff(7643,plain,
% 3.34/3.60 (r(s(s(z)), s(s(s(z))))),
% 3.34/3.60 inference(modus_ponens,[status(thm)],[7642, 7521])).
% 3.34/3.60 tff(7644,plain,
% 3.34/3.60 (b(z, s(s(s(z))))),
% 3.34/3.60 inference(unit_resolution,[status(thm)],[1238, 818, 1117])).
% 3.44/3.60 tff(7645,plain,
% 3.44/3.60 (~b(s(s(z)), s(s(s(z))))),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[7639, 178, 3461, 273, 7644, 1127])).
% 3.44/3.60 tff(7646,plain,
% 3.44/3.60 (~b(s(s(z)), elem!1)),
% 3.44/3.60 inference(modus_ponens,[status(thm)],[7645, 1221])).
% 3.44/3.60 tff(7647,plain,
% 3.44/3.60 (r(s(s(z)), elem!1)),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[448, 7646, 12])).
% 3.44/3.60 tff(7648,plain,
% 3.44/3.60 (r(s(s(z)), s(s(s(z))))),
% 3.44/3.60 inference(modus_ponens,[status(thm)],[7647, 7223])).
% 3.44/3.60 tff(7649,plain,
% 3.44/3.60 (~r(z, elem!1)),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[1284, 1426, 844])).
% 3.44/3.60 tff(7650,plain,
% 3.44/3.60 (b(z, elem!1)),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[585, 7649, 507])).
% 3.44/3.60 tff(7651,plain,
% 3.44/3.60 (b(z, s(s(s(z))))),
% 3.44/3.60 inference(modus_ponens,[status(thm)],[7650, 1234])).
% 3.44/3.60 tff(7652,plain,
% 3.44/3.60 (~b(s(s(z)), s(s(s(z))))),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[7639, 178, 3461, 273, 7651, 1127])).
% 3.44/3.60 tff(7653,plain,
% 3.44/3.60 (~b(s(s(z)), elem!1)),
% 3.44/3.60 inference(modus_ponens,[status(thm)],[7652, 1221])).
% 3.44/3.60 tff(7654,plain,
% 3.44/3.60 (r(s(s(z)), elem!1)),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[448, 7653, 12])).
% 3.44/3.60 tff(7655,plain,
% 3.44/3.60 (r(s(s(z)), s(s(s(z))))),
% 3.44/3.60 inference(modus_ponens,[status(thm)],[7654, 7223])).
% 3.44/3.60 tff(7656,plain,
% 3.44/3.60 (r(s(elem!1), elem!1) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 3.44/3.60 inference(transitivity,[status(thm)],[7213, 7216])).
% 3.44/3.60 tff(7657,plain,
% 3.44/3.60 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.44/3.60 inference(modus_ponens,[status(thm)],[1426, 7656])).
% 3.44/3.60 tff(7658,plain,
% 3.44/3.60 ($false),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[7239, 118, 147, 7657, 7655])).
% 3.44/3.60 tff(7659,plain,((~r(s(elem!1), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~(s(elem!1) = s(s(s(s(z)))))) | (s(s(z)) = elem!1) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (z = elem!1) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.60 tff(7660,plain,
% 3.44/3.60 (~r(s(elem!1), elem!1)),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[7659, 147, 1117, 12, 3461, 273, 1127, 507, 844])).
% 3.44/3.60 tff(7661,plain,
% 3.44/3.60 (b(s(elem!1), elem!1)),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[677, 7660, 1548])).
% 3.44/3.60 tff(7662,plain,
% 3.44/3.60 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.44/3.60 inference(modus_ponens,[status(thm)],[7661, 1280])).
% 3.44/3.60 tff(7663,plain,
% 3.44/3.60 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[6178, 7548, 6047, 7662, 1117, 7528, 450, 202])).
% 3.44/3.60 tff(7664,plain,
% 3.44/3.60 (~b(elem!1, s(s(s(elem!1))))),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[6974, 7663, 1117])).
% 3.44/3.60 tff(7665,plain,
% 3.44/3.60 (r(elem!1, s(s(s(elem!1))))),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[2054, 7664, 7526])).
% 3.44/3.60 tff(7666,plain,
% 3.44/3.60 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.44/3.60 inference(modus_ponens,[status(thm)],[7605, 1188])).
% 3.44/3.60 tff(7667,plain,
% 3.44/3.60 (r(z, s(s(s(s(s(s(z))))))) <=> r(z, s(s(s(elem!1))))),
% 3.44/3.60 inference(monotonicity,[status(thm)],[6036])).
% 3.44/3.60 tff(7668,plain,
% 3.44/3.60 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(s(s(z)))))))),
% 3.44/3.60 inference(symmetry,[status(thm)],[7667])).
% 3.44/3.60 tff(7669,plain,
% 3.44/3.60 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 3.44/3.60 inference(modus_ponens,[status(thm)],[556, 7199])).
% 3.44/3.60 tff(7670,assumption,(r(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 3.44/3.60 tff(7671,plain,
% 3.44/3.60 ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[7411, 118, 7670])).
% 3.44/3.60 tff(7672,plain,
% 3.44/3.60 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[7671, 7669])).
% 3.44/3.60 tff(7673,plain,
% 3.44/3.60 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.44/3.60 inference(modus_ponens,[status(thm)],[7672, 7197])).
% 3.44/3.60 tff(7674,plain,
% 3.44/3.60 (b(s(s(z)), s(s(s(elem!1))))),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[4223, 7673])).
% 3.44/3.60 tff(7675,plain,
% 3.44/3.60 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[7268, 7674, 1117])).
% 3.44/3.60 tff(7676,plain,
% 3.44/3.60 (~r(s(s(s(elem!1))), s(s(z)))),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[4205, 556, 450])).
% 3.44/3.60 tff(7677,plain,
% 3.44/3.60 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[6165, 7676, 1117])).
% 3.44/3.60 tff(7678,plain,
% 3.44/3.60 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[6139, 7677, 6059])).
% 3.44/3.60 tff(7679,plain,
% 3.44/3.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 3.44/3.60 inference(rewrite,[status(thm)],[])).
% 3.44/3.60 tff(7680,plain,
% 3.44/3.60 (((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 3.44/3.60 inference(rewrite,[status(thm)],[])).
% 3.44/3.60 tff(7681,plain,
% 3.44/3.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 3.44/3.60 inference(monotonicity,[status(thm)],[7680])).
% 3.44/3.60 tff(7682,plain,
% 3.44/3.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 3.44/3.60 inference(transitivity,[status(thm)],[7681, 7679])).
% 3.44/3.60 tff(7683,plain,
% 3.44/3.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)))),
% 3.44/3.60 inference(quant_inst,[status(thm)],[])).
% 3.44/3.60 tff(7684,plain,
% 3.44/3.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))),
% 3.44/3.60 inference(modus_ponens,[status(thm)],[7683, 7682])).
% 3.44/3.60 tff(7685,plain,
% 3.44/3.60 (~b(z, s(s(s(s(s(s(z)))))))),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[7684, 178, 3461, 273, 7678, 7675])).
% 3.44/3.60 tff(7686,plain,
% 3.44/3.60 (~b(z, s(s(s(elem!1))))),
% 3.44/3.60 inference(modus_ponens,[status(thm)],[7685, 7251])).
% 3.44/3.60 tff(7687,plain,
% 3.44/3.60 (r(z, s(s(s(elem!1))))),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[2095, 7686])).
% 3.44/3.60 tff(7688,plain,
% 3.44/3.60 (r(z, s(s(s(s(s(s(z)))))))),
% 3.44/3.60 inference(modus_ponens,[status(thm)],[7687, 7668])).
% 3.44/3.60 tff(7689,plain,
% 3.44/3.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 3.44/3.60 inference(rewrite,[status(thm)],[])).
% 3.44/3.60 tff(7690,plain,
% 3.44/3.60 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), 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(z)))) | (~b(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(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 3.44/3.60 inference(rewrite,[status(thm)],[])).
% 3.44/3.60 tff(7691,plain,
% 3.44/3.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(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(s(z))))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 3.44/3.60 inference(monotonicity,[status(thm)],[7690])).
% 3.44/3.60 tff(7692,plain,
% 3.44/3.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(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(s(z))))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 3.44/3.60 inference(transitivity,[status(thm)],[7691, 7689])).
% 3.44/3.60 tff(7693,plain,
% 3.44/3.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(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(s(z))))))), s(s(s(s(s(s(z)))))))))),
% 3.44/3.60 inference(quant_inst,[status(thm)],[])).
% 3.44/3.60 tff(7694,plain,
% 3.44/3.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))),
% 3.44/3.60 inference(modus_ponens,[status(thm)],[7693, 7692])).
% 3.44/3.60 tff(7695,plain,
% 3.44/3.60 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[7694, 178, 104, 202, 6154, 7678])).
% 3.44/3.60 tff(7696,plain,
% 3.44/3.60 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.44/3.60 inference(modus_ponens,[status(thm)],[7695, 7558])).
% 3.44/3.60 tff(7697,plain,
% 3.44/3.60 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[1988, 7696, 1693])).
% 3.44/3.60 tff(7698,plain,
% 3.44/3.60 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 3.44/3.60 inference(modus_ponens,[status(thm)],[7697, 7555])).
% 3.44/3.60 tff(7699,plain,
% 3.44/3.60 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 3.44/3.60 inference(rewrite,[status(thm)],[])).
% 3.44/3.60 tff(7700,plain,
% 3.44/3.60 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 3.44/3.60 inference(rewrite,[status(thm)],[])).
% 3.44/3.60 tff(7701,plain,
% 3.44/3.60 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z))))))))))),
% 3.44/3.60 inference(monotonicity,[status(thm)],[7700])).
% 3.44/3.60 tff(7702,plain,
% 3.44/3.60 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 3.44/3.60 inference(transitivity,[status(thm)],[7701, 7699])).
% 3.44/3.60 tff(7703,plain,
% 3.44/3.60 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.60 inference(quant_inst,[status(thm)],[])).
% 3.44/3.60 tff(7704,plain,
% 3.44/3.60 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z))))))))),
% 3.44/3.60 inference(modus_ponens,[status(thm)],[7703, 7702])).
% 3.44/3.60 tff(7705,plain,
% 3.44/3.60 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[7704, 118, 7698, 7688])).
% 3.44/3.60 tff(7706,plain,
% 3.44/3.60 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[271, 7705])).
% 3.44/3.60 tff(7707,plain,
% 3.44/3.60 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[1309, 7706, 1301, 818, 104])).
% 3.44/3.60 tff(7708,plain,
% 3.44/3.60 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[691, 7707, 7666])).
% 3.44/3.60 tff(7709,plain,
% 3.44/3.60 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.60 inference(modus_ponens,[status(thm)],[7708, 1264])).
% 3.44/3.60 tff(7710,plain,
% 3.44/3.60 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 3.44/3.60 inference(modus_ponens,[status(thm)],[3311, 6795])).
% 3.44/3.60 tff(7711,plain,
% 3.44/3.60 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(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(s(s(s(z))))))))))),
% 3.44/3.60 inference(rewrite,[status(thm)],[])).
% 3.44/3.60 tff(7712,plain,
% 3.44/3.60 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.60 inference(quant_inst,[status(thm)],[])).
% 3.44/3.60 tff(7713,plain,
% 3.44/3.60 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.44/3.60 inference(modus_ponens,[status(thm)],[7712, 7711])).
% 3.44/3.60 tff(7714,plain,
% 3.44/3.60 ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[7713, 118, 7698])).
% 3.44/3.60 tff(7715,plain,
% 3.44/3.60 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[7714, 7710])).
% 3.44/3.60 tff(7716,plain,
% 3.44/3.60 ($false),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[7715, 7709])).
% 3.44/3.60 tff(7717,plain,((~r(s(s(s(elem!1))), elem!1)) | (~(s(elem!1) = s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.60 tff(7718,plain,
% 3.44/3.60 (~r(s(s(s(elem!1))), elem!1)),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[7717, 7560, 1301, 818, 1117, 7665, 1658, 3461, 273, 202, 7548, 7648, 450])).
% 3.44/3.60 tff(7719,plain,
% 3.44/3.60 (b(s(s(s(elem!1))), elem!1)),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[570, 7718, 7528])).
% 3.44/3.60 tff(7720,plain,
% 3.44/3.60 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 3.44/3.60 inference(modus_ponens,[status(thm)],[7719, 7527])).
% 3.44/3.60 tff(7721,plain,
% 3.44/3.60 (~r(z, s(s(s(elem!1))))),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[7389, 7719, 854, 7661, 356, 7529])).
% 3.44/3.60 tff(7722,plain,
% 3.44/3.60 (b(z, s(s(s(elem!1))))),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[2095, 7721])).
% 3.44/3.60 tff(7723,plain,
% 3.44/3.60 (b(z, s(s(s(s(s(s(z)))))))),
% 3.44/3.60 inference(modus_ponens,[status(thm)],[7722, 6075])).
% 3.44/3.60 tff(7724,plain,
% 3.44/3.60 ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[7258, 178, 7548, 6047, 7644])).
% 3.44/3.60 tff(7725,plain,
% 3.44/3.60 ($false),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[7724, 7723, 7720])).
% 3.44/3.60 tff(7726,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~(s(elem!1) = s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (s(s(z)) = elem!1) | (~b(s(s(s(z))), z)) | (z = elem!1) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.60 tff(7727,plain,
% 3.44/3.60 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[7726, 7487, 5725, 356, 5722, 7632, 5619, 7456, 202, 7510, 7522, 7516, 7505, 7490, 7464])).
% 3.44/3.60 tff(7728,plain,
% 3.44/3.60 (b(s(s(z)), s(s(s(s(z)))))),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[164, 7727])).
% 3.44/3.60 tff(7729,plain,
% 3.44/3.60 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 3.44/3.60 inference(modus_ponens,[status(thm)],[1597, 7527])).
% 3.44/3.60 tff(7730,plain,
% 3.44/3.60 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[6966, 683, 1547, 1650, 273, 202, 3461, 1117, 507, 5396, 854, 7526, 450, 167, 844])).
% 3.44/3.60 tff(7731,plain,
% 3.44/3.60 (b(s(s(s(elem!1))), s(elem!1))),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[373, 7730, 356])).
% 3.44/3.60 tff(7732,plain,
% 3.44/3.60 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 3.44/3.60 inference(modus_ponens,[status(thm)],[7731, 6039])).
% 3.44/3.60 tff(7733,plain,
% 3.44/3.60 (~r(z, s(s(s(elem!1))))),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[7389, 683, 854, 1597, 356, 2333])).
% 3.44/3.60 tff(7734,plain,
% 3.44/3.60 (b(z, s(s(s(elem!1))))),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[2095, 7733])).
% 3.44/3.60 tff(7735,plain,
% 3.44/3.60 (b(z, s(s(s(s(s(s(z)))))))),
% 3.44/3.60 inference(modus_ponens,[status(thm)],[7734, 6075])).
% 3.44/3.60 tff(7736,plain,
% 3.44/3.60 ($false),
% 3.44/3.60 inference(unit_resolution,[status(thm)],[7258, 178, 7735, 7732, 1126, 3008, 7729])).
% 3.44/3.60 tff(7737,plain,((~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~(s(elem!1) = s(s(s(s(z)))))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~r(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (z = elem!1) | (~r(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.61 tff(7738,plain,
% 3.44/3.61 (~b(s(elem!1), elem!1)),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[7737, 1597, 3008, 1117, 356, 854, 1126, 2333, 273, 202, 3461, 507, 450, 167, 6062])).
% 3.44/3.61 tff(7739,plain,
% 3.44/3.61 (r(s(elem!1), elem!1)),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[677, 7738, 1548])).
% 3.44/3.61 tff(7740,plain,
% 3.44/3.61 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[7350, 7739, 1127, 1117, 7528, 6062, 2333, 3008])).
% 3.44/3.61 tff(7741,plain,
% 3.44/3.61 (b(s(s(s(elem!1))), s(elem!1))),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[373, 7740, 356])).
% 3.44/3.61 tff(7742,plain,
% 3.44/3.61 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 3.44/3.61 inference(modus_ponens,[status(thm)],[7741, 6039])).
% 3.44/3.61 tff(7743,plain,
% 3.44/3.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)))),
% 3.44/3.61 inference(rewrite,[status(thm)],[])).
% 3.44/3.61 tff(7744,plain,
% 3.44/3.61 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)))),
% 3.44/3.61 inference(rewrite,[status(thm)],[])).
% 3.44/3.61 tff(7745,plain,
% 3.44/3.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z))))),
% 3.44/3.61 inference(monotonicity,[status(thm)],[7744])).
% 3.44/3.61 tff(7746,plain,
% 3.44/3.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)))),
% 3.44/3.61 inference(transitivity,[status(thm)],[7745, 7743])).
% 3.44/3.61 tff(7747,plain,
% 3.44/3.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 3.44/3.61 inference(quant_inst,[status(thm)],[])).
% 3.44/3.61 tff(7748,plain,
% 3.44/3.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z))),
% 3.44/3.61 inference(modus_ponens,[status(thm)],[7747, 7746])).
% 3.44/3.61 tff(7749,plain,
% 3.44/3.61 ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[7748, 178, 3008, 1127, 7252])).
% 3.44/3.61 tff(7750,plain,
% 3.44/3.61 (~b(s(s(s(s(s(s(z)))))), z)),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[7749, 6155])).
% 3.44/3.61 tff(7751,plain,
% 3.44/3.61 (~b(s(s(s(elem!1))), z)),
% 3.44/3.61 inference(modus_ponens,[status(thm)],[7750, 7277])).
% 3.44/3.61 tff(7752,plain,
% 3.44/3.61 (r(s(s(s(elem!1))), z)),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[1565, 7751])).
% 3.44/3.61 tff(7753,plain,
% 3.44/3.61 (r(s(s(s(s(s(s(z)))))), z)),
% 3.44/3.61 inference(modus_ponens,[status(thm)],[7752, 7276])).
% 3.44/3.61 tff(7754,plain,
% 3.44/3.61 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[7295, 7753])).
% 3.44/3.61 tff(7755,plain,
% 3.44/3.61 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[7299, 41, 7754])).
% 3.44/3.61 tff(7756,plain,
% 3.44/3.61 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[7755, 7274])).
% 3.44/3.61 tff(7757,plain,
% 3.44/3.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 3.44/3.61 inference(rewrite,[status(thm)],[])).
% 3.44/3.61 tff(7758,plain,
% 3.44/3.61 (((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~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(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 3.44/3.61 inference(rewrite,[status(thm)],[])).
% 3.44/3.61 tff(7759,plain,
% 3.44/3.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~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(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 3.44/3.61 inference(monotonicity,[status(thm)],[7758])).
% 3.44/3.61 tff(7760,plain,
% 3.44/3.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~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(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 3.44/3.61 inference(transitivity,[status(thm)],[7759, 7757])).
% 3.44/3.61 tff(7761,plain,
% 3.44/3.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~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(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 3.44/3.61 inference(quant_inst,[status(thm)],[])).
% 3.44/3.61 tff(7762,plain,
% 3.44/3.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 3.44/3.61 inference(modus_ponens,[status(thm)],[7761, 7760])).
% 3.44/3.61 tff(7763,plain,
% 3.44/3.61 ($false),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[7762, 178, 6154, 1126, 6155, 7252, 7756])).
% 3.44/3.61 tff(7764,plain,((~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)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~(s(elem!1) = s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.61 tff(7765,plain,
% 3.44/3.61 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[7764, 7742, 1126, 7729, 7211, 1117, 194, 3008, 1127])).
% 3.44/3.61 tff(7766,plain,
% 3.44/3.61 (~b(elem!1, s(s(s(elem!1))))),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[6974, 7765, 1117])).
% 3.44/3.61 tff(7767,plain,
% 3.44/3.61 (r(elem!1, s(s(s(elem!1))))),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[2054, 7766, 7526])).
% 3.44/3.61 tff(7768,assumption,(~r(s(s(s(z))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 3.44/3.61 tff(7769,plain,
% 3.44/3.61 ($false),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[7768, 7710])).
% 3.44/3.61 tff(7770,plain,(r(s(s(s(z))), s(s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(elem!1))))) | (~(s(elem!1) = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.61 tff(7771,plain,
% 3.44/3.61 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[7770, 7767, 1117])).
% 3.44/3.61 tff(7772,assumption,(r(s(s(s(z))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 3.44/3.61 tff(7773,plain,
% 3.44/3.61 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(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)))))))))),
% 3.44/3.61 inference(rewrite,[status(thm)],[])).
% 3.44/3.61 tff(7774,plain,
% 3.44/3.61 (((~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(z)), s(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)))))))))),
% 3.44/3.61 inference(rewrite,[status(thm)],[])).
% 3.44/3.61 tff(7775,plain,
% 3.44/3.61 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(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))))))))))),
% 3.44/3.61 inference(monotonicity,[status(thm)],[7774])).
% 3.44/3.61 tff(7776,plain,
% 3.44/3.61 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(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)))))))))),
% 3.44/3.61 inference(transitivity,[status(thm)],[7775, 7773])).
% 3.44/3.61 tff(7777,plain,
% 3.44/3.61 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(z))))))),
% 3.44/3.61 inference(quant_inst,[status(thm)],[])).
% 3.44/3.61 tff(7778,plain,
% 3.44/3.61 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 3.44/3.61 inference(modus_ponens,[status(thm)],[7777, 7776])).
% 3.44/3.61 tff(7779,plain,
% 3.44/3.61 ($false),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[7778, 118, 6939, 7670, 7772])).
% 3.44/3.61 tff(7780,plain,((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.61 tff(7781,plain,
% 3.44/3.61 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[7780, 7771, 7670])).
% 3.44/3.61 tff(7782,plain,
% 3.44/3.61 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.44/3.61 inference(modus_ponens,[status(thm)],[7781, 7197])).
% 3.44/3.61 tff(7783,plain,
% 3.44/3.61 (b(s(s(z)), s(s(s(elem!1))))),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[4223, 7782])).
% 3.44/3.61 tff(7784,plain,
% 3.44/3.61 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[7268, 7783, 1117])).
% 3.44/3.61 tff(7785,plain,
% 3.44/3.61 ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[7283, 178, 3461, 3008, 7729])).
% 3.44/3.61 tff(7786,plain,
% 3.44/3.61 (~b(s(s(s(s(s(s(z)))))), z)),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[7785, 7784])).
% 3.44/3.61 tff(7787,plain,
% 3.44/3.61 (~b(s(s(s(elem!1))), z)),
% 3.44/3.61 inference(modus_ponens,[status(thm)],[7786, 7277])).
% 3.44/3.61 tff(7788,plain,
% 3.44/3.61 (r(s(s(s(elem!1))), z)),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[1565, 7787])).
% 3.44/3.61 tff(7789,plain,
% 3.44/3.61 (r(s(s(s(s(s(s(z)))))), z)),
% 3.44/3.61 inference(modus_ponens,[status(thm)],[7788, 7276])).
% 3.44/3.61 tff(7790,plain,
% 3.44/3.61 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[7295, 7789])).
% 3.44/3.61 tff(7791,plain,
% 3.44/3.61 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[7299, 41, 7790])).
% 3.44/3.61 tff(7792,plain,
% 3.44/3.61 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[7791, 7579])).
% 3.44/3.61 tff(7793,plain,
% 3.44/3.61 ($false),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[7307, 178, 167, 202, 7742, 7784, 7792])).
% 3.44/3.61 tff(7794,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~(s(elem!1) = s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, s(s(z)))) | (z = elem!1) | (~r(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.61 tff(7795,plain,
% 3.44/3.61 (~b(s(s(s(elem!1))), elem!1)),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[7794, 7728, 202, 7487, 3244, 5619, 7633, 7643, 7519, 7516, 356, 7513, 5725, 7456, 7505, 7510])).
% 3.44/3.61 tff(7796,plain,
% 3.44/3.61 (r(s(s(s(elem!1))), elem!1)),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[570, 7795, 7508])).
% 3.44/3.61 tff(7797,plain,
% 3.44/3.61 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 3.44/3.61 inference(modus_ponens,[status(thm)],[7796, 7504])).
% 3.44/3.61 tff(7798,plain,
% 3.44/3.61 ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[7411, 118, 7643])).
% 3.44/3.61 tff(7799,plain,
% 3.44/3.61 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[7798, 7797])).
% 3.44/3.61 tff(7800,plain,
% 3.44/3.61 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.44/3.61 inference(modus_ponens,[status(thm)],[7799, 7498])).
% 3.44/3.61 tff(7801,plain,
% 3.44/3.61 (b(s(s(z)), s(s(s(elem!1))))),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[4223, 7800])).
% 3.44/3.61 tff(7802,plain,
% 3.44/3.61 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[7268, 7801, 7487])).
% 3.44/3.61 tff(7803,plain,
% 3.44/3.61 (~(s(s(s(s(s(s(z)))))) = s(s(z)))),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[6058, 7487])).
% 3.44/3.61 tff(7804,plain,
% 3.44/3.61 (~r(s(s(s(elem!1))), s(s(z)))),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[4205, 7796, 7510])).
% 3.44/3.61 tff(7805,plain,
% 3.44/3.61 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[6165, 7804, 7487])).
% 3.44/3.61 tff(7806,plain,
% 3.44/3.61 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[6139, 7805, 7803])).
% 3.44/3.61 tff(7807,plain,
% 3.44/3.61 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[7428, 178, 7728, 202, 7806])).
% 3.44/3.61 tff(7808,plain,
% 3.44/3.61 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[7807, 7802])).
% 3.44/3.61 tff(7809,plain,
% 3.44/3.61 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.44/3.61 inference(modus_ponens,[status(thm)],[7808, 7495])).
% 3.44/3.61 tff(7810,plain,
% 3.44/3.61 (r(s(s(s(elem!1))), s(elem!1))),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[373, 7809, 356])).
% 3.44/3.61 tff(7811,plain,
% 3.44/3.61 (b(s(s(s(s(s(s(z)))))), z) <=> b(s(s(s(elem!1))), z)),
% 3.44/3.61 inference(monotonicity,[status(thm)],[7502])).
% 3.44/3.61 tff(7812,plain,
% 3.44/3.61 ((~b(s(s(s(s(s(s(z)))))), z)) <=> (~b(s(s(s(elem!1))), z))),
% 3.44/3.61 inference(monotonicity,[status(thm)],[7811])).
% 3.44/3.61 tff(7813,plain,
% 3.44/3.61 ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[6107, 178, 5619, 7456, 7806])).
% 3.44/3.61 tff(7814,plain,
% 3.44/3.61 (~b(s(s(s(s(s(s(z)))))), z)),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[7813, 7802])).
% 3.44/3.61 tff(7815,plain,
% 3.44/3.61 (~b(s(s(s(elem!1))), z)),
% 3.44/3.61 inference(modus_ponens,[status(thm)],[7814, 7812])).
% 3.44/3.61 tff(7816,plain,
% 3.44/3.61 (r(s(s(s(elem!1))), z)),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[1565, 7815])).
% 3.44/3.61 tff(7817,plain,
% 3.44/3.61 ($false),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[1557, 7816, 7810, 7490])).
% 3.44/3.61 tff(7818,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (s(s(s(elem!1))) = s(elem!1)) | r(elem!1, s(elem!1)) | b(elem!1, s(s(z))) | b(s(elem!1), s(s(s(s(z))))) | b(s(s(s(s(z)))), z) | r(s(s(z)), z) | r(elem!1, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.61 tff(7819,plain,
% 3.44/3.61 (r(elem!1, s(elem!1))),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[7818, 5719, 3170, 202, 5710, 5618, 5707, 461])).
% 3.44/3.61 tff(7820,plain,
% 3.44/3.61 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[2935, 7819, 5701])).
% 3.44/3.61 tff(7821,plain,
% 3.44/3.61 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[395, 7820, 5697])).
% 3.44/3.61 tff(7822,plain,
% 3.44/3.61 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.44/3.61 inference(monotonicity,[status(thm)],[5694])).
% 3.44/3.61 tff(7823,plain,
% 3.44/3.61 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.44/3.61 inference(modus_ponens,[status(thm)],[3831, 7822])).
% 3.44/3.61 tff(7824,plain,
% 3.44/3.61 (b(elem!1, z)),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[498, 4357, 5631])).
% 3.44/3.61 tff(7825,plain,
% 3.44/3.61 (~r(s(elem!1), s(s(s(elem!1))))),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[5423, 5283, 557, 5633, 3311, 7824])).
% 3.44/3.61 tff(7826,plain,
% 3.44/3.61 (~(s(elem!1) = s(s(s(elem!1))))),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[5395, 5707])).
% 3.44/3.61 tff(7827,plain,
% 3.44/3.61 (b(s(elem!1), s(s(s(elem!1))))),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[5432, 7826, 7825])).
% 3.44/3.61 tff(7828,plain,
% 3.44/3.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(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(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(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(s(elem!1)))))),
% 3.44/3.61 inference(rewrite,[status(thm)],[])).
% 3.44/3.61 tff(7829,plain,
% 3.44/3.61 (((~b(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)))) | (~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(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(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(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(s(elem!1)))))),
% 3.44/3.61 inference(rewrite,[status(thm)],[])).
% 3.44/3.61 tff(7830,plain,
% 3.44/3.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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)))) | (~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(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(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(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(s(elem!1))))))),
% 3.44/3.61 inference(monotonicity,[status(thm)],[7829])).
% 3.44/3.61 tff(7831,plain,
% 3.44/3.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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)))) | (~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(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(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(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(s(elem!1)))))),
% 3.44/3.61 inference(transitivity,[status(thm)],[7830, 7828])).
% 3.44/3.61 tff(7832,plain,
% 3.44/3.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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)))) | (~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(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(elem!1), s(s(s(elem!1))))))),
% 3.44/3.61 inference(quant_inst,[status(thm)],[])).
% 3.44/3.61 tff(7833,plain,
% 3.44/3.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(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(s(elem!1))))),
% 3.44/3.61 inference(modus_ponens,[status(thm)],[7832, 7831])).
% 3.44/3.61 tff(7834,plain,
% 3.44/3.61 (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.61 inference(unit_resolution,[status(thm)],[7833, 178, 7827, 7823, 7821, 5696])).
% 3.44/3.61 tff(7835,plain,
% 3.44/3.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(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(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(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(z)))))),
% 3.44/3.61 inference(rewrite,[status(thm)],[])).
% 3.44/3.61 tff(7836,plain,
% 3.44/3.61 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(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(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(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(z)))))),
% 3.44/3.62 inference(rewrite,[status(thm)],[])).
% 3.44/3.62 tff(7837,plain,
% 3.44/3.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(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(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(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(z))))))),
% 3.44/3.62 inference(monotonicity,[status(thm)],[7836])).
% 3.44/3.62 tff(7838,plain,
% 3.44/3.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(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(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(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(z)))))),
% 3.44/3.62 inference(transitivity,[status(thm)],[7837, 7835])).
% 3.44/3.62 tff(7839,plain,
% 3.44/3.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(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(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.62 inference(quant_inst,[status(thm)],[])).
% 3.44/3.62 tff(7840,plain,
% 3.44/3.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(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(z))))),
% 3.44/3.62 inference(modus_ponens,[status(thm)],[7839, 7838])).
% 3.44/3.62 tff(7841,plain,
% 3.44/3.62 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.44/3.62 inference(unit_resolution,[status(thm)],[7840, 178, 5630, 104, 5688, 5628])).
% 3.44/3.62 tff(7842,plain,
% 3.44/3.62 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.44/3.62 inference(unit_resolution,[status(thm)],[3578, 7841])).
% 3.44/3.62 tff(7843,plain,
% 3.44/3.62 (~b(s(s(s(elem!1))), s(s(z)))),
% 3.44/3.62 inference(unit_resolution,[status(thm)],[5595, 178, 5688, 202, 3828, 3831])).
% 3.44/3.62 tff(7844,plain,
% 3.44/3.62 (r(s(s(s(elem!1))), s(s(z)))),
% 3.44/3.62 inference(unit_resolution,[status(thm)],[4209, 41, 7843, 4181])).
% 3.44/3.62 tff(7845,plain,
% 3.44/3.62 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.62 inference(rewrite,[status(thm)],[])).
% 3.44/3.62 tff(7846,plain,
% 3.44/3.62 (((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(elem!1))), 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(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.62 inference(rewrite,[status(thm)],[])).
% 3.44/3.62 tff(7847,plain,
% 3.44/3.62 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))))),
% 3.44/3.62 inference(monotonicity,[status(thm)],[7846])).
% 3.44/3.62 tff(7848,plain,
% 3.44/3.62 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.62 inference(transitivity,[status(thm)],[7847, 7845])).
% 3.44/3.62 tff(7849,plain,
% 3.44/3.62 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.62 inference(quant_inst,[status(thm)],[])).
% 3.44/3.62 tff(7850,plain,
% 3.44/3.62 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 3.44/3.62 inference(modus_ponens,[status(thm)],[7849, 7848])).
% 3.44/3.62 tff(7851,plain,
% 3.44/3.62 (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.62 inference(unit_resolution,[status(thm)],[7850, 118, 7844, 7842])).
% 3.44/3.62 tff(7852,plain,
% 3.44/3.62 ((s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.62 inference(unit_resolution,[status(thm)],[3612, 41, 7851])).
% 3.44/3.62 tff(7853,plain,
% 3.44/3.62 ($false),
% 3.44/3.62 inference(unit_resolution,[status(thm)],[7852, 7834, 5617])).
% 3.44/3.62 tff(7854,plain,(r(s(s(z)), z) | b(s(s(s(s(z)))), z) | (~b(s(s(s(s(z)))), s(s(z)))) | b(elem!1, s(s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (s(s(s(elem!1))) = elem!1) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | b(s(s(z)), elem!1) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.62 tff(7855,plain,
% 3.44/3.62 (r(s(s(z)), z)),
% 3.44/3.62 inference(unit_resolution,[status(thm)],[7854, 5145, 4503, 461, 3170, 5600, 5161, 3243, 5151, 5143, 3241, 47, 5616])).
% 3.44/3.62 tff(7856,plain,
% 3.44/3.62 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.62 inference(unit_resolution,[status(thm)],[3102, 106, 108])).
% 3.44/3.62 tff(7857,plain,
% 3.44/3.62 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.62 inference(unit_resolution,[status(thm)],[249, 7856])).
% 3.44/3.62 tff(7858,plain,
% 3.44/3.62 ($false),
% 3.44/3.62 inference(unit_resolution,[status(thm)],[279, 178, 273, 104, 7857, 165, 595])).
% 3.44/3.62 tff(7859,plain,((~r(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.62 tff(7860,plain,
% 3.44/3.62 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.44/3.62 inference(unit_resolution,[status(thm)],[7859, 7855, 5600, 5153, 5155, 47])).
% 3.44/3.62 tff(7861,plain,
% 3.44/3.62 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.44/3.62 inference(unit_resolution,[status(thm)],[133, 7860])).
% 3.44/3.62 tff(7862,plain,
% 3.44/3.62 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.44/3.62 inference(unit_resolution,[status(thm)],[5277, 7861, 4503, 1, 3170, 5153, 5143, 461, 3243])).
% 3.44/3.62 tff(7863,plain,
% 3.44/3.62 (~r(elem!1, z)),
% 3.44/3.62 inference(unit_resolution,[status(thm)],[3421, 5143, 3243])).
% 3.44/3.62 tff(7864,plain,
% 3.44/3.62 (~(s(elem!1) = elem!1)),
% 3.44/3.62 inference(unit_resolution,[status(thm)],[2150, 5161])).
% 3.44/3.62 tff(7865,plain,
% 3.44/3.62 (~(elem!1 = s(s(s(s(z)))))),
% 3.44/3.62 inference(unit_resolution,[status(thm)],[325, 5146])).
% 3.44/3.62 tff(7866,plain,
% 3.44/3.62 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.44/3.62 inference(unit_resolution,[status(thm)],[5293, 7861, 7865, 3244, 5155, 7864, 5156, 5153, 47, 7855, 3241, 7863])).
% 3.44/3.62 tff(7867,plain,
% 3.44/3.62 ($false),
% 3.44/3.62 inference(unit_resolution,[status(thm)],[691, 7866, 7862, 701])).
% 3.44/3.62 tff(7868,plain,((elem!1 = s(s(s(s(s(s(s(z)))))))) | b(s(s(z)), elem!1) | b(z, s(s(s(s(z))))) | b(s(s(s(s(z)))), z) | b(elem!1, s(s(z))) | b(z, s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.62 tff(7869,plain,
% 3.44/3.62 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 3.44/3.62 inference(unit_resolution,[status(thm)],[7868, 3242, 1, 3170, 461, 3241, 3240])).
% 3.44/3.62 tff(7870,plain,
% 3.44/3.62 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 3.44/3.62 inference(monotonicity,[status(thm)],[7869])).
% 3.44/3.62 tff(7871,plain,
% 3.44/3.62 (s(s(elem!1)) = s(s(s(s(s(s(s(s(s(z)))))))))),
% 3.44/3.62 inference(monotonicity,[status(thm)],[7870])).
% 3.44/3.62 tff(7872,plain,
% 3.44/3.62 (s(s(s(elem!1))) = s(s(s(s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.62 inference(monotonicity,[status(thm)],[7871])).
% 3.44/3.62 tff(7873,plain,
% 3.44/3.62 (s(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(s(elem!1)))),
% 3.44/3.62 inference(symmetry,[status(thm)],[7872])).
% 3.44/3.62 tff(7874,plain,
% 3.44/3.62 (b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z))))))))))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 3.44/3.62 inference(monotonicity,[status(thm)],[7873])).
% 3.44/3.62 tff(7875,plain,
% 3.44/3.62 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 3.44/3.62 inference(symmetry,[status(thm)],[7874])).
% 3.44/3.62 tff(7876,plain,
% 3.44/3.62 (r(s(s(z)), s(s(s(s(s(s(s(s(s(s(z))))))))))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 3.44/3.62 inference(monotonicity,[status(thm)],[7873])).
% 3.44/3.62 tff(7877,plain,
% 3.44/3.62 ((~r(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) <=> (~r(s(s(z)), s(s(s(elem!1)))))),
% 3.44/3.62 inference(monotonicity,[status(thm)],[7876])).
% 3.44/3.62 tff(7878,plain,
% 3.44/3.62 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.44/3.62 inference(monotonicity,[status(thm)],[7869])).
% 3.44/3.62 tff(7879,plain,
% 3.44/3.62 (~(s(elem!1) = s(s(z)))),
% 3.44/3.62 inference(unit_resolution,[status(thm)],[2832, 7869])).
% 3.44/3.62 tff(7880,plain,
% 3.44/3.62 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.44/3.62 inference(unit_resolution,[status(thm)],[2840, 7879])).
% 3.44/3.62 tff(7881,plain,
% 3.44/3.62 (~(elem!1 = s(s(s(elem!1))))),
% 3.44/3.62 inference(unit_resolution,[status(thm)],[2859, 7880, 7869])).
% 3.44/3.62 tff(7882,plain,
% 3.44/3.62 (r(elem!1, s(s(s(elem!1))))),
% 3.44/3.62 inference(unit_resolution,[status(thm)],[2054, 7881, 3240])).
% 3.44/3.62 tff(7883,plain,
% 3.44/3.62 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.44/3.62 inference(modus_ponens,[status(thm)],[7882, 7878])).
% 3.44/3.62 tff(7884,plain,
% 3.44/3.62 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z))))))))))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.44/3.62 inference(monotonicity,[status(thm)],[4345])).
% 3.44/3.62 tff(7885,plain,
% 3.44/3.62 (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(s(s(s(s(s(s(s(z)))))))))))),
% 3.44/3.62 inference(symmetry,[status(thm)],[7884])).
% 3.44/3.62 tff(7886,plain,
% 3.44/3.62 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 3.44/3.62 inference(modus_ponens,[status(thm)],[5128, 7885])).
% 3.44/3.62 tff(7887,assumption,(~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))), introduced(assumption)).
% 3.44/3.62 tff(7888,plain,
% 3.44/3.62 ($false),
% 3.44/3.62 inference(unit_resolution,[status(thm)],[7887, 7886])).
% 3.44/3.62 tff(7889,plain,(r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z))))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~(elem!1 = s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.62 tff(7890,plain,
% 3.44/3.62 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 3.44/3.62 inference(unit_resolution,[status(thm)],[7889, 7883, 7869])).
% 3.44/3.62 tff(7891,plain,
% 3.44/3.62 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.62 inference(monotonicity,[status(thm)],[7869])).
% 3.44/3.62 tff(7892,plain,
% 3.44/3.62 ((~b(s(s(z)), elem!1)) <=> (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 3.44/3.62 inference(monotonicity,[status(thm)],[7891])).
% 3.44/3.62 tff(7893,plain,
% 3.44/3.62 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.62 inference(modus_ponens,[status(thm)],[3241, 7892])).
% 3.44/3.62 tff(7894,plain,
% 3.44/3.62 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.62 inference(unit_resolution,[status(thm)],[249, 7893])).
% 3.44/3.62 tff(7895,assumption,(r(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))), introduced(assumption)).
% 3.44/3.62 tff(7896,assumption,(r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))), introduced(assumption)).
% 3.44/3.62 tff(7897,plain,
% 3.44/3.62 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 3.44/3.62 inference(rewrite,[status(thm)],[])).
% 3.44/3.62 tff(7898,plain,
% 3.44/3.62 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 3.44/3.62 inference(rewrite,[status(thm)],[])).
% 3.44/3.62 tff(7899,plain,
% 3.44/3.62 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z))))))))))))))),
% 3.44/3.62 inference(monotonicity,[status(thm)],[7898])).
% 3.44/3.62 tff(7900,plain,
% 3.44/3.62 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 3.44/3.62 inference(transitivity,[status(thm)],[7899, 7897])).
% 3.44/3.62 tff(7901,plain,
% 3.44/3.62 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.62 inference(quant_inst,[status(thm)],[])).
% 3.44/3.62 tff(7902,plain,
% 3.44/3.62 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z))))))))))))),
% 3.44/3.62 inference(modus_ponens,[status(thm)],[7901, 7900])).
% 3.44/3.62 tff(7903,plain,
% 3.44/3.62 ($false),
% 3.44/3.62 inference(unit_resolution,[status(thm)],[7902, 118, 224, 7896, 7895])).
% 3.44/3.62 tff(7904,plain,((~r(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z))))))))))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.62 tff(7905,plain,
% 3.44/3.62 (~r(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 3.44/3.62 inference(unit_resolution,[status(thm)],[7904, 7894, 7890])).
% 3.44/3.62 tff(7906,plain,
% 3.44/3.62 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.44/3.62 inference(modus_ponens,[status(thm)],[7905, 7877])).
% 3.44/3.62 tff(7907,plain,
% 3.44/3.62 (b(s(s(z)), s(s(s(elem!1))))),
% 3.44/3.62 inference(unit_resolution,[status(thm)],[4223, 7906])).
% 3.44/3.62 tff(7908,plain,
% 3.44/3.62 (b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 3.44/3.62 inference(modus_ponens,[status(thm)],[7907, 7875])).
% 3.44/3.62 tff(7909,plain,
% 3.44/3.62 (b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.44/3.62 inference(monotonicity,[status(thm)],[7873])).
% 3.44/3.62 tff(7910,plain,
% 3.44/3.62 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))),
% 3.44/3.62 inference(symmetry,[status(thm)],[7909])).
% 3.44/3.62 tff(7911,plain,
% 3.44/3.62 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.44/3.62 inference(unit_resolution,[status(thm)],[4173, 7880, 3260])).
% 3.44/3.62 tff(7912,plain,
% 3.44/3.62 (b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))),
% 3.44/3.62 inference(modus_ponens,[status(thm)],[7911, 7910])).
% 3.44/3.62 tff(7913,plain,
% 3.44/3.62 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(s(s(z))))))))))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.44/3.62 inference(monotonicity,[status(thm)],[7873])).
% 3.44/3.62 tff(7914,plain,
% 3.44/3.62 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 3.44/3.62 inference(symmetry,[status(thm)],[7913])).
% 3.44/3.62 tff(7915,plain,
% 3.44/3.62 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 3.44/3.62 inference(modus_ponens,[status(thm)],[4156, 3289])).
% 3.44/3.62 tff(7916,plain,
% 3.44/3.62 ($false),
% 3.44/3.62 inference(unit_resolution,[status(thm)],[2857, 7915])).
% 3.44/3.62 tff(7917,plain,((~(s(s(s(s(z)))) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.62 tff(7918,plain,
% 3.44/3.62 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 3.44/3.62 inference(unit_resolution,[status(thm)],[7917, 7880])).
% 3.44/3.62 tff(7919,plain,
% 3.44/3.62 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.44/3.62 inference(unit_resolution,[status(thm)],[5150, 7918])).
% 3.44/3.62 tff(7920,plain,
% 3.44/3.62 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 3.44/3.62 inference(modus_ponens,[status(thm)],[7919, 7914])).
% 3.44/3.62 tff(7921,plain,
% 3.44/3.62 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(z)) = s(s(s(elem!1))))),
% 3.44/3.62 inference(commutativity,[status(thm)],[])).
% 3.44/3.62 tff(7922,plain,
% 3.44/3.62 ((s(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 3.44/3.62 inference(monotonicity,[status(thm)],[7873])).
% 3.44/3.62 tff(7923,plain,
% 3.44/3.62 ((s(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(z))) <=> (s(s(z)) = s(s(s(elem!1))))),
% 3.44/3.62 inference(transitivity,[status(thm)],[7922, 7921])).
% 3.44/3.62 tff(7924,plain,
% 3.44/3.62 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(z)))),
% 3.44/3.62 inference(symmetry,[status(thm)],[7923])).
% 3.44/3.62 tff(7925,plain,
% 3.44/3.62 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(z))))),
% 3.44/3.62 inference(monotonicity,[status(thm)],[7924])).
% 3.44/3.62 tff(7926,plain,
% 3.44/3.62 (~(s(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(z)))),
% 3.44/3.62 inference(modus_ponens,[status(thm)],[1683, 7925])).
% 3.44/3.62 tff(7927,plain,
% 3.44/3.62 (b(elem!1, s(s(z))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.44/3.62 inference(monotonicity,[status(thm)],[7869])).
% 3.44/3.62 tff(7928,plain,
% 3.44/3.62 ((~b(elem!1, s(s(z)))) <=> (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 3.44/3.62 inference(monotonicity,[status(thm)],[7927])).
% 3.44/3.62 tff(7929,plain,
% 3.44/3.62 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.44/3.62 inference(modus_ponens,[status(thm)],[461, 7928])).
% 3.44/3.62 tff(7930,plain,
% 3.44/3.62 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.44/3.62 inference(unit_resolution,[status(thm)],[2960, 41, 7929, 3574])).
% 3.44/3.62 tff(7931,assumption,(r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))), introduced(assumption)).
% 3.44/3.62 tff(7932,plain,
% 3.44/3.62 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 3.44/3.62 inference(rewrite,[status(thm)],[])).
% 3.44/3.62 tff(7933,plain,
% 3.44/3.62 (((~r(s(s(s(s(s(s(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(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z))))))))))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 3.44/3.62 inference(rewrite,[status(thm)],[])).
% 3.44/3.62 tff(7934,plain,
% 3.44/3.62 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(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(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z))))))))))))))),
% 3.44/3.62 inference(monotonicity,[status(thm)],[7933])).
% 3.44/3.62 tff(7935,plain,
% 3.44/3.62 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(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(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 3.44/3.62 inference(transitivity,[status(thm)],[7934, 7932])).
% 3.44/3.62 tff(7936,plain,
% 3.44/3.62 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(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(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 3.44/3.62 inference(quant_inst,[status(thm)],[])).
% 3.44/3.62 tff(7937,plain,
% 3.44/3.62 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z))))))))))))),
% 3.44/3.62 inference(modus_ponens,[status(thm)],[7936, 7935])).
% 3.44/3.62 tff(7938,plain,
% 3.44/3.62 ($false),
% 3.44/3.62 inference(unit_resolution,[status(thm)],[7937, 118, 107, 7896, 7931])).
% 3.44/3.62 tff(7939,plain,((~r(s(s(s(s(s(s(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(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z))))))))))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.62 tff(7940,plain,
% 3.44/3.62 (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))),
% 3.44/3.62 inference(unit_resolution,[status(thm)],[7939, 7930, 7890])).
% 3.44/3.62 tff(7941,plain,
% 3.44/3.62 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(z))) | b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z))) | r(s(s(s(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(s(s(s(z)))))))))) = s(s(z))) | b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z))) | r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z))))),
% 3.44/3.62 inference(rewrite,[status(thm)],[])).
% 3.44/3.62 tff(7942,plain,
% 3.44/3.62 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(z))) | b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z))) | r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z))))),
% 3.44/3.62 inference(quant_inst,[status(thm)],[])).
% 3.44/3.62 tff(7943,plain,
% 3.44/3.62 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(z))) | b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z))) | r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))),
% 3.44/3.62 inference(modus_ponens,[status(thm)],[7942, 7941])).
% 3.44/3.62 tff(7944,plain,
% 3.44/3.62 ((s(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(z))) | b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))),
% 3.44/3.62 inference(unit_resolution,[status(thm)],[7943, 41, 7940])).
% 3.44/3.62 tff(7945,plain,
% 3.44/3.62 (b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))),
% 3.44/3.62 inference(unit_resolution,[status(thm)],[7944, 7926])).
% 3.44/3.62 tff(7946,plain,
% 3.44/3.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(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(s(s(s(z)))))))))))) | (~b(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(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(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))))),
% 3.44/3.62 inference(rewrite,[status(thm)],[])).
% 3.44/3.62 tff(7947,plain,
% 3.44/3.62 (((~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(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(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))))),
% 3.44/3.62 inference(rewrite,[status(thm)],[])).
% 3.44/3.62 tff(7948,plain,
% 3.44/3.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(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(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z))))))),
% 3.44/3.63 inference(monotonicity,[status(thm)],[7947])).
% 3.44/3.63 tff(7949,plain,
% 3.44/3.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(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(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))))),
% 3.44/3.63 inference(transitivity,[status(thm)],[7948, 7946])).
% 3.44/3.63 tff(7950,plain,
% 3.44/3.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))))),
% 3.44/3.63 inference(quant_inst,[status(thm)],[])).
% 3.44/3.63 tff(7951,plain,
% 3.44/3.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z))))),
% 3.44/3.63 inference(modus_ponens,[status(thm)],[7950, 7949])).
% 3.44/3.63 tff(7952,plain,
% 3.44/3.63 ($false),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[7951, 178, 4503, 7945, 7920, 7912, 7908])).
% 3.44/3.63 tff(7953,plain,(b(z, s(s(s(elem!1)))) | b(elem!1, s(s(z))) | b(s(s(z)), elem!1) | b(elem!1, s(s(s(elem!1)))) | b(z, s(s(s(s(z))))) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 3.44/3.63 tff(7954,plain,
% 3.44/3.63 (b(z, s(s(s(elem!1))))),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[7953, 3241, 461, 3240, 1, 3170])).
% 3.44/3.63 tff(7955,plain,
% 3.44/3.63 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(elem!1))))),
% 3.44/3.63 inference(monotonicity,[status(thm)],[1527])).
% 3.44/3.63 tff(7956,plain,
% 3.44/3.63 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 3.44/3.63 inference(symmetry,[status(thm)],[7955])).
% 3.44/3.63 tff(7957,plain,
% 3.44/3.63 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(z)))),
% 3.44/3.63 inference(transitivity,[status(thm)],[7956, 1666])).
% 3.44/3.63 tff(7958,plain,
% 3.44/3.63 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(z))))),
% 3.44/3.63 inference(monotonicity,[status(thm)],[7957])).
% 3.44/3.63 tff(7959,plain,
% 3.44/3.63 (~(elem!1 = s(s(z)))),
% 3.44/3.63 inference(modus_ponens,[status(thm)],[1683, 7958])).
% 3.44/3.63 tff(7960,plain,
% 3.44/3.63 (r(elem!1, s(s(z)))),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[467, 7959, 461])).
% 3.44/3.63 tff(7961,plain,
% 3.44/3.63 (b(z, elem!1)),
% 3.44/3.63 inference(modus_ponens,[status(thm)],[2043, 4183])).
% 3.44/3.63 tff(7962,plain,
% 3.44/3.63 (~(elem!1 = s(s(s(s(z)))))),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[1846, 7961, 1])).
% 3.44/3.63 tff(7963,plain,
% 3.44/3.63 ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) <=> (~b(elem!1, s(s(s(s(z))))))),
% 3.44/3.63 inference(monotonicity,[status(thm)],[3878])).
% 3.44/3.63 tff(7964,plain,
% 3.44/3.63 (~b(elem!1, s(s(s(s(z)))))),
% 3.44/3.63 inference(modus_ponens,[status(thm)],[4170, 7963])).
% 3.44/3.63 tff(7965,plain,
% 3.44/3.63 (r(elem!1, s(s(s(s(z)))))),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[483, 7964, 7962])).
% 3.44/3.63 tff(7966,plain,
% 3.44/3.63 ($false),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[3785, 7965, 7960, 193])).
% 3.44/3.63 tff(7967,plain,((~(elem!1 = s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(z)))) | b(elem!1, s(s(z))) | b(z, s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.63 tff(7968,plain,
% 3.44/3.63 (~(elem!1 = s(s(s(elem!1))))),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[7967, 103, 461, 1, 4170, 7954])).
% 3.44/3.63 tff(7969,plain,
% 3.44/3.63 (r(elem!1, s(s(s(elem!1))))),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[2054, 7968, 3240])).
% 3.44/3.63 tff(7970,plain,
% 3.44/3.63 (~r(s(s(z)), z)),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[199, 193, 3244])).
% 3.44/3.63 tff(7971,plain,
% 3.44/3.63 (b(s(s(z)), z)),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[3249, 7970])).
% 3.44/3.63 tff(7972,plain,
% 3.44/3.63 ($false),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[5684, 118, 3311, 438, 1823])).
% 3.44/3.63 tff(7973,plain,((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.63 tff(7974,plain,
% 3.44/3.63 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[7973, 4256, 3311])).
% 3.44/3.63 tff(7975,plain,
% 3.44/3.63 (b(s(s(z)), s(s(s(elem!1))))),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[4223, 7974])).
% 3.44/3.63 tff(7976,assumption,(b(s(s(s(elem!1))), z)), introduced(assumption)).
% 3.44/3.63 tff(7977,plain,
% 3.44/3.63 ($false),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[6292, 178, 2043, 7976, 3461, 273, 4291])).
% 3.44/3.63 tff(7978,plain,((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.63 tff(7979,plain,
% 3.44/3.63 (~b(s(s(s(elem!1))), z)),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[7978, 7975, 7971, 273, 2043])).
% 3.44/3.63 tff(7980,plain,
% 3.44/3.63 (r(s(s(s(elem!1))), z)),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[1565, 7979])).
% 3.44/3.63 tff(7981,plain,
% 3.44/3.63 (~r(elem!1, z)),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[6071, 7980, 3311])).
% 3.44/3.63 tff(7982,plain,
% 3.44/3.63 (b(elem!1, z)),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[498, 7981, 3873])).
% 3.44/3.63 tff(7983,plain,
% 3.44/3.63 (~(elem!1 = s(s(s(s(z)))))),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[3172, 7982, 3170])).
% 3.44/3.63 tff(7984,plain,
% 3.44/3.63 (b(elem!1, s(s(s(s(z)))))),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[483, 7983, 4246])).
% 3.44/3.63 tff(7985,plain,
% 3.44/3.63 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[4162, 7984, 3240])).
% 3.44/3.63 tff(7986,plain,
% 3.44/3.63 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[4168, 7985])).
% 3.44/3.63 tff(7987,plain,
% 3.44/3.63 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[4173, 7986, 4170])).
% 3.44/3.63 tff(7988,plain,
% 3.44/3.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.44/3.63 inference(rewrite,[status(thm)],[])).
% 3.44/3.63 tff(7989,plain,
% 3.44/3.63 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.44/3.63 inference(rewrite,[status(thm)],[])).
% 3.44/3.63 tff(7990,plain,
% 3.44/3.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 3.44/3.63 inference(monotonicity,[status(thm)],[7989])).
% 3.44/3.63 tff(7991,plain,
% 3.44/3.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.44/3.63 inference(transitivity,[status(thm)],[7990, 7988])).
% 3.44/3.63 tff(7992,plain,
% 3.44/3.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.44/3.63 inference(quant_inst,[status(thm)],[])).
% 3.44/3.63 tff(7993,plain,
% 3.44/3.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.44/3.63 inference(modus_ponens,[status(thm)],[7992, 7991])).
% 3.44/3.63 tff(7994,plain,
% 3.44/3.63 ($false),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[7993, 118, 7980, 3244, 7987])).
% 3.44/3.63 tff(7995,plain,((s(s(z)) = elem!1) | b(s(s(s(elem!1))), s(s(s(s(z))))) | b(elem!1, s(s(s(elem!1)))) | b(s(s(s(s(z)))), z) | (~r(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(z)))) | b(elem!1, s(s(z))) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.44/3.63 tff(7996,plain,
% 3.44/3.63 (s(s(z)) = elem!1),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[7995, 7969, 3240, 3170, 4170, 3271, 7954, 103, 461, 3241])).
% 3.44/3.63 tff(7997,plain,
% 3.44/3.63 ((s(elem!1) = s(s(z))) <=> (s(elem!1) = elem!1)),
% 3.44/3.63 inference(monotonicity,[status(thm)],[7996])).
% 3.44/3.63 tff(7998,plain,
% 3.44/3.63 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(z)))),
% 3.44/3.63 inference(symmetry,[status(thm)],[7997])).
% 3.44/3.63 tff(7999,plain,
% 3.44/3.63 ((~(s(elem!1) = elem!1)) <=> (~(s(elem!1) = s(s(z))))),
% 3.44/3.63 inference(monotonicity,[status(thm)],[7998])).
% 3.44/3.63 tff(8000,plain,
% 3.44/3.63 (~(s(s(s(elem!1))) = elem!1)),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[2489, 7968])).
% 3.44/3.63 tff(8001,plain,
% 3.44/3.63 (~(s(elem!1) = elem!1)),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[2150, 8000])).
% 3.44/3.63 tff(8002,plain,
% 3.44/3.63 (~(s(elem!1) = s(s(z)))),
% 3.44/3.63 inference(modus_ponens,[status(thm)],[8001, 7999])).
% 3.44/3.63 tff(8003,plain,
% 3.44/3.63 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[2840, 8002])).
% 3.44/3.63 tff(8004,plain,
% 3.44/3.63 (~b(s(s(s(s(z)))), elem!1)),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[3774, 7996, 86])).
% 3.44/3.63 tff(8005,plain,
% 3.44/3.63 (~r(s(s(z)), z)),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[199, 103, 3244])).
% 3.44/3.63 tff(8006,plain,
% 3.44/3.63 (~r(elem!1, z)),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[6206, 7996, 8005])).
% 3.44/3.63 tff(8007,plain,
% 3.44/3.63 (b(elem!1, z)),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[498, 8006, 3277])).
% 3.44/3.63 tff(8008,plain,
% 3.44/3.63 (~(elem!1 = s(s(s(s(z)))))),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[3172, 8007, 3170])).
% 3.44/3.63 tff(8009,plain,
% 3.44/3.63 (~(s(s(s(s(z)))) = elem!1)),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[504, 8008])).
% 3.44/3.63 tff(8010,plain,
% 3.44/3.63 (r(s(s(s(s(z)))), elem!1)),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[3142, 8009, 8004])).
% 3.44/3.63 tff(8011,plain,
% 3.44/3.63 (b(z, s(s(z))) <=> b(z, elem!1)),
% 3.44/3.63 inference(monotonicity,[status(thm)],[7996])).
% 3.44/3.63 tff(8012,plain,
% 3.44/3.63 (b(z, elem!1)),
% 3.44/3.63 inference(modus_ponens,[status(thm)],[3271, 8011])).
% 3.44/3.63 tff(8013,plain,
% 3.44/3.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.44/3.63 inference(rewrite,[status(thm)],[])).
% 3.44/3.63 tff(8014,plain,
% 3.44/3.63 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.44/3.63 inference(rewrite,[status(thm)],[])).
% 3.44/3.63 tff(8015,plain,
% 3.44/3.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 3.44/3.63 inference(monotonicity,[status(thm)],[8014])).
% 3.44/3.63 tff(8016,plain,
% 3.44/3.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.44/3.63 inference(transitivity,[status(thm)],[8015, 8013])).
% 3.44/3.63 tff(8017,plain,
% 3.44/3.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), z)))),
% 3.44/3.63 inference(quant_inst,[status(thm)],[])).
% 3.44/3.63 tff(8018,plain,
% 3.44/3.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.44/3.63 inference(modus_ponens,[status(thm)],[8017, 8016])).
% 3.44/3.63 tff(8019,plain,
% 3.44/3.63 (~r(s(s(s(elem!1))), z)),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[8018, 118, 145, 3251])).
% 3.44/3.63 tff(8020,plain,
% 3.44/3.63 (b(s(s(s(elem!1))), z)),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[1565, 8019])).
% 3.44/3.63 tff(8021,plain,
% 3.44/3.63 (~r(z, s(s(s(elem!1))))),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[3259, 3251, 145])).
% 3.44/3.63 tff(8022,plain,
% 3.44/3.63 (b(z, s(s(s(elem!1))))),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[2095, 8021])).
% 3.44/3.63 tff(8023,plain,
% 3.44/3.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 3.44/3.63 inference(rewrite,[status(thm)],[])).
% 3.44/3.63 tff(8024,plain,
% 3.44/3.63 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 3.44/3.63 inference(rewrite,[status(thm)],[])).
% 3.44/3.63 tff(8025,plain,
% 3.44/3.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1))))),
% 3.44/3.63 inference(monotonicity,[status(thm)],[8024])).
% 3.44/3.63 tff(8026,plain,
% 3.44/3.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 3.44/3.63 inference(transitivity,[status(thm)],[8025, 8023])).
% 3.44/3.63 tff(8027,plain,
% 3.44/3.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 3.44/3.63 inference(quant_inst,[status(thm)],[])).
% 3.44/3.63 tff(8028,plain,
% 3.44/3.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1))),
% 3.44/3.63 inference(modus_ponens,[status(thm)],[8027, 8026])).
% 3.44/3.63 tff(8029,plain,
% 3.44/3.63 (~b(s(s(s(elem!1))), elem!1)),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[8028, 178, 818, 506, 8022, 8020])).
% 3.44/3.63 tff(8030,plain,
% 3.44/3.63 (r(s(s(s(elem!1))), elem!1)),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[570, 8029, 949])).
% 3.44/3.63 tff(8031,plain,
% 3.44/3.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.44/3.63 inference(rewrite,[status(thm)],[])).
% 3.44/3.63 tff(8032,plain,
% 3.44/3.63 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~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)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.44/3.63 inference(rewrite,[status(thm)],[])).
% 3.44/3.63 tff(8033,plain,
% 3.44/3.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 3.44/3.63 inference(monotonicity,[status(thm)],[8032])).
% 3.44/3.63 tff(8034,plain,
% 3.44/3.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.44/3.63 inference(transitivity,[status(thm)],[8033, 8031])).
% 3.44/3.63 tff(8035,plain,
% 3.44/3.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.44/3.63 inference(quant_inst,[status(thm)],[])).
% 3.44/3.63 tff(8036,plain,
% 3.44/3.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.44/3.63 inference(modus_ponens,[status(thm)],[8035, 8034])).
% 3.44/3.63 tff(8037,plain,
% 3.44/3.63 ($false),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[8036, 118, 8030, 3132, 3251])).
% 3.44/3.63 tff(8038,plain,((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (s(s(s(elem!1))) = elem!1) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.63 tff(8039,plain,
% 3.44/3.63 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[8038, 8012, 8000, 8007, 8010, 47])).
% 3.44/3.63 tff(8040,plain,
% 3.44/3.63 ($false),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[4173, 8039, 8003, 4170])).
% 3.44/3.63 tff(8041,plain,(b(s(s(s(s(z)))), s(s(z))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | b(s(s(s(s(z)))), z) | b(elem!1, s(s(s(elem!1)))) | b(elem!1, s(s(z))) | b(s(s(z)), elem!1) | b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.63 tff(8042,plain,
% 3.44/3.63 (b(s(s(s(s(z)))), s(s(z)))),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[8041, 4170, 3170, 3240, 461, 3241, 1])).
% 3.44/3.63 tff(8043,plain,
% 3.44/3.63 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[4796, 8042, 701, 47, 3241, 461, 3244, 3240])).
% 3.44/3.63 tff(8044,plain,
% 3.44/3.63 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[4173, 8043, 4170])).
% 3.44/3.63 tff(8045,plain,
% 3.44/3.63 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[7917, 8043])).
% 3.44/3.63 tff(8046,plain,
% 3.44/3.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(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(elem!1))))))),
% 3.44/3.63 inference(rewrite,[status(thm)],[])).
% 3.44/3.63 tff(8047,plain,
% 3.44/3.63 (((~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(s(s(s(s(z))))))), s(s(s(elem!1)))))) <=> ((~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(elem!1))))))),
% 3.44/3.63 inference(rewrite,[status(thm)],[])).
% 3.44/3.63 tff(8048,plain,
% 3.44/3.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))))),
% 3.44/3.63 inference(monotonicity,[status(thm)],[8047])).
% 3.44/3.63 tff(8049,plain,
% 3.44/3.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.44/3.63 inference(transitivity,[status(thm)],[8048, 8046])).
% 3.44/3.63 tff(8050,plain,
% 3.44/3.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.44/3.63 inference(quant_inst,[status(thm)],[])).
% 3.44/3.63 tff(8051,plain,
% 3.44/3.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 3.44/3.63 inference(modus_ponens,[status(thm)],[8050, 8049])).
% 3.44/3.63 tff(8052,plain,
% 3.44/3.63 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[8051, 118, 1130, 3251])).
% 3.44/3.63 tff(8053,plain,
% 3.44/3.63 (b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.44/3.63 inference(unit_resolution,[status(thm)],[5118, 8052, 3521])).
% 3.44/3.63 tff(8054,plain,
% 3.44/3.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(s(s(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))))))),
% 3.44/3.63 inference(rewrite,[status(thm)],[])).
% 3.44/3.63 tff(8055,plain,
% 3.44/3.63 (((~b(s(s(s(elem!1))), 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(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(s(s(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))))))),
% 3.44/3.63 inference(rewrite,[status(thm)],[])).
% 3.44/3.63 tff(8056,plain,
% 3.44/3.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(s(s(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)))))))),
% 3.44/3.63 inference(monotonicity,[status(thm)],[8055])).
% 3.44/3.63 tff(8057,plain,
% 3.44/3.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(s(s(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))))))),
% 3.44/3.64 inference(transitivity,[status(thm)],[8056, 8054])).
% 3.44/3.64 tff(8058,plain,
% 3.44/3.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.64 inference(quant_inst,[status(thm)],[])).
% 3.44/3.64 tff(8059,plain,
% 3.44/3.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 3.44/3.64 inference(modus_ponens,[status(thm)],[8058, 8057])).
% 3.44/3.64 tff(8060,plain,
% 3.44/3.64 ($false),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[8059, 178, 2043, 8020, 4845, 1140, 8053])).
% 3.44/3.64 tff(8061,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.64 tff(8062,plain,
% 3.44/3.64 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[8061, 4511, 2043, 3251, 145])).
% 3.44/3.64 tff(8063,plain,
% 3.44/3.64 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[84, 8062])).
% 3.44/3.64 tff(8064,plain,
% 3.44/3.64 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[4690, 203, 3261])).
% 3.44/3.64 tff(8065,plain,
% 3.44/3.64 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[249, 8064])).
% 3.44/3.64 tff(8066,plain,
% 3.44/3.64 ($false),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[259, 8065, 223, 202, 4803, 104])).
% 3.44/3.64 tff(8067,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.64 tff(8068,plain,
% 3.44/3.64 (~r(z, s(s(z)))),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[8067, 203, 202, 8063, 145])).
% 3.44/3.64 tff(8069,plain,
% 3.44/3.64 (b(z, s(s(z)))),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[143, 8068])).
% 3.44/3.64 tff(8070,plain,
% 3.44/3.64 (~r(s(s(z)), z)),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[155, 147, 145])).
% 3.44/3.64 tff(8071,plain,
% 3.44/3.64 (b(s(s(z)), z)),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[3249, 8070])).
% 3.44/3.64 tff(8072,plain,
% 3.44/3.64 (~b(s(s(z)), s(s(s(elem!1))))),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[7978, 8071, 8020, 273, 2043])).
% 3.44/3.64 tff(8073,plain,
% 3.44/3.64 (r(s(s(z)), s(s(s(elem!1))))),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[4223, 8072])).
% 3.44/3.64 tff(8074,plain,
% 3.44/3.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.44/3.64 inference(rewrite,[status(thm)],[])).
% 3.44/3.64 tff(8075,plain,
% 3.44/3.64 (((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(elem!1)))))) <=> ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.44/3.64 inference(rewrite,[status(thm)],[])).
% 3.44/3.64 tff(8076,plain,
% 3.44/3.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 3.44/3.64 inference(monotonicity,[status(thm)],[8075])).
% 3.44/3.64 tff(8077,plain,
% 3.44/3.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.44/3.64 inference(transitivity,[status(thm)],[8076, 8074])).
% 3.44/3.64 tff(8078,plain,
% 3.44/3.64 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 3.44/3.64 inference(quant_inst,[status(thm)],[])).
% 3.44/3.64 tff(8079,plain,
% 3.44/3.64 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.44/3.64 inference(modus_ponens,[status(thm)],[8078, 8077])).
% 3.44/3.64 tff(8080,plain,
% 3.44/3.64 ($false),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[8079, 118, 8073, 147, 3251])).
% 3.44/3.64 tff(8081,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.64 tff(8082,plain,
% 3.44/3.64 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[8081, 8069, 3251, 2043, 145])).
% 3.44/3.64 tff(8083,plain,
% 3.44/3.64 (b(s(s(z)), s(s(s(s(z)))))),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[164, 8082])).
% 3.44/3.64 tff(8084,plain,
% 3.44/3.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 3.44/3.64 inference(rewrite,[status(thm)],[])).
% 3.44/3.64 tff(8085,plain,
% 3.44/3.64 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(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(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(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(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 3.44/3.64 inference(rewrite,[status(thm)],[])).
% 3.44/3.64 tff(8086,plain,
% 3.44/3.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(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(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 3.44/3.64 inference(monotonicity,[status(thm)],[8085])).
% 3.44/3.64 tff(8087,plain,
% 3.44/3.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(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(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 3.44/3.64 inference(transitivity,[status(thm)],[8086, 8084])).
% 3.44/3.64 tff(8088,plain,
% 3.44/3.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(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(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.64 inference(quant_inst,[status(thm)],[])).
% 3.44/3.64 tff(8089,plain,
% 3.44/3.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 3.44/3.64 inference(modus_ponens,[status(thm)],[8088, 8087])).
% 3.44/3.64 tff(8090,plain,
% 3.44/3.64 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[8089, 178, 8063, 8083, 223, 202])).
% 3.44/3.64 tff(8091,plain,
% 3.44/3.64 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[3578, 8090])).
% 3.44/3.64 tff(8092,plain,
% 3.44/3.64 (~(elem!1 = z)),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[3276, 8069, 461])).
% 3.44/3.64 tff(8093,plain,
% 3.44/3.64 (~(z = elem!1)),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[317, 8092])).
% 3.44/3.64 tff(8094,plain,
% 3.44/3.64 (~(s(s(elem!1)) = s(s(z)))),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[2386, 8093])).
% 3.44/3.64 tff(8095,plain,
% 3.44/3.64 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[259, 8083, 202, 223, 8063])).
% 3.44/3.64 tff(8096,plain,
% 3.44/3.64 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[249, 8095])).
% 3.44/3.64 tff(8097,plain,
% 3.44/3.64 (~r(s(s(z)), z)),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[232, 8096, 203])).
% 3.44/3.64 tff(8098,plain,
% 3.44/3.64 (b(s(s(z)), z)),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[3249, 8097])).
% 3.44/3.64 tff(8099,plain,
% 3.44/3.64 (~b(s(s(z)), s(s(s(elem!1))))),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[7978, 8098, 8020, 8069, 2043])).
% 3.44/3.64 tff(8100,plain,
% 3.44/3.64 (r(s(s(z)), s(s(s(elem!1))))),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[4223, 8099])).
% 3.44/3.64 tff(8101,plain,
% 3.44/3.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 3.44/3.64 inference(rewrite,[status(thm)],[])).
% 3.44/3.64 tff(8102,plain,
% 3.44/3.64 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 3.44/3.64 inference(rewrite,[status(thm)],[])).
% 3.44/3.64 tff(8103,plain,
% 3.44/3.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 3.44/3.64 inference(monotonicity,[status(thm)],[8102])).
% 3.44/3.64 tff(8104,plain,
% 3.44/3.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 3.44/3.64 inference(transitivity,[status(thm)],[8103, 8101])).
% 3.44/3.64 tff(8105,plain,
% 3.44/3.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))))),
% 3.44/3.64 inference(quant_inst,[status(thm)],[])).
% 3.44/3.64 tff(8106,plain,
% 3.44/3.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z))))),
% 3.44/3.64 inference(modus_ponens,[status(thm)],[8105, 8104])).
% 3.44/3.64 tff(8107,plain,
% 3.44/3.64 (~b(s(s(s(elem!1))), s(s(z)))),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[8106, 178, 2043, 8020, 8098, 8069])).
% 3.44/3.64 tff(8108,plain,
% 3.44/3.64 (r(s(s(s(elem!1))), s(s(z)))),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[4209, 41, 8107, 4181])).
% 3.44/3.64 tff(8109,plain,
% 3.44/3.64 (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[7850, 118, 8108, 8091])).
% 3.44/3.64 tff(8110,plain,
% 3.44/3.64 ((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))))))))),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[3612, 41, 8109])).
% 3.44/3.64 tff(8111,plain,
% 3.44/3.64 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[8110, 5617])).
% 3.44/3.64 tff(8112,plain,
% 3.44/3.64 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[5361, 1324])).
% 3.44/3.64 tff(8113,plain,
% 3.44/3.64 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.44/3.64 inference(modus_ponens,[status(thm)],[107, 3547])).
% 3.44/3.64 tff(8114,plain,
% 3.44/3.64 (r(s(s(s(z))), elem!1) <=> r(s(elem!1), elem!1)),
% 3.44/3.64 inference(monotonicity,[status(thm)],[3505])).
% 3.44/3.64 tff(8115,plain,
% 3.44/3.64 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(z))), elem!1)),
% 3.44/3.64 inference(monotonicity,[status(thm)],[1324])).
% 3.44/3.64 tff(8116,plain,
% 3.44/3.64 (r(s(s(s(z))), s(s(z))) <=> r(s(elem!1), elem!1)),
% 3.44/3.64 inference(transitivity,[status(thm)],[8115, 8114])).
% 3.44/3.64 tff(8117,plain,
% 3.44/3.64 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[8081, 273, 3251, 2043, 145])).
% 3.44/3.64 tff(8118,plain,
% 3.44/3.64 (b(s(s(z)), s(s(s(s(z)))))),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[164, 8117])).
% 3.44/3.64 tff(8119,plain,
% 3.44/3.64 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 3.44/3.64 inference(monotonicity,[status(thm)],[3505])).
% 3.44/3.64 tff(8120,plain,
% 3.44/3.64 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 3.44/3.64 inference(symmetry,[status(thm)],[8119])).
% 3.44/3.64 tff(8121,plain,
% 3.44/3.64 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 3.44/3.64 inference(monotonicity,[status(thm)],[3507])).
% 3.44/3.64 tff(8122,plain,
% 3.44/3.64 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 3.44/3.64 inference(transitivity,[status(thm)],[8121, 8120])).
% 3.44/3.64 tff(8123,plain,
% 3.44/3.64 ((s(elem!1) = s(s(elem!1))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 3.44/3.64 inference(monotonicity,[status(thm)],[3507])).
% 3.44/3.64 tff(8124,plain,
% 3.44/3.64 ((s(elem!1) = s(s(elem!1))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 3.44/3.64 inference(transitivity,[status(thm)],[8123, 2163])).
% 3.44/3.64 tff(8125,plain,
% 3.44/3.64 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(elem!1) = s(s(elem!1)))),
% 3.44/3.64 inference(symmetry,[status(thm)],[8124])).
% 3.44/3.64 tff(8126,plain,
% 3.44/3.64 ((~(s(s(s(s(z)))) = s(elem!1))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 3.44/3.64 inference(monotonicity,[status(thm)],[8125])).
% 3.44/3.64 tff(8127,plain,
% 3.44/3.64 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 3.44/3.64 inference(monotonicity,[status(thm)],[3505])).
% 3.44/3.64 tff(8128,plain,
% 3.44/3.64 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 3.44/3.64 inference(monotonicity,[status(thm)],[8127])).
% 3.44/3.64 tff(8129,plain,
% 3.44/3.64 (~(s(s(s(s(z)))) = s(elem!1))),
% 3.44/3.64 inference(modus_ponens,[status(thm)],[4938, 8128])).
% 3.44/3.64 tff(8130,plain,
% 3.44/3.64 (~(s(elem!1) = s(s(elem!1)))),
% 3.44/3.64 inference(modus_ponens,[status(thm)],[8129, 8126])).
% 3.44/3.64 tff(8131,plain,
% 3.44/3.64 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.44/3.64 inference(monotonicity,[status(thm)],[3506])).
% 3.44/3.64 tff(8132,plain,
% 3.44/3.64 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.44/3.64 inference(modus_ponens,[status(thm)],[3251, 8131])).
% 3.44/3.64 tff(8133,plain,
% 3.44/3.64 (r(z, s(s(s(s(z))))) <=> r(z, s(s(elem!1)))),
% 3.44/3.64 inference(monotonicity,[status(thm)],[3506])).
% 3.44/3.64 tff(8134,plain,
% 3.44/3.64 (r(z, s(s(elem!1)))),
% 3.44/3.64 inference(modus_ponens,[status(thm)],[145, 8133])).
% 3.44/3.64 tff(8135,plain,
% 3.44/3.64 (elem!1 = s(s(z))),
% 3.44/3.64 inference(symmetry,[status(thm)],[1324])).
% 3.44/3.64 tff(8136,plain,
% 3.44/3.64 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(z)) = s(s(s(s(elem!1)))))),
% 3.44/3.64 inference(monotonicity,[status(thm)],[8135])).
% 3.44/3.64 tff(8137,plain,
% 3.44/3.64 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 3.44/3.64 inference(symmetry,[status(thm)],[8136])).
% 3.44/3.64 tff(8138,plain,
% 3.44/3.64 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 3.44/3.64 inference(monotonicity,[status(thm)],[8137])).
% 3.44/3.64 tff(8139,plain,
% 3.44/3.64 (~(elem!1 = s(s(s(s(elem!1)))))),
% 3.44/3.64 inference(modus_ponens,[status(thm)],[2131, 8138])).
% 3.44/3.64 tff(8140,plain,
% 3.44/3.64 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[1509, 8139])).
% 3.44/3.64 tff(8141,plain,
% 3.44/3.64 (~r(z, s(elem!1))),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[5550, 118, 5972, 5226])).
% 3.44/3.64 tff(8142,plain,
% 3.44/3.64 (b(z, s(elem!1))),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[2351, 8141])).
% 3.44/3.64 tff(8143,plain,
% 3.44/3.64 (~r(s(elem!1), z)),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[5542, 118, 5972, 5226])).
% 3.44/3.64 tff(8144,plain,
% 3.44/3.64 (b(s(elem!1), z)),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[774, 8143])).
% 3.44/3.64 tff(8145,plain,
% 3.44/3.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.44/3.64 inference(rewrite,[status(thm)],[])).
% 3.44/3.64 tff(8146,plain,
% 3.44/3.64 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(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)))))),
% 3.44/3.64 inference(rewrite,[status(thm)],[])).
% 3.44/3.64 tff(8147,plain,
% 3.44/3.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))))),
% 3.44/3.64 inference(monotonicity,[status(thm)],[8146])).
% 3.44/3.64 tff(8148,plain,
% 3.44/3.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.44/3.64 inference(transitivity,[status(thm)],[8147, 8145])).
% 3.44/3.64 tff(8149,plain,
% 3.44/3.64 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 3.44/3.64 inference(quant_inst,[status(thm)],[])).
% 3.44/3.64 tff(8150,plain,
% 3.44/3.64 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 3.44/3.64 inference(modus_ponens,[status(thm)],[8149, 8148])).
% 3.44/3.64 tff(8151,plain,
% 3.44/3.64 (~r(s(elem!1), s(s(s(elem!1))))),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[8150, 118, 5227, 5972])).
% 3.44/3.64 tff(8152,plain,
% 3.44/3.64 (b(s(elem!1), s(s(s(elem!1))))),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[5432, 8151, 5396])).
% 3.44/3.64 tff(8153,plain,
% 3.44/3.64 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[5978, 118, 5227, 5972])).
% 3.44/3.64 tff(8154,plain,
% 3.44/3.64 (b(s(s(s(elem!1))), s(elem!1))),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[373, 8153, 356])).
% 3.44/3.64 tff(8155,plain,
% 3.44/3.64 ($false),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[6736, 8154, 8152, 2043, 8144, 8142])).
% 3.44/3.64 tff(8156,plain,((~r(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.64 tff(8157,plain,
% 3.44/3.64 (~r(s(elem!1), s(s(elem!1)))),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[8156, 8140, 2043, 8134, 8132])).
% 3.44/3.64 tff(8158,plain,
% 3.44/3.64 (b(s(elem!1), s(s(elem!1)))),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[1028, 8157, 8130])).
% 3.44/3.64 tff(8159,plain,
% 3.44/3.64 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.44/3.64 inference(modus_ponens,[status(thm)],[8158, 8122])).
% 3.44/3.64 tff(8160,plain,
% 3.44/3.64 (~b(s(s(s(z))), s(s(z)))),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[4963, 8159, 194, 202, 273, 8118])).
% 3.44/3.64 tff(8161,plain,
% 3.44/3.64 (r(s(s(s(z))), s(s(z)))),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[4966, 8160])).
% 3.44/3.64 tff(8162,plain,
% 3.44/3.64 (r(s(elem!1), elem!1)),
% 3.44/3.64 inference(modus_ponens,[status(thm)],[8161, 8116])).
% 3.44/3.64 tff(8163,plain,
% 3.44/3.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(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)))),
% 3.44/3.64 inference(rewrite,[status(thm)],[])).
% 3.44/3.64 tff(8164,plain,
% 3.44/3.64 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), 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)))),
% 3.44/3.64 inference(rewrite,[status(thm)],[])).
% 3.44/3.64 tff(8165,plain,
% 3.44/3.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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))))),
% 3.44/3.64 inference(monotonicity,[status(thm)],[8164])).
% 3.44/3.64 tff(8166,plain,
% 3.44/3.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(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)))),
% 3.44/3.64 inference(transitivity,[status(thm)],[8165, 8163])).
% 3.44/3.64 tff(8167,plain,
% 3.44/3.64 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.64 inference(quant_inst,[status(thm)],[])).
% 3.44/3.64 tff(8168,plain,
% 3.44/3.64 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 3.44/3.64 inference(modus_ponens,[status(thm)],[8167, 8166])).
% 3.44/3.64 tff(8169,plain,
% 3.44/3.64 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[8168, 118, 8162, 8113])).
% 3.44/3.64 tff(8170,plain,
% 3.44/3.64 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[395, 8169, 8112])).
% 3.44/3.64 tff(8171,plain,
% 3.44/3.64 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), elem!1)),
% 3.44/3.64 inference(monotonicity,[status(thm)],[1324])).
% 3.44/3.64 tff(8172,plain,
% 3.44/3.64 (r(s(s(s(elem!1))), elem!1)),
% 3.44/3.64 inference(modus_ponens,[status(thm)],[3859, 8171])).
% 3.44/3.64 tff(8173,plain,
% 3.44/3.64 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[1574, 118, 8162, 8172])).
% 3.44/3.64 tff(8174,plain,
% 3.44/3.64 (b(s(s(s(elem!1))), s(elem!1))),
% 3.44/3.64 inference(unit_resolution,[status(thm)],[373, 8173, 8140])).
% 3.44/3.64 tff(8175,plain,
% 3.44/3.64 (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)))),
% 3.44/3.64 inference(monotonicity,[status(thm)],[3506])).
% 3.44/3.64 tff(8176,plain,
% 3.44/3.64 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.44/3.64 inference(modus_ponens,[status(thm)],[104, 8175])).
% 3.44/3.64 tff(8177,plain,
% 3.44/3.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(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(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(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(s(elem!1)))))),
% 3.44/3.64 inference(rewrite,[status(thm)],[])).
% 3.44/3.64 tff(8178,plain,
% 3.44/3.64 (((~b(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)))) | (~b(s(elem!1), s(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(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(elem!1), s(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(s(elem!1)))))),
% 3.44/3.64 inference(rewrite,[status(thm)],[])).
% 3.44/3.64 tff(8179,plain,
% 3.44/3.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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)))) | (~b(s(elem!1), s(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(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(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(s(elem!1))))))),
% 3.44/3.65 inference(monotonicity,[status(thm)],[8178])).
% 3.44/3.65 tff(8180,plain,
% 3.44/3.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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)))) | (~b(s(elem!1), s(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(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(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(s(elem!1)))))),
% 3.44/3.65 inference(transitivity,[status(thm)],[8179, 8177])).
% 3.44/3.65 tff(8181,plain,
% 3.44/3.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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)))) | (~b(s(elem!1), s(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(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 3.44/3.65 inference(quant_inst,[status(thm)],[])).
% 3.44/3.65 tff(8182,plain,
% 3.44/3.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 3.44/3.65 inference(modus_ponens,[status(thm)],[8181, 8180])).
% 3.44/3.65 tff(8183,plain,
% 3.44/3.65 ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[8182, 178, 8158, 3830, 8176])).
% 3.44/3.65 tff(8184,plain,
% 3.44/3.65 ($false),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[8183, 8174, 8170])).
% 3.44/3.65 tff(8185,plain,((~(s(s(z)) = elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(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(z)))) | (~r(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.65 tff(8186,plain,
% 3.44/3.65 (~(s(s(z)) = elem!1)),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[8185, 8111, 194, 202, 8069, 2043, 3251, 145, 8063, 8091, 8108])).
% 3.44/3.65 tff(8187,plain,
% 3.44/3.65 (r(s(s(z)), elem!1)),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[448, 8186, 3241])).
% 3.44/3.65 tff(8188,plain,
% 3.44/3.65 (~r(elem!1, s(s(s(elem!1))))),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[7973, 8187, 8100])).
% 3.44/3.65 tff(8189,plain,
% 3.44/3.65 (elem!1 = s(s(s(elem!1)))),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[2054, 8188, 3240])).
% 3.44/3.65 tff(8190,plain,
% 3.44/3.65 (~(s(s(s(z))) = elem!1)),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[4830, 8189, 8094])).
% 3.44/3.65 tff(8191,plain,
% 3.44/3.65 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 3.44/3.65 inference(monotonicity,[status(thm)],[1527])).
% 3.44/3.65 tff(8192,plain,
% 3.44/3.65 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 3.44/3.65 inference(monotonicity,[status(thm)],[1527])).
% 3.44/3.65 tff(8193,plain,
% 3.44/3.65 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), elem!1)),
% 3.44/3.65 inference(symmetry,[status(thm)],[8192])).
% 3.44/3.65 tff(8194,plain,
% 3.44/3.65 ((~r(s(s(s(z))), s(s(s(elem!1))))) <=> (~r(s(s(s(z))), elem!1))),
% 3.44/3.65 inference(monotonicity,[status(thm)],[8193])).
% 3.44/3.65 tff(8195,plain,
% 3.44/3.65 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 3.44/3.65 inference(rewrite,[status(thm)],[])).
% 3.44/3.65 tff(8196,plain,
% 3.44/3.65 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 3.44/3.65 inference(quant_inst,[status(thm)],[])).
% 3.44/3.65 tff(8197,plain,
% 3.44/3.65 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 3.44/3.65 inference(modus_ponens,[status(thm)],[8196, 8195])).
% 3.44/3.65 tff(8198,plain,
% 3.44/3.65 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[8197, 118, 3251, 4891])).
% 3.44/3.65 tff(8199,plain,
% 3.44/3.65 (~r(s(s(s(z))), elem!1)),
% 3.44/3.65 inference(modus_ponens,[status(thm)],[8198, 8194])).
% 3.44/3.65 tff(8200,plain,
% 3.44/3.65 (b(s(s(s(z))), elem!1)),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[4981, 8199, 4970])).
% 3.44/3.65 tff(8201,plain,
% 3.44/3.65 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.44/3.65 inference(modus_ponens,[status(thm)],[8200, 8191])).
% 3.44/3.65 tff(8202,plain,
% 3.44/3.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 3.44/3.65 inference(rewrite,[status(thm)],[])).
% 3.44/3.65 tff(8203,plain,
% 3.44/3.65 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 3.44/3.65 inference(rewrite,[status(thm)],[])).
% 3.44/3.65 tff(8204,plain,
% 3.44/3.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 3.44/3.65 inference(monotonicity,[status(thm)],[8203])).
% 3.44/3.65 tff(8205,plain,
% 3.44/3.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 3.44/3.65 inference(transitivity,[status(thm)],[8204, 8202])).
% 3.44/3.65 tff(8206,plain,
% 3.44/3.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))))),
% 3.44/3.65 inference(quant_inst,[status(thm)],[])).
% 3.44/3.65 tff(8207,plain,
% 3.44/3.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 3.44/3.65 inference(modus_ponens,[status(thm)],[8206, 8205])).
% 3.44/3.65 tff(8208,plain,
% 3.44/3.65 ($false),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[8207, 178, 2043, 8020, 4921, 4904, 8201])).
% 3.44/3.65 tff(8209,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~(elem!1 = s(s(s(elem!1))))) | (s(s(s(z))) = elem!1) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.65 tff(8210,plain,
% 3.44/3.65 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[8209, 8189, 2043, 8190, 145, 3251])).
% 3.44/3.65 tff(8211,plain,
% 3.44/3.65 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[4928, 8210, 4890])).
% 3.44/3.65 tff(8212,plain,
% 3.44/3.65 (~b(s(s(s(z))), s(s(z)))),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[4963, 8211, 194, 202, 8069, 8083])).
% 3.44/3.65 tff(8213,plain,
% 3.44/3.65 (r(s(s(s(z))), s(s(z)))),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[4966, 8212])).
% 3.44/3.65 tff(8214,plain,
% 3.44/3.65 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[1175, 118, 8213, 8091])).
% 3.44/3.65 tff(8215,plain,
% 3.44/3.65 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 8214])).
% 3.44/3.65 tff(8216,assumption,(r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 3.44/3.65 tff(8217,plain,
% 3.44/3.65 ($false),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[1197, 118, 1125, 107, 8216])).
% 3.44/3.65 tff(8218,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.65 tff(8219,plain,
% 3.44/3.65 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[8218, 8213, 8091])).
% 3.44/3.65 tff(8220,plain,
% 3.44/3.65 ((s(s(s(z))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[5031, 41, 8219])).
% 3.44/3.65 tff(8221,plain,
% 3.44/3.65 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[8220, 5021])).
% 3.44/3.65 tff(8222,plain,
% 3.44/3.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(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(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(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(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.65 inference(rewrite,[status(thm)],[])).
% 3.44/3.65 tff(8223,plain,
% 3.44/3.65 (((~b(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))))))))) | (~b(s(s(s(z))), s(s(s(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(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)))))) | (~b(s(s(s(s(z)))), s(s(s(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(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.65 inference(rewrite,[status(thm)],[])).
% 3.44/3.65 tff(8224,plain,
% 3.44/3.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(s(z))), s(s(s(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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(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(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 3.44/3.65 inference(monotonicity,[status(thm)],[8223])).
% 3.44/3.65 tff(8225,plain,
% 3.44/3.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(s(z))), s(s(s(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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(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(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.65 inference(transitivity,[status(thm)],[8224, 8222])).
% 3.44/3.65 tff(8226,plain,
% 3.44/3.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(s(z))), s(s(s(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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 3.44/3.65 inference(quant_inst,[status(thm)],[])).
% 3.44/3.65 tff(8227,plain,
% 3.44/3.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.44/3.65 inference(modus_ponens,[status(thm)],[8226, 8225])).
% 3.44/3.65 tff(8228,plain,
% 3.44/3.65 ($false),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[8227, 178, 8063, 223, 8211, 8221, 8215])).
% 3.44/3.65 tff(8229,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | b(elem!1, s(s(s(elem!1)))) | b(s(s(z)), elem!1) | b(elem!1, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.65 tff(8230,plain,
% 3.44/3.65 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[8229, 8042, 3244, 7954, 47, 8044, 3240, 3241, 461])).
% 3.44/3.65 tff(8231,plain,
% 3.44/3.65 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[271, 8230])).
% 3.44/3.65 tff(8232,plain,
% 3.44/3.65 (~b(z, s(s(z)))),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[8081, 147, 3251, 2043, 145])).
% 3.44/3.65 tff(8233,plain,
% 3.44/3.65 ($false),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[143, 8232, 3479])).
% 3.44/3.65 tff(8234,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.65 tff(8235,plain,
% 3.44/3.65 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[8234, 3251, 2043, 145])).
% 3.44/3.65 tff(8236,plain,
% 3.44/3.65 (b(s(s(z)), s(s(s(s(z)))))),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[164, 8235])).
% 3.44/3.65 tff(8237,plain,
% 3.44/3.65 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[7840, 178, 273, 8063, 8236, 595])).
% 3.44/3.65 tff(8238,plain,
% 3.44/3.65 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[3578, 8237])).
% 3.44/3.65 tff(8239,assumption,(s(s(s(z))) = s(s(s(elem!1)))), introduced(assumption)).
% 3.44/3.65 tff(8240,plain,
% 3.44/3.65 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 3.44/3.65 inference(monotonicity,[status(thm)],[8239])).
% 3.44/3.65 tff(8241,plain,
% 3.44/3.65 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 3.44/3.65 inference(symmetry,[status(thm)],[8240])).
% 3.44/3.65 tff(8242,plain,
% 3.44/3.65 (s(s(elem!1)) = s(s(z))),
% 3.44/3.65 inference(transitivity,[status(thm)],[344, 8241, 65])).
% 3.44/3.65 tff(8243,plain,
% 3.44/3.65 ($false),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[2484, 8242])).
% 3.44/3.65 tff(8244,plain,((~(s(s(s(z))) = s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.65 tff(8245,plain,
% 3.44/3.65 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[8244, 3875])).
% 3.44/3.65 tff(8246,assumption,(~(s(s(s(z))) = s(s(s(elem!1))))), introduced(assumption)).
% 3.44/3.65 tff(8247,plain,
% 3.44/3.65 (((~![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)))))),
% 3.44/3.65 inference(rewrite,[status(thm)],[])).
% 3.44/3.65 tff(8248,plain,
% 3.44/3.65 ((~![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)))))),
% 3.44/3.65 inference(quant_inst,[status(thm)],[])).
% 3.44/3.65 tff(8249,plain,
% 3.44/3.65 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1))))),
% 3.44/3.65 inference(modus_ponens,[status(thm)],[8248, 8247])).
% 3.44/3.65 tff(8250,plain,
% 3.44/3.65 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[8249, 41, 8198, 8246])).
% 3.44/3.65 tff(8251,plain,
% 3.44/3.65 ($false),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[8207, 178, 2043, 8020, 4921, 4904, 8250])).
% 3.44/3.65 tff(8252,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.65 tff(8253,plain,
% 3.44/3.65 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[8252, 8245, 2043, 145, 3251])).
% 3.44/3.65 tff(8254,plain,
% 3.44/3.65 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[4928, 8253, 4890])).
% 3.44/3.65 tff(8255,plain,
% 3.44/3.65 (~b(s(s(s(z))), s(s(z)))),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[4963, 8254, 194, 202, 273, 8236])).
% 3.44/3.65 tff(8256,plain,
% 3.44/3.65 (r(s(s(s(z))), s(s(z)))),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[4966, 8255])).
% 3.44/3.65 tff(8257,plain,
% 3.44/3.65 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[1175, 118, 8256, 8238])).
% 3.44/3.65 tff(8258,plain,
% 3.44/3.65 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 8257])).
% 3.44/3.65 tff(8259,plain,
% 3.44/3.65 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[8218, 8238, 8256])).
% 3.44/3.65 tff(8260,plain,
% 3.44/3.65 ((s(s(s(z))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[5031, 41, 8259])).
% 3.44/3.65 tff(8261,plain,
% 3.44/3.65 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[8260, 5021])).
% 3.44/3.65 tff(8262,plain,
% 3.44/3.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.65 inference(rewrite,[status(thm)],[])).
% 3.44/3.65 tff(8263,plain,
% 3.44/3.65 (((~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(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z)))))) <=> ((~b(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(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.65 inference(rewrite,[status(thm)],[])).
% 3.44/3.65 tff(8264,plain,
% 3.44/3.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 3.44/3.65 inference(monotonicity,[status(thm)],[8263])).
% 3.44/3.65 tff(8265,plain,
% 3.44/3.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.65 inference(transitivity,[status(thm)],[8264, 8262])).
% 3.44/3.65 tff(8266,plain,
% 3.44/3.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))))),
% 3.44/3.65 inference(quant_inst,[status(thm)],[])).
% 3.44/3.65 tff(8267,plain,
% 3.44/3.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.44/3.65 inference(modus_ponens,[status(thm)],[8266, 8265])).
% 3.44/3.65 tff(8268,plain,
% 3.44/3.65 ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[8267, 178, 8063, 595, 8254])).
% 3.44/3.65 tff(8269,plain,
% 3.44/3.65 (~b(z, s(s(s(z))))),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[8268, 8261])).
% 3.44/3.65 tff(8270,plain,
% 3.44/3.65 (r(z, s(s(s(z))))),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[4920, 8269])).
% 3.44/3.65 tff(8271,plain,
% 3.44/3.65 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[4961, 8270, 194])).
% 3.44/3.65 tff(8272,plain,
% 3.44/3.65 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.44/3.65 inference(unit_resolution,[status(thm)],[4950, 8271, 4938])).
% 3.44/3.65 tff(8273,plain,
% 3.44/3.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(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(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(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(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.65 inference(rewrite,[status(thm)],[])).
% 3.44/3.65 tff(8274,plain,
% 3.44/3.65 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(s(s(s(z))))))), 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(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.66 inference(rewrite,[status(thm)],[])).
% 3.44/3.66 tff(8275,plain,
% 3.44/3.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(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(z))), s(s(s(s(s(s(s(z)))))))))))),
% 3.44/3.66 inference(monotonicity,[status(thm)],[8274])).
% 3.44/3.66 tff(8276,plain,
% 3.44/3.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(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(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.66 inference(transitivity,[status(thm)],[8275, 8273])).
% 3.44/3.66 tff(8277,plain,
% 3.44/3.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.66 inference(quant_inst,[status(thm)],[])).
% 3.44/3.66 tff(8278,plain,
% 3.44/3.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.44/3.66 inference(modus_ponens,[status(thm)],[8277, 8276])).
% 3.44/3.66 tff(8279,plain,
% 3.44/3.66 ($false),
% 3.44/3.66 inference(unit_resolution,[status(thm)],[8278, 178, 8063, 8254, 8272, 8261, 8258])).
% 3.44/3.66 tff(8280,plain,((~b(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | b(elem!1, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.66 tff(8281,plain,
% 3.44/3.66 (~b(z, s(s(z)))),
% 3.44/3.66 inference(unit_resolution,[status(thm)],[8280, 8231, 3244, 8042, 7954, 47, 8044, 461])).
% 3.44/3.66 tff(8282,plain,
% 3.44/3.66 (r(z, s(s(z)))),
% 3.44/3.66 inference(unit_resolution,[status(thm)],[143, 8281])).
% 3.44/3.66 tff(8283,plain,
% 3.44/3.66 ((z = elem!1) <=> (z = s(s(s(elem!1))))),
% 3.44/3.66 inference(monotonicity,[status(thm)],[1527])).
% 3.44/3.66 tff(8284,plain,
% 3.44/3.66 ((z = elem!1) <=> (s(s(s(elem!1))) = z)),
% 3.44/3.66 inference(transitivity,[status(thm)],[8283, 2087])).
% 3.44/3.66 tff(8285,plain,
% 3.44/3.66 ((s(s(s(elem!1))) = z) <=> (z = elem!1)),
% 3.44/3.66 inference(symmetry,[status(thm)],[8284])).
% 3.44/3.66 tff(8286,plain,
% 3.44/3.66 ((~(s(s(s(elem!1))) = z)) <=> (~(z = elem!1))),
% 3.44/3.66 inference(monotonicity,[status(thm)],[8285])).
% 3.44/3.66 tff(8287,plain,
% 3.44/3.66 (~(z = elem!1)),
% 3.44/3.66 inference(modus_ponens,[status(thm)],[940, 8286])).
% 3.44/3.66 tff(8288,plain,
% 3.44/3.66 (~(s(s(elem!1)) = s(s(z)))),
% 3.44/3.66 inference(unit_resolution,[status(thm)],[2386, 8287])).
% 3.44/3.66 tff(8289,plain,
% 3.44/3.66 (~(s(s(s(z))) = elem!1)),
% 3.44/3.66 inference(unit_resolution,[status(thm)],[4830, 8288, 1527])).
% 3.44/3.66 tff(8290,plain,
% 3.44/3.66 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(elem!1))))),
% 3.44/3.66 inference(monotonicity,[status(thm)],[1527])).
% 3.44/3.66 tff(8291,plain,
% 3.44/3.66 ((~b(s(s(z)), elem!1)) <=> (~b(s(s(z)), s(s(s(elem!1)))))),
% 3.44/3.66 inference(monotonicity,[status(thm)],[8290])).
% 3.44/3.66 tff(8292,plain,
% 3.44/3.66 (~b(s(s(z)), s(s(s(elem!1))))),
% 3.44/3.66 inference(modus_ponens,[status(thm)],[3241, 8291])).
% 3.44/3.66 tff(8293,plain,
% 3.44/3.66 (r(s(s(z)), s(s(s(elem!1))))),
% 3.44/3.66 inference(unit_resolution,[status(thm)],[4221, 41, 1683, 8292])).
% 3.44/3.66 tff(8294,plain,
% 3.44/3.66 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(z)) = elem!1))),
% 3.44/3.66 inference(monotonicity,[status(thm)],[7956])).
% 3.44/3.66 tff(8295,plain,
% 3.44/3.66 (~(s(s(z)) = elem!1)),
% 3.44/3.66 inference(modus_ponens,[status(thm)],[1683, 8294])).
% 3.44/3.66 tff(8296,plain,
% 3.44/3.66 (r(s(s(z)), elem!1)),
% 3.44/3.66 inference(unit_resolution,[status(thm)],[448, 8295, 3241])).
% 3.44/3.66 tff(8297,plain,
% 3.44/3.66 (r(z, s(s(s(elem!1)))) <=> r(z, elem!1)),
% 3.44/3.66 inference(symmetry,[status(thm)],[6445])).
% 3.44/3.66 tff(8298,plain,
% 3.44/3.66 ((~r(z, s(s(s(elem!1))))) <=> (~r(z, elem!1))),
% 3.44/3.66 inference(monotonicity,[status(thm)],[8297])).
% 3.44/3.66 tff(8299,plain,
% 3.44/3.66 (~r(z, elem!1)),
% 3.44/3.66 inference(modus_ponens,[status(thm)],[8021, 8298])).
% 3.44/3.66 tff(8300,plain,
% 3.44/3.66 (r(elem!1, z) <=> r(s(s(s(elem!1))), z)),
% 3.44/3.66 inference(monotonicity,[status(thm)],[1527])).
% 3.44/3.66 tff(8301,plain,
% 3.44/3.66 (r(s(s(s(elem!1))), z) <=> r(elem!1, z)),
% 3.44/3.66 inference(symmetry,[status(thm)],[8300])).
% 3.44/3.66 tff(8302,plain,
% 3.44/3.66 ((~r(s(s(s(elem!1))), z)) <=> (~r(elem!1, z))),
% 3.44/3.66 inference(monotonicity,[status(thm)],[8301])).
% 3.44/3.66 tff(8303,plain,
% 3.44/3.66 (~r(elem!1, z)),
% 3.44/3.66 inference(modus_ponens,[status(thm)],[8019, 8302])).
% 3.44/3.66 tff(8304,plain,
% 3.44/3.66 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.44/3.66 inference(unit_resolution,[status(thm)],[2820, 1140, 4845, 8303, 8299, 8287])).
% 3.44/3.66 tff(8305,plain,
% 3.44/3.66 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.44/3.66 inference(unit_resolution,[status(thm)],[691, 8304, 701])).
% 3.44/3.66 tff(8306,plain,
% 3.44/3.66 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.66 inference(modus_ponens,[status(thm)],[8305, 5004])).
% 3.44/3.66 tff(8307,plain,
% 3.44/3.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), 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))))))))))),
% 3.44/3.66 inference(rewrite,[status(thm)],[])).
% 3.44/3.66 tff(8308,plain,
% 3.44/3.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.66 inference(quant_inst,[status(thm)],[])).
% 3.44/3.66 tff(8309,plain,
% 3.44/3.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 3.44/3.66 inference(modus_ponens,[status(thm)],[8308, 8307])).
% 3.44/3.66 tff(8310,plain,
% 3.44/3.66 ($false),
% 3.44/3.66 inference(unit_resolution,[status(thm)],[8309, 118, 1130, 3251, 8306])).
% 3.44/3.66 tff(8311,plain,((~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)))))) | (~(elem!1 = s(s(s(elem!1))))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.66 tff(8312,plain,
% 3.44/3.66 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.44/3.66 inference(unit_resolution,[status(thm)],[8311, 1527, 3251, 701, 145])).
% 3.44/3.66 tff(8313,plain,
% 3.44/3.66 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.44/3.66 inference(unit_resolution,[status(thm)],[84, 8312])).
% 3.44/3.66 tff(8314,plain,
% 3.44/3.66 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.66 inference(modus_ponens,[status(thm)],[1265, 5004])).
% 3.44/3.66 tff(8315,plain,
% 3.44/3.66 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.66 inference(unit_resolution,[status(thm)],[259, 3865, 202, 167, 104])).
% 3.44/3.66 tff(8316,plain,
% 3.44/3.66 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.66 inference(unit_resolution,[status(thm)],[222, 8315])).
% 3.44/3.66 tff(8317,plain,
% 3.44/3.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(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))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(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))))))))))),
% 3.44/3.66 inference(rewrite,[status(thm)],[])).
% 3.44/3.66 tff(8318,plain,
% 3.44/3.66 (((~r(s(s(s(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(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), 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))))))))))),
% 3.44/3.66 inference(rewrite,[status(thm)],[])).
% 3.44/3.66 tff(8319,plain,
% 3.44/3.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(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)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(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)))))))))))),
% 3.44/3.66 inference(monotonicity,[status(thm)],[8318])).
% 3.44/3.66 tff(8320,plain,
% 3.44/3.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(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)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(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))))))))))),
% 3.44/3.66 inference(transitivity,[status(thm)],[8319, 8317])).
% 3.44/3.66 tff(8321,plain,
% 3.44/3.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(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)))))))),
% 3.44/3.66 inference(quant_inst,[status(thm)],[])).
% 3.44/3.66 tff(8322,plain,
% 3.44/3.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 3.44/3.66 inference(modus_ponens,[status(thm)],[8321, 8320])).
% 3.44/3.66 tff(8323,plain,
% 3.44/3.66 ($false),
% 3.44/3.66 inference(unit_resolution,[status(thm)],[8322, 118, 8316, 3251, 8314])).
% 3.44/3.66 tff(8324,plain,((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~(elem!1 = s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(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(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.66 tff(8325,plain,
% 3.44/3.66 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.44/3.66 inference(unit_resolution,[status(thm)],[8324, 1527, 3251, 202, 4803, 8313, 8296])).
% 3.44/3.66 tff(8326,plain,
% 3.44/3.66 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.44/3.66 inference(unit_resolution,[status(thm)],[691, 8325, 701])).
% 3.44/3.66 tff(8327,plain,
% 3.44/3.66 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.66 inference(modus_ponens,[status(thm)],[8326, 3810])).
% 3.44/3.66 tff(8328,plain,
% 3.44/3.66 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.44/3.66 inference(unit_resolution,[status(thm)],[8067, 8313, 202, 3261, 145])).
% 3.44/3.66 tff(8329,plain,
% 3.44/3.66 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.44/3.66 inference(unit_resolution,[status(thm)],[271, 8328])).
% 3.44/3.66 tff(8330,plain,
% 3.44/3.66 (~r(s(s(s(z))), elem!1)),
% 3.44/3.66 inference(modus_ponens,[status(thm)],[8198, 4972])).
% 3.44/3.66 tff(8331,plain,
% 3.44/3.66 (b(s(s(s(z))), elem!1)),
% 3.44/3.66 inference(unit_resolution,[status(thm)],[4981, 8330, 8289])).
% 3.44/3.66 tff(8332,plain,
% 3.44/3.66 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.44/3.66 inference(modus_ponens,[status(thm)],[8331, 4969])).
% 3.44/3.66 tff(8333,plain,
% 3.44/3.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 3.44/3.66 inference(rewrite,[status(thm)],[])).
% 3.44/3.66 tff(8334,plain,
% 3.44/3.66 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(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(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(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(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 3.44/3.66 inference(rewrite,[status(thm)],[])).
% 3.44/3.66 tff(8335,plain,
% 3.44/3.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 3.44/3.66 inference(monotonicity,[status(thm)],[8334])).
% 3.44/3.66 tff(8336,plain,
% 3.44/3.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 3.44/3.66 inference(transitivity,[status(thm)],[8335, 8333])).
% 3.44/3.66 tff(8337,plain,
% 3.44/3.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 3.44/3.66 inference(quant_inst,[status(thm)],[])).
% 3.44/3.66 tff(8338,plain,
% 3.44/3.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 3.44/3.66 inference(modus_ponens,[status(thm)],[8337, 8336])).
% 3.44/3.66 tff(8339,plain,
% 3.44/3.66 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 3.44/3.66 inference(unit_resolution,[status(thm)],[8338, 178, 8020, 595, 4904, 3830])).
% 3.44/3.66 tff(8340,plain,
% 3.44/3.66 ($false),
% 3.44/3.66 inference(unit_resolution,[status(thm)],[8339, 8332])).
% 3.44/3.66 tff(8341,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~(elem!1 = s(s(s(elem!1))))) | (~b(z, 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(z)))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.66 tff(8342,plain,
% 3.44/3.66 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 3.44/3.66 inference(unit_resolution,[status(thm)],[8341, 8329, 1527, 8327, 3251, 145])).
% 3.44/3.66 tff(8343,plain,
% 3.44/3.66 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.44/3.66 inference(unit_resolution,[status(thm)],[4928, 8342, 4890])).
% 3.44/3.66 tff(8344,assumption,(r(s(s(s(z))), s(s(s(elem!1))))), introduced(assumption)).
% 3.44/3.66 tff(8345,plain,
% 3.44/3.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 3.44/3.66 inference(rewrite,[status(thm)],[])).
% 3.44/3.66 tff(8346,plain,
% 3.44/3.66 (((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 3.44/3.66 inference(rewrite,[status(thm)],[])).
% 3.44/3.66 tff(8347,plain,
% 3.44/3.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1)))))))),
% 3.44/3.66 inference(monotonicity,[status(thm)],[8346])).
% 3.44/3.66 tff(8348,plain,
% 3.44/3.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 3.44/3.66 inference(transitivity,[status(thm)],[8347, 8345])).
% 3.44/3.66 tff(8349,plain,
% 3.44/3.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z)))))),
% 3.44/3.66 inference(quant_inst,[status(thm)],[])).
% 3.44/3.66 tff(8350,plain,
% 3.44/3.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 3.44/3.66 inference(modus_ponens,[status(thm)],[8349, 8348])).
% 3.44/3.66 tff(8351,plain,
% 3.44/3.66 ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 3.44/3.66 inference(unit_resolution,[status(thm)],[8350, 118, 1823])).
% 3.44/3.66 tff(8352,plain,
% 3.44/3.66 (~r(s(s(s(z))), s(s(z)))),
% 3.44/3.66 inference(unit_resolution,[status(thm)],[8351, 8344])).
% 3.44/3.66 tff(8353,plain,
% 3.44/3.66 (b(s(s(s(z))), s(s(z)))),
% 3.44/3.66 inference(unit_resolution,[status(thm)],[4966, 8352])).
% 3.44/3.66 tff(8354,plain,
% 3.44/3.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 3.44/3.66 inference(rewrite,[status(thm)],[])).
% 3.44/3.66 tff(8355,plain,
% 3.44/3.66 (((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 3.44/3.66 inference(rewrite,[status(thm)],[])).
% 3.44/3.66 tff(8356,plain,
% 3.44/3.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1)))))))),
% 3.44/3.66 inference(monotonicity,[status(thm)],[8355])).
% 3.44/3.66 tff(8357,plain,
% 3.44/3.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 3.44/3.66 inference(transitivity,[status(thm)],[8356, 8354])).
% 3.44/3.66 tff(8358,plain,
% 3.44/3.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))))),
% 3.44/3.66 inference(quant_inst,[status(thm)],[])).
% 3.44/3.66 tff(8359,plain,
% 3.44/3.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 3.44/3.66 inference(modus_ponens,[status(thm)],[8358, 8357])).
% 3.44/3.66 tff(8360,plain,
% 3.44/3.66 ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 3.44/3.66 inference(unit_resolution,[status(thm)],[8359, 118, 1823])).
% 3.44/3.66 tff(8361,plain,
% 3.44/3.66 (~r(s(s(z)), s(s(s(z))))),
% 3.44/3.66 inference(unit_resolution,[status(thm)],[8360, 8344])).
% 3.44/3.66 tff(8362,plain,
% 3.44/3.66 (b(s(s(z)), s(s(s(z))))),
% 3.44/3.66 inference(unit_resolution,[status(thm)],[5088, 8361])).
% 3.44/3.66 tff(8363,plain,
% 3.44/3.66 ($false),
% 3.44/3.66 inference(unit_resolution,[status(thm)],[5253, 178, 167, 202, 1126, 8362, 8353])).
% 3.44/3.66 tff(8364,plain,((~r(s(s(s(z))), s(s(s(elem!1))))) | (~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)))))) | (~r(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.66 tff(8365,plain,
% 3.44/3.66 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 3.44/3.66 inference(unit_resolution,[status(thm)],[8364, 8343, 202, 4803, 8293])).
% 3.44/3.66 tff(8366,plain,
% 3.44/3.66 (~r(s(s(s(z))), elem!1)),
% 3.44/3.66 inference(modus_ponens,[status(thm)],[8365, 4972])).
% 3.44/3.66 tff(8367,plain,
% 3.44/3.66 (b(s(s(s(z))), elem!1)),
% 3.44/3.66 inference(unit_resolution,[status(thm)],[4981, 8366, 8289])).
% 3.44/3.66 tff(8368,plain,
% 3.44/3.66 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.44/3.66 inference(modus_ponens,[status(thm)],[8367, 4969])).
% 3.44/3.66 tff(8369,plain,
% 3.44/3.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 3.44/3.66 inference(rewrite,[status(thm)],[])).
% 3.44/3.66 tff(8370,plain,
% 3.44/3.66 (((~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(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(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(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 3.44/3.66 inference(rewrite,[status(thm)],[])).
% 3.44/3.66 tff(8371,plain,
% 3.44/3.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 3.44/3.66 inference(monotonicity,[status(thm)],[8370])).
% 3.44/3.66 tff(8372,plain,
% 3.44/3.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 3.44/3.67 inference(transitivity,[status(thm)],[8371, 8369])).
% 3.44/3.67 tff(8373,plain,
% 3.44/3.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)))),
% 3.44/3.67 inference(quant_inst,[status(thm)],[])).
% 3.44/3.67 tff(8374,plain,
% 3.44/3.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 3.44/3.67 inference(modus_ponens,[status(thm)],[8373, 8372])).
% 3.44/3.67 tff(8375,plain,
% 3.44/3.67 (~b(s(s(s(z))), z)),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[8374, 178, 2043, 8329, 8327, 8368])).
% 3.44/3.67 tff(8376,plain,
% 3.44/3.67 (r(s(s(s(z))), z)),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[4903, 41, 77, 8375])).
% 3.44/3.67 tff(8377,plain,
% 3.44/3.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 3.44/3.67 inference(rewrite,[status(thm)],[])).
% 3.44/3.67 tff(8378,plain,
% 3.44/3.67 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 3.44/3.67 inference(quant_inst,[status(thm)],[])).
% 3.44/3.67 tff(8379,plain,
% 3.44/3.67 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 3.44/3.67 inference(modus_ponens,[status(thm)],[8378, 8377])).
% 3.44/3.67 tff(8380,plain,
% 3.44/3.67 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[8379, 118, 194, 8376])).
% 3.44/3.67 tff(8381,plain,
% 3.44/3.67 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[4950, 8380, 4938])).
% 3.44/3.67 tff(8382,plain,
% 3.44/3.67 ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[4944, 178, 4803, 202, 8343])).
% 3.44/3.67 tff(8383,plain,
% 3.44/3.67 (~b(s(s(s(z))), s(s(z)))),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[8382, 8381])).
% 3.44/3.67 tff(8384,plain,
% 3.44/3.67 (r(s(s(s(z))), s(s(z)))),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[4966, 8383])).
% 3.44/3.67 tff(8385,plain,
% 3.44/3.67 ($false),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[6019, 118, 3261, 8384, 8376])).
% 3.44/3.67 tff(8386,plain,((~(elem!1 = s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.44/3.67 tff(8387,plain,
% 3.44/3.67 (~(elem!1 = s(s(s(elem!1))))),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[8386, 8282, 8042, 3244, 7954, 8044, 47, 701, 3241])).
% 3.44/3.67 tff(8388,plain,
% 3.44/3.67 (~(s(s(s(elem!1))) = elem!1)),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[2489, 8387])).
% 3.44/3.67 tff(8389,plain,
% 3.44/3.67 (r(elem!1, s(s(s(elem!1))))),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[2054, 8387, 3240])).
% 3.44/3.67 tff(8390,plain,
% 3.44/3.67 (~r(s(s(s(elem!1))), z)),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[8018, 118, 47, 3251])).
% 3.44/3.67 tff(8391,plain,
% 3.44/3.67 (b(s(s(s(elem!1))), z)),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[1565, 8390])).
% 3.44/3.67 tff(8392,plain,
% 3.44/3.67 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[8061, 4511, 2043, 3251, 47])).
% 3.44/3.67 tff(8393,plain,
% 3.44/3.67 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[84, 8392])).
% 3.44/3.67 tff(8394,plain,
% 3.44/3.67 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[8234, 3251, 2043, 47])).
% 3.44/3.67 tff(8395,plain,
% 3.44/3.67 (b(s(s(z)), s(s(s(s(z)))))),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[164, 8394])).
% 3.44/3.67 tff(8396,plain,
% 3.44/3.67 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[951, 949])).
% 3.44/3.67 tff(8397,plain,
% 3.44/3.67 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[4343, 8396])).
% 3.44/3.67 tff(8398,plain,
% 3.44/3.67 (~(z = elem!1)),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[5266, 3261, 8397, 202, 3311, 461, 1, 3170])).
% 3.44/3.67 tff(8399,plain,
% 3.44/3.67 (b(s(s(z)), s(s(s(elem!1))))),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[4223, 1836])).
% 3.44/3.67 tff(8400,assumption,(s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 3.44/3.67 tff(8401,plain,
% 3.44/3.67 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 3.44/3.67 inference(symmetry,[status(thm)],[8400])).
% 3.44/3.67 tff(8402,plain,
% 3.44/3.67 ($false),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[3521, 8401])).
% 3.44/3.67 tff(8403,plain,((~(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))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.67 tff(8404,plain,
% 3.44/3.67 (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[8403, 4511])).
% 3.44/3.67 tff(8405,plain,
% 3.44/3.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))))),
% 3.44/3.67 inference(rewrite,[status(thm)],[])).
% 3.44/3.67 tff(8406,plain,
% 3.44/3.67 (((~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(z))))) <=> ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))))),
% 3.44/3.67 inference(rewrite,[status(thm)],[])).
% 3.44/3.67 tff(8407,plain,
% 3.44/3.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z))))))),
% 3.44/3.67 inference(monotonicity,[status(thm)],[8406])).
% 3.44/3.67 tff(8408,plain,
% 3.44/3.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))))),
% 3.44/3.67 inference(transitivity,[status(thm)],[8407, 8405])).
% 3.44/3.67 tff(8409,plain,
% 3.44/3.67 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(z)))))),
% 3.44/3.67 inference(quant_inst,[status(thm)],[])).
% 3.44/3.67 tff(8410,plain,
% 3.44/3.67 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z))))),
% 3.44/3.67 inference(modus_ponens,[status(thm)],[8409, 8408])).
% 3.44/3.67 tff(8411,plain,
% 3.44/3.67 ($false),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[8410, 118, 521, 438, 3261])).
% 3.44/3.67 tff(8412,plain,((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.67 tff(8413,plain,
% 3.44/3.67 (~r(z, elem!1)),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[8412, 4256, 3261])).
% 3.44/3.67 tff(8414,plain,
% 3.44/3.67 (b(z, elem!1)),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[585, 8413, 507])).
% 3.44/3.67 tff(8415,plain,
% 3.44/3.67 ($false),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[5737, 118, 437, 3261, 450])).
% 3.44/3.67 tff(8416,plain,((~r(elem!1, s(s(z)))) | (~r(elem!1, z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.67 tff(8417,plain,
% 3.44/3.67 (~r(elem!1, z)),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[8416, 1042, 3261])).
% 3.44/3.67 tff(8418,plain,
% 3.44/3.67 (b(elem!1, z)),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[498, 8417, 2809])).
% 3.44/3.67 tff(8419,plain,
% 3.44/3.67 (~b(s(s(s(elem!1))), elem!1)),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[8028, 178, 8414, 8418, 2043, 7976])).
% 3.44/3.67 tff(8420,plain,
% 3.44/3.67 (r(s(s(s(elem!1))), elem!1)),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[570, 8419, 949])).
% 3.44/3.67 tff(8421,plain,
% 3.44/3.67 (~r(s(s(s(elem!1))), s(s(z)))),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[4205, 8420, 1042])).
% 3.44/3.67 tff(8422,plain,
% 3.44/3.67 (b(s(s(s(elem!1))), s(s(z)))),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[4209, 41, 8421, 4181])).
% 3.44/3.67 tff(8423,plain,
% 3.44/3.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.44/3.67 inference(rewrite,[status(thm)],[])).
% 3.44/3.67 tff(8424,plain,
% 3.44/3.67 (((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.44/3.67 inference(rewrite,[status(thm)],[])).
% 3.44/3.67 tff(8425,plain,
% 3.44/3.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 3.44/3.67 inference(monotonicity,[status(thm)],[8424])).
% 3.44/3.67 tff(8426,plain,
% 3.44/3.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.44/3.67 inference(transitivity,[status(thm)],[8425, 8423])).
% 3.44/3.67 tff(8427,plain,
% 3.44/3.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 3.44/3.67 inference(quant_inst,[status(thm)],[])).
% 3.44/3.67 tff(8428,plain,
% 3.44/3.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 3.44/3.67 inference(modus_ponens,[status(thm)],[8427, 8426])).
% 3.44/3.67 tff(8429,plain,
% 3.44/3.67 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[8428, 178, 4291, 167, 202, 8422])).
% 3.44/3.67 tff(8430,plain,
% 3.44/3.67 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[3296, 41, 8429, 4166])).
% 3.44/3.67 tff(8431,plain,
% 3.44/3.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.44/3.67 inference(rewrite,[status(thm)],[])).
% 3.44/3.67 tff(8432,plain,
% 3.44/3.67 (((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.44/3.67 inference(rewrite,[status(thm)],[])).
% 3.44/3.67 tff(8433,plain,
% 3.44/3.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 3.44/3.67 inference(monotonicity,[status(thm)],[8432])).
% 3.44/3.67 tff(8434,plain,
% 3.44/3.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.44/3.67 inference(transitivity,[status(thm)],[8433, 8431])).
% 3.44/3.67 tff(8435,plain,
% 3.44/3.67 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 3.44/3.67 inference(quant_inst,[status(thm)],[])).
% 3.44/3.67 tff(8436,plain,
% 3.44/3.67 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 3.44/3.67 inference(modus_ponens,[status(thm)],[8435, 8434])).
% 3.44/3.67 tff(8437,plain,
% 3.44/3.67 (~r(elem!1, s(s(s(s(z)))))),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[8436, 118, 3311, 8430])).
% 3.44/3.67 tff(8438,plain,
% 3.44/3.67 (b(elem!1, s(s(s(s(z)))))),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[483, 8437, 4520])).
% 3.44/3.67 tff(8439,plain,
% 3.44/3.67 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[1309, 8438, 595, 8414, 104])).
% 3.44/3.67 tff(8440,plain,
% 3.44/3.67 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[691, 8439, 701])).
% 3.44/3.67 tff(8441,plain,
% 3.44/3.67 (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[3623, 8440, 3311])).
% 3.44/3.67 tff(8442,plain,
% 3.44/3.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(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)))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(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)))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 3.44/3.67 inference(rewrite,[status(thm)],[])).
% 3.44/3.67 tff(8443,plain,
% 3.44/3.67 (((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(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)))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 3.44/3.67 inference(rewrite,[status(thm)],[])).
% 3.44/3.67 tff(8444,plain,
% 3.44/3.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(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)))))) | (~b(elem!1, s(s(s(s(z))))))))),
% 3.44/3.67 inference(monotonicity,[status(thm)],[8443])).
% 3.44/3.67 tff(8445,plain,
% 3.44/3.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(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)))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 3.44/3.67 inference(transitivity,[status(thm)],[8444, 8442])).
% 3.44/3.67 tff(8446,plain,
% 3.44/3.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.67 inference(quant_inst,[status(thm)],[])).
% 3.44/3.67 tff(8447,plain,
% 3.44/3.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(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)))))) | (~b(elem!1, s(s(s(s(z))))))),
% 3.44/3.67 inference(modus_ponens,[status(thm)],[8446, 8445])).
% 3.44/3.67 tff(8448,plain,
% 3.44/3.67 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[8447, 178, 8414, 104, 8438, 595])).
% 3.44/3.67 tff(8449,plain,
% 3.44/3.67 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[3444, 8448, 4245])).
% 3.44/3.67 tff(8450,plain,
% 3.44/3.67 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[2956, 118, 4256, 8449])).
% 3.44/3.67 tff(8451,plain,
% 3.44/3.67 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.44/3.67 inference(unit_resolution,[status(thm)],[3578, 8450])).
% 3.44/3.67 tff(8452,plain,
% 3.44/3.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(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(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(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(z)))))),
% 3.44/3.67 inference(rewrite,[status(thm)],[])).
% 3.44/3.67 tff(8453,plain,
% 3.44/3.67 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(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(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(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(z)))))),
% 3.44/3.68 inference(rewrite,[status(thm)],[])).
% 3.44/3.68 tff(8454,plain,
% 3.44/3.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(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(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(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(z))))))),
% 3.44/3.68 inference(monotonicity,[status(thm)],[8453])).
% 3.44/3.68 tff(8455,plain,
% 3.44/3.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(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(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(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(z)))))),
% 3.44/3.68 inference(transitivity,[status(thm)],[8454, 8452])).
% 3.44/3.68 tff(8456,plain,
% 3.44/3.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(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(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.68 inference(quant_inst,[status(thm)],[])).
% 3.44/3.68 tff(8457,plain,
% 3.44/3.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 3.44/3.68 inference(modus_ponens,[status(thm)],[8456, 8455])).
% 3.44/3.68 tff(8458,plain,
% 3.44/3.68 ((~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[8457, 178, 104, 167, 8422])).
% 3.44/3.68 tff(8459,plain,
% 3.44/3.68 (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[8458, 8451])).
% 3.44/3.68 tff(8460,plain,
% 3.44/3.68 ($false),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[3612, 41, 8459, 8441, 8404])).
% 3.44/3.68 tff(8461,plain,((s(s(z)) = elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(elem!1))))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (s(s(s(elem!1))) = elem!1) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (z = elem!1) | (~r(z, s(s(z)))) | b(elem!1, s(s(z))) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.44/3.68 tff(8462,plain,
% 3.44/3.68 (s(s(z)) = elem!1),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[8461, 8399, 167, 595, 3311, 701, 4166, 104, 202, 949, 2043, 7976, 507, 3261, 461, 3241])).
% 3.44/3.68 tff(8463,plain,
% 3.44/3.68 (r(s(s(z)), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 3.44/3.68 inference(monotonicity,[status(thm)],[8462])).
% 3.44/3.68 tff(8464,plain,
% 3.44/3.68 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 3.44/3.68 inference(symmetry,[status(thm)],[8463])).
% 3.44/3.68 tff(8465,plain,
% 3.44/3.68 (r(s(s(z)), s(s(s(elem!1))))),
% 3.44/3.68 inference(modus_ponens,[status(thm)],[3311, 8464])).
% 3.44/3.68 tff(8466,plain,
% 3.44/3.68 ($false),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[1836, 8465])).
% 3.44/3.68 tff(8467,plain,(r(s(s(z)), s(s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (s(s(s(s(z)))) = s(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(z)))) | (s(s(s(elem!1))) = elem!1) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (z = elem!1) | (~r(z, s(s(z)))) | b(elem!1, s(s(z))) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.44/3.68 tff(8468,plain,
% 3.44/3.68 (r(s(s(z)), s(s(s(elem!1))))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[8467, 8398, 8395, 595, 701, 4166, 8393, 202, 949, 2043, 8391, 3311, 3261, 461, 3241])).
% 3.44/3.68 tff(8469,plain,
% 3.44/3.68 (~r(s(s(z)), elem!1)),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[7973, 8468, 3311])).
% 3.44/3.68 tff(8470,plain,
% 3.44/3.68 (s(s(z)) = elem!1),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[448, 8469, 3241])).
% 3.44/3.68 tff(8471,plain,
% 3.44/3.68 (r(z, elem!1)),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[7053, 8470, 3261])).
% 3.44/3.68 tff(8472,plain,
% 3.44/3.68 (~r(elem!1, s(s(s(s(z)))))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[529, 8471, 47])).
% 3.44/3.68 tff(8473,plain,
% 3.44/3.68 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(z)))), elem!1)),
% 3.44/3.68 inference(monotonicity,[status(thm)],[8470])).
% 3.44/3.68 tff(8474,plain,
% 3.44/3.68 ((~r(s(s(s(s(z)))), s(s(z)))) <=> (~r(s(s(s(s(z)))), elem!1))),
% 3.44/3.68 inference(monotonicity,[status(thm)],[8473])).
% 3.44/3.68 tff(8475,plain,
% 3.44/3.68 (~r(s(s(s(s(z)))), s(s(z)))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[3269, 3261, 47])).
% 3.44/3.68 tff(8476,plain,
% 3.44/3.68 (~r(s(s(s(s(z)))), elem!1)),
% 3.44/3.68 inference(modus_ponens,[status(thm)],[8475, 8474])).
% 3.44/3.68 tff(8477,plain,
% 3.44/3.68 (~(s(s(elem!1)) = s(s(z)))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[2386, 8398])).
% 3.44/3.68 tff(8478,plain,
% 3.44/3.68 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[8244, 8477])).
% 3.44/3.68 tff(8479,plain,
% 3.44/3.68 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[8252, 8478, 2043, 47, 3251])).
% 3.44/3.68 tff(8480,plain,
% 3.44/3.68 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[4928, 8479, 4890])).
% 3.44/3.68 tff(8481,plain,
% 3.44/3.68 (s(s(s(z))) = s(elem!1)),
% 3.44/3.68 inference(monotonicity,[status(thm)],[8470])).
% 3.44/3.68 tff(8482,plain,
% 3.44/3.68 (s(s(s(s(z)))) = s(s(elem!1))),
% 3.44/3.68 inference(monotonicity,[status(thm)],[8481])).
% 3.44/3.68 tff(8483,plain,
% 3.44/3.68 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(elem!1)))),
% 3.44/3.68 inference(monotonicity,[status(thm)],[8482])).
% 3.44/3.68 tff(8484,plain,
% 3.44/3.68 (b(elem!1, s(s(s(s(z)))))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[483, 8472, 4520])).
% 3.44/3.68 tff(8485,plain,
% 3.44/3.68 (b(elem!1, s(s(elem!1)))),
% 3.44/3.68 inference(modus_ponens,[status(thm)],[8484, 8483])).
% 3.44/3.68 tff(8486,plain,
% 3.44/3.68 (b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.68 inference(monotonicity,[status(thm)],[3505])).
% 3.44/3.68 tff(8487,plain,
% 3.44/3.68 ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 3.44/3.68 inference(monotonicity,[status(thm)],[8486])).
% 3.44/3.68 tff(8488,plain,
% 3.44/3.68 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), s(s(elem!1)))),
% 3.44/3.68 inference(symmetry,[status(thm)],[8121])).
% 3.44/3.68 tff(8489,plain,
% 3.44/3.68 (b(s(elem!1), s(s(s(s(z)))))),
% 3.44/3.68 inference(modus_ponens,[status(thm)],[1126, 8119])).
% 3.44/3.68 tff(8490,plain,
% 3.44/3.68 (b(s(elem!1), s(s(elem!1)))),
% 3.44/3.68 inference(modus_ponens,[status(thm)],[8489, 8488])).
% 3.44/3.68 tff(8491,plain,
% 3.44/3.68 (r(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.44/3.68 inference(monotonicity,[status(thm)],[1324])).
% 3.44/3.68 tff(8492,plain,
% 3.44/3.68 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.68 inference(symmetry,[status(thm)],[8491])).
% 3.44/3.68 tff(8493,plain,
% 3.44/3.68 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.68 inference(modus_ponens,[status(thm)],[1265, 8492])).
% 3.44/3.68 tff(8494,plain,
% 3.44/3.68 (r(s(elem!1), elem!1)),
% 3.44/3.68 inference(modus_ponens,[status(thm)],[1125, 8116])).
% 3.44/3.68 tff(8495,plain,
% 3.44/3.68 (~r(z, s(elem!1))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[7068, 118, 521, 8494])).
% 3.44/3.68 tff(8496,plain,
% 3.44/3.68 (b(z, s(elem!1))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[2351, 8495])).
% 3.44/3.68 tff(8497,plain,
% 3.44/3.68 (r(s(elem!1), s(s(z))) <=> r(s(elem!1), elem!1)),
% 3.44/3.68 inference(monotonicity,[status(thm)],[1324])).
% 3.44/3.68 tff(8498,plain,
% 3.44/3.68 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(z)))),
% 3.44/3.68 inference(symmetry,[status(thm)],[8497])).
% 3.44/3.68 tff(8499,plain,
% 3.44/3.68 (r(s(s(s(z))), s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 3.44/3.68 inference(transitivity,[status(thm)],[8115, 8114, 8498])).
% 3.44/3.68 tff(8500,plain,
% 3.44/3.68 (r(s(elem!1), s(s(z)))),
% 3.44/3.68 inference(modus_ponens,[status(thm)],[1125, 8499])).
% 3.44/3.68 tff(8501,plain,
% 3.44/3.68 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[390, 8500, 224])).
% 3.44/3.68 tff(8502,plain,
% 3.44/3.68 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[395, 8501, 8112])).
% 3.44/3.68 tff(8503,plain,
% 3.44/3.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~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))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~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))))))), s(s(elem!1)))))),
% 3.44/3.68 inference(rewrite,[status(thm)],[])).
% 3.44/3.68 tff(8504,plain,
% 3.44/3.68 (((~b(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)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), 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(z, s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~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))))))), s(s(elem!1)))))),
% 3.44/3.68 inference(rewrite,[status(thm)],[])).
% 3.44/3.68 tff(8505,plain,
% 3.44/3.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), 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(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~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))))))), s(s(elem!1))))))),
% 3.44/3.68 inference(monotonicity,[status(thm)],[8504])).
% 3.44/3.68 tff(8506,plain,
% 3.44/3.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), 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(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~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))))))), s(s(elem!1)))))),
% 3.44/3.68 inference(transitivity,[status(thm)],[8505, 8503])).
% 3.44/3.68 tff(8507,plain,
% 3.44/3.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), 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(z, s(elem!1))))),
% 3.44/3.68 inference(quant_inst,[status(thm)],[])).
% 3.44/3.68 tff(8508,plain,
% 3.44/3.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 3.44/3.68 inference(modus_ponens,[status(thm)],[8507, 8506])).
% 3.44/3.68 tff(8509,plain,
% 3.44/3.68 ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[8508, 178, 5391, 595, 3504])).
% 3.44/3.68 tff(8510,plain,
% 3.44/3.68 ($false),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[8509, 8502, 8496])).
% 3.44/3.68 tff(8511,plain,((~r(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(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(z, elem!1)) | (~(s(s(z)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.68 tff(8512,plain,
% 3.44/3.68 (~r(s(s(s(z))), s(s(z)))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[8511, 8493, 595, 8176, 8490, 521, 1324])).
% 3.44/3.68 tff(8513,plain,
% 3.44/3.68 (b(s(s(s(z))), s(s(z)))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[4966, 8512])).
% 3.44/3.68 tff(8514,plain,
% 3.44/3.68 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[4945, 8513])).
% 3.44/3.68 tff(8515,plain,
% 3.44/3.68 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[4950, 8514, 4938])).
% 3.44/3.68 tff(8516,plain,
% 3.44/3.68 (~r(z, s(s(s(z))))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[4961, 8515, 194])).
% 3.44/3.68 tff(8517,plain,
% 3.44/3.68 (b(z, s(s(s(z))))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[4920, 8516])).
% 3.44/3.68 tff(8518,plain,
% 3.44/3.68 ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[8267, 178, 104, 595, 1126])).
% 3.44/3.68 tff(8519,plain,
% 3.44/3.68 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[8518, 8517])).
% 3.44/3.68 tff(8520,plain,
% 3.44/3.68 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.68 inference(modus_ponens,[status(thm)],[8519, 8487])).
% 3.44/3.68 tff(8521,plain,
% 3.44/3.68 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[395, 8520, 8112])).
% 3.44/3.68 tff(8522,plain,
% 3.44/3.68 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 3.44/3.68 inference(monotonicity,[status(thm)],[3506])).
% 3.44/3.68 tff(8523,plain,
% 3.44/3.68 ((~b(s(s(s(s(z)))), elem!1)) <=> (~b(s(s(s(s(z)))), s(s(z))))),
% 3.44/3.68 inference(monotonicity,[status(thm)],[3770])).
% 3.44/3.68 tff(8524,plain,
% 3.44/3.68 (~b(s(s(s(s(z)))), s(s(z)))),
% 3.44/3.68 inference(modus_ponens,[status(thm)],[3278, 8523])).
% 3.44/3.68 tff(8525,plain,
% 3.44/3.68 ($false),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[202, 8524])).
% 3.44/3.68 tff(8526,plain,((~(s(s(z)) = elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | b(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.44/3.68 tff(8527,plain,
% 3.44/3.68 (b(s(s(s(s(z)))), elem!1)),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[8526, 1324, 202])).
% 3.44/3.68 tff(8528,plain,
% 3.44/3.68 (b(s(s(elem!1)), elem!1)),
% 3.44/3.68 inference(modus_ponens,[status(thm)],[8527, 8522])).
% 3.44/3.68 tff(8529,plain,
% 3.44/3.68 (b(s(s(s(z))), elem!1) <=> b(s(elem!1), elem!1)),
% 3.44/3.68 inference(monotonicity,[status(thm)],[3505])).
% 3.44/3.68 tff(8530,plain,
% 3.44/3.68 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), elem!1)),
% 3.44/3.68 inference(monotonicity,[status(thm)],[1324])).
% 3.44/3.68 tff(8531,plain,
% 3.44/3.68 (b(s(s(s(z))), s(s(z))) <=> b(s(elem!1), elem!1)),
% 3.44/3.68 inference(transitivity,[status(thm)],[8530, 8529])).
% 3.44/3.68 tff(8532,plain,
% 3.44/3.68 (b(s(elem!1), elem!1)),
% 3.44/3.68 inference(modus_ponens,[status(thm)],[8513, 8531])).
% 3.44/3.68 tff(8533,plain,
% 3.44/3.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))))),
% 3.44/3.68 inference(rewrite,[status(thm)],[])).
% 3.44/3.68 tff(8534,plain,
% 3.44/3.68 (((~b(s(s(elem!1)), 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(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))))),
% 3.44/3.68 inference(rewrite,[status(thm)],[])).
% 3.44/3.68 tff(8535,plain,
% 3.44/3.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1))))))),
% 3.44/3.68 inference(monotonicity,[status(thm)],[8534])).
% 3.44/3.68 tff(8536,plain,
% 3.44/3.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))))),
% 3.44/3.68 inference(transitivity,[status(thm)],[8535, 8533])).
% 3.44/3.68 tff(8537,plain,
% 3.44/3.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))),
% 3.44/3.68 inference(quant_inst,[status(thm)],[])).
% 3.44/3.68 tff(8538,plain,
% 3.44/3.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1))))),
% 3.44/3.68 inference(modus_ponens,[status(thm)],[8537, 8536])).
% 3.44/3.68 tff(8539,plain,
% 3.44/3.68 (~b(elem!1, s(elem!1))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[8538, 178, 8532, 8528, 8490, 6572])).
% 3.44/3.68 tff(8540,plain,
% 3.44/3.68 (r(elem!1, s(elem!1))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[756, 8539, 750])).
% 3.44/3.68 tff(8541,plain,
% 3.44/3.68 ($false),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[2935, 8540, 8521, 1265])).
% 3.44/3.68 tff(8542,plain,((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~(s(s(z)) = elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.68 tff(8543,plain,
% 3.44/3.68 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[8542, 8485, 5450, 8470, 8393, 595, 8480, 3244, 8395, 202, 8471])).
% 3.44/3.68 tff(8544,plain,
% 3.44/3.68 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[691, 8543, 701])).
% 3.44/3.68 tff(8545,plain,
% 3.44/3.68 (b(elem!1, s(s(s(s(z)))))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[483, 469, 5721])).
% 3.44/3.68 tff(8546,plain,
% 3.44/3.68 (b(s(s(s(s(z)))), elem!1)),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[3142, 551, 5369])).
% 3.44/3.68 tff(8547,plain,
% 3.44/3.68 ($false),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[4266, 178, 104, 8546, 869, 8545, 251])).
% 3.44/3.68 tff(8548,plain,((elem!1 = s(s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, 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)))), elem!1) | r(elem!1, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.68 tff(8549,plain,
% 3.44/3.68 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[8548, 8544, 8393, 4520, 8476, 8472])).
% 3.44/3.68 tff(8550,plain,
% 3.44/3.68 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[222, 8549])).
% 3.44/3.68 tff(8551,plain,
% 3.44/3.68 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[3586, 8550, 8470])).
% 3.44/3.68 tff(8552,plain,
% 3.44/3.68 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[5361, 8470])).
% 3.44/3.68 tff(8553,plain,
% 3.44/3.68 (r(s(s(s(z))), elem!1) <=> r(s(elem!1), elem!1)),
% 3.44/3.68 inference(monotonicity,[status(thm)],[8481])).
% 3.44/3.68 tff(8554,plain,
% 3.44/3.68 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(z))), elem!1)),
% 3.44/3.68 inference(monotonicity,[status(thm)],[8470])).
% 3.44/3.68 tff(8555,plain,
% 3.44/3.68 (r(s(s(s(z))), s(s(z))) <=> r(s(elem!1), elem!1)),
% 3.44/3.68 inference(transitivity,[status(thm)],[8554, 8553])).
% 3.44/3.68 tff(8556,plain,
% 3.44/3.68 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 3.44/3.68 inference(monotonicity,[status(thm)],[8481])).
% 3.44/3.68 tff(8557,plain,
% 3.44/3.68 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 3.44/3.68 inference(transitivity,[status(thm)],[8556, 3881])).
% 3.44/3.68 tff(8558,plain,
% 3.44/3.68 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 3.44/3.68 inference(transitivity,[status(thm)],[8557, 7104])).
% 3.44/3.68 tff(8559,plain,
% 3.44/3.68 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 3.44/3.68 inference(monotonicity,[status(thm)],[8558])).
% 3.44/3.68 tff(8560,plain,
% 3.44/3.68 (~(s(elem!1) = s(s(s(elem!1))))),
% 3.44/3.68 inference(modus_ponens,[status(thm)],[8478, 8559])).
% 3.44/3.68 tff(8561,plain,
% 3.44/3.68 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 3.44/3.68 inference(monotonicity,[status(thm)],[8481])).
% 3.44/3.68 tff(8562,plain,
% 3.44/3.68 ((~r(s(s(s(z))), s(s(s(elem!1))))) <=> (~r(s(elem!1), s(s(s(elem!1)))))),
% 3.44/3.68 inference(monotonicity,[status(thm)],[8561])).
% 3.44/3.68 tff(8563,plain,
% 3.44/3.68 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[8364, 8468, 202, 8395, 8480])).
% 3.44/3.68 tff(8564,plain,
% 3.44/3.68 (~r(s(elem!1), s(s(s(elem!1))))),
% 3.44/3.68 inference(modus_ponens,[status(thm)],[8563, 8562])).
% 3.44/3.68 tff(8565,plain,
% 3.44/3.68 (b(s(elem!1), s(s(s(elem!1))))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[5432, 8564, 8560])).
% 3.44/3.68 tff(8566,plain,
% 3.44/3.68 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 3.44/3.68 inference(monotonicity,[status(thm)],[8557])).
% 3.44/3.68 tff(8567,plain,
% 3.44/3.68 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.44/3.68 inference(modus_ponens,[status(thm)],[8478, 8566])).
% 3.44/3.68 tff(8568,plain,
% 3.44/3.68 (b(s(elem!1), elem!1)),
% 3.44/3.68 inference(modus_ponens,[status(thm)],[4932, 8531])).
% 3.44/3.68 tff(8569,plain,
% 3.44/3.68 (~b(elem!1, s(elem!1))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[8538, 178, 8568, 8528, 8490, 6572])).
% 3.44/3.68 tff(8570,plain,
% 3.44/3.68 (r(elem!1, s(elem!1))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[756, 8569, 750])).
% 3.44/3.68 tff(8571,plain,
% 3.44/3.68 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[1591, 8570, 3311])).
% 3.44/3.68 tff(8572,plain,
% 3.44/3.68 (b(z, s(s(s(z)))) <=> b(z, s(elem!1))),
% 3.44/3.68 inference(monotonicity,[status(thm)],[3505])).
% 3.44/3.68 tff(8573,plain,
% 3.44/3.68 (~r(z, s(s(s(z))))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[4961, 4951, 194])).
% 3.44/3.68 tff(8574,plain,
% 3.44/3.68 (b(z, s(s(s(z))))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[4920, 8573])).
% 3.44/3.68 tff(8575,plain,
% 3.44/3.68 (b(z, s(elem!1))),
% 3.44/3.68 inference(modus_ponens,[status(thm)],[8574, 8572])).
% 3.44/3.68 tff(8576,plain,
% 3.44/3.68 (r(s(s(s(s(z)))), z) <=> r(s(s(elem!1)), z)),
% 3.44/3.68 inference(monotonicity,[status(thm)],[3506])).
% 3.44/3.68 tff(8577,plain,
% 3.44/3.68 (r(s(s(elem!1)), z)),
% 3.44/3.68 inference(modus_ponens,[status(thm)],[194, 8576])).
% 3.44/3.68 tff(8578,plain,
% 3.44/3.68 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(s(z)))), s(elem!1))),
% 3.44/3.68 inference(monotonicity,[status(thm)],[3507])).
% 3.44/3.68 tff(8579,plain,
% 3.44/3.68 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 3.44/3.68 inference(symmetry,[status(thm)],[8578])).
% 3.44/3.68 tff(8580,plain,
% 3.44/3.68 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 3.44/3.68 inference(monotonicity,[status(thm)],[3505])).
% 3.44/3.68 tff(8581,plain,
% 3.44/3.68 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(elem!1)), s(elem!1))),
% 3.44/3.68 inference(transitivity,[status(thm)],[8580, 8579])).
% 3.44/3.68 tff(8582,plain,
% 3.44/3.68 (r(s(s(elem!1)), s(elem!1))),
% 3.44/3.68 inference(modus_ponens,[status(thm)],[4951, 8581])).
% 3.44/3.68 tff(8583,plain,
% 3.44/3.68 (~r(s(elem!1), z)),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[997, 8582, 8577])).
% 3.44/3.68 tff(8584,plain,
% 3.44/3.68 (b(s(elem!1), z)),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[774, 8583])).
% 3.44/3.68 tff(8585,plain,
% 3.44/3.68 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[6736, 8584, 2043, 5888, 8575])).
% 3.44/3.68 tff(8586,plain,
% 3.44/3.68 ($false),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[373, 8585, 8571, 356])).
% 3.44/3.68 tff(8587,plain,((~b(s(s(s(z))), s(s(z)))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (elem!1 = s(elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~(s(s(z)) = elem!1)) | (~r(s(s(s(s(z)))), 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))))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.68 tff(8588,plain,
% 3.44/3.68 (~b(s(s(s(z))), s(s(z)))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[8587, 8567, 2043, 8565, 3311, 5450, 8485, 8470, 3244, 8395, 202, 8480])).
% 3.44/3.68 tff(8589,plain,
% 3.44/3.68 (r(s(s(s(z))), s(s(z)))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[4966, 8588])).
% 3.44/3.68 tff(8590,plain,
% 3.44/3.68 (r(s(elem!1), elem!1)),
% 3.44/3.68 inference(modus_ponens,[status(thm)],[8589, 8555])).
% 3.44/3.68 tff(8591,plain,
% 3.44/3.68 (~r(z, s(elem!1))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[7068, 118, 8471, 8590])).
% 3.44/3.68 tff(8592,plain,
% 3.44/3.68 (b(z, s(elem!1))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[2351, 8591])).
% 3.44/3.68 tff(8593,plain,
% 3.44/3.68 (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)))),
% 3.44/3.68 inference(monotonicity,[status(thm)],[8482])).
% 3.44/3.68 tff(8594,plain,
% 3.44/3.68 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.44/3.68 inference(modus_ponens,[status(thm)],[8393, 8593])).
% 3.44/3.68 tff(8595,plain,
% 3.44/3.68 (s(s(elem!1)) = s(s(s(s(z))))),
% 3.44/3.68 inference(symmetry,[status(thm)],[8482])).
% 3.44/3.68 tff(8596,plain,
% 3.44/3.68 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 3.44/3.68 inference(monotonicity,[status(thm)],[8595])).
% 3.44/3.68 tff(8597,plain,
% 3.44/3.68 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), s(s(elem!1)))),
% 3.44/3.68 inference(symmetry,[status(thm)],[8596])).
% 3.44/3.68 tff(8598,plain,
% 3.44/3.68 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 3.44/3.68 inference(monotonicity,[status(thm)],[8481])).
% 3.44/3.68 tff(8599,plain,
% 3.44/3.68 (b(s(elem!1), s(s(s(s(z)))))),
% 3.44/3.68 inference(modus_ponens,[status(thm)],[8480, 8598])).
% 3.44/3.68 tff(8600,plain,
% 3.44/3.68 (b(s(elem!1), s(s(elem!1)))),
% 3.44/3.68 inference(modus_ponens,[status(thm)],[8599, 8597])).
% 3.44/3.68 tff(8601,plain,
% 3.44/3.68 ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[8508, 178, 8600, 595, 8594])).
% 3.44/3.68 tff(8602,plain,
% 3.44/3.68 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[8601, 8592])).
% 3.44/3.68 tff(8603,plain,
% 3.44/3.68 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[395, 8602, 8552])).
% 3.44/3.68 tff(8604,plain,
% 3.44/3.68 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(s(z)))), s(elem!1))),
% 3.44/3.68 inference(monotonicity,[status(thm)],[8595])).
% 3.44/3.68 tff(8605,plain,
% 3.44/3.68 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 3.44/3.68 inference(symmetry,[status(thm)],[8604])).
% 3.44/3.68 tff(8606,plain,
% 3.44/3.68 (~r(elem!1, s(s(z)))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[4862, 8471, 3261])).
% 3.44/3.68 tff(8607,plain,
% 3.44/3.68 (elem!1 = s(s(z))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[467, 8606, 461])).
% 3.44/3.68 tff(8608,plain,
% 3.44/3.68 (~(s(elem!1) = s(s(s(s(z)))))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[1353, 8607, 4510])).
% 3.44/3.68 tff(8609,plain,
% 3.44/3.68 (~(s(s(s(s(z)))) = s(elem!1))),
% 3.44/3.68 inference(unit_resolution,[status(thm)],[2168, 8608])).
% 3.44/3.68 tff(8610,plain,
% 3.44/3.68 (r(s(elem!1), s(s(z))) <=> r(s(elem!1), elem!1)),
% 3.44/3.68 inference(monotonicity,[status(thm)],[8470])).
% 3.44/3.68 tff(8611,plain,
% 3.44/3.68 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(z)))),
% 3.44/3.68 inference(symmetry,[status(thm)],[8610])).
% 3.44/3.68 tff(8612,plain,
% 3.44/3.68 (r(s(s(s(z))), s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 3.44/3.68 inference(transitivity,[status(thm)],[8554, 8553, 8611])).
% 3.44/3.68 tff(8613,plain,
% 3.44/3.68 (r(s(elem!1), s(s(z)))),
% 3.44/3.68 inference(modus_ponens,[status(thm)],[8589, 8612])).
% 3.44/3.68 tff(8614,plain,
% 3.44/3.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z)))))),
% 3.44/3.68 inference(rewrite,[status(thm)],[])).
% 3.44/3.68 tff(8615,plain,
% 3.44/3.68 (((~r(z, s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z)))))),
% 3.44/3.69 inference(rewrite,[status(thm)],[])).
% 3.44/3.69 tff(8616,plain,
% 3.44/3.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z))))))),
% 3.44/3.69 inference(monotonicity,[status(thm)],[8615])).
% 3.44/3.69 tff(8617,plain,
% 3.44/3.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z)))))),
% 3.44/3.69 inference(transitivity,[status(thm)],[8616, 8614])).
% 3.44/3.69 tff(8618,plain,
% 3.44/3.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), z)))),
% 3.44/3.69 inference(quant_inst,[status(thm)],[])).
% 3.44/3.69 tff(8619,plain,
% 3.44/3.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z))))),
% 3.44/3.69 inference(modus_ponens,[status(thm)],[8618, 8617])).
% 3.44/3.69 tff(8620,plain,
% 3.44/3.69 ($false),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[8619, 118, 844, 3261, 363])).
% 3.44/3.69 tff(8621,plain,((~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.69 tff(8622,plain,
% 3.44/3.69 (~r(s(elem!1), z)),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[8621, 8613, 3261])).
% 3.44/3.69 tff(8623,plain,
% 3.44/3.69 (b(s(elem!1), z)),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[774, 8622])).
% 3.44/3.69 tff(8624,plain,
% 3.44/3.69 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[6736, 8623, 2043, 8565, 8592])).
% 3.44/3.69 tff(8625,plain,
% 3.44/3.69 (r(s(s(s(elem!1))), s(elem!1))),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[373, 8624, 8567])).
% 3.44/3.69 tff(8626,plain,
% 3.44/3.69 (~r(elem!1, s(elem!1))),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[1591, 8625, 3311])).
% 3.44/3.69 tff(8627,plain,
% 3.44/3.69 (b(elem!1, s(elem!1))),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[756, 8626, 5450])).
% 3.44/3.69 tff(8628,plain,
% 3.44/3.69 (~(elem!1 = z)),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[2808, 8398])).
% 3.44/3.69 tff(8629,plain,
% 3.44/3.69 (~r(s(s(s(elem!1))), elem!1)),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[1576, 8625, 8590])).
% 3.44/3.69 tff(8630,plain,
% 3.44/3.69 (b(s(s(s(elem!1))), elem!1)),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[570, 8629, 949])).
% 3.44/3.69 tff(8631,plain,
% 3.44/3.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.69 inference(rewrite,[status(thm)],[])).
% 3.44/3.69 tff(8632,plain,
% 3.44/3.69 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.69 inference(rewrite,[status(thm)],[])).
% 3.44/3.69 tff(8633,plain,
% 3.44/3.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.44/3.69 inference(monotonicity,[status(thm)],[8632])).
% 3.44/3.69 tff(8634,plain,
% 3.44/3.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.44/3.69 inference(transitivity,[status(thm)],[8633, 8631])).
% 3.44/3.69 tff(8635,plain,
% 3.44/3.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 3.44/3.69 inference(quant_inst,[status(thm)],[])).
% 3.44/3.69 tff(8636,plain,
% 3.44/3.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.44/3.69 inference(modus_ponens,[status(thm)],[8635, 8634])).
% 3.44/3.69 tff(8637,plain,
% 3.44/3.69 ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1))),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[8636, 178, 8391, 8544, 595])).
% 3.44/3.69 tff(8638,plain,
% 3.44/3.69 (~b(elem!1, z)),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[8637, 8630])).
% 3.44/3.69 tff(8639,plain,
% 3.44/3.69 (r(elem!1, z)),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[498, 8638, 8628])).
% 3.44/3.69 tff(8640,assumption,(b(s(s(s(s(z)))), s(elem!1))), introduced(assumption)).
% 3.44/3.69 tff(8641,plain,
% 3.44/3.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 3.44/3.69 inference(rewrite,[status(thm)],[])).
% 3.44/3.69 tff(8642,plain,
% 3.44/3.69 (((~b(s(elem!1), s(s(s(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(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 3.44/3.69 inference(rewrite,[status(thm)],[])).
% 3.44/3.69 tff(8643,plain,
% 3.44/3.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 3.44/3.69 inference(monotonicity,[status(thm)],[8642])).
% 3.44/3.69 tff(8644,plain,
% 3.44/3.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 3.44/3.69 inference(transitivity,[status(thm)],[8643, 8641])).
% 3.44/3.69 tff(8645,plain,
% 3.44/3.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))),
% 3.44/3.69 inference(quant_inst,[status(thm)],[])).
% 3.44/3.69 tff(8646,plain,
% 3.44/3.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 3.44/3.69 inference(modus_ponens,[status(thm)],[8645, 8644])).
% 3.44/3.69 tff(8647,plain,
% 3.44/3.69 ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1))),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[8646, 178, 8640, 1301, 1069])).
% 3.44/3.69 tff(8648,plain,
% 3.44/3.69 (~b(s(s(s(s(z)))), elem!1)),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[8647, 854])).
% 3.44/3.69 tff(8649,plain,
% 3.44/3.69 (r(s(s(s(s(z)))), elem!1)),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[3142, 8648, 323])).
% 3.44/3.69 tff(8650,plain,
% 3.44/3.69 (~r(s(s(s(s(z)))), z)),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[6033, 8649, 437])).
% 3.44/3.69 tff(8651,plain,
% 3.44/3.69 (b(s(s(s(s(z)))), z)),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[191, 8650])).
% 3.44/3.69 tff(8652,plain,
% 3.44/3.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 3.44/3.69 inference(rewrite,[status(thm)],[])).
% 3.44/3.69 tff(8653,plain,
% 3.44/3.69 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(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(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 3.44/3.69 inference(rewrite,[status(thm)],[])).
% 3.44/3.69 tff(8654,plain,
% 3.44/3.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(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(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 3.44/3.69 inference(monotonicity,[status(thm)],[8653])).
% 3.44/3.69 tff(8655,plain,
% 3.44/3.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(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(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 3.44/3.69 inference(transitivity,[status(thm)],[8654, 8652])).
% 3.44/3.69 tff(8656,plain,
% 3.44/3.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(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(elem!1, s(elem!1))))),
% 3.44/3.69 inference(quant_inst,[status(thm)],[])).
% 3.44/3.69 tff(8657,plain,
% 3.44/3.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 3.44/3.69 inference(modus_ponens,[status(thm)],[8656, 8655])).
% 3.44/3.69 tff(8658,plain,
% 3.44/3.69 ($false),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[8657, 178, 854, 853, 8651, 1301, 1069])).
% 3.44/3.69 tff(8659,plain,((~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, z)) | (s(s(s(s(z)))) = elem!1) | (~b(s(s(s(s(z)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.69 tff(8660,plain,
% 3.44/3.69 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[8659, 8639, 8484, 4510, 8623, 8599, 8627])).
% 3.44/3.69 tff(8661,plain,
% 3.44/3.69 (r(s(s(s(s(z)))), s(elem!1))),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[2173, 8660, 8609])).
% 3.44/3.69 tff(8662,plain,
% 3.44/3.69 (r(s(s(elem!1)), s(elem!1))),
% 3.44/3.69 inference(modus_ponens,[status(thm)],[8661, 8605])).
% 3.44/3.69 tff(8663,plain,
% 3.44/3.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~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))))))))))),
% 3.44/3.69 inference(rewrite,[status(thm)],[])).
% 3.44/3.69 tff(8664,plain,
% 3.44/3.69 (((~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(s(elem!1)), s(elem!1)))) <=> ((~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(s(s(s(s(s(s(z))))))))))),
% 3.44/3.69 inference(rewrite,[status(thm)],[])).
% 3.44/3.69 tff(8665,plain,
% 3.44/3.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(s(s(s(s(s(s(z)))))))))))),
% 3.44/3.69 inference(monotonicity,[status(thm)],[8664])).
% 3.44/3.69 tff(8666,plain,
% 3.44/3.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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(s(s(s(s(s(s(z))))))))))),
% 3.44/3.69 inference(transitivity,[status(thm)],[8665, 8663])).
% 3.44/3.69 tff(8667,plain,
% 3.44/3.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(s(elem!1)), s(elem!1))))),
% 3.44/3.69 inference(quant_inst,[status(thm)],[])).
% 3.44/3.69 tff(8668,plain,
% 3.44/3.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 3.44/3.69 inference(modus_ponens,[status(thm)],[8667, 8666])).
% 3.44/3.69 tff(8669,plain,
% 3.44/3.69 ($false),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[8668, 118, 8662, 8603, 8551])).
% 3.44/3.69 tff(8670,plain,((~r(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (s(s(s(elem!1))) = elem!1) | (~r(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | b(elem!1, s(s(z))) | b(s(s(z)), elem!1) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | b(z, s(s(s(s(z))))) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 3.44/3.69 tff(8671,plain,
% 3.44/3.69 ($false),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[8670, 8389, 8388, 8231, 8282, 7954, 8042, 701, 461, 3241, 8045, 8044, 1, 3170])).
% 3.44/3.69 tff(8672,plain,(b(s(s(s(elem!1))), s(s(s(s(z))))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | b(elem!1, s(s(z))) | b(s(s(z)), elem!1) | b(z, s(s(s(s(z))))) | b(s(s(s(s(z)))), z) | b(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.69 tff(8673,plain,
% 3.44/3.69 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[8672, 701, 461, 3241, 1, 3170, 3240])).
% 3.44/3.69 tff(8674,plain,
% 3.44/3.69 (b(s(s(z)), z)),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[3249, 8005])).
% 3.44/3.69 tff(8675,plain,
% 3.44/3.69 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[4093, 1130, 193, 3461, 145])).
% 3.44/3.69 tff(8676,plain,
% 3.44/3.69 ($false),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[271, 8675, 4844])).
% 3.44/3.69 tff(8677,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.69 tff(8678,plain,
% 3.44/3.69 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[8677, 8674, 103, 47])).
% 3.44/3.69 tff(8679,plain,
% 3.44/3.69 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[84, 8678])).
% 3.44/3.69 tff(8680,plain,
% 3.44/3.69 (~r(z, s(s(z)))),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[3269, 103, 145])).
% 3.44/3.69 tff(8681,plain,
% 3.44/3.69 (b(z, s(s(z)))),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[143, 8680])).
% 3.44/3.69 tff(8682,plain,
% 3.44/3.69 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[8677, 7971, 193, 145])).
% 3.44/3.69 tff(8683,plain,
% 3.44/3.69 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[84, 8682])).
% 3.44/3.69 tff(8684,plain,
% 3.44/3.69 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[5101, 147, 7971, 145])).
% 3.44/3.69 tff(8685,plain,
% 3.44/3.69 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[4928, 8684, 4890])).
% 3.44/3.69 tff(8686,plain,
% 3.44/3.69 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[8244, 2484])).
% 3.44/3.69 tff(8687,plain,
% 3.44/3.69 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[4162, 3879, 3240])).
% 3.44/3.69 tff(8688,plain,
% 3.44/3.69 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.44/3.69 inference(monotonicity,[status(thm)],[1527])).
% 3.44/3.69 tff(8689,plain,
% 3.44/3.69 ((~r(s(s(s(s(z)))), elem!1)) <=> (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 3.44/3.69 inference(monotonicity,[status(thm)],[8688])).
% 3.44/3.69 tff(8690,plain,
% 3.44/3.69 (~r(s(s(s(s(z)))), elem!1)),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[3329, 438, 193])).
% 3.44/3.69 tff(8691,plain,
% 3.44/3.69 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.44/3.69 inference(modus_ponens,[status(thm)],[8690, 8689])).
% 3.44/3.69 tff(8692,plain,
% 3.44/3.69 ((s(s(s(s(z)))) = s(s(s(elem!1)))) | b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[3296, 41, 8691])).
% 3.44/3.69 tff(8693,plain,
% 3.44/3.69 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[8692, 8687])).
% 3.44/3.69 tff(8694,plain,
% 3.44/3.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 3.44/3.69 inference(rewrite,[status(thm)],[])).
% 3.44/3.69 tff(8695,plain,
% 3.44/3.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 3.44/3.69 inference(quant_inst,[status(thm)],[])).
% 3.44/3.69 tff(8696,plain,
% 3.44/3.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 3.44/3.69 inference(modus_ponens,[status(thm)],[8695, 8694])).
% 3.44/3.69 tff(8697,plain,
% 3.44/3.69 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[8696, 118, 193, 1125])).
% 3.44/3.69 tff(8698,plain,
% 3.44/3.69 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[4950, 8697, 4938])).
% 3.44/3.69 tff(8699,plain,
% 3.44/3.69 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[5051, 8698])).
% 3.44/3.69 tff(8700,plain,
% 3.44/3.69 ($false),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[8249, 41, 8699, 4976, 8246])).
% 3.44/3.69 tff(8701,plain,((~r(s(s(s(z))), s(s(z)))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.69 tff(8702,plain,
% 3.44/3.69 (~r(s(s(s(z))), s(s(z)))),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[8701, 8693, 1126, 8686, 3831, 193, 6448])).
% 3.44/3.69 tff(8703,plain,
% 3.44/3.69 (b(s(s(s(z))), s(s(z)))),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[4966, 8702])).
% 3.44/3.69 tff(8704,plain,
% 3.44/3.69 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[8677, 3425, 193, 145])).
% 3.44/3.69 tff(8705,plain,
% 3.44/3.69 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[84, 8704])).
% 3.44/3.69 tff(8706,plain,
% 3.44/3.69 ((elem!1 = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 3.44/3.69 inference(monotonicity,[status(thm)],[1527])).
% 3.44/3.69 tff(8707,plain,
% 3.44/3.69 ((elem!1 = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 3.44/3.69 inference(transitivity,[status(thm)],[8706, 3539])).
% 3.44/3.69 tff(8708,plain,
% 3.44/3.69 ((~(elem!1 = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))))),
% 3.44/3.69 inference(monotonicity,[status(thm)],[8707])).
% 3.44/3.69 tff(8709,plain,
% 3.44/3.69 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 3.44/3.69 inference(modus_ponens,[status(thm)],[701, 8708])).
% 3.44/3.69 tff(8710,plain,
% 3.44/3.69 (~(s(s(s(z))) = elem!1)),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[4830, 1527, 2484])).
% 3.44/3.69 tff(8711,plain,
% 3.44/3.69 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[5113, 8693, 701, 3831, 145, 3425, 1527, 8710, 438, 8705])).
% 3.44/3.69 tff(8712,plain,
% 3.44/3.69 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[5118, 8711, 8709])).
% 3.44/3.69 tff(8713,plain,
% 3.44/3.69 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[5051, 6170])).
% 3.44/3.69 tff(8714,plain,
% 3.44/3.69 (r(s(s(s(z))), s(s(s(elem!1))))),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[8249, 41, 8713, 8246])).
% 3.44/3.69 tff(8715,plain,
% 3.44/3.69 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[7596, 178, 104, 251, 1126, 6170])).
% 3.44/3.69 tff(8716,plain,
% 3.44/3.69 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 8715])).
% 3.44/3.69 tff(8717,plain,
% 3.44/3.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(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(s(s(z))))))),
% 3.44/3.69 inference(rewrite,[status(thm)],[])).
% 3.44/3.69 tff(8718,plain,
% 3.44/3.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(s(s(z))))))),
% 3.44/3.69 inference(quant_inst,[status(thm)],[])).
% 3.44/3.69 tff(8719,plain,
% 3.44/3.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 3.44/3.69 inference(modus_ponens,[status(thm)],[8718, 8717])).
% 3.44/3.69 tff(8720,plain,
% 3.44/3.69 ($false),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[8719, 118, 8716, 5128, 8714])).
% 3.44/3.69 tff(8721,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (s(s(s(z))) = s(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))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.44/3.69 tff(8722,plain,
% 3.44/3.69 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[8721, 8712, 8686, 8705, 251, 1126, 8693, 3831])).
% 3.44/3.69 tff(8723,plain,
% 3.44/3.69 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[4950, 8722, 4938])).
% 3.44/3.69 tff(8724,plain,
% 3.44/3.69 (~r(z, s(s(s(z))))),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[4961, 8723, 194])).
% 3.44/3.69 tff(8725,plain,
% 3.44/3.69 (b(z, s(s(s(z))))),
% 3.44/3.69 inference(unit_resolution,[status(thm)],[4920, 8724])).
% 3.44/3.69 tff(8726,plain,
% 3.44/3.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 3.44/3.69 inference(rewrite,[status(thm)],[])).
% 3.44/3.69 tff(8727,plain,
% 3.44/3.69 (((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(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(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 3.44/3.69 inference(rewrite,[status(thm)],[])).
% 3.44/3.69 tff(8728,plain,
% 3.44/3.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(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(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 3.54/3.70 inference(monotonicity,[status(thm)],[8727])).
% 3.54/3.70 tff(8729,plain,
% 3.54/3.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(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(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 3.54/3.70 inference(transitivity,[status(thm)],[8728, 8726])).
% 3.54/3.70 tff(8730,plain,
% 3.54/3.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(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(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))))),
% 3.54/3.70 inference(quant_inst,[status(thm)],[])).
% 3.54/3.70 tff(8731,plain,
% 3.54/3.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 3.54/3.70 inference(modus_ponens,[status(thm)],[8730, 8729])).
% 3.54/3.70 tff(8732,plain,
% 3.54/3.70 ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[8731, 178, 2043, 1126, 3831])).
% 3.54/3.70 tff(8733,plain,
% 3.54/3.70 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[8732, 8725])).
% 3.54/3.70 tff(8734,plain,
% 3.54/3.70 (r(s(s(s(z))), s(s(s(elem!1))))),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[8249, 41, 8733, 8686])).
% 3.54/3.70 tff(8735,plain,
% 3.54/3.70 (~r(s(s(z)), s(s(s(z))))),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[8359, 118, 3863, 8734])).
% 3.54/3.70 tff(8736,plain,
% 3.54/3.70 (b(s(s(z)), s(s(s(z))))),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[5088, 8735])).
% 3.54/3.70 tff(8737,plain,
% 3.54/3.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 3.54/3.70 inference(rewrite,[status(thm)],[])).
% 3.54/3.70 tff(8738,plain,
% 3.54/3.70 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 3.54/3.70 inference(rewrite,[status(thm)],[])).
% 3.54/3.70 tff(8739,plain,
% 3.54/3.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))))),
% 3.54/3.70 inference(monotonicity,[status(thm)],[8738])).
% 3.54/3.70 tff(8740,plain,
% 3.54/3.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 3.54/3.70 inference(transitivity,[status(thm)],[8739, 8737])).
% 3.54/3.70 tff(8741,plain,
% 3.54/3.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)))),
% 3.54/3.70 inference(quant_inst,[status(thm)],[])).
% 3.54/3.70 tff(8742,plain,
% 3.54/3.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 3.54/3.70 inference(modus_ponens,[status(thm)],[8741, 8740])).
% 3.54/3.70 tff(8743,plain,
% 3.54/3.70 ($false),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[8742, 178, 3425, 3549, 8725, 8736, 8703])).
% 3.54/3.70 tff(8744,plain,((~(elem!1 = s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | b(elem!1, s(s(s(elem!1)))) | (~r(elem!1, s(s(z)))) | (s(s(elem!1)) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.70 tff(8745,plain,
% 3.54/3.70 (~(elem!1 = s(s(s(elem!1))))),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[8744, 4256, 8685, 3831, 3244, 251, 193, 701, 145, 2043, 3240, 1042, 3791])).
% 3.54/3.70 tff(8746,plain,
% 3.54/3.70 (r(elem!1, s(s(s(elem!1))))),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[2054, 8745, 3240])).
% 3.54/3.70 tff(8747,plain,
% 3.54/3.70 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[7973, 8746, 4256])).
% 3.54/3.70 tff(8748,plain,
% 3.54/3.70 (b(s(s(z)), s(s(s(elem!1))))),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[4223, 8747])).
% 3.54/3.70 tff(8749,plain,
% 3.54/3.70 (~b(s(s(s(elem!1))), z)),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[7978, 8748, 7971, 3549, 2043])).
% 3.54/3.70 tff(8750,plain,
% 3.54/3.70 (r(s(s(s(elem!1))), z)),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[1565, 8749])).
% 3.54/3.70 tff(8751,plain,
% 3.54/3.70 (~r(elem!1, z)),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[6071, 8750, 8746])).
% 3.54/3.70 tff(8752,plain,
% 3.54/3.70 (b(elem!1, z)),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[498, 8751, 3789])).
% 3.54/3.70 tff(8753,plain,
% 3.54/3.70 (~(elem!1 = s(s(s(s(z)))))),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[3172, 8752, 3170])).
% 3.54/3.70 tff(8754,plain,
% 3.54/3.70 (~(s(s(s(s(z)))) = elem!1)),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[504, 8753])).
% 3.54/3.70 tff(8755,plain,
% 3.54/3.70 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[3502, 8754])).
% 3.54/3.70 tff(8756,plain,
% 3.54/3.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.54/3.70 inference(rewrite,[status(thm)],[])).
% 3.54/3.70 tff(8757,plain,
% 3.54/3.70 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1))) <=> ((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.54/3.70 inference(rewrite,[status(thm)],[])).
% 3.54/3.70 tff(8758,plain,
% 3.54/3.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 3.54/3.70 inference(monotonicity,[status(thm)],[8757])).
% 3.54/3.70 tff(8759,plain,
% 3.54/3.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.54/3.70 inference(transitivity,[status(thm)],[8758, 8756])).
% 3.54/3.70 tff(8760,plain,
% 3.54/3.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))),
% 3.54/3.70 inference(quant_inst,[status(thm)],[])).
% 3.54/3.70 tff(8761,plain,
% 3.54/3.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 3.54/3.70 inference(modus_ponens,[status(thm)],[8760, 8759])).
% 3.54/3.70 tff(8762,plain,
% 3.54/3.70 ($false),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[8761, 118, 438, 470, 147])).
% 3.54/3.70 tff(8763,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.70 tff(8764,plain,
% 3.54/3.70 (~r(elem!1, s(s(s(s(z)))))),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[8763, 4256, 147])).
% 3.54/3.70 tff(8765,plain,
% 3.54/3.70 (~r(s(s(s(s(z)))), elem!1)),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[3329, 4256, 193])).
% 3.54/3.70 tff(8766,plain,
% 3.54/3.70 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[8548, 8753, 8683, 251, 8765, 8764])).
% 3.54/3.70 tff(8767,plain,
% 3.54/3.70 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[4307, 8766, 3831, 8746, 8755, 8748, 8683, 3241])).
% 3.54/3.70 tff(8768,plain,
% 3.54/3.70 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[691, 8766, 701])).
% 3.54/3.70 tff(8769,plain,
% 3.54/3.70 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[2803, 8768, 4256])).
% 3.54/3.70 tff(8770,plain,
% 3.54/3.70 ($false),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[249, 8769, 8767])).
% 3.54/3.70 tff(8771,plain,((s(s(z)) = elem!1) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | b(s(s(z)), elem!1) | (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)))), z) | (~b(z, s(s(s(elem!1))))) | b(elem!1, s(s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | b(elem!1, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.70 tff(8772,plain,
% 3.54/3.70 (s(s(z)) = elem!1),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[8771, 251, 3241, 701, 3831, 3170, 2043, 3240, 103, 145, 147, 461])).
% 3.54/3.70 tff(8773,plain,
% 3.54/3.70 (r(s(s(elem!1)), s(s(z))) <=> r(s(s(elem!1)), elem!1)),
% 3.54/3.70 inference(monotonicity,[status(thm)],[8772])).
% 3.54/3.70 tff(8774,plain,
% 3.54/3.70 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(s(z)))),
% 3.54/3.70 inference(symmetry,[status(thm)],[8773])).
% 3.54/3.70 tff(8775,plain,
% 3.54/3.70 (s(s(s(z))) = s(elem!1)),
% 3.54/3.70 inference(monotonicity,[status(thm)],[8772])).
% 3.54/3.70 tff(8776,plain,
% 3.54/3.70 (s(s(s(s(z)))) = s(s(elem!1))),
% 3.54/3.70 inference(monotonicity,[status(thm)],[8775])).
% 3.54/3.70 tff(8777,plain,
% 3.54/3.70 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 3.54/3.70 inference(monotonicity,[status(thm)],[8776])).
% 3.54/3.70 tff(8778,plain,
% 3.54/3.70 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(elem!1)), s(s(z)))),
% 3.54/3.70 inference(transitivity,[status(thm)],[8777, 8774])).
% 3.54/3.70 tff(8779,plain,
% 3.54/3.70 (~b(s(s(s(s(z)))), elem!1)),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[3774, 8772, 86])).
% 3.54/3.70 tff(8780,plain,
% 3.54/3.70 (~(elem!1 = z)),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[3276, 8681, 461])).
% 3.54/3.70 tff(8781,plain,
% 3.54/3.70 (~r(elem!1, z)),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[6206, 8772, 8005])).
% 3.54/3.70 tff(8782,plain,
% 3.54/3.70 (b(elem!1, z)),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[498, 8781, 8780])).
% 3.54/3.70 tff(8783,plain,
% 3.54/3.70 (~(elem!1 = s(s(s(s(z)))))),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[3172, 8782, 3170])).
% 3.54/3.70 tff(8784,plain,
% 3.54/3.70 (~(s(s(s(s(z)))) = elem!1)),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[504, 8783])).
% 3.54/3.70 tff(8785,plain,
% 3.54/3.70 (r(s(s(s(s(z)))), elem!1)),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[3142, 8784, 8779])).
% 3.54/3.70 tff(8786,plain,
% 3.54/3.70 (r(s(s(elem!1)), s(s(z)))),
% 3.54/3.70 inference(modus_ponens,[status(thm)],[8785, 8778])).
% 3.54/3.70 tff(8787,plain,
% 3.54/3.70 (s(s(elem!1)) = s(s(s(s(z))))),
% 3.54/3.70 inference(symmetry,[status(thm)],[8776])).
% 3.54/3.70 tff(8788,plain,
% 3.54/3.70 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(s(z)))), s(elem!1))),
% 3.54/3.70 inference(monotonicity,[status(thm)],[8787])).
% 3.54/3.70 tff(8789,plain,
% 3.54/3.70 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 3.54/3.70 inference(symmetry,[status(thm)],[8788])).
% 3.54/3.70 tff(8790,plain,
% 3.54/3.70 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 3.54/3.70 inference(monotonicity,[status(thm)],[8775])).
% 3.54/3.70 tff(8791,plain,
% 3.54/3.70 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(elem!1)), s(elem!1))),
% 3.54/3.70 inference(transitivity,[status(thm)],[8790, 8789])).
% 3.54/3.70 tff(8792,plain,
% 3.54/3.70 (~(z = elem!1)),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[317, 8780])).
% 3.54/3.70 tff(8793,plain,
% 3.54/3.70 (~(s(s(elem!1)) = s(s(z)))),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[2386, 8792])).
% 3.54/3.70 tff(8794,plain,
% 3.54/3.70 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 3.54/3.70 inference(monotonicity,[status(thm)],[8772])).
% 3.54/3.70 tff(8795,plain,
% 3.54/3.70 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 3.54/3.70 inference(transitivity,[status(thm)],[8794, 1526])).
% 3.54/3.70 tff(8796,plain,
% 3.54/3.70 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 3.54/3.70 inference(transitivity,[status(thm)],[8795, 2486])).
% 3.54/3.70 tff(8797,plain,
% 3.54/3.70 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 3.54/3.70 inference(monotonicity,[status(thm)],[8796])).
% 3.54/3.70 tff(8798,plain,
% 3.54/3.70 (~(elem!1 = s(s(s(elem!1))))),
% 3.54/3.70 inference(modus_ponens,[status(thm)],[1683, 8797])).
% 3.54/3.70 tff(8799,plain,
% 3.54/3.70 (r(elem!1, s(s(s(elem!1))))),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[2054, 8798, 3240])).
% 3.54/3.70 tff(8800,plain,
% 3.54/3.70 ((s(s(elem!1)) = s(s(z))) <=> (s(s(elem!1)) = elem!1)),
% 3.54/3.70 inference(monotonicity,[status(thm)],[1324])).
% 3.54/3.70 tff(8801,plain,
% 3.54/3.70 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(elem!1)) = elem!1))),
% 3.54/3.70 inference(monotonicity,[status(thm)],[8800])).
% 3.54/3.70 tff(8802,plain,
% 3.54/3.70 (~(s(s(elem!1)) = elem!1)),
% 3.54/3.70 inference(modus_ponens,[status(thm)],[2484, 8801])).
% 3.54/3.70 tff(8803,plain,
% 3.54/3.70 ((~b(s(s(s(s(z)))), elem!1)) <=> (~b(s(s(elem!1)), elem!1))),
% 3.54/3.70 inference(monotonicity,[status(thm)],[8522])).
% 3.54/3.70 tff(8804,plain,
% 3.54/3.70 (~b(s(s(s(s(z)))), elem!1)),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[3774, 1324, 86])).
% 3.54/3.70 tff(8805,plain,
% 3.54/3.70 (~b(s(s(elem!1)), elem!1)),
% 3.54/3.70 inference(modus_ponens,[status(thm)],[8804, 8803])).
% 3.54/3.70 tff(8806,plain,
% 3.54/3.70 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.54/3.70 inference(monotonicity,[status(thm)],[3506])).
% 3.54/3.70 tff(8807,plain,
% 3.54/3.70 ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) <=> (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 3.54/3.70 inference(monotonicity,[status(thm)],[8806])).
% 3.54/3.70 tff(8808,assumption,(~b(s(s(s(s(z)))), s(s(s(elem!1))))), introduced(assumption)).
% 3.54/3.70 tff(8809,plain,
% 3.54/3.70 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.54/3.70 inference(modus_ponens,[status(thm)],[8808, 8807])).
% 3.54/3.70 tff(8810,plain,
% 3.54/3.70 ($false),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[3377, 8809, 8805, 3311, 8802])).
% 3.54/3.70 tff(8811,plain,((~(s(s(z)) = elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | b(s(s(s(s(z)))), s(s(s(elem!1)))) | (s(s(elem!1)) = s(s(z))) | b(s(s(s(s(z)))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.70 tff(8812,plain,
% 3.54/3.70 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[8811, 8799, 86, 8793, 8772])).
% 3.54/3.70 tff(8813,plain,
% 3.54/3.70 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[5101, 147, 8674, 145])).
% 3.54/3.70 tff(8814,plain,
% 3.54/3.70 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[4928, 8813, 4890])).
% 3.54/3.70 tff(8815,plain,
% 3.54/3.70 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[8677, 8674, 103, 145])).
% 3.54/3.70 tff(8816,plain,
% 3.54/3.70 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[84, 8815])).
% 3.54/3.70 tff(8817,plain,
% 3.54/3.70 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[8244, 8793])).
% 3.54/3.70 tff(8818,plain,
% 3.54/3.70 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[3502, 8784])).
% 3.54/3.70 tff(8819,plain,
% 3.54/3.70 (b(s(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))))))))),
% 3.54/3.70 inference(monotonicity,[status(thm)],[8787])).
% 3.54/3.70 tff(8820,plain,
% 3.54/3.70 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.54/3.70 inference(symmetry,[status(thm)],[8819])).
% 3.54/3.70 tff(8821,plain,
% 3.54/3.70 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.54/3.70 inference(modus_ponens,[status(thm)],[251, 8820])).
% 3.54/3.70 tff(8822,plain,
% 3.54/3.70 (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)))),
% 3.54/3.70 inference(monotonicity,[status(thm)],[8776])).
% 3.54/3.70 tff(8823,plain,
% 3.54/3.70 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.54/3.70 inference(modus_ponens,[status(thm)],[8816, 8822])).
% 3.54/3.70 tff(8824,plain,
% 3.54/3.70 ((s(s(elem!1)) = s(s(z))) <=> (s(s(elem!1)) = elem!1)),
% 3.54/3.70 inference(monotonicity,[status(thm)],[8772])).
% 3.54/3.70 tff(8825,plain,
% 3.54/3.70 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(elem!1)) = elem!1))),
% 3.54/3.70 inference(monotonicity,[status(thm)],[8824])).
% 3.54/3.70 tff(8826,plain,
% 3.54/3.70 (~(s(s(elem!1)) = elem!1)),
% 3.54/3.70 inference(modus_ponens,[status(thm)],[8793, 8825])).
% 3.54/3.70 tff(8827,plain,
% 3.54/3.70 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 3.54/3.70 inference(monotonicity,[status(thm)],[8776])).
% 3.54/3.70 tff(8828,plain,
% 3.54/3.70 ((~b(s(s(s(s(z)))), elem!1)) <=> (~b(s(s(elem!1)), elem!1))),
% 3.54/3.70 inference(monotonicity,[status(thm)],[8827])).
% 3.54/3.70 tff(8829,plain,
% 3.54/3.70 (~b(s(s(elem!1)), elem!1)),
% 3.54/3.70 inference(modus_ponens,[status(thm)],[8779, 8828])).
% 3.54/3.70 tff(8830,plain,
% 3.54/3.70 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[3377, 8829, 8799, 8826])).
% 3.54/3.70 tff(8831,plain,
% 3.54/3.70 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.54/3.70 inference(monotonicity,[status(thm)],[8776])).
% 3.54/3.70 tff(8832,plain,
% 3.54/3.70 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.54/3.70 inference(modus_ponens,[status(thm)],[3831, 8831])).
% 3.54/3.70 tff(8833,plain,
% 3.54/3.70 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[3518, 178, 8832, 8830, 8823, 8821])).
% 3.54/3.70 tff(8834,plain,
% 3.54/3.70 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[5118, 8833, 8818])).
% 3.54/3.70 tff(8835,plain,
% 3.54/3.70 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[8721, 8834, 8817, 8816, 251, 8814, 8812, 3831])).
% 3.54/3.70 tff(8836,plain,
% 3.54/3.70 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[4950, 8835, 4938])).
% 3.54/3.70 tff(8837,plain,
% 3.54/3.70 (r(s(s(elem!1)), s(elem!1))),
% 3.54/3.70 inference(modus_ponens,[status(thm)],[8836, 8791])).
% 3.54/3.70 tff(8838,assumption,(r(s(s(elem!1)), s(s(z)))), introduced(assumption)).
% 3.54/3.70 tff(8839,plain,
% 3.54/3.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 3.54/3.70 inference(rewrite,[status(thm)],[])).
% 3.54/3.70 tff(8840,plain,
% 3.54/3.70 (((~r(s(elem!1), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 3.54/3.70 inference(rewrite,[status(thm)],[])).
% 3.54/3.70 tff(8841,plain,
% 3.54/3.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(elem!1)), s(s(z))))))),
% 3.54/3.70 inference(monotonicity,[status(thm)],[8840])).
% 3.54/3.70 tff(8842,plain,
% 3.54/3.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 3.54/3.70 inference(transitivity,[status(thm)],[8841, 8839])).
% 3.54/3.70 tff(8843,plain,
% 3.54/3.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 3.54/3.70 inference(quant_inst,[status(thm)],[])).
% 3.54/3.70 tff(8844,plain,
% 3.54/3.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(elem!1)), s(s(z))))),
% 3.54/3.70 inference(modus_ponens,[status(thm)],[8843, 8842])).
% 3.54/3.70 tff(8845,plain,
% 3.54/3.70 ($false),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[8844, 118, 363, 8838, 992])).
% 3.54/3.70 tff(8846,plain,((~r(s(s(elem!1)), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.70 tff(8847,plain,
% 3.54/3.70 (~r(s(elem!1), s(s(z)))),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[8846, 8837, 8786])).
% 3.54/3.70 tff(8848,plain,
% 3.54/3.70 ((s(elem!1) = s(s(z))) <=> (s(elem!1) = elem!1)),
% 3.54/3.70 inference(monotonicity,[status(thm)],[8772])).
% 3.54/3.70 tff(8849,plain,
% 3.54/3.70 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(z)))),
% 3.54/3.70 inference(symmetry,[status(thm)],[8848])).
% 3.54/3.70 tff(8850,plain,
% 3.54/3.70 ((elem!1 = s(s(s(z)))) <=> (elem!1 = s(elem!1))),
% 3.54/3.70 inference(monotonicity,[status(thm)],[8775])).
% 3.54/3.70 tff(8851,plain,
% 3.54/3.70 ((elem!1 = s(s(s(z)))) <=> (s(elem!1) = elem!1)),
% 3.54/3.70 inference(transitivity,[status(thm)],[8850, 3190])).
% 3.54/3.70 tff(8852,plain,
% 3.54/3.70 ((elem!1 = s(s(s(z)))) <=> (s(elem!1) = s(s(z)))),
% 3.54/3.70 inference(transitivity,[status(thm)],[8851, 8849])).
% 3.54/3.70 tff(8853,plain,
% 3.54/3.70 ((~(elem!1 = s(s(s(z))))) <=> (~(s(elem!1) = s(s(z))))),
% 3.54/3.70 inference(monotonicity,[status(thm)],[8852])).
% 3.54/3.70 tff(8854,plain,
% 3.54/3.70 ((s(s(z)) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 3.54/3.70 inference(monotonicity,[status(thm)],[8772])).
% 3.54/3.70 tff(8855,plain,
% 3.54/3.70 ((~(s(s(z)) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 3.54/3.70 inference(monotonicity,[status(thm)],[8854])).
% 3.54/3.70 tff(8856,plain,
% 3.54/3.70 (~(elem!1 = s(s(s(z))))),
% 3.54/3.70 inference(modus_ponens,[status(thm)],[3205, 8855])).
% 3.54/3.70 tff(8857,plain,
% 3.54/3.70 (~(s(elem!1) = s(s(z)))),
% 3.54/3.70 inference(modus_ponens,[status(thm)],[8856, 8853])).
% 3.54/3.70 tff(8858,plain,
% 3.54/3.70 (b(s(s(z)), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 3.54/3.70 inference(monotonicity,[status(thm)],[8772])).
% 3.54/3.70 tff(8859,plain,
% 3.54/3.70 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 3.54/3.70 inference(symmetry,[status(thm)],[8858])).
% 3.54/3.70 tff(8860,plain,
% 3.54/3.70 ((~b(elem!1, s(s(s(elem!1))))) <=> (~b(s(s(z)), s(s(s(elem!1)))))),
% 3.54/3.70 inference(monotonicity,[status(thm)],[8859])).
% 3.54/3.70 tff(8861,plain,
% 3.54/3.70 (~b(s(s(z)), s(s(s(elem!1))))),
% 3.54/3.70 inference(modus_ponens,[status(thm)],[3240, 8860])).
% 3.54/3.70 tff(8862,plain,
% 3.54/3.70 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 3.54/3.70 inference(monotonicity,[status(thm)],[8775])).
% 3.54/3.70 tff(8863,plain,
% 3.54/3.70 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 3.54/3.70 inference(transitivity,[status(thm)],[8862, 3881])).
% 3.54/3.70 tff(8864,plain,
% 3.54/3.70 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 3.54/3.70 inference(transitivity,[status(thm)],[8863, 7104])).
% 3.54/3.70 tff(8865,plain,
% 3.54/3.70 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 3.54/3.70 inference(monotonicity,[status(thm)],[8864])).
% 3.54/3.70 tff(8866,plain,
% 3.54/3.70 (~(s(elem!1) = s(s(s(elem!1))))),
% 3.54/3.70 inference(modus_ponens,[status(thm)],[8817, 8865])).
% 3.54/3.70 tff(8867,plain,
% 3.54/3.70 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 3.54/3.70 inference(monotonicity,[status(thm)],[8775])).
% 3.54/3.70 tff(8868,plain,
% 3.54/3.70 ((~b(s(s(s(z))), s(s(s(elem!1))))) <=> (~b(s(elem!1), s(s(s(elem!1)))))),
% 3.54/3.70 inference(monotonicity,[status(thm)],[8867])).
% 3.54/3.70 tff(8869,plain,
% 3.54/3.70 (~r(z, s(s(s(z))))),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[4961, 8836, 3244])).
% 3.54/3.70 tff(8870,plain,
% 3.54/3.70 (b(z, s(s(s(z))))),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[4920, 8869])).
% 3.54/3.70 tff(8871,plain,
% 3.54/3.70 ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[8731, 178, 2043, 8814, 3831])).
% 3.54/3.70 tff(8872,plain,
% 3.54/3.70 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 3.54/3.70 inference(unit_resolution,[status(thm)],[8871, 8870])).
% 3.54/3.70 tff(8873,plain,
% 3.54/3.70 (~b(s(elem!1), s(s(s(elem!1))))),
% 3.54/3.70 inference(modus_ponens,[status(thm)],[8872, 8868])).
% 3.54/3.70 tff(8874,plain,
% 3.54/3.71 (~r(s(s(z)), s(elem!1))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[6127, 8873, 8866, 8861])).
% 3.54/3.71 tff(8875,plain,
% 3.54/3.71 (r(s(s(s(s(z)))), z) <=> r(s(s(elem!1)), z)),
% 3.54/3.71 inference(monotonicity,[status(thm)],[8776])).
% 3.54/3.71 tff(8876,plain,
% 3.54/3.71 (r(s(s(elem!1)), z)),
% 3.54/3.71 inference(modus_ponens,[status(thm)],[3244, 8875])).
% 3.54/3.71 tff(8877,plain,
% 3.54/3.71 (~r(s(elem!1), z)),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[997, 8837, 8876])).
% 3.54/3.71 tff(8878,plain,
% 3.54/3.71 (b(s(elem!1), z)),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[774, 8877])).
% 3.54/3.71 tff(8879,plain,
% 3.54/3.71 ($false),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[6767, 8878, 8874, 8681, 8857, 8674, 8847])).
% 3.54/3.71 tff(8880,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(z))) | b(elem!1, s(s(s(elem!1)))) | b(s(s(s(s(z)))), z) | b(s(s(z)), elem!1) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | b(elem!1, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.71 tff(8881,plain,
% 3.54/3.71 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[8880, 147, 3831, 86, 3240, 3170, 3241, 701, 145, 2043, 461])).
% 3.54/3.71 tff(8882,plain,
% 3.54/3.71 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[222, 8881])).
% 3.54/3.71 tff(8883,plain,
% 3.54/3.71 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[3569, 8882, 145, 103, 8674, 8681])).
% 3.54/3.71 tff(8884,plain,
% 3.54/3.71 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[3578, 8883])).
% 3.54/3.71 tff(8885,plain,
% 3.54/3.71 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[212, 8882, 145])).
% 3.54/3.71 tff(8886,plain,
% 3.54/3.71 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[271, 8885])).
% 3.54/3.71 tff(8887,plain,
% 3.54/3.71 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[5624, 8882, 147])).
% 3.54/3.71 tff(8888,plain,
% 3.54/3.71 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[249, 8887])).
% 3.54/3.71 tff(8889,plain,
% 3.54/3.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(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(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(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(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.54/3.71 inference(rewrite,[status(thm)],[])).
% 3.54/3.71 tff(8890,plain,
% 3.54/3.71 (((~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(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(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(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.54/3.71 inference(rewrite,[status(thm)],[])).
% 3.54/3.71 tff(8891,plain,
% 3.54/3.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(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(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(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(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 3.54/3.71 inference(monotonicity,[status(thm)],[8890])).
% 3.54/3.71 tff(8892,plain,
% 3.54/3.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(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(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(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(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.54/3.71 inference(transitivity,[status(thm)],[8891, 8889])).
% 3.54/3.71 tff(8893,plain,
% 3.54/3.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(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(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(elem!1))))))),
% 3.54/3.71 inference(quant_inst,[status(thm)],[])).
% 3.54/3.71 tff(8894,plain,
% 3.54/3.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(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(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.54/3.71 inference(modus_ponens,[status(thm)],[8893, 8892])).
% 3.54/3.71 tff(8895,plain,
% 3.54/3.71 (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[8894, 178, 2043, 104, 595, 3831])).
% 3.54/3.71 tff(8896,plain,
% 3.54/3.71 (b(s(s(s(s(z)))), s(s(s(s(elem!1))))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 3.54/3.71 inference(monotonicity,[status(thm)],[4021])).
% 3.54/3.71 tff(8897,plain,
% 3.54/3.71 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 3.54/3.71 inference(symmetry,[status(thm)],[8896])).
% 3.54/3.71 tff(8898,plain,
% 3.54/3.71 (r(s(s(s(s(z)))), s(s(s(s(elem!1))))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 3.54/3.71 inference(monotonicity,[status(thm)],[4021])).
% 3.54/3.71 tff(8899,plain,
% 3.54/3.71 ((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) <=> (~r(s(s(s(s(z)))), s(elem!1)))),
% 3.54/3.71 inference(monotonicity,[status(thm)],[8898])).
% 3.54/3.71 tff(8900,plain,
% 3.54/3.71 (b(s(s(s(s(z)))), elem!1)),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[3308, 8691, 1527])).
% 3.54/3.71 tff(8901,plain,
% 3.54/3.71 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[3936, 8900, 193, 107, 1527, 3879, 461])).
% 3.54/3.71 tff(8902,plain,
% 3.54/3.71 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[1649, 8901])).
% 3.54/3.71 tff(8903,plain,
% 3.54/3.71 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[1657, 8902])).
% 3.54/3.71 tff(8904,plain,
% 3.54/3.71 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[3975, 8903, 3831, 193, 6448, 1527, 3876, 8693, 3863])).
% 3.54/3.71 tff(8905,plain,
% 3.54/3.71 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[1170, 8904])).
% 3.54/3.71 tff(8906,plain,
% 3.54/3.71 (~b(s(s(s(s(elem!1)))), z)),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[3983, 178, 273, 8905, 166, 595])).
% 3.54/3.71 tff(8907,plain,
% 3.54/3.71 (r(s(s(s(s(elem!1)))), z)),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[1716, 8906])).
% 3.54/3.71 tff(8908,plain,
% 3.54/3.71 (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[4147, 118, 8907, 194])).
% 3.54/3.71 tff(8909,plain,
% 3.54/3.71 (~r(s(s(s(s(z)))), s(elem!1))),
% 3.54/3.71 inference(modus_ponens,[status(thm)],[8908, 8899])).
% 3.54/3.71 tff(8910,plain,
% 3.54/3.71 (b(s(s(s(s(z)))), s(elem!1))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[2173, 8909, 4008])).
% 3.54/3.71 tff(8911,plain,
% 3.54/3.71 (b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 3.54/3.71 inference(modus_ponens,[status(thm)],[8910, 8897])).
% 3.54/3.71 tff(8912,plain,
% 3.54/3.71 (r(s(elem!1), z)),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[3991, 8907, 1527])).
% 3.54/3.71 tff(8913,plain,
% 3.54/3.71 (~r(s(elem!1), s(s(s(s(z)))))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[916, 8912, 194])).
% 3.54/3.71 tff(8914,plain,
% 3.54/3.71 (b(s(elem!1), s(s(s(s(z)))))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[1084, 8913, 3876])).
% 3.54/3.71 tff(8915,plain,
% 3.54/3.71 (b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 3.54/3.71 inference(modus_ponens,[status(thm)],[8914, 3872])).
% 3.54/3.71 tff(8916,plain,
% 3.54/3.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(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)))))))),
% 3.54/3.71 inference(rewrite,[status(thm)],[])).
% 3.54/3.71 tff(8917,plain,
% 3.54/3.71 (((~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(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(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(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)))))))),
% 3.54/3.71 inference(rewrite,[status(thm)],[])).
% 3.54/3.71 tff(8918,plain,
% 3.54/3.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(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(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(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))))))))),
% 3.54/3.71 inference(monotonicity,[status(thm)],[8917])).
% 3.54/3.71 tff(8919,plain,
% 3.54/3.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(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(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(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)))))))),
% 3.54/3.71 inference(transitivity,[status(thm)],[8918, 8916])).
% 3.54/3.71 tff(8920,plain,
% 3.54/3.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(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(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.54/3.71 inference(quant_inst,[status(thm)],[])).
% 3.54/3.71 tff(8921,plain,
% 3.54/3.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(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))))))),
% 3.54/3.71 inference(modus_ponens,[status(thm)],[8920, 8919])).
% 3.54/3.71 tff(8922,plain,
% 3.54/3.71 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[8921, 178, 8693, 3831, 8915, 8911])).
% 3.54/3.71 tff(8923,plain,
% 3.54/3.71 (~b(elem!1, s(elem!1))),
% 3.54/3.71 inference(modus_ponens,[status(thm)],[8922, 3871])).
% 3.54/3.71 tff(8924,plain,
% 3.54/3.71 (~(elem!1 = s(s(elem!1)))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[1539, 8901])).
% 3.54/3.71 tff(8925,plain,
% 3.54/3.71 (~(s(s(elem!1)) = elem!1)),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[1546, 8924])).
% 3.54/3.71 tff(8926,plain,
% 3.54/3.71 (~(s(elem!1) = elem!1)),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[672, 8925])).
% 3.54/3.71 tff(8927,plain,
% 3.54/3.71 (~(elem!1 = s(elem!1))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[748, 8926])).
% 3.54/3.71 tff(8928,assumption,(~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 3.54/3.71 tff(8929,plain,
% 3.54/3.71 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.54/3.71 inference(modus_ponens,[status(thm)],[8928, 5006])).
% 3.54/3.71 tff(8930,plain,
% 3.54/3.71 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[691, 8929, 701])).
% 3.54/3.71 tff(8931,plain,
% 3.54/3.71 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[1695, 8903])).
% 3.54/3.71 tff(8932,plain,
% 3.54/3.71 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[1750, 8922, 8931])).
% 3.54/3.71 tff(8933,plain,
% 3.54/3.71 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[4036, 8932, 3863])).
% 3.54/3.71 tff(8934,plain,
% 3.54/3.71 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[2136, 8933])).
% 3.54/3.71 tff(8935,plain,
% 3.54/3.71 (b(s(s(z)), s(elem!1))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[1524, 8934, 3894])).
% 3.54/3.71 tff(8936,plain,
% 3.54/3.71 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[2529, 8935, 104, 8914, 166])).
% 3.54/3.71 tff(8937,plain,
% 3.54/3.71 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[395, 8936, 4020])).
% 3.54/3.71 tff(8938,plain,
% 3.54/3.71 (~r(elem!1, s(elem!1))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[2935, 8937, 8930])).
% 3.54/3.71 tff(8939,plain,
% 3.54/3.71 (b(elem!1, s(elem!1))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[756, 8938, 8927])).
% 3.54/3.71 tff(8940,plain,
% 3.54/3.71 ($false),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[8939, 8923])).
% 3.54/3.71 tff(8941,plain,((~(elem!1 = s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | b(elem!1, s(s(z))) | b(elem!1, s(s(s(elem!1)))) | (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(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.71 tff(8942,plain,
% 3.54/3.71 (~(elem!1 = s(s(s(elem!1))))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[8941, 1042, 166, 3831, 3244, 273, 595, 193, 107, 461, 3240, 701, 8895, 104, 4256])).
% 3.54/3.71 tff(8943,plain,
% 3.54/3.71 (r(elem!1, s(s(s(elem!1))))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[2054, 8942, 3240])).
% 3.54/3.71 tff(8944,plain,
% 3.54/3.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(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(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(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(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.54/3.71 inference(rewrite,[status(thm)],[])).
% 3.54/3.71 tff(8945,plain,
% 3.54/3.71 (((~b(s(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(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(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(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.54/3.71 inference(rewrite,[status(thm)],[])).
% 3.54/3.71 tff(8946,plain,
% 3.54/3.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(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(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))))),
% 3.54/3.71 inference(monotonicity,[status(thm)],[8945])).
% 3.54/3.71 tff(8947,plain,
% 3.54/3.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(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(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.54/3.71 inference(transitivity,[status(thm)],[8946, 8944])).
% 3.54/3.71 tff(8948,plain,
% 3.54/3.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.54/3.71 inference(quant_inst,[status(thm)],[])).
% 3.54/3.71 tff(8949,plain,
% 3.54/3.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(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(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 3.54/3.71 inference(modus_ponens,[status(thm)],[8948, 8947])).
% 3.54/3.71 tff(8950,plain,
% 3.54/3.71 ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[8949, 178, 2043, 104, 3831])).
% 3.54/3.71 tff(8951,plain,
% 3.54/3.71 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[8950, 595])).
% 3.54/3.71 tff(8952,plain,
% 3.54/3.71 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[7973, 8943, 4256])).
% 3.54/3.71 tff(8953,plain,
% 3.54/3.71 (b(s(s(z)), s(s(s(elem!1))))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[4223, 8952])).
% 3.54/3.71 tff(8954,plain,
% 3.54/3.71 (~b(s(s(s(elem!1))), z)),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[7978, 8953, 7971, 273, 2043])).
% 3.54/3.71 tff(8955,plain,
% 3.54/3.71 (r(s(s(s(elem!1))), z)),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[1565, 8954])).
% 3.54/3.71 tff(8956,plain,
% 3.54/3.71 (~r(elem!1, z)),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[6071, 8955, 8943])).
% 3.54/3.71 tff(8957,plain,
% 3.54/3.71 (b(elem!1, z)),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[498, 8956, 3873])).
% 3.54/3.71 tff(8958,plain,
% 3.54/3.71 (~(elem!1 = s(s(s(s(z)))))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[3172, 8957, 3170])).
% 3.54/3.71 tff(8959,plain,
% 3.54/3.71 (~(s(s(s(s(z)))) = elem!1)),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[504, 8958])).
% 3.54/3.71 tff(8960,plain,
% 3.54/3.71 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[3502, 8959])).
% 3.54/3.71 tff(8961,plain,
% 3.54/3.71 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[5118, 8960, 8951])).
% 3.54/3.71 tff(8962,plain,
% 3.54/3.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(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))))))),
% 3.54/3.71 inference(rewrite,[status(thm)],[])).
% 3.54/3.71 tff(8963,plain,
% 3.54/3.71 (((~r(elem!1, 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))))))), elem!1))) <=> ((~r(elem!1, s(s(s(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))))))),
% 3.54/3.71 inference(rewrite,[status(thm)],[])).
% 3.54/3.71 tff(8964,plain,
% 3.54/3.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(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)))))))),
% 3.54/3.71 inference(monotonicity,[status(thm)],[8963])).
% 3.54/3.71 tff(8965,plain,
% 3.54/3.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(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))))))),
% 3.54/3.71 inference(transitivity,[status(thm)],[8964, 8962])).
% 3.54/3.71 tff(8966,plain,
% 3.54/3.71 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.54/3.71 inference(quant_inst,[status(thm)],[])).
% 3.54/3.71 tff(8967,plain,
% 3.54/3.71 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 3.54/3.71 inference(modus_ponens,[status(thm)],[8966, 8965])).
% 3.54/3.71 tff(8968,plain,
% 3.54/3.71 ($false),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[8967, 118, 3311, 2953, 5128])).
% 3.54/3.71 tff(8969,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.71 tff(8970,plain,
% 3.54/3.71 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[8969, 8961, 8943])).
% 3.54/3.71 tff(8971,plain,
% 3.54/3.71 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[3444, 8970, 4245])).
% 3.54/3.71 tff(8972,plain,
% 3.54/3.71 (b(elem!1, s(s(s(s(z)))))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[483, 8958, 8764])).
% 3.54/3.71 tff(8973,plain,
% 3.54/3.71 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[4307, 8960, 3831, 166, 8943, 8953, 104, 3241])).
% 3.54/3.71 tff(8974,plain,
% 3.54/3.71 (b(s(s(s(s(z)))), elem!1)),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[3142, 8959, 8765])).
% 3.54/3.71 tff(8975,plain,
% 3.54/3.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.54/3.71 inference(rewrite,[status(thm)],[])).
% 3.54/3.71 tff(8976,plain,
% 3.54/3.71 (((~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(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(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(s(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)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.54/3.71 inference(rewrite,[status(thm)],[])).
% 3.54/3.71 tff(8977,plain,
% 3.54/3.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(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(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.54/3.71 inference(monotonicity,[status(thm)],[8976])).
% 3.54/3.71 tff(8978,plain,
% 3.54/3.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(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(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.54/3.71 inference(transitivity,[status(thm)],[8977, 8975])).
% 3.54/3.71 tff(8979,plain,
% 3.54/3.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(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(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.54/3.71 inference(quant_inst,[status(thm)],[])).
% 3.54/3.71 tff(8980,plain,
% 3.54/3.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.54/3.71 inference(modus_ponens,[status(thm)],[8979, 8978])).
% 3.54/3.71 tff(8981,plain,
% 3.54/3.71 ($false),
% 3.54/3.71 inference(unit_resolution,[status(thm)],[8980, 178, 104, 8974, 8973, 8972, 8971])).
% 3.54/3.71 tff(8982,plain,((s(s(z)) = elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | b(s(s(z)), elem!1) | b(s(s(s(s(z)))), z) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | b(elem!1, s(s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | b(elem!1, s(s(z))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.72 tff(8983,plain,
% 3.54/3.72 (s(s(z)) = elem!1),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[8982, 8888, 3831, 8816, 3241, 3170, 8681, 2043, 3240, 8886, 103, 8884, 461, 701, 147])).
% 3.54/3.72 tff(8984,plain,
% 3.54/3.72 (s(s(s(z))) = s(elem!1)),
% 3.54/3.72 inference(monotonicity,[status(thm)],[8983])).
% 3.54/3.72 tff(8985,plain,
% 3.54/3.72 (s(s(s(s(z)))) = s(s(elem!1))),
% 3.54/3.72 inference(monotonicity,[status(thm)],[8984])).
% 3.54/3.72 tff(8986,plain,
% 3.54/3.72 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 3.54/3.72 inference(monotonicity,[status(thm)],[8985])).
% 3.54/3.72 tff(8987,plain,
% 3.54/3.72 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 3.54/3.72 inference(symmetry,[status(thm)],[8986])).
% 3.54/3.72 tff(8988,plain,
% 3.54/3.72 ((~r(s(s(elem!1)), elem!1)) <=> (~r(s(s(s(s(z)))), elem!1))),
% 3.54/3.72 inference(monotonicity,[status(thm)],[8987])).
% 3.54/3.72 tff(8989,plain,
% 3.54/3.72 (~r(s(s(elem!1)), elem!1)),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[3599, 8983, 103, 145, 8882, 8674])).
% 3.54/3.72 tff(8990,plain,
% 3.54/3.72 (~r(s(s(s(s(z)))), elem!1)),
% 3.54/3.72 inference(modus_ponens,[status(thm)],[8989, 8988])).
% 3.54/3.72 tff(8991,plain,
% 3.54/3.72 (~b(s(s(s(s(z)))), elem!1)),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[3774, 8983, 86])).
% 3.54/3.72 tff(8992,plain,
% 3.54/3.72 (~r(elem!1, z)),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[6206, 8983, 8005])).
% 3.54/3.72 tff(8993,plain,
% 3.54/3.72 (b(elem!1, z)),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[498, 8992, 8780])).
% 3.54/3.72 tff(8994,plain,
% 3.54/3.72 (~(elem!1 = s(s(s(s(z)))))),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[3172, 8993, 3170])).
% 3.54/3.72 tff(8995,plain,
% 3.54/3.72 (~(s(s(s(s(z)))) = elem!1)),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[504, 8994])).
% 3.54/3.72 tff(8996,plain,
% 3.54/3.72 (r(s(s(s(s(z)))), elem!1)),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[3142, 8995, 8991])).
% 3.54/3.72 tff(8997,plain,
% 3.54/3.72 ($false),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[8996, 8990])).
% 3.54/3.72 tff(8998,plain,((~r(s(s(z)), s(s(s(s(z)))))) | b(s(s(s(s(z)))), z) | (~r(z, s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | b(s(s(z)), elem!1) | (~b(z, s(s(s(elem!1))))) | b(elem!1, s(s(s(elem!1)))) | b(elem!1, s(s(z))) | (elem!1 = s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.72 tff(8999,plain,
% 3.54/3.72 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[8998, 86, 47, 3170, 8673, 3241, 7954, 3240, 461, 701])).
% 3.54/3.72 tff(9000,plain,
% 3.54/3.72 (b(s(s(z)), s(s(s(s(z)))))),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[164, 8999])).
% 3.54/3.72 tff(9001,plain,
% 3.54/3.72 (~r(z, s(s(z)))),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[3269, 193, 47])).
% 3.54/3.72 tff(9002,plain,
% 3.54/3.72 (b(z, s(s(z)))),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[143, 9001])).
% 3.54/3.72 tff(9003,plain,
% 3.54/3.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.54/3.72 inference(rewrite,[status(thm)],[])).
% 3.54/3.72 tff(9004,plain,
% 3.54/3.72 (((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.54/3.72 inference(rewrite,[status(thm)],[])).
% 3.54/3.72 tff(9005,plain,
% 3.54/3.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 3.54/3.72 inference(monotonicity,[status(thm)],[9004])).
% 3.54/3.72 tff(9006,plain,
% 3.54/3.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.54/3.72 inference(transitivity,[status(thm)],[9005, 9003])).
% 3.54/3.72 tff(9007,plain,
% 3.54/3.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(z)))))),
% 3.54/3.72 inference(quant_inst,[status(thm)],[])).
% 3.54/3.72 tff(9008,plain,
% 3.54/3.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.54/3.72 inference(modus_ponens,[status(thm)],[9007, 9006])).
% 3.54/3.72 tff(9009,plain,
% 3.54/3.72 (~b(s(s(z)), s(s(s(elem!1))))),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[9008, 178, 2043, 9002, 167, 3831])).
% 3.54/3.72 tff(9010,plain,
% 3.54/3.72 (r(s(s(z)), s(s(s(elem!1))))),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[4223, 9009])).
% 3.54/3.72 tff(9011,plain,
% 3.54/3.72 (~r(elem!1, s(s(s(elem!1))))),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[7973, 4256, 9010])).
% 3.54/3.72 tff(9012,plain,
% 3.54/3.72 (elem!1 = s(s(s(elem!1)))),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[2054, 9011, 3240])).
% 3.54/3.72 tff(9013,plain,
% 3.54/3.72 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.54/3.72 inference(monotonicity,[status(thm)],[9012])).
% 3.54/3.72 tff(9014,plain,
% 3.54/3.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.54/3.72 inference(rewrite,[status(thm)],[])).
% 3.54/3.72 tff(9015,plain,
% 3.54/3.72 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.54/3.72 inference(rewrite,[status(thm)],[])).
% 3.54/3.72 tff(9016,plain,
% 3.54/3.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 3.54/3.72 inference(monotonicity,[status(thm)],[9015])).
% 3.54/3.72 tff(9017,plain,
% 3.54/3.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.54/3.72 inference(transitivity,[status(thm)],[9016, 9014])).
% 3.54/3.72 tff(9018,plain,
% 3.54/3.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))))),
% 3.54/3.72 inference(quant_inst,[status(thm)],[])).
% 3.54/3.72 tff(9019,plain,
% 3.54/3.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.54/3.72 inference(modus_ponens,[status(thm)],[9018, 9017])).
% 3.54/3.72 tff(9020,plain,
% 3.54/3.72 (~b(s(s(s(elem!1))), s(s(z)))),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[9019, 178, 2043, 9002, 167, 3831])).
% 3.54/3.72 tff(9021,plain,
% 3.54/3.72 (r(s(s(s(elem!1))), s(s(z)))),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[4209, 41, 9020, 4181])).
% 3.54/3.72 tff(9022,plain,
% 3.54/3.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.54/3.72 inference(rewrite,[status(thm)],[])).
% 3.54/3.72 tff(9023,plain,
% 3.54/3.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.54/3.72 inference(quant_inst,[status(thm)],[])).
% 3.54/3.72 tff(9024,plain,
% 3.54/3.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 3.54/3.72 inference(modus_ponens,[status(thm)],[9023, 9022])).
% 3.54/3.72 tff(9025,plain,
% 3.54/3.72 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[9024, 118, 9021, 193])).
% 3.54/3.72 tff(9026,plain,
% 3.54/3.72 (b(s(s(s(s(z)))), elem!1)),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[3308, 9012, 9025])).
% 3.54/3.72 tff(9027,plain,
% 3.54/3.72 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.54/3.72 inference(modus_ponens,[status(thm)],[9026, 9013])).
% 3.54/3.72 tff(9028,plain,
% 3.54/3.72 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[4067, 178, 104, 251, 9027, 3831])).
% 3.54/3.72 tff(9029,plain,
% 3.54/3.72 ((elem!1 = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 3.54/3.72 inference(monotonicity,[status(thm)],[9012])).
% 3.54/3.72 tff(9030,plain,
% 3.54/3.72 ((elem!1 = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 3.54/3.72 inference(transitivity,[status(thm)],[9029, 3539])).
% 3.54/3.72 tff(9031,plain,
% 3.54/3.72 ((~(elem!1 = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))))),
% 3.54/3.72 inference(monotonicity,[status(thm)],[9030])).
% 3.54/3.72 tff(9032,plain,
% 3.54/3.72 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 3.54/3.72 inference(modus_ponens,[status(thm)],[701, 9031])).
% 3.54/3.72 tff(9033,plain,
% 3.54/3.72 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[5118, 9032, 9028])).
% 3.54/3.72 tff(9034,plain,
% 3.54/3.72 (b(z, elem!1) <=> b(z, s(s(s(elem!1))))),
% 3.54/3.72 inference(monotonicity,[status(thm)],[9012])).
% 3.54/3.72 tff(9035,plain,
% 3.54/3.72 (b(z, s(s(s(elem!1)))) <=> b(z, elem!1)),
% 3.54/3.72 inference(symmetry,[status(thm)],[9034])).
% 3.54/3.72 tff(9036,plain,
% 3.54/3.72 (b(z, elem!1)),
% 3.54/3.72 inference(modus_ponens,[status(thm)],[2043, 9035])).
% 3.54/3.72 tff(9037,plain,
% 3.54/3.72 (~(elem!1 = s(s(s(s(z)))))),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[1846, 9036, 1])).
% 3.54/3.72 tff(9038,plain,
% 3.54/3.72 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[8548, 9037, 104, 251, 8765, 4246])).
% 3.54/3.72 tff(9039,plain,
% 3.54/3.72 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[691, 9038, 701])).
% 3.54/3.72 tff(9040,plain,
% 3.54/3.72 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[2803, 9039, 4256])).
% 3.54/3.72 tff(9041,plain,
% 3.54/3.72 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[249, 9040])).
% 3.54/3.72 tff(9042,plain,
% 3.54/3.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), 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(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), 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(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.54/3.72 inference(rewrite,[status(thm)],[])).
% 3.54/3.72 tff(9043,plain,
% 3.54/3.72 (((~b(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))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~b(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(z)), 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(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.54/3.72 inference(rewrite,[status(thm)],[])).
% 3.54/3.72 tff(9044,plain,
% 3.54/3.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(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(z)), s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), 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(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 3.54/3.72 inference(monotonicity,[status(thm)],[9043])).
% 3.54/3.72 tff(9045,plain,
% 3.54/3.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(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(z)), s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), 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(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.54/3.72 inference(transitivity,[status(thm)],[9044, 9042])).
% 3.54/3.72 tff(9046,plain,
% 3.54/3.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 3.54/3.72 inference(quant_inst,[status(thm)],[])).
% 3.54/3.72 tff(9047,plain,
% 3.54/3.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 3.54/3.72 inference(modus_ponens,[status(thm)],[9046, 9045])).
% 3.54/3.72 tff(9048,plain,
% 3.54/3.72 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[9047, 178, 104, 9041, 167, 251])).
% 3.54/3.72 tff(9049,plain,
% 3.54/3.72 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[3578, 9048])).
% 3.54/3.72 tff(9050,plain,
% 3.54/3.72 ($false),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[5140, 118, 9010, 9049, 9033])).
% 3.54/3.72 tff(9051,plain,((s(s(z)) = elem!1) | (~b(s(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(s(z))))))))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | b(z, s(s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | b(elem!1, s(s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | b(elem!1, s(s(z))) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.54/3.72 tff(9052,plain,
% 3.54/3.72 (s(s(z)) = elem!1),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[9051, 251, 9000, 8679, 701, 1, 8673, 7954, 3240, 103, 461, 3241])).
% 3.54/3.72 tff(9053,plain,
% 3.54/3.72 (b(s(s(z)), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 3.54/3.72 inference(monotonicity,[status(thm)],[9052])).
% 3.54/3.72 tff(9054,plain,
% 3.54/3.72 (b(elem!1, s(s(s(s(z)))))),
% 3.54/3.72 inference(modus_ponens,[status(thm)],[9000, 9053])).
% 3.54/3.72 tff(9055,plain,
% 3.54/3.72 (~r(elem!1, z)),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[6206, 9052, 8005])).
% 3.54/3.72 tff(9056,plain,
% 3.54/3.72 (b(elem!1, z)),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[498, 9055, 3277])).
% 3.54/3.72 tff(9057,plain,
% 3.54/3.72 (~(elem!1 = s(s(s(s(z)))))),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[3172, 9056, 3170])).
% 3.54/3.72 tff(9058,plain,
% 3.54/3.72 (~(s(s(s(s(z)))) = elem!1)),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[504, 9057])).
% 3.54/3.72 tff(9059,plain,
% 3.54/3.72 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[3502, 9058])).
% 3.54/3.72 tff(9060,plain,
% 3.54/3.72 (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[8403, 9059])).
% 3.54/3.72 tff(9061,plain,
% 3.54/3.72 (~b(s(s(s(elem!1))), s(s(z)))),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[9019, 178, 7954, 3271, 9000, 8673])).
% 3.54/3.72 tff(9062,plain,
% 3.54/3.72 (r(s(s(s(elem!1))), s(s(z)))),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[4209, 41, 9061, 4181])).
% 3.54/3.72 tff(9063,plain,
% 3.54/3.72 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[9024, 118, 9062, 103])).
% 3.54/3.72 tff(9064,plain,
% 3.54/3.72 (~b(s(s(s(s(z)))), elem!1)),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[3774, 9052, 86])).
% 3.54/3.72 tff(9065,plain,
% 3.54/3.72 (~(elem!1 = s(s(s(elem!1))))),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[3308, 9064, 9063])).
% 3.54/3.72 tff(9066,plain,
% 3.54/3.72 (r(elem!1, s(s(s(elem!1))))),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[2054, 9065, 3240])).
% 3.54/3.72 tff(9067,plain,
% 3.54/3.72 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[8811, 9066, 86, 4320, 9052])).
% 3.54/3.72 tff(9068,plain,
% 3.54/3.72 (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[4103, 9067, 8673, 251, 8679])).
% 3.54/3.72 tff(9069,plain,
% 3.54/3.72 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[3612, 41, 9068, 9060])).
% 3.54/3.72 tff(9070,plain,
% 3.54/3.72 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), elem!1)),
% 3.54/3.72 inference(monotonicity,[status(thm)],[9052])).
% 3.54/3.72 tff(9071,plain,
% 3.54/3.72 (r(s(s(s(elem!1))), elem!1)),
% 3.54/3.72 inference(modus_ponens,[status(thm)],[9062, 9070])).
% 3.54/3.72 tff(9072,plain,
% 3.54/3.72 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[3682, 9071, 9069])).
% 3.54/3.72 tff(9073,plain,
% 3.54/3.72 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[3444, 9072, 4245])).
% 3.54/3.72 tff(9074,plain,
% 3.54/3.72 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[3623, 9069, 9066])).
% 3.54/3.72 tff(9075,plain,
% 3.54/3.72 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.54/3.72 inference(unit_resolution,[status(thm)],[691, 9074, 701])).
% 3.54/3.72 tff(9076,plain,
% 3.54/3.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.54/3.72 inference(rewrite,[status(thm)],[])).
% 3.54/3.72 tff(9077,plain,
% 3.54/3.72 (((~b(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))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(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)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.54/3.72 inference(rewrite,[status(thm)],[])).
% 3.54/3.72 tff(9078,plain,
% 3.54/3.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.54/3.72 inference(monotonicity,[status(thm)],[9077])).
% 3.54/3.72 tff(9079,plain,
% 3.54/3.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.54/3.72 inference(transitivity,[status(thm)],[9078, 9076])).
% 3.54/3.72 tff(9080,plain,
% 3.54/3.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.54/3.73 inference(quant_inst,[status(thm)],[])).
% 3.54/3.73 tff(9081,plain,
% 3.54/3.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.54/3.73 inference(modus_ponens,[status(thm)],[9080, 9079])).
% 3.54/3.73 tff(9082,plain,
% 3.54/3.73 ($false),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[9081, 178, 104, 869, 1301, 251, 3664])).
% 3.54/3.73 tff(9083,plain,((~b(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(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))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.73 tff(9084,plain,
% 3.54/3.73 ($false),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[9083, 9075, 9073, 251, 8679, 9054])).
% 3.54/3.73 tff(9085,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(z)))), s(s(z))) | b(s(s(s(s(z)))), z) | b(elem!1, s(s(s(elem!1)))) | b(z, s(s(s(s(z))))) | b(elem!1, s(s(z))) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.54/3.73 tff(9086,plain,
% 3.54/3.73 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[9085, 86, 701, 3170, 3240, 1, 461, 3241])).
% 3.54/3.73 tff(9087,plain,
% 3.54/3.73 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[222, 9086])).
% 3.54/3.73 tff(9088,plain,
% 3.54/3.73 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[212, 9087, 47])).
% 3.54/3.73 tff(9089,plain,
% 3.54/3.73 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[271, 9088])).
% 3.54/3.73 tff(9090,plain,
% 3.54/3.73 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[3559, 9087, 103])).
% 3.54/3.73 tff(9091,plain,
% 3.54/3.73 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[249, 9090])).
% 3.54/3.73 tff(9092,plain,
% 3.54/3.73 ($false),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[279, 178, 3271, 8679, 9091, 9000, 9089])).
% 3.54/3.73 tff(9093,plain,(b(s(s(s(s(z)))), s(s(z))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(z)))), z) | b(elem!1, s(s(s(elem!1)))) | b(z, s(s(s(s(z))))) | b(elem!1, s(s(z))) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.54/3.73 tff(9094,plain,
% 3.54/3.73 (b(s(s(s(s(z)))), s(s(z)))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[9093, 701, 3170, 3240, 1, 461, 3241])).
% 3.54/3.73 tff(9095,plain,
% 3.54/3.73 (~(s(s(s(s(z)))) = elem!1)),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[4509, 9094, 461])).
% 3.54/3.73 tff(9096,plain,
% 3.54/3.73 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[3502, 9095])).
% 3.54/3.73 tff(9097,plain,
% 3.54/3.73 (r(elem!1, s(s(s(elem!1))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[2054, 1586, 3240])).
% 3.54/3.73 tff(9098,plain,
% 3.54/3.73 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[4923, 3437, 47])).
% 3.54/3.73 tff(9099,plain,
% 3.54/3.73 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[4928, 9098, 4890])).
% 3.54/3.73 tff(9100,plain,
% 3.54/3.73 (~b(s(s(z)), z)),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[3488, 147, 145, 1130])).
% 3.54/3.73 tff(9101,plain,
% 3.54/3.73 ($false),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[3249, 9100, 8070])).
% 3.54/3.73 tff(9102,plain,((~r(s(s(z)), 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))))))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.73 tff(9103,plain,
% 3.54/3.73 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[9102, 3437, 47])).
% 3.54/3.73 tff(9104,plain,
% 3.54/3.73 (b(s(s(z)), s(s(s(s(z)))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[164, 9103])).
% 3.54/3.73 tff(9105,plain,
% 3.54/3.73 (~(s(elem!1) = elem!1)),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[2150, 6403])).
% 3.54/3.73 tff(9106,plain,
% 3.54/3.73 (~(elem!1 = s(elem!1))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[748, 9105])).
% 3.54/3.73 tff(9107,plain,
% 3.54/3.73 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.54/3.73 inference(monotonicity,[status(thm)],[3506])).
% 3.54/3.73 tff(9108,plain,
% 3.54/3.73 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.54/3.73 inference(modus_ponens,[status(thm)],[3831, 9107])).
% 3.54/3.73 tff(9109,plain,
% 3.54/3.73 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 3.54/3.73 inference(monotonicity,[status(thm)],[3507])).
% 3.54/3.73 tff(9110,plain,
% 3.54/3.73 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 3.54/3.73 inference(symmetry,[status(thm)],[9109])).
% 3.54/3.73 tff(9111,plain,
% 3.54/3.73 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 3.54/3.73 inference(monotonicity,[status(thm)],[3505])).
% 3.54/3.73 tff(9112,plain,
% 3.54/3.73 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(elem!1)), s(elem!1))),
% 3.54/3.73 inference(transitivity,[status(thm)],[9111, 9110])).
% 3.54/3.73 tff(9113,plain,
% 3.54/3.73 ((s(s(elem!1)) = elem!1) <=> (s(s(elem!1)) = s(s(z)))),
% 3.54/3.73 inference(symmetry,[status(thm)],[8800])).
% 3.54/3.73 tff(9114,plain,
% 3.54/3.73 ((s(s(s(s(z)))) = elem!1) <=> (s(s(elem!1)) = elem!1)),
% 3.54/3.73 inference(monotonicity,[status(thm)],[3506])).
% 3.54/3.73 tff(9115,plain,
% 3.54/3.73 ((s(s(s(s(z)))) = elem!1) <=> (s(s(elem!1)) = s(s(z)))),
% 3.54/3.73 inference(transitivity,[status(thm)],[9114, 9113])).
% 3.54/3.73 tff(9116,plain,
% 3.54/3.73 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(s(s(elem!1)) = s(s(z))))),
% 3.54/3.73 inference(monotonicity,[status(thm)],[9115])).
% 3.54/3.73 tff(9117,plain,
% 3.54/3.73 (~(s(s(elem!1)) = s(s(z)))),
% 3.54/3.73 inference(modus_ponens,[status(thm)],[323, 9116])).
% 3.54/3.73 tff(9118,plain,
% 3.54/3.73 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[8244, 9117])).
% 3.54/3.73 tff(9119,plain,
% 3.54/3.73 (r(s(s(z)), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 3.54/3.73 inference(monotonicity,[status(thm)],[1324])).
% 3.54/3.73 tff(9120,plain,
% 3.54/3.73 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 3.54/3.73 inference(symmetry,[status(thm)],[9119])).
% 3.54/3.73 tff(9121,plain,
% 3.54/3.73 (r(s(s(z)), s(s(s(elem!1))))),
% 3.54/3.73 inference(modus_ponens,[status(thm)],[3311, 9120])).
% 3.54/3.73 tff(9122,plain,
% 3.54/3.73 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[8364, 9121, 202, 1126, 167])).
% 3.54/3.73 tff(9123,assumption,(~r(s(s(s(z))), s(s(s(elem!1))))), introduced(assumption)).
% 3.54/3.73 tff(9124,assumption,(~b(s(s(s(z))), s(s(s(elem!1))))), introduced(assumption)).
% 3.54/3.73 tff(9125,plain,
% 3.54/3.73 ($false),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[8249, 41, 9124, 9123, 8246])).
% 3.54/3.73 tff(9126,plain,(b(s(s(s(z))), s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1)))) | (s(s(s(z))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.73 tff(9127,plain,
% 3.54/3.73 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[9126, 9122, 9118])).
% 3.54/3.73 tff(9128,plain,
% 3.54/3.73 (~b(z, s(s(s(z))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[8732, 9127])).
% 3.54/3.73 tff(9129,plain,
% 3.54/3.73 (r(z, s(s(s(z))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[4920, 9128])).
% 3.54/3.73 tff(9130,plain,
% 3.54/3.73 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[4961, 9129, 194])).
% 3.54/3.73 tff(9131,plain,
% 3.54/3.73 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[4950, 9130, 4938])).
% 3.54/3.73 tff(9132,plain,
% 3.54/3.73 (b(s(s(elem!1)), s(elem!1))),
% 3.54/3.73 inference(modus_ponens,[status(thm)],[9131, 9112])).
% 3.54/3.73 tff(9133,plain,
% 3.54/3.73 (~(s(elem!1) = s(s(s(elem!1))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[5395, 8140])).
% 3.54/3.73 tff(9134,plain,
% 3.54/3.73 (~b(s(s(s(z))), s(s(z)))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[4945, 9131])).
% 3.54/3.73 tff(9135,plain,
% 3.54/3.73 (r(s(s(s(z))), s(s(z)))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[4966, 9134])).
% 3.54/3.73 tff(9136,plain,
% 3.54/3.73 (r(s(elem!1), elem!1)),
% 3.54/3.73 inference(modus_ponens,[status(thm)],[9135, 8116])).
% 3.54/3.73 tff(9137,plain,
% 3.54/3.73 ($false),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[5403, 118, 1426, 3311, 2102])).
% 3.54/3.73 tff(9138,plain,((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.73 tff(9139,plain,
% 3.54/3.73 (~r(s(elem!1), s(s(s(elem!1))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[9138, 9136, 3311])).
% 3.54/3.73 tff(9140,plain,
% 3.54/3.73 (b(s(elem!1), s(s(s(elem!1))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[5432, 9139, 9133])).
% 3.54/3.73 tff(9141,plain,
% 3.54/3.73 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(elem!1)))),
% 3.54/3.73 inference(monotonicity,[status(thm)],[3506])).
% 3.54/3.73 tff(9142,plain,
% 3.54/3.73 (b(s(s(z)), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 3.54/3.73 inference(monotonicity,[status(thm)],[1324])).
% 3.54/3.73 tff(9143,plain,
% 3.54/3.73 (b(elem!1, s(s(s(s(z)))))),
% 3.54/3.73 inference(modus_ponens,[status(thm)],[167, 9142])).
% 3.54/3.73 tff(9144,plain,
% 3.54/3.73 (b(elem!1, s(s(elem!1)))),
% 3.54/3.73 inference(modus_ponens,[status(thm)],[9143, 9141])).
% 3.54/3.73 tff(9145,plain,
% 3.54/3.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))))),
% 3.54/3.73 inference(rewrite,[status(thm)],[])).
% 3.54/3.73 tff(9146,plain,
% 3.54/3.73 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))))),
% 3.54/3.73 inference(rewrite,[status(thm)],[])).
% 3.54/3.73 tff(9147,plain,
% 3.54/3.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1))))))),
% 3.54/3.73 inference(monotonicity,[status(thm)],[9146])).
% 3.54/3.73 tff(9148,plain,
% 3.54/3.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))))),
% 3.54/3.73 inference(transitivity,[status(thm)],[9147, 9145])).
% 3.54/3.73 tff(9149,plain,
% 3.54/3.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 3.54/3.73 inference(quant_inst,[status(thm)],[])).
% 3.54/3.73 tff(9150,plain,
% 3.54/3.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1))))),
% 3.54/3.73 inference(modus_ponens,[status(thm)],[9149, 9148])).
% 3.54/3.73 tff(9151,plain,
% 3.54/3.73 (~b(elem!1, s(elem!1))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[9150, 178, 8528, 9132, 8490, 9144])).
% 3.54/3.73 tff(9152,plain,
% 3.54/3.73 (r(elem!1, s(elem!1))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[756, 9151, 750])).
% 3.54/3.73 tff(9153,plain,
% 3.54/3.73 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[1591, 9152, 3311])).
% 3.54/3.73 tff(9154,plain,
% 3.54/3.73 (b(s(s(s(elem!1))), s(elem!1))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[373, 9153, 8140])).
% 3.54/3.73 tff(9155,plain,
% 3.54/3.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.54/3.73 inference(rewrite,[status(thm)],[])).
% 3.54/3.73 tff(9156,plain,
% 3.54/3.73 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.54/3.73 inference(rewrite,[status(thm)],[])).
% 3.54/3.73 tff(9157,plain,
% 3.54/3.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 3.54/3.73 inference(monotonicity,[status(thm)],[9156])).
% 3.54/3.73 tff(9158,plain,
% 3.54/3.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.54/3.73 inference(transitivity,[status(thm)],[9157, 9155])).
% 3.54/3.73 tff(9159,plain,
% 3.54/3.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 3.54/3.73 inference(quant_inst,[status(thm)],[])).
% 3.54/3.73 tff(9160,plain,
% 3.54/3.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 3.54/3.73 inference(modus_ponens,[status(thm)],[9159, 9158])).
% 3.54/3.73 tff(9161,plain,
% 3.54/3.73 ($false),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[9160, 178, 9154, 9140, 9132, 9108, 8490])).
% 3.54/3.73 tff(9162,plain,((~(s(s(z)) = elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (elem!1 = s(elem!1)) | (~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)))))) | (~r(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.54/3.73 tff(9163,plain,
% 3.54/3.73 (~(s(s(z)) = elem!1)),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[9162, 9097, 9106, 9104, 9094, 9099, 3244, 7954, 8673, 9095])).
% 3.54/3.73 tff(9164,plain,
% 3.54/3.73 (r(s(s(z)), elem!1)),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[448, 9163, 3241])).
% 3.54/3.73 tff(9165,plain,
% 3.54/3.73 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[7973, 9164, 9097])).
% 3.54/3.73 tff(9166,plain,
% 3.54/3.73 (b(s(s(z)), s(s(s(elem!1))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[4223, 9165])).
% 3.54/3.73 tff(9167,plain,
% 3.54/3.73 (~(elem!1 = s(s(z)))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[311, 9163])).
% 3.54/3.73 tff(9168,plain,
% 3.54/3.73 (r(elem!1, s(s(z)))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[467, 9167, 461])).
% 3.54/3.73 tff(9169,plain,
% 3.54/3.73 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[1138, 3437, 47])).
% 3.54/3.73 tff(9170,plain,
% 3.54/3.73 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[133, 9169])).
% 3.54/3.73 tff(9171,plain,
% 3.54/3.73 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[4843, 3437, 47])).
% 3.54/3.73 tff(9172,plain,
% 3.54/3.73 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[271, 9171])).
% 3.54/3.73 tff(9173,plain,
% 3.54/3.73 (~r(elem!1, z)),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[8416, 3261, 450])).
% 3.54/3.73 tff(9174,plain,
% 3.54/3.73 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[3478, 3261, 47])).
% 3.54/3.73 tff(9175,plain,
% 3.54/3.73 (b(s(s(z)), s(s(s(s(z)))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[164, 9174])).
% 3.54/3.73 tff(9176,plain,
% 3.54/3.73 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[8244, 8288])).
% 3.54/3.73 tff(9177,plain,
% 3.54/3.73 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[4923, 3437, 145])).
% 3.54/3.73 tff(9178,plain,
% 3.54/3.73 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[4928, 9177, 4890])).
% 3.54/3.73 tff(9179,plain,
% 3.54/3.73 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[8364, 3863, 202, 9178, 167])).
% 3.54/3.73 tff(9180,plain,
% 3.54/3.73 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[9126, 9179, 9176])).
% 3.54/3.73 tff(9181,plain,
% 3.54/3.73 ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[8731, 178, 2043, 9178, 3831])).
% 3.54/3.73 tff(9182,plain,
% 3.54/3.73 (~b(z, s(s(s(z))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[9181, 9180])).
% 3.54/3.73 tff(9183,plain,
% 3.54/3.73 (r(z, s(s(s(z))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[4920, 9182])).
% 3.54/3.73 tff(9184,plain,
% 3.54/3.73 ((s(s(s(elem!1))) = z) <=> (elem!1 = z)),
% 3.54/3.73 inference(transitivity,[status(thm)],[8285, 314])).
% 3.54/3.73 tff(9185,plain,
% 3.54/3.73 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = z))),
% 3.54/3.73 inference(monotonicity,[status(thm)],[9184])).
% 3.54/3.73 tff(9186,plain,
% 3.54/3.73 (~(elem!1 = z)),
% 3.54/3.73 inference(modus_ponens,[status(thm)],[940, 9185])).
% 3.54/3.73 tff(9187,plain,
% 3.54/3.73 (b(elem!1, z)),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[498, 9186, 1342])).
% 3.54/3.73 tff(9188,plain,
% 3.54/3.73 (~r(s(s(s(s(z)))), elem!1)),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[3457, 3879, 3428, 145, 7961, 9187])).
% 3.54/3.73 tff(9189,plain,
% 3.54/3.73 (b(s(s(s(s(z)))), elem!1)),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[3142, 9188, 323])).
% 3.54/3.73 tff(9190,plain,
% 3.54/3.73 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.54/3.73 inference(modus_ponens,[status(thm)],[9189, 3290])).
% 3.54/3.73 tff(9191,plain,
% 3.54/3.73 ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[5050, 178, 9178, 9190, 3831])).
% 3.54/3.73 tff(9192,plain,
% 3.54/3.73 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[9191, 9180])).
% 3.54/3.73 tff(9193,plain,
% 3.54/3.73 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[4950, 9192, 4938])).
% 3.54/3.73 tff(9194,plain,
% 3.54/3.73 ($false),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[4961, 9193, 9183, 194])).
% 3.54/3.73 tff(9195,plain,((~(elem!1 = s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (s(s(s(s(z)))) = elem!1) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | (~r(z, 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, z) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.73 tff(9196,plain,
% 3.54/3.73 (~(elem!1 = s(s(s(elem!1))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[9195, 9175, 3831, 2043, 4510, 3428, 47, 202, 3244, 9173, 438])).
% 3.54/3.73 tff(9197,plain,
% 3.54/3.73 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[951, 6403])).
% 3.54/3.73 tff(9198,plain,
% 3.54/3.73 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[4343, 9197])).
% 3.54/3.73 tff(9199,plain,
% 3.54/3.73 (~(z = elem!1)),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[5266, 9198, 3261, 202, 9097, 461, 1, 3170])).
% 3.54/3.73 tff(9200,plain,
% 3.54/3.73 (~(elem!1 = z)),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[2808, 9199])).
% 3.54/3.73 tff(9201,plain,
% 3.54/3.73 (b(elem!1, z)),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[498, 9200, 9173])).
% 3.54/3.73 tff(9202,plain,
% 3.54/3.73 (~r(z, elem!1)),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[8412, 3261, 438])).
% 3.54/3.73 tff(9203,plain,
% 3.54/3.73 (b(z, elem!1)),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[585, 9199, 9202])).
% 3.54/3.73 tff(9204,plain,
% 3.54/3.73 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[3455, 178, 9203, 9201, 595, 146])).
% 3.54/3.73 tff(9205,plain,
% 3.54/3.73 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[3444, 9204, 4245])).
% 3.54/3.73 tff(9206,plain,
% 3.54/3.73 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[8969, 9205, 9097])).
% 3.54/3.73 tff(9207,plain,
% 3.54/3.73 (b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[5118, 9206, 4511])).
% 3.54/3.73 tff(9208,plain,
% 3.54/3.73 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[2956, 118, 438, 9205])).
% 3.54/3.73 tff(9209,plain,
% 3.54/3.73 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[3578, 9208])).
% 3.54/3.73 tff(9210,plain,
% 3.54/3.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.54/3.73 inference(rewrite,[status(thm)],[])).
% 3.54/3.73 tff(9211,plain,
% 3.54/3.73 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(elem!1))), 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(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.54/3.73 inference(rewrite,[status(thm)],[])).
% 3.54/3.73 tff(9212,plain,
% 3.54/3.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))))),
% 3.54/3.73 inference(monotonicity,[status(thm)],[9211])).
% 3.54/3.73 tff(9213,plain,
% 3.54/3.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.54/3.73 inference(transitivity,[status(thm)],[9212, 9210])).
% 3.54/3.73 tff(9214,plain,
% 3.54/3.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.54/3.73 inference(quant_inst,[status(thm)],[])).
% 3.54/3.73 tff(9215,plain,
% 3.54/3.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 3.54/3.73 inference(modus_ponens,[status(thm)],[9214, 9213])).
% 3.54/3.73 tff(9216,plain,
% 3.54/3.73 (~b(s(s(s(elem!1))), s(s(z)))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[9215, 178, 9175, 9209, 3831, 9207])).
% 3.54/3.73 tff(9217,plain,
% 3.54/3.73 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[2820, 9199, 595, 146, 9202, 9173])).
% 3.54/3.73 tff(9218,plain,
% 3.54/3.73 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[691, 9217, 701])).
% 3.54/3.73 tff(9219,plain,
% 3.54/3.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 3.54/3.73 inference(rewrite,[status(thm)],[])).
% 3.54/3.73 tff(9220,plain,
% 3.54/3.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 3.54/3.73 inference(quant_inst,[status(thm)],[])).
% 3.54/3.73 tff(9221,plain,
% 3.54/3.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(z))))))),
% 3.54/3.73 inference(modus_ponens,[status(thm)],[9220, 9219])).
% 3.54/3.73 tff(9222,plain,
% 3.54/3.73 (~r(elem!1, s(s(s(s(z)))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[9221, 118, 9218, 204])).
% 3.54/3.73 tff(9223,plain,
% 3.54/3.73 (b(elem!1, s(s(s(s(z)))))),
% 3.54/3.73 inference(unit_resolution,[status(thm)],[483, 9222, 4520])).
% 3.54/3.73 tff(9224,plain,
% 3.54/3.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~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)))))))),
% 3.54/3.73 inference(rewrite,[status(thm)],[])).
% 3.54/3.73 tff(9225,plain,
% 3.54/3.73 (((~b(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(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~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)))))))),
% 3.54/3.74 inference(rewrite,[status(thm)],[])).
% 3.54/3.74 tff(9226,plain,
% 3.54/3.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~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))))))))),
% 3.54/3.74 inference(monotonicity,[status(thm)],[9225])).
% 3.54/3.74 tff(9227,plain,
% 3.54/3.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~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)))))))),
% 3.54/3.74 inference(transitivity,[status(thm)],[9226, 9224])).
% 3.54/3.74 tff(9228,plain,
% 3.54/3.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 3.54/3.74 inference(quant_inst,[status(thm)],[])).
% 3.54/3.74 tff(9229,plain,
% 3.54/3.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.54/3.74 inference(modus_ponens,[status(thm)],[9228, 9227])).
% 3.54/3.74 tff(9230,plain,
% 3.54/3.74 (~b(s(s(s(elem!1))), elem!1)),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[9229, 178, 9203, 2043, 9223, 3831])).
% 3.54/3.74 tff(9231,plain,
% 3.54/3.74 (r(s(s(s(elem!1))), elem!1)),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[570, 9230, 6403])).
% 3.54/3.74 tff(9232,plain,
% 3.54/3.74 (~r(s(s(s(elem!1))), s(s(z)))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[4205, 9231, 450])).
% 3.54/3.74 tff(9233,plain,
% 3.54/3.74 ($false),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[4209, 41, 9232, 9216, 4181])).
% 3.54/3.74 tff(9234,plain,((elem!1 = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(z)), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~r(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | b(elem!1, s(s(z))) | b(z, s(s(s(s(z))))) | b(s(s(s(s(z)))), z) | b(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.74 tff(9235,plain,
% 3.54/3.74 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[9234, 9196, 450, 2043, 438, 9172, 9170, 3831, 701, 3261, 202, 461, 1, 3170, 3240])).
% 3.54/3.74 tff(9236,plain,
% 3.54/3.74 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[222, 9235])).
% 3.54/3.74 tff(9237,plain,
% 3.54/3.74 (r(elem!1, s(s(s(elem!1))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[2054, 9196, 3240])).
% 3.54/3.74 tff(9238,plain,
% 3.54/3.74 (~(s(s(s(elem!1))) = elem!1)),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[2489, 9196])).
% 3.54/3.74 tff(9239,plain,
% 3.54/3.74 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[951, 9238])).
% 3.54/3.74 tff(9240,plain,
% 3.54/3.74 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[4343, 9239])).
% 3.54/3.74 tff(9241,plain,
% 3.54/3.74 (~(z = elem!1)),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[5266, 9240, 3261, 202, 9237, 461, 1, 3170])).
% 3.54/3.74 tff(9242,plain,
% 3.54/3.74 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[2820, 9241, 9172, 9170, 9202, 9173])).
% 3.54/3.74 tff(9243,plain,
% 3.54/3.74 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[691, 9242, 701])).
% 3.54/3.74 tff(9244,plain,
% 3.54/3.74 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[2803, 9243, 438])).
% 3.54/3.74 tff(9245,plain,
% 3.54/3.74 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[249, 9244])).
% 3.54/3.74 tff(9246,plain,
% 3.54/3.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(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))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(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))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.54/3.74 inference(rewrite,[status(thm)],[])).
% 3.54/3.74 tff(9247,plain,
% 3.54/3.74 (((~b(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))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(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))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.54/3.74 inference(rewrite,[status(thm)],[])).
% 3.54/3.74 tff(9248,plain,
% 3.54/3.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(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))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 3.54/3.74 inference(monotonicity,[status(thm)],[9247])).
% 3.54/3.74 tff(9249,plain,
% 3.54/3.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(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))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.54/3.74 inference(transitivity,[status(thm)],[9248, 9246])).
% 3.54/3.74 tff(9250,plain,
% 3.54/3.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 3.54/3.74 inference(quant_inst,[status(thm)],[])).
% 3.54/3.74 tff(9251,plain,
% 3.54/3.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(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))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.54/3.74 inference(modus_ponens,[status(thm)],[9250, 9249])).
% 3.54/3.74 tff(9252,plain,
% 3.54/3.74 (~b(s(s(s(elem!1))), s(s(z)))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[9251, 178, 9245, 9175, 9236, 3831])).
% 3.54/3.74 tff(9253,plain,
% 3.54/3.74 (r(s(s(s(elem!1))), s(s(z)))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[4209, 41, 9252, 4181])).
% 3.54/3.74 tff(9254,plain,
% 3.54/3.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 3.54/3.74 inference(rewrite,[status(thm)],[])).
% 3.54/3.74 tff(9255,plain,
% 3.54/3.74 (((~r(s(s(s(elem!1))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 3.54/3.74 inference(rewrite,[status(thm)],[])).
% 3.54/3.74 tff(9256,plain,
% 3.54/3.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 3.54/3.74 inference(monotonicity,[status(thm)],[9255])).
% 3.54/3.74 tff(9257,plain,
% 3.54/3.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 3.54/3.74 inference(transitivity,[status(thm)],[9256, 9254])).
% 3.54/3.74 tff(9258,plain,
% 3.54/3.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(elem!1))))))),
% 3.54/3.74 inference(quant_inst,[status(thm)],[])).
% 3.54/3.74 tff(9259,plain,
% 3.54/3.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 3.54/3.74 inference(modus_ponens,[status(thm)],[9258, 9257])).
% 3.54/3.74 tff(9260,plain,
% 3.54/3.74 ($false),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[9259, 118, 9237, 450, 9253])).
% 3.54/3.74 tff(9261,plain,((~r(z, s(s(z)))) | (~r(elem!1, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | b(elem!1, s(s(z))) | b(z, s(s(s(s(z))))) | b(s(s(s(s(z)))), z) | (~b(z, s(s(s(elem!1))))) | b(elem!1, s(s(s(elem!1)))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.74 tff(9262,plain,
% 3.54/3.74 (~r(z, s(s(z)))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[9261, 9168, 8673, 9164, 701, 9094, 461, 1, 3170, 7954, 3240, 3428])).
% 3.54/3.74 tff(9263,plain,
% 3.54/3.74 (b(z, s(s(z)))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[143, 9262])).
% 3.54/3.74 tff(9264,plain,
% 3.54/3.74 ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[9008, 178, 7954, 9104, 8673])).
% 3.54/3.74 tff(9265,plain,
% 3.54/3.74 ($false),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[9264, 9263, 9166])).
% 3.54/3.74 tff(9266,plain,((elem!1 = s(s(s(elem!1)))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | b(elem!1, s(s(z))) | b(z, s(s(s(s(z))))) | b(s(s(s(s(z)))), z) | b(elem!1, s(s(s(elem!1)))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.54/3.74 tff(9267,plain,
% 3.54/3.74 (elem!1 = s(s(s(elem!1)))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[9266, 3428, 461, 1, 3170, 3240, 701, 3241])).
% 3.54/3.74 tff(9268,plain,
% 3.54/3.74 ((z = elem!1) <=> (z = s(s(s(elem!1))))),
% 3.54/3.74 inference(monotonicity,[status(thm)],[9267])).
% 3.54/3.74 tff(9269,plain,
% 3.54/3.74 ((z = elem!1) <=> (s(s(s(elem!1))) = z)),
% 3.54/3.74 inference(transitivity,[status(thm)],[9268, 2087])).
% 3.54/3.74 tff(9270,plain,
% 3.54/3.74 ((s(s(s(elem!1))) = z) <=> (z = elem!1)),
% 3.54/3.74 inference(symmetry,[status(thm)],[9269])).
% 3.54/3.74 tff(9271,plain,
% 3.54/3.74 ((~(s(s(s(elem!1))) = z)) <=> (~(z = elem!1))),
% 3.54/3.74 inference(monotonicity,[status(thm)],[9270])).
% 3.54/3.74 tff(9272,plain,
% 3.54/3.74 (~(z = elem!1)),
% 3.54/3.74 inference(modus_ponens,[status(thm)],[940, 9271])).
% 3.54/3.74 tff(9273,plain,
% 3.54/3.74 (~(s(s(elem!1)) = s(s(z)))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[2386, 9272])).
% 3.54/3.74 tff(9274,plain,
% 3.54/3.74 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[8244, 9273])).
% 3.54/3.74 tff(9275,plain,
% 3.54/3.74 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(elem!1))))),
% 3.54/3.74 inference(monotonicity,[status(thm)],[9267])).
% 3.54/3.74 tff(9276,plain,
% 3.54/3.74 ((~b(s(s(z)), elem!1)) <=> (~b(s(s(z)), s(s(s(elem!1)))))),
% 3.54/3.74 inference(monotonicity,[status(thm)],[9275])).
% 3.54/3.74 tff(9277,plain,
% 3.54/3.74 (~b(s(s(z)), s(s(s(elem!1))))),
% 3.54/3.74 inference(modus_ponens,[status(thm)],[3241, 9276])).
% 3.54/3.74 tff(9278,plain,
% 3.54/3.74 (r(s(s(z)), s(s(s(elem!1))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[4221, 41, 1683, 9277])).
% 3.54/3.74 tff(9279,plain,
% 3.54/3.74 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[8364, 9278, 9094, 9099, 9104])).
% 3.54/3.74 tff(9280,plain,
% 3.54/3.74 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[9126, 9279, 9274])).
% 3.54/3.74 tff(9281,plain,
% 3.54/3.74 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.54/3.74 inference(monotonicity,[status(thm)],[9267])).
% 3.54/3.74 tff(9282,plain,
% 3.54/3.74 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(elem!1))))),
% 3.54/3.74 inference(monotonicity,[status(thm)],[9267])).
% 3.54/3.74 tff(9283,plain,
% 3.54/3.74 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 3.54/3.74 inference(symmetry,[status(thm)],[9282])).
% 3.54/3.74 tff(9284,plain,
% 3.54/3.74 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(z)) = elem!1))),
% 3.54/3.74 inference(monotonicity,[status(thm)],[9283])).
% 3.54/3.74 tff(9285,plain,
% 3.54/3.74 (~(s(s(z)) = elem!1)),
% 3.54/3.74 inference(modus_ponens,[status(thm)],[1683, 9284])).
% 3.54/3.74 tff(9286,plain,
% 3.54/3.74 (r(s(s(z)), elem!1)),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[448, 9285, 3241])).
% 3.54/3.74 tff(9287,plain,
% 3.54/3.74 (r(elem!1, z)),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[9195, 9286, 8673, 7954, 9095, 3428, 47, 9094, 3244, 9104, 9267])).
% 3.54/3.74 tff(9288,plain,
% 3.54/3.74 (~r(s(s(s(s(z)))), elem!1)),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[6033, 9287, 3244])).
% 3.54/3.74 tff(9289,plain,
% 3.54/3.74 (b(s(s(s(s(z)))), elem!1)),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[3142, 9288, 9095])).
% 3.54/3.74 tff(9290,plain,
% 3.54/3.74 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.54/3.74 inference(modus_ponens,[status(thm)],[9289, 9281])).
% 3.54/3.74 tff(9291,plain,
% 3.54/3.74 ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[8731, 178, 7954, 9099, 8673])).
% 3.54/3.74 tff(9292,plain,
% 3.54/3.74 (~b(z, s(s(s(z))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[9291, 9280])).
% 3.54/3.74 tff(9293,plain,
% 3.54/3.74 (r(z, s(s(s(z))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[4920, 9292])).
% 3.54/3.74 tff(9294,plain,
% 3.54/3.74 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[4961, 9293, 3244])).
% 3.54/3.74 tff(9295,plain,
% 3.54/3.74 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[4950, 9294, 4938])).
% 3.54/3.74 tff(9296,plain,
% 3.54/3.74 ($false),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[5050, 178, 9099, 9295, 9290, 8673, 9280])).
% 3.54/3.74 tff(9297,plain,(b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | b(s(s(z)), elem!1) | b(elem!1, s(s(z))) | b(z, s(s(s(s(z))))) | b(s(s(s(s(z)))), z) | b(elem!1, s(s(s(elem!1)))) | (elem!1 = s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.74 tff(9298,plain,
% 3.54/3.74 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[9297, 701, 461, 1, 3170, 3240, 3241])).
% 3.54/3.74 tff(9299,plain,
% 3.54/3.74 (~(elem!1 = z)),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[3276, 3480, 461])).
% 3.54/3.74 tff(9300,plain,
% 3.54/3.74 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[4796, 202, 701, 145, 3241, 461, 194, 3240])).
% 3.54/3.74 tff(9301,plain,
% 3.54/3.74 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[7917, 2857])).
% 3.54/3.74 tff(9302,plain,
% 3.54/3.74 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[7973, 438, 3311])).
% 3.54/3.74 tff(9303,plain,
% 3.54/3.74 (b(s(s(z)), s(s(s(elem!1))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[4223, 9302])).
% 3.54/3.74 tff(9304,plain,
% 3.54/3.74 (~b(s(s(s(elem!1))), z)),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[7978, 9303, 8071, 3480, 2043])).
% 3.54/3.74 tff(9305,plain,
% 3.54/3.74 (r(s(s(s(elem!1))), z)),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[1565, 9304])).
% 3.54/3.74 tff(9306,plain,
% 3.54/3.74 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[5340, 118, 9305, 194])).
% 3.54/3.74 tff(9307,plain,
% 3.54/3.74 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[3296, 41, 9306, 4166])).
% 3.54/3.74 tff(9308,plain,
% 3.54/3.74 (~r(elem!1, s(s(s(s(z)))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[8763, 438, 147])).
% 3.54/3.74 tff(9309,plain,
% 3.54/3.74 (b(elem!1, s(s(s(s(z)))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[483, 9308, 3130])).
% 3.54/3.74 tff(9310,plain,
% 3.54/3.74 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[3502, 323])).
% 3.54/3.74 tff(9311,plain,
% 3.54/3.74 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[4307, 4289, 3831, 104, 3521, 3311, 9303, 3241])).
% 3.54/3.74 tff(9312,plain,
% 3.54/3.74 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[691, 4289, 701])).
% 3.54/3.74 tff(9313,plain,
% 3.54/3.74 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[2803, 9312, 438])).
% 3.54/3.74 tff(9314,plain,
% 3.54/3.74 ($false),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[249, 9313, 9311])).
% 3.54/3.74 tff(9315,plain,(b(elem!1, s(s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | b(s(s(z)), elem!1) | (elem!1 = s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.74 tff(9316,plain,
% 3.54/3.74 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[9315, 438, 3831, 104, 9310, 3311, 3241, 701])).
% 3.54/3.74 tff(9317,plain,
% 3.54/3.74 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[5034, 251])).
% 3.54/3.74 tff(9318,plain,
% 3.54/3.74 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[5118, 9317, 3521])).
% 3.54/3.74 tff(9319,plain,
% 3.54/3.74 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[9083, 251, 869, 104, 1301])).
% 3.54/3.74 tff(9320,plain,
% 3.54/3.74 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[3444, 9319, 3914])).
% 3.54/3.74 tff(9321,plain,
% 3.54/3.74 ($false),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[8969, 9320, 9318, 3311])).
% 3.54/3.74 tff(9322,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(elem!1))))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | (~b(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(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))))))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.74 tff(9323,plain,
% 3.54/3.74 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[9322, 9316, 4245, 9310, 3311, 104, 9309, 9307, 3831])).
% 3.54/3.74 tff(9324,plain,
% 3.54/3.74 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[222, 9323])).
% 3.54/3.74 tff(9325,plain,
% 3.54/3.74 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[212, 9324, 145])).
% 3.54/3.74 tff(9326,plain,
% 3.54/3.74 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[271, 9325])).
% 3.54/3.74 tff(9327,plain,
% 3.54/3.74 (~b(z, elem!1)),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[1309, 9326, 104, 9309, 9316])).
% 3.54/3.74 tff(9328,plain,
% 3.54/3.74 (r(z, elem!1)),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[585, 9327, 507])).
% 3.54/3.74 tff(9329,plain,
% 3.54/3.74 (~r(s(s(s(s(z)))), elem!1)),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[3137, 9328, 194])).
% 3.54/3.74 tff(9330,plain,
% 3.54/3.74 (b(s(s(s(s(z)))), elem!1)),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[3142, 9329, 323])).
% 3.54/3.74 tff(9331,plain,
% 3.54/3.74 (~r(s(s(s(elem!1))), elem!1)),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[6384, 9328, 3480, 8071, 9303])).
% 3.54/3.74 tff(9332,plain,
% 3.54/3.74 (b(s(s(s(elem!1))), elem!1)),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[570, 9331, 949])).
% 3.54/3.74 tff(9333,plain,
% 3.54/3.74 ($false),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[4195, 178, 9332, 9330, 9309, 9307, 3831])).
% 3.54/3.74 tff(9334,plain,((~r(s(s(z)), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (s(s(s(s(z)))) = elem!1) | (~r(s(s(s(s(z)))), z)) | (s(s(s(elem!1))) = elem!1) | (z = elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(elem!1))))) | b(s(s(z)), elem!1) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.74 tff(9335,plain,
% 3.54/3.74 (~r(s(s(z)), elem!1)),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[9334, 6403, 323, 194, 3831, 318, 104, 145, 9097, 3241, 701, 9301, 2043, 147])).
% 3.54/3.74 tff(9336,plain,
% 3.54/3.74 (s(s(z)) = elem!1),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[448, 9335, 3241])).
% 3.54/3.74 tff(9337,plain,
% 3.54/3.74 (s(s(s(z))) = s(elem!1)),
% 3.54/3.74 inference(monotonicity,[status(thm)],[9336])).
% 3.54/3.74 tff(9338,plain,
% 3.54/3.74 (s(s(s(s(z)))) = s(s(elem!1))),
% 3.54/3.74 inference(monotonicity,[status(thm)],[9337])).
% 3.54/3.74 tff(9339,plain,
% 3.54/3.74 (s(s(elem!1)) = s(s(s(s(z))))),
% 3.54/3.74 inference(symmetry,[status(thm)],[9338])).
% 3.54/3.74 tff(9340,plain,
% 3.54/3.74 (b(s(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))))))))),
% 3.54/3.74 inference(monotonicity,[status(thm)],[9339])).
% 3.54/3.74 tff(9341,plain,
% 3.54/3.74 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.54/3.74 inference(symmetry,[status(thm)],[9340])).
% 3.54/3.74 tff(9342,plain,
% 3.54/3.74 (~r(elem!1, z)),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[6206, 9336, 8070])).
% 3.54/3.74 tff(9343,plain,
% 3.54/3.74 (b(elem!1, z)),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[498, 9342, 290])).
% 3.54/3.74 tff(9344,plain,
% 3.54/3.74 (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[8403, 9310])).
% 3.54/3.74 tff(9345,plain,
% 3.54/3.74 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.54/3.74 inference(monotonicity,[status(thm)],[9338])).
% 3.54/3.74 tff(9346,plain,
% 3.54/3.74 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.54/3.74 inference(symmetry,[status(thm)],[9345])).
% 3.54/3.74 tff(9347,plain,
% 3.54/3.74 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(s(z)))))),
% 3.54/3.74 inference(monotonicity,[status(thm)],[3507])).
% 3.54/3.74 tff(9348,plain,
% 3.54/3.74 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(s(elem!1)))),
% 3.54/3.74 inference(symmetry,[status(thm)],[9347])).
% 3.54/3.74 tff(9349,plain,
% 3.54/3.74 (r(elem!1, s(s(s(s(z)))))),
% 3.54/3.74 inference(modus_ponens,[status(thm)],[147, 3426])).
% 3.54/3.74 tff(9350,plain,
% 3.54/3.74 (r(elem!1, s(s(elem!1)))),
% 3.54/3.74 inference(modus_ponens,[status(thm)],[9349, 9348])).
% 3.54/3.74 tff(9351,plain,
% 3.54/3.74 ($false),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[5467, 9350])).
% 3.54/3.74 tff(9352,plain,((~(s(s(z)) = elem!1)) | r(elem!1, s(s(elem!1))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.74 tff(9353,plain,
% 3.54/3.74 (r(elem!1, s(s(elem!1)))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[9352, 9336, 147])).
% 3.54/3.74 tff(9354,plain,
% 3.54/3.74 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[5845, 9353, 9097])).
% 3.54/3.74 tff(9355,plain,
% 3.54/3.74 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 3.54/3.74 inference(monotonicity,[status(thm)],[9338])).
% 3.54/3.74 tff(9356,plain,
% 3.54/3.74 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 3.54/3.74 inference(transitivity,[status(thm)],[9355, 3400])).
% 3.54/3.74 tff(9357,plain,
% 3.54/3.74 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 3.54/3.74 inference(monotonicity,[status(thm)],[9356])).
% 3.54/3.74 tff(9358,plain,
% 3.54/3.74 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 3.54/3.74 inference(modus_ponens,[status(thm)],[2857, 9357])).
% 3.54/3.74 tff(9359,plain,
% 3.54/3.74 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[3375, 9358, 9354])).
% 3.54/3.74 tff(9360,plain,
% 3.54/3.74 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.54/3.74 inference(modus_ponens,[status(thm)],[9359, 9346])).
% 3.54/3.74 tff(9361,assumption,(~(s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 3.54/3.74 tff(9362,plain,
% 3.54/3.74 (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[3623, 1265, 3311])).
% 3.54/3.74 tff(9363,plain,
% 3.54/3.74 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[5624, 8493, 147])).
% 3.54/3.74 tff(9364,plain,
% 3.54/3.74 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[222, 9363])).
% 3.54/3.74 tff(9365,plain,
% 3.54/3.74 (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[4103, 9364, 3831, 3828, 104])).
% 3.54/3.74 tff(9366,plain,
% 3.54/3.74 ($false),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[3612, 41, 9365, 9362, 9361])).
% 3.54/3.74 tff(9367,plain,((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~(s(s(z)) = elem!1)) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.74 tff(9368,plain,
% 3.54/3.74 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[9367, 9360, 3831, 9344, 104, 147, 9336, 9097])).
% 3.54/3.74 tff(9369,plain,
% 3.54/3.74 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[691, 9368, 701])).
% 3.54/3.74 tff(9370,plain,
% 3.54/3.74 (b(z, s(s(z))) <=> b(z, elem!1)),
% 3.54/3.74 inference(monotonicity,[status(thm)],[9336])).
% 3.54/3.74 tff(9371,plain,
% 3.54/3.74 (b(z, elem!1)),
% 3.54/3.74 inference(modus_ponens,[status(thm)],[3480, 9370])).
% 3.54/3.74 tff(9372,plain,
% 3.54/3.74 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[5118, 8951, 3521])).
% 3.54/3.74 tff(9373,plain,
% 3.54/3.74 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[3672, 595, 818, 869, 506])).
% 3.54/3.74 tff(9374,plain,
% 3.54/3.74 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[3444, 9373, 3914])).
% 3.54/3.74 tff(9375,plain,
% 3.54/3.74 ($false),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[8969, 9374, 9372, 3311])).
% 3.54/3.74 tff(9376,plain,((~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(elem!1))))) | (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, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.74 tff(9377,plain,
% 3.54/3.74 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[9376, 9097, 4245, 9310, 9371, 9369, 9343, 2043, 104, 3831])).
% 3.54/3.74 tff(9378,plain,
% 3.54/3.74 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[271, 9377])).
% 3.54/3.74 tff(9379,plain,
% 3.54/3.74 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[212, 9378, 145])).
% 3.54/3.74 tff(9380,plain,
% 3.54/3.74 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[222, 9379])).
% 3.54/3.74 tff(9381,plain,
% 3.54/3.74 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.54/3.74 inference(modus_ponens,[status(thm)],[9380, 9341])).
% 3.54/3.74 tff(9382,plain,
% 3.54/3.74 (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)))),
% 3.54/3.74 inference(monotonicity,[status(thm)],[9338])).
% 3.54/3.74 tff(9383,plain,
% 3.54/3.74 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.54/3.74 inference(modus_ponens,[status(thm)],[104, 9382])).
% 3.54/3.74 tff(9384,plain,
% 3.54/3.74 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.54/3.74 inference(monotonicity,[status(thm)],[9338])).
% 3.54/3.74 tff(9385,plain,
% 3.54/3.74 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.54/3.74 inference(modus_ponens,[status(thm)],[3831, 9384])).
% 3.54/3.74 tff(9386,plain,
% 3.54/3.74 ((~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)))))),
% 3.54/3.74 inference(unit_resolution,[status(thm)],[3518, 178, 9385, 9359, 9383])).
% 3.54/3.74 tff(9387,plain,
% 3.54/3.74 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[9386, 9381])).
% 3.54/3.75 tff(9388,plain,
% 3.54/3.75 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[5118, 9387, 9310])).
% 3.54/3.75 tff(9389,plain,
% 3.54/3.75 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[8969, 9388, 9097])).
% 3.54/3.75 tff(9390,plain,
% 3.54/3.75 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[3444, 9389, 4245])).
% 3.54/3.75 tff(9391,plain,
% 3.54/3.75 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 3.54/3.75 inference(monotonicity,[status(thm)],[9338])).
% 3.54/3.75 tff(9392,plain,
% 3.54/3.75 (b(s(s(s(s(z)))), elem!1)),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[8526, 9336, 202])).
% 3.54/3.75 tff(9393,plain,
% 3.54/3.75 (b(s(s(elem!1)), elem!1)),
% 3.54/3.75 inference(modus_ponens,[status(thm)],[9392, 9391])).
% 3.54/3.75 tff(9394,plain,
% 3.54/3.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(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(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(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(elem!1)))))),
% 3.54/3.75 inference(rewrite,[status(thm)],[])).
% 3.54/3.75 tff(9395,plain,
% 3.54/3.75 (((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(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)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), 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(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(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(elem!1)))))),
% 3.54/3.75 inference(rewrite,[status(thm)],[])).
% 3.54/3.75 tff(9396,plain,
% 3.54/3.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(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)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(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(elem!1))))))),
% 3.54/3.75 inference(monotonicity,[status(thm)],[9395])).
% 3.54/3.75 tff(9397,plain,
% 3.54/3.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(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)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(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(elem!1)))))),
% 3.54/3.75 inference(transitivity,[status(thm)],[9396, 9394])).
% 3.54/3.75 tff(9398,plain,
% 3.54/3.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(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)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 3.54/3.75 inference(quant_inst,[status(thm)],[])).
% 3.54/3.75 tff(9399,plain,
% 3.54/3.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 3.54/3.75 inference(modus_ponens,[status(thm)],[9398, 9397])).
% 3.54/3.75 tff(9400,plain,
% 3.54/3.75 ($false),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[9399, 178, 9393, 9369, 9390, 9383, 9381])).
% 3.54/3.75 tff(9401,plain,((elem!1 = s(s(s(elem!1)))) | (~r(z, s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (elem!1 = z) | (~b(s(s(s(s(z)))), s(s(z)))) | b(s(s(z)), elem!1) | (s(s(s(s(z)))) = elem!1) | (~r(s(s(s(s(z)))), z)) | b(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.75 tff(9402,plain,
% 3.54/3.75 (elem!1 = s(s(s(elem!1)))),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[9401, 147, 2043, 104, 3831, 701, 145, 9300, 9299, 202, 3241, 4510, 194, 3240])).
% 3.54/3.75 tff(9403,plain,
% 3.54/3.75 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.54/3.75 inference(monotonicity,[status(thm)],[9402])).
% 3.54/3.75 tff(9404,plain,
% 3.54/3.75 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(elem!1))))),
% 3.54/3.75 inference(monotonicity,[status(thm)],[9402])).
% 3.54/3.75 tff(9405,plain,
% 3.54/3.75 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 3.54/3.75 inference(symmetry,[status(thm)],[9404])).
% 3.54/3.75 tff(9406,plain,
% 3.54/3.75 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(z)) = elem!1))),
% 3.54/3.75 inference(monotonicity,[status(thm)],[9405])).
% 3.54/3.75 tff(9407,plain,
% 3.54/3.75 (~(s(s(z)) = elem!1)),
% 3.54/3.75 inference(modus_ponens,[status(thm)],[1683, 9406])).
% 3.54/3.75 tff(9408,plain,
% 3.54/3.75 (r(s(s(z)), elem!1)),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[448, 9407, 3241])).
% 3.54/3.75 tff(9409,plain,
% 3.54/3.75 (~(z = elem!1)),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[317, 9299])).
% 3.54/3.75 tff(9410,plain,
% 3.54/3.75 (~(s(s(elem!1)) = s(s(z)))),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[2386, 9409])).
% 3.54/3.75 tff(9411,plain,
% 3.54/3.75 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[8244, 9410])).
% 3.54/3.75 tff(9412,plain,
% 3.54/3.75 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(elem!1))))),
% 3.54/3.75 inference(monotonicity,[status(thm)],[9402])).
% 3.54/3.75 tff(9413,plain,
% 3.54/3.75 ((~b(s(s(z)), elem!1)) <=> (~b(s(s(z)), s(s(s(elem!1)))))),
% 3.54/3.75 inference(monotonicity,[status(thm)],[9412])).
% 3.54/3.75 tff(9414,plain,
% 3.54/3.75 (~b(s(s(z)), s(s(s(elem!1))))),
% 3.54/3.75 inference(modus_ponens,[status(thm)],[3241, 9413])).
% 3.54/3.75 tff(9415,plain,
% 3.54/3.75 (r(s(s(z)), s(s(s(elem!1))))),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[4221, 41, 1683, 9414])).
% 3.54/3.75 tff(9416,plain,
% 3.54/3.75 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[5101, 8071, 147, 145])).
% 3.54/3.75 tff(9417,plain,
% 3.54/3.75 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[4928, 9416, 4890])).
% 3.54/3.75 tff(9418,plain,
% 3.54/3.75 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[8950, 3551])).
% 3.54/3.75 tff(9419,plain,
% 3.54/3.75 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[5118, 9418, 3521])).
% 3.54/3.75 tff(9420,plain,
% 3.54/3.75 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[8732, 3008])).
% 3.54/3.75 tff(9421,plain,
% 3.54/3.75 (r(s(s(s(z))), s(s(s(elem!1))))),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[9126, 9420, 8246])).
% 3.54/3.75 tff(9422,plain,
% 3.54/3.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 3.54/3.75 inference(rewrite,[status(thm)],[])).
% 3.54/3.75 tff(9423,plain,
% 3.54/3.75 (((~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(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(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(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 3.54/3.75 inference(rewrite,[status(thm)],[])).
% 3.54/3.75 tff(9424,plain,
% 3.54/3.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))))),
% 3.54/3.75 inference(monotonicity,[status(thm)],[9423])).
% 3.54/3.75 tff(9425,plain,
% 3.54/3.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 3.54/3.75 inference(transitivity,[status(thm)],[9424, 9422])).
% 3.54/3.75 tff(9426,plain,
% 3.54/3.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.54/3.75 inference(quant_inst,[status(thm)],[])).
% 3.54/3.75 tff(9427,plain,
% 3.54/3.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 3.54/3.75 inference(modus_ponens,[status(thm)],[9426, 9425])).
% 3.54/3.75 tff(9428,plain,
% 3.54/3.75 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[9427, 178, 104, 595, 1126, 3008])).
% 3.54/3.75 tff(9429,plain,
% 3.54/3.75 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 9428])).
% 3.54/3.75 tff(9430,plain,
% 3.54/3.75 ($false),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[8719, 118, 9429, 5128, 9421])).
% 3.54/3.75 tff(9431,plain,((~b(z, s(s(s(z))))) | (~r(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(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.75 tff(9432,plain,
% 3.54/3.75 (~b(z, s(s(s(z))))),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[9431, 9419, 104, 3551, 1126, 8246, 2043, 3831])).
% 3.54/3.75 tff(9433,plain,
% 3.54/3.75 (r(z, s(s(s(z))))),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[4920, 9432])).
% 3.54/3.75 tff(9434,plain,
% 3.54/3.75 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[4961, 9433, 194])).
% 3.54/3.75 tff(9435,plain,
% 3.54/3.75 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[4950, 9434, 4938])).
% 3.54/3.75 tff(9436,plain,
% 3.54/3.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 3.54/3.75 inference(rewrite,[status(thm)],[])).
% 3.54/3.75 tff(9437,plain,
% 3.54/3.75 (((~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 3.54/3.75 inference(rewrite,[status(thm)],[])).
% 3.54/3.75 tff(9438,plain,
% 3.54/3.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))))),
% 3.54/3.75 inference(monotonicity,[status(thm)],[9437])).
% 3.54/3.75 tff(9439,plain,
% 3.54/3.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 3.54/3.75 inference(transitivity,[status(thm)],[9438, 9436])).
% 3.54/3.75 tff(9440,plain,
% 3.54/3.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.54/3.75 inference(quant_inst,[status(thm)],[])).
% 3.54/3.75 tff(9441,plain,
% 3.54/3.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 3.54/3.75 inference(modus_ponens,[status(thm)],[9440, 9439])).
% 3.54/3.75 tff(9442,plain,
% 3.54/3.75 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[9441, 118, 204, 3615])).
% 3.54/3.75 tff(9443,plain,
% 3.54/3.75 (b(s(s(s(s(z)))), elem!1)),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[3308, 9442, 1527])).
% 3.54/3.75 tff(9444,plain,
% 3.54/3.75 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.54/3.75 inference(modus_ponens,[status(thm)],[9443, 3290])).
% 3.54/3.75 tff(9445,plain,
% 3.54/3.75 ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[5050, 178, 1126, 9444, 3831])).
% 3.54/3.75 tff(9446,plain,
% 3.54/3.75 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[9445, 9435])).
% 3.54/3.75 tff(9447,plain,
% 3.54/3.75 (r(s(s(s(z))), s(s(s(elem!1))))),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[9126, 9446, 8246])).
% 3.54/3.75 tff(9448,plain,
% 3.54/3.75 (~r(s(s(s(z))), s(s(z)))),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[8350, 118, 1823, 9447])).
% 3.54/3.75 tff(9449,plain,
% 3.54/3.75 (b(s(s(s(z))), s(s(z)))),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[4966, 9448])).
% 3.54/3.75 tff(9450,plain,
% 3.54/3.75 (~r(s(s(z)), s(s(s(z))))),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[8359, 118, 1823, 9447])).
% 3.54/3.75 tff(9451,plain,
% 3.54/3.75 (b(s(s(z)), s(s(s(z))))),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[5088, 9450])).
% 3.54/3.75 tff(9452,plain,
% 3.54/3.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 3.54/3.75 inference(rewrite,[status(thm)],[])).
% 3.54/3.75 tff(9453,plain,
% 3.54/3.75 (((~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(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 3.54/3.75 inference(rewrite,[status(thm)],[])).
% 3.54/3.75 tff(9454,plain,
% 3.54/3.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))))),
% 3.54/3.75 inference(monotonicity,[status(thm)],[9453])).
% 3.54/3.75 tff(9455,plain,
% 3.54/3.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 3.54/3.75 inference(transitivity,[status(thm)],[9454, 9452])).
% 3.54/3.75 tff(9456,plain,
% 3.54/3.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 3.54/3.75 inference(quant_inst,[status(thm)],[])).
% 3.54/3.75 tff(9457,plain,
% 3.54/3.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 3.54/3.75 inference(modus_ponens,[status(thm)],[9456, 9455])).
% 3.54/3.75 tff(9458,plain,
% 3.54/3.75 ($false),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[9457, 178, 202, 1126, 9435, 9451, 9449])).
% 3.54/3.75 tff(9459,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~(elem!1 = s(s(s(elem!1))))) | (~r(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)))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.75 tff(9460,plain,
% 3.54/3.75 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[9459, 8314, 1126, 1823, 8246, 3831, 194, 104, 2043, 1527, 202, 9310, 145])).
% 3.54/3.75 tff(9461,plain,
% 3.54/3.75 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[222, 9460])).
% 3.54/3.75 tff(9462,plain,
% 3.54/3.75 (~b(s(s(z)), s(s(s(s(z)))))),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[259, 5345, 202, 251, 104])).
% 3.54/3.75 tff(9463,plain,
% 3.54/3.75 (r(s(s(z)), s(s(s(s(z)))))),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[164, 9462])).
% 3.54/3.75 tff(9464,plain,
% 3.54/3.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.54/3.75 inference(rewrite,[status(thm)],[])).
% 3.54/3.75 tff(9465,plain,
% 3.54/3.75 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.54/3.75 inference(rewrite,[status(thm)],[])).
% 3.54/3.75 tff(9466,plain,
% 3.54/3.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))))),
% 3.54/3.75 inference(monotonicity,[status(thm)],[9465])).
% 3.54/3.75 tff(9467,plain,
% 3.54/3.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.54/3.75 inference(transitivity,[status(thm)],[9466, 9464])).
% 3.54/3.75 tff(9468,plain,
% 3.54/3.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.54/3.75 inference(quant_inst,[status(thm)],[])).
% 3.54/3.75 tff(9469,plain,
% 3.54/3.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))),
% 3.54/3.75 inference(modus_ponens,[status(thm)],[9468, 9467])).
% 3.54/3.75 tff(9470,plain,
% 3.54/3.75 ($false),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[9469, 118, 438, 3132, 9463])).
% 3.54/3.75 tff(9471,plain,((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), 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)))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.75 tff(9472,plain,
% 3.54/3.75 (~r(s(s(s(s(z)))), elem!1)),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[9471, 9461, 202, 104, 438, 1265])).
% 3.54/3.75 tff(9473,plain,
% 3.54/3.75 (b(s(s(s(s(z)))), elem!1)),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[3142, 9472, 323])).
% 3.54/3.75 tff(9474,plain,
% 3.54/3.75 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.54/3.75 inference(modus_ponens,[status(thm)],[9473, 3290])).
% 3.54/3.75 tff(9475,plain,
% 3.54/3.75 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[4067, 178, 104, 9461, 9474, 3831])).
% 3.54/3.75 tff(9476,plain,
% 3.54/3.75 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[5118, 9475, 9310])).
% 3.54/3.75 tff(9477,plain,
% 3.54/3.75 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[8721, 9476, 104, 1126, 8246, 9461, 9474, 3831])).
% 3.54/3.75 tff(9478,plain,
% 3.54/3.75 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[4950, 9477, 4938])).
% 3.54/3.75 tff(9479,plain,
% 3.54/3.75 (~r(z, s(s(s(z))))),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[4961, 9478, 194])).
% 3.54/3.75 tff(9480,plain,
% 3.54/3.75 (b(z, s(s(s(z))))),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[4920, 9479])).
% 3.54/3.75 tff(9481,plain,
% 3.54/3.75 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 3.54/3.75 inference(unit_resolution,[status(thm)],[8732, 9480])).
% 3.54/3.75 tff(9482,plain,
% 3.54/3.75 (r(s(s(s(z))), s(s(s(elem!1))))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[9126, 9481, 8246])).
% 3.54/3.76 tff(9483,plain,
% 3.54/3.76 (~r(s(s(s(z))), s(s(z)))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[8350, 118, 1823, 9482])).
% 3.54/3.76 tff(9484,plain,
% 3.54/3.76 (b(s(s(s(z))), s(s(z)))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[4966, 9483])).
% 3.54/3.76 tff(9485,plain,
% 3.54/3.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 3.54/3.76 inference(rewrite,[status(thm)],[])).
% 3.54/3.76 tff(9486,plain,
% 3.54/3.76 (((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(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))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(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))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 3.54/3.76 inference(rewrite,[status(thm)],[])).
% 3.54/3.76 tff(9487,plain,
% 3.54/3.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(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))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z))))))),
% 3.54/3.76 inference(monotonicity,[status(thm)],[9486])).
% 3.54/3.76 tff(9488,plain,
% 3.54/3.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(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))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 3.54/3.76 inference(transitivity,[status(thm)],[9487, 9485])).
% 3.54/3.76 tff(9489,plain,
% 3.54/3.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(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))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 3.54/3.76 inference(quant_inst,[status(thm)],[])).
% 3.54/3.76 tff(9490,plain,
% 3.54/3.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z))))),
% 3.54/3.76 inference(modus_ponens,[status(thm)],[9489, 9488])).
% 3.54/3.76 tff(9491,plain,
% 3.54/3.76 ($false),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[9490, 178, 3865, 9461, 202, 1126, 9484])).
% 3.54/3.76 tff(9492,plain,((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~(elem!1 = s(s(s(elem!1))))) | (s(s(s(s(z)))) = elem!1) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.76 tff(9493,plain,
% 3.54/3.76 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[9492, 9417, 202, 9415, 9411, 2043, 3831, 194, 104, 9402, 4510, 9408, 145])).
% 3.54/3.76 tff(9494,plain,
% 3.54/3.76 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[691, 9493, 701])).
% 3.54/3.76 tff(9495,plain,
% 3.54/3.76 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.54/3.76 inference(monotonicity,[status(thm)],[9402])).
% 3.54/3.76 tff(9496,plain,
% 3.54/3.76 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 3.54/3.76 inference(symmetry,[status(thm)],[9495])).
% 3.54/3.76 tff(9497,plain,
% 3.54/3.76 ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) <=> (~r(elem!1, s(s(s(s(z))))))),
% 3.54/3.76 inference(monotonicity,[status(thm)],[9496])).
% 3.54/3.76 tff(9498,plain,
% 3.54/3.76 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[8234, 147, 2043, 145])).
% 3.54/3.76 tff(9499,plain,
% 3.54/3.76 (~r(elem!1, s(s(s(s(z)))))),
% 3.54/3.76 inference(modus_ponens,[status(thm)],[9498, 9497])).
% 3.54/3.76 tff(9500,plain,
% 3.54/3.76 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.54/3.76 inference(monotonicity,[status(thm)],[9402])).
% 3.54/3.76 tff(9501,plain,
% 3.54/3.76 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 3.54/3.76 inference(symmetry,[status(thm)],[9500])).
% 3.54/3.76 tff(9502,plain,
% 3.54/3.76 (b(elem!1, s(s(s(s(z)))))),
% 3.54/3.76 inference(modus_ponens,[status(thm)],[3831, 9501])).
% 3.54/3.76 tff(9503,plain,
% 3.54/3.76 (b(z, elem!1) <=> b(z, s(s(s(elem!1))))),
% 3.54/3.76 inference(monotonicity,[status(thm)],[9402])).
% 3.54/3.76 tff(9504,plain,
% 3.54/3.76 (b(z, s(s(s(elem!1)))) <=> b(z, elem!1)),
% 3.54/3.76 inference(symmetry,[status(thm)],[9503])).
% 3.54/3.76 tff(9505,plain,
% 3.54/3.76 (b(z, elem!1)),
% 3.54/3.76 inference(modus_ponens,[status(thm)],[2043, 9504])).
% 3.54/3.76 tff(9506,plain,
% 3.54/3.76 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[1309, 9494, 104, 9505, 9502])).
% 3.54/3.76 tff(9507,plain,
% 3.54/3.76 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[271, 9506])).
% 3.54/3.76 tff(9508,plain,
% 3.54/3.76 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[212, 9507, 145])).
% 3.54/3.76 tff(9509,plain,
% 3.54/3.76 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[222, 9508])).
% 3.54/3.76 tff(9510,plain,
% 3.54/3.76 (r(s(s(s(s(z)))), elem!1)),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[8548, 9509, 104, 9499, 4520, 9494])).
% 3.54/3.76 tff(9511,plain,
% 3.54/3.76 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.54/3.76 inference(modus_ponens,[status(thm)],[9510, 9403])).
% 3.54/3.76 tff(9512,plain,
% 3.54/3.76 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.54/3.76 inference(rewrite,[status(thm)],[])).
% 3.54/3.76 tff(9513,plain,
% 3.54/3.76 (((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.54/3.76 inference(rewrite,[status(thm)],[])).
% 3.54/3.76 tff(9514,plain,
% 3.54/3.76 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 3.54/3.76 inference(monotonicity,[status(thm)],[9513])).
% 3.54/3.76 tff(9515,plain,
% 3.54/3.76 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.54/3.76 inference(transitivity,[status(thm)],[9514, 9512])).
% 3.54/3.76 tff(9516,plain,
% 3.54/3.76 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.54/3.76 inference(quant_inst,[status(thm)],[])).
% 3.54/3.76 tff(9517,plain,
% 3.54/3.76 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 3.54/3.76 inference(modus_ponens,[status(thm)],[9516, 9515])).
% 3.54/3.76 tff(9518,plain,
% 3.54/3.76 ($false),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[9517, 118, 9415, 147, 9511])).
% 3.54/3.76 tff(9519,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | b(s(s(z)), elem!1) | b(elem!1, s(s(s(elem!1)))) | b(elem!1, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.76 tff(9520,plain,
% 3.54/3.76 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[9519, 9298, 47, 701, 9094, 7954, 8673, 3244, 3241, 3240, 461])).
% 3.54/3.76 tff(9521,plain,
% 3.54/3.76 (b(s(s(z)), s(s(s(s(z)))))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[164, 9520])).
% 3.54/3.76 tff(9522,plain,
% 3.54/3.76 (~r(z, s(s(z)))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[8067, 203, 202, 104, 145])).
% 3.54/3.76 tff(9523,plain,
% 3.54/3.76 (b(z, s(s(z)))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[143, 9522])).
% 3.54/3.76 tff(9524,plain,
% 3.54/3.76 ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[9008, 178, 2043, 167, 3831])).
% 3.54/3.76 tff(9525,plain,
% 3.54/3.76 (~b(s(s(z)), s(s(s(elem!1))))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[9524, 9523])).
% 3.54/3.76 tff(9526,plain,
% 3.54/3.76 (r(s(s(z)), s(s(s(elem!1))))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[4223, 9525])).
% 3.54/3.76 tff(9527,plain,
% 3.54/3.76 (~r(s(s(z)), elem!1)),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[7973, 9526, 3311])).
% 3.54/3.76 tff(9528,plain,
% 3.54/3.76 (s(s(z)) = elem!1),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[448, 9527, 3241])).
% 3.54/3.76 tff(9529,plain,
% 3.54/3.76 (s(s(s(z))) = s(elem!1)),
% 3.54/3.76 inference(monotonicity,[status(thm)],[9528])).
% 3.54/3.76 tff(9530,plain,
% 3.54/3.76 (s(s(s(s(z)))) = s(s(elem!1))),
% 3.54/3.76 inference(monotonicity,[status(thm)],[9529])).
% 3.54/3.76 tff(9531,plain,
% 3.54/3.76 (r(z, s(s(s(s(z))))) <=> r(z, s(s(elem!1)))),
% 3.54/3.76 inference(monotonicity,[status(thm)],[9530])).
% 3.54/3.76 tff(9532,plain,
% 3.54/3.76 (r(z, s(s(elem!1)))),
% 3.54/3.76 inference(modus_ponens,[status(thm)],[145, 9531])).
% 3.54/3.76 tff(9533,plain,
% 3.54/3.76 (s(s(elem!1)) = s(s(s(s(z))))),
% 3.54/3.76 inference(symmetry,[status(thm)],[9530])).
% 3.54/3.76 tff(9534,plain,
% 3.54/3.76 (r(s(elem!1), s(s(elem!1))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 3.54/3.76 inference(monotonicity,[status(thm)],[9533])).
% 3.54/3.76 tff(9535,plain,
% 3.54/3.76 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(elem!1), s(s(elem!1)))),
% 3.54/3.76 inference(symmetry,[status(thm)],[9534])).
% 3.54/3.76 tff(9536,plain,
% 3.54/3.76 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 3.54/3.76 inference(monotonicity,[status(thm)],[9529])).
% 3.54/3.76 tff(9537,plain,
% 3.54/3.76 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[9162, 9528, 167, 3311, 202, 750, 3244, 2043, 3831, 4510])).
% 3.54/3.76 tff(9538,plain,
% 3.54/3.76 (r(s(s(s(z))), s(s(s(s(z)))))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[4928, 9537, 4890])).
% 3.54/3.76 tff(9539,plain,
% 3.54/3.76 (r(s(elem!1), s(s(s(s(z)))))),
% 3.54/3.76 inference(modus_ponens,[status(thm)],[9538, 9536])).
% 3.54/3.76 tff(9540,plain,
% 3.54/3.76 (r(s(elem!1), s(s(elem!1)))),
% 3.54/3.76 inference(modus_ponens,[status(thm)],[9539, 9535])).
% 3.54/3.76 tff(9541,plain,
% 3.54/3.76 (~r(s(elem!1), z)),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[5542, 118, 9540, 9532])).
% 3.54/3.76 tff(9542,plain,
% 3.54/3.76 (b(s(elem!1), z)),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[774, 9541])).
% 3.54/3.76 tff(9543,plain,
% 3.54/3.76 (~r(z, s(elem!1))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[5550, 118, 9540, 9532])).
% 3.54/3.76 tff(9544,plain,
% 3.54/3.76 (b(z, s(elem!1))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[2351, 9543])).
% 3.54/3.76 tff(9545,plain,
% 3.54/3.76 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 3.54/3.76 inference(monotonicity,[status(thm)],[9529])).
% 3.54/3.76 tff(9546,plain,
% 3.54/3.76 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 3.54/3.76 inference(transitivity,[status(thm)],[9545, 3881])).
% 3.54/3.76 tff(9547,plain,
% 3.54/3.76 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 3.54/3.76 inference(transitivity,[status(thm)],[9546, 7104])).
% 3.54/3.76 tff(9548,plain,
% 3.54/3.76 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 3.54/3.76 inference(monotonicity,[status(thm)],[9547])).
% 3.54/3.76 tff(9549,plain,
% 3.54/3.76 (~(elem!1 = z)),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[3276, 9523, 461])).
% 3.54/3.76 tff(9550,plain,
% 3.54/3.76 (~(z = elem!1)),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[317, 9549])).
% 3.54/3.76 tff(9551,plain,
% 3.54/3.76 (~(s(s(elem!1)) = s(s(z)))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[2386, 9550])).
% 3.54/3.76 tff(9552,plain,
% 3.54/3.76 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[8244, 9551])).
% 3.54/3.76 tff(9553,plain,
% 3.54/3.76 (~(s(elem!1) = s(s(s(elem!1))))),
% 3.54/3.76 inference(modus_ponens,[status(thm)],[9552, 9548])).
% 3.54/3.76 tff(9554,plain,
% 3.54/3.76 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[259, 223, 202, 104, 167])).
% 3.54/3.76 tff(9555,plain,
% 3.54/3.76 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[249, 9554])).
% 3.54/3.76 tff(9556,plain,
% 3.54/3.76 (~r(s(s(z)), z)),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[232, 9555, 203])).
% 3.54/3.76 tff(9557,plain,
% 3.54/3.76 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 3.54/3.76 inference(monotonicity,[status(thm)],[9546])).
% 3.54/3.76 tff(9558,plain,
% 3.54/3.76 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.54/3.76 inference(modus_ponens,[status(thm)],[9552, 9557])).
% 3.54/3.76 tff(9559,plain,
% 3.54/3.76 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 3.54/3.76 inference(monotonicity,[status(thm)],[9529])).
% 3.54/3.76 tff(9560,plain,
% 3.54/3.76 ((~b(s(s(s(z))), s(s(s(s(z)))))) <=> (~b(s(elem!1), s(s(s(s(z))))))),
% 3.54/3.76 inference(monotonicity,[status(thm)],[9559])).
% 3.54/3.76 tff(9561,plain,
% 3.54/3.76 (~b(s(elem!1), s(s(s(s(z)))))),
% 3.54/3.76 inference(modus_ponens,[status(thm)],[9537, 9560])).
% 3.54/3.76 tff(9562,plain,
% 3.54/3.76 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 3.54/3.76 inference(rewrite,[status(thm)],[])).
% 3.54/3.76 tff(9563,plain,
% 3.54/3.76 (((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 3.54/3.76 inference(rewrite,[status(thm)],[])).
% 3.54/3.76 tff(9564,plain,
% 3.54/3.76 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 3.54/3.76 inference(monotonicity,[status(thm)],[9563])).
% 3.54/3.76 tff(9565,plain,
% 3.54/3.76 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 3.54/3.76 inference(transitivity,[status(thm)],[9564, 9562])).
% 3.54/3.76 tff(9566,plain,
% 3.54/3.76 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 3.54/3.76 inference(quant_inst,[status(thm)],[])).
% 3.54/3.76 tff(9567,plain,
% 3.54/3.76 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))),
% 3.54/3.76 inference(modus_ponens,[status(thm)],[9566, 9565])).
% 3.54/3.76 tff(9568,plain,
% 3.54/3.76 ($false),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[9567, 118, 3261, 194, 193])).
% 3.54/3.76 tff(9569,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.76 tff(9570,plain,
% 3.54/3.76 (~r(z, s(s(z)))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[9569, 193, 194])).
% 3.54/3.76 tff(9571,plain,
% 3.54/3.76 (b(z, s(s(z)))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[143, 9570])).
% 3.54/3.76 tff(9572,plain,
% 3.54/3.76 (~r(s(elem!1), s(s(z)))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[3949, 908, 193])).
% 3.54/3.76 tff(9573,plain,
% 3.54/3.76 (b(z, elem!1) <=> b(z, s(s(z)))),
% 3.54/3.76 inference(monotonicity,[status(thm)],[308])).
% 3.54/3.76 tff(9574,plain,
% 3.54/3.76 (b(z, s(s(z))) <=> b(z, elem!1)),
% 3.54/3.76 inference(symmetry,[status(thm)],[9573])).
% 3.54/3.76 tff(9575,plain,
% 3.54/3.76 (b(z, elem!1)),
% 3.54/3.76 inference(modus_ponens,[status(thm)],[144, 9574])).
% 3.54/3.76 tff(9576,plain,
% 3.54/3.76 (b(elem!1, z)),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[6641, 308, 5618])).
% 3.54/3.76 tff(9577,plain,
% 3.54/3.76 (~r(s(s(z)), s(elem!1))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[1331, 6634, 744])).
% 3.54/3.76 tff(9578,plain,
% 3.54/3.76 (s(elem!1) = s(s(z))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[6767, 144, 853, 3461, 1062, 927])).
% 3.54/3.76 tff(9579,plain,
% 3.54/3.76 (r(z, s(elem!1)) <=> r(z, s(s(z)))),
% 3.54/3.76 inference(monotonicity,[status(thm)],[9578])).
% 3.54/3.76 tff(9580,plain,
% 3.54/3.76 (r(z, s(s(z))) <=> r(z, s(elem!1))),
% 3.54/3.76 inference(symmetry,[status(thm)],[9579])).
% 3.54/3.76 tff(9581,plain,
% 3.54/3.76 ((~r(z, s(s(z)))) <=> (~r(z, s(elem!1)))),
% 3.54/3.76 inference(monotonicity,[status(thm)],[9580])).
% 3.54/3.76 tff(9582,plain,
% 3.54/3.76 (~r(z, s(elem!1))),
% 3.54/3.76 inference(modus_ponens,[status(thm)],[48, 9581])).
% 3.54/3.76 tff(9583,plain,
% 3.54/3.76 ($false),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[2333, 9582])).
% 3.54/3.76 tff(9584,plain,(r(z, s(s(z))) | (~r(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | r(s(s(z)), s(elem!1)) | r(s(elem!1), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.76 tff(9585,plain,
% 3.54/3.76 (~r(z, s(elem!1))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[9584, 9577, 5619, 48, 927, 853])).
% 3.54/3.76 tff(9586,plain,
% 3.54/3.76 (b(z, s(elem!1))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[2351, 9585])).
% 3.54/3.76 tff(9587,plain,
% 3.54/3.76 (~b(z, elem!1)),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[863, 9586, 9576, 854, 853])).
% 3.54/3.76 tff(9588,plain,
% 3.54/3.76 ($false),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[9587, 9575])).
% 3.54/3.76 tff(9589,plain,((~(elem!1 = s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | r(z, s(s(z))) | r(s(elem!1), s(s(z))) | r(elem!1, s(elem!1)) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 3.54/3.76 tff(9590,plain,
% 3.54/3.76 (~(elem!1 = s(s(z)))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[9589, 6752, 854, 9570, 9572, 744, 5618])).
% 3.54/3.76 tff(9591,plain,
% 3.54/3.76 (r(elem!1, s(s(z)))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[467, 9590, 461])).
% 3.54/3.76 tff(9592,plain,
% 3.54/3.76 (~(s(elem!1) = s(s(z)))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[1047, 9591, 744])).
% 3.54/3.76 tff(9593,plain,
% 3.54/3.76 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[6776, 9592, 5619, 9571, 908, 6752])).
% 3.54/3.76 tff(9594,plain,
% 3.54/3.76 (b(s(s(z)), s(s(s(s(z)))))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[164, 9593])).
% 3.54/3.76 tff(9595,plain,
% 3.54/3.76 (b(s(elem!1), s(s(z)))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[421, 9592, 9572])).
% 3.54/3.76 tff(9596,plain,
% 3.54/3.76 ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(z))))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[6363, 178, 6752, 5619, 9571])).
% 3.54/3.76 tff(9597,plain,
% 3.54/3.76 (~b(z, s(elem!1))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[9596, 9595])).
% 3.54/3.76 tff(9598,plain,
% 3.54/3.76 (r(z, s(elem!1))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[2351, 9597])).
% 3.54/3.76 tff(9599,plain,
% 3.54/3.76 (~r(z, s(s(s(s(z)))))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[2766, 9598, 908])).
% 3.54/3.76 tff(9600,plain,
% 3.54/3.76 (b(z, s(s(s(s(z)))))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[46, 9599])).
% 3.54/3.76 tff(9601,plain,
% 3.54/3.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 3.54/3.76 inference(rewrite,[status(thm)],[])).
% 3.54/3.76 tff(9602,plain,
% 3.54/3.76 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 3.54/3.76 inference(rewrite,[status(thm)],[])).
% 3.54/3.76 tff(9603,plain,
% 3.54/3.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 3.54/3.76 inference(monotonicity,[status(thm)],[9602])).
% 3.54/3.76 tff(9604,plain,
% 3.54/3.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 3.54/3.76 inference(transitivity,[status(thm)],[9603, 9601])).
% 3.54/3.76 tff(9605,plain,
% 3.54/3.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)))),
% 3.54/3.76 inference(quant_inst,[status(thm)],[])).
% 3.54/3.76 tff(9606,plain,
% 3.54/3.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 3.54/3.76 inference(modus_ponens,[status(thm)],[9605, 9604])).
% 3.54/3.76 tff(9607,plain,
% 3.54/3.76 ($false),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[9606, 178, 6752, 9571, 9595, 9600, 9594])).
% 3.54/3.76 tff(9608,plain,((~r(s(elem!1), s(s(s(s(z)))))) | r(elem!1, s(elem!1)) | b(elem!1, s(s(z))) | (~b(elem!1, s(elem!1))) | r(s(s(z)), z) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.76 tff(9609,plain,
% 3.54/3.76 (~r(s(elem!1), s(s(s(s(z)))))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[9608, 193, 461, 5725, 5618, 744, 194])).
% 3.54/3.76 tff(9610,plain,
% 3.54/3.76 (s(elem!1) = s(s(s(s(z))))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[1084, 9609, 5720])).
% 3.54/3.76 tff(9611,plain,
% 3.54/3.76 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 3.54/3.76 inference(monotonicity,[status(thm)],[9610])).
% 3.54/3.76 tff(9612,plain,
% 3.54/3.76 (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))),
% 3.54/3.76 inference(monotonicity,[status(thm)],[9611])).
% 3.54/3.76 tff(9613,plain,
% 3.54/3.76 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 3.54/3.76 inference(symmetry,[status(thm)],[9612])).
% 3.54/3.76 tff(9614,plain,
% 3.54/3.76 (r(s(s(s(s(s(s(z)))))), z) <=> r(s(s(s(elem!1))), z)),
% 3.54/3.76 inference(monotonicity,[status(thm)],[9613])).
% 3.54/3.76 tff(9615,plain,
% 3.54/3.76 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(s(s(z)))))), z)),
% 3.54/3.76 inference(symmetry,[status(thm)],[9614])).
% 3.54/3.76 tff(9616,plain,
% 3.54/3.76 (b(s(s(s(s(s(s(z)))))), z) <=> b(s(s(s(elem!1))), z)),
% 3.54/3.76 inference(monotonicity,[status(thm)],[9613])).
% 3.54/3.76 tff(9617,plain,
% 3.54/3.76 ((~b(s(s(s(s(s(s(z)))))), z)) <=> (~b(s(s(s(elem!1))), z))),
% 3.54/3.76 inference(monotonicity,[status(thm)],[9616])).
% 3.54/3.76 tff(9618,plain,
% 3.54/3.76 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 3.54/3.76 inference(monotonicity,[status(thm)],[9610])).
% 3.54/3.76 tff(9619,plain,
% 3.54/3.76 (elem!1 = s(s(s(z)))),
% 3.54/3.76 inference(transitivity,[status(thm)],[517, 9618, 11])).
% 3.54/3.76 tff(9620,plain,
% 3.54/3.76 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 3.54/3.76 inference(monotonicity,[status(thm)],[9612, 9619])).
% 3.54/3.76 tff(9621,plain,
% 3.54/3.76 (~(elem!1 = z)),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[3276, 9571, 461])).
% 3.54/3.76 tff(9622,plain,
% 3.54/3.76 (~(z = elem!1)),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[317, 9621])).
% 3.54/3.76 tff(9623,plain,
% 3.54/3.76 (~(s(s(elem!1)) = s(s(z)))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[2386, 9622])).
% 3.54/3.76 tff(9624,plain,
% 3.54/3.76 (~(elem!1 = s(s(s(elem!1))))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[2498, 9610, 9623])).
% 3.54/3.76 tff(9625,plain,
% 3.54/3.76 (~(s(s(s(elem!1))) = elem!1)),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[2489, 9624])).
% 3.54/3.76 tff(9626,plain,
% 3.54/3.76 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 3.54/3.76 inference(symmetry,[status(thm)],[9618])).
% 3.54/3.76 tff(9627,plain,
% 3.54/3.76 (s(s(s(z))) = elem!1),
% 3.54/3.76 inference(transitivity,[status(thm)],[61, 9626, 304])).
% 3.54/3.76 tff(9628,plain,
% 3.54/3.76 (r(s(s(s(z))), s(s(z))) <=> r(elem!1, s(s(z)))),
% 3.54/3.76 inference(monotonicity,[status(thm)],[9627])).
% 3.54/3.76 tff(9629,plain,
% 3.54/3.76 (r(elem!1, s(s(z))) <=> r(s(s(s(z))), s(s(z)))),
% 3.54/3.76 inference(symmetry,[status(thm)],[9628])).
% 3.54/3.76 tff(9630,plain,
% 3.54/3.76 ((s(elem!1) = elem!1) <=> (s(s(s(s(z)))) = elem!1)),
% 3.54/3.76 inference(monotonicity,[status(thm)],[9610])).
% 3.54/3.76 tff(9631,plain,
% 3.54/3.76 ((~(s(elem!1) = elem!1)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 3.54/3.76 inference(monotonicity,[status(thm)],[9630])).
% 3.54/3.76 tff(9632,plain,
% 3.54/3.76 (~(s(s(s(s(z)))) = elem!1)),
% 3.54/3.76 inference(modus_ponens,[status(thm)],[1548, 9631])).
% 3.54/3.76 tff(9633,plain,
% 3.54/3.76 (~(elem!1 = s(s(z)))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[1353, 9632, 9610])).
% 3.54/3.76 tff(9634,plain,
% 3.54/3.76 (r(elem!1, s(s(z)))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[467, 9633, 461])).
% 3.54/3.76 tff(9635,plain,
% 3.54/3.76 (r(s(s(s(z))), s(s(z)))),
% 3.54/3.76 inference(modus_ponens,[status(thm)],[9634, 9629])).
% 3.54/3.76 tff(9636,plain,
% 3.54/3.76 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 3.54/3.76 inference(monotonicity,[status(thm)],[9627])).
% 3.54/3.76 tff(9637,plain,
% 3.54/3.76 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 3.54/3.76 inference(symmetry,[status(thm)],[9636])).
% 3.54/3.76 tff(9638,plain,
% 3.54/3.76 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(s(z)))))),
% 3.54/3.76 inference(monotonicity,[status(thm)],[9610])).
% 3.54/3.76 tff(9639,plain,
% 3.54/3.76 (b(elem!1, s(s(s(s(z)))))),
% 3.54/3.76 inference(modus_ponens,[status(thm)],[5725, 9638])).
% 3.54/3.76 tff(9640,plain,
% 3.54/3.76 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.54/3.76 inference(modus_ponens,[status(thm)],[9639, 9637])).
% 3.54/3.76 tff(9641,plain,
% 3.54/3.76 (~(s(s(s(s(s(s(z)))))) = s(s(z)))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[6058, 9610])).
% 3.54/3.76 tff(9642,plain,
% 3.54/3.76 (b(s(elem!1), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 3.54/3.76 inference(monotonicity,[status(thm)],[9610])).
% 3.54/3.76 tff(9643,plain,
% 3.54/3.76 (b(s(s(s(s(z)))), elem!1) <=> b(s(elem!1), elem!1)),
% 3.54/3.76 inference(symmetry,[status(thm)],[9642])).
% 3.54/3.76 tff(9644,plain,
% 3.54/3.76 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[8696, 118, 193, 9635])).
% 3.54/3.76 tff(9645,plain,
% 3.54/3.76 (~r(s(s(s(s(z)))), elem!1)),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[7220, 9644, 9610])).
% 3.54/3.76 tff(9646,plain,
% 3.54/3.76 (b(s(s(s(s(z)))), elem!1)),
% 3.54/3.76 inference(unit_resolution,[status(thm)],[3142, 9645, 9632])).
% 3.54/3.76 tff(9647,plain,
% 3.54/3.76 (b(s(elem!1), elem!1)),
% 3.54/3.76 inference(modus_ponens,[status(thm)],[9646, 9643])).
% 3.54/3.76 tff(9648,plain,
% 3.54/3.76 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 3.54/3.76 inference(monotonicity,[status(thm)],[1117, 1119])).
% 3.54/3.76 tff(9649,plain,
% 3.54/3.76 (r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 3.54/3.76 inference(symmetry,[status(thm)],[9648])).
% 3.54/3.76 tff(9650,plain,
% 3.54/3.76 ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) <=> (~r(s(elem!1), s(s(s(elem!1)))))),
% 3.54/3.76 inference(monotonicity,[status(thm)],[9649])).
% 3.54/3.76 tff(9651,plain,
% 3.54/3.76 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 3.54/3.77 inference(rewrite,[status(thm)],[])).
% 3.54/3.77 tff(9652,plain,
% 3.54/3.77 (((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 3.54/3.77 inference(rewrite,[status(thm)],[])).
% 3.54/3.77 tff(9653,plain,
% 3.54/3.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 3.54/3.77 inference(monotonicity,[status(thm)],[9652])).
% 3.54/3.77 tff(9654,plain,
% 3.54/3.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 3.54/3.77 inference(transitivity,[status(thm)],[9653, 9651])).
% 3.54/3.77 tff(9655,plain,
% 3.54/3.77 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 3.54/3.77 inference(quant_inst,[status(thm)],[])).
% 3.54/3.77 tff(9656,plain,
% 3.54/3.77 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 3.54/3.77 inference(modus_ponens,[status(thm)],[9655, 9654])).
% 3.54/3.77 tff(9657,plain,
% 3.54/3.77 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[9656, 118, 193, 2405])).
% 3.54/3.77 tff(9658,plain,
% 3.54/3.77 (~r(s(elem!1), s(s(s(elem!1))))),
% 3.54/3.77 inference(modus_ponens,[status(thm)],[9657, 9650])).
% 3.54/3.77 tff(9659,plain,
% 3.54/3.77 (r(s(s(s(elem!1))), s(s(z)))),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[6165, 2405, 1117])).
% 3.54/3.77 tff(9660,plain,
% 3.54/3.77 (~r(s(s(s(elem!1))), elem!1)),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[4205, 9659, 450])).
% 3.54/3.77 tff(9661,plain,
% 3.54/3.77 (b(s(s(s(elem!1))), elem!1)),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[570, 9660, 6403])).
% 3.54/3.77 tff(9662,plain,
% 3.54/3.77 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[6146, 118, 2405, 6053])).
% 3.54/3.77 tff(9663,plain,
% 3.54/3.77 (~r(elem!1, s(s(s(elem!1))))),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[7770, 9662, 1117])).
% 3.54/3.77 tff(9664,plain,
% 3.54/3.77 (b(elem!1, s(s(s(elem!1))))),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[2054, 9663, 1586])).
% 3.54/3.77 tff(9665,plain,
% 3.54/3.77 (~b(s(elem!1), s(s(s(elem!1))))),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[6834, 9664, 854, 683, 9661])).
% 3.54/3.77 tff(9666,plain,
% 3.54/3.77 (r(s(elem!1), s(s(s(elem!1))))),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[5432, 9665, 5425])).
% 3.54/3.77 tff(9667,plain,
% 3.54/3.77 ($false),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[9666, 9658])).
% 3.54/3.77 tff(9668,plain,((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~(s(elem!1) = s(s(s(s(z)))))) | (s(elem!1) = s(s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (elem!1 = s(s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.77 tff(9669,plain,
% 3.54/3.77 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[9668, 9610, 5396, 5725, 9647, 9624, 193, 9634])).
% 3.54/3.77 tff(9670,plain,
% 3.54/3.77 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[6139, 9669, 9641])).
% 3.54/3.77 tff(9671,plain,
% 3.54/3.77 (r(z, s(s(elem!1))) <=> r(z, s(s(s(s(s(z))))))),
% 3.54/3.77 inference(monotonicity,[status(thm)],[1118])).
% 3.54/3.77 tff(9672,plain,
% 3.54/3.77 (r(z, s(s(s(s(s(z)))))) <=> r(z, s(s(elem!1)))),
% 3.54/3.77 inference(symmetry,[status(thm)],[9671])).
% 3.54/3.77 tff(9673,assumption,(z = s(s(s(s(s(z)))))), introduced(assumption)).
% 3.54/3.77 tff(9674,plain,
% 3.54/3.77 (s(s(s(s(s(z))))) = z),
% 3.54/3.77 inference(symmetry,[status(thm)],[9673])).
% 3.54/3.77 tff(9675,plain,
% 3.54/3.77 ($false),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[242, 9674])).
% 3.54/3.77 tff(9676,plain,(~(z = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.77 tff(9677,plain,
% 3.54/3.77 ((s(elem!1) = elem!1) <=> (s(s(s(s(z)))) = elem!1)),
% 3.54/3.77 inference(monotonicity,[status(thm)],[1117])).
% 3.54/3.77 tff(9678,plain,
% 3.54/3.77 ((~(s(elem!1) = elem!1)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 3.54/3.77 inference(monotonicity,[status(thm)],[9677])).
% 3.54/3.77 tff(9679,plain,
% 3.54/3.77 (~(s(s(s(s(z)))) = elem!1)),
% 3.54/3.77 inference(modus_ponens,[status(thm)],[1548, 9678])).
% 3.54/3.77 tff(9680,plain,
% 3.54/3.77 (~(elem!1 = s(s(z)))),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[1353, 9679, 1117])).
% 3.54/3.77 tff(9681,plain,
% 3.54/3.77 (~(s(s(z)) = s(s(s(z))))),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[2196, 9680, 1117])).
% 3.54/3.77 tff(9682,plain,
% 3.54/3.77 ((~r(s(s(s(s(s(s(z)))))), z)) <=> (~r(s(s(s(elem!1))), z))),
% 3.54/3.77 inference(monotonicity,[status(thm)],[7275])).
% 3.54/3.77 tff(9683,plain,
% 3.54/3.77 (r(z, s(s(s(z)))) <=> r(z, elem!1)),
% 3.54/3.77 inference(monotonicity,[status(thm)],[1183])).
% 3.54/3.77 tff(9684,plain,
% 3.54/3.77 (r(z, elem!1) <=> r(z, s(s(s(z))))),
% 3.54/3.77 inference(symmetry,[status(thm)],[9683])).
% 3.54/3.77 tff(9685,plain,
% 3.54/3.77 (r(z, s(s(s(z))))),
% 3.54/3.77 inference(modus_ponens,[status(thm)],[521, 9684])).
% 3.54/3.77 tff(9686,plain,
% 3.54/3.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 3.54/3.77 inference(rewrite,[status(thm)],[])).
% 3.54/3.77 tff(9687,plain,
% 3.54/3.77 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z))) <=> ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 3.54/3.77 inference(rewrite,[status(thm)],[])).
% 3.54/3.77 tff(9688,plain,
% 3.54/3.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z))))),
% 3.54/3.77 inference(monotonicity,[status(thm)],[9687])).
% 3.54/3.77 tff(9689,plain,
% 3.54/3.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 3.54/3.77 inference(transitivity,[status(thm)],[9688, 9686])).
% 3.54/3.77 tff(9690,plain,
% 3.54/3.77 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 3.54/3.77 inference(quant_inst,[status(thm)],[])).
% 3.54/3.77 tff(9691,plain,
% 3.54/3.77 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z))),
% 3.54/3.77 inference(modus_ponens,[status(thm)],[9690, 9689])).
% 3.54/3.77 tff(9692,plain,
% 3.54/3.77 ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z))),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[9691, 118, 7669])).
% 3.54/3.77 tff(9693,plain,
% 3.54/3.77 (~r(s(s(s(s(s(s(z)))))), z)),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[9692, 9685])).
% 3.54/3.77 tff(9694,plain,
% 3.54/3.77 (~r(s(s(s(elem!1))), z)),
% 3.54/3.77 inference(modus_ponens,[status(thm)],[9693, 9682])).
% 3.54/3.77 tff(9695,plain,
% 3.54/3.77 (b(s(s(s(elem!1))), z)),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[1565, 9694])).
% 3.54/3.77 tff(9696,plain,
% 3.54/3.77 (b(s(s(s(s(s(s(z)))))), z)),
% 3.54/3.77 inference(modus_ponens,[status(thm)],[9695, 6066])).
% 3.54/3.77 tff(9697,plain,
% 3.54/3.77 (~r(z, s(s(s(elem!1))))),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[565, 521, 556])).
% 3.54/3.77 tff(9698,plain,
% 3.54/3.77 (b(z, s(s(s(elem!1))))),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[2095, 9697])).
% 3.54/3.77 tff(9699,plain,
% 3.54/3.77 (b(z, s(s(s(s(s(s(z)))))))),
% 3.54/3.77 inference(modus_ponens,[status(thm)],[9698, 6075])).
% 3.54/3.77 tff(9700,plain,
% 3.54/3.77 ($false),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[6084, 178, 3461, 273, 9699, 6067, 9696])).
% 3.54/3.77 tff(9701,plain,((~r(z, elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~(s(elem!1) = s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.77 tff(9702,plain,
% 3.54/3.77 (~r(z, elem!1)),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[9701, 556, 9571, 3461, 1117, 6067])).
% 3.54/3.77 tff(9703,plain,
% 3.54/3.77 (b(z, elem!1)),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[585, 9702, 318])).
% 3.54/3.77 tff(9704,plain,
% 3.54/3.77 (b(z, s(s(s(z))))),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[1238, 9703, 1117])).
% 3.54/3.77 tff(9705,assumption,(b(s(s(s(s(s(s(z)))))), z)), introduced(assumption)).
% 3.54/3.77 tff(9706,assumption,(r(s(s(s(s(s(s(z)))))), s(s(s(z))))), introduced(assumption)).
% 3.54/3.77 tff(9707,plain,
% 3.54/3.77 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(z)))),
% 3.54/3.77 inference(commutativity,[status(thm)],[])).
% 3.54/3.77 tff(9708,plain,
% 3.54/3.77 ((s(s(s(s(s(s(z)))))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(s(z)))))))),
% 3.54/3.77 inference(symmetry,[status(thm)],[9707])).
% 3.54/3.77 tff(9709,plain,
% 3.54/3.77 ((~(s(s(s(s(s(s(z)))))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(s(s(z))))))))),
% 3.54/3.77 inference(monotonicity,[status(thm)],[9708])).
% 3.54/3.77 tff(9710,plain,
% 3.54/3.77 (~(s(s(z)) = s(s(s(s(s(s(z)))))))),
% 3.54/3.77 inference(modus_ponens,[status(thm)],[6134, 9709])).
% 3.54/3.77 tff(9711,plain,
% 3.54/3.77 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[6108, 9705])).
% 3.54/3.77 tff(9712,plain,
% 3.54/3.77 (((~![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))))))))),
% 3.54/3.77 inference(rewrite,[status(thm)],[])).
% 3.54/3.77 tff(9713,plain,
% 3.54/3.77 ((~![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))))))))),
% 3.54/3.77 inference(quant_inst,[status(thm)],[])).
% 3.54/3.77 tff(9714,plain,
% 3.54/3.77 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(s(z))))))) | b(s(s(z)), s(s(s(s(s(s(z))))))) | r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 3.54/3.77 inference(modus_ponens,[status(thm)],[9713, 9712])).
% 3.54/3.77 tff(9715,plain,
% 3.54/3.77 ((s(s(z)) = s(s(s(s(s(s(z))))))) | r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[9714, 41, 9711])).
% 3.54/3.77 tff(9716,plain,
% 3.54/3.77 (r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[9715, 9710])).
% 3.54/3.77 tff(9717,plain,
% 3.54/3.77 ($false),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[7411, 118, 6939, 7670, 9706])).
% 3.54/3.77 tff(9718,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.77 tff(9719,plain,
% 3.54/3.77 (~r(s(s(z)), s(s(s(z))))),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[9718, 9716, 9706])).
% 3.54/3.77 tff(9720,plain,
% 3.54/3.77 (b(s(s(z)), s(s(s(z))))),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[5087, 9719, 3006])).
% 3.54/3.77 tff(9721,plain,
% 3.54/3.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 3.54/3.77 inference(rewrite,[status(thm)],[])).
% 3.54/3.77 tff(9722,plain,
% 3.54/3.77 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 3.54/3.77 inference(rewrite,[status(thm)],[])).
% 3.54/3.77 tff(9723,plain,
% 3.54/3.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 3.54/3.77 inference(monotonicity,[status(thm)],[9722])).
% 3.54/3.77 tff(9724,plain,
% 3.54/3.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 3.54/3.77 inference(transitivity,[status(thm)],[9723, 9721])).
% 3.54/3.77 tff(9725,plain,
% 3.54/3.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 3.54/3.77 inference(quant_inst,[status(thm)],[])).
% 3.54/3.77 tff(9726,plain,
% 3.54/3.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))),
% 3.54/3.77 inference(modus_ponens,[status(thm)],[9725, 9724])).
% 3.54/3.77 tff(9727,plain,
% 3.54/3.77 ($false),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[9726, 178, 3461, 3008, 6067, 9720, 9705])).
% 3.54/3.77 tff(9728,plain,((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (s(s(z)) = s(s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (s(s(s(s(s(s(z)))))) = s(s(z))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.77 tff(9729,plain,
% 3.54/3.77 (~b(s(s(s(s(s(s(z)))))), z)),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[9728, 9704, 3461, 6067, 9681, 7669, 6059, 9571])).
% 3.54/3.77 tff(9730,plain,
% 3.54/3.77 (~b(s(s(s(elem!1))), z)),
% 3.54/3.77 inference(modus_ponens,[status(thm)],[9729, 7277])).
% 3.54/3.77 tff(9731,plain,
% 3.54/3.77 (r(s(s(s(elem!1))), z)),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[1565, 9730])).
% 3.54/3.77 tff(9732,plain,
% 3.54/3.77 (r(s(s(s(s(s(s(z)))))), z)),
% 3.54/3.77 inference(modus_ponens,[status(thm)],[9731, 7276])).
% 3.54/3.77 tff(9733,plain,
% 3.54/3.77 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[7295, 9732])).
% 3.54/3.77 tff(9734,plain,
% 3.54/3.77 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[7299, 41, 9733])).
% 3.54/3.77 tff(9735,plain,
% 3.54/3.77 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[9734, 7579])).
% 3.54/3.77 tff(9736,plain,
% 3.54/3.77 (~(elem!1 = s(s(s(elem!1))))),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[2498, 1117, 3340])).
% 3.54/3.77 tff(9737,plain,
% 3.54/3.77 (~r(s(s(s(s(z)))), elem!1)),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[7220, 8697, 1117])).
% 3.54/3.77 tff(9738,plain,
% 3.54/3.77 (b(s(s(s(s(z)))), elem!1)),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[3142, 9737, 9679])).
% 3.54/3.77 tff(9739,plain,
% 3.54/3.77 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.54/3.77 inference(modus_ponens,[status(thm)],[9738, 1278])).
% 3.54/3.77 tff(9740,plain,
% 3.54/3.77 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[1557, 9731, 6062])).
% 3.54/3.77 tff(9741,plain,
% 3.54/3.77 (b(s(s(s(elem!1))), s(elem!1))),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[373, 9740, 356])).
% 3.54/3.77 tff(9742,plain,
% 3.54/3.77 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 3.54/3.77 inference(modus_ponens,[status(thm)],[9741, 6039])).
% 3.54/3.77 tff(9743,plain,
% 3.54/3.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(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(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(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(z))), s(s(s(s(s(s(z)))))))))),
% 3.54/3.77 inference(rewrite,[status(thm)],[])).
% 3.54/3.77 tff(9744,plain,
% 3.54/3.77 (((~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(z))), s(s(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(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(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)))))))))),
% 3.54/3.77 inference(rewrite,[status(thm)],[])).
% 3.54/3.77 tff(9745,plain,
% 3.54/3.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))), s(s(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(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(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(z))), s(s(s(s(s(s(z))))))))))),
% 3.54/3.77 inference(monotonicity,[status(thm)],[9744])).
% 3.54/3.77 tff(9746,plain,
% 3.54/3.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))), s(s(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(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(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(z))), s(s(s(s(s(s(z)))))))))),
% 3.54/3.77 inference(transitivity,[status(thm)],[9745, 9743])).
% 3.54/3.77 tff(9747,plain,
% 3.54/3.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))), s(s(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(z)))), s(s(s(z))))))),
% 3.54/3.77 inference(quant_inst,[status(thm)],[])).
% 3.54/3.77 tff(9748,plain,
% 3.54/3.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(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(z))), s(s(s(s(s(s(z))))))))),
% 3.54/3.77 inference(modus_ponens,[status(thm)],[9747, 9746])).
% 3.54/3.77 tff(9749,plain,
% 3.54/3.77 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[9748, 178, 9742, 1126, 9739, 9735])).
% 3.54/3.77 tff(9750,plain,
% 3.54/3.77 (~b(elem!1, s(s(s(elem!1))))),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[6974, 9749, 1117])).
% 3.54/3.77 tff(9751,plain,
% 3.54/3.77 (r(elem!1, s(s(s(elem!1))))),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[2054, 9750, 9736])).
% 3.54/3.77 tff(9752,plain,
% 3.54/3.77 (r(s(s(s(z))), z) <=> r(elem!1, z)),
% 3.54/3.77 inference(monotonicity,[status(thm)],[1183])).
% 3.54/3.77 tff(9753,plain,
% 3.54/3.77 (r(elem!1, z) <=> r(s(s(s(z))), z)),
% 3.54/3.77 inference(symmetry,[status(thm)],[9752])).
% 3.54/3.77 tff(9754,plain,
% 3.54/3.77 (r(s(s(s(z))), z)),
% 3.54/3.77 inference(modus_ponens,[status(thm)],[437, 9753])).
% 3.54/3.77 tff(9755,plain,
% 3.54/3.77 (r(s(s(s(s(s(s(z)))))), z)),
% 3.54/3.77 inference(modus_ponens,[status(thm)],[1552, 7276])).
% 3.54/3.77 tff(9756,plain,
% 3.54/3.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 3.54/3.77 inference(rewrite,[status(thm)],[])).
% 3.54/3.77 tff(9757,plain,
% 3.54/3.77 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 3.54/3.77 inference(quant_inst,[status(thm)],[])).
% 3.54/3.77 tff(9758,plain,
% 3.54/3.77 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 3.54/3.77 inference(modus_ponens,[status(thm)],[9757, 9756])).
% 3.54/3.77 tff(9759,plain,
% 3.54/3.77 ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z))),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[9758, 118, 9706])).
% 3.54/3.77 tff(9760,plain,
% 3.54/3.77 ($false),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[9759, 9755, 9754])).
% 3.54/3.77 tff(9761,plain,((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~(s(elem!1) = s(s(s(s(z)))))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.77 tff(9762,plain,
% 3.54/3.77 (~r(elem!1, z)),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[9761, 9731, 1117, 7669])).
% 3.54/3.77 tff(9763,plain,
% 3.54/3.77 (b(elem!1, z)),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[498, 9762, 290])).
% 3.54/3.77 tff(9764,plain,
% 3.54/3.77 (b(s(s(s(z))), z)),
% 3.54/3.77 inference(modus_ponens,[status(thm)],[9763, 7205])).
% 3.54/3.77 tff(9765,plain,
% 3.54/3.77 (~b(s(s(z)), s(s(s(z))))),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[7639, 178, 3461, 9571, 9704, 9764])).
% 3.54/3.77 tff(9766,plain,
% 3.54/3.77 (r(s(s(z)), s(s(s(z))))),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[5087, 9765, 9681])).
% 3.54/3.77 tff(9767,plain,
% 3.54/3.77 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[9718, 9766, 7669])).
% 3.54/3.77 tff(9768,plain,
% 3.54/3.77 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.54/3.77 inference(modus_ponens,[status(thm)],[9767, 7197])).
% 3.54/3.77 tff(9769,plain,
% 3.54/3.77 (b(s(s(z)), s(s(s(elem!1))))),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[4223, 9768])).
% 3.54/3.77 tff(9770,plain,
% 3.54/3.77 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[7268, 9769, 1117])).
% 3.54/3.77 tff(9771,plain,
% 3.54/3.77 (~b(z, s(s(s(s(s(s(z)))))))),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[7684, 178, 3461, 9571, 6067, 9770])).
% 3.54/3.77 tff(9772,plain,
% 3.54/3.77 (~b(z, s(s(s(elem!1))))),
% 3.54/3.77 inference(modus_ponens,[status(thm)],[9771, 7251])).
% 3.54/3.77 tff(9773,plain,
% 3.54/3.77 (r(z, s(s(s(elem!1))))),
% 3.54/3.77 inference(unit_resolution,[status(thm)],[2095, 9772])).
% 3.54/3.77 tff(9774,plain,
% 3.54/3.77 (r(z, s(s(s(s(s(s(z)))))))),
% 3.54/3.77 inference(modus_ponens,[status(thm)],[9773, 7668])).
% 3.54/3.77 tff(9775,plain,
% 3.54/3.77 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(elem!1, s(s(elem!1)))),
% 3.54/3.77 inference(monotonicity,[status(thm)],[1183, 6803])).
% 3.54/3.77 tff(9776,plain,
% 3.54/3.77 (b(elem!1, s(s(elem!1))) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.54/3.77 inference(symmetry,[status(thm)],[9775])).
% 3.54/3.78 tff(9777,plain,
% 3.54/3.78 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.54/3.78 inference(unit_resolution,[status(thm)],[3375, 3347, 1655])).
% 3.54/3.78 tff(9778,plain,
% 3.54/3.78 (~r(elem!1, s(s(elem!1)))),
% 3.54/3.78 inference(unit_resolution,[status(thm)],[5845, 9777, 3311])).
% 3.54/3.78 tff(9779,assumption,(~b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 3.54/3.78 tff(9780,plain,
% 3.54/3.78 ($false),
% 3.54/3.78 inference(unit_resolution,[status(thm)],[5470, 41, 1544, 5467, 9779])).
% 3.54/3.78 tff(9781,plain,(b(elem!1, s(s(elem!1))) | (elem!1 = s(s(elem!1))) | r(elem!1, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.78 tff(9782,plain,
% 3.54/3.78 (b(elem!1, s(s(elem!1)))),
% 3.54/3.78 inference(unit_resolution,[status(thm)],[9781, 9778, 1544])).
% 3.54/3.78 tff(9783,plain,
% 3.54/3.78 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.54/3.78 inference(modus_ponens,[status(thm)],[9782, 9776])).
% 3.54/3.78 tff(9784,plain,
% 3.54/3.78 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(elem!1)), elem!1)),
% 3.54/3.78 inference(monotonicity,[status(thm)],[6803, 1183])).
% 3.54/3.78 tff(9785,plain,
% 3.54/3.78 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.54/3.78 inference(symmetry,[status(thm)],[9784])).
% 3.54/3.78 tff(9786,plain,
% 3.54/3.78 (~(s(s(elem!1)) = elem!1)),
% 3.54/3.78 inference(unit_resolution,[status(thm)],[1546, 1544])).
% 3.54/3.78 tff(9787,plain,
% 3.54/3.78 (b(s(s(elem!1)), elem!1)),
% 3.54/3.78 inference(unit_resolution,[status(thm)],[3377, 3347, 9786, 3311])).
% 3.54/3.78 tff(9788,plain,
% 3.54/3.78 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.54/3.78 inference(modus_ponens,[status(thm)],[9787, 9785])).
% 3.54/3.78 tff(9789,assumption,(r(z, s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 3.54/3.78 tff(9790,plain,
% 3.54/3.78 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 3.54/3.78 inference(monotonicity,[status(thm)],[1118, 1119])).
% 3.54/3.78 tff(9791,plain,
% 3.54/3.78 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 3.54/3.78 inference(modus_ponens,[status(thm)],[9777, 9790])).
% 3.54/3.78 tff(9792,plain,
% 3.54/3.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 3.54/3.78 inference(rewrite,[status(thm)],[])).
% 3.54/3.78 tff(9793,plain,
% 3.54/3.78 (((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 3.54/3.78 inference(rewrite,[status(thm)],[])).
% 3.54/3.78 tff(9794,plain,
% 3.54/3.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))))),
% 3.54/3.78 inference(monotonicity,[status(thm)],[9793])).
% 3.54/3.78 tff(9795,plain,
% 3.54/3.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 3.54/3.78 inference(transitivity,[status(thm)],[9794, 9792])).
% 3.54/3.78 tff(9796,plain,
% 3.54/3.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), z)))),
% 3.54/3.78 inference(quant_inst,[status(thm)],[])).
% 3.54/3.78 tff(9797,plain,
% 3.54/3.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 3.54/3.78 inference(modus_ponens,[status(thm)],[9796, 9795])).
% 3.54/3.78 tff(9798,plain,
% 3.54/3.78 (~r(s(s(s(s(s(z))))), z)),
% 3.54/3.78 inference(unit_resolution,[status(thm)],[9797, 118, 9791, 9789])).
% 3.54/3.78 tff(9799,plain,
% 3.54/3.78 (b(s(s(s(s(s(z))))), z)),
% 3.54/3.78 inference(unit_resolution,[status(thm)],[410, 41, 242, 9798])).
% 3.54/3.78 tff(9800,plain,
% 3.54/3.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.54/3.78 inference(rewrite,[status(thm)],[])).
% 3.54/3.78 tff(9801,plain,
% 3.54/3.78 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.54/3.78 inference(rewrite,[status(thm)],[])).
% 3.54/3.78 tff(9802,plain,
% 3.54/3.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 3.54/3.78 inference(monotonicity,[status(thm)],[9801])).
% 3.54/3.78 tff(9803,plain,
% 3.54/3.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.54/3.78 inference(transitivity,[status(thm)],[9802, 9800])).
% 3.54/3.78 tff(9804,plain,
% 3.54/3.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.54/3.78 inference(quant_inst,[status(thm)],[])).
% 3.54/3.78 tff(9805,plain,
% 3.54/3.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 3.54/3.78 inference(modus_ponens,[status(thm)],[9804, 9803])).
% 3.54/3.78 tff(9806,plain,
% 3.54/3.78 ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 3.54/3.78 inference(unit_resolution,[status(thm)],[9805, 178, 3008, 1127])).
% 3.54/3.78 tff(9807,plain,
% 3.54/3.78 ($false),
% 3.54/3.78 inference(unit_resolution,[status(thm)],[9806, 9799, 9788, 9783])).
% 3.54/3.78 tff(9808,plain,(b(s(s(elem!1)), s(s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~(s(elem!1) = s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (elem!1 = s(s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.78 tff(9809,plain,
% 3.54/3.78 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.54/3.78 inference(unit_resolution,[status(thm)],[9808, 9704, 9764, 1117, 9774, 1540, 9751, 1650])).
% 3.54/3.78 tff(9810,plain,
% 3.54/3.78 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 3.54/3.78 inference(modus_ponens,[status(thm)],[9809, 6863])).
% 3.54/3.78 tff(9811,assumption,(b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 3.54/3.78 tff(9812,plain,
% 3.54/3.78 (~(s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 3.54/3.78 inference(modus_ponens,[status(thm)],[6871, 6881])).
% 3.54/3.78 tff(9813,plain,
% 3.54/3.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.54/3.78 inference(rewrite,[status(thm)],[])).
% 3.54/3.78 tff(9814,plain,
% 3.54/3.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.54/3.78 inference(quant_inst,[status(thm)],[])).
% 3.54/3.78 tff(9815,plain,
% 3.54/3.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 3.54/3.78 inference(modus_ponens,[status(thm)],[9814, 9813])).
% 3.54/3.78 tff(9816,plain,
% 3.54/3.78 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.54/3.78 inference(unit_resolution,[status(thm)],[9815, 118, 193, 1902])).
% 3.54/3.78 tff(9817,plain,
% 3.54/3.78 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.54/3.78 inference(unit_resolution,[status(thm)],[6895, 41, 9816])).
% 3.54/3.78 tff(9818,plain,
% 3.54/3.78 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.54/3.78 inference(unit_resolution,[status(thm)],[9817, 9812])).
% 3.54/3.78 tff(9819,plain,
% 3.54/3.78 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(elem!1)))),
% 3.54/3.78 inference(monotonicity,[status(thm)],[1183, 6803])).
% 3.54/3.78 tff(9820,plain,
% 3.54/3.78 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(elem!1)) = elem!1)),
% 3.54/3.78 inference(transitivity,[status(thm)],[9819, 1541])).
% 3.54/3.78 tff(9821,plain,
% 3.54/3.78 ((s(s(elem!1)) = elem!1) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 3.54/3.78 inference(symmetry,[status(thm)],[9820])).
% 3.54/3.78 tff(9822,plain,
% 3.54/3.78 ((~(s(s(elem!1)) = elem!1)) <=> (~(s(s(s(z))) = s(s(s(s(s(z)))))))),
% 3.54/3.78 inference(monotonicity,[status(thm)],[9821])).
% 3.54/3.78 tff(9823,plain,
% 3.54/3.78 (~(s(s(s(z))) = s(s(s(s(s(z))))))),
% 3.54/3.78 inference(modus_ponens,[status(thm)],[346, 9822])).
% 3.54/3.78 tff(9824,plain,
% 3.54/3.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.54/3.78 inference(rewrite,[status(thm)],[])).
% 3.54/3.78 tff(9825,plain,
% 3.54/3.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.54/3.78 inference(quant_inst,[status(thm)],[])).
% 3.54/3.78 tff(9826,plain,
% 3.54/3.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 3.54/3.78 inference(modus_ponens,[status(thm)],[9825, 9824])).
% 3.54/3.78 tff(9827,plain,
% 3.54/3.78 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.54/3.78 inference(unit_resolution,[status(thm)],[9826, 118, 1902, 1125])).
% 3.54/3.78 tff(9828,plain,
% 3.54/3.78 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 3.54/3.78 inference(rewrite,[status(thm)],[])).
% 3.54/3.78 tff(9829,plain,
% 3.54/3.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 3.54/3.78 inference(quant_inst,[status(thm)],[])).
% 3.54/3.78 tff(9830,plain,
% 3.54/3.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.54/3.78 inference(modus_ponens,[status(thm)],[9829, 9828])).
% 3.54/3.78 tff(9831,plain,
% 3.54/3.78 ((s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.54/3.78 inference(unit_resolution,[status(thm)],[9830, 41, 9827])).
% 3.54/3.78 tff(9832,plain,
% 3.54/3.78 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.54/3.78 inference(unit_resolution,[status(thm)],[9831, 9823])).
% 3.54/3.78 tff(9833,assumption,(b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 3.54/3.78 tff(9834,plain,
% 3.54/3.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(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(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(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(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.54/3.78 inference(rewrite,[status(thm)],[])).
% 3.54/3.78 tff(9835,plain,
% 3.54/3.78 (((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(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(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.54/3.78 inference(rewrite,[status(thm)],[])).
% 3.54/3.78 tff(9836,plain,
% 3.54/3.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(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(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 3.54/3.78 inference(monotonicity,[status(thm)],[9835])).
% 3.54/3.78 tff(9837,plain,
% 3.54/3.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(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(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.54/3.78 inference(transitivity,[status(thm)],[9836, 9834])).
% 3.54/3.78 tff(9838,plain,
% 3.54/3.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.54/3.78 inference(quant_inst,[status(thm)],[])).
% 3.54/3.78 tff(9839,plain,
% 3.54/3.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 3.54/3.78 inference(modus_ponens,[status(thm)],[9838, 9837])).
% 3.54/3.78 tff(9840,plain,
% 3.54/3.78 ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 3.54/3.78 inference(unit_resolution,[status(thm)],[9839, 178, 1126, 9833])).
% 3.54/3.78 tff(9841,plain,
% 3.54/3.78 ($false),
% 3.54/3.78 inference(unit_resolution,[status(thm)],[9840, 9832, 9818, 9811])).
% 3.54/3.78 tff(9842,plain,((~r(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (s(s(elem!1)) = elem!1) | (~(s(elem!1) = s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.78 tff(9843,plain,
% 3.54/3.78 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 3.54/3.78 inference(unit_resolution,[status(thm)],[9842, 9810, 1126, 9735, 1547, 1117, 1125, 193])).
% 3.54/3.78 tff(9844,plain,
% 3.54/3.78 (r(s(s(elem!1)), s(s(z))) <=> r(s(s(s(s(s(z))))), s(s(z)))),
% 3.54/3.78 inference(monotonicity,[status(thm)],[1118])).
% 3.54/3.78 tff(9845,plain,
% 3.54/3.78 (r(s(s(s(s(s(z))))), s(s(z))) <=> r(s(s(elem!1)), s(s(z)))),
% 3.54/3.78 inference(symmetry,[status(thm)],[9844])).
% 3.54/3.78 tff(9846,plain,
% 3.54/3.78 ((~r(s(s(s(s(s(z))))), s(s(z)))) <=> (~r(s(s(elem!1)), s(s(z))))),
% 3.54/3.78 inference(monotonicity,[status(thm)],[9845])).
% 3.54/3.78 tff(9847,assumption,(~r(s(s(s(s(s(z))))), s(s(z)))), introduced(assumption)).
% 3.54/3.78 tff(9848,plain,
% 3.54/3.78 (~r(s(s(elem!1)), s(s(z)))),
% 3.54/3.78 inference(modus_ponens,[status(thm)],[9847, 9846])).
% 3.54/3.78 tff(9849,plain,
% 3.54/3.78 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 3.54/3.78 inference(monotonicity,[status(thm)],[1118])).
% 3.54/3.78 tff(9850,plain,
% 3.54/3.78 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 3.54/3.78 inference(symmetry,[status(thm)],[9849])).
% 3.54/3.78 tff(9851,plain,
% 3.54/3.78 ((~b(s(s(s(s(s(z))))), s(s(z)))) <=> (~b(s(s(elem!1)), s(s(z))))),
% 3.54/3.78 inference(monotonicity,[status(thm)],[9850])).
% 3.54/3.78 tff(9852,plain,
% 3.54/3.78 (~b(s(s(elem!1)), s(s(z)))),
% 3.54/3.78 inference(modus_ponens,[status(thm)],[4696, 9851])).
% 3.54/3.78 tff(9853,plain,
% 3.54/3.78 ($false),
% 3.54/3.78 inference(unit_resolution,[status(thm)],[6494, 9852, 9848, 2484])).
% 3.54/3.78 tff(9854,plain,(b(s(s(s(s(s(z))))), s(s(z))) | (s(s(elem!1)) = s(s(z))) | (~(s(elem!1) = s(s(s(s(z)))))) | r(s(s(s(s(s(z))))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.78 tff(9855,plain,
% 3.54/3.78 (b(s(s(s(s(s(z))))), s(s(z)))),
% 3.54/3.78 inference(unit_resolution,[status(thm)],[9854, 9843, 1117, 3340])).
% 3.54/3.78 tff(9856,plain,
% 3.54/3.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 3.54/3.78 inference(rewrite,[status(thm)],[])).
% 3.54/3.78 tff(9857,plain,
% 3.54/3.78 (((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 3.54/3.78 inference(rewrite,[status(thm)],[])).
% 3.54/3.78 tff(9858,plain,
% 3.54/3.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))))),
% 3.54/3.78 inference(monotonicity,[status(thm)],[9857])).
% 3.54/3.78 tff(9859,plain,
% 3.54/3.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 3.54/3.78 inference(transitivity,[status(thm)],[9858, 9856])).
% 3.54/3.78 tff(9860,plain,
% 3.54/3.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))))),
% 3.54/3.78 inference(quant_inst,[status(thm)],[])).
% 3.54/3.78 tff(9861,plain,
% 3.54/3.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 3.54/3.78 inference(modus_ponens,[status(thm)],[9860, 9859])).
% 3.54/3.78 tff(9862,plain,
% 3.54/3.78 ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 3.54/3.78 inference(unit_resolution,[status(thm)],[9861, 178, 9571, 9770, 9810])).
% 3.54/3.78 tff(9863,plain,
% 3.54/3.78 (~b(z, s(s(s(s(s(z))))))),
% 3.54/3.78 inference(unit_resolution,[status(thm)],[9862, 9855])).
% 3.54/3.78 tff(9864,plain,
% 3.54/3.78 (r(z, s(s(s(s(s(z))))))),
% 3.54/3.78 inference(unit_resolution,[status(thm)],[1490, 41, 9863, 9676])).
% 3.54/3.78 tff(9865,plain,
% 3.54/3.78 (r(z, s(s(elem!1)))),
% 3.54/3.78 inference(modus_ponens,[status(thm)],[9864, 9672])).
% 3.54/3.78 tff(9866,plain,
% 3.54/3.78 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) <=> (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 3.54/3.78 inference(monotonicity,[status(thm)],[6804])).
% 3.54/3.78 tff(9867,plain,
% 3.54/3.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 3.54/3.78 inference(rewrite,[status(thm)],[])).
% 3.54/3.78 tff(9868,plain,
% 3.54/3.78 (((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 3.54/3.79 inference(rewrite,[status(thm)],[])).
% 3.54/3.79 tff(9869,plain,
% 3.54/3.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))))),
% 3.54/3.79 inference(monotonicity,[status(thm)],[9868])).
% 3.54/3.79 tff(9870,plain,
% 3.54/3.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 3.54/3.79 inference(transitivity,[status(thm)],[9869, 9867])).
% 3.54/3.79 tff(9871,plain,
% 3.54/3.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 3.54/3.79 inference(quant_inst,[status(thm)],[])).
% 3.54/3.79 tff(9872,plain,
% 3.54/3.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[9871, 9870])).
% 3.54/3.79 tff(9873,plain,
% 3.54/3.79 ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[9872, 178, 6067, 9770, 9810])).
% 3.54/3.79 tff(9874,plain,
% 3.54/3.79 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[9873, 9855])).
% 3.54/3.79 tff(9875,plain,
% 3.54/3.79 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[9874, 9866])).
% 3.54/3.79 tff(9876,plain,
% 3.54/3.79 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[3409, 9875, 5807])).
% 3.54/3.79 tff(9877,plain,
% 3.54/3.79 (~r(z, s(s(elem!1)))),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[5235, 9876, 9773])).
% 3.54/3.79 tff(9878,plain,
% 3.54/3.79 ($false),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[9877, 9865])).
% 3.54/3.79 tff(9879,plain,((~r(s(s(s(elem!1))), elem!1)) | (~(s(elem!1) = s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (elem!1 = z) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.79 tff(9880,plain,
% 3.54/3.79 (~r(s(s(s(elem!1))), elem!1)),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[9879, 9610, 9670, 9640, 9635, 193, 5619, 194, 9621, 356])).
% 3.54/3.79 tff(9881,plain,
% 3.54/3.79 (b(s(s(s(elem!1))), elem!1)),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[570, 9880, 9625])).
% 3.54/3.79 tff(9882,plain,
% 3.54/3.79 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[9881, 9620])).
% 3.54/3.79 tff(9883,plain,
% 3.54/3.79 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), elem!1)),
% 3.54/3.79 inference(monotonicity,[status(thm)],[9627])).
% 3.54/3.79 tff(9884,plain,
% 3.54/3.79 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 3.54/3.79 inference(symmetry,[status(thm)],[9883])).
% 3.54/3.79 tff(9885,plain,
% 3.54/3.79 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[9646, 9884])).
% 3.54/3.79 tff(9886,plain,
% 3.54/3.79 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[6176, 178, 1126, 6170, 7252])).
% 3.54/3.79 tff(9887,plain,
% 3.54/3.79 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[9886, 6155])).
% 3.54/3.79 tff(9888,plain,
% 3.54/3.79 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[9887, 6041])).
% 3.54/3.79 tff(9889,plain,
% 3.54/3.79 (r(s(s(s(elem!1))), s(elem!1))),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[373, 9888, 356])).
% 3.54/3.79 tff(9890,plain,
% 3.54/3.79 (~r(s(s(s(elem!1))), z)),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[1557, 9889, 6062])).
% 3.54/3.79 tff(9891,plain,
% 3.54/3.79 (b(s(s(s(elem!1))), z)),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[1565, 9890])).
% 3.54/3.79 tff(9892,plain,
% 3.54/3.79 (b(s(s(s(s(s(s(z)))))), z)),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[9891, 6066])).
% 3.54/3.79 tff(9893,plain,
% 3.54/3.79 (~b(z, s(s(s(s(s(s(z)))))))),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[6084, 178, 3461, 273, 6067, 9892])).
% 3.54/3.79 tff(9894,plain,
% 3.54/3.79 (~b(z, s(s(s(elem!1))))),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[9893, 7251])).
% 3.54/3.79 tff(9895,plain,
% 3.54/3.79 (r(z, s(s(s(elem!1))))),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[2095, 9894])).
% 3.54/3.79 tff(9896,plain,
% 3.54/3.79 (r(z, s(s(s(s(s(s(z)))))))),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[9895, 7668])).
% 3.54/3.79 tff(9897,plain,
% 3.54/3.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 3.54/3.79 inference(rewrite,[status(thm)],[])).
% 3.54/3.79 tff(9898,plain,
% 3.54/3.79 (((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), 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(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(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 3.54/3.79 inference(rewrite,[status(thm)],[])).
% 3.54/3.79 tff(9899,plain,
% 3.54/3.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), 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(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 3.54/3.79 inference(monotonicity,[status(thm)],[9898])).
% 3.54/3.79 tff(9900,plain,
% 3.54/3.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), 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(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 3.54/3.79 inference(transitivity,[status(thm)],[9899, 9897])).
% 3.54/3.79 tff(9901,plain,
% 3.54/3.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), 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(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 3.54/3.79 inference(quant_inst,[status(thm)],[])).
% 3.54/3.79 tff(9902,plain,
% 3.54/3.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[9901, 9900])).
% 3.54/3.79 tff(9903,plain,
% 3.54/3.79 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[9902, 178, 1126, 6155, 6170, 7252])).
% 3.54/3.79 tff(9904,plain,
% 3.54/3.79 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[7299, 41, 9903])).
% 3.54/3.79 tff(9905,plain,
% 3.54/3.79 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[9904, 7579])).
% 3.54/3.79 tff(9906,plain,
% 3.54/3.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 3.54/3.79 inference(rewrite,[status(thm)],[])).
% 3.54/3.79 tff(9907,plain,
% 3.54/3.79 (((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 3.54/3.79 inference(rewrite,[status(thm)],[])).
% 3.54/3.79 tff(9908,plain,
% 3.54/3.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 3.54/3.79 inference(monotonicity,[status(thm)],[9907])).
% 3.54/3.79 tff(9909,plain,
% 3.54/3.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 3.54/3.79 inference(transitivity,[status(thm)],[9908, 9906])).
% 3.54/3.79 tff(9910,plain,
% 3.54/3.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), z)))),
% 3.54/3.79 inference(quant_inst,[status(thm)],[])).
% 3.54/3.79 tff(9911,plain,
% 3.54/3.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[9910, 9909])).
% 3.54/3.79 tff(9912,plain,
% 3.54/3.79 ($false),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[9911, 118, 194, 9905, 9896])).
% 3.54/3.79 tff(9913,plain,((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), z)) | (~(s(elem!1) = s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.79 tff(9914,plain,
% 3.54/3.79 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[9913, 9610, 194, 5619, 9571, 9670, 356, 9640, 9885, 9882])).
% 3.54/3.79 tff(9915,plain,
% 3.54/3.79 (~b(elem!1, s(s(s(elem!1))))),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[6974, 9914, 9610])).
% 3.54/3.79 tff(9916,plain,
% 3.54/3.79 (r(elem!1, s(s(s(elem!1))))),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[2054, 9915, 9624])).
% 3.54/3.79 tff(9917,plain,
% 3.54/3.79 (~r(elem!1, z)),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[6086, 9916, 9571, 9670, 9610, 5619])).
% 3.54/3.79 tff(9918,plain,
% 3.54/3.79 (b(elem!1, z)),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[498, 9917, 9621])).
% 3.54/3.79 tff(9919,plain,
% 3.54/3.79 (~b(z, s(s(s(s(s(s(z)))))))),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[6084, 178, 3461, 273, 6067, 9705])).
% 3.54/3.79 tff(9920,plain,
% 3.54/3.79 (~b(z, s(s(s(elem!1))))),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[9919, 7251])).
% 3.54/3.79 tff(9921,plain,
% 3.54/3.79 (r(z, s(s(s(elem!1))))),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[2095, 9920])).
% 3.54/3.79 tff(9922,plain,
% 3.54/3.79 (~r(z, elem!1)),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[3319, 9921, 3311])).
% 3.54/3.79 tff(9923,plain,
% 3.54/3.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 3.54/3.79 inference(rewrite,[status(thm)],[])).
% 3.54/3.79 tff(9924,plain,
% 3.54/3.79 (((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 3.54/3.79 inference(rewrite,[status(thm)],[])).
% 3.54/3.79 tff(9925,plain,
% 3.54/3.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 3.54/3.79 inference(monotonicity,[status(thm)],[9924])).
% 3.54/3.79 tff(9926,plain,
% 3.54/3.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 3.54/3.79 inference(transitivity,[status(thm)],[9925, 9923])).
% 3.54/3.79 tff(9927,plain,
% 3.54/3.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 3.54/3.79 inference(quant_inst,[status(thm)],[])).
% 3.54/3.79 tff(9928,plain,
% 3.54/3.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[9927, 9926])).
% 3.54/3.79 tff(9929,plain,
% 3.54/3.79 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[9928, 178, 3461, 6067, 6170, 7206, 7252, 9705])).
% 3.54/3.79 tff(9930,plain,
% 3.54/3.79 (~b(s(elem!1), s(s(s(elem!1))))),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[9929, 7248])).
% 3.54/3.79 tff(9931,plain,
% 3.54/3.79 (r(s(elem!1), s(s(s(elem!1))))),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[5432, 9930, 5425])).
% 3.54/3.79 tff(9932,plain,
% 3.54/3.79 (~b(z, elem!1)),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[5423, 9931, 3311, 725, 9921, 506])).
% 3.54/3.79 tff(9933,plain,
% 3.54/3.79 ($false),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[585, 9932, 9922, 507])).
% 3.54/3.79 tff(9934,plain,((~b(s(s(s(s(s(s(z)))))), z)) | (z = elem!1) | (~r(elem!1, s(s(s(elem!1))))) | (s(elem!1) = elem!1) | (~b(elem!1, z)) | (s(elem!1) = s(s(s(elem!1)))) | (~(s(elem!1) = s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.79 tff(9935,plain,
% 3.54/3.79 (~b(s(s(s(s(s(s(z)))))), z)),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[9934, 9622, 9916, 1548, 9918, 5396, 9610, 5619, 9670, 9885, 9882, 9571])).
% 3.54/3.79 tff(9936,plain,
% 3.54/3.79 (~b(s(s(s(elem!1))), z)),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[9935, 9617])).
% 3.54/3.79 tff(9937,plain,
% 3.54/3.79 (r(s(s(s(elem!1))), z)),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[1565, 9936])).
% 3.54/3.79 tff(9938,plain,
% 3.54/3.79 (r(s(s(s(s(s(s(z)))))), z)),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[9937, 9615])).
% 3.54/3.79 tff(9939,plain,
% 3.54/3.79 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[7295, 9938])).
% 3.54/3.79 tff(9940,plain,
% 3.54/3.79 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 3.54/3.79 inference(monotonicity,[status(thm)],[9612, 9610])).
% 3.54/3.79 tff(9941,plain,
% 3.54/3.79 (r(s(elem!1), z) <=> r(s(s(s(s(z)))), z)),
% 3.54/3.79 inference(monotonicity,[status(thm)],[9610])).
% 3.54/3.79 tff(9942,plain,
% 3.54/3.79 (r(s(s(s(s(z)))), z) <=> r(s(elem!1), z)),
% 3.54/3.79 inference(symmetry,[status(thm)],[9941])).
% 3.54/3.79 tff(9943,plain,
% 3.54/3.79 (r(s(elem!1), z)),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[194, 9942])).
% 3.54/3.79 tff(9944,plain,
% 3.54/3.79 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[1557, 9937, 9943])).
% 3.54/3.79 tff(9945,plain,
% 3.54/3.79 (b(s(s(s(elem!1))), s(elem!1))),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[373, 9944, 356])).
% 3.54/3.79 tff(9946,plain,
% 3.54/3.79 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[9945, 9940])).
% 3.54/3.79 tff(9947,plain,
% 3.54/3.79 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[6323, 178, 9946, 9640, 9885, 9882])).
% 3.54/3.79 tff(9948,plain,
% 3.54/3.79 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[7299, 41, 9947])).
% 3.54/3.79 tff(9949,plain,
% 3.54/3.79 (s(s(s(s(z)))) = s(s(s(s(s(s(z))))))),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[9948, 9939])).
% 3.54/3.79 tff(9950,plain,
% 3.54/3.79 (s(s(s(s(s(s(z)))))) = s(s(s(s(z))))),
% 3.54/3.79 inference(symmetry,[status(thm)],[9949])).
% 3.54/3.79 tff(9951,plain,
% 3.54/3.79 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 3.54/3.79 inference(transitivity,[status(thm)],[9612, 9950])).
% 3.54/3.79 tff(9952,plain,
% 3.54/3.79 (s(s(s(s(z)))) = s(elem!1)),
% 3.54/3.79 inference(symmetry,[status(thm)],[9610])).
% 3.54/3.79 tff(9953,plain,
% 3.54/3.79 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 3.54/3.79 inference(monotonicity,[status(thm)],[9952])).
% 3.54/3.79 tff(9954,plain,
% 3.54/3.79 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.54/3.79 inference(symmetry,[status(thm)],[9953])).
% 3.54/3.79 tff(9955,plain,
% 3.54/3.79 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(s(s(elem!1))) = s(s(s(s(z))))))),
% 3.54/3.79 inference(monotonicity,[status(thm)],[9954])).
% 3.54/3.79 tff(9956,plain,
% 3.54/3.79 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[356, 9955])).
% 3.54/3.79 tff(9957,plain,
% 3.54/3.79 ($false),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[9956, 9951])).
% 3.54/3.79 tff(9958,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (s(s(s(elem!1))) = s(elem!1)) | b(elem!1, s(s(z))) | b(s(elem!1), s(s(s(s(z))))) | r(s(s(z)), z) | r(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.54/3.79 tff(9959,plain,
% 3.54/3.79 (~r(s(s(s(s(z)))), s(s(z)))),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[9958, 5618, 356, 461, 5720, 3244, 744])).
% 3.54/3.79 tff(9960,plain,
% 3.54/3.79 (b(s(s(s(s(z)))), s(s(z)))),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[102, 9959])).
% 3.54/3.79 tff(9961,plain,
% 3.54/3.79 (r(elem!1, s(s(s(s(z)))))),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[7818, 9960, 744, 461, 5720, 3170, 5618, 356])).
% 3.54/3.79 tff(9962,plain,
% 3.54/3.79 (r(s(elem!1), s(s(s(s(z)))))),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[1084, 1369, 5720])).
% 3.54/3.79 tff(9963,plain,
% 3.54/3.79 (~r(s(elem!1), z)),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[916, 9962, 194])).
% 3.54/3.79 tff(9964,plain,
% 3.54/3.79 (b(s(elem!1), z)),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[774, 9963])).
% 3.54/3.79 tff(9965,plain,
% 3.54/3.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 3.54/3.79 inference(rewrite,[status(thm)],[])).
% 3.54/3.79 tff(9966,plain,
% 3.54/3.79 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 3.54/3.79 inference(rewrite,[status(thm)],[])).
% 3.54/3.79 tff(9967,plain,
% 3.54/3.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 3.54/3.79 inference(monotonicity,[status(thm)],[9966])).
% 3.54/3.79 tff(9968,plain,
% 3.54/3.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 3.54/3.79 inference(transitivity,[status(thm)],[9967, 9965])).
% 3.54/3.79 tff(9969,plain,
% 3.54/3.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)))),
% 3.54/3.79 inference(quant_inst,[status(thm)],[])).
% 3.54/3.79 tff(9970,plain,
% 3.54/3.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[9969, 9968])).
% 3.54/3.79 tff(9971,plain,
% 3.54/3.79 (~r(s(elem!1), elem!1)),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[9970, 118, 470, 9962])).
% 3.54/3.80 tff(9972,plain,
% 3.54/3.80 (b(s(elem!1), elem!1)),
% 3.54/3.80 inference(unit_resolution,[status(thm)],[677, 9971, 1548])).
% 3.54/3.80 tff(9973,plain,
% 3.54/3.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 3.54/3.80 inference(rewrite,[status(thm)],[])).
% 3.54/3.80 tff(9974,plain,
% 3.54/3.80 (((~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 3.54/3.80 inference(rewrite,[status(thm)],[])).
% 3.54/3.80 tff(9975,plain,
% 3.54/3.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z))))))))),
% 3.54/3.80 inference(monotonicity,[status(thm)],[9974])).
% 3.54/3.80 tff(9976,plain,
% 3.54/3.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 3.54/3.80 inference(transitivity,[status(thm)],[9975, 9973])).
% 3.54/3.80 tff(9977,plain,
% 3.54/3.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 3.54/3.80 inference(quant_inst,[status(thm)],[])).
% 3.54/3.80 tff(9978,plain,
% 3.54/3.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z))))))),
% 3.54/3.80 inference(modus_ponens,[status(thm)],[9977, 9976])).
% 3.54/3.80 tff(9979,plain,
% 3.54/3.80 ($false),
% 3.54/3.80 inference(unit_resolution,[status(thm)],[9978, 118, 437, 194, 470])).
% 3.64/3.80 tff(9980,plain,((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.80 tff(9981,plain,
% 3.64/3.80 (~r(elem!1, z)),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[9980, 470, 194])).
% 3.64/3.80 tff(9982,plain,
% 3.64/3.80 (~r(s(s(s(s(z)))), s(s(z)))),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[9958, 5618, 356, 461, 5720, 194, 744])).
% 3.64/3.80 tff(9983,plain,
% 3.64/3.80 (b(s(s(s(s(z)))), s(s(z)))),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[102, 9982])).
% 3.64/3.80 tff(9984,plain,
% 3.64/3.80 (r(z, s(s(s(z)))) <=> r(z, s(elem!1))),
% 3.64/3.80 inference(monotonicity,[status(thm)],[7036])).
% 3.64/3.80 tff(9985,plain,
% 3.64/3.80 (r(z, s(elem!1)) <=> r(z, s(s(s(z))))),
% 3.64/3.80 inference(symmetry,[status(thm)],[9984])).
% 3.64/3.80 tff(9986,plain,
% 3.64/3.80 (b(s(elem!1), s(s(z)))),
% 3.64/3.80 inference(modus_ponens,[status(thm)],[683, 7046])).
% 3.64/3.80 tff(9987,plain,
% 3.64/3.80 (b(s(s(s(z))), s(s(z)))),
% 3.64/3.80 inference(modus_ponens,[status(thm)],[9986, 7045])).
% 3.64/3.80 tff(9988,plain,
% 3.64/3.80 (b(s(s(s(z))), z)),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[7042, 308, 853])).
% 3.64/3.80 tff(9989,plain,
% 3.64/3.80 (b(s(s(z)), s(elem!1))),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[1337, 6634, 725, 744])).
% 3.64/3.80 tff(9990,plain,
% 3.64/3.80 (b(s(s(z)), s(s(s(z))))),
% 3.64/3.80 inference(modus_ponens,[status(thm)],[9989, 7059])).
% 3.64/3.80 tff(9991,plain,
% 3.64/3.80 (~b(z, s(s(s(z))))),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[5098, 9990, 9988, 9987, 3461])).
% 3.64/3.80 tff(9992,plain,
% 3.64/3.80 (~b(z, s(elem!1))),
% 3.64/3.80 inference(modus_ponens,[status(thm)],[9991, 7158])).
% 3.64/3.80 tff(9993,plain,
% 3.64/3.80 (r(z, s(elem!1))),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[2351, 9992])).
% 3.64/3.80 tff(9994,plain,
% 3.64/3.80 (r(z, s(s(s(z))))),
% 3.64/3.80 inference(modus_ponens,[status(thm)],[9993, 9985])).
% 3.64/3.80 tff(9995,plain,
% 3.64/3.80 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 3.64/3.80 inference(monotonicity,[status(thm)],[5636])).
% 3.64/3.80 tff(9996,plain,
% 3.64/3.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 3.64/3.80 inference(rewrite,[status(thm)],[])).
% 3.64/3.80 tff(9997,plain,
% 3.64/3.80 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 3.64/3.80 inference(rewrite,[status(thm)],[])).
% 3.64/3.80 tff(9998,plain,
% 3.64/3.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 3.64/3.80 inference(monotonicity,[status(thm)],[9997])).
% 3.64/3.80 tff(9999,plain,
% 3.64/3.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 3.64/3.80 inference(transitivity,[status(thm)],[9998, 9996])).
% 3.64/3.80 tff(10000,plain,
% 3.64/3.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 3.64/3.80 inference(quant_inst,[status(thm)],[])).
% 3.64/3.80 tff(10001,plain,
% 3.64/3.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 3.64/3.80 inference(modus_ponens,[status(thm)],[10000, 9999])).
% 3.64/3.80 tff(10002,plain,
% 3.64/3.80 ((~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[10001, 178, 853, 3461, 202])).
% 3.64/3.80 tff(10003,plain,
% 3.64/3.80 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[10002, 9986])).
% 3.64/3.80 tff(10004,plain,
% 3.64/3.80 (r(s(s(s(s(z)))), s(elem!1))),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[2173, 10003, 2508])).
% 3.64/3.80 tff(10005,plain,
% 3.64/3.80 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.64/3.80 inference(modus_ponens,[status(thm)],[10004, 9995])).
% 3.64/3.80 tff(10006,plain,
% 3.64/3.80 ($false),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[4959, 118, 194, 10005, 9994])).
% 3.64/3.80 tff(10007,plain,((~(elem!1 = s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (s(s(s(s(z)))) = s(elem!1)) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(elem!1), elem!1)) | (s(elem!1) = elem!1) | r(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.80 tff(10008,plain,
% 3.64/3.80 (~(elem!1 = s(s(z)))),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[10007, 2169, 194, 5619, 9964, 9983, 9972, 1548, 744])).
% 3.64/3.80 tff(10009,plain,
% 3.64/3.80 (r(elem!1, s(s(z)))),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[467, 10008, 461])).
% 3.64/3.80 tff(10010,plain,
% 3.64/3.80 (~(s(elem!1) = s(s(z)))),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[1047, 10009, 744])).
% 3.64/3.80 tff(10011,plain,
% 3.64/3.80 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[6776, 273, 3461, 908, 1056, 6752])).
% 3.64/3.80 tff(10012,plain,
% 3.64/3.80 (b(s(s(z)), s(s(s(s(z)))))),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[164, 10011])).
% 3.64/3.80 tff(10013,plain,
% 3.64/3.80 (b(elem!1, z)),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[498, 3873, 1342])).
% 3.64/3.80 tff(10014,plain,
% 3.64/3.80 (~r(z, s(s(s(s(z)))))),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[7485, 10013, 461, 725, 3461, 744, 908, 273, 194])).
% 3.64/3.80 tff(10015,plain,
% 3.64/3.80 (b(z, s(s(s(s(z)))))),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[46, 10014])).
% 3.64/3.80 tff(10016,plain,
% 3.64/3.80 ($false),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[6228, 178, 3461, 273, 10015, 10012, 202])).
% 3.64/3.80 tff(10017,plain,((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | b(elem!1, s(s(z))) | (s(elem!1) = elem!1) | r(elem!1, s(elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | r(elem!1, z) | (s(elem!1) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.80 tff(10018,plain,
% 3.64/3.80 (~b(z, s(s(z)))),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[10017, 9962, 9983, 461, 1548, 744, 5619, 194, 9981, 10010])).
% 3.64/3.80 tff(10019,plain,
% 3.64/3.80 (r(z, s(s(z)))),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[143, 10018])).
% 3.64/3.80 tff(10020,plain,
% 3.64/3.80 (b(s(elem!1), z)),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[774, 767])).
% 3.64/3.80 tff(10021,plain,
% 3.64/3.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 3.64/3.80 inference(rewrite,[status(thm)],[])).
% 3.64/3.80 tff(10022,plain,
% 3.64/3.80 (((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 3.64/3.80 inference(rewrite,[status(thm)],[])).
% 3.64/3.80 tff(10023,plain,
% 3.64/3.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(elem!1)))))))),
% 3.64/3.80 inference(monotonicity,[status(thm)],[10022])).
% 3.64/3.80 tff(10024,plain,
% 3.64/3.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 3.64/3.80 inference(transitivity,[status(thm)],[10023, 10021])).
% 3.64/3.80 tff(10025,plain,
% 3.64/3.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 3.64/3.80 inference(quant_inst,[status(thm)],[])).
% 3.64/3.80 tff(10026,plain,
% 3.64/3.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(elem!1)))))),
% 3.64/3.80 inference(modus_ponens,[status(thm)],[10025, 10024])).
% 3.64/3.80 tff(10027,plain,
% 3.64/3.80 ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[10026, 178, 854, 7976, 10020])).
% 3.64/3.80 tff(10028,plain,
% 3.64/3.80 (~b(elem!1, s(s(s(elem!1))))),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[10027, 2044])).
% 3.64/3.80 tff(10029,plain,
% 3.64/3.80 (elem!1 = s(s(s(elem!1)))),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[2054, 10028, 4512])).
% 3.64/3.80 tff(10030,plain,
% 3.64/3.80 (s(elem!1) = s(s(s(s(elem!1))))),
% 3.64/3.80 inference(monotonicity,[status(thm)],[10029])).
% 3.64/3.80 tff(10031,plain,
% 3.64/3.80 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.64/3.80 inference(monotonicity,[status(thm)],[10030])).
% 3.64/3.80 tff(10032,plain,
% 3.64/3.80 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(elem!1))))),
% 3.64/3.80 inference(monotonicity,[status(thm)],[10029])).
% 3.64/3.80 tff(10033,plain,
% 3.64/3.80 (b(s(elem!1), s(s(s(elem!1))))),
% 3.64/3.80 inference(modus_ponens,[status(thm)],[683, 10032])).
% 3.64/3.80 tff(10034,plain,
% 3.64/3.80 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.64/3.80 inference(modus_ponens,[status(thm)],[10033, 10031])).
% 3.64/3.80 tff(10035,plain,
% 3.64/3.80 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.64/3.80 inference(monotonicity,[status(thm)],[10030])).
% 3.64/3.80 tff(10036,plain,
% 3.64/3.80 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.64/3.80 inference(modus_ponens,[status(thm)],[2044, 10035])).
% 3.64/3.80 tff(10037,plain,
% 3.64/3.80 (~r(s(s(s(s(elem!1)))), z)),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[3991, 10029, 767])).
% 3.64/3.80 tff(10038,plain,
% 3.64/3.80 (b(s(s(s(s(elem!1)))), z)),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[1716, 10037])).
% 3.64/3.80 tff(10039,plain,
% 3.64/3.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 3.64/3.80 inference(rewrite,[status(thm)],[])).
% 3.64/3.80 tff(10040,plain,
% 3.64/3.80 (((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 3.64/3.80 inference(rewrite,[status(thm)],[])).
% 3.64/3.80 tff(10041,plain,
% 3.64/3.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 3.64/3.80 inference(monotonicity,[status(thm)],[10040])).
% 3.64/3.80 tff(10042,plain,
% 3.64/3.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 3.64/3.80 inference(transitivity,[status(thm)],[10041, 10039])).
% 3.64/3.80 tff(10043,plain,
% 3.64/3.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 3.64/3.80 inference(quant_inst,[status(thm)],[])).
% 3.64/3.80 tff(10044,plain,
% 3.64/3.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 3.64/3.80 inference(modus_ponens,[status(thm)],[10043, 10042])).
% 3.64/3.80 tff(10045,plain,
% 3.64/3.80 ($false),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[10044, 178, 2043, 7976, 10038, 10036, 10034])).
% 3.64/3.80 tff(10046,plain,((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), elem!1)) | r(s(elem!1), z) | r(elem!1, s(s(s(elem!1)))) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.80 tff(10047,plain,
% 3.64/3.80 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[10046, 2043, 7976, 683, 767, 4512, 5725])).
% 3.64/3.80 tff(10048,plain,
% 3.64/3.80 (r(s(s(s(elem!1))), s(elem!1))),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[373, 10047, 356])).
% 3.64/3.80 tff(10049,plain,
% 3.64/3.80 (r(elem!1, s(elem!1)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 3.64/3.80 inference(monotonicity,[status(thm)],[1527])).
% 3.64/3.80 tff(10050,plain,
% 3.64/3.80 (r(s(s(s(elem!1))), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 3.64/3.80 inference(symmetry,[status(thm)],[10049])).
% 3.64/3.80 tff(10051,plain,
% 3.64/3.80 (r(elem!1, s(elem!1))),
% 3.64/3.80 inference(modus_ponens,[status(thm)],[1551, 10050])).
% 3.64/3.80 tff(10052,plain,
% 3.64/3.80 ($false),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[744, 10051])).
% 3.64/3.80 tff(10053,plain,((~r(s(s(s(elem!1))), s(elem!1))) | r(elem!1, s(elem!1)) | (~(elem!1 = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.80 tff(10054,plain,
% 3.64/3.80 (~(elem!1 = s(s(s(elem!1))))),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[10053, 10048, 744])).
% 3.64/3.80 tff(10055,plain,
% 3.64/3.80 (b(elem!1, s(s(s(elem!1))))),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[2054, 10054, 4512])).
% 3.64/3.80 tff(10056,plain,
% 3.64/3.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 3.64/3.80 inference(rewrite,[status(thm)],[])).
% 3.64/3.80 tff(10057,plain,
% 3.64/3.80 (((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 3.64/3.80 inference(rewrite,[status(thm)],[])).
% 3.64/3.80 tff(10058,plain,
% 3.64/3.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1)))))))),
% 3.64/3.80 inference(monotonicity,[status(thm)],[10057])).
% 3.64/3.80 tff(10059,plain,
% 3.64/3.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 3.64/3.80 inference(transitivity,[status(thm)],[10058, 10056])).
% 3.64/3.80 tff(10060,plain,
% 3.64/3.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)))),
% 3.64/3.80 inference(quant_inst,[status(thm)],[])).
% 3.64/3.80 tff(10061,plain,
% 3.64/3.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1)))))),
% 3.64/3.80 inference(modus_ponens,[status(thm)],[10060, 10059])).
% 3.64/3.80 tff(10062,plain,
% 3.64/3.80 (~b(elem!1, z)),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[10061, 178, 2043, 683, 10020, 10055])).
% 3.64/3.80 tff(10063,plain,
% 3.64/3.80 (elem!1 = z),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[498, 10062, 1342])).
% 3.64/3.80 tff(10064,plain,
% 3.64/3.80 (s(elem!1) = s(z)),
% 3.64/3.80 inference(monotonicity,[status(thm)],[10063])).
% 3.64/3.80 tff(10065,plain,
% 3.64/3.80 (s(z) = s(elem!1)),
% 3.64/3.80 inference(symmetry,[status(thm)],[10064])).
% 3.64/3.80 tff(10066,plain,
% 3.64/3.80 (r(s(s(z)), s(z)) <=> r(s(s(z)), s(elem!1))),
% 3.64/3.80 inference(monotonicity,[status(thm)],[10065])).
% 3.64/3.80 tff(10067,plain,
% 3.64/3.80 (r(s(s(z)), s(elem!1)) <=> r(s(s(z)), s(z))),
% 3.64/3.80 inference(symmetry,[status(thm)],[10066])).
% 3.64/3.80 tff(10068,plain,
% 3.64/3.80 (~(elem!1 = s(s(z)))),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[6641, 10062, 5618])).
% 3.64/3.80 tff(10069,plain,
% 3.64/3.80 (r(elem!1, s(s(z)))),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[467, 10068, 461])).
% 3.64/3.80 tff(10070,plain,
% 3.64/3.80 (~(s(elem!1) = s(s(z)))),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[1047, 10069, 744])).
% 3.64/3.80 tff(10071,plain,
% 3.64/3.80 (~(s(s(z)) = s(elem!1))),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[1058, 10070])).
% 3.64/3.80 tff(10072,plain,
% 3.64/3.80 (b(z, s(z)) <=> b(z, s(elem!1))),
% 3.64/3.80 inference(monotonicity,[status(thm)],[10065])).
% 3.64/3.80 tff(10073,plain,
% 3.64/3.80 (b(z, s(elem!1)) <=> b(z, s(z))),
% 3.64/3.80 inference(symmetry,[status(thm)],[10072])).
% 3.64/3.80 tff(10074,plain,
% 3.64/3.80 (~r(z, s(elem!1))),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[6201, 10063, 744])).
% 3.64/3.80 tff(10075,plain,
% 3.64/3.80 (b(z, s(elem!1))),
% 3.64/3.80 inference(unit_resolution,[status(thm)],[2351, 10074])).
% 3.64/3.80 tff(10076,plain,
% 3.64/3.80 (b(z, s(z))),
% 3.64/3.80 inference(modus_ponens,[status(thm)],[10075, 10073])).
% 3.64/3.80 tff(10077,plain,
% 3.64/3.80 (b(s(z), z) <=> b(s(elem!1), z)),
% 3.64/3.80 inference(monotonicity,[status(thm)],[10065])).
% 3.64/3.80 tff(10078,plain,
% 3.64/3.80 (b(s(elem!1), z) <=> b(s(z), z)),
% 3.64/3.80 inference(symmetry,[status(thm)],[10077])).
% 3.64/3.80 tff(10079,plain,
% 3.64/3.80 (b(s(z), z)),
% 3.64/3.80 inference(modus_ponens,[status(thm)],[10020, 10078])).
% 3.64/3.80 tff(10080,plain,
% 3.64/3.81 (s(s(elem!1)) = s(s(z))),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10064])).
% 3.64/3.81 tff(10081,plain,
% 3.64/3.81 (b(s(elem!1), s(s(elem!1))) <=> b(s(z), s(s(z)))),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10064, 10080])).
% 3.64/3.81 tff(10082,plain,
% 3.64/3.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 3.64/3.81 inference(rewrite,[status(thm)],[])).
% 3.64/3.81 tff(10083,plain,
% 3.64/3.81 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(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(elem!1, s(elem!1)))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 3.64/3.81 inference(rewrite,[status(thm)],[])).
% 3.64/3.81 tff(10084,plain,
% 3.64/3.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(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(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10083])).
% 3.64/3.81 tff(10085,plain,
% 3.64/3.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(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(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 3.64/3.81 inference(transitivity,[status(thm)],[10084, 10082])).
% 3.64/3.81 tff(10086,plain,
% 3.64/3.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(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(elem!1, s(elem!1))))),
% 3.64/3.81 inference(quant_inst,[status(thm)],[])).
% 3.64/3.81 tff(10087,plain,
% 3.64/3.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))),
% 3.64/3.81 inference(modus_ponens,[status(thm)],[10086, 10085])).
% 3.64/3.81 tff(10088,plain,
% 3.64/3.81 (~b(s(elem!1), s(s(s(elem!1))))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[10087, 178, 5725, 7976, 10020, 10055])).
% 3.64/3.81 tff(10089,plain,
% 3.64/3.81 (r(s(elem!1), s(s(s(elem!1))))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[5432, 10088, 5396])).
% 3.64/3.81 tff(10090,plain,
% 3.64/3.81 (z = elem!1),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[2808, 10063])).
% 3.64/3.81 tff(10091,plain,
% 3.64/3.81 (b(s(s(elem!1)), elem!1)),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[5878, 10090, 5619])).
% 3.64/3.81 tff(10092,plain,
% 3.64/3.81 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), z)),
% 3.64/3.81 inference(monotonicity,[status(thm)],[928])).
% 3.64/3.81 tff(10093,plain,
% 3.64/3.81 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 3.64/3.81 inference(symmetry,[status(thm)],[10092])).
% 3.64/3.81 tff(10094,plain,
% 3.64/3.81 (b(s(s(s(elem!1))), elem!1)),
% 3.64/3.81 inference(modus_ponens,[status(thm)],[7976, 10093])).
% 3.64/3.81 tff(10095,plain,
% 3.64/3.81 ($false),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[5308, 10094])).
% 3.64/3.81 tff(10096,plain,((~(elem!1 = z)) | b(s(s(s(elem!1))), elem!1) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.81 tff(10097,plain,
% 3.64/3.81 (b(s(s(s(elem!1))), elem!1)),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[10096, 10063, 7976])).
% 3.64/3.81 tff(10098,plain,
% 3.64/3.81 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[5980, 5972, 1551])).
% 3.64/3.81 tff(10099,plain,
% 3.64/3.81 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[3409, 10098, 6444])).
% 3.64/3.81 tff(10100,plain,
% 3.64/3.81 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[5994, 5972, 2102])).
% 3.64/3.81 tff(10101,plain,
% 3.64/3.81 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[3375, 10100, 1655])).
% 3.64/3.81 tff(10102,plain,
% 3.64/3.81 ($false),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[5500, 10101, 10099, 1597, 2042, 5434])).
% 3.64/3.81 tff(10103,plain,((~r(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.81 tff(10104,plain,
% 3.64/3.81 (~r(s(elem!1), s(s(elem!1)))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[10103, 10097, 10055, 10091, 1650, 10089, 10048])).
% 3.64/3.81 tff(10105,plain,
% 3.64/3.81 (b(s(elem!1), s(s(elem!1)))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[1028, 10104, 5389])).
% 3.64/3.81 tff(10106,plain,
% 3.64/3.81 (b(s(z), s(s(z)))),
% 3.64/3.81 inference(modus_ponens,[status(thm)],[10105, 10081])).
% 3.64/3.81 tff(10107,plain,
% 3.64/3.81 (b(s(s(z)), s(z)) <=> b(s(s(z)), s(elem!1))),
% 3.64/3.81 inference(monotonicity,[status(thm)],[6683])).
% 3.64/3.81 tff(10108,plain,
% 3.64/3.81 (b(s(s(z)), s(elem!1)) <=> b(s(s(z)), s(z))),
% 3.64/3.81 inference(symmetry,[status(thm)],[10107])).
% 3.64/3.81 tff(10109,plain,
% 3.64/3.81 (b(s(s(z)), s(z))),
% 3.64/3.81 inference(modus_ponens,[status(thm)],[1071, 10108])).
% 3.64/3.81 tff(10110,assumption,(b(s(z), s(s(z)))), introduced(assumption)).
% 3.64/3.81 tff(10111,plain,
% 3.64/3.81 ($false),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[6676, 178, 3461, 10110, 1791, 1790, 10109])).
% 3.64/3.81 tff(10112,plain,((~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(elem!1))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.81 tff(10113,plain,
% 3.64/3.81 (~b(s(s(z)), s(elem!1))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[10112, 10106, 10079, 10076, 5619, 10063])).
% 3.64/3.81 tff(10114,plain,
% 3.64/3.81 (r(s(s(z)), s(elem!1))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[1067, 10113, 10071])).
% 3.64/3.81 tff(10115,plain,
% 3.64/3.81 (r(s(s(z)), s(z))),
% 3.64/3.81 inference(modus_ponens,[status(thm)],[10114, 10067])).
% 3.64/3.81 tff(10116,plain,
% 3.64/3.81 (s(s(s(elem!1))) = s(s(s(z)))),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10080])).
% 3.64/3.81 tff(10117,plain,
% 3.64/3.81 (s(s(s(z))) = s(s(s(elem!1)))),
% 3.64/3.81 inference(symmetry,[status(thm)],[10116])).
% 3.64/3.81 tff(10118,plain,
% 3.64/3.81 (r(s(z), s(s(s(z)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10065, 10117])).
% 3.64/3.81 tff(10119,plain,
% 3.64/3.81 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(z), s(s(s(z))))),
% 3.64/3.81 inference(symmetry,[status(thm)],[10118])).
% 3.64/3.81 tff(10120,plain,
% 3.64/3.81 (r(s(z), s(s(s(z))))),
% 3.64/3.81 inference(modus_ponens,[status(thm)],[10089, 10119])).
% 3.64/3.81 tff(10121,plain,
% 3.64/3.81 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10117])).
% 3.64/3.81 tff(10122,plain,
% 3.64/3.81 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(z))))),
% 3.64/3.81 inference(symmetry,[status(thm)],[10121])).
% 3.64/3.81 tff(10123,plain,
% 3.64/3.81 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10080])).
% 3.64/3.81 tff(10124,plain,
% 3.64/3.81 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(z))))),
% 3.64/3.81 inference(transitivity,[status(thm)],[10123, 10122])).
% 3.64/3.81 tff(10125,plain,
% 3.64/3.81 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[5490, 10105, 10055, 683, 10091])).
% 3.64/3.81 tff(10126,plain,
% 3.64/3.81 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[3375, 10125, 1650])).
% 3.64/3.81 tff(10127,plain,
% 3.64/3.81 (r(s(s(z)), s(s(s(z))))),
% 3.64/3.81 inference(modus_ponens,[status(thm)],[10126, 10124])).
% 3.64/3.81 tff(10128,plain,
% 3.64/3.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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))))))),
% 3.64/3.81 inference(rewrite,[status(thm)],[])).
% 3.64/3.81 tff(10129,plain,
% 3.64/3.81 (((~r(s(z), s(s(s(z))))) | (~r(s(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))))))),
% 3.64/3.81 inference(rewrite,[status(thm)],[])).
% 3.64/3.81 tff(10130,plain,
% 3.64/3.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))))),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10129])).
% 3.64/3.81 tff(10131,plain,
% 3.64/3.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 3.64/3.81 inference(transitivity,[status(thm)],[10130, 10128])).
% 3.64/3.81 tff(10132,plain,
% 3.64/3.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 3.64/3.81 inference(quant_inst,[status(thm)],[])).
% 3.64/3.81 tff(10133,plain,
% 3.64/3.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 3.64/3.81 inference(modus_ponens,[status(thm)],[10132, 10131])).
% 3.64/3.81 tff(10134,plain,
% 3.64/3.81 (~r(s(s(z)), s(z))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[10133, 118, 10127, 10120])).
% 3.64/3.81 tff(10135,plain,
% 3.64/3.81 ($false),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[10134, 10115])).
% 3.64/3.81 tff(10136,plain,((~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | r(elem!1, s(elem!1)) | (~b(s(s(s(elem!1))), z)) | b(elem!1, s(s(z))) | r(elem!1, z) | r(s(s(z)), z) | r(elem!1, s(s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1)) | r(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 3.64/3.81 tff(10137,plain,
% 3.64/3.81 (~b(z, s(s(s(elem!1))))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[10136, 7976, 744, 683, 461, 1342, 5618, 4512, 356, 767])).
% 3.64/3.81 tff(10138,plain,
% 3.64/3.81 (r(z, s(s(s(elem!1))))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[2095, 10137])).
% 3.64/3.81 tff(10139,plain,
% 3.64/3.81 (~(elem!1 = z)),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[4850, 10138, 4512])).
% 3.64/3.81 tff(10140,plain,
% 3.64/3.81 (~(z = elem!1)),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[317, 10139])).
% 3.64/3.81 tff(10141,plain,
% 3.64/3.81 (b(elem!1, z)),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[498, 10139, 1342])).
% 3.64/3.81 tff(10142,plain,
% 3.64/3.81 (~(elem!1 = s(s(s(elem!1))))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[4868, 10140, 3261, 461, 10137])).
% 3.64/3.81 tff(10143,plain,
% 3.64/3.81 (b(elem!1, s(s(s(elem!1))))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[2054, 10142, 4512])).
% 3.64/3.81 tff(10144,plain,
% 3.64/3.81 ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[10026, 178, 5725, 7976, 10020])).
% 3.64/3.81 tff(10145,plain,
% 3.64/3.81 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[10144, 10143])).
% 3.64/3.81 tff(10146,plain,
% 3.64/3.81 (r(s(s(s(elem!1))), s(elem!1))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[373, 10145, 356])).
% 3.64/3.81 tff(10147,plain,
% 3.64/3.81 (~r(z, s(elem!1))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[5447, 10146, 10138])).
% 3.64/3.81 tff(10148,plain,
% 3.64/3.81 (b(z, s(elem!1))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[2351, 10147])).
% 3.64/3.81 tff(10149,plain,
% 3.64/3.81 (~b(z, elem!1)),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[863, 10148, 10020, 5725, 10141])).
% 3.64/3.81 tff(10150,plain,
% 3.64/3.81 (r(z, elem!1)),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[585, 10149, 10140])).
% 3.64/3.81 tff(10151,plain,
% 3.64/3.81 (~r(elem!1, s(s(z)))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[4862, 10150, 3261])).
% 3.64/3.81 tff(10152,plain,
% 3.64/3.81 (elem!1 = s(s(z))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[467, 10151, 461])).
% 3.64/3.81 tff(10153,plain,
% 3.64/3.81 (s(elem!1) = s(s(s(z)))),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10152])).
% 3.64/3.81 tff(10154,plain,
% 3.64/3.81 (s(s(s(z))) = s(elem!1)),
% 3.64/3.81 inference(symmetry,[status(thm)],[10153])).
% 3.64/3.81 tff(10155,plain,
% 3.64/3.81 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), s(elem!1))),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10154])).
% 3.64/3.81 tff(10156,plain,
% 3.64/3.81 (b(s(s(z)), s(elem!1)) <=> b(s(s(z)), s(s(s(z))))),
% 3.64/3.81 inference(symmetry,[status(thm)],[10155])).
% 3.64/3.81 tff(10157,plain,
% 3.64/3.81 (s(s(z)) = elem!1),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[311, 10152])).
% 3.64/3.81 tff(10158,plain,
% 3.64/3.81 (b(s(s(z)), s(elem!1))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[1337, 10157, 1548, 744])).
% 3.64/3.81 tff(10159,plain,
% 3.64/3.81 (b(s(s(z)), s(s(s(z))))),
% 3.64/3.81 inference(modus_ponens,[status(thm)],[10158, 10156])).
% 3.64/3.81 tff(10160,plain,
% 3.64/3.81 (b(z, s(elem!1)) <=> b(z, s(s(s(z))))),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10153])).
% 3.64/3.81 tff(10161,plain,
% 3.64/3.81 (b(z, s(s(s(z))))),
% 3.64/3.81 inference(modus_ponens,[status(thm)],[10148, 10160])).
% 3.64/3.81 tff(10162,plain,
% 3.64/3.81 (s(s(elem!1)) = s(s(s(s(z))))),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10153])).
% 3.64/3.81 tff(10163,plain,
% 3.64/3.81 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10162])).
% 3.64/3.81 tff(10164,plain,
% 3.64/3.81 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(s(z))))), z)),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10163])).
% 3.64/3.81 tff(10165,plain,
% 3.64/3.81 (b(s(s(s(s(s(z))))), z)),
% 3.64/3.81 inference(modus_ponens,[status(thm)],[7976, 10164])).
% 3.64/3.81 tff(10166,plain,
% 3.64/3.81 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 3.64/3.81 inference(symmetry,[status(thm)],[10163])).
% 3.64/3.81 tff(10167,plain,
% 3.64/3.81 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10166])).
% 3.64/3.81 tff(10168,plain,
% 3.64/3.81 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 3.64/3.81 inference(symmetry,[status(thm)],[10167])).
% 3.64/3.81 tff(10169,plain,
% 3.64/3.81 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(z)))),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10152])).
% 3.64/3.81 tff(10170,plain,
% 3.64/3.81 (~(s(s(s(elem!1))) = elem!1)),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[2489, 10142])).
% 3.64/3.81 tff(10171,plain,
% 3.64/3.81 (~r(s(s(s(elem!1))), elem!1)),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[565, 10150, 10138])).
% 3.64/3.81 tff(10172,plain,
% 3.64/3.81 (b(s(s(s(elem!1))), elem!1)),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[570, 10171, 10170])).
% 3.64/3.81 tff(10173,plain,
% 3.64/3.81 (b(s(s(s(elem!1))), s(s(z)))),
% 3.64/3.81 inference(modus_ponens,[status(thm)],[10172, 10169])).
% 3.64/3.81 tff(10174,plain,
% 3.64/3.81 (b(s(s(s(s(s(z))))), s(s(z)))),
% 3.64/3.81 inference(modus_ponens,[status(thm)],[10173, 10168])).
% 3.64/3.81 tff(10175,plain,
% 3.64/3.81 ($false),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[7151, 178, 5619, 10174, 10165, 10161, 10159])).
% 3.64/3.81 tff(10176,plain,((~b(s(s(s(elem!1))), z)) | r(elem!1, s(elem!1)) | b(elem!1, s(s(z))) | (~r(z, s(s(z)))) | (s(s(s(elem!1))) = s(elem!1)) | r(elem!1, s(s(s(elem!1)))) | r(elem!1, z) | (~b(s(elem!1), elem!1)) | r(s(s(z)), z) | r(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 3.64/3.81 tff(10177,plain,
% 3.64/3.81 (~b(s(s(s(elem!1))), z)),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[10176, 4512, 461, 3261, 356, 744, 9981, 683, 5618, 767])).
% 3.64/3.81 tff(10178,plain,
% 3.64/3.81 (r(s(s(s(elem!1))), z)),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[1565, 10177])).
% 3.64/3.81 tff(10179,plain,
% 3.64/3.81 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[7993, 118, 10178, 194])).
% 3.64/3.81 tff(10180,plain,
% 3.64/3.81 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[5340, 118, 10178, 194])).
% 3.64/3.81 tff(10181,plain,
% 3.64/3.81 (elem!1 = z),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[498, 5723, 1342])).
% 3.64/3.81 tff(10182,plain,
% 3.64/3.81 (s(elem!1) = s(z)),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10181])).
% 3.64/3.81 tff(10183,plain,
% 3.64/3.81 (s(s(elem!1)) = s(s(z))),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10182])).
% 3.64/3.81 tff(10184,plain,
% 3.64/3.81 (s(s(s(elem!1))) = s(s(s(z)))),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10183])).
% 3.64/3.81 tff(10185,plain,
% 3.64/3.81 (s(s(s(z))) = s(s(s(elem!1)))),
% 3.64/3.81 inference(symmetry,[status(thm)],[10184])).
% 3.64/3.81 tff(10186,plain,
% 3.64/3.81 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10185])).
% 3.64/3.81 tff(10187,plain,
% 3.64/3.81 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(z))), s(s(z)))),
% 3.64/3.81 inference(symmetry,[status(thm)],[10186])).
% 3.64/3.81 tff(10188,plain,
% 3.64/3.81 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10183])).
% 3.64/3.81 tff(10189,plain,
% 3.64/3.81 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(z)))),
% 3.64/3.81 inference(transitivity,[status(thm)],[10188, 10187])).
% 3.64/3.81 tff(10190,plain,
% 3.64/3.81 (r(elem!1, s(s(elem!1))) <=> r(z, s(s(elem!1)))),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10181])).
% 3.64/3.81 tff(10191,plain,
% 3.64/3.81 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 3.64/3.81 inference(symmetry,[status(thm)],[10190])).
% 3.64/3.81 tff(10192,plain,
% 3.64/3.81 (r(z, s(s(elem!1))) <=> r(z, s(s(z)))),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10183])).
% 3.64/3.81 tff(10193,plain,
% 3.64/3.81 (r(z, s(s(z))) <=> r(z, s(s(elem!1)))),
% 3.64/3.81 inference(symmetry,[status(thm)],[10192])).
% 3.64/3.81 tff(10194,plain,
% 3.64/3.81 (r(z, s(s(z))) <=> r(elem!1, s(s(elem!1)))),
% 3.64/3.81 inference(transitivity,[status(thm)],[10193, 10191])).
% 3.64/3.81 tff(10195,plain,
% 3.64/3.81 (r(elem!1, s(s(elem!1)))),
% 3.64/3.81 inference(modus_ponens,[status(thm)],[3261, 10194])).
% 3.64/3.81 tff(10196,plain,
% 3.64/3.81 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), z)),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10181])).
% 3.64/3.81 tff(10197,plain,
% 3.64/3.81 (r(s(s(s(elem!1))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 3.64/3.81 inference(symmetry,[status(thm)],[10196])).
% 3.64/3.81 tff(10198,plain,
% 3.64/3.81 (r(s(s(s(elem!1))), elem!1)),
% 3.64/3.81 inference(modus_ponens,[status(thm)],[1552, 10197])).
% 3.64/3.81 tff(10199,plain,
% 3.64/3.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.64/3.81 inference(rewrite,[status(thm)],[])).
% 3.64/3.81 tff(10200,plain,
% 3.64/3.81 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~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)))))),
% 3.64/3.81 inference(rewrite,[status(thm)],[])).
% 3.64/3.81 tff(10201,plain,
% 3.64/3.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))))),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10200])).
% 3.64/3.81 tff(10202,plain,
% 3.64/3.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.64/3.81 inference(transitivity,[status(thm)],[10201, 10199])).
% 3.64/3.81 tff(10203,plain,
% 3.64/3.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 3.64/3.81 inference(quant_inst,[status(thm)],[])).
% 3.64/3.81 tff(10204,plain,
% 3.64/3.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 3.64/3.81 inference(modus_ponens,[status(thm)],[10203, 10202])).
% 3.64/3.81 tff(10205,plain,
% 3.64/3.81 ($false),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[10204, 118, 556, 5227, 5816])).
% 3.64/3.81 tff(10206,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.81 tff(10207,plain,
% 3.64/3.81 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[10206, 10198, 10195])).
% 3.64/3.81 tff(10208,plain,
% 3.64/3.81 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[3409, 10207, 5222])).
% 3.64/3.81 tff(10209,plain,
% 3.64/3.81 (b(s(s(s(z))), s(s(z)))),
% 3.64/3.81 inference(modus_ponens,[status(thm)],[10208, 10189])).
% 3.64/3.81 tff(10210,plain,
% 3.64/3.81 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10184])).
% 3.64/3.81 tff(10211,plain,
% 3.64/3.81 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10210, 10184])).
% 3.64/3.81 tff(10212,plain,
% 3.64/3.81 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10210, 10184])).
% 3.64/3.81 tff(10213,plain,
% 3.64/3.81 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.64/3.81 inference(symmetry,[status(thm)],[10212])).
% 3.64/3.81 tff(10214,plain,
% 3.64/3.81 ((~r(s(s(s(s(z)))), s(s(s(z))))) <=> (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10213])).
% 3.64/3.81 tff(10215,plain,
% 3.64/3.81 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10184])).
% 3.64/3.81 tff(10216,plain,
% 3.64/3.81 ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10215])).
% 3.64/3.81 tff(10217,plain,
% 3.64/3.81 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.64/3.81 inference(modus_ponens,[status(thm)],[3293, 10216])).
% 3.64/3.81 tff(10218,plain,
% 3.64/3.81 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.64/3.81 inference(modus_ponens,[status(thm)],[10217, 10214])).
% 3.64/3.81 tff(10219,plain,
% 3.64/3.81 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[1988, 10218, 1693])).
% 3.64/3.81 tff(10220,plain,
% 3.64/3.81 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.64/3.81 inference(modus_ponens,[status(thm)],[10219, 10211])).
% 3.64/3.81 tff(10221,plain,
% 3.64/3.81 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10184])).
% 3.64/3.81 tff(10222,plain,
% 3.64/3.81 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[2840, 6750])).
% 3.64/3.81 tff(10223,plain,
% 3.64/3.81 ((s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[3825, 41, 4171])).
% 3.64/3.81 tff(10224,plain,
% 3.64/3.81 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[10223, 10222])).
% 3.64/3.81 tff(10225,plain,
% 3.64/3.81 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.64/3.81 inference(modus_ponens,[status(thm)],[10224, 10221])).
% 3.64/3.81 tff(10226,plain,
% 3.64/3.81 (r(elem!1, s(s(s(s(z))))) <=> r(z, s(s(s(s(z)))))),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10181])).
% 3.64/3.81 tff(10227,plain,
% 3.64/3.81 (r(z, s(s(s(s(z)))))),
% 3.64/3.81 inference(modus_ponens,[status(thm)],[470, 10226])).
% 3.64/3.81 tff(10228,plain,
% 3.64/3.81 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[3478, 10227, 3261])).
% 3.64/3.81 tff(10229,plain,
% 3.64/3.81 (b(s(s(z)), s(s(s(s(z)))))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[164, 10228])).
% 3.64/3.81 tff(10230,plain,
% 3.64/3.81 ($false),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[4944, 178, 10229, 202, 10225, 10220, 10209])).
% 3.64/3.81 tff(10231,plain,(b(elem!1, z) | (~b(s(s(s(s(z)))), s(s(z)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(z, s(s(z)))) | r(s(s(s(s(z)))), s(s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), z)) | r(s(s(s(elem!1))), s(s(s(s(z))))) | r(elem!1, s(elem!1)) | b(elem!1, s(s(z))) | r(elem!1, z) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 3.64/3.81 tff(10232,plain,
% 3.64/3.81 (b(elem!1, z)),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[10231, 10180, 5807, 1658, 3261, 202, 470, 10178, 10179, 744, 461, 9981, 5618])).
% 3.64/3.81 tff(10233,plain,
% 3.64/3.81 (~b(z, elem!1)),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[2429, 10232, 683, 5725, 10020])).
% 3.64/3.81 tff(10234,plain,
% 3.64/3.81 (~(z = elem!1)),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[6991, 10232])).
% 3.64/3.81 tff(10235,plain,
% 3.64/3.81 (r(z, elem!1)),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[585, 10234, 10233])).
% 3.64/3.81 tff(10236,plain,
% 3.64/3.81 (~r(elem!1, s(s(z)))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[4862, 10235, 3261])).
% 3.64/3.81 tff(10237,plain,
% 3.64/3.81 (elem!1 = s(s(z))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[467, 10236, 461])).
% 3.64/3.81 tff(10238,plain,
% 3.64/3.81 (s(elem!1) = s(s(s(z)))),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10237])).
% 3.64/3.81 tff(10239,plain,
% 3.64/3.81 (s(s(elem!1)) = s(s(s(s(z))))),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10238])).
% 3.64/3.81 tff(10240,plain,
% 3.64/3.81 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10239])).
% 3.64/3.81 tff(10241,plain,
% 3.64/3.81 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(s(s(z))))))),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10240])).
% 3.64/3.81 tff(10242,plain,
% 3.64/3.81 (~(elem!1 = z)),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[4850, 3243, 4512])).
% 3.64/3.81 tff(10243,plain,
% 3.64/3.81 (~(z = elem!1)),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[317, 10242])).
% 3.64/3.81 tff(10244,plain,
% 3.64/3.81 (b(elem!1, z)),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[498, 10242, 1342])).
% 3.64/3.81 tff(10245,plain,
% 3.64/3.81 (~b(z, elem!1)),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[2429, 10244, 683, 5725, 853])).
% 3.64/3.81 tff(10246,plain,
% 3.64/3.81 (r(z, elem!1)),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[585, 10245, 10243])).
% 3.64/3.81 tff(10247,plain,
% 3.64/3.81 (~r(elem!1, s(s(z)))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[4862, 10246, 3261])).
% 3.64/3.81 tff(10248,plain,
% 3.64/3.81 (elem!1 = s(s(z))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[467, 10247, 461])).
% 3.64/3.81 tff(10249,plain,
% 3.64/3.81 (s(elem!1) = s(s(s(z)))),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10248])).
% 3.64/3.81 tff(10250,plain,
% 3.64/3.81 (s(s(s(z))) = s(elem!1)),
% 3.64/3.81 inference(symmetry,[status(thm)],[10249])).
% 3.64/3.81 tff(10251,plain,
% 3.64/3.81 (b(s(s(s(z))), s(s(z))) <=> b(s(elem!1), s(s(z)))),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10250])).
% 3.64/3.81 tff(10252,plain,
% 3.64/3.81 (b(s(elem!1), s(s(z))) <=> b(s(s(s(z))), s(s(z)))),
% 3.64/3.81 inference(symmetry,[status(thm)],[10251])).
% 3.64/3.81 tff(10253,plain,
% 3.64/3.81 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(z)))),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10248])).
% 3.64/3.81 tff(10254,plain,
% 3.64/3.81 (b(s(elem!1), s(s(z)))),
% 3.64/3.81 inference(modus_ponens,[status(thm)],[683, 10253])).
% 3.64/3.81 tff(10255,plain,
% 3.64/3.81 (b(s(s(s(z))), s(s(z)))),
% 3.64/3.81 inference(modus_ponens,[status(thm)],[10254, 10252])).
% 3.64/3.81 tff(10256,plain,
% 3.64/3.81 (b(s(s(s(z))), z)),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[7042, 10248, 853])).
% 3.64/3.81 tff(10257,plain,
% 3.64/3.81 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), s(elem!1))),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10250])).
% 3.64/3.81 tff(10258,plain,
% 3.64/3.81 (b(s(s(z)), s(elem!1)) <=> b(s(s(z)), s(s(s(z))))),
% 3.64/3.81 inference(symmetry,[status(thm)],[10257])).
% 3.64/3.81 tff(10259,plain,
% 3.64/3.81 (s(s(z)) = elem!1),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[311, 10248])).
% 3.64/3.81 tff(10260,plain,
% 3.64/3.81 (b(s(s(z)), s(elem!1))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[1337, 10259, 1548, 744])).
% 3.64/3.81 tff(10261,plain,
% 3.64/3.81 (b(s(s(z)), s(s(s(z))))),
% 3.64/3.81 inference(modus_ponens,[status(thm)],[10260, 10258])).
% 3.64/3.81 tff(10262,plain,
% 3.64/3.81 (b(z, s(elem!1)) <=> b(z, s(s(s(z))))),
% 3.64/3.81 inference(monotonicity,[status(thm)],[10249])).
% 3.64/3.81 tff(10263,plain,
% 3.64/3.81 (~(elem!1 = s(s(s(elem!1))))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[4868, 10243, 3261, 461, 3242])).
% 3.64/3.81 tff(10264,plain,
% 3.64/3.81 (~(s(s(s(elem!1))) = elem!1)),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[2489, 10263])).
% 3.64/3.81 tff(10265,plain,
% 3.64/3.81 (~r(s(s(s(elem!1))), elem!1)),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[565, 10246, 3243])).
% 3.64/3.81 tff(10266,plain,
% 3.64/3.81 (b(s(s(s(elem!1))), elem!1)),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[570, 10265, 10264])).
% 3.64/3.81 tff(10267,plain,
% 3.64/3.81 (~r(z, s(elem!1))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[7389, 10266, 5725, 683, 356, 3243])).
% 3.64/3.81 tff(10268,plain,
% 3.64/3.81 (b(z, s(elem!1))),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[2351, 10267])).
% 3.64/3.81 tff(10269,plain,
% 3.64/3.81 (b(z, s(s(s(z))))),
% 3.64/3.81 inference(modus_ponens,[status(thm)],[10268, 10262])).
% 3.64/3.81 tff(10270,plain,
% 3.64/3.81 ($false),
% 3.64/3.81 inference(unit_resolution,[status(thm)],[5096, 178, 3461, 10269, 10261, 10256, 10255])).
% 3.64/3.81 tff(10271,plain,(b(z, s(s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(elem!1), elem!1)) | r(elem!1, s(elem!1)) | (~b(s(elem!1), z)) | (s(s(s(elem!1))) = s(elem!1)) | b(elem!1, s(s(z))) | (~r(z, s(s(z)))) | r(elem!1, z) | r(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.82 tff(10272,plain,
% 3.64/3.82 (b(z, s(s(s(elem!1))))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[10271, 4512, 683, 744, 10020, 356, 461, 3261, 9981, 5619])).
% 3.64/3.82 tff(10273,plain,
% 3.64/3.82 (b(z, s(s(s(s(s(z))))))),
% 3.64/3.82 inference(modus_ponens,[status(thm)],[10272, 10241])).
% 3.64/3.82 tff(10274,plain,
% 3.64/3.82 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 3.64/3.82 inference(symmetry,[status(thm)],[10240])).
% 3.64/3.82 tff(10275,plain,
% 3.64/3.82 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.64/3.82 inference(monotonicity,[status(thm)],[10274])).
% 3.64/3.82 tff(10276,plain,
% 3.64/3.82 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.64/3.82 inference(symmetry,[status(thm)],[10275])).
% 3.64/3.82 tff(10277,plain,
% 3.64/3.82 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 3.64/3.82 inference(monotonicity,[status(thm)],[10239])).
% 3.64/3.82 tff(10278,plain,
% 3.64/3.82 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.64/3.82 inference(transitivity,[status(thm)],[10277, 3289])).
% 3.64/3.82 tff(10279,plain,
% 3.64/3.82 ((~(s(s(elem!1)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(z))))))),
% 3.64/3.82 inference(monotonicity,[status(thm)],[10278])).
% 3.64/3.82 tff(10280,plain,
% 3.64/3.82 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.64/3.82 inference(modus_ponens,[status(thm)],[1650, 10279])).
% 3.64/3.82 tff(10281,plain,
% 3.64/3.82 ((s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[3825, 41, 10179])).
% 3.64/3.82 tff(10282,plain,
% 3.64/3.82 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[10281, 10280])).
% 3.64/3.82 tff(10283,plain,
% 3.64/3.82 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.64/3.82 inference(modus_ponens,[status(thm)],[10282, 10276])).
% 3.64/3.82 tff(10284,plain,
% 3.64/3.82 (b(s(s(z)), s(s(s(s(s(z)))))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 3.64/3.82 inference(monotonicity,[status(thm)],[10274])).
% 3.64/3.82 tff(10285,plain,
% 3.64/3.82 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(s(z))))))),
% 3.64/3.82 inference(symmetry,[status(thm)],[10284])).
% 3.64/3.82 tff(10286,plain,
% 3.64/3.82 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 3.64/3.82 inference(monotonicity,[status(thm)],[10237])).
% 3.64/3.82 tff(10287,plain,
% 3.64/3.82 ((~r(elem!1, s(s(s(elem!1))))) <=> (~r(s(s(z)), s(s(s(elem!1)))))),
% 3.64/3.82 inference(monotonicity,[status(thm)],[10286])).
% 3.64/3.82 tff(10288,plain,
% 3.64/3.82 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.64/3.82 inference(modus_ponens,[status(thm)],[4512, 10287])).
% 3.64/3.82 tff(10289,plain,
% 3.64/3.82 (b(s(s(z)), s(s(s(elem!1))))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[4223, 10288])).
% 3.64/3.82 tff(10290,plain,
% 3.64/3.82 (b(s(s(z)), s(s(s(s(s(z))))))),
% 3.64/3.82 inference(modus_ponens,[status(thm)],[10289, 10285])).
% 3.64/3.82 tff(10291,plain,
% 3.64/3.82 (~r(z, s(s(s(s(z)))))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[529, 10235, 470])).
% 3.64/3.82 tff(10292,plain,
% 3.64/3.82 (b(z, s(s(s(s(z)))))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[46, 10291])).
% 3.64/3.82 tff(10293,plain,
% 3.64/3.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))),
% 3.64/3.82 inference(rewrite,[status(thm)],[])).
% 3.64/3.82 tff(10294,plain,
% 3.64/3.82 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))),
% 3.64/3.82 inference(rewrite,[status(thm)],[])).
% 3.64/3.82 tff(10295,plain,
% 3.64/3.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z))))))))),
% 3.64/3.82 inference(monotonicity,[status(thm)],[10294])).
% 3.64/3.82 tff(10296,plain,
% 3.64/3.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))),
% 3.64/3.82 inference(transitivity,[status(thm)],[10295, 10293])).
% 3.64/3.82 tff(10297,plain,
% 3.64/3.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)))),
% 3.64/3.82 inference(quant_inst,[status(thm)],[])).
% 3.64/3.82 tff(10298,plain,
% 3.64/3.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z))))))),
% 3.64/3.82 inference(modus_ponens,[status(thm)],[10297, 10296])).
% 3.64/3.82 tff(10299,plain,
% 3.64/3.82 ($false),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[10298, 178, 5619, 10292, 10290, 10283, 10273])).
% 3.64/3.82 tff(10300,plain,(r(elem!1, s(s(s(elem!1)))) | b(elem!1, s(s(z))) | (~r(z, s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | r(elem!1, s(elem!1)) | r(s(s(z)), z) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(s(z)))), z)) | r(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 3.64/3.82 tff(10301,plain,
% 3.64/3.82 (r(elem!1, s(s(s(elem!1))))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[10300, 10019, 461, 470, 9972, 9983, 744, 5618, 356, 194, 9963])).
% 3.64/3.82 tff(10302,plain,
% 3.64/3.82 (~(elem!1 = z)),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[5261, 10019, 9983, 5807, 1696, 470, 10301])).
% 3.64/3.82 tff(10303,plain,
% 3.64/3.82 (b(elem!1, z)),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[498, 10302, 9981])).
% 3.64/3.82 tff(10304,plain,
% 3.64/3.82 (~(z = elem!1)),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[317, 10302])).
% 3.64/3.82 tff(10305,plain,
% 3.64/3.82 (~r(z, elem!1)),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[4862, 10019, 10009])).
% 3.64/3.82 tff(10306,plain,
% 3.64/3.82 (b(z, elem!1)),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[585, 10305, 10304])).
% 3.64/3.82 tff(10307,plain,
% 3.64/3.82 ($false),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[2429, 10306, 10303, 9972, 5725, 9964])).
% 3.64/3.82 tff(10308,plain,((s(elem!1) = s(s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))) | b(elem!1, s(s(z))) | r(elem!1, s(elem!1)) | r(s(s(z)), z) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(s(z)))), z)) | b(s(elem!1), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.82 tff(10309,plain,
% 3.64/3.82 (s(elem!1) = s(s(s(s(z))))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[10308, 9961, 461, 744, 5618, 356, 3244, 5720])).
% 3.64/3.82 tff(10310,plain,
% 3.64/3.82 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(s(z)))))),
% 3.64/3.82 inference(monotonicity,[status(thm)],[10309])).
% 3.64/3.82 tff(10311,plain,
% 3.64/3.82 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(elem!1))),
% 3.64/3.82 inference(symmetry,[status(thm)],[10310])).
% 3.64/3.82 tff(10312,plain,
% 3.64/3.82 (r(elem!1, s(elem!1))),
% 3.64/3.82 inference(modus_ponens,[status(thm)],[9961, 10311])).
% 3.64/3.82 tff(10313,plain,
% 3.64/3.82 ($false),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[744, 10312])).
% 3.64/3.82 tff(10314,plain,(r(s(s(z)), z) | r(elem!1, s(elem!1)) | b(elem!1, s(s(z))) | (s(s(s(elem!1))) = s(elem!1)) | b(s(elem!1), s(s(s(s(z))))) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 3.64/3.82 tff(10315,plain,
% 3.64/3.82 (r(elem!1, s(elem!1))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[10314, 9561, 461, 3170, 9558, 9556])).
% 3.64/3.82 tff(10316,plain,
% 3.64/3.82 ($false),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[5420, 118, 1587, 3311, 2102])).
% 3.64/3.82 tff(10317,plain,((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.82 tff(10318,plain,
% 3.64/3.82 (~r(s(elem!1), s(s(s(elem!1))))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[10317, 10315, 3311])).
% 3.64/3.82 tff(10319,plain,
% 3.64/3.82 (b(s(elem!1), s(s(s(elem!1))))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[5432, 10318, 9553])).
% 3.64/3.82 tff(10320,plain,
% 3.64/3.82 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[1591, 10315, 3311])).
% 3.64/3.82 tff(10321,plain,
% 3.64/3.82 (b(s(s(s(elem!1))), s(elem!1))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[373, 10320, 9558])).
% 3.64/3.82 tff(10322,plain,
% 3.64/3.82 ($false),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[6736, 10321, 10319, 2043, 9544, 9542])).
% 3.64/3.82 tff(10323,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | b(elem!1, s(s(z))) | b(s(s(s(s(z)))), z) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (elem!1 = s(elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | b(s(s(z)), elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.82 tff(10324,plain,
% 3.64/3.82 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[10323, 9097, 7954, 461, 3170, 47, 9521, 9094, 9106, 8673, 3241, 9298])).
% 3.64/3.82 tff(10325,plain,
% 3.64/3.82 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[271, 10324])).
% 3.64/3.82 tff(10326,plain,
% 3.64/3.82 ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[8949, 178, 7954, 9298, 8673])).
% 3.64/3.82 tff(10327,plain,
% 3.64/3.82 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[10326, 10325])).
% 3.64/3.82 tff(10328,plain,
% 3.64/3.82 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[5118, 10327, 9096])).
% 3.64/3.82 tff(10329,plain,
% 3.64/3.82 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[8969, 10328, 9097])).
% 3.64/3.82 tff(10330,plain,
% 3.64/3.82 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[3444, 10329, 4245])).
% 3.64/3.82 tff(10331,plain,
% 3.64/3.82 (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[8403, 9096])).
% 3.64/3.82 tff(10332,plain,
% 3.64/3.82 (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[8894, 178, 7954, 9298, 10325, 8673])).
% 3.64/3.82 tff(10333,plain,
% 3.64/3.82 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[3612, 41, 10332, 10331])).
% 3.64/3.82 tff(10334,plain,
% 3.64/3.82 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[3623, 10333, 9097])).
% 3.64/3.82 tff(10335,plain,
% 3.64/3.82 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[691, 10334, 701])).
% 3.64/3.82 tff(10336,plain,
% 3.64/3.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 3.64/3.82 inference(rewrite,[status(thm)],[])).
% 3.64/3.82 tff(10337,plain,
% 3.64/3.82 (((~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(s(s(s(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(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 3.64/3.82 inference(rewrite,[status(thm)],[])).
% 3.64/3.82 tff(10338,plain,
% 3.64/3.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(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(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 3.64/3.82 inference(monotonicity,[status(thm)],[10337])).
% 3.64/3.82 tff(10339,plain,
% 3.64/3.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(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(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 3.64/3.82 inference(transitivity,[status(thm)],[10338, 10336])).
% 3.64/3.82 tff(10340,plain,
% 3.64/3.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(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(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.64/3.82 inference(quant_inst,[status(thm)],[])).
% 3.64/3.82 tff(10341,plain,
% 3.64/3.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 3.64/3.82 inference(modus_ponens,[status(thm)],[10340, 10339])).
% 3.64/3.82 tff(10342,plain,
% 3.64/3.82 ($false),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[10341, 178, 8528, 869, 9144, 3664, 8176])).
% 3.64/3.82 tff(10343,plain,((~(s(s(z)) = elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(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)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.82 tff(10344,plain,
% 3.64/3.82 (~(s(s(z)) = elem!1)),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[10343, 10335, 10330, 9298, 9521, 9094])).
% 3.64/3.82 tff(10345,plain,
% 3.64/3.82 (~(elem!1 = s(s(z)))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[311, 10344])).
% 3.64/3.82 tff(10346,plain,
% 3.64/3.82 (r(elem!1, s(s(z)))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[467, 10345, 461])).
% 3.64/3.82 tff(10347,plain,
% 3.64/3.82 (r(s(s(z)), elem!1)),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[448, 10344, 3241])).
% 3.64/3.82 tff(10348,plain,
% 3.64/3.82 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[7973, 10347, 9097])).
% 3.64/3.82 tff(10349,plain,
% 3.64/3.82 (b(s(s(z)), s(s(s(elem!1))))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[4223, 10348])).
% 3.64/3.82 tff(10350,plain,
% 3.64/3.82 ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[9008, 178, 7954, 9521, 8673])).
% 3.64/3.82 tff(10351,plain,
% 3.64/3.82 (~b(z, s(s(z)))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[10350, 10349])).
% 3.64/3.82 tff(10352,plain,
% 3.64/3.82 (r(z, s(s(z)))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[143, 10351])).
% 3.64/3.82 tff(10353,plain,
% 3.64/3.82 (~r(elem!1, z)),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[8416, 10352, 10346])).
% 3.64/3.82 tff(10354,plain,
% 3.64/3.82 (~(z = elem!1)),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[5266, 10352, 9198, 9094, 9097, 461, 1, 3170])).
% 3.64/3.82 tff(10355,plain,
% 3.64/3.82 (~(elem!1 = z)),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[2808, 10354])).
% 3.64/3.82 tff(10356,plain,
% 3.64/3.82 (~r(z, elem!1)),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[8412, 10352, 10347])).
% 3.64/3.82 tff(10357,plain,
% 3.64/3.82 (b(z, elem!1)),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[585, 10356, 10354])).
% 3.64/3.82 tff(10358,plain,
% 3.64/3.82 (~b(elem!1, z)),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[9376, 10357, 4245, 9096, 9097, 10325, 10335, 7954, 9298, 8673])).
% 3.64/3.82 tff(10359,plain,
% 3.64/3.82 ($false),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[498, 10358, 10355, 10353])).
% 3.64/3.82 tff(10360,plain,((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(z))) | b(z, s(s(s(s(z))))) | b(s(s(s(s(z)))), z) | b(s(s(z)), elem!1) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | b(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.82 tff(10361,plain,
% 3.64/3.82 (elem!1 = s(s(s(elem!1)))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[10360, 701, 1, 3170, 3241, 461, 3240])).
% 3.64/3.82 tff(10362,plain,
% 3.64/3.82 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(elem!1))))),
% 3.64/3.82 inference(monotonicity,[status(thm)],[10361])).
% 3.64/3.82 tff(10363,plain,
% 3.64/3.82 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 3.64/3.82 inference(symmetry,[status(thm)],[10362])).
% 3.64/3.82 tff(10364,plain,
% 3.64/3.82 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(z)) = elem!1))),
% 3.64/3.82 inference(monotonicity,[status(thm)],[10363])).
% 3.64/3.82 tff(10365,plain,
% 3.64/3.82 (~(s(s(z)) = elem!1)),
% 3.64/3.82 inference(modus_ponens,[status(thm)],[1683, 10364])).
% 3.64/3.82 tff(10366,plain,
% 3.64/3.82 (r(s(s(z)), elem!1)),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[448, 10365, 3241])).
% 3.64/3.82 tff(10367,plain,
% 3.64/3.82 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.64/3.82 inference(monotonicity,[status(thm)],[10361])).
% 3.64/3.82 tff(10368,plain,
% 3.64/3.82 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 3.64/3.82 inference(symmetry,[status(thm)],[10367])).
% 3.64/3.82 tff(10369,plain,
% 3.64/3.82 (b(elem!1, s(s(s(s(z)))))),
% 3.64/3.82 inference(modus_ponens,[status(thm)],[8673, 10368])).
% 3.64/3.82 tff(10370,plain,
% 3.64/3.82 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(elem!1))))),
% 3.64/3.82 inference(monotonicity,[status(thm)],[10361])).
% 3.64/3.82 tff(10371,plain,
% 3.64/3.82 ((~b(s(s(z)), elem!1)) <=> (~b(s(s(z)), s(s(s(elem!1)))))),
% 3.64/3.82 inference(monotonicity,[status(thm)],[10370])).
% 3.64/3.82 tff(10372,plain,
% 3.64/3.82 (~b(s(s(z)), s(s(s(elem!1))))),
% 3.64/3.82 inference(modus_ponens,[status(thm)],[3241, 10371])).
% 3.64/3.82 tff(10373,plain,
% 3.64/3.82 (r(s(s(z)), s(s(s(elem!1))))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[4221, 41, 1683, 10372])).
% 3.64/3.82 tff(10374,plain,
% 3.64/3.82 (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))))),
% 3.64/3.82 inference(monotonicity,[status(thm)],[1527])).
% 3.64/3.82 tff(10375,plain,
% 3.64/3.82 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[259, 251, 202, 104, 167])).
% 3.64/3.82 tff(10376,plain,
% 3.64/3.82 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[249, 10375])).
% 3.64/3.82 tff(10377,plain,
% 3.64/3.82 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[2803, 10376, 438])).
% 3.64/3.82 tff(10378,plain,
% 3.64/3.82 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[691, 10377, 701])).
% 3.64/3.82 tff(10379,plain,
% 3.64/3.82 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[9083, 10378, 1301, 104, 251])).
% 3.64/3.82 tff(10380,plain,
% 3.64/3.82 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[3444, 10379, 4245])).
% 3.64/3.82 tff(10381,plain,
% 3.64/3.82 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.64/3.82 inference(modus_ponens,[status(thm)],[10380, 10374])).
% 3.64/3.82 tff(10382,plain,
% 3.64/3.82 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(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(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(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(s(elem!1))))))),
% 3.64/3.82 inference(rewrite,[status(thm)],[])).
% 3.64/3.82 tff(10383,plain,
% 3.64/3.82 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 3.64/3.82 inference(rewrite,[status(thm)],[])).
% 3.64/3.82 tff(10384,plain,
% 3.64/3.82 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(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(s(elem!1)))))))),
% 3.64/3.82 inference(monotonicity,[status(thm)],[10383])).
% 3.64/3.82 tff(10385,plain,
% 3.64/3.82 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(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(s(elem!1))))))),
% 3.64/3.82 inference(transitivity,[status(thm)],[10384, 10382])).
% 3.64/3.82 tff(10386,plain,
% 3.64/3.82 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.64/3.82 inference(quant_inst,[status(thm)],[])).
% 3.64/3.82 tff(10387,plain,
% 3.64/3.82 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 3.64/3.82 inference(modus_ponens,[status(thm)],[10386, 10385])).
% 3.64/3.82 tff(10388,plain,
% 3.64/3.82 ($false),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[10387, 118, 1823, 10376, 10381])).
% 3.64/3.82 tff(10389,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~(elem!1 = s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.82 tff(10390,plain,
% 3.64/3.82 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[10389, 10373, 10361, 10369, 9298, 701, 10366, 9094, 9521])).
% 3.64/3.82 tff(10391,plain,
% 3.64/3.82 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[222, 10390])).
% 3.64/3.82 tff(10392,plain,
% 3.64/3.82 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[212, 10391, 47])).
% 3.64/3.82 tff(10393,plain,
% 3.64/3.82 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[271, 10392])).
% 3.64/3.82 tff(10394,plain,
% 3.64/3.82 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[10326, 10393])).
% 3.64/3.82 tff(10395,plain,
% 3.64/3.82 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[5118, 10394, 9096])).
% 3.64/3.82 tff(10396,plain,
% 3.64/3.82 (b(elem!1, s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 3.64/3.82 inference(monotonicity,[status(thm)],[10361])).
% 3.64/3.82 tff(10397,plain,
% 3.64/3.82 ((~b(elem!1, s(s(z)))) <=> (~b(s(s(s(elem!1))), s(s(z))))),
% 3.64/3.82 inference(monotonicity,[status(thm)],[10396])).
% 3.64/3.82 tff(10398,plain,
% 3.64/3.82 (~b(s(s(s(elem!1))), s(s(z)))),
% 3.64/3.82 inference(modus_ponens,[status(thm)],[461, 10397])).
% 3.64/3.82 tff(10399,plain,
% 3.64/3.82 (r(s(s(s(elem!1))), s(s(z)))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[4209, 41, 10398, 4181])).
% 3.64/3.82 tff(10400,plain,
% 3.64/3.82 ($false),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[4881, 118, 3859, 107, 5128])).
% 3.64/3.82 tff(10401,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.82 tff(10402,plain,
% 3.64/3.82 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[10401, 10399, 10395])).
% 3.64/3.82 tff(10403,plain,
% 3.64/3.82 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[3578, 10402])).
% 3.64/3.82 tff(10404,plain,
% 3.64/3.82 (b(z, elem!1) <=> b(z, s(s(s(elem!1))))),
% 3.64/3.82 inference(monotonicity,[status(thm)],[10361])).
% 3.64/3.82 tff(10405,plain,
% 3.64/3.82 (b(z, s(s(s(elem!1)))) <=> b(z, elem!1)),
% 3.64/3.82 inference(symmetry,[status(thm)],[10404])).
% 3.64/3.82 tff(10406,plain,
% 3.64/3.82 (b(z, elem!1)),
% 3.64/3.82 inference(modus_ponens,[status(thm)],[7954, 10405])).
% 3.64/3.82 tff(10407,plain,
% 3.64/3.82 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[1309, 10393, 9298, 10406, 10369])).
% 3.64/3.82 tff(10408,plain,
% 3.64/3.82 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[691, 10407, 701])).
% 3.64/3.82 tff(10409,plain,
% 3.64/3.82 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[2803, 10408, 10366])).
% 3.64/3.82 tff(10410,plain,
% 3.64/3.82 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[249, 10409])).
% 3.64/3.82 tff(10411,plain,
% 3.64/3.82 ($false),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[1259, 178, 9298, 10410, 9521, 9094, 10403])).
% 3.64/3.82 tff(10412,plain,((elem!1 = s(s(s(s(s(s(s(z)))))))) | b(s(s(z)), elem!1) | b(elem!1, s(s(z))) | b(z, s(s(s(s(z))))) | b(s(s(s(s(z)))), z) | b(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.82 tff(10413,plain,
% 3.64/3.82 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[10412, 3241, 461, 1, 3170, 3240])).
% 3.64/3.82 tff(10414,plain,
% 3.64/3.82 ((z = elem!1) <=> (z = s(s(s(s(s(s(s(z))))))))),
% 3.64/3.82 inference(monotonicity,[status(thm)],[10413])).
% 3.64/3.82 tff(10415,plain,
% 3.64/3.82 ((z = elem!1) <=> (s(s(s(s(s(s(s(z))))))) = z)),
% 3.64/3.82 inference(transitivity,[status(thm)],[10414, 263])).
% 3.64/3.82 tff(10416,plain,
% 3.64/3.82 ((s(s(s(s(s(s(s(z))))))) = z) <=> (z = elem!1)),
% 3.64/3.82 inference(symmetry,[status(thm)],[10415])).
% 3.64/3.82 tff(10417,plain,
% 3.64/3.82 ((~(s(s(s(s(s(s(s(z))))))) = z)) <=> (~(z = elem!1))),
% 3.64/3.82 inference(monotonicity,[status(thm)],[10416])).
% 3.64/3.82 tff(10418,plain,
% 3.64/3.82 (~(z = elem!1)),
% 3.64/3.82 inference(modus_ponens,[status(thm)],[128, 10417])).
% 3.64/3.82 tff(10419,plain,
% 3.64/3.82 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.82 inference(monotonicity,[status(thm)],[10413])).
% 3.64/3.82 tff(10420,plain,
% 3.64/3.82 ((s(s(s(z))) = elem!1) <=> (elem!1 = s(s(s(z))))),
% 3.64/3.82 inference(commutativity,[status(thm)],[])).
% 3.64/3.82 tff(10421,plain,
% 3.64/3.82 ((elem!1 = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 3.64/3.82 inference(symmetry,[status(thm)],[10420])).
% 3.64/3.82 tff(10422,plain,
% 3.64/3.82 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 3.64/3.82 inference(symmetry,[status(thm)],[10413])).
% 3.64/3.82 tff(10423,plain,
% 3.64/3.82 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 3.64/3.82 inference(monotonicity,[status(thm)],[10422])).
% 3.64/3.82 tff(10424,plain,
% 3.64/3.82 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 3.64/3.82 inference(transitivity,[status(thm)],[10423, 10421])).
% 3.64/3.82 tff(10425,plain,
% 3.64/3.82 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(s(s(s(z))) = elem!1))),
% 3.64/3.82 inference(monotonicity,[status(thm)],[10424])).
% 3.64/3.82 tff(10426,plain,
% 3.64/3.82 (~(s(s(s(z))) = elem!1)),
% 3.64/3.82 inference(modus_ponens,[status(thm)],[1104, 10425])).
% 3.64/3.82 tff(10427,plain,
% 3.64/3.82 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.82 inference(monotonicity,[status(thm)],[10413])).
% 3.64/3.82 tff(10428,plain,
% 3.64/3.82 (b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(z))), elem!1)),
% 3.64/3.82 inference(symmetry,[status(thm)],[10427])).
% 3.64/3.82 tff(10429,plain,
% 3.64/3.82 ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(s(s(z))), elem!1))),
% 3.64/3.82 inference(monotonicity,[status(thm)],[10428])).
% 3.64/3.82 tff(10430,plain,
% 3.64/3.82 (~(s(s(elem!1)) = s(s(z)))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[2386, 10418])).
% 3.64/3.82 tff(10431,plain,
% 3.64/3.82 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 3.64/3.82 inference(unit_resolution,[status(thm)],[8244, 10430])).
% 3.64/3.82 tff(10432,plain,
% 3.64/3.82 (~(s(elem!1) = s(s(z)))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[2832, 10413])).
% 3.64/3.83 tff(10433,plain,
% 3.64/3.83 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[2840, 10432])).
% 3.64/3.83 tff(10434,plain,
% 3.64/3.83 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[4173, 4170, 10433])).
% 3.64/3.83 tff(10435,plain,
% 3.64/3.83 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[8252, 10434, 10431, 47, 7954])).
% 3.64/3.83 tff(10436,plain,
% 3.64/3.83 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[4928, 10435, 4890])).
% 3.64/3.83 tff(10437,plain,
% 3.64/3.83 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[8234, 10434, 7954, 47])).
% 3.64/3.83 tff(10438,plain,
% 3.64/3.83 (b(s(s(z)), s(s(s(s(z)))))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[164, 10437])).
% 3.64/3.83 tff(10439,plain,
% 3.64/3.83 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[8229, 10434, 3244, 7954, 47, 8042, 3240, 3241, 461])).
% 3.64/3.83 tff(10440,plain,
% 3.64/3.83 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[271, 10439])).
% 3.64/3.83 tff(10441,plain,
% 3.64/3.83 (~b(z, s(s(z)))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[8280, 10440, 3244, 8042, 7954, 47, 10434, 461])).
% 3.64/3.83 tff(10442,plain,
% 3.64/3.83 (r(z, s(s(z)))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[143, 10441])).
% 3.64/3.83 tff(10443,plain,
% 3.64/3.83 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[4961, 4952, 194])).
% 3.64/3.83 tff(10444,plain,
% 3.64/3.83 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[4950, 10443, 4938])).
% 3.64/3.83 tff(10445,plain,
% 3.64/3.83 (~b(s(s(s(z))), s(s(z)))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[4945, 10444])).
% 3.64/3.83 tff(10446,plain,
% 3.64/3.83 (r(s(s(s(z))), s(s(z)))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[4966, 10445])).
% 3.64/3.83 tff(10447,plain,
% 3.64/3.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 3.64/3.83 inference(rewrite,[status(thm)],[])).
% 3.64/3.83 tff(10448,plain,
% 3.64/3.83 (((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 3.64/3.83 inference(rewrite,[status(thm)],[])).
% 3.64/3.83 tff(10449,plain,
% 3.64/3.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))))),
% 3.64/3.83 inference(monotonicity,[status(thm)],[10448])).
% 3.64/3.83 tff(10450,plain,
% 3.64/3.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 3.64/3.83 inference(transitivity,[status(thm)],[10449, 10447])).
% 3.64/3.83 tff(10451,plain,
% 3.64/3.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))))),
% 3.64/3.83 inference(quant_inst,[status(thm)],[])).
% 3.64/3.83 tff(10452,plain,
% 3.64/3.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))),
% 3.64/3.83 inference(modus_ponens,[status(thm)],[10451, 10450])).
% 3.64/3.83 tff(10453,plain,
% 3.64/3.83 ($false),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[10452, 118, 3261, 10446, 4952])).
% 3.64/3.83 tff(10454,plain,((~r(z, s(s(s(z))))) | (~r(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(s(s(z)))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.83 tff(10455,plain,
% 3.64/3.83 (~r(z, s(s(s(z))))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[10454, 10442, 10438, 8042, 10436, 3244])).
% 3.64/3.83 tff(10456,plain,
% 3.64/3.83 (b(z, s(s(s(z))))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[4920, 10455])).
% 3.64/3.83 tff(10457,plain,
% 3.64/3.83 (b(elem!1, s(s(z))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.64/3.83 inference(monotonicity,[status(thm)],[10413])).
% 3.64/3.83 tff(10458,plain,
% 3.64/3.83 ((~b(elem!1, s(s(z)))) <=> (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 3.64/3.83 inference(monotonicity,[status(thm)],[10457])).
% 3.64/3.83 tff(10459,plain,
% 3.64/3.83 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.64/3.83 inference(modus_ponens,[status(thm)],[461, 10458])).
% 3.64/3.83 tff(10460,plain,
% 3.64/3.83 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[2960, 41, 10459, 3574])).
% 3.64/3.83 tff(10461,plain,
% 3.64/3.83 (~(elem!1 = s(s(s(elem!1))))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[2859, 10433, 10413])).
% 3.64/3.83 tff(10462,plain,
% 3.64/3.83 (r(elem!1, s(s(s(elem!1))))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[2054, 10461, 3240])).
% 3.64/3.83 tff(10463,plain,
% 3.64/3.83 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(s(s(s(s(z))))))))),
% 3.64/3.83 inference(monotonicity,[status(thm)],[10413])).
% 3.64/3.83 tff(10464,plain,
% 3.64/3.83 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(z)) = elem!1)),
% 3.64/3.83 inference(symmetry,[status(thm)],[10463])).
% 3.64/3.83 tff(10465,plain,
% 3.64/3.83 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(z)) = elem!1))),
% 3.64/3.83 inference(monotonicity,[status(thm)],[10464])).
% 3.64/3.83 tff(10466,plain,
% 3.64/3.83 (~(s(s(z)) = elem!1)),
% 3.64/3.83 inference(modus_ponens,[status(thm)],[244, 10465])).
% 3.64/3.83 tff(10467,plain,
% 3.64/3.83 (r(s(s(z)), elem!1)),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[448, 10466, 3241])).
% 3.64/3.83 tff(10468,plain,
% 3.64/3.83 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[7973, 10467, 10462])).
% 3.64/3.83 tff(10469,plain,
% 3.64/3.83 (b(s(s(z)), s(s(s(elem!1))))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[4223, 10468])).
% 3.64/3.83 tff(10470,plain,
% 3.64/3.83 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 3.64/3.83 inference(monotonicity,[status(thm)],[10413])).
% 3.64/3.83 tff(10471,plain,
% 3.64/3.83 (s(s(elem!1)) = s(s(s(s(s(s(s(s(s(z)))))))))),
% 3.64/3.83 inference(monotonicity,[status(thm)],[10470])).
% 3.64/3.83 tff(10472,plain,
% 3.64/3.83 (s(s(s(elem!1))) = s(s(s(s(s(s(s(s(s(s(z))))))))))),
% 3.64/3.83 inference(monotonicity,[status(thm)],[10471])).
% 3.64/3.83 tff(10473,plain,
% 3.64/3.83 (s(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(s(elem!1)))),
% 3.64/3.83 inference(symmetry,[status(thm)],[10472])).
% 3.64/3.83 tff(10474,plain,
% 3.64/3.83 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z))))))))))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.64/3.83 inference(monotonicity,[status(thm)],[10473])).
% 3.64/3.83 tff(10475,plain,
% 3.64/3.83 (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(s(s(s(s(s(s(s(z)))))))))))),
% 3.64/3.83 inference(symmetry,[status(thm)],[10474])).
% 3.64/3.83 tff(10476,plain,
% 3.64/3.83 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.64/3.83 inference(monotonicity,[status(thm)],[10413])).
% 3.64/3.83 tff(10477,plain,
% 3.64/3.83 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.64/3.83 inference(modus_ponens,[status(thm)],[10462, 10476])).
% 3.64/3.83 tff(10478,plain,
% 3.64/3.83 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 3.64/3.83 inference(modus_ponens,[status(thm)],[10477, 10475])).
% 3.64/3.83 tff(10479,plain,
% 3.64/3.83 (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[7939, 10478, 10460])).
% 3.64/3.83 tff(10480,plain,
% 3.64/3.83 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[9102, 1130, 145])).
% 3.64/3.83 tff(10481,plain,
% 3.64/3.83 (b(s(s(z)), s(s(s(s(z)))))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[164, 10480])).
% 3.64/3.83 tff(10482,assumption,(~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))), introduced(assumption)).
% 3.64/3.83 tff(10483,plain,
% 3.64/3.83 (~(s(elem!1) = s(s(z)))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[2832, 679])).
% 3.64/3.83 tff(10484,plain,
% 3.64/3.83 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[2840, 10483])).
% 3.64/3.83 tff(10485,plain,
% 3.64/3.83 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 3.64/3.83 inference(monotonicity,[status(thm)],[679])).
% 3.64/3.83 tff(10486,plain,
% 3.64/3.83 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 3.64/3.83 inference(transitivity,[status(thm)],[10485, 3539])).
% 3.64/3.83 tff(10487,plain,
% 3.64/3.83 ((~(s(s(s(elem!1))) = elem!1)) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))))),
% 3.64/3.83 inference(monotonicity,[status(thm)],[10486])).
% 3.64/3.83 tff(10488,plain,
% 3.64/3.83 (~(elem!1 = s(s(s(elem!1))))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[2859, 10484, 679])).
% 3.64/3.83 tff(10489,plain,
% 3.64/3.83 (~(s(s(s(elem!1))) = elem!1)),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[2489, 10488])).
% 3.64/3.83 tff(10490,plain,
% 3.64/3.83 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 3.64/3.83 inference(modus_ponens,[status(thm)],[10489, 10487])).
% 3.64/3.83 tff(10491,plain,
% 3.64/3.83 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[8061, 1130, 2043, 10490, 145])).
% 3.64/3.83 tff(10492,plain,
% 3.64/3.83 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[4173, 10491, 10484])).
% 3.64/3.83 tff(10493,plain,
% 3.64/3.83 (~r(s(s(s(s(z)))), s(s(z)))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[3891, 1130, 107])).
% 3.64/3.83 tff(10494,plain,
% 3.64/3.83 (b(s(s(s(s(z)))), s(s(z)))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[102, 10493])).
% 3.64/3.83 tff(10495,plain,
% 3.64/3.83 (b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.64/3.83 inference(monotonicity,[status(thm)],[4345])).
% 3.64/3.83 tff(10496,plain,
% 3.64/3.83 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))),
% 3.64/3.83 inference(symmetry,[status(thm)],[10495])).
% 3.64/3.83 tff(10497,plain,
% 3.64/3.83 (b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))),
% 3.64/3.83 inference(modus_ponens,[status(thm)],[3831, 10496])).
% 3.64/3.83 tff(10498,plain,
% 3.64/3.83 ((s(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 3.64/3.83 inference(monotonicity,[status(thm)],[4345])).
% 3.64/3.83 tff(10499,plain,
% 3.64/3.83 ((s(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(z))) <=> (s(s(z)) = s(s(s(elem!1))))),
% 3.64/3.83 inference(transitivity,[status(thm)],[10498, 7921])).
% 3.64/3.83 tff(10500,plain,
% 3.64/3.83 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(z)))),
% 3.64/3.83 inference(symmetry,[status(thm)],[10499])).
% 3.64/3.83 tff(10501,plain,
% 3.64/3.83 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(z))))),
% 3.64/3.83 inference(monotonicity,[status(thm)],[10500])).
% 3.64/3.83 tff(10502,plain,
% 3.64/3.83 (~(s(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(z)))),
% 3.64/3.83 inference(modus_ponens,[status(thm)],[1683, 10501])).
% 3.64/3.83 tff(10503,plain,
% 3.64/3.83 ((s(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(z))) | b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[7943, 41, 10482])).
% 3.64/3.83 tff(10504,plain,
% 3.64/3.83 (b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[10503, 10502])).
% 3.64/3.83 tff(10505,plain,
% 3.64/3.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))))),
% 3.64/3.83 inference(rewrite,[status(thm)],[])).
% 3.64/3.83 tff(10506,plain,
% 3.64/3.83 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))) | (~b(s(s(s(s(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(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z))))))))))))) <=> ((~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))))),
% 3.64/3.83 inference(rewrite,[status(thm)],[])).
% 3.64/3.83 tff(10507,plain,
% 3.64/3.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))) | (~b(s(s(s(s(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(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z))))))),
% 3.64/3.83 inference(monotonicity,[status(thm)],[10506])).
% 3.64/3.83 tff(10508,plain,
% 3.64/3.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))) | (~b(s(s(s(s(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(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))))),
% 3.64/3.83 inference(transitivity,[status(thm)],[10507, 10505])).
% 3.64/3.83 tff(10509,plain,
% 3.64/3.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))) | (~b(s(s(s(s(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(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 3.64/3.83 inference(quant_inst,[status(thm)],[])).
% 3.64/3.83 tff(10510,plain,
% 3.64/3.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z))))),
% 3.64/3.83 inference(modus_ponens,[status(thm)],[10509, 10508])).
% 3.64/3.83 tff(10511,plain,
% 3.64/3.83 ($false),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[10510, 178, 167, 202, 10504, 10497, 4419])).
% 3.64/3.83 tff(10512,plain,(r(s(s(s(s(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(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.83 tff(10513,plain,
% 3.64/3.83 ($false),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[10512, 10494, 10492, 679, 10482, 4291, 10481])).
% 3.64/3.83 tff(10514,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.83 tff(10515,plain,
% 3.64/3.83 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[10514, 10413, 10479, 10469, 10460, 47, 7954])).
% 3.64/3.83 tff(10516,plain,
% 3.64/3.83 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[84, 10515])).
% 3.64/3.83 tff(10517,plain,
% 3.64/3.83 ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[8267, 178, 10516, 10440, 10436])).
% 3.64/3.83 tff(10518,plain,
% 3.64/3.83 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[10517, 10456])).
% 3.64/3.83 tff(10519,plain,
% 3.64/3.83 (~b(s(s(s(z))), elem!1)),
% 3.64/3.83 inference(modus_ponens,[status(thm)],[10518, 10429])).
% 3.64/3.83 tff(10520,plain,
% 3.64/3.83 (r(s(s(s(z))), elem!1)),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[4981, 10519, 10426])).
% 3.64/3.83 tff(10521,plain,
% 3.64/3.83 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.83 inference(modus_ponens,[status(thm)],[10520, 10419])).
% 3.64/3.83 tff(10522,plain,
% 3.64/3.83 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.83 inference(monotonicity,[status(thm)],[10413])).
% 3.64/3.83 tff(10523,plain,
% 3.64/3.83 ((~b(s(s(z)), elem!1)) <=> (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 3.64/3.83 inference(monotonicity,[status(thm)],[10522])).
% 3.64/3.83 tff(10524,plain,
% 3.64/3.83 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.83 inference(modus_ponens,[status(thm)],[3241, 10523])).
% 3.64/3.83 tff(10525,plain,
% 3.64/3.83 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[249, 10524])).
% 3.64/3.83 tff(10526,plain,
% 3.64/3.83 (~r(s(s(s(z))), s(s(z)))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[1269, 118, 10525, 10521])).
% 3.64/3.83 tff(10527,plain,
% 3.64/3.83 (b(s(s(s(z))), s(s(z)))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[4966, 10526])).
% 3.64/3.83 tff(10528,plain,
% 3.64/3.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.64/3.83 inference(rewrite,[status(thm)],[])).
% 3.64/3.83 tff(10529,plain,
% 3.64/3.83 (((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.64/3.83 inference(rewrite,[status(thm)],[])).
% 3.64/3.83 tff(10530,plain,
% 3.64/3.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 3.64/3.83 inference(monotonicity,[status(thm)],[10529])).
% 3.64/3.83 tff(10531,plain,
% 3.64/3.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.64/3.83 inference(transitivity,[status(thm)],[10530, 10528])).
% 3.64/3.83 tff(10532,plain,
% 3.64/3.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(z))))))),
% 3.64/3.83 inference(quant_inst,[status(thm)],[])).
% 3.64/3.83 tff(10533,plain,
% 3.64/3.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.64/3.83 inference(modus_ponens,[status(thm)],[10532, 10531])).
% 3.64/3.83 tff(10534,plain,
% 3.64/3.83 (~r(s(s(z)), s(s(s(z))))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[10533, 118, 10525, 10521])).
% 3.64/3.83 tff(10535,plain,
% 3.64/3.83 (b(s(s(z)), s(s(s(z))))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[5088, 10534])).
% 3.64/3.83 tff(10536,plain,
% 3.64/3.83 ($false),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[5253, 178, 10438, 8042, 10436, 10535, 10527])).
% 3.64/3.83 tff(10537,plain,(b(s(s(s(elem!1))), s(s(s(s(z))))) | b(elem!1, s(s(z))) | b(elem!1, s(s(s(elem!1)))) | b(s(s(z)), elem!1) | b(s(s(s(s(z)))), z) | b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.83 tff(10538,plain,
% 3.64/3.83 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[10537, 3241, 3240, 461, 3170, 1])).
% 3.64/3.83 tff(10539,plain,
% 3.64/3.83 (b(z, s(s(s(s(s(s(s(s(s(s(z))))))))))) <=> b(z, s(s(s(elem!1))))),
% 3.64/3.83 inference(monotonicity,[status(thm)],[4345])).
% 3.64/3.83 tff(10540,plain,
% 3.64/3.83 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 3.64/3.83 inference(symmetry,[status(thm)],[10539])).
% 3.64/3.83 tff(10541,plain,
% 3.64/3.83 (b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 3.64/3.83 inference(modus_ponens,[status(thm)],[2043, 10540])).
% 3.64/3.83 tff(10542,assumption,(~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))), introduced(assumption)).
% 3.64/3.83 tff(10543,plain,
% 3.64/3.83 ($false),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[10542, 4419])).
% 3.64/3.83 tff(10544,plain,(b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z))))))))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~(elem!1 = s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.83 tff(10545,plain,
% 3.64/3.83 (b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[10544, 4291, 679])).
% 3.64/3.83 tff(10546,plain,
% 3.64/3.83 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(s(s(z))))))))))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.64/3.83 inference(monotonicity,[status(thm)],[4345])).
% 3.64/3.83 tff(10547,plain,
% 3.64/3.83 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(s(s(s(z))))))))))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 3.64/3.83 inference(monotonicity,[status(thm)],[4345])).
% 3.64/3.83 tff(10548,plain,
% 3.64/3.83 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(s(s(s(z))))))))))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.64/3.83 inference(transitivity,[status(thm)],[10547, 3289])).
% 3.64/3.83 tff(10549,plain,
% 3.64/3.83 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 3.64/3.83 inference(symmetry,[status(thm)],[10548])).
% 3.64/3.83 tff(10550,plain,
% 3.64/3.83 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(s(s(s(s(s(s(s(s(z))))))))))))),
% 3.64/3.83 inference(monotonicity,[status(thm)],[10549])).
% 3.64/3.83 tff(10551,plain,
% 3.64/3.83 (~(s(s(s(s(z)))) = s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 3.64/3.83 inference(modus_ponens,[status(thm)],[10484, 10550])).
% 3.64/3.83 tff(10552,plain,
% 3.64/3.83 (r(s(s(s(s(s(s(s(s(s(s(z)))))))))), z) <=> r(s(s(s(elem!1))), z)),
% 3.64/3.83 inference(monotonicity,[status(thm)],[4345])).
% 3.64/3.83 tff(10553,plain,
% 3.64/3.83 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)),
% 3.64/3.83 inference(symmetry,[status(thm)],[10552])).
% 3.64/3.83 tff(10554,plain,
% 3.64/3.83 (~b(s(s(s(elem!1))), z)),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[7978, 3425, 4291, 3549, 2043])).
% 3.64/3.83 tff(10555,plain,
% 3.64/3.83 (r(s(s(s(elem!1))), z)),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[1565, 10554])).
% 3.64/3.83 tff(10556,plain,
% 3.64/3.83 (r(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)),
% 3.64/3.83 inference(modus_ponens,[status(thm)],[10555, 10553])).
% 3.64/3.83 tff(10557,plain,
% 3.64/3.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 3.64/3.83 inference(rewrite,[status(thm)],[])).
% 3.64/3.83 tff(10558,plain,
% 3.64/3.83 (((~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(s(s(z))))))))))))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 3.64/3.83 inference(rewrite,[status(thm)],[])).
% 3.64/3.83 tff(10559,plain,
% 3.64/3.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(s(s(z))))))))))))))),
% 3.64/3.83 inference(monotonicity,[status(thm)],[10558])).
% 3.64/3.83 tff(10560,plain,
% 3.64/3.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 3.64/3.83 inference(transitivity,[status(thm)],[10559, 10557])).
% 3.64/3.83 tff(10561,plain,
% 3.64/3.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 3.64/3.83 inference(quant_inst,[status(thm)],[])).
% 3.64/3.83 tff(10562,plain,
% 3.64/3.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(s(s(z))))))))))))),
% 3.64/3.83 inference(modus_ponens,[status(thm)],[10561, 10560])).
% 3.64/3.83 tff(10563,plain,
% 3.64/3.83 ((~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(s(s(z))))))))))))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[10562, 118, 194])).
% 3.64/3.83 tff(10564,plain,
% 3.64/3.83 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[10563, 10556])).
% 3.64/3.83 tff(10565,plain,
% 3.64/3.83 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(s(s(s(s(s(z))))))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(s(s(z))))))))))) | r(s(s(s(s(z)))), s(s(s(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(s(s(s(z))))))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(s(s(z))))))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(s(s(z))))))))))))),
% 3.64/3.83 inference(rewrite,[status(thm)],[])).
% 3.64/3.83 tff(10566,plain,
% 3.64/3.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(s(s(s(s(s(z))))))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(s(s(z))))))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(s(s(z))))))))))))),
% 3.64/3.83 inference(quant_inst,[status(thm)],[])).
% 3.64/3.83 tff(10567,plain,
% 3.64/3.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(s(s(s(s(s(z))))))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(s(s(z))))))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 3.64/3.83 inference(modus_ponens,[status(thm)],[10566, 10565])).
% 3.64/3.83 tff(10568,plain,
% 3.64/3.83 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(s(s(s(z))))))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[10567, 41, 10564])).
% 3.64/3.83 tff(10569,plain,
% 3.64/3.83 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[10568, 10551])).
% 3.64/3.83 tff(10570,plain,
% 3.64/3.83 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.64/3.83 inference(modus_ponens,[status(thm)],[10569, 10546])).
% 3.64/3.83 tff(10571,plain,
% 3.64/3.83 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[3559, 193, 224])).
% 3.64/3.83 tff(10572,plain,
% 3.64/3.83 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[222, 10571])).
% 3.64/3.83 tff(10573,plain,
% 3.64/3.83 ((z = elem!1) <=> (z = s(s(s(s(s(s(s(z))))))))),
% 3.64/3.83 inference(monotonicity,[status(thm)],[679])).
% 3.64/3.83 tff(10574,plain,
% 3.64/3.83 ((z = elem!1) <=> (s(s(s(s(s(s(s(z))))))) = z)),
% 3.64/3.83 inference(transitivity,[status(thm)],[10573, 263])).
% 3.64/3.83 tff(10575,plain,
% 3.64/3.83 ((s(s(s(s(s(s(s(z))))))) = z) <=> (z = elem!1)),
% 3.64/3.83 inference(symmetry,[status(thm)],[10574])).
% 3.64/3.83 tff(10576,plain,
% 3.64/3.83 ((~(s(s(s(s(s(s(s(z))))))) = z)) <=> (~(z = elem!1))),
% 3.64/3.83 inference(monotonicity,[status(thm)],[10575])).
% 3.64/3.83 tff(10577,plain,
% 3.64/3.83 (~(z = elem!1)),
% 3.64/3.83 inference(modus_ponens,[status(thm)],[128, 10576])).
% 3.64/3.83 tff(10578,plain,
% 3.64/3.83 (~(s(s(elem!1)) = s(s(z)))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[2386, 10577])).
% 3.64/3.83 tff(10579,plain,
% 3.64/3.83 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[8244, 10578])).
% 3.64/3.83 tff(10580,plain,
% 3.64/3.83 (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[4103, 10570, 3831, 10572, 104])).
% 3.64/3.83 tff(10581,plain,
% 3.64/3.83 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.83 inference(monotonicity,[status(thm)],[679])).
% 3.64/3.83 tff(10582,plain,
% 3.64/3.83 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.83 inference(modus_ponens,[status(thm)],[1597, 10581])).
% 3.64/3.83 tff(10583,plain,
% 3.64/3.83 ($false),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[8928, 10582])).
% 3.64/3.83 tff(10584,plain,((~b(s(s(s(elem!1))), elem!1)) | b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))) | (~(elem!1 = s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.83 tff(10585,plain,
% 3.64/3.83 (~b(s(s(s(elem!1))), elem!1)),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[10584, 10580, 679])).
% 3.64/3.83 tff(10586,plain,
% 3.64/3.83 (r(s(s(s(elem!1))), elem!1)),
% 3.64/3.83 inference(unit_resolution,[status(thm)],[570, 10585, 10489])).
% 3.64/3.83 tff(10587,plain,
% 3.64/3.84 (~r(z, elem!1)),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[6384, 10586, 3549, 3425, 4291])).
% 3.64/3.84 tff(10588,plain,
% 3.64/3.84 (b(z, elem!1)),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[585, 10587, 10577])).
% 3.64/3.84 tff(10589,plain,
% 3.64/3.84 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[4243, 10588, 679])).
% 3.64/3.84 tff(10590,plain,
% 3.64/3.84 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[8721, 1126, 8246, 104, 3831, 251, 3828, 5128])).
% 3.64/3.84 tff(10591,plain,
% 3.64/3.84 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[4950, 10590, 4938])).
% 3.64/3.84 tff(10592,plain,
% 3.64/3.84 (~b(z, s(s(s(z))))),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[9431, 1126, 104, 3831, 595, 8246, 2043, 5128])).
% 3.64/3.84 tff(10593,plain,
% 3.64/3.84 (r(z, s(s(s(z))))),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[4920, 10592])).
% 3.64/3.84 tff(10594,plain,
% 3.64/3.84 ($false),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[4961, 10593, 10591, 194])).
% 3.64/3.84 tff(10595,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), 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(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.84 tff(10596,plain,
% 3.64/3.84 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[10595, 10589, 104, 3831, 194, 10579, 2043, 5128, 10572, 10570])).
% 3.64/3.84 tff(10597,plain,
% 3.64/3.84 (r(s(s(s(z))), s(s(s(s(z)))))),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[4928, 10596, 4890])).
% 3.64/3.84 tff(10598,plain,
% 3.64/3.84 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[5101, 10597, 3425, 145])).
% 3.64/3.84 tff(10599,plain,
% 3.64/3.84 (b(s(s(z)), s(s(s(s(z)))))),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[164, 10598])).
% 3.64/3.84 tff(10600,plain,
% 3.64/3.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 3.64/3.84 inference(rewrite,[status(thm)],[])).
% 3.64/3.84 tff(10601,plain,
% 3.64/3.84 (((~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(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(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 3.64/3.84 inference(rewrite,[status(thm)],[])).
% 3.64/3.84 tff(10602,plain,
% 3.64/3.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(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(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z))))))))))))))),
% 3.64/3.84 inference(monotonicity,[status(thm)],[10601])).
% 3.64/3.84 tff(10603,plain,
% 3.64/3.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(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(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 3.64/3.84 inference(transitivity,[status(thm)],[10602, 10600])).
% 3.64/3.84 tff(10604,plain,
% 3.64/3.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(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(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(z)))))),
% 3.64/3.84 inference(quant_inst,[status(thm)],[])).
% 3.64/3.84 tff(10605,plain,
% 3.64/3.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z))))))))))))),
% 3.64/3.84 inference(modus_ponens,[status(thm)],[10604, 10603])).
% 3.64/3.84 tff(10606,plain,
% 3.64/3.84 ($false),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[10605, 178, 3549, 10599, 10545, 10497, 10541])).
% 3.64/3.84 tff(10607,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(z, 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(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.84 tff(10608,plain,
% 3.64/3.84 (~r(s(s(s(s(z)))), s(s(z)))),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[10607, 7954, 10413, 47, 10516, 10538, 3244, 10477, 10469, 10525])).
% 3.64/3.84 tff(10609,plain,
% 3.64/3.84 (b(s(s(s(s(z)))), s(s(z)))),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[102, 10608])).
% 3.64/3.84 tff(10610,plain,
% 3.64/3.84 (~b(s(s(z)), s(s(s(s(z)))))),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[10512, 10609, 10413, 10479, 10469, 10538])).
% 3.64/3.84 tff(10611,plain,
% 3.64/3.84 (r(s(s(z)), s(s(s(s(z)))))),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[164, 10610])).
% 3.64/3.84 tff(10612,plain,
% 3.64/3.84 (~r(s(s(z)), z)),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[155, 10611, 47])).
% 3.64/3.84 tff(10613,plain,
% 3.64/3.84 (b(s(s(z)), z)),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[3249, 10612])).
% 3.64/3.84 tff(10614,plain,
% 3.64/3.84 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[5101, 10613, 10611, 47])).
% 3.64/3.84 tff(10615,plain,
% 3.64/3.84 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[4928, 10614, 4890])).
% 3.64/3.84 tff(10616,plain,
% 3.64/3.84 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[5624, 10611, 10525])).
% 3.64/3.84 tff(10617,plain,
% 3.64/3.84 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[222, 10616])).
% 3.64/3.84 tff(10618,plain,
% 3.64/3.84 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(s(s(z))))))))))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.64/3.84 inference(monotonicity,[status(thm)],[10473])).
% 3.64/3.84 tff(10619,plain,
% 3.64/3.84 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(s(s(s(z))))))))))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 3.64/3.84 inference(monotonicity,[status(thm)],[10473])).
% 3.64/3.84 tff(10620,plain,
% 3.64/3.84 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(s(s(s(z))))))))))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.64/3.84 inference(transitivity,[status(thm)],[10619, 3289])).
% 3.64/3.84 tff(10621,plain,
% 3.64/3.84 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 3.64/3.84 inference(symmetry,[status(thm)],[10620])).
% 3.64/3.84 tff(10622,plain,
% 3.64/3.84 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(s(s(s(s(s(s(s(s(z))))))))))))),
% 3.64/3.84 inference(monotonicity,[status(thm)],[10621])).
% 3.64/3.84 tff(10623,plain,
% 3.64/3.84 (~(s(s(s(s(z)))) = s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 3.64/3.84 inference(modus_ponens,[status(thm)],[10433, 10622])).
% 3.64/3.84 tff(10624,plain,
% 3.64/3.84 (r(s(s(s(s(s(s(s(s(s(s(z)))))))))), z) <=> r(s(s(s(elem!1))), z)),
% 3.64/3.84 inference(monotonicity,[status(thm)],[10473])).
% 3.64/3.84 tff(10625,plain,
% 3.64/3.84 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)),
% 3.64/3.84 inference(symmetry,[status(thm)],[10624])).
% 3.64/3.84 tff(10626,plain,
% 3.64/3.84 (~r(z, s(s(z)))),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[3478, 10611, 47])).
% 3.64/3.84 tff(10627,plain,
% 3.64/3.84 (b(z, s(s(z)))),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[143, 10626])).
% 3.64/3.84 tff(10628,plain,
% 3.64/3.84 (~b(s(s(s(elem!1))), z)),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[7978, 10613, 10469, 10627, 7954])).
% 3.64/3.84 tff(10629,plain,
% 3.64/3.84 (r(s(s(s(elem!1))), z)),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[1565, 10628])).
% 3.64/3.84 tff(10630,plain,
% 3.64/3.84 (r(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)),
% 3.64/3.84 inference(modus_ponens,[status(thm)],[10629, 10625])).
% 3.64/3.84 tff(10631,plain,
% 3.64/3.84 ((~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(s(s(z))))))))))))),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[10562, 118, 3244])).
% 3.64/3.84 tff(10632,plain,
% 3.64/3.84 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[10631, 10630])).
% 3.64/3.84 tff(10633,plain,
% 3.64/3.84 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(s(s(s(z))))))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[10567, 41, 10632])).
% 3.64/3.84 tff(10634,plain,
% 3.64/3.84 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[10633, 10623])).
% 3.64/3.84 tff(10635,plain,
% 3.64/3.84 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.64/3.84 inference(modus_ponens,[status(thm)],[10634, 10618])).
% 3.64/3.84 tff(10636,plain,
% 3.64/3.84 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[10595, 10635, 10516, 10538, 3244, 10431, 7954, 10477, 10617, 10615])).
% 3.64/3.84 tff(10637,plain,
% 3.64/3.84 (~b(z, elem!1)),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[4243, 10636, 10413])).
% 3.64/3.84 tff(10638,plain,
% 3.64/3.84 (~(s(s(s(elem!1))) = elem!1)),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[2489, 10461])).
% 3.64/3.84 tff(10639,plain,
% 3.64/3.84 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.84 inference(monotonicity,[status(thm)],[10413])).
% 3.64/3.84 tff(10640,plain,
% 3.64/3.84 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(elem!1))), elem!1)),
% 3.64/3.84 inference(symmetry,[status(thm)],[10639])).
% 3.64/3.84 tff(10641,plain,
% 3.64/3.84 (b(s(s(s(s(s(s(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))))))))),
% 3.64/3.84 inference(monotonicity,[status(thm)],[10473])).
% 3.64/3.84 tff(10642,plain,
% 3.64/3.84 (b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(elem!1))), elem!1)),
% 3.64/3.84 inference(transitivity,[status(thm)],[10641, 10640])).
% 3.64/3.84 tff(10643,plain,
% 3.64/3.84 ((~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(s(s(elem!1))), elem!1))),
% 3.64/3.84 inference(monotonicity,[status(thm)],[10642])).
% 3.64/3.84 tff(10644,plain,
% 3.64/3.84 (b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.64/3.84 inference(monotonicity,[status(thm)],[10473])).
% 3.64/3.84 tff(10645,plain,
% 3.64/3.84 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))),
% 3.64/3.84 inference(symmetry,[status(thm)],[10644])).
% 3.64/3.84 tff(10646,plain,
% 3.64/3.84 (b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))),
% 3.64/3.84 inference(modus_ponens,[status(thm)],[10538, 10645])).
% 3.64/3.84 tff(10647,plain,
% 3.64/3.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(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(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(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(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))))),
% 3.64/3.84 inference(rewrite,[status(thm)],[])).
% 3.64/3.84 tff(10648,plain,
% 3.64/3.84 (((~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(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(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))))))))) | (~b(s(s(s(s(s(s(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(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(s(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(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))))),
% 3.64/3.84 inference(rewrite,[status(thm)],[])).
% 3.64/3.84 tff(10649,plain,
% 3.64/3.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(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))))))))) | (~b(s(s(s(s(s(s(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(s(s(s(z)))))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(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(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z)))))))))))),
% 3.64/3.84 inference(monotonicity,[status(thm)],[10648])).
% 3.64/3.84 tff(10650,plain,
% 3.64/3.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(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))))))))) | (~b(s(s(s(s(s(s(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(s(s(s(z)))))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(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(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))))),
% 3.64/3.84 inference(transitivity,[status(thm)],[10649, 10647])).
% 3.64/3.84 tff(10651,plain,
% 3.64/3.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(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))))))))) | (~b(s(s(s(s(s(s(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(s(s(s(z)))))))))))))),
% 3.64/3.84 inference(quant_inst,[status(thm)],[])).
% 3.64/3.84 tff(10652,plain,
% 3.64/3.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z)))))))))),
% 3.64/3.84 inference(modus_ponens,[status(thm)],[10651, 10650])).
% 3.64/3.84 tff(10653,plain,
% 3.64/3.84 ((~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z)))))))))),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[10652, 178, 10516, 10617])).
% 3.64/3.84 tff(10654,plain,
% 3.64/3.84 (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[10653, 10634, 10646])).
% 3.64/3.84 tff(10655,plain,
% 3.64/3.84 (~b(s(s(s(elem!1))), elem!1)),
% 3.64/3.84 inference(modus_ponens,[status(thm)],[10654, 10643])).
% 3.64/3.84 tff(10656,plain,
% 3.64/3.84 (r(s(s(s(elem!1))), elem!1)),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[570, 10655, 10638])).
% 3.64/3.84 tff(10657,plain,
% 3.64/3.84 (~r(z, elem!1)),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[6384, 10656, 10627, 10613, 10469])).
% 3.64/3.84 tff(10658,plain,
% 3.64/3.84 ($false),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[585, 10657, 10637, 10418])).
% 3.64/3.84 tff(10659,plain,(b(s(s(z)), elem!1) | b(elem!1, s(s(s(elem!1)))) | b(elem!1, s(s(z))) | b(s(s(s(s(z)))), z) | b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.84 tff(10660,plain,
% 3.64/3.84 (b(elem!1, s(s(s(elem!1))))),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[10659, 3239, 1, 299, 3224])).
% 3.64/3.84 tff(10661,plain,
% 3.64/3.84 (b(s(s(z)), s(s(s(elem!1))))),
% 3.64/3.84 inference(modus_ponens,[status(thm)],[10660, 3226])).
% 3.64/3.84 tff(10662,plain,
% 3.64/3.84 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[4173, 3822, 2857])).
% 3.64/3.84 tff(10663,plain,
% 3.64/3.84 ($false),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[3296, 41, 8808, 3293, 4166])).
% 3.64/3.84 tff(10664,plain,(b(s(s(s(s(z)))), s(s(s(elem!1)))) | r(s(s(s(s(z)))), s(s(s(elem!1)))) | (s(s(s(s(z)))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.84 tff(10665,plain,
% 3.64/3.84 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[10664, 3288, 9301])).
% 3.64/3.84 tff(10666,plain,
% 3.64/3.84 ($false),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[4816, 178, 4291, 167, 202, 3828, 3831])).
% 3.64/3.84 tff(10667,plain,((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.84 tff(10668,plain,
% 3.64/3.84 ($false),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[10667, 10665, 10662, 202, 167, 4291])).
% 3.64/3.84 tff(10669,plain,((~r(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.84 tff(10670,plain,
% 3.64/3.84 (~r(z, s(s(s(elem!1))))),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[10669, 10661, 302, 202, 3208, 300, 47])).
% 3.64/3.84 tff(10671,plain,
% 3.64/3.84 (b(z, s(s(s(elem!1))))),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[2095, 10670])).
% 3.64/3.84 tff(10672,plain,
% 3.64/3.84 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[8280, 10671, 273, 202, 289, 47, 300, 3224])).
% 3.64/3.84 tff(10673,plain,
% 3.64/3.84 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[4173, 10672, 3208])).
% 3.64/3.84 tff(10674,plain,
% 3.64/3.84 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.64/3.84 inference(symmetry,[status(thm)],[9107])).
% 3.64/3.84 tff(10675,plain,
% 3.64/3.84 ((~b(s(s(s(elem!1))), s(s(elem!1)))) <=> (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.64/3.84 inference(monotonicity,[status(thm)],[10674])).
% 3.64/3.84 tff(10676,assumption,(~b(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 3.64/3.84 tff(10677,plain,
% 3.64/3.84 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.64/3.84 inference(modus_ponens,[status(thm)],[10676, 10675])).
% 3.64/3.84 tff(10678,plain,
% 3.64/3.84 ($false),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[3831, 10677])).
% 3.64/3.84 tff(10679,plain,(b(s(s(s(elem!1))), s(s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~(s(s(z)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.84 tff(10680,plain,
% 3.64/3.84 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[10679, 10673, 3180])).
% 3.64/3.84 tff(10681,plain,
% 3.64/3.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.64/3.84 inference(rewrite,[status(thm)],[])).
% 3.64/3.84 tff(10682,plain,
% 3.64/3.84 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.64/3.84 inference(rewrite,[status(thm)],[])).
% 3.64/3.84 tff(10683,plain,
% 3.64/3.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 3.64/3.84 inference(monotonicity,[status(thm)],[10682])).
% 3.64/3.84 tff(10684,plain,
% 3.64/3.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.64/3.84 inference(transitivity,[status(thm)],[10683, 10681])).
% 3.64/3.84 tff(10685,plain,
% 3.64/3.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)))),
% 3.64/3.84 inference(quant_inst,[status(thm)],[])).
% 3.64/3.84 tff(10686,plain,
% 3.64/3.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 3.64/3.84 inference(modus_ponens,[status(thm)],[10685, 10684])).
% 3.64/3.84 tff(10687,plain,
% 3.64/3.84 ($false),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[10686, 178, 818, 10671, 10660, 10680, 3187])).
% 3.64/3.84 tff(10688,plain,((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | b(z, s(s(s(s(z))))) | (~r(s(s(z)), z)) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | (elem!1 = z) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.84 tff(10689,plain,
% 3.64/3.84 (~b(z, elem!1)),
% 3.64/3.84 inference(unit_resolution,[status(thm)],[10688, 202, 144, 1, 106, 286, 290, 107, 104])).
% 3.64/3.85 tff(10690,plain,
% 3.64/3.85 (r(z, elem!1)),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[585, 10689, 318])).
% 3.64/3.85 tff(10691,plain,
% 3.64/3.85 (r(z, s(s(z)))),
% 3.64/3.85 inference(modus_ponens,[status(thm)],[10690, 3178])).
% 3.64/3.85 tff(10692,plain,
% 3.64/3.85 ($false),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[48, 10691])).
% 3.64/3.85 tff(10693,plain,((~b(s(s(s(s(z)))), s(s(z)))) | r(z, s(s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | (elem!1 = z) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.85 tff(10694,plain,
% 3.64/3.85 (~b(s(s(s(s(z)))), s(s(z)))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[10693, 286, 106, 107, 48, 290, 104, 1])).
% 3.64/3.85 tff(10695,plain,
% 3.64/3.85 (r(s(s(s(s(z)))), s(s(z)))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[102, 10694])).
% 3.64/3.85 tff(10696,plain,
% 3.64/3.85 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[3559, 10695, 287])).
% 3.64/3.85 tff(10697,plain,
% 3.64/3.85 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[222, 10696])).
% 3.64/3.85 tff(10698,plain,
% 3.64/3.85 (~r(s(s(s(s(z)))), z)),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[199, 10695, 106])).
% 3.64/3.85 tff(10699,plain,
% 3.64/3.85 (b(s(s(s(s(z)))), z)),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[191, 10698])).
% 3.64/3.85 tff(10700,plain,
% 3.64/3.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.64/3.85 inference(rewrite,[status(thm)],[])).
% 3.64/3.85 tff(10701,plain,
% 3.64/3.85 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, 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)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))) <=> ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.64/3.85 inference(rewrite,[status(thm)],[])).
% 3.64/3.85 tff(10702,plain,
% 3.64/3.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 3.64/3.85 inference(monotonicity,[status(thm)],[10701])).
% 3.64/3.85 tff(10703,plain,
% 3.64/3.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.64/3.85 inference(transitivity,[status(thm)],[10702, 10700])).
% 3.64/3.85 tff(10704,plain,
% 3.64/3.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 3.64/3.85 inference(quant_inst,[status(thm)],[])).
% 3.64/3.85 tff(10705,plain,
% 3.64/3.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 3.64/3.85 inference(modus_ponens,[status(thm)],[10704, 10703])).
% 3.64/3.85 tff(10706,plain,
% 3.64/3.85 ($false),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[10705, 178, 104, 10699, 10697, 289, 134])).
% 3.64/3.85 tff(10707,plain,(b(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)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | r(z, s(s(z))) | (elem!1 = z) | b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.85 tff(10708,plain,
% 3.64/3.85 (elem!1 = z),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[10707, 282, 106, 107, 48, 104, 1])).
% 3.64/3.85 tff(10709,assumption,(s(s(s(z))) = s(s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 3.64/3.85 tff(10710,plain,
% 3.64/3.85 (s(s(s(s(s(s(s(z))))))) = s(s(s(z)))),
% 3.64/3.85 inference(symmetry,[status(thm)],[10709])).
% 3.64/3.85 tff(10711,plain,
% 3.64/3.85 ($false),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[1104, 10710])).
% 3.64/3.85 tff(10712,plain,(~(s(s(s(z))) = s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.85 tff(10713,plain,
% 3.64/3.85 (~r(s(s(s(s(z)))), s(s(z)))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[199, 194, 106])).
% 3.64/3.85 tff(10714,plain,
% 3.64/3.85 (b(s(s(s(s(z)))), s(s(z)))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[102, 10713])).
% 3.64/3.85 tff(10715,plain,
% 3.64/3.85 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[281, 134, 104, 106, 145, 273])).
% 3.64/3.85 tff(10716,plain,
% 3.64/3.85 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[249, 10715])).
% 3.64/3.85 tff(10717,plain,
% 3.64/3.85 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[232, 10716, 106])).
% 3.64/3.85 tff(10718,plain,
% 3.64/3.85 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[271, 10717])).
% 3.64/3.85 tff(10719,plain,
% 3.64/3.85 (r(s(s(z)), elem!1) <=> r(s(s(z)), z)),
% 3.64/3.85 inference(monotonicity,[status(thm)],[928])).
% 3.64/3.85 tff(10720,plain,
% 3.64/3.85 (r(s(s(z)), z) <=> r(s(s(z)), elem!1)),
% 3.64/3.85 inference(symmetry,[status(thm)],[10719])).
% 3.64/3.85 tff(10721,plain,
% 3.64/3.85 (r(s(s(z)), elem!1)),
% 3.64/3.85 inference(modus_ponens,[status(thm)],[106, 10720])).
% 3.64/3.85 tff(10722,plain,
% 3.64/3.85 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(z))))),
% 3.64/3.85 inference(monotonicity,[status(thm)],[931])).
% 3.64/3.85 tff(10723,plain,
% 3.64/3.85 (r(z, s(s(s(z)))) <=> r(z, s(s(s(elem!1))))),
% 3.64/3.85 inference(symmetry,[status(thm)],[10722])).
% 3.64/3.85 tff(10724,plain,
% 3.64/3.85 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 3.64/3.85 inference(transitivity,[status(thm)],[10723, 4847])).
% 3.64/3.85 tff(10725,plain,
% 3.64/3.85 (r(elem!1, s(s(s(elem!1))))),
% 3.64/3.85 inference(modus_ponens,[status(thm)],[4952, 10724])).
% 3.64/3.85 tff(10726,plain,
% 3.64/3.85 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[7973, 10725, 438])).
% 3.64/3.85 tff(10727,plain,
% 3.64/3.85 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(z))) = s(s(s(s(z)))))),
% 3.64/3.85 inference(monotonicity,[status(thm)],[931])).
% 3.64/3.85 tff(10728,plain,
% 3.64/3.85 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 3.64/3.85 inference(transitivity,[status(thm)],[10727, 4936])).
% 3.64/3.85 tff(10729,plain,
% 3.64/3.85 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.64/3.85 inference(symmetry,[status(thm)],[10728])).
% 3.64/3.85 tff(10730,plain,
% 3.64/3.85 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(z))))))),
% 3.64/3.85 inference(monotonicity,[status(thm)],[10729])).
% 3.64/3.85 tff(10731,plain,
% 3.64/3.85 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.64/3.85 inference(modus_ponens,[status(thm)],[4938, 10730])).
% 3.64/3.85 tff(10732,plain,
% 3.64/3.85 (r(z, s(s(s(elem!1))))),
% 3.64/3.85 inference(modus_ponens,[status(thm)],[4952, 10723])).
% 3.64/3.85 tff(10733,plain,
% 3.64/3.85 (~b(s(s(z)), s(s(s(elem!1))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[10669, 10732, 167, 202, 10731, 194, 145])).
% 3.64/3.85 tff(10734,plain,
% 3.64/3.85 ($false),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[4223, 10733, 10726])).
% 3.64/3.85 tff(10735,plain,((~r(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.85 tff(10736,plain,
% 3.64/3.85 (~r(z, s(s(s(z))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[10735, 10714, 165, 194, 145, 10721, 928])).
% 3.64/3.85 tff(10737,plain,
% 3.64/3.85 (b(z, s(s(s(z))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[4920, 10736])).
% 3.64/3.85 tff(10738,plain,
% 3.64/3.85 (b(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(z))))),
% 3.64/3.85 inference(monotonicity,[status(thm)],[931])).
% 3.64/3.85 tff(10739,plain,
% 3.64/3.85 (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(elem!1))))),
% 3.64/3.85 inference(symmetry,[status(thm)],[10738])).
% 3.64/3.85 tff(10740,plain,
% 3.64/3.85 ((~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(elem!1)))))),
% 3.64/3.85 inference(monotonicity,[status(thm)],[10739])).
% 3.64/3.85 tff(10741,plain,
% 3.64/3.85 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.64/3.85 inference(modus_ponens,[status(thm)],[9428, 10740])).
% 3.64/3.85 tff(10742,plain,
% 3.64/3.85 ((s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(z))))),
% 3.64/3.85 inference(monotonicity,[status(thm)],[931])).
% 3.64/3.85 tff(10743,plain,
% 3.64/3.85 ((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))))),
% 3.64/3.85 inference(symmetry,[status(thm)],[10742])).
% 3.64/3.85 tff(10744,plain,
% 3.64/3.85 ((~(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)))))),
% 3.64/3.85 inference(monotonicity,[status(thm)],[10743])).
% 3.64/3.85 tff(10745,plain,
% 3.64/3.85 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 3.64/3.85 inference(modus_ponens,[status(thm)],[1104, 10744])).
% 3.64/3.85 tff(10746,plain,
% 3.64/3.85 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 3.64/3.85 inference(monotonicity,[status(thm)],[5207])).
% 3.64/3.85 tff(10747,plain,
% 3.64/3.85 (~b(s(s(s(z))), s(s(z)))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[4963, 1126, 273, 202, 167, 194])).
% 3.64/3.85 tff(10748,plain,
% 3.64/3.85 (r(s(s(s(z))), s(s(z)))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[4966, 10747])).
% 3.64/3.85 tff(10749,plain,
% 3.64/3.85 (r(s(s(s(elem!1))), s(s(z)))),
% 3.64/3.85 inference(modus_ponens,[status(thm)],[10748, 10746])).
% 3.64/3.85 tff(10750,plain,
% 3.64/3.85 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[10401, 10749, 107])).
% 3.64/3.85 tff(10751,plain,
% 3.64/3.85 (b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[5118, 10750, 10745])).
% 3.64/3.85 tff(10752,plain,
% 3.64/3.85 ($false),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[10751, 10741])).
% 3.64/3.85 tff(10753,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~(elem!1 = z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.85 tff(10754,plain,
% 3.64/3.85 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[10753, 10737, 107, 104, 10718, 928, 273, 10714, 165, 194])).
% 3.64/3.85 tff(10755,plain,
% 3.64/3.85 (b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[4928, 4890])).
% 3.64/3.85 tff(10756,plain,
% 3.64/3.85 (r(s(s(s(z))), s(s(s(s(z)))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[10755, 10754])).
% 3.64/3.85 tff(10757,plain,
% 3.64/3.85 (~r(s(s(s(z))), z)),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[4899, 118, 145, 10756])).
% 3.64/3.85 tff(10758,plain,
% 3.64/3.85 (b(s(s(s(z))), z)),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[4903, 41, 77, 10757])).
% 3.64/3.85 tff(10759,plain,
% 3.64/3.85 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[1319, 178, 10718, 134, 10737, 10758])).
% 3.64/3.85 tff(10760,plain,
% 3.64/3.85 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[5031, 41, 10759, 10712])).
% 3.64/3.85 tff(10761,plain,
% 3.64/3.85 (~r(s(s(s(z))), s(s(z)))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[8218, 10760, 107])).
% 3.64/3.85 tff(10762,plain,
% 3.64/3.85 (b(s(s(s(z))), s(s(z)))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[4966, 10761])).
% 3.64/3.85 tff(10763,plain,
% 3.64/3.85 (~r(s(s(z)), s(s(s(z))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[10533, 118, 10716, 10760])).
% 3.64/3.85 tff(10764,plain,
% 3.64/3.85 (b(s(s(z)), s(s(s(z))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[5088, 10763])).
% 3.64/3.85 tff(10765,plain,
% 3.64/3.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 3.64/3.85 inference(rewrite,[status(thm)],[])).
% 3.64/3.85 tff(10766,plain,
% 3.64/3.85 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 3.64/3.85 inference(rewrite,[status(thm)],[])).
% 3.64/3.85 tff(10767,plain,
% 3.64/3.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))))),
% 3.64/3.85 inference(monotonicity,[status(thm)],[10766])).
% 3.64/3.85 tff(10768,plain,
% 3.64/3.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 3.64/3.85 inference(transitivity,[status(thm)],[10767, 10765])).
% 3.64/3.85 tff(10769,plain,
% 3.64/3.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)))),
% 3.64/3.85 inference(quant_inst,[status(thm)],[])).
% 3.64/3.85 tff(10770,plain,
% 3.64/3.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))),
% 3.64/3.85 inference(modus_ponens,[status(thm)],[10769, 10768])).
% 3.64/3.85 tff(10771,plain,
% 3.64/3.85 ($false),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[10770, 178, 273, 10737, 10764, 10758, 10762])).
% 3.64/3.85 tff(10772,plain,((~r(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~(elem!1 = z)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.85 tff(10773,plain,
% 3.64/3.85 (~r(s(s(s(s(z)))), z)),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[10772, 107, 144, 47, 104, 10708, 106])).
% 3.64/3.85 tff(10774,plain,
% 3.64/3.85 (b(s(s(s(s(z)))), z)),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[191, 10773])).
% 3.64/3.85 tff(10775,plain,
% 3.64/3.85 (~b(s(s(s(s(z)))), s(s(z)))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[298, 10774, 104, 144, 134])).
% 3.64/3.85 tff(10776,plain,
% 3.64/3.85 (r(s(s(s(s(z)))), s(s(z)))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[102, 10775])).
% 3.64/3.85 tff(10777,plain,
% 3.64/3.85 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[3559, 10776, 283])).
% 3.64/3.85 tff(10778,plain,
% 3.64/3.85 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[222, 10777])).
% 3.64/3.85 tff(10779,plain,
% 3.64/3.85 ($false),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[10705, 178, 104, 10774, 10778, 285, 134])).
% 3.64/3.85 tff(10780,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | r(z, s(s(z))) | b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.85 tff(10781,plain,
% 3.64/3.85 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[10780, 106, 104, 48, 1])).
% 3.64/3.85 tff(10782,plain,
% 3.64/3.85 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[3578, 10781])).
% 3.64/3.85 tff(10783,plain,
% 3.64/3.85 ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[7840, 178, 144, 104, 302])).
% 3.64/3.85 tff(10784,plain,
% 3.64/3.85 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[10783, 10782])).
% 3.64/3.85 tff(10785,plain,
% 3.64/3.85 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[271, 10784])).
% 3.64/3.85 tff(10786,plain,
% 3.64/3.85 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[212, 10785, 47])).
% 3.64/3.85 tff(10787,plain,
% 3.64/3.85 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[222, 10786])).
% 3.64/3.85 tff(10788,plain,
% 3.64/3.85 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[232, 10785, 106])).
% 3.64/3.85 tff(10789,plain,
% 3.64/3.85 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[249, 10788])).
% 3.64/3.85 tff(10790,plain,
% 3.64/3.85 ($false),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[9047, 178, 104, 10789, 302, 10787, 10782])).
% 3.64/3.85 tff(10791,plain,((~r(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | r(z, s(s(z))) | b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.85 tff(10792,plain,
% 3.64/3.85 (~r(s(s(z)), z)),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[10791, 1, 48, 104])).
% 3.64/3.85 tff(10793,plain,
% 3.64/3.85 (b(s(s(z)), z)),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[3249, 10792])).
% 3.64/3.85 tff(10794,plain,
% 3.64/3.85 (r(s(s(z)), s(s(s(s(z)))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[164, 105])).
% 3.64/3.85 tff(10795,plain,
% 3.64/3.85 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[5101, 10794, 47, 5619])).
% 3.64/3.85 tff(10796,plain,
% 3.64/3.85 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[10755, 10795])).
% 3.64/3.85 tff(10797,plain,
% 3.64/3.85 (~b(z, s(s(s(elem!1))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[8234, 3251, 145, 147])).
% 3.64/3.85 tff(10798,plain,
% 3.64/3.85 ($false),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[2095, 10797, 8021])).
% 3.64/3.85 tff(10799,plain,((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.85 tff(10800,plain,
% 3.64/3.85 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[10799, 10794, 47])).
% 3.64/3.85 tff(10801,plain,
% 3.64/3.85 (r(elem!1, z)),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[498, 5723, 290])).
% 3.64/3.85 tff(10802,plain,
% 3.64/3.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.64/3.85 inference(rewrite,[status(thm)],[])).
% 3.64/3.85 tff(10803,plain,
% 3.64/3.85 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.64/3.85 inference(rewrite,[status(thm)],[])).
% 3.64/3.85 tff(10804,plain,
% 3.64/3.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.64/3.85 inference(monotonicity,[status(thm)],[10803])).
% 3.64/3.85 tff(10805,plain,
% 3.64/3.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.64/3.85 inference(transitivity,[status(thm)],[10804, 10802])).
% 3.64/3.85 tff(10806,plain,
% 3.64/3.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)))),
% 3.64/3.85 inference(quant_inst,[status(thm)],[])).
% 3.64/3.85 tff(10807,plain,
% 3.64/3.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.64/3.85 inference(modus_ponens,[status(thm)],[10806, 10805])).
% 3.64/3.85 tff(10808,plain,
% 3.64/3.85 ($false),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[10807, 118, 437, 1265, 203])).
% 3.64/3.85 tff(10809,plain,((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.85 tff(10810,plain,
% 3.64/3.85 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[10809, 10801, 4236])).
% 3.64/3.85 tff(10811,plain,
% 3.64/3.85 (~r(elem!1, s(s(s(s(z)))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[478, 10801, 145])).
% 3.64/3.85 tff(10812,plain,
% 3.64/3.85 (b(elem!1, s(s(s(s(z)))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[483, 10811, 469])).
% 3.64/3.85 tff(10813,plain,
% 3.64/3.85 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[222, 4237])).
% 3.64/3.85 tff(10814,plain,
% 3.64/3.85 (~(s(s(z)) = elem!1)),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[3230, 6642])).
% 3.64/3.85 tff(10815,plain,
% 3.64/3.85 (~r(s(s(s(s(z)))), elem!1)),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[6033, 194, 10801])).
% 3.64/3.85 tff(10816,plain,
% 3.64/3.85 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[8548, 10815, 104, 10813, 469, 10811])).
% 3.64/3.85 tff(10817,plain,
% 3.64/3.85 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[691, 10816, 10810])).
% 3.64/3.85 tff(10818,plain,
% 3.64/3.85 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 3.64/3.85 inference(monotonicity,[status(thm)],[10817])).
% 3.64/3.85 tff(10819,plain,
% 3.64/3.85 (s(s(elem!1)) = s(s(s(s(s(s(s(s(s(z)))))))))),
% 3.64/3.85 inference(monotonicity,[status(thm)],[10818])).
% 3.64/3.85 tff(10820,plain,
% 3.64/3.85 (s(s(s(elem!1))) = s(s(s(s(s(s(s(s(s(s(z))))))))))),
% 3.64/3.85 inference(monotonicity,[status(thm)],[10819])).
% 3.64/3.85 tff(10821,plain,
% 3.64/3.85 (s(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(s(elem!1)))),
% 3.64/3.85 inference(symmetry,[status(thm)],[10820])).
% 3.64/3.85 tff(10822,plain,
% 3.64/3.85 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z))))))))))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.64/3.85 inference(monotonicity,[status(thm)],[10821])).
% 3.64/3.85 tff(10823,plain,
% 3.64/3.85 (b(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(s(s(s(s(s(s(s(z)))))))))))),
% 3.64/3.85 inference(symmetry,[status(thm)],[10822])).
% 3.64/3.85 tff(10824,plain,
% 3.64/3.85 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.64/3.85 inference(monotonicity,[status(thm)],[10817])).
% 3.64/3.85 tff(10825,plain,
% 3.64/3.85 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[10809, 10801, 203])).
% 3.64/3.85 tff(10826,plain,
% 3.64/3.85 (~r(s(s(s(s(z)))), elem!1)),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[6033, 10801, 194])).
% 3.64/3.85 tff(10827,plain,
% 3.64/3.85 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[8548, 10826, 104, 223, 469, 10811])).
% 3.64/3.85 tff(10828,assumption,(~r(s(s(z)), elem!1)), introduced(assumption)).
% 3.64/3.85 tff(10829,plain,
% 3.64/3.85 (b(s(s(z)), elem!1)),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[448, 10814, 10828])).
% 3.64/3.85 tff(10830,plain,
% 3.64/3.85 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.85 inference(monotonicity,[status(thm)],[679])).
% 3.64/3.85 tff(10831,plain,
% 3.64/3.85 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(z)), elem!1)),
% 3.64/3.85 inference(symmetry,[status(thm)],[10830])).
% 3.64/3.85 tff(10832,plain,
% 3.64/3.85 ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(s(z)), elem!1))),
% 3.64/3.85 inference(monotonicity,[status(thm)],[10831])).
% 3.64/3.85 tff(10833,plain,
% 3.64/3.85 (~b(s(s(z)), elem!1)),
% 3.64/3.85 inference(modus_ponens,[status(thm)],[286, 10832])).
% 3.64/3.85 tff(10834,plain,
% 3.64/3.85 ($false),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[817, 10833])).
% 3.64/3.85 tff(10835,plain,((~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), elem!1)) | b(s(s(z)), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.85 tff(10836,plain,
% 3.64/3.85 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[10835, 10829, 286])).
% 3.64/3.85 tff(10837,plain,
% 3.64/3.85 ($false),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[691, 10836, 10827, 10825])).
% 3.64/3.85 tff(10838,plain,(b(elem!1, z) | b(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)))))) | (elem!1 = s(s(s(s(z))))) | r(s(s(z)), elem!1) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(z)))))) | (elem!1 = z) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 3.64/3.85 tff(10839,plain,
% 3.64/3.85 (r(s(s(z)), elem!1)),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[10838, 194, 104, 286, 5723, 469, 4236, 145, 290, 5618])).
% 3.64/3.85 tff(10840,plain,
% 3.64/3.85 (~b(z, elem!1)),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[4243, 10817, 4235])).
% 3.64/3.85 tff(10841,plain,
% 3.64/3.85 (r(z, elem!1)),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[585, 10840, 318])).
% 3.64/3.85 tff(10842,plain,
% 3.64/3.85 (~r(z, s(s(s(elem!1))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[3319, 3311, 521])).
% 3.64/3.85 tff(10843,plain,
% 3.64/3.85 (b(z, s(s(s(elem!1))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[2095, 10842])).
% 3.64/3.85 tff(10844,plain,
% 3.64/3.85 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[7973, 3311, 438])).
% 3.64/3.85 tff(10845,plain,
% 3.64/3.85 (b(s(s(z)), s(s(s(elem!1))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[4223, 10844])).
% 3.64/3.85 tff(10846,plain,
% 3.64/3.85 ($false),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[7978, 6073, 10845, 273, 3461, 10843])).
% 3.64/3.85 tff(10847,plain,((~r(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.85 tff(10848,plain,
% 3.64/3.85 (~r(elem!1, s(s(s(elem!1))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[10847, 10841, 5619, 273, 10801, 10839])).
% 3.64/3.85 tff(10849,plain,
% 3.64/3.85 (~(s(elem!1) = s(s(z)))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[2832, 10817])).
% 3.64/3.85 tff(10850,plain,
% 3.64/3.85 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[2840, 10849])).
% 3.64/3.85 tff(10851,plain,
% 3.64/3.85 (~(elem!1 = s(s(s(elem!1))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[2859, 10850, 10817])).
% 3.64/3.85 tff(10852,plain,
% 3.64/3.85 (b(elem!1, s(s(s(elem!1))))),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[2054, 10851, 10848])).
% 3.64/3.85 tff(10853,plain,
% 3.64/3.85 (b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.64/3.85 inference(modus_ponens,[status(thm)],[10852, 10824])).
% 3.64/3.85 tff(10854,plain,
% 3.64/3.85 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 3.64/3.85 inference(modus_ponens,[status(thm)],[10853, 10823])).
% 3.64/3.85 tff(10855,plain,
% 3.64/3.85 (b(s(s(s(s(s(s(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))))))))),
% 3.64/3.85 inference(monotonicity,[status(thm)],[10821])).
% 3.64/3.85 tff(10856,plain,
% 3.64/3.85 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.85 inference(symmetry,[status(thm)],[10855])).
% 3.64/3.85 tff(10857,plain,
% 3.64/3.85 (~r(s(s(s(elem!1))), elem!1)),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[6388, 10841, 10839, 5619, 273])).
% 3.64/3.85 tff(10858,plain,
% 3.64/3.85 (~(s(s(s(elem!1))) = elem!1)),
% 3.64/3.85 inference(unit_resolution,[status(thm)],[2489, 10851])).
% 3.64/3.85 tff(10859,plain,
% 3.64/3.86 (b(s(s(s(elem!1))), elem!1)),
% 3.64/3.86 inference(unit_resolution,[status(thm)],[570, 10858, 10857])).
% 3.64/3.86 tff(10860,plain,
% 3.64/3.86 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.86 inference(unit_resolution,[status(thm)],[10584, 10859, 10817])).
% 3.64/3.86 tff(10861,plain,
% 3.64/3.86 (b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.86 inference(modus_ponens,[status(thm)],[10860, 10856])).
% 3.64/3.86 tff(10862,plain,
% 3.64/3.86 (b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.64/3.86 inference(monotonicity,[status(thm)],[10821])).
% 3.64/3.86 tff(10863,plain,
% 3.64/3.86 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))),
% 3.64/3.86 inference(symmetry,[status(thm)],[10862])).
% 3.64/3.86 tff(10864,plain,
% 3.64/3.86 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.64/3.86 inference(unit_resolution,[status(thm)],[4173, 10850, 4171])).
% 3.64/3.86 tff(10865,plain,
% 3.64/3.86 (b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))),
% 3.64/3.86 inference(modus_ponens,[status(thm)],[10864, 10863])).
% 3.64/3.86 tff(10866,plain,
% 3.64/3.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(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(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(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(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))))),
% 3.64/3.86 inference(rewrite,[status(thm)],[])).
% 3.64/3.86 tff(10867,plain,
% 3.64/3.86 (((~b(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))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(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(s(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(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))))))))) | (~b(s(s(s(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(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))))),
% 3.64/3.86 inference(rewrite,[status(thm)],[])).
% 3.64/3.86 tff(10868,plain,
% 3.64/3.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(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(s(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(s(s(s(s(s(s(z)))))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(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(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z)))))))))))),
% 3.64/3.86 inference(monotonicity,[status(thm)],[10867])).
% 3.64/3.86 tff(10869,plain,
% 3.64/3.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(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(s(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(s(s(s(s(s(s(z)))))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(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(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))))),
% 3.64/3.86 inference(transitivity,[status(thm)],[10868, 10866])).
% 3.64/3.86 tff(10870,plain,
% 3.64/3.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(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(s(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(s(s(s(s(s(s(z)))))))))))))),
% 3.64/3.86 inference(quant_inst,[status(thm)],[])).
% 3.64/3.86 tff(10871,plain,
% 3.64/3.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z)))))))))),
% 3.64/3.86 inference(modus_ponens,[status(thm)],[10870, 10869])).
% 3.64/3.86 tff(10872,plain,
% 3.64/3.86 ((~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z)))))))))),
% 3.64/3.86 inference(unit_resolution,[status(thm)],[10871, 178, 104, 10813])).
% 3.64/3.86 tff(10873,plain,
% 3.64/3.86 ($false),
% 3.64/3.86 inference(unit_resolution,[status(thm)],[10872, 10865, 10861, 10854])).
% 3.64/3.86 tff(10874,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | r(s(s(s(elem!1))), s(s(s(s(z))))) | b(z, s(s(s(s(s(s(s(z)))))))) | (elem!1 = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | b(elem!1, z) | (~r(z, s(s(s(s(z)))))) | (elem!1 = z) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 3.64/3.86 tff(10875,plain,
% 3.64/3.86 (~r(s(s(s(s(z)))), z)),
% 3.64/3.86 inference(unit_resolution,[status(thm)],[10874, 5723, 273, 4171, 4235, 469, 286, 104, 145, 290, 5618])).
% 3.64/3.86 tff(10876,plain,
% 3.64/3.86 (b(s(s(s(s(z)))), z)),
% 3.64/3.86 inference(unit_resolution,[status(thm)],[191, 10875])).
% 3.64/3.86 tff(10877,plain,
% 3.64/3.86 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.64/3.86 inference(unit_resolution,[status(thm)],[691, 10836, 10825])).
% 3.64/3.86 tff(10878,plain,
% 3.64/3.86 (r(s(s(s(s(z)))), elem!1)),
% 3.64/3.86 inference(unit_resolution,[status(thm)],[8548, 10877, 104, 223, 469, 10811])).
% 3.64/3.86 tff(10879,plain,
% 3.64/3.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.64/3.86 inference(rewrite,[status(thm)],[])).
% 3.64/3.86 tff(10880,plain,
% 3.64/3.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.64/3.86 inference(quant_inst,[status(thm)],[])).
% 3.64/3.86 tff(10881,plain,
% 3.64/3.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), elem!1))),
% 3.64/3.86 inference(modus_ponens,[status(thm)],[10880, 10879])).
% 3.64/3.86 tff(10882,plain,
% 3.64/3.86 ($false),
% 3.64/3.86 inference(unit_resolution,[status(thm)],[10881, 118, 450, 3132, 193])).
% 3.64/3.86 tff(10883,plain,((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.86 tff(10884,plain,
% 3.64/3.86 (~r(elem!1, s(s(z)))),
% 3.64/3.86 inference(unit_resolution,[status(thm)],[10883, 10878, 193])).
% 3.64/3.86 tff(10885,plain,
% 3.64/3.86 (b(elem!1, s(s(z)))),
% 3.64/3.86 inference(unit_resolution,[status(thm)],[467, 10884, 6642])).
% 3.64/3.86 tff(10886,plain,
% 3.64/3.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))),
% 3.64/3.86 inference(rewrite,[status(thm)],[])).
% 3.64/3.86 tff(10887,plain,
% 3.64/3.86 (((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), z))) <=> ((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))),
% 3.64/3.86 inference(rewrite,[status(thm)],[])).
% 3.64/3.86 tff(10888,plain,
% 3.64/3.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z))))),
% 3.64/3.86 inference(monotonicity,[status(thm)],[10887])).
% 3.64/3.86 tff(10889,plain,
% 3.64/3.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))),
% 3.64/3.86 inference(transitivity,[status(thm)],[10888, 10886])).
% 3.64/3.86 tff(10890,plain,
% 3.64/3.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), z)))),
% 3.64/3.86 inference(quant_inst,[status(thm)],[])).
% 3.64/3.86 tff(10891,plain,
% 3.64/3.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z))),
% 3.64/3.86 inference(modus_ponens,[status(thm)],[10890, 10889])).
% 3.64/3.86 tff(10892,plain,
% 3.64/3.86 ($false),
% 3.64/3.86 inference(unit_resolution,[status(thm)],[10891, 178, 818, 817, 3461, 273, 812])).
% 3.64/3.86 tff(10893,plain,((~b(elem!1, s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.86 tff(10894,plain,
% 3.64/3.86 (~b(z, elem!1)),
% 3.64/3.86 inference(unit_resolution,[status(thm)],[10893, 10885, 273, 5619, 10829])).
% 3.64/3.86 tff(10895,plain,
% 3.64/3.86 (r(z, elem!1)),
% 3.64/3.86 inference(unit_resolution,[status(thm)],[585, 10894, 318])).
% 3.64/3.86 tff(10896,plain,
% 3.64/3.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.64/3.86 inference(rewrite,[status(thm)],[])).
% 3.64/3.86 tff(10897,plain,
% 3.64/3.86 (((~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.64/3.86 inference(rewrite,[status(thm)],[])).
% 3.64/3.86 tff(10898,plain,
% 3.64/3.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))))),
% 3.64/3.86 inference(monotonicity,[status(thm)],[10897])).
% 3.64/3.86 tff(10899,plain,
% 3.64/3.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.64/3.86 inference(transitivity,[status(thm)],[10898, 10896])).
% 3.64/3.86 tff(10900,plain,
% 3.64/3.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))))),
% 3.64/3.86 inference(quant_inst,[status(thm)],[])).
% 3.64/3.86 tff(10901,plain,
% 3.64/3.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))),
% 3.64/3.86 inference(modus_ponens,[status(thm)],[10900, 10899])).
% 3.64/3.86 tff(10902,plain,
% 3.64/3.86 ($false),
% 3.64/3.86 inference(unit_resolution,[status(thm)],[10901, 118, 10895, 10878, 145])).
% 3.64/3.86 tff(10903,plain,(b(elem!1, z) | (~r(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (elem!1 = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | r(s(s(z)), elem!1) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (elem!1 = z) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 3.64/3.86 tff(10904,plain,
% 3.64/3.86 (b(elem!1, z)),
% 3.64/3.86 inference(unit_resolution,[status(thm)],[10903, 469, 273, 103, 104, 145, 286, 10828, 203, 290, 5618])).
% 3.64/3.86 tff(10905,plain,
% 3.64/3.86 (r(s(s(s(s(z)))), elem!1)),
% 3.64/3.86 inference(unit_resolution,[status(thm)],[3142, 8804, 323])).
% 3.64/3.86 tff(10906,plain,
% 3.64/3.86 ((elem!1 = s(s(s(z)))) <=> (elem!1 = s(elem!1))),
% 3.64/3.86 inference(monotonicity,[status(thm)],[3505])).
% 3.64/3.86 tff(10907,plain,
% 3.64/3.86 ((elem!1 = s(s(s(z)))) <=> (s(elem!1) = elem!1)),
% 3.64/3.86 inference(transitivity,[status(thm)],[10906, 3190])).
% 3.64/3.86 tff(10908,plain,
% 3.64/3.86 ((elem!1 = s(s(s(z)))) <=> (elem!1 = s(elem!1))),
% 3.64/3.86 inference(transitivity,[status(thm)],[10907, 3880])).
% 3.64/3.86 tff(10909,plain,
% 3.64/3.86 ((~(elem!1 = s(s(s(z))))) <=> (~(elem!1 = s(elem!1)))),
% 3.64/3.86 inference(monotonicity,[status(thm)],[10908])).
% 3.64/3.86 tff(10910,plain,
% 3.64/3.86 ((s(s(z)) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 3.64/3.86 inference(monotonicity,[status(thm)],[1324])).
% 3.64/3.86 tff(10911,plain,
% 3.64/3.86 ((~(s(s(z)) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 3.64/3.86 inference(monotonicity,[status(thm)],[10910])).
% 3.64/3.86 tff(10912,plain,
% 3.64/3.86 (~(elem!1 = s(s(s(z))))),
% 3.64/3.86 inference(modus_ponens,[status(thm)],[3205, 10911])).
% 3.64/3.86 tff(10913,plain,
% 3.64/3.86 (~(elem!1 = s(elem!1))),
% 3.64/3.86 inference(modus_ponens,[status(thm)],[10912, 10909])).
% 3.64/3.86 tff(10914,plain,
% 3.64/3.86 ((~(elem!1 = s(s(s(z))))) <=> (~(s(elem!1) = elem!1))),
% 3.64/3.86 inference(monotonicity,[status(thm)],[10907])).
% 3.64/3.86 tff(10915,plain,
% 3.64/3.86 (~(s(elem!1) = elem!1)),
% 3.64/3.86 inference(modus_ponens,[status(thm)],[10912, 10914])).
% 3.64/3.86 tff(10916,plain,
% 3.64/3.86 (elem!1 = s(s(z))),
% 3.64/3.86 inference(unit_resolution,[status(thm)],[3230, 1324])).
% 3.64/3.86 tff(10917,plain,
% 3.64/3.86 (r(s(s(elem!1)), s(s(z))) <=> r(s(s(elem!1)), elem!1)),
% 3.64/3.86 inference(monotonicity,[status(thm)],[1324])).
% 3.64/3.86 tff(10918,plain,
% 3.64/3.86 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(s(z)))),
% 3.64/3.86 inference(symmetry,[status(thm)],[10917])).
% 3.64/3.86 tff(10919,plain,
% 3.64/3.86 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 3.64/3.86 inference(monotonicity,[status(thm)],[3506])).
% 3.64/3.86 tff(10920,plain,
% 3.64/3.86 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(elem!1)), s(s(z)))),
% 3.64/3.86 inference(transitivity,[status(thm)],[10919, 10918])).
% 3.64/3.86 tff(10921,plain,
% 3.64/3.86 (r(s(s(elem!1)), s(s(z)))),
% 3.64/3.86 inference(modus_ponens,[status(thm)],[10905, 10920])).
% 3.64/3.86 tff(10922,plain,
% 3.64/3.86 ((s(elem!1) = s(s(elem!1))) <=> (s(s(elem!1)) = s(elem!1))),
% 3.64/3.86 inference(symmetry,[status(thm)],[981])).
% 3.64/3.86 tff(10923,plain,
% 3.64/3.86 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(elem!1)) = s(elem!1))),
% 3.64/3.86 inference(transitivity,[status(thm)],[8125, 10922])).
% 3.64/3.86 tff(10924,plain,
% 3.64/3.86 ((~(s(s(s(s(z)))) = s(elem!1))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 3.64/3.86 inference(monotonicity,[status(thm)],[10923])).
% 3.64/3.86 tff(10925,plain,
% 3.64/3.86 (~(s(elem!1) = s(s(s(s(z)))))),
% 3.64/3.86 inference(unit_resolution,[status(thm)],[1353, 10916, 323])).
% 3.64/3.86 tff(10926,plain,
% 3.64/3.86 (~(s(s(s(s(z)))) = s(elem!1))),
% 3.64/3.86 inference(unit_resolution,[status(thm)],[2168, 10925])).
% 3.64/3.86 tff(10927,plain,
% 3.64/3.86 (~(s(s(elem!1)) = s(elem!1))),
% 3.64/3.86 inference(modus_ponens,[status(thm)],[10926, 10924])).
% 3.64/3.86 tff(10928,plain,
% 3.64/3.86 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.64/3.86 inference(modus_ponens,[status(thm)],[224, 8491])).
% 3.64/3.86 tff(10929,plain,
% 3.64/3.86 (b(z, s(s(z))) <=> b(z, elem!1)),
% 3.64/3.86 inference(monotonicity,[status(thm)],[1324])).
% 3.64/3.86 tff(10930,plain,
% 3.64/3.86 (b(z, elem!1)),
% 3.64/3.86 inference(modus_ponens,[status(thm)],[273, 10929])).
% 3.64/3.86 tff(10931,plain,
% 3.64/3.86 (~r(s(elem!1), s(s(z)))),
% 3.64/3.86 inference(unit_resolution,[status(thm)],[390, 382, 224])).
% 3.64/3.86 tff(10932,plain,
% 3.64/3.86 (~r(s(elem!1), elem!1)),
% 3.64/3.86 inference(unit_resolution,[status(thm)],[7028, 10931, 308])).
% 3.64/3.86 tff(10933,plain,
% 3.64/3.86 (b(s(elem!1), elem!1)),
% 3.64/3.86 inference(unit_resolution,[status(thm)],[677, 10932, 725])).
% 3.64/3.86 tff(10934,plain,
% 3.64/3.86 (~r(elem!1, s(elem!1))),
% 3.64/3.86 inference(unit_resolution,[status(thm)],[2935, 382, 1265])).
% 3.64/3.86 tff(10935,plain,
% 3.64/3.86 (b(elem!1, s(elem!1))),
% 3.64/3.86 inference(unit_resolution,[status(thm)],[756, 10934, 750])).
% 3.64/3.86 tff(10936,plain,
% 3.64/3.86 (~b(s(elem!1), z)),
% 3.64/3.86 inference(unit_resolution,[status(thm)],[2429, 10935, 818, 506, 10933])).
% 3.64/3.86 tff(10937,plain,
% 3.64/3.86 (r(s(elem!1), z)),
% 3.64/3.86 inference(unit_resolution,[status(thm)],[774, 10936])).
% 3.64/3.86 tff(10938,plain,
% 3.64/3.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.64/3.86 inference(rewrite,[status(thm)],[])).
% 3.64/3.86 tff(10939,plain,
% 3.64/3.86 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.64/3.86 inference(rewrite,[status(thm)],[])).
% 3.64/3.86 tff(10940,plain,
% 3.64/3.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 3.64/3.86 inference(monotonicity,[status(thm)],[10939])).
% 3.64/3.86 tff(10941,plain,
% 3.64/3.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.64/3.86 inference(transitivity,[status(thm)],[10940, 10938])).
% 3.64/3.86 tff(10942,plain,
% 3.64/3.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), z)))),
% 3.64/3.86 inference(quant_inst,[status(thm)],[])).
% 3.64/3.86 tff(10943,plain,
% 3.64/3.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 3.64/3.86 inference(modus_ponens,[status(thm)],[10942, 10941])).
% 3.64/3.86 tff(10944,plain,
% 3.64/3.86 ($false),
% 3.64/3.86 inference(unit_resolution,[status(thm)],[10943, 118, 10937, 382, 203])).
% 3.64/3.86 tff(10945,plain,((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(elem!1) = elem!1) | (elem!1 = s(elem!1)) | (~(elem!1 = s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.86 tff(10946,plain,
% 3.64/3.86 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.86 inference(unit_resolution,[status(thm)],[10945, 10915, 203, 506, 10930, 10913, 10916, 10928, 224])).
% 3.64/3.86 tff(10947,plain,
% 3.64/3.86 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.86 inference(unit_resolution,[status(thm)],[395, 10946, 8112])).
% 3.64/3.86 tff(10948,plain,
% 3.64/3.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(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(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(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(elem!1)))))),
% 3.64/3.86 inference(rewrite,[status(thm)],[])).
% 3.64/3.86 tff(10949,plain,
% 3.64/3.86 (((~b(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)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(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(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(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(elem!1)))))),
% 3.64/3.86 inference(rewrite,[status(thm)],[])).
% 3.64/3.86 tff(10950,plain,
% 3.64/3.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(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(elem!1), s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(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(elem!1))))))),
% 3.64/3.86 inference(monotonicity,[status(thm)],[10949])).
% 3.64/3.86 tff(10951,plain,
% 3.64/3.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(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(elem!1), s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(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(elem!1)))))),
% 3.64/3.86 inference(transitivity,[status(thm)],[10950, 10948])).
% 3.64/3.86 tff(10952,plain,
% 3.64/3.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(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(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 3.64/3.86 inference(quant_inst,[status(thm)],[])).
% 3.64/3.86 tff(10953,plain,
% 3.64/3.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(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(elem!1))))),
% 3.64/3.87 inference(modus_ponens,[status(thm)],[10952, 10951])).
% 3.64/3.87 tff(10954,plain,
% 3.64/3.87 ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[10953, 178, 8490, 8176])).
% 3.64/3.87 tff(10955,plain,
% 3.64/3.87 (~b(s(s(elem!1)), s(elem!1))),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[10954, 3510, 10947])).
% 3.64/3.87 tff(10956,plain,
% 3.64/3.87 (r(s(s(elem!1)), s(elem!1))),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[1006, 10955, 10927])).
% 3.64/3.87 tff(10957,plain,
% 3.64/3.87 (~r(s(elem!1), s(s(z)))),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[8846, 10956, 10921])).
% 3.64/3.87 tff(10958,plain,
% 3.64/3.87 (~r(s(elem!1), elem!1)),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[7028, 10957, 10916])).
% 3.64/3.87 tff(10959,plain,
% 3.64/3.87 (b(s(elem!1), elem!1)),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[677, 10958, 10915])).
% 3.64/3.87 tff(10960,plain,
% 3.64/3.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 3.64/3.87 inference(rewrite,[status(thm)],[])).
% 3.64/3.87 tff(10961,plain,
% 3.64/3.87 (((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 3.64/3.87 inference(rewrite,[status(thm)],[])).
% 3.64/3.87 tff(10962,plain,
% 3.64/3.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1))))))),
% 3.64/3.87 inference(monotonicity,[status(thm)],[10961])).
% 3.64/3.87 tff(10963,plain,
% 3.64/3.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 3.64/3.87 inference(transitivity,[status(thm)],[10962, 10960])).
% 3.64/3.87 tff(10964,plain,
% 3.64/3.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 3.64/3.87 inference(quant_inst,[status(thm)],[])).
% 3.64/3.87 tff(10965,plain,
% 3.64/3.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1))))),
% 3.64/3.87 inference(modus_ponens,[status(thm)],[10964, 10963])).
% 3.64/3.87 tff(10966,plain,
% 3.64/3.87 ($false),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[10965, 118, 2333, 992, 5226])).
% 3.64/3.87 tff(10967,plain,((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.87 tff(10968,plain,
% 3.64/3.87 (~r(z, s(elem!1))),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[10967, 10956, 8134])).
% 3.64/3.87 tff(10969,plain,
% 3.64/3.87 (b(z, s(elem!1))),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[2351, 10968])).
% 3.64/3.87 tff(10970,plain,
% 3.64/3.87 (~b(elem!1, s(elem!1))),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[1396, 10969, 10930, 506, 10959])).
% 3.64/3.87 tff(10971,plain,
% 3.64/3.87 (r(elem!1, s(elem!1))),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[756, 10970, 10913])).
% 3.64/3.87 tff(10972,plain,
% 3.64/3.87 ((s(elem!1) = s(s(z))) <=> (s(elem!1) = elem!1)),
% 3.64/3.87 inference(monotonicity,[status(thm)],[1324])).
% 3.64/3.87 tff(10973,plain,
% 3.64/3.87 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(z)))),
% 3.64/3.87 inference(symmetry,[status(thm)],[10972])).
% 3.64/3.87 tff(10974,plain,
% 3.64/3.87 ((elem!1 = s(s(s(z)))) <=> (s(elem!1) = s(s(z)))),
% 3.64/3.87 inference(transitivity,[status(thm)],[10907, 10973])).
% 3.64/3.87 tff(10975,plain,
% 3.64/3.87 ((~(elem!1 = s(s(s(z))))) <=> (~(s(elem!1) = s(s(z))))),
% 3.64/3.87 inference(monotonicity,[status(thm)],[10974])).
% 3.64/3.87 tff(10976,plain,
% 3.64/3.87 (~(s(elem!1) = s(s(z)))),
% 3.64/3.87 inference(modus_ponens,[status(thm)],[10912, 10975])).
% 3.64/3.87 tff(10977,plain,
% 3.64/3.87 (b(s(elem!1), s(s(z)))),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[421, 10957, 10976])).
% 3.64/3.87 tff(10978,plain,
% 3.64/3.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 3.64/3.87 inference(rewrite,[status(thm)],[])).
% 3.64/3.87 tff(10979,plain,
% 3.64/3.87 (((~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 3.64/3.87 inference(rewrite,[status(thm)],[])).
% 3.64/3.87 tff(10980,plain,
% 3.64/3.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 3.64/3.87 inference(monotonicity,[status(thm)],[10979])).
% 3.64/3.87 tff(10981,plain,
% 3.64/3.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 3.64/3.87 inference(transitivity,[status(thm)],[10980, 10978])).
% 3.64/3.87 tff(10982,plain,
% 3.64/3.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)))),
% 3.64/3.87 inference(quant_inst,[status(thm)],[])).
% 3.64/3.87 tff(10983,plain,
% 3.64/3.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 3.64/3.87 inference(modus_ponens,[status(thm)],[10982, 10981])).
% 3.64/3.87 tff(10984,plain,
% 3.64/3.87 ($false),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[10983, 178, 855, 273, 1070, 168, 8640])).
% 3.64/3.87 tff(10985,plain,((~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.87 tff(10986,plain,
% 3.64/3.87 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[10985, 10969, 273, 168, 10977])).
% 3.64/3.87 tff(10987,plain,
% 3.64/3.87 (r(s(s(s(s(z)))), s(elem!1))),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[2173, 10986, 10926])).
% 3.64/3.87 tff(10988,plain,
% 3.64/3.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.64/3.87 inference(rewrite,[status(thm)],[])).
% 3.64/3.87 tff(10989,plain,
% 3.64/3.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.64/3.87 inference(quant_inst,[status(thm)],[])).
% 3.64/3.87 tff(10990,plain,
% 3.64/3.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), elem!1))),
% 3.64/3.87 inference(modus_ponens,[status(thm)],[10989, 10988])).
% 3.64/3.87 tff(10991,plain,
% 3.64/3.87 ($false),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[10990, 118, 1587, 3132, 6400])).
% 3.64/3.87 tff(10992,plain,((~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.87 tff(10993,plain,
% 3.64/3.87 ($false),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[10992, 10987, 10971, 10905])).
% 3.64/3.87 tff(10994,plain,((~(s(s(z)) = elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.87 tff(10995,plain,
% 3.64/3.87 (~(s(s(z)) = elem!1)),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[10994, 10904, 168, 273, 203, 287, 145, 104, 1126, 551, 86])).
% 3.64/3.87 tff(10996,plain,
% 3.64/3.87 (b(s(s(z)), elem!1)),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[448, 10995, 10828])).
% 3.64/3.87 tff(10997,plain,
% 3.64/3.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 3.64/3.87 inference(rewrite,[status(thm)],[])).
% 3.64/3.87 tff(10998,plain,
% 3.64/3.87 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z))))) <=> ((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 3.64/3.87 inference(rewrite,[status(thm)],[])).
% 3.64/3.87 tff(10999,plain,
% 3.64/3.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))))),
% 3.64/3.87 inference(monotonicity,[status(thm)],[10998])).
% 3.64/3.87 tff(11000,plain,
% 3.64/3.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 3.64/3.87 inference(transitivity,[status(thm)],[10999, 10997])).
% 3.64/3.87 tff(11001,plain,
% 3.64/3.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))))),
% 3.64/3.87 inference(quant_inst,[status(thm)],[])).
% 3.64/3.87 tff(11002,plain,
% 3.64/3.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))),
% 3.64/3.87 inference(modus_ponens,[status(thm)],[11001, 11000])).
% 3.64/3.87 tff(11003,plain,
% 3.64/3.87 ($false),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[11002, 178, 818, 506, 817, 3461, 273])).
% 3.64/3.87 tff(11004,plain,((~b(s(s(z)), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.87 tff(11005,plain,
% 3.64/3.87 (~b(z, elem!1)),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[11004, 10996, 5619, 273, 10904])).
% 3.64/3.87 tff(11006,plain,
% 3.64/3.87 (r(z, elem!1)),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[585, 11005, 318])).
% 3.64/3.87 tff(11007,plain,
% 3.64/3.87 (~r(elem!1, s(s(s(s(z)))))),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[529, 11006, 145])).
% 3.64/3.87 tff(11008,plain,
% 3.64/3.87 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[10835, 10996, 286])).
% 3.64/3.87 tff(11009,plain,
% 3.64/3.87 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[3818, 11006, 203])).
% 3.64/3.87 tff(11010,plain,
% 3.64/3.87 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[691, 11009, 11008])).
% 3.64/3.87 tff(11011,plain,
% 3.64/3.87 (r(s(s(s(s(z)))), elem!1)),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[8548, 11010, 104, 223, 469, 11007])).
% 3.64/3.87 tff(11012,plain,
% 3.64/3.87 ($false),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[10901, 118, 11006, 11011, 145])).
% 3.64/3.87 tff(11013,plain,((elem!1 = s(s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | r(s(s(z)), elem!1) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(z))) | (elem!1 = z) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 3.64/3.87 tff(11014,plain,
% 3.64/3.87 (b(s(s(s(s(z)))), s(s(z)))),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[11013, 10828, 104, 203, 273, 286, 145, 469, 1126, 168, 290, 5618])).
% 3.64/3.87 tff(11015,plain,
% 3.64/3.87 (b(s(s(z)), elem!1)),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[448, 10828, 12])).
% 3.64/3.87 tff(11016,plain,
% 3.64/3.87 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[298, 11014, 104, 273, 168])).
% 3.64/3.87 tff(11017,plain,
% 3.64/3.87 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[133, 11016])).
% 3.64/3.87 tff(11018,plain,
% 3.64/3.87 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[10835, 11015, 286])).
% 3.64/3.87 tff(11019,plain,
% 3.64/3.87 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[703, 11018])).
% 3.64/3.87 tff(11020,plain,
% 3.64/3.87 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[691, 11018, 644])).
% 3.64/3.87 tff(11021,plain,
% 3.64/3.87 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[9083, 11020, 104, 223, 1301])).
% 3.64/3.87 tff(11022,plain,
% 3.64/3.87 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[3444, 11021, 11019])).
% 3.64/3.87 tff(11023,plain,
% 3.64/3.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 3.64/3.87 inference(rewrite,[status(thm)],[])).
% 3.64/3.87 tff(11024,plain,
% 3.64/3.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 3.64/3.87 inference(quant_inst,[status(thm)],[])).
% 3.64/3.87 tff(11025,plain,
% 3.64/3.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 3.64/3.87 inference(modus_ponens,[status(thm)],[11024, 11023])).
% 3.64/3.87 tff(11026,plain,
% 3.64/3.87 ($false),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[11025, 118, 521, 108, 2953])).
% 3.64/3.87 tff(11027,plain,((~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))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.87 tff(11028,plain,
% 3.64/3.87 (~r(z, elem!1)),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[11027, 11022, 11017])).
% 3.64/3.87 tff(11029,plain,
% 3.64/3.87 (b(z, elem!1)),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[585, 11028, 318])).
% 3.64/3.87 tff(11030,plain,
% 3.64/3.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 3.64/3.87 inference(rewrite,[status(thm)],[])).
% 3.64/3.87 tff(11031,plain,
% 3.64/3.87 (((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 3.64/3.87 inference(rewrite,[status(thm)],[])).
% 3.64/3.87 tff(11032,plain,
% 3.64/3.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 3.64/3.87 inference(monotonicity,[status(thm)],[11031])).
% 3.64/3.87 tff(11033,plain,
% 3.64/3.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 3.64/3.87 inference(transitivity,[status(thm)],[11032, 11030])).
% 3.64/3.87 tff(11034,plain,
% 3.64/3.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 3.64/3.87 inference(quant_inst,[status(thm)],[])).
% 3.64/3.87 tff(11035,plain,
% 3.64/3.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))),
% 3.64/3.87 inference(modus_ponens,[status(thm)],[11034, 11033])).
% 3.64/3.87 tff(11036,plain,
% 3.64/3.87 ($false),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[11035, 178, 11029, 11015, 273, 168, 11014])).
% 3.64/3.87 tff(11037,plain,(r(s(s(z)), elem!1) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | (s(s(z)) = elem!1) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(z)))))) | (elem!1 = s(s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (elem!1 = z) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 3.64/3.87 tff(11038,plain,
% 3.64/3.87 (r(s(s(z)), elem!1)),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[11037, 10876, 273, 104, 10812, 10810, 286, 10814, 4236, 145, 469, 1126, 290, 5618])).
% 3.64/3.87 tff(11039,plain,
% 3.64/3.87 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[8548, 469, 104, 10813, 8690, 5721])).
% 3.64/3.87 tff(11040,plain,
% 3.64/3.87 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[691, 11039, 2804])).
% 3.64/3.87 tff(11041,plain,
% 3.64/3.87 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 3.64/3.87 inference(monotonicity,[status(thm)],[11040])).
% 3.64/3.87 tff(11042,plain,
% 3.64/3.87 (s(s(elem!1)) = s(s(s(s(s(s(s(s(s(z)))))))))),
% 3.64/3.87 inference(monotonicity,[status(thm)],[11041])).
% 3.64/3.87 tff(11043,plain,
% 3.64/3.87 (s(s(s(elem!1))) = s(s(s(s(s(s(s(s(s(s(z))))))))))),
% 3.64/3.87 inference(monotonicity,[status(thm)],[11042])).
% 3.64/3.87 tff(11044,plain,
% 3.64/3.87 (s(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(s(elem!1)))),
% 3.64/3.87 inference(symmetry,[status(thm)],[11043])).
% 3.64/3.87 tff(11045,plain,
% 3.64/3.87 (b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.64/3.87 inference(monotonicity,[status(thm)],[11044])).
% 3.64/3.87 tff(11046,plain,
% 3.64/3.87 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))),
% 3.64/3.87 inference(symmetry,[status(thm)],[11045])).
% 3.64/3.87 tff(11047,plain,
% 3.64/3.87 (~(s(elem!1) = s(s(z)))),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[2832, 11040])).
% 3.64/3.87 tff(11048,plain,
% 3.64/3.87 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[2840, 11047])).
% 3.64/3.87 tff(11049,plain,
% 3.64/3.87 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[4173, 11048, 4171])).
% 3.64/3.87 tff(11050,plain,
% 3.64/3.87 (b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))),
% 3.64/3.87 inference(modus_ponens,[status(thm)],[11049, 11046])).
% 3.64/3.87 tff(11051,plain,
% 3.64/3.87 (b(s(s(s(s(s(s(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))))))))),
% 3.64/3.87 inference(monotonicity,[status(thm)],[11044])).
% 3.64/3.87 tff(11052,plain,
% 3.64/3.87 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.87 inference(symmetry,[status(thm)],[11051])).
% 3.64/3.87 tff(11053,plain,
% 3.64/3.87 (~b(z, elem!1)),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[4243, 11040, 4235])).
% 3.64/3.87 tff(11054,plain,
% 3.64/3.87 (r(z, elem!1)),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[585, 11053, 318])).
% 3.64/3.87 tff(11055,plain,
% 3.64/3.87 (~r(s(s(s(elem!1))), elem!1)),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[6388, 11054, 438, 3461, 273])).
% 3.64/3.87 tff(11056,plain,
% 3.64/3.87 (~(elem!1 = s(s(s(elem!1))))),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[2859, 11048, 11040])).
% 3.64/3.87 tff(11057,plain,
% 3.64/3.87 (~(s(s(s(elem!1))) = elem!1)),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[2489, 11056])).
% 3.64/3.87 tff(11058,plain,
% 3.64/3.87 (b(s(s(s(elem!1))), elem!1)),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[570, 11057, 11055])).
% 3.64/3.87 tff(11059,plain,
% 3.64/3.87 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.87 inference(unit_resolution,[status(thm)],[10584, 11058, 11040])).
% 3.64/3.87 tff(11060,plain,
% 3.64/3.87 (b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.87 inference(modus_ponens,[status(thm)],[11059, 11052])).
% 3.64/3.87 tff(11061,plain,
% 3.64/3.87 (b(elem!1, z) <=> b(s(s(s(s(s(s(s(z))))))), z)),
% 3.64/3.87 inference(monotonicity,[status(thm)],[11040])).
% 3.64/3.87 tff(11062,plain,
% 3.64/3.87 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.64/3.87 inference(monotonicity,[status(thm)],[11040])).
% 3.64/3.87 tff(11063,plain,
% 3.64/3.87 (b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 3.64/3.87 inference(symmetry,[status(thm)],[11062])).
% 3.64/3.87 tff(11064,plain,
% 3.64/3.87 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z))))))))))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.64/3.87 inference(monotonicity,[status(thm)],[11044])).
% 3.64/3.87 tff(11065,plain,
% 3.64/3.87 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z))))))))))) <=> b(elem!1, s(s(s(elem!1))))),
% 3.64/3.87 inference(transitivity,[status(thm)],[11064, 11063])).
% 3.64/3.87 tff(11066,plain,
% 3.64/3.87 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) <=> (~b(elem!1, s(s(s(elem!1)))))),
% 3.64/3.87 inference(monotonicity,[status(thm)],[11065])).
% 3.64/3.87 tff(11067,plain,
% 3.64/3.87 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[10872, 11050, 11060])).
% 3.64/3.88 tff(11068,plain,
% 3.64/3.88 (~b(elem!1, s(s(s(elem!1))))),
% 3.64/3.88 inference(modus_ponens,[status(thm)],[11067, 11066])).
% 3.64/3.88 tff(11069,plain,
% 3.64/3.88 (r(elem!1, s(s(s(elem!1))))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[2054, 11068, 11056])).
% 3.64/3.88 tff(11070,plain,
% 3.64/3.88 (~r(elem!1, z)),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[10847, 11069, 3461, 273, 438, 11054])).
% 3.64/3.88 tff(11071,plain,
% 3.64/3.88 (b(elem!1, z)),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[498, 11070, 290])).
% 3.64/3.88 tff(11072,plain,
% 3.64/3.88 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.64/3.88 inference(modus_ponens,[status(thm)],[11071, 11061])).
% 3.64/3.88 tff(11073,plain,
% 3.64/3.88 (~r(z, s(s(s(elem!1))))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[3319, 11069, 11054])).
% 3.64/3.88 tff(11074,plain,
% 3.64/3.88 (b(z, s(s(s(elem!1))))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[2095, 11073])).
% 3.64/3.88 tff(11075,plain,
% 3.64/3.88 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) <=> (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 3.64/3.88 inference(monotonicity,[status(thm)],[11064])).
% 3.64/3.88 tff(11076,plain,
% 3.64/3.88 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.64/3.88 inference(modus_ponens,[status(thm)],[11067, 11075])).
% 3.64/3.88 tff(11077,plain,
% 3.64/3.88 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[5118, 11076, 4254])).
% 3.64/3.88 tff(11078,plain,
% 3.64/3.88 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[7973, 11069, 438])).
% 3.64/3.88 tff(11079,plain,
% 3.64/3.88 (b(s(s(z)), s(s(s(elem!1))))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[4223, 11078])).
% 3.64/3.88 tff(11080,plain,
% 3.64/3.88 (~r(s(s(s(s(z)))), z)),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[10607, 11079, 145, 224, 104, 193, 11040, 11049, 11077, 11074])).
% 3.64/3.88 tff(11081,plain,
% 3.64/3.88 (b(s(s(s(s(z)))), z)),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[191, 11080])).
% 3.64/3.88 tff(11082,plain,
% 3.64/3.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))))),
% 3.64/3.88 inference(rewrite,[status(thm)],[])).
% 3.64/3.88 tff(11083,plain,
% 3.64/3.88 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(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))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))))),
% 3.64/3.88 inference(rewrite,[status(thm)],[])).
% 3.64/3.88 tff(11084,plain,
% 3.64/3.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(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))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z)))))))))))),
% 3.64/3.88 inference(monotonicity,[status(thm)],[11083])).
% 3.64/3.88 tff(11085,plain,
% 3.64/3.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(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))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))))),
% 3.64/3.88 inference(transitivity,[status(thm)],[11084, 11082])).
% 3.64/3.88 tff(11086,plain,
% 3.64/3.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(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))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))))),
% 3.64/3.88 inference(quant_inst,[status(thm)],[])).
% 3.64/3.88 tff(11087,plain,
% 3.64/3.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z)))))))))),
% 3.64/3.88 inference(modus_ponens,[status(thm)],[11086, 11085])).
% 3.64/3.88 tff(11088,plain,
% 3.64/3.88 ($false),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[11087, 178, 11081, 10813, 11072, 11060, 11050])).
% 3.64/3.88 tff(11089,plain,((elem!1 = s(s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(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)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (elem!1 = z) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(s(s(z)), elem!1)) | r(s(s(s(elem!1))), s(s(s(s(z))))) | b(z, s(s(s(s(s(s(s(z)))))))) | r(elem!1, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.88 tff(11090,plain,
% 3.64/3.88 (~r(s(s(s(s(z)))), s(s(z)))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[11089, 11038, 287, 104, 145, 290, 5619, 273, 469, 4171, 4235, 10811])).
% 3.64/3.88 tff(11091,plain,
% 3.64/3.88 (b(s(s(s(s(z)))), s(s(z)))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[102, 11090])).
% 3.64/3.88 tff(11092,plain,
% 3.64/3.88 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[298, 11091, 104, 273, 10876])).
% 3.64/3.88 tff(11093,plain,
% 3.64/3.88 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[133, 11092])).
% 3.64/3.88 tff(11094,plain,
% 3.64/3.88 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[11027, 521, 108])).
% 3.64/3.88 tff(11095,plain,
% 3.64/3.88 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[691, 701, 644])).
% 3.64/3.88 tff(11096,plain,
% 3.64/3.88 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[3444, 4245, 605])).
% 3.64/3.88 tff(11097,plain,
% 3.64/3.88 ($false),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[9083, 11096, 11095, 104, 251, 1301])).
% 3.64/3.88 tff(11098,plain,((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))))))))) | (~b(elem!1, s(s(s(s(z)))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.88 tff(11099,plain,
% 3.64/3.88 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[11098, 11094, 251, 1301, 104, 644])).
% 3.64/3.88 tff(11100,plain,
% 3.64/3.88 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 3.64/3.88 inference(monotonicity,[status(thm)],[11099])).
% 3.64/3.88 tff(11101,plain,
% 3.64/3.88 (s(s(elem!1)) = s(s(s(s(s(s(s(s(s(z)))))))))),
% 3.64/3.88 inference(monotonicity,[status(thm)],[11100])).
% 3.64/3.88 tff(11102,plain,
% 3.64/3.88 (s(s(s(elem!1))) = s(s(s(s(s(s(s(s(s(s(z))))))))))),
% 3.64/3.88 inference(monotonicity,[status(thm)],[11101])).
% 3.64/3.88 tff(11103,plain,
% 3.64/3.88 (s(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(s(elem!1)))),
% 3.64/3.88 inference(symmetry,[status(thm)],[11102])).
% 3.64/3.88 tff(11104,plain,
% 3.64/3.88 (b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.64/3.88 inference(monotonicity,[status(thm)],[11103])).
% 3.64/3.88 tff(11105,plain,
% 3.64/3.88 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))),
% 3.64/3.88 inference(symmetry,[status(thm)],[11104])).
% 3.64/3.88 tff(11106,plain,
% 3.64/3.88 (~(s(elem!1) = s(s(z)))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[2832, 11099])).
% 3.64/3.88 tff(11107,plain,
% 3.64/3.88 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[2840, 11106])).
% 3.64/3.88 tff(11108,plain,
% 3.64/3.88 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[4173, 11107, 4171])).
% 3.64/3.88 tff(11109,plain,
% 3.64/3.88 (b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))),
% 3.64/3.88 inference(modus_ponens,[status(thm)],[11108, 11105])).
% 3.64/3.88 tff(11110,plain,
% 3.64/3.88 (b(s(s(s(s(s(s(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))))))))),
% 3.64/3.88 inference(monotonicity,[status(thm)],[11103])).
% 3.64/3.88 tff(11111,plain,
% 3.64/3.88 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.88 inference(symmetry,[status(thm)],[11110])).
% 3.64/3.88 tff(11112,plain,
% 3.64/3.88 (~r(s(s(s(elem!1))), elem!1)),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[6388, 521, 438, 3461, 273])).
% 3.64/3.88 tff(11113,plain,
% 3.64/3.88 (~(elem!1 = s(s(s(elem!1))))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[2859, 11107, 11099])).
% 3.64/3.88 tff(11114,plain,
% 3.64/3.88 (~(s(s(s(elem!1))) = elem!1)),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[2489, 11113])).
% 3.64/3.88 tff(11115,plain,
% 3.64/3.88 (b(s(s(s(elem!1))), elem!1)),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[570, 11114, 11112])).
% 3.64/3.88 tff(11116,plain,
% 3.64/3.88 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[10584, 11115, 11099])).
% 3.64/3.88 tff(11117,plain,
% 3.64/3.88 (b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.88 inference(modus_ponens,[status(thm)],[11116, 11111])).
% 3.64/3.88 tff(11118,plain,
% 3.64/3.88 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z))))))))))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.64/3.88 inference(monotonicity,[status(thm)],[11103])).
% 3.64/3.88 tff(11119,plain,
% 3.64/3.88 (b(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(s(s(s(s(s(s(s(z)))))))))))),
% 3.64/3.88 inference(symmetry,[status(thm)],[11118])).
% 3.64/3.88 tff(11120,plain,
% 3.64/3.88 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.64/3.88 inference(monotonicity,[status(thm)],[11099])).
% 3.64/3.88 tff(11121,plain,
% 3.64/3.88 (~r(elem!1, s(s(s(elem!1))))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[10847, 521, 3461, 273, 437, 438])).
% 3.64/3.88 tff(11122,plain,
% 3.64/3.88 (b(elem!1, s(s(s(elem!1))))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[2054, 11113, 11121])).
% 3.64/3.88 tff(11123,plain,
% 3.64/3.88 (b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.64/3.88 inference(modus_ponens,[status(thm)],[11122, 11120])).
% 3.64/3.88 tff(11124,plain,
% 3.64/3.88 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 3.64/3.88 inference(modus_ponens,[status(thm)],[11123, 11119])).
% 3.64/3.88 tff(11125,plain,
% 3.64/3.88 ((~b(s(s(s(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(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z)))))))))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[10871, 178, 104, 251])).
% 3.64/3.88 tff(11126,plain,
% 3.64/3.88 ($false),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[11125, 11124, 11117, 11109])).
% 3.64/3.88 tff(11127,plain,((~r(z, 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))))))))) | r(s(s(s(elem!1))), s(s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.88 tff(11128,plain,
% 3.64/3.88 (~r(z, elem!1)),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[11127, 10812, 10813, 4171, 104, 10810, 11093, 5619, 273, 10801, 11038])).
% 3.64/3.88 tff(11129,plain,
% 3.64/3.88 (b(z, elem!1)),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[585, 11128, 318])).
% 3.64/3.88 tff(11130,plain,
% 3.64/3.88 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[4243, 11129, 4235])).
% 3.64/3.88 tff(11131,plain,
% 3.64/3.88 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[11098, 11130, 10813, 10812, 104, 10810])).
% 3.64/3.88 tff(11132,plain,
% 3.64/3.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.64/3.88 inference(rewrite,[status(thm)],[])).
% 3.64/3.88 tff(11133,plain,
% 3.64/3.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.64/3.88 inference(quant_inst,[status(thm)],[])).
% 3.64/3.88 tff(11134,plain,
% 3.64/3.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 3.64/3.88 inference(modus_ponens,[status(thm)],[11133, 11132])).
% 3.64/3.88 tff(11135,plain,
% 3.64/3.88 ($false),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[11134, 118, 10801, 11093, 11131])).
% 3.64/3.88 tff(11136,plain,(b(elem!1, z) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | b(z, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(elem!1))), s(s(s(s(z))))) | (~b(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (elem!1 = z) | (elem!1 = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 3.64/3.88 tff(11137,plain,
% 3.64/3.88 (b(elem!1, z)),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[11136, 469, 4235, 10800, 273, 47, 290, 104, 286, 10796, 5618])).
% 3.64/3.88 tff(11138,plain,
% 3.64/3.88 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[5101, 10794, 145, 5619])).
% 3.64/3.88 tff(11139,plain,
% 3.64/3.88 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[10755, 11138])).
% 3.64/3.88 tff(11140,plain,
% 3.64/3.88 (b(elem!1, z)),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[10838, 469, 104, 286, 10828, 194, 203, 145, 290, 5618])).
% 3.64/3.88 tff(11141,plain,
% 3.64/3.88 (~b(z, elem!1)),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[11004, 817, 3461, 273, 506])).
% 3.64/3.88 tff(11142,plain,
% 3.64/3.88 (r(z, elem!1)),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[585, 11141, 507])).
% 3.64/3.88 tff(11143,plain,
% 3.64/3.88 (~r(elem!1, s(s(s(s(z)))))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[529, 11142, 145])).
% 3.64/3.88 tff(11144,plain,
% 3.64/3.88 (~r(s(s(s(s(z)))), elem!1)),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[3137, 11142, 194])).
% 3.64/3.88 tff(11145,plain,
% 3.64/3.88 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[10835, 817, 286])).
% 3.64/3.88 tff(11146,plain,
% 3.64/3.88 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[3818, 11142, 203])).
% 3.64/3.88 tff(11147,plain,
% 3.64/3.88 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[691, 11146, 11145])).
% 3.64/3.88 tff(11148,plain,
% 3.64/3.88 ($false),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[8548, 11147, 11144, 104, 223, 469, 11143])).
% 3.64/3.88 tff(11149,plain,((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (elem!1 = s(s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(z)))))) | (z = elem!1) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | b(s(s(z)), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.88 tff(11150,plain,
% 3.64/3.88 (~b(s(s(z)), elem!1)),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[11149, 469, 104, 194, 203, 145, 318, 5619, 273, 11140, 286])).
% 3.64/3.88 tff(11151,plain,
% 3.64/3.88 (s(s(z)) = elem!1),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[448, 11150, 10828])).
% 3.64/3.88 tff(11152,plain,
% 3.64/3.88 (s(s(s(z))) = s(elem!1)),
% 3.64/3.88 inference(monotonicity,[status(thm)],[11151])).
% 3.64/3.88 tff(11153,plain,
% 3.64/3.88 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 3.64/3.88 inference(monotonicity,[status(thm)],[11152])).
% 3.64/3.88 tff(11154,plain,
% 3.64/3.88 (b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.88 inference(monotonicity,[status(thm)],[11152])).
% 3.64/3.88 tff(11155,plain,
% 3.64/3.88 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.88 inference(symmetry,[status(thm)],[11154])).
% 3.64/3.88 tff(11156,plain,
% 3.64/3.88 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[5361, 11151])).
% 3.64/3.88 tff(11157,plain,
% 3.64/3.88 (r(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.64/3.88 inference(monotonicity,[status(thm)],[11151])).
% 3.64/3.88 tff(11158,plain,
% 3.64/3.88 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.64/3.88 inference(modus_ponens,[status(thm)],[287, 11157])).
% 3.64/3.88 tff(11159,plain,
% 3.64/3.88 (elem!1 = s(s(z))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[3230, 11151])).
% 3.64/3.88 tff(11160,plain,
% 3.64/3.88 ((elem!1 = s(s(s(z)))) <=> (elem!1 = s(elem!1))),
% 3.64/3.88 inference(monotonicity,[status(thm)],[11152])).
% 3.64/3.88 tff(11161,plain,
% 3.64/3.88 ((elem!1 = s(s(s(z)))) <=> (s(elem!1) = elem!1)),
% 3.64/3.88 inference(transitivity,[status(thm)],[11160, 3190])).
% 3.64/3.88 tff(11162,plain,
% 3.64/3.88 ((elem!1 = s(s(s(z)))) <=> (elem!1 = s(elem!1))),
% 3.64/3.88 inference(transitivity,[status(thm)],[11161, 3880])).
% 3.64/3.88 tff(11163,plain,
% 3.64/3.88 ((~(elem!1 = s(s(s(z))))) <=> (~(elem!1 = s(elem!1)))),
% 3.64/3.88 inference(monotonicity,[status(thm)],[11162])).
% 3.64/3.88 tff(11164,plain,
% 3.64/3.88 ((s(s(z)) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 3.64/3.88 inference(monotonicity,[status(thm)],[11151])).
% 3.64/3.88 tff(11165,plain,
% 3.64/3.88 ((~(s(s(z)) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 3.64/3.88 inference(monotonicity,[status(thm)],[11164])).
% 3.64/3.88 tff(11166,plain,
% 3.64/3.88 (~(elem!1 = s(s(s(z))))),
% 3.64/3.88 inference(modus_ponens,[status(thm)],[3205, 11165])).
% 3.64/3.88 tff(11167,plain,
% 3.64/3.88 (~(elem!1 = s(elem!1))),
% 3.64/3.88 inference(modus_ponens,[status(thm)],[11166, 11163])).
% 3.64/3.88 tff(11168,plain,
% 3.64/3.88 (~b(s(s(s(s(z)))), elem!1)),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[3774, 11151, 86])).
% 3.64/3.88 tff(11169,plain,
% 3.64/3.88 (r(s(s(s(s(z)))), elem!1)),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[3142, 11168, 551])).
% 3.64/3.88 tff(11170,plain,
% 3.64/3.88 (~r(z, elem!1)),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[3137, 11169, 194])).
% 3.64/3.88 tff(11171,plain,
% 3.64/3.88 (b(z, elem!1)),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[585, 11170, 318])).
% 3.64/3.88 tff(11172,plain,
% 3.64/3.88 ((~(elem!1 = s(s(s(z))))) <=> (~(s(elem!1) = elem!1))),
% 3.64/3.88 inference(monotonicity,[status(thm)],[11161])).
% 3.64/3.88 tff(11173,plain,
% 3.64/3.88 (~(s(elem!1) = elem!1)),
% 3.64/3.88 inference(modus_ponens,[status(thm)],[11166, 11172])).
% 3.64/3.88 tff(11174,plain,
% 3.64/3.88 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[10945, 11173, 203, 11140, 11171, 11167, 11159, 11158, 287])).
% 3.64/3.88 tff(11175,plain,
% 3.64/3.88 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[395, 11174, 11156])).
% 3.64/3.88 tff(11176,plain,
% 3.64/3.88 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.88 inference(modus_ponens,[status(thm)],[11175, 11155])).
% 3.64/3.88 tff(11177,plain,
% 3.64/3.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.64/3.88 inference(rewrite,[status(thm)],[])).
% 3.64/3.88 tff(11178,plain,
% 3.64/3.88 (((~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(s(z))), s(s(s(s(z)))))) | (~b(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))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.64/3.88 inference(rewrite,[status(thm)],[])).
% 3.64/3.88 tff(11179,plain,
% 3.64/3.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), 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(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 3.64/3.88 inference(monotonicity,[status(thm)],[11178])).
% 3.64/3.88 tff(11180,plain,
% 3.64/3.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), 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(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.64/3.88 inference(transitivity,[status(thm)],[11179, 11177])).
% 3.64/3.88 tff(11181,plain,
% 3.64/3.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), 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(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.64/3.88 inference(quant_inst,[status(thm)],[])).
% 3.64/3.88 tff(11182,plain,
% 3.64/3.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.64/3.88 inference(modus_ponens,[status(thm)],[11181, 11180])).
% 3.64/3.88 tff(11183,plain,
% 3.64/3.88 ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[11182, 178, 104, 223, 1126])).
% 3.64/3.88 tff(11184,plain,
% 3.64/3.88 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[11183, 11176])).
% 3.64/3.88 tff(11185,plain,
% 3.64/3.88 (b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[4950, 4938])).
% 3.64/3.88 tff(11186,plain,
% 3.64/3.88 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[11185, 11184])).
% 3.64/3.88 tff(11187,plain,
% 3.64/3.88 (r(s(s(s(s(z)))), s(elem!1))),
% 3.64/3.88 inference(modus_ponens,[status(thm)],[11186, 11153])).
% 3.64/3.88 tff(11188,plain,
% 3.64/3.88 (r(s(s(elem!1)), s(s(z))) <=> r(s(s(elem!1)), elem!1)),
% 3.64/3.88 inference(monotonicity,[status(thm)],[11151])).
% 3.64/3.88 tff(11189,plain,
% 3.64/3.88 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(s(z)))),
% 3.64/3.88 inference(symmetry,[status(thm)],[11188])).
% 3.64/3.88 tff(11190,plain,
% 3.64/3.88 (s(s(s(s(z)))) = s(s(elem!1))),
% 3.64/3.88 inference(monotonicity,[status(thm)],[11152])).
% 3.64/3.88 tff(11191,plain,
% 3.64/3.88 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 3.64/3.88 inference(monotonicity,[status(thm)],[11190])).
% 3.64/3.88 tff(11192,plain,
% 3.64/3.88 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(elem!1)), s(s(z)))),
% 3.64/3.88 inference(transitivity,[status(thm)],[11191, 11189])).
% 3.64/3.88 tff(11193,plain,
% 3.64/3.88 (r(s(s(elem!1)), s(s(z)))),
% 3.64/3.88 inference(modus_ponens,[status(thm)],[11169, 11192])).
% 3.64/3.88 tff(11194,plain,
% 3.64/3.88 (s(s(elem!1)) = s(s(s(s(z))))),
% 3.64/3.88 inference(symmetry,[status(thm)],[11190])).
% 3.64/3.88 tff(11195,plain,
% 3.64/3.88 ((s(elem!1) = s(s(elem!1))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 3.64/3.88 inference(monotonicity,[status(thm)],[11194])).
% 3.64/3.88 tff(11196,plain,
% 3.64/3.88 ((s(elem!1) = s(s(elem!1))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 3.64/3.88 inference(transitivity,[status(thm)],[11195, 2163])).
% 3.64/3.88 tff(11197,plain,
% 3.64/3.88 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(elem!1) = s(s(elem!1)))),
% 3.64/3.88 inference(symmetry,[status(thm)],[11196])).
% 3.64/3.88 tff(11198,plain,
% 3.64/3.88 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(elem!1)) = s(elem!1))),
% 3.64/3.88 inference(transitivity,[status(thm)],[11197, 10922])).
% 3.64/3.88 tff(11199,plain,
% 3.64/3.88 ((~(s(s(s(s(z)))) = s(elem!1))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 3.64/3.88 inference(monotonicity,[status(thm)],[11198])).
% 3.64/3.88 tff(11200,plain,
% 3.64/3.88 (~(s(elem!1) = s(s(s(s(z)))))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[1353, 11159, 551])).
% 3.64/3.88 tff(11201,plain,
% 3.64/3.88 (~(s(s(s(s(z)))) = s(elem!1))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[2168, 11200])).
% 3.64/3.88 tff(11202,plain,
% 3.64/3.88 (~(s(s(elem!1)) = s(elem!1))),
% 3.64/3.88 inference(modus_ponens,[status(thm)],[11201, 11199])).
% 3.64/3.88 tff(11203,plain,
% 3.64/3.88 (b(s(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))))))))),
% 3.64/3.88 inference(monotonicity,[status(thm)],[11194])).
% 3.64/3.88 tff(11204,plain,
% 3.64/3.88 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.88 inference(symmetry,[status(thm)],[11203])).
% 3.64/3.88 tff(11205,plain,
% 3.64/3.88 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.88 inference(modus_ponens,[status(thm)],[223, 11204])).
% 3.64/3.88 tff(11206,plain,
% 3.64/3.88 (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)))),
% 3.64/3.88 inference(monotonicity,[status(thm)],[11190])).
% 3.64/3.88 tff(11207,plain,
% 3.64/3.88 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.64/3.88 inference(modus_ponens,[status(thm)],[104, 11206])).
% 3.64/3.88 tff(11208,plain,
% 3.64/3.88 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 3.64/3.88 inference(monotonicity,[status(thm)],[11194])).
% 3.64/3.88 tff(11209,plain,
% 3.64/3.88 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), s(s(elem!1)))),
% 3.64/3.88 inference(symmetry,[status(thm)],[11208])).
% 3.64/3.88 tff(11210,plain,
% 3.64/3.88 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 3.64/3.88 inference(monotonicity,[status(thm)],[11152])).
% 3.64/3.88 tff(11211,plain,
% 3.64/3.88 (b(s(elem!1), s(s(s(s(z)))))),
% 3.64/3.88 inference(modus_ponens,[status(thm)],[1126, 11210])).
% 3.64/3.88 tff(11212,plain,
% 3.64/3.88 (b(s(elem!1), s(s(elem!1)))),
% 3.64/3.88 inference(modus_ponens,[status(thm)],[11211, 11209])).
% 3.64/3.88 tff(11213,plain,
% 3.64/3.88 ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[10953, 178, 11212, 11207])).
% 3.64/3.88 tff(11214,plain,
% 3.64/3.88 (~b(s(s(elem!1)), s(elem!1))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[11213, 11205, 11175])).
% 3.64/3.88 tff(11215,plain,
% 3.64/3.88 (r(s(s(elem!1)), s(elem!1))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[1006, 11214, 11202])).
% 3.64/3.88 tff(11216,plain,
% 3.64/3.88 (~r(s(elem!1), s(s(z)))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[8846, 11215, 11193])).
% 3.64/3.88 tff(11217,plain,
% 3.64/3.88 (~r(s(elem!1), elem!1)),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[7028, 11216, 11159])).
% 3.64/3.88 tff(11218,plain,
% 3.64/3.88 (b(s(elem!1), elem!1)),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[677, 11217, 11173])).
% 3.64/3.88 tff(11219,plain,
% 3.64/3.88 (r(z, s(s(s(s(z))))) <=> r(z, s(s(elem!1)))),
% 3.64/3.88 inference(monotonicity,[status(thm)],[11190])).
% 3.64/3.88 tff(11220,plain,
% 3.64/3.88 (r(z, s(s(elem!1)))),
% 3.64/3.88 inference(modus_ponens,[status(thm)],[145, 11219])).
% 3.64/3.88 tff(11221,plain,
% 3.64/3.88 (~r(z, s(elem!1))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[10967, 11215, 11220])).
% 3.64/3.88 tff(11222,plain,
% 3.64/3.88 (b(z, s(elem!1))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[2351, 11221])).
% 3.64/3.88 tff(11223,plain,
% 3.64/3.88 (~b(elem!1, s(elem!1))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[1396, 11222, 11171, 11140, 11218])).
% 3.64/3.88 tff(11224,plain,
% 3.64/3.88 (r(elem!1, s(elem!1))),
% 3.64/3.88 inference(unit_resolution,[status(thm)],[756, 11223, 11167])).
% 3.64/3.89 tff(11225,plain,
% 3.64/3.89 (~r(s(s(s(s(z)))), s(elem!1))),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[10992, 11224, 11169])).
% 3.64/3.89 tff(11226,plain,
% 3.64/3.89 ($false),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[11225, 11187])).
% 3.64/3.89 tff(11227,plain,((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(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(z)), elem!1) | (~b(z, s(s(z)))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | (elem!1 = z) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 3.64/3.89 tff(11228,plain,
% 3.64/3.89 (elem!1 = s(s(s(s(z))))),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[11227, 3244, 11139, 203, 145, 104, 86, 10828, 273, 286, 290, 5618])).
% 3.64/3.89 tff(11229,plain,
% 3.64/3.89 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(s(z)))))),
% 3.64/3.89 inference(monotonicity,[status(thm)],[11228])).
% 3.64/3.89 tff(11230,plain,
% 3.64/3.89 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), elem!1)),
% 3.64/3.89 inference(symmetry,[status(thm)],[11229])).
% 3.64/3.89 tff(11231,plain,
% 3.64/3.89 ((~b(s(s(z)), s(s(s(s(z)))))) <=> (~b(s(s(z)), elem!1))),
% 3.64/3.89 inference(monotonicity,[status(thm)],[11230])).
% 3.64/3.89 tff(11232,plain,
% 3.64/3.89 (~b(s(s(z)), elem!1)),
% 3.64/3.89 inference(modus_ponens,[status(thm)],[105, 11231])).
% 3.64/3.89 tff(11233,plain,
% 3.64/3.89 (~b(elem!1, z)),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[3172, 11228, 3170])).
% 3.64/3.89 tff(11234,plain,
% 3.64/3.89 (~(elem!1 = s(s(z)))),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[6641, 11233, 5618])).
% 3.64/3.89 tff(11235,plain,
% 3.64/3.89 (~(s(s(z)) = elem!1)),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[3230, 11234])).
% 3.64/3.89 tff(11236,plain,
% 3.64/3.89 (b(s(s(z)), elem!1)),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[448, 11235, 10828])).
% 3.64/3.89 tff(11237,plain,
% 3.64/3.89 ($false),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[11236, 11232])).
% 3.64/3.89 tff(11238,plain,(b(s(s(s(s(z)))), z) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), elem!1) | r(s(s(z)), z) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(z))) | (~b(z, s(s(z)))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 3.64/3.89 tff(11239,plain,
% 3.64/3.89 (b(s(s(s(s(z)))), z)),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[11238, 10828, 105, 5618, 203, 145, 104, 86, 273, 286, 290])).
% 3.64/3.89 tff(11240,plain,
% 3.64/3.89 (elem!1 = s(s(s(s(z))))),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[11013, 10828, 104, 203, 273, 286, 145, 11239, 11139, 86, 290, 5618])).
% 3.64/3.89 tff(11241,plain,
% 3.64/3.89 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(s(s(z)))))),
% 3.64/3.89 inference(monotonicity,[status(thm)],[11240])).
% 3.64/3.89 tff(11242,plain,
% 3.64/3.89 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(z)), elem!1)),
% 3.64/3.89 inference(symmetry,[status(thm)],[11241])).
% 3.64/3.89 tff(11243,plain,
% 3.64/3.89 (r(s(s(z)), elem!1)),
% 3.64/3.89 inference(modus_ponens,[status(thm)],[10794, 11242])).
% 3.64/3.89 tff(11244,plain,
% 3.64/3.89 ($false),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[10828, 11243])).
% 3.64/3.89 tff(11245,plain,(r(s(s(z)), elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(z))) | (elem!1 = z) | r(s(s(z)), z) | b(s(s(z)), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.89 tff(11246,plain,
% 3.64/3.89 (b(s(s(s(s(z)))), s(s(z)))),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[11245, 10828, 203, 273, 286, 145, 104, 290, 5618, 105])).
% 3.64/3.89 tff(11247,plain,
% 3.64/3.89 (~r(s(s(s(s(z)))), z)),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[11149, 817, 104, 469, 203, 145, 507, 3461, 273, 506, 286])).
% 3.64/3.89 tff(11248,plain,
% 3.64/3.89 (b(s(s(s(s(z)))), z)),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[191, 11247])).
% 3.64/3.89 tff(11249,plain,
% 3.64/3.89 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[703, 11145])).
% 3.64/3.89 tff(11250,plain,
% 3.64/3.89 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[11027, 11142, 108])).
% 3.64/3.89 tff(11251,plain,
% 3.64/3.89 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[3444, 11250, 11249])).
% 3.64/3.89 tff(11252,plain,
% 3.64/3.89 (b(elem!1, s(s(s(s(z)))))),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[483, 11143, 469])).
% 3.64/3.89 tff(11253,plain,
% 3.64/3.89 ($false),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[9083, 11147, 11252, 104, 223, 11251])).
% 3.64/3.89 tff(11254,plain,((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (elem!1 = s(s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(z)))))) | (z = elem!1) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | b(s(s(z)), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.89 tff(11255,plain,
% 3.64/3.89 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[11254, 817, 469, 506, 203, 145, 507, 3461, 273, 104, 286])).
% 3.64/3.89 tff(11256,plain,
% 3.64/3.89 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[133, 11255])).
% 3.64/3.89 tff(11257,plain,
% 3.64/3.89 ($false),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[298, 11256, 11248, 104, 273, 202])).
% 3.64/3.89 tff(11258,plain,((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (elem!1 = s(s(s(s(z))))) | (~b(elem!1, z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(z)))))) | (z = elem!1) | (~b(s(s(z)), z)) | b(s(s(z)), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.89 tff(11259,plain,
% 3.64/3.89 (~b(s(s(z)), elem!1)),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[11258, 11246, 273, 104, 469, 506, 203, 145, 318, 5619, 286])).
% 3.64/3.89 tff(11260,plain,
% 3.64/3.89 (s(s(z)) = elem!1),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[448, 11259, 10828])).
% 3.64/3.89 tff(11261,plain,
% 3.64/3.89 (s(s(s(z))) = s(elem!1)),
% 3.64/3.89 inference(monotonicity,[status(thm)],[11260])).
% 3.64/3.89 tff(11262,plain,
% 3.64/3.89 (s(s(s(s(z)))) = s(s(elem!1))),
% 3.64/3.89 inference(monotonicity,[status(thm)],[11261])).
% 3.64/3.89 tff(11263,plain,
% 3.64/3.89 (s(s(elem!1)) = s(s(s(s(z))))),
% 3.64/3.89 inference(symmetry,[status(thm)],[11262])).
% 3.64/3.89 tff(11264,plain,
% 3.64/3.89 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(s(z)))), s(elem!1))),
% 3.64/3.89 inference(monotonicity,[status(thm)],[11263])).
% 3.64/3.89 tff(11265,plain,
% 3.64/3.89 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 3.64/3.89 inference(symmetry,[status(thm)],[11264])).
% 3.64/3.89 tff(11266,plain,
% 3.64/3.89 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 3.64/3.89 inference(monotonicity,[status(thm)],[11261])).
% 3.64/3.89 tff(11267,plain,
% 3.64/3.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.64/3.89 inference(rewrite,[status(thm)],[])).
% 3.64/3.89 tff(11268,plain,
% 3.64/3.89 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.64/3.89 inference(rewrite,[status(thm)],[])).
% 3.64/3.89 tff(11269,plain,
% 3.64/3.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 3.64/3.89 inference(monotonicity,[status(thm)],[11268])).
% 3.64/3.89 tff(11270,plain,
% 3.64/3.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.64/3.89 inference(transitivity,[status(thm)],[11269, 11267])).
% 3.64/3.89 tff(11271,plain,
% 3.64/3.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z)))),
% 3.64/3.89 inference(quant_inst,[status(thm)],[])).
% 3.64/3.89 tff(11272,plain,
% 3.64/3.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.64/3.89 inference(modus_ponens,[status(thm)],[11271, 11270])).
% 3.64/3.89 tff(11273,plain,
% 3.64/3.89 (~r(s(s(s(z))), z)),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[11272, 118, 203, 8216])).
% 3.64/3.89 tff(11274,assumption,(~(s(s(s(z))) = s(s(z)))), introduced(assumption)).
% 3.64/3.89 tff(11275,plain,
% 3.64/3.89 (~r(s(s(s(z))), s(s(z)))),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[1269, 118, 224, 8216])).
% 3.64/3.89 tff(11276,plain,
% 3.64/3.89 (b(s(s(s(z))), s(s(z)))),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[4965, 11275, 11274])).
% 3.64/3.89 tff(11277,plain,
% 3.64/3.89 (~r(s(s(z)), s(s(s(z))))),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[10533, 118, 224, 8216])).
% 3.64/3.89 tff(11278,plain,
% 3.64/3.89 (b(s(s(z)), s(s(s(z))))),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[5087, 11277, 3006])).
% 3.64/3.89 tff(11279,plain,
% 3.64/3.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 3.64/3.89 inference(rewrite,[status(thm)],[])).
% 3.64/3.89 tff(11280,plain,
% 3.64/3.89 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 3.64/3.89 inference(rewrite,[status(thm)],[])).
% 3.64/3.89 tff(11281,plain,
% 3.64/3.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))))),
% 3.64/3.89 inference(monotonicity,[status(thm)],[11280])).
% 3.64/3.89 tff(11282,plain,
% 3.64/3.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 3.64/3.89 inference(transitivity,[status(thm)],[11281, 11279])).
% 3.64/3.89 tff(11283,plain,
% 3.64/3.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 3.64/3.89 inference(quant_inst,[status(thm)],[])).
% 3.64/3.89 tff(11284,plain,
% 3.64/3.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))),
% 3.64/3.89 inference(modus_ponens,[status(thm)],[11283, 11282])).
% 3.64/3.89 tff(11285,plain,
% 3.64/3.89 ($false),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[11284, 178, 3461, 273, 11278, 1127, 11276])).
% 3.64/3.89 tff(11286,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (s(s(s(z))) = s(s(z))) | (s(s(z)) = s(s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.89 tff(11287,plain,
% 3.64/3.89 ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[11286, 3204, 3205])).
% 3.64/3.89 tff(11288,plain,
% 3.64/3.89 (~b(s(s(s(z))), z)),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[11287, 8216, 3461, 273, 224])).
% 3.64/3.89 tff(11289,plain,
% 3.64/3.89 ($false),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[4903, 41, 77, 11288, 11273])).
% 3.64/3.89 tff(11290,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.89 tff(11291,plain,
% 3.64/3.89 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[11290, 287, 5619, 273, 203])).
% 3.64/3.89 tff(11292,plain,
% 3.64/3.89 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[5031, 41, 11291, 10712])).
% 3.64/3.89 tff(11293,plain,
% 3.64/3.89 ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[11182, 178, 104, 223, 11139])).
% 3.64/3.89 tff(11294,plain,
% 3.64/3.89 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[11293, 11292])).
% 3.64/3.89 tff(11295,plain,
% 3.64/3.89 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[11185, 11294])).
% 3.64/3.89 tff(11296,plain,
% 3.64/3.89 (r(s(s(s(s(z)))), s(elem!1))),
% 3.64/3.89 inference(modus_ponens,[status(thm)],[11295, 11266])).
% 3.64/3.89 tff(11297,plain,
% 3.64/3.89 (r(s(s(elem!1)), s(elem!1))),
% 3.64/3.89 inference(modus_ponens,[status(thm)],[11296, 11265])).
% 3.64/3.89 tff(11298,plain,
% 3.64/3.89 (r(z, s(s(s(s(z))))) <=> r(z, s(s(elem!1)))),
% 3.64/3.89 inference(monotonicity,[status(thm)],[11262])).
% 3.64/3.89 tff(11299,plain,
% 3.64/3.89 (r(z, s(s(elem!1)))),
% 3.64/3.89 inference(modus_ponens,[status(thm)],[145, 11298])).
% 3.64/3.89 tff(11300,plain,
% 3.64/3.89 (~r(z, s(elem!1))),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[10967, 11297, 11299])).
% 3.64/3.89 tff(11301,plain,
% 3.64/3.89 (b(z, s(elem!1))),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[2351, 11300])).
% 3.64/3.89 tff(11302,plain,
% 3.64/3.89 ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) <=> (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 3.64/3.89 inference(monotonicity,[status(thm)],[8492])).
% 3.64/3.89 tff(11303,plain,
% 3.64/3.89 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.89 inference(modus_ponens,[status(thm)],[644, 11302])).
% 3.64/3.89 tff(11304,plain,
% 3.64/3.89 ($false),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[224, 11303])).
% 3.64/3.89 tff(11305,plain,((~(s(s(z)) = elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.89 tff(11306,plain,
% 3.64/3.89 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[11305, 11260, 287])).
% 3.64/3.89 tff(11307,plain,
% 3.64/3.89 (~r(z, elem!1)),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[3818, 11306, 203])).
% 3.64/3.89 tff(11308,plain,
% 3.64/3.89 (b(z, elem!1)),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[585, 11307, 318])).
% 3.64/3.89 tff(11309,plain,
% 3.64/3.89 ((elem!1 = s(s(s(z)))) <=> (elem!1 = s(elem!1))),
% 3.64/3.89 inference(monotonicity,[status(thm)],[11261])).
% 3.64/3.89 tff(11310,plain,
% 3.64/3.89 ((elem!1 = s(s(s(z)))) <=> (s(elem!1) = elem!1)),
% 3.64/3.89 inference(transitivity,[status(thm)],[11309, 3190])).
% 3.64/3.89 tff(11311,plain,
% 3.64/3.89 ((elem!1 = s(s(s(z)))) <=> (elem!1 = s(elem!1))),
% 3.64/3.89 inference(transitivity,[status(thm)],[11310, 3880])).
% 3.64/3.89 tff(11312,plain,
% 3.64/3.89 ((~(elem!1 = s(s(s(z))))) <=> (~(elem!1 = s(elem!1)))),
% 3.64/3.89 inference(monotonicity,[status(thm)],[11311])).
% 3.64/3.89 tff(11313,plain,
% 3.64/3.89 ((s(s(z)) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 3.64/3.89 inference(monotonicity,[status(thm)],[11260])).
% 3.64/3.89 tff(11314,plain,
% 3.64/3.89 ((~(s(s(z)) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 3.64/3.89 inference(monotonicity,[status(thm)],[11313])).
% 3.64/3.89 tff(11315,plain,
% 3.64/3.89 (~(elem!1 = s(s(s(z))))),
% 3.64/3.89 inference(modus_ponens,[status(thm)],[3205, 11314])).
% 3.64/3.89 tff(11316,plain,
% 3.64/3.89 (~(elem!1 = s(elem!1))),
% 3.64/3.89 inference(modus_ponens,[status(thm)],[11315, 11312])).
% 3.64/3.89 tff(11317,plain,
% 3.64/3.89 (r(s(s(z)), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 3.64/3.89 inference(monotonicity,[status(thm)],[11260])).
% 3.64/3.89 tff(11318,plain,
% 3.64/3.89 (r(elem!1, s(s(s(s(z)))))),
% 3.64/3.89 inference(modus_ponens,[status(thm)],[10794, 11317])).
% 3.64/3.89 tff(11319,plain,
% 3.64/3.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 3.64/3.89 inference(rewrite,[status(thm)],[])).
% 3.64/3.89 tff(11320,plain,
% 3.64/3.89 (((~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 3.64/3.89 inference(rewrite,[status(thm)],[])).
% 3.64/3.89 tff(11321,plain,
% 3.64/3.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1)))))),
% 3.64/3.89 inference(monotonicity,[status(thm)],[11320])).
% 3.64/3.89 tff(11322,plain,
% 3.64/3.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 3.64/3.89 inference(transitivity,[status(thm)],[11321, 11319])).
% 3.64/3.89 tff(11323,plain,
% 3.64/3.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))))),
% 3.64/3.89 inference(quant_inst,[status(thm)],[])).
% 3.64/3.89 tff(11324,plain,
% 3.64/3.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 3.64/3.89 inference(modus_ponens,[status(thm)],[11323, 11322])).
% 3.64/3.89 tff(11325,plain,
% 3.64/3.89 ($false),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[11324, 118, 1587, 6400, 470])).
% 3.64/3.89 tff(11326,plain,((~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.89 tff(11327,plain,
% 3.64/3.89 (~r(elem!1, s(elem!1))),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[11326, 11296, 11318])).
% 3.64/3.89 tff(11328,plain,
% 3.64/3.89 (b(elem!1, s(elem!1))),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[756, 11327, 11316])).
% 3.64/3.89 tff(11329,plain,
% 3.64/3.89 (~b(s(elem!1), z)),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[863, 11328, 11308, 506, 11301])).
% 3.64/3.89 tff(11330,plain,
% 3.64/3.89 (r(s(elem!1), z)),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[774, 11329])).
% 3.64/3.89 tff(11331,plain,
% 3.64/3.89 (~r(s(s(elem!1)), z)),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[997, 11330, 11297])).
% 3.64/3.89 tff(11332,plain,
% 3.64/3.89 (b(s(s(elem!1)), z)),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[6600, 11331])).
% 3.64/3.89 tff(11333,plain,
% 3.64/3.89 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 3.64/3.89 inference(monotonicity,[status(thm)],[11262])).
% 3.64/3.89 tff(11334,plain,
% 3.64/3.89 (b(s(s(s(s(z)))), elem!1)),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[8526, 11260, 11246])).
% 3.64/3.89 tff(11335,plain,
% 3.64/3.89 (b(s(s(elem!1)), elem!1)),
% 3.64/3.89 inference(modus_ponens,[status(thm)],[11334, 11333])).
% 3.64/3.89 tff(11336,plain,
% 3.64/3.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 3.64/3.89 inference(rewrite,[status(thm)],[])).
% 3.64/3.89 tff(11337,plain,
% 3.64/3.89 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z))) <=> ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 3.64/3.89 inference(rewrite,[status(thm)],[])).
% 3.64/3.89 tff(11338,plain,
% 3.64/3.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))))),
% 3.64/3.89 inference(monotonicity,[status(thm)],[11337])).
% 3.64/3.89 tff(11339,plain,
% 3.64/3.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 3.64/3.89 inference(transitivity,[status(thm)],[11338, 11336])).
% 3.64/3.89 tff(11340,plain,
% 3.64/3.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))),
% 3.64/3.89 inference(quant_inst,[status(thm)],[])).
% 3.64/3.89 tff(11341,plain,
% 3.64/3.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))),
% 3.64/3.89 inference(modus_ponens,[status(thm)],[11340, 11339])).
% 3.64/3.89 tff(11342,plain,
% 3.64/3.89 ($false),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[11341, 178, 11308, 11301, 11328, 11335, 11332])).
% 3.64/3.89 tff(11343,plain,(r(s(s(z)), elem!1) | (~b(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (elem!1 = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | (elem!1 = z) | r(s(s(z)), z) | b(s(s(z)), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.89 tff(11344,plain,
% 3.64/3.89 (r(s(s(z)), elem!1)),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[11343, 11137, 47, 4236, 273, 104, 469, 286, 290, 5618, 105])).
% 3.64/3.89 tff(11345,plain,
% 3.64/3.89 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[2803, 11344, 287])).
% 3.64/3.89 tff(11346,plain,
% 3.64/3.89 (~r(elem!1, s(s(s(s(z)))))),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[8763, 11344, 10794])).
% 3.64/3.89 tff(11347,plain,
% 3.64/3.89 (b(elem!1, s(s(s(s(z)))))),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[483, 11346, 469])).
% 3.64/3.89 tff(11348,plain,
% 3.64/3.89 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[212, 4236, 47])).
% 3.64/3.89 tff(11349,plain,
% 3.64/3.89 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[222, 11348])).
% 3.64/3.89 tff(11350,plain,
% 3.64/3.89 ($false),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[2968, 118, 438, 224, 2953])).
% 3.64/3.89 tff(11351,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.64/3.89 tff(11352,plain,
% 3.64/3.89 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[11351, 11344, 287])).
% 3.64/3.89 tff(11353,plain,
% 3.64/3.89 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[11098, 11352, 11349, 11347, 104, 11345])).
% 3.64/3.89 tff(11354,plain,
% 3.64/3.89 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 3.64/3.89 inference(monotonicity,[status(thm)],[11353])).
% 3.64/3.89 tff(11355,plain,
% 3.64/3.89 (s(s(elem!1)) = s(s(s(s(s(s(s(s(s(z)))))))))),
% 3.64/3.89 inference(monotonicity,[status(thm)],[11354])).
% 3.64/3.89 tff(11356,plain,
% 3.64/3.89 (s(s(s(elem!1))) = s(s(s(s(s(s(s(s(s(s(z))))))))))),
% 3.64/3.89 inference(monotonicity,[status(thm)],[11355])).
% 3.64/3.89 tff(11357,plain,
% 3.64/3.89 (s(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(s(elem!1)))),
% 3.64/3.89 inference(symmetry,[status(thm)],[11356])).
% 3.64/3.89 tff(11358,plain,
% 3.64/3.89 (b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.64/3.89 inference(monotonicity,[status(thm)],[11357])).
% 3.64/3.89 tff(11359,plain,
% 3.64/3.89 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))),
% 3.64/3.89 inference(symmetry,[status(thm)],[11358])).
% 3.64/3.89 tff(11360,plain,
% 3.64/3.89 (~(s(elem!1) = s(s(z)))),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[2832, 11353])).
% 3.64/3.89 tff(11361,plain,
% 3.64/3.89 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[2840, 11360])).
% 3.64/3.89 tff(11362,plain,
% 3.64/3.89 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[4173, 11361, 10800])).
% 3.64/3.89 tff(11363,plain,
% 3.64/3.89 (b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))),
% 3.64/3.89 inference(modus_ponens,[status(thm)],[11362, 11359])).
% 3.64/3.89 tff(11364,plain,
% 3.64/3.89 (b(s(s(s(s(s(s(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))))))))),
% 3.64/3.89 inference(monotonicity,[status(thm)],[11357])).
% 3.64/3.89 tff(11365,plain,
% 3.64/3.89 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.89 inference(symmetry,[status(thm)],[11364])).
% 3.64/3.89 tff(11366,plain,
% 3.64/3.89 (~(elem!1 = s(s(s(elem!1))))),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[2859, 11361, 11353])).
% 3.64/3.89 tff(11367,plain,
% 3.64/3.89 (~(s(s(s(elem!1))) = elem!1)),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[2489, 11366])).
% 3.64/3.89 tff(11368,plain,
% 3.64/3.89 (~b(z, elem!1)),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[4243, 11353, 4235])).
% 3.64/3.89 tff(11369,plain,
% 3.64/3.89 (r(z, elem!1)),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[585, 11368, 318])).
% 3.64/3.89 tff(11370,plain,
% 3.64/3.89 (~r(s(s(s(elem!1))), elem!1)),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[6388, 11369, 11344, 5619, 273])).
% 3.64/3.89 tff(11371,plain,
% 3.64/3.89 (b(s(s(s(elem!1))), elem!1)),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[570, 11370, 11367])).
% 3.64/3.89 tff(11372,plain,
% 3.64/3.89 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[10584, 11371, 11353])).
% 3.64/3.89 tff(11373,plain,
% 3.64/3.89 (b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))),
% 3.64/3.89 inference(modus_ponens,[status(thm)],[11372, 11365])).
% 3.64/3.89 tff(11374,plain,
% 3.64/3.89 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z))))))))))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.64/3.89 inference(monotonicity,[status(thm)],[11357])).
% 3.64/3.89 tff(11375,plain,
% 3.64/3.89 (b(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(s(s(s(s(s(s(s(z)))))))))))),
% 3.64/3.89 inference(symmetry,[status(thm)],[11374])).
% 3.64/3.89 tff(11376,plain,
% 3.64/3.89 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.64/3.89 inference(monotonicity,[status(thm)],[11353])).
% 3.64/3.89 tff(11377,plain,
% 3.64/3.89 (~r(s(s(s(s(z)))), s(s(z)))),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[11089, 11344, 287, 104, 47, 290, 5619, 273, 469, 10800, 4235, 11346])).
% 3.64/3.89 tff(11378,plain,
% 3.64/3.89 (b(s(s(s(s(z)))), s(s(z)))),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[102, 11377])).
% 3.64/3.89 tff(11379,plain,
% 3.64/3.89 (~b(s(s(z)), elem!1)),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[11258, 11378, 273, 104, 469, 11137, 4236, 47, 318, 5619, 286])).
% 3.64/3.89 tff(11380,plain,
% 3.64/3.89 (~b(s(s(s(s(z)))), z)),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[3159, 178, 11137, 273, 11347, 11378])).
% 3.64/3.89 tff(11381,plain,
% 3.64/3.89 (r(s(s(s(s(z)))), z)),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[191, 11380])).
% 3.64/3.89 tff(11382,plain,
% 3.64/3.89 (~r(s(s(s(s(z)))), elem!1)),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[3137, 11369, 11381])).
% 3.64/3.89 tff(11383,plain,
% 3.64/3.89 (b(s(s(s(s(z)))), elem!1)),
% 3.64/3.89 inference(unit_resolution,[status(thm)],[3142, 11382, 551])).
% 3.64/3.89 tff(11384,plain,
% 3.64/3.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 3.74/3.90 inference(rewrite,[status(thm)],[])).
% 3.74/3.90 tff(11385,plain,
% 3.74/3.90 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 3.74/3.90 inference(rewrite,[status(thm)],[])).
% 3.74/3.90 tff(11386,plain,
% 3.74/3.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 3.74/3.90 inference(monotonicity,[status(thm)],[11385])).
% 3.74/3.90 tff(11387,plain,
% 3.74/3.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 3.74/3.90 inference(transitivity,[status(thm)],[11386, 11384])).
% 3.74/3.90 tff(11388,plain,
% 3.74/3.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 3.74/3.90 inference(quant_inst,[status(thm)],[])).
% 3.74/3.90 tff(11389,plain,
% 3.74/3.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z))))),
% 3.74/3.90 inference(modus_ponens,[status(thm)],[11388, 11387])).
% 3.74/3.90 tff(11390,plain,
% 3.74/3.90 ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1))),
% 3.74/3.90 inference(unit_resolution,[status(thm)],[11389, 178, 11137, 5619, 11378])).
% 3.74/3.90 tff(11391,plain,
% 3.74/3.90 (~b(elem!1, s(s(z)))),
% 3.74/3.90 inference(unit_resolution,[status(thm)],[11390, 11383])).
% 3.74/3.90 tff(11392,plain,
% 3.74/3.90 (b(elem!1, s(s(s(elem!1))))),
% 3.74/3.90 inference(unit_resolution,[status(thm)],[10659, 11391, 1, 11380, 11379])).
% 3.74/3.90 tff(11393,plain,
% 3.74/3.90 (b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.74/3.90 inference(modus_ponens,[status(thm)],[11392, 11376])).
% 3.74/3.90 tff(11394,plain,
% 3.74/3.90 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 3.74/3.90 inference(modus_ponens,[status(thm)],[11393, 11375])).
% 3.74/3.90 tff(11395,plain,
% 3.74/3.90 ((~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z)))))))))),
% 3.74/3.90 inference(unit_resolution,[status(thm)],[10871, 178, 104, 11349])).
% 3.74/3.90 tff(11396,plain,
% 3.74/3.90 ($false),
% 3.74/3.90 inference(unit_resolution,[status(thm)],[11395, 11394, 11373, 11363])).
% 3.74/3.90 tff(11397,plain,((elem!1 = s(s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | b(z, s(s(s(s(z))))) | (~b(z, s(s(z)))) | b(z, s(s(s(s(s(s(s(z)))))))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | (elem!1 = z) | r(s(s(z)), z) | b(s(s(z)), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.90 tff(11398,plain,
% 3.74/3.90 (elem!1 = s(s(s(s(z))))),
% 3.74/3.90 inference(unit_resolution,[status(thm)],[11397, 286, 1, 273, 4235, 104, 290, 5618, 105])).
% 3.74/3.90 tff(11399,plain,
% 3.74/3.90 (r(elem!1, s(elem!1)) <=> r(s(s(s(s(z)))), s(elem!1))),
% 3.74/3.90 inference(monotonicity,[status(thm)],[11398])).
% 3.74/3.90 tff(11400,plain,
% 3.74/3.90 (r(s(s(s(s(z)))), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 3.74/3.90 inference(symmetry,[status(thm)],[11399])).
% 3.74/3.90 tff(11401,plain,
% 3.74/3.90 (s(elem!1) = s(s(s(s(s(z)))))),
% 3.74/3.90 inference(monotonicity,[status(thm)],[11398])).
% 3.74/3.90 tff(11402,plain,
% 3.74/3.90 (s(s(s(s(s(z))))) = s(elem!1)),
% 3.74/3.90 inference(symmetry,[status(thm)],[11401])).
% 3.74/3.90 tff(11403,plain,
% 3.74/3.90 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 3.74/3.90 inference(monotonicity,[status(thm)],[11402])).
% 3.74/3.90 tff(11404,plain,
% 3.74/3.90 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(elem!1, s(elem!1))),
% 3.74/3.90 inference(transitivity,[status(thm)],[11403, 11400])).
% 3.74/3.90 tff(11405,plain,
% 3.74/3.90 ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) <=> (~r(elem!1, s(elem!1)))),
% 3.74/3.90 inference(monotonicity,[status(thm)],[11404])).
% 3.74/3.90 tff(11406,plain,
% 3.74/3.90 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 3.74/3.90 inference(commutativity,[status(thm)],[])).
% 3.74/3.90 tff(11407,plain,
% 3.74/3.90 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 3.74/3.90 inference(symmetry,[status(thm)],[11406])).
% 3.74/3.90 tff(11408,plain,
% 3.74/3.90 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(s(s(z)))))),
% 3.74/3.90 inference(monotonicity,[status(thm)],[11407])).
% 3.74/3.90 tff(11409,assumption,(s(s(s(z))) = s(s(s(s(s(z)))))), introduced(assumption)).
% 3.74/3.90 tff(11410,plain,
% 3.74/3.90 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 3.74/3.90 inference(monotonicity,[status(thm)],[11409])).
% 3.74/3.90 tff(11411,plain,
% 3.74/3.90 (s(s(z)) = s(s(s(s(z))))),
% 3.74/3.90 inference(transitivity,[status(thm)],[66, 11410, 53])).
% 3.74/3.90 tff(11412,plain,
% 3.74/3.90 ($false),
% 3.74/3.90 inference(unit_resolution,[status(thm)],[159, 11411])).
% 3.74/3.90 tff(11413,plain,(~(s(s(s(z))) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.90 tff(11414,plain,
% 3.74/3.90 (~(s(s(s(s(s(z))))) = s(s(s(z))))),
% 3.74/3.90 inference(modus_ponens,[status(thm)],[11413, 11408])).
% 3.74/3.90 tff(11415,plain,
% 3.74/3.90 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.74/3.90 inference(unit_resolution,[status(thm)],[11290, 287, 5619, 273, 4236])).
% 3.74/3.90 tff(11416,plain,
% 3.74/3.90 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.74/3.90 inference(unit_resolution,[status(thm)],[5031, 41, 11415, 10712])).
% 3.74/3.90 tff(11417,plain,
% 3.74/3.90 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 3.74/3.90 inference(monotonicity,[status(thm)],[11402])).
% 3.74/3.90 tff(11418,plain,
% 3.74/3.90 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.74/3.90 inference(symmetry,[status(thm)],[11417])).
% 3.74/3.90 tff(11419,plain,
% 3.74/3.90 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(s(z)))))),
% 3.74/3.90 inference(monotonicity,[status(thm)],[11398])).
% 3.74/3.90 tff(11420,plain,
% 3.74/3.90 (b(s(elem!1), elem!1) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.74/3.90 inference(transitivity,[status(thm)],[11419, 11418])).
% 3.74/3.90 tff(11421,plain,
% 3.74/3.90 (s(s(s(s(z)))) = elem!1),
% 3.74/3.90 inference(unit_resolution,[status(thm)],[325, 11398])).
% 3.74/3.90 tff(11422,plain,
% 3.74/3.90 (~b(z, elem!1)),
% 3.74/3.90 inference(unit_resolution,[status(thm)],[1846, 11398, 1])).
% 3.74/3.90 tff(11423,plain,
% 3.74/3.90 (r(z, elem!1)),
% 3.74/3.90 inference(unit_resolution,[status(thm)],[585, 11422, 318])).
% 3.74/3.90 tff(11424,plain,
% 3.74/3.90 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.74/3.90 inference(unit_resolution,[status(thm)],[3818, 11423, 4236])).
% 3.74/3.90 tff(11425,plain,
% 3.74/3.90 (~(s(s(z)) = elem!1)),
% 3.74/3.90 inference(unit_resolution,[status(thm)],[11305, 11424, 287])).
% 3.74/3.90 tff(11426,plain,
% 3.74/3.90 (~(s(s(elem!1)) = elem!1)),
% 3.74/3.90 inference(unit_resolution,[status(thm)],[338, 11425, 11421])).
% 3.74/3.90 tff(11427,plain,
% 3.74/3.90 (~(s(elem!1) = elem!1)),
% 3.74/3.90 inference(unit_resolution,[status(thm)],[672, 11426])).
% 3.74/3.90 tff(11428,plain,
% 3.74/3.90 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(s(s(z)))))),
% 3.74/3.90 inference(monotonicity,[status(thm)],[319])).
% 3.74/3.90 tff(11429,plain,
% 3.74/3.90 (r(s(elem!1), s(s(s(s(z)))))),
% 3.74/3.90 inference(modus_ponens,[status(thm)],[1426, 11428])).
% 3.74/3.90 tff(11430,plain,
% 3.74/3.90 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(z))))))),
% 3.74/3.90 inference(monotonicity,[status(thm)],[2290])).
% 3.74/3.90 tff(11431,plain,
% 3.74/3.90 (s(z) = s(s(s(s(z))))),
% 3.74/3.90 inference(transitivity,[status(thm)],[71, 11430, 53])).
% 3.74/3.90 tff(11432,plain,
% 3.74/3.90 (inj_0(s(z)) = inj_0(s(s(s(s(z)))))),
% 3.74/3.90 inference(monotonicity,[status(thm)],[11431])).
% 3.74/3.90 tff(11433,plain,
% 3.74/3.90 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 3.74/3.90 inference(symmetry,[status(thm)],[11432])).
% 3.74/3.90 tff(11434,plain,
% 3.74/3.90 (s(s(s(z))) = s(s(s(s(s(s(z))))))),
% 3.74/3.90 inference(monotonicity,[status(thm)],[2290])).
% 3.74/3.90 tff(11435,plain,
% 3.74/3.90 (s(s(s(s(s(s(z)))))) = s(s(s(z)))),
% 3.74/3.90 inference(symmetry,[status(thm)],[11434])).
% 3.74/3.90 tff(11436,plain,
% 3.74/3.90 (s(s(s(s(s(s(z)))))) = z),
% 3.74/3.90 inference(transitivity,[status(thm)],[11435, 61, 11433, 51])).
% 3.74/3.90 tff(11437,plain,
% 3.74/3.90 ($false),
% 3.74/3.90 inference(unit_resolution,[status(thm)],[433, 11436])).
% 3.74/3.90 tff(11438,plain,((~(s(elem!1) = s(s(z)))) | (~(elem!1 = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.90 tff(11439,plain,
% 3.74/3.90 (~(s(elem!1) = s(s(z)))),
% 3.74/3.90 inference(unit_resolution,[status(thm)],[11438, 319])).
% 3.74/3.90 tff(11440,plain,
% 3.74/3.90 (~r(s(elem!1), z)),
% 3.74/3.90 inference(unit_resolution,[status(thm)],[1284, 1426, 521])).
% 3.74/3.90 tff(11441,plain,
% 3.74/3.90 (b(s(elem!1), z)),
% 3.74/3.90 inference(unit_resolution,[status(thm)],[774, 11440])).
% 3.74/3.90 tff(11442,plain,
% 3.74/3.90 (~r(s(elem!1), s(s(s(s(z)))))),
% 3.74/3.90 inference(unit_resolution,[status(thm)],[6776, 11441, 273, 147, 11439, 3461])).
% 3.74/3.90 tff(11443,plain,
% 3.74/3.90 ($false),
% 3.74/3.90 inference(unit_resolution,[status(thm)],[11442, 11429])).
% 3.74/3.90 tff(11444,plain,((~r(s(elem!1), elem!1)) | (~(elem!1 = s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.90 tff(11445,plain,
% 3.74/3.90 (~r(s(elem!1), elem!1)),
% 3.74/3.90 inference(unit_resolution,[status(thm)],[11444, 11398, 273, 10794, 5619, 11423])).
% 3.74/3.90 tff(11446,plain,
% 3.74/3.90 (b(s(elem!1), elem!1)),
% 3.74/3.90 inference(unit_resolution,[status(thm)],[677, 11445, 11427])).
% 3.74/3.90 tff(11447,plain,
% 3.74/3.90 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.74/3.90 inference(modus_ponens,[status(thm)],[11446, 11420])).
% 3.74/3.90 tff(11448,plain,
% 3.74/3.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.74/3.90 inference(rewrite,[status(thm)],[])).
% 3.74/3.90 tff(11449,plain,
% 3.74/3.90 (((~b(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))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.74/3.90 inference(rewrite,[status(thm)],[])).
% 3.74/3.90 tff(11450,plain,
% 3.74/3.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 3.74/3.90 inference(monotonicity,[status(thm)],[11449])).
% 3.74/3.90 tff(11451,plain,
% 3.74/3.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.74/3.90 inference(transitivity,[status(thm)],[11450, 11448])).
% 3.74/3.90 tff(11452,plain,
% 3.74/3.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.74/3.90 inference(quant_inst,[status(thm)],[])).
% 3.74/3.90 tff(11453,plain,
% 3.74/3.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 3.74/3.90 inference(modus_ponens,[status(thm)],[11452, 11451])).
% 3.74/3.90 tff(11454,plain,
% 3.74/3.90 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.74/3.90 inference(unit_resolution,[status(thm)],[11453, 178, 11349, 11447, 10796, 11416])).
% 3.74/3.90 tff(11455,plain,
% 3.74/3.90 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 3.74/3.90 inference(rewrite,[status(thm)],[])).
% 3.74/3.90 tff(11456,plain,
% 3.74/3.90 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 3.74/3.90 inference(quant_inst,[status(thm)],[])).
% 3.74/3.90 tff(11457,plain,
% 3.74/3.90 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.74/3.90 inference(modus_ponens,[status(thm)],[11456, 11455])).
% 3.74/3.90 tff(11458,plain,
% 3.74/3.90 ((s(s(s(s(s(z))))) = s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.74/3.90 inference(unit_resolution,[status(thm)],[11457, 41, 11454])).
% 3.74/3.90 tff(11459,plain,
% 3.74/3.90 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.74/3.90 inference(unit_resolution,[status(thm)],[11458, 11414])).
% 3.74/3.90 tff(11460,plain,
% 3.74/3.90 ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.74/3.90 inference(unit_resolution,[status(thm)],[11182, 178, 104, 11349, 10796])).
% 3.74/3.90 tff(11461,plain,
% 3.74/3.90 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.74/3.90 inference(unit_resolution,[status(thm)],[11460, 11416])).
% 3.74/3.90 tff(11462,plain,
% 3.74/3.90 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.74/3.90 inference(unit_resolution,[status(thm)],[11185, 11461])).
% 3.74/3.90 tff(11463,plain,
% 3.74/3.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.74/3.90 inference(rewrite,[status(thm)],[])).
% 3.74/3.90 tff(11464,plain,
% 3.74/3.90 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.74/3.90 inference(rewrite,[status(thm)],[])).
% 3.74/3.90 tff(11465,plain,
% 3.74/3.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 3.74/3.90 inference(monotonicity,[status(thm)],[11464])).
% 3.74/3.90 tff(11466,plain,
% 3.74/3.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.74/3.90 inference(transitivity,[status(thm)],[11465, 11463])).
% 3.74/3.90 tff(11467,plain,
% 3.74/3.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.74/3.90 inference(quant_inst,[status(thm)],[])).
% 3.74/3.90 tff(11468,plain,
% 3.74/3.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 3.74/3.90 inference(modus_ponens,[status(thm)],[11467, 11466])).
% 3.74/3.90 tff(11469,plain,
% 3.74/3.90 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.74/3.90 inference(unit_resolution,[status(thm)],[11468, 118, 11462, 11459])).
% 3.74/3.90 tff(11470,plain,
% 3.74/3.90 (~r(elem!1, s(elem!1))),
% 3.74/3.90 inference(modus_ponens,[status(thm)],[11469, 11405])).
% 3.74/3.90 tff(11471,plain,
% 3.74/3.90 (~(elem!1 = s(elem!1))),
% 3.74/3.90 inference(unit_resolution,[status(thm)],[748, 11427])).
% 3.74/3.90 tff(11472,plain,
% 3.74/3.90 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(s(s(s(s(z))))))))),
% 3.74/3.90 inference(monotonicity,[status(thm)],[352])).
% 3.74/3.90 tff(11473,plain,
% 3.74/3.90 (b(z, s(s(s(s(s(s(s(z)))))))) <=> b(z, s(s(s(elem!1))))),
% 3.74/3.90 inference(symmetry,[status(thm)],[11472])).
% 3.74/3.90 tff(11474,plain,
% 3.74/3.90 ((~b(z, s(s(s(s(s(s(s(z))))))))) <=> (~b(z, s(s(s(elem!1)))))),
% 3.74/3.90 inference(monotonicity,[status(thm)],[11473])).
% 3.74/3.90 tff(11475,plain,
% 3.74/3.90 (~b(z, s(s(s(elem!1))))),
% 3.74/3.90 inference(modus_ponens,[status(thm)],[4235, 11474])).
% 3.74/3.90 tff(11476,plain,
% 3.74/3.90 ($false),
% 3.74/3.90 inference(unit_resolution,[status(thm)],[2043, 11475])).
% 3.74/3.90 tff(11477,plain,((~(elem!1 = s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | b(z, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.90 tff(11478,plain,
% 3.74/3.90 (~b(z, s(s(s(elem!1))))),
% 3.74/3.90 inference(unit_resolution,[status(thm)],[11477, 11398, 4235])).
% 3.74/3.90 tff(11479,plain,
% 3.74/3.90 (r(z, s(s(s(elem!1))))),
% 3.74/3.90 inference(unit_resolution,[status(thm)],[2095, 11478])).
% 3.74/3.90 tff(11480,plain,
% 3.74/3.90 (~(s(elem!1) = s(s(elem!1)))),
% 3.74/3.90 inference(unit_resolution,[status(thm)],[979, 11426])).
% 3.74/3.90 tff(11481,plain,
% 3.74/3.90 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 3.74/3.90 inference(monotonicity,[status(thm)],[11401])).
% 3.74/3.90 tff(11482,plain,
% 3.74/3.90 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 3.74/3.90 inference(monotonicity,[status(thm)],[11481, 11398])).
% 3.74/3.90 tff(11483,plain,
% 3.74/3.90 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> r(s(s(elem!1)), elem!1)),
% 3.74/3.90 inference(symmetry,[status(thm)],[11482])).
% 3.74/3.90 tff(11484,plain,
% 3.74/3.90 ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) <=> (~r(s(s(elem!1)), elem!1))),
% 3.74/3.90 inference(monotonicity,[status(thm)],[11483])).
% 3.74/3.90 tff(11485,plain,
% 3.74/3.90 (b(z, s(s(elem!1))) <=> b(z, s(s(s(s(s(s(z)))))))),
% 3.74/3.90 inference(monotonicity,[status(thm)],[351])).
% 3.74/3.90 tff(11486,plain,
% 3.74/3.90 (b(z, s(s(s(s(s(s(z))))))) <=> b(z, s(s(elem!1)))),
% 3.74/3.90 inference(symmetry,[status(thm)],[11485])).
% 3.74/3.90 tff(11487,plain,
% 3.74/3.90 ((z = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = z)),
% 3.74/3.90 inference(commutativity,[status(thm)],[])).
% 3.74/3.90 tff(11488,plain,
% 3.74/3.90 ((s(s(s(s(s(s(z)))))) = z) <=> (z = s(s(s(s(s(s(z)))))))),
% 3.74/3.90 inference(symmetry,[status(thm)],[11487])).
% 3.74/3.90 tff(11489,plain,
% 3.74/3.90 ((~(s(s(s(s(s(s(z)))))) = z)) <=> (~(z = s(s(s(s(s(s(z))))))))),
% 3.74/3.90 inference(monotonicity,[status(thm)],[11488])).
% 3.74/3.90 tff(11490,plain,
% 3.74/3.90 (~(z = s(s(s(s(s(s(z)))))))),
% 3.74/3.90 inference(modus_ponens,[status(thm)],[433, 11489])).
% 3.74/3.90 tff(11491,assumption,(r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))), introduced(assumption)).
% 3.74/3.90 tff(11492,plain,
% 3.74/3.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 3.74/3.90 inference(rewrite,[status(thm)],[])).
% 3.74/3.90 tff(11493,plain,
% 3.74/3.90 (((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z))))))))) <=> ((~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 3.74/3.90 inference(rewrite,[status(thm)],[])).
% 3.74/3.90 tff(11494,plain,
% 3.74/3.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 3.74/3.90 inference(monotonicity,[status(thm)],[11493])).
% 3.74/3.90 tff(11495,plain,
% 3.74/3.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 3.74/3.90 inference(transitivity,[status(thm)],[11494, 11492])).
% 3.74/3.90 tff(11496,plain,
% 3.74/3.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 3.74/3.90 inference(quant_inst,[status(thm)],[])).
% 3.74/3.90 tff(11497,plain,
% 3.74/3.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 3.74/3.90 inference(modus_ponens,[status(thm)],[11496, 11495])).
% 3.74/3.90 tff(11498,plain,
% 3.74/3.90 ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 3.74/3.90 inference(unit_resolution,[status(thm)],[11497, 118, 145])).
% 3.74/3.90 tff(11499,plain,
% 3.74/3.90 (~r(z, s(s(s(s(s(s(z)))))))),
% 3.74/3.90 inference(unit_resolution,[status(thm)],[11498, 11491])).
% 3.74/3.90 tff(11500,plain,
% 3.74/3.90 (((~![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))))))))),
% 3.74/3.90 inference(rewrite,[status(thm)],[])).
% 3.74/3.90 tff(11501,plain,
% 3.74/3.90 ((~![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))))))))),
% 3.74/3.90 inference(quant_inst,[status(thm)],[])).
% 3.74/3.90 tff(11502,plain,
% 3.74/3.90 ((~![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)))))))),
% 3.74/3.90 inference(modus_ponens,[status(thm)],[11501, 11500])).
% 3.74/3.90 tff(11503,plain,
% 3.74/3.90 ((z = s(s(s(s(s(s(z))))))) | b(z, s(s(s(s(s(s(z)))))))),
% 3.74/3.90 inference(unit_resolution,[status(thm)],[11502, 41, 11499])).
% 3.74/3.90 tff(11504,plain,
% 3.74/3.90 (b(z, s(s(s(s(s(s(z)))))))),
% 3.74/3.90 inference(unit_resolution,[status(thm)],[11503, 11490])).
% 3.74/3.90 tff(11505,plain,
% 3.74/3.90 (b(z, s(s(elem!1)))),
% 3.74/3.90 inference(modus_ponens,[status(thm)],[11504, 11486])).
% 3.74/3.90 tff(11506,plain,
% 3.74/3.90 (r(s(s(z)), s(s(elem!1))) <=> r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 3.74/3.90 inference(monotonicity,[status(thm)],[351])).
% 3.74/3.91 tff(11507,plain,
% 3.74/3.91 (r(s(s(z)), s(s(s(s(s(s(z))))))) <=> r(s(s(z)), s(s(elem!1)))),
% 3.74/3.91 inference(symmetry,[status(thm)],[11506])).
% 3.74/3.91 tff(11508,plain,
% 3.74/3.91 ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) <=> (~r(s(s(z)), s(s(elem!1))))),
% 3.74/3.91 inference(monotonicity,[status(thm)],[11507])).
% 3.74/3.91 tff(11509,plain,
% 3.74/3.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 3.74/3.91 inference(rewrite,[status(thm)],[])).
% 3.74/3.91 tff(11510,plain,
% 3.74/3.91 (((~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(z)), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 3.74/3.91 inference(rewrite,[status(thm)],[])).
% 3.74/3.91 tff(11511,plain,
% 3.74/3.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 3.74/3.91 inference(monotonicity,[status(thm)],[11510])).
% 3.74/3.91 tff(11512,plain,
% 3.74/3.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 3.74/3.91 inference(transitivity,[status(thm)],[11511, 11509])).
% 3.74/3.91 tff(11513,plain,
% 3.74/3.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 3.74/3.91 inference(quant_inst,[status(thm)],[])).
% 3.74/3.91 tff(11514,plain,
% 3.74/3.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 3.74/3.91 inference(modus_ponens,[status(thm)],[11513, 11512])).
% 3.74/3.91 tff(11515,plain,
% 3.74/3.91 ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[11514, 118, 147])).
% 3.74/3.91 tff(11516,plain,
% 3.74/3.91 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[11515, 11491])).
% 3.74/3.91 tff(11517,plain,
% 3.74/3.91 (~r(s(s(z)), s(s(elem!1)))),
% 3.74/3.91 inference(modus_ponens,[status(thm)],[11516, 11508])).
% 3.74/3.91 tff(11518,plain,
% 3.74/3.91 ((z = elem!1) <=> (z = s(s(s(s(z)))))),
% 3.74/3.91 inference(monotonicity,[status(thm)],[319])).
% 3.74/3.91 tff(11519,plain,
% 3.74/3.91 ((z = elem!1) <=> (s(s(s(s(z)))) = z)),
% 3.74/3.91 inference(transitivity,[status(thm)],[11518, 19])).
% 3.74/3.91 tff(11520,plain,
% 3.74/3.91 ((s(s(s(s(z)))) = z) <=> (z = elem!1)),
% 3.74/3.91 inference(symmetry,[status(thm)],[11519])).
% 3.74/3.91 tff(11521,plain,
% 3.74/3.91 ((~(s(s(s(s(z)))) = z)) <=> (~(z = elem!1))),
% 3.74/3.91 inference(monotonicity,[status(thm)],[11520])).
% 3.74/3.91 tff(11522,plain,
% 3.74/3.91 (~(z = elem!1)),
% 3.74/3.91 inference(modus_ponens,[status(thm)],[30, 11521])).
% 3.74/3.91 tff(11523,plain,
% 3.74/3.91 (~(s(s(elem!1)) = s(s(z)))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[2386, 11522])).
% 3.74/3.91 tff(11524,plain,
% 3.74/3.91 (~(s(s(z)) = s(s(elem!1)))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[6460, 11523])).
% 3.74/3.91 tff(11525,plain,
% 3.74/3.91 (r(s(s(elem!1)), s(s(z))) <=> r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 3.74/3.91 inference(monotonicity,[status(thm)],[351])).
% 3.74/3.91 tff(11526,plain,
% 3.74/3.91 (r(s(s(s(s(s(s(z)))))), s(s(z))) <=> r(s(s(elem!1)), s(s(z)))),
% 3.74/3.91 inference(symmetry,[status(thm)],[11525])).
% 3.74/3.91 tff(11527,plain,
% 3.74/3.91 ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) <=> (~r(s(s(elem!1)), s(s(z))))),
% 3.74/3.91 inference(monotonicity,[status(thm)],[11526])).
% 3.74/3.91 tff(11528,plain,
% 3.74/3.91 ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[6190, 118, 147])).
% 3.74/3.91 tff(11529,plain,
% 3.74/3.91 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[11528, 11491])).
% 3.74/3.91 tff(11530,plain,
% 3.74/3.91 (~r(s(s(elem!1)), s(s(z)))),
% 3.74/3.91 inference(modus_ponens,[status(thm)],[11529, 11527])).
% 3.74/3.91 tff(11531,plain,
% 3.74/3.91 (b(s(s(elem!1)), s(s(z)))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[6494, 11530, 11523])).
% 3.74/3.91 tff(11532,plain,
% 3.74/3.91 (~b(z, s(s(elem!1)))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[6486, 11531, 3461, 273, 11524, 11517])).
% 3.74/3.91 tff(11533,plain,
% 3.74/3.91 ($false),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[11532, 11505])).
% 3.74/3.91 tff(11534,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~(elem!1 = s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.91 tff(11535,plain,
% 3.74/3.91 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[11534, 11398, 47, 10794, 5619, 273])).
% 3.74/3.91 tff(11536,plain,
% 3.74/3.91 (~r(s(s(elem!1)), elem!1)),
% 3.74/3.91 inference(modus_ponens,[status(thm)],[11535, 11484])).
% 3.74/3.91 tff(11537,plain,
% 3.74/3.91 (b(s(s(elem!1)), elem!1)),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[3362, 11536, 11426])).
% 3.74/3.91 tff(11538,plain,
% 3.74/3.91 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.74/3.91 inference(monotonicity,[status(thm)],[11398])).
% 3.74/3.91 tff(11539,plain,
% 3.74/3.91 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), elem!1)),
% 3.74/3.91 inference(symmetry,[status(thm)],[11538])).
% 3.74/3.91 tff(11540,plain,
% 3.74/3.91 (~(s(elem!1) = s(s(z)))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[11438, 11398])).
% 3.74/3.91 tff(11541,plain,
% 3.74/3.91 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[2840, 11540])).
% 3.74/3.91 tff(11542,plain,
% 3.74/3.91 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[4173, 11541, 10800])).
% 3.74/3.91 tff(11543,plain,
% 3.74/3.91 (b(s(s(s(elem!1))), elem!1)),
% 3.74/3.91 inference(modus_ponens,[status(thm)],[11542, 11539])).
% 3.74/3.91 tff(11544,plain,
% 3.74/3.91 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.74/3.91 inference(monotonicity,[status(thm)],[11398])).
% 3.74/3.91 tff(11545,plain,
% 3.74/3.91 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 3.74/3.91 inference(symmetry,[status(thm)],[11544])).
% 3.74/3.91 tff(11546,plain,
% 3.74/3.91 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 3.74/3.91 inference(monotonicity,[status(thm)],[11481])).
% 3.74/3.91 tff(11547,plain,
% 3.74/3.91 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.74/3.91 inference(monotonicity,[status(thm)],[11546])).
% 3.74/3.91 tff(11548,plain,
% 3.74/3.91 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.74/3.91 inference(symmetry,[status(thm)],[11547])).
% 3.74/3.91 tff(11549,plain,
% 3.74/3.91 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(elem!1))))),
% 3.74/3.91 inference(transitivity,[status(thm)],[11548, 11545])).
% 3.74/3.91 tff(11550,plain,
% 3.74/3.91 (b(elem!1, s(s(s(elem!1))))),
% 3.74/3.91 inference(modus_ponens,[status(thm)],[11349, 11549])).
% 3.74/3.91 tff(11551,plain,
% 3.74/3.91 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[348, 11426])).
% 3.74/3.91 tff(11552,plain,
% 3.74/3.91 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[3404, 5889])).
% 3.74/3.91 tff(11553,plain,
% 3.74/3.91 (~b(s(elem!1), s(s(s(elem!1))))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[6834, 854, 1597, 683, 2042])).
% 3.74/3.91 tff(11554,plain,
% 3.74/3.91 (r(s(elem!1), s(s(s(elem!1))))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[5432, 11553, 5396])).
% 3.74/3.91 tff(11555,plain,
% 3.74/3.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))))),
% 3.74/3.91 inference(rewrite,[status(thm)],[])).
% 3.74/3.91 tff(11556,plain,
% 3.74/3.91 (((~r(z, s(s(s(elem!1))))) | (~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(elem!1), z)) | (~r(z, s(s(s(elem!1))))))),
% 3.74/3.91 inference(rewrite,[status(thm)],[])).
% 3.74/3.91 tff(11557,plain,
% 3.74/3.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1)))))))),
% 3.74/3.91 inference(monotonicity,[status(thm)],[11556])).
% 3.74/3.91 tff(11558,plain,
% 3.74/3.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))))),
% 3.74/3.91 inference(transitivity,[status(thm)],[11557, 11555])).
% 3.74/3.91 tff(11559,plain,
% 3.74/3.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))),
% 3.74/3.91 inference(quant_inst,[status(thm)],[])).
% 3.74/3.91 tff(11560,plain,
% 3.74/3.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1)))))),
% 3.74/3.91 inference(modus_ponens,[status(thm)],[11559, 11558])).
% 3.74/3.91 tff(11561,plain,
% 3.74/3.91 (~r(s(elem!1), z)),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[11560, 118, 557, 2102])).
% 3.74/3.91 tff(11562,plain,
% 3.74/3.91 (b(s(elem!1), z)),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[774, 11561])).
% 3.74/3.91 tff(11563,plain,
% 3.74/3.91 (~(s(s(elem!1)) = s(elem!1))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[986, 984])).
% 3.74/3.91 tff(11564,plain,
% 3.74/3.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 3.74/3.91 inference(rewrite,[status(thm)],[])).
% 3.74/3.91 tff(11565,plain,
% 3.74/3.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 3.74/3.91 inference(quant_inst,[status(thm)],[])).
% 3.74/3.91 tff(11566,plain,
% 3.74/3.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1)))),
% 3.74/3.91 inference(modus_ponens,[status(thm)],[11565, 11564])).
% 3.74/3.91 tff(11567,plain,
% 3.74/3.91 (~r(s(s(elem!1)), s(elem!1))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[11566, 118, 2102, 3364])).
% 3.74/3.91 tff(11568,plain,
% 3.74/3.91 (b(s(s(elem!1)), s(elem!1))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[1006, 11567, 11563])).
% 3.74/3.91 tff(11569,plain,
% 3.74/3.91 (~r(s(elem!1), s(s(elem!1)))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[5994, 2102, 3364])).
% 3.74/3.91 tff(11570,plain,
% 3.74/3.91 (b(s(elem!1), s(s(elem!1)))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[1028, 11569, 984])).
% 3.74/3.91 tff(11571,plain,
% 3.74/3.91 ((z = s(s(elem!1))) <=> (s(s(elem!1)) = z)),
% 3.74/3.91 inference(commutativity,[status(thm)],[])).
% 3.74/3.91 tff(11572,plain,
% 3.74/3.91 ((s(s(elem!1)) = z) <=> (z = s(s(elem!1)))),
% 3.74/3.91 inference(symmetry,[status(thm)],[11571])).
% 3.74/3.91 tff(11573,plain,
% 3.74/3.91 ((~(s(s(elem!1)) = z)) <=> (~(z = s(s(elem!1))))),
% 3.74/3.91 inference(monotonicity,[status(thm)],[11572])).
% 3.74/3.91 tff(11574,plain,
% 3.74/3.91 (~(z = s(s(elem!1)))),
% 3.74/3.91 inference(modus_ponens,[status(thm)],[970, 11573])).
% 3.74/3.91 tff(11575,plain,
% 3.74/3.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))),
% 3.74/3.91 inference(rewrite,[status(thm)],[])).
% 3.74/3.91 tff(11576,plain,
% 3.74/3.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))),
% 3.74/3.91 inference(quant_inst,[status(thm)],[])).
% 3.74/3.91 tff(11577,plain,
% 3.74/3.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1))))),
% 3.74/3.91 inference(modus_ponens,[status(thm)],[11576, 11575])).
% 3.74/3.91 tff(11578,plain,
% 3.74/3.91 (~r(z, s(s(elem!1)))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[11577, 118, 557, 3364])).
% 3.74/3.91 tff(11579,plain,
% 3.74/3.91 ((z = s(s(elem!1))) | b(z, s(s(elem!1)))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[6469, 41, 11578])).
% 3.74/3.91 tff(11580,plain,
% 3.74/3.91 (b(z, s(s(elem!1)))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[11579, 11574])).
% 3.74/3.91 tff(11581,plain,
% 3.74/3.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))),
% 3.74/3.91 inference(rewrite,[status(thm)],[])).
% 3.74/3.91 tff(11582,plain,
% 3.74/3.91 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))),
% 3.74/3.91 inference(rewrite,[status(thm)],[])).
% 3.74/3.91 tff(11583,plain,
% 3.74/3.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z))))),
% 3.74/3.91 inference(monotonicity,[status(thm)],[11582])).
% 3.74/3.91 tff(11584,plain,
% 3.74/3.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))),
% 3.74/3.91 inference(transitivity,[status(thm)],[11583, 11581])).
% 3.74/3.91 tff(11585,plain,
% 3.74/3.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))),
% 3.74/3.91 inference(quant_inst,[status(thm)],[])).
% 3.74/3.91 tff(11586,plain,
% 3.74/3.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z))),
% 3.74/3.91 inference(modus_ponens,[status(thm)],[11585, 11584])).
% 3.74/3.91 tff(11587,plain,
% 3.74/3.91 (~r(s(s(elem!1)), z)),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[11586, 118, 557, 3364])).
% 3.74/3.91 tff(11588,plain,
% 3.74/3.91 (b(s(s(elem!1)), z)),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[6600, 11587])).
% 3.74/3.91 tff(11589,plain,
% 3.74/3.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 3.74/3.91 inference(rewrite,[status(thm)],[])).
% 3.74/3.91 tff(11590,plain,
% 3.74/3.91 (((~b(z, s(s(elem!1)))) | (~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(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 3.74/3.91 inference(rewrite,[status(thm)],[])).
% 3.74/3.91 tff(11591,plain,
% 3.74/3.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1))))))),
% 3.74/3.91 inference(monotonicity,[status(thm)],[11590])).
% 3.74/3.91 tff(11592,plain,
% 3.74/3.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 3.74/3.91 inference(transitivity,[status(thm)],[11591, 11589])).
% 3.74/3.91 tff(11593,plain,
% 3.74/3.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 3.74/3.91 inference(quant_inst,[status(thm)],[])).
% 3.74/3.91 tff(11594,plain,
% 3.74/3.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1))))),
% 3.74/3.91 inference(modus_ponens,[status(thm)],[11593, 11592])).
% 3.74/3.91 tff(11595,plain,
% 3.74/3.91 ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[11594, 178, 11588, 11580, 11570])).
% 3.74/3.91 tff(11596,plain,
% 3.74/3.91 ($false),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[11595, 11568, 11562])).
% 3.74/3.91 tff(11597,plain,((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.91 tff(11598,plain,
% 3.74/3.91 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[11597, 11554, 557, 984])).
% 3.74/3.91 tff(11599,plain,
% 3.74/3.91 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[3375, 11598, 5889])).
% 3.74/3.91 tff(11600,plain,
% 3.74/3.91 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[5500, 11599, 2042, 1597, 5434])).
% 3.74/3.91 tff(11601,plain,
% 3.74/3.91 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[3409, 11600, 11552])).
% 3.74/3.91 tff(11602,plain,
% 3.74/3.91 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[5897, 11599, 1597, 854, 5434])).
% 3.74/3.91 tff(11603,plain,
% 3.74/3.91 (r(s(s(s(elem!1))), s(elem!1))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[373, 11602, 356])).
% 3.74/3.91 tff(11604,plain,
% 3.74/3.91 (~b(s(elem!1), s(s(elem!1)))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[5490, 11599, 2042, 5434, 683])).
% 3.74/3.91 tff(11605,plain,
% 3.74/3.91 (r(s(elem!1), s(s(elem!1)))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[1028, 11604, 984])).
% 3.74/3.91 tff(11606,plain,
% 3.74/3.91 ($false),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[5980, 11605, 11603, 11601])).
% 3.74/3.91 tff(11607,plain,((~b(elem!1, s(elem!1))) | (s(elem!1) = s(s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.91 tff(11608,plain,
% 3.74/3.91 (~b(elem!1, s(elem!1))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[11607, 11446, 11551, 11550, 11543, 11537, 11480, 11479])).
% 3.74/3.91 tff(11609,plain,
% 3.74/3.91 (r(elem!1, s(elem!1))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[756, 11608, 11471])).
% 3.74/3.91 tff(11610,plain,
% 3.74/3.91 ($false),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[11609, 11470])).
% 3.74/3.91 tff(11611,plain,(b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | (~b(z, s(s(z)))) | b(z, s(s(s(s(s(s(s(z)))))))) | b(z, s(s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (elem!1 = z) | r(s(s(z)), z) | b(s(s(z)), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.91 tff(11612,plain,
% 3.74/3.91 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[11611, 105, 4235, 1, 104, 290, 10792, 144])).
% 3.74/3.91 tff(11613,plain,
% 3.74/3.91 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[8244, 3340])).
% 3.74/3.91 tff(11614,plain,
% 3.74/3.91 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[4243, 818, 4235])).
% 3.74/3.91 tff(11615,plain,
% 3.74/3.91 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[691, 11614, 644])).
% 3.74/3.91 tff(11616,plain,
% 3.74/3.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.74/3.91 inference(rewrite,[status(thm)],[])).
% 3.74/3.91 tff(11617,plain,
% 3.74/3.91 (((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z))))) <=> ((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.74/3.91 inference(rewrite,[status(thm)],[])).
% 3.74/3.91 tff(11618,plain,
% 3.74/3.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.74/3.91 inference(monotonicity,[status(thm)],[11617])).
% 3.74/3.91 tff(11619,plain,
% 3.74/3.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.74/3.91 inference(transitivity,[status(thm)],[11618, 11616])).
% 3.74/3.91 tff(11620,plain,
% 3.74/3.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))))),
% 3.74/3.91 inference(quant_inst,[status(thm)],[])).
% 3.74/3.91 tff(11621,plain,
% 3.74/3.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.74/3.91 inference(modus_ponens,[status(thm)],[11620, 11619])).
% 3.74/3.91 tff(11622,plain,
% 3.74/3.91 (~b(s(s(z)), elem!1)),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[11621, 178, 818, 273, 166, 11615])).
% 3.74/3.91 tff(11623,plain,
% 3.74/3.91 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 3.74/3.91 inference(monotonicity,[status(thm)],[1324])).
% 3.74/3.91 tff(11624,plain,
% 3.74/3.91 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 3.74/3.91 inference(transitivity,[status(thm)],[11623, 1526])).
% 3.74/3.91 tff(11625,plain,
% 3.74/3.91 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 3.74/3.91 inference(transitivity,[status(thm)],[11624, 2486])).
% 3.74/3.91 tff(11626,plain,
% 3.74/3.91 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 3.74/3.91 inference(monotonicity,[status(thm)],[11625])).
% 3.74/3.91 tff(11627,plain,
% 3.74/3.91 (~(elem!1 = s(s(s(elem!1))))),
% 3.74/3.91 inference(modus_ponens,[status(thm)],[1683, 11626])).
% 3.74/3.91 tff(11628,plain,
% 3.74/3.91 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[10799, 147, 145])).
% 3.74/3.91 tff(11629,plain,
% 3.74/3.91 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[2840, 10976])).
% 3.74/3.91 tff(11630,plain,
% 3.74/3.91 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[4173, 11629, 11628])).
% 3.74/3.91 tff(11631,plain,
% 3.74/3.91 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[10679, 11630, 1324])).
% 3.74/3.91 tff(11632,plain,
% 3.74/3.91 (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 3.74/3.91 inference(unit_resolution,[status(thm)],[8403, 3521])).
% 3.74/3.91 tff(11633,plain,
% 3.74/3.91 (b(s(s(z)), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 3.74/3.91 inference(monotonicity,[status(thm)],[1324])).
% 3.74/3.91 tff(11634,plain,
% 3.74/3.91 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 3.74/3.91 inference(symmetry,[status(thm)],[11633])).
% 3.74/3.91 tff(11635,plain,
% 3.74/3.91 (b(s(s(z)), s(s(s(elem!1))))),
% 3.74/3.91 inference(modus_ponens,[status(thm)],[2042, 11634])).
% 3.74/3.91 tff(11636,plain,
% 3.74/3.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 3.74/3.91 inference(rewrite,[status(thm)],[])).
% 3.74/3.91 tff(11637,plain,
% 3.74/3.91 (((~b(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)))) | (~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(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(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 3.74/3.91 inference(rewrite,[status(thm)],[])).
% 3.74/3.91 tff(11638,plain,
% 3.74/3.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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)))) | (~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(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(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 3.74/3.92 inference(monotonicity,[status(thm)],[11637])).
% 3.74/3.92 tff(11639,plain,
% 3.74/3.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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)))) | (~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(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(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 3.74/3.92 inference(transitivity,[status(thm)],[11638, 11636])).
% 3.74/3.92 tff(11640,plain,
% 3.74/3.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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)))) | (~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(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(elem!1, s(s(s(elem!1))))))),
% 3.74/3.92 inference(quant_inst,[status(thm)],[])).
% 3.74/3.92 tff(11641,plain,
% 3.74/3.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 3.74/3.92 inference(modus_ponens,[status(thm)],[11640, 11639])).
% 3.74/3.92 tff(11642,plain,
% 3.74/3.92 ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[11641, 178, 3512, 869, 3504])).
% 3.74/3.92 tff(11643,plain,
% 3.74/3.92 (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[11642, 2042])).
% 3.74/3.92 tff(11644,plain,
% 3.74/3.92 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[3612, 41, 11643, 9361])).
% 3.74/3.92 tff(11645,plain,
% 3.74/3.92 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 3.74/3.92 inference(rewrite,[status(thm)],[])).
% 3.74/3.92 tff(11646,plain,
% 3.74/3.92 (((~r(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(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 3.74/3.92 inference(rewrite,[status(thm)],[])).
% 3.74/3.92 tff(11647,plain,
% 3.74/3.92 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))))),
% 3.74/3.92 inference(monotonicity,[status(thm)],[11646])).
% 3.74/3.92 tff(11648,plain,
% 3.74/3.92 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 3.74/3.92 inference(transitivity,[status(thm)],[11647, 11645])).
% 3.74/3.92 tff(11649,plain,
% 3.74/3.92 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(s(s(elem!1))), z)))),
% 3.74/3.92 inference(quant_inst,[status(thm)],[])).
% 3.74/3.92 tff(11650,plain,
% 3.74/3.92 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 3.74/3.92 inference(modus_ponens,[status(thm)],[11649, 11648])).
% 3.74/3.92 tff(11651,plain,
% 3.74/3.92 (~r(s(s(s(elem!1))), z)),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[11650, 118, 203, 11644])).
% 3.74/3.92 tff(11652,plain,
% 3.74/3.92 (b(s(s(s(elem!1))), z)),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[1565, 11651])).
% 3.74/3.92 tff(11653,plain,
% 3.74/3.92 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 3.74/3.92 inference(rewrite,[status(thm)],[])).
% 3.74/3.92 tff(11654,plain,
% 3.74/3.92 (((~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 3.74/3.92 inference(rewrite,[status(thm)],[])).
% 3.74/3.92 tff(11655,plain,
% 3.74/3.92 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))))),
% 3.74/3.92 inference(monotonicity,[status(thm)],[11654])).
% 3.74/3.92 tff(11656,plain,
% 3.74/3.92 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 3.74/3.92 inference(transitivity,[status(thm)],[11655, 11653])).
% 3.74/3.92 tff(11657,plain,
% 3.74/3.92 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(elem!1))))))),
% 3.74/3.92 inference(quant_inst,[status(thm)],[])).
% 3.74/3.92 tff(11658,plain,
% 3.74/3.92 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 3.74/3.92 inference(modus_ponens,[status(thm)],[11657, 11656])).
% 3.74/3.92 tff(11659,plain,
% 3.74/3.92 (~r(z, s(s(s(elem!1))))),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[11658, 118, 203, 11644])).
% 3.74/3.92 tff(11660,plain,
% 3.74/3.92 (b(z, s(s(s(elem!1))))),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[2095, 11659])).
% 3.74/3.92 tff(11661,plain,
% 3.74/3.92 ($false),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[7978, 11660, 11652, 273, 3461, 11635])).
% 3.74/3.92 tff(11662,plain,((~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))) | (~(s(s(z)) = elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.92 tff(11663,plain,
% 3.74/3.92 (~b(elem!1, s(s(s(elem!1))))),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[11662, 1324, 5619, 203, 11632, 273, 11631, 869, 8176])).
% 3.74/3.92 tff(11664,plain,
% 3.74/3.92 (r(elem!1, s(s(s(elem!1))))),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[2054, 11663, 11627])).
% 3.74/3.92 tff(11665,plain,
% 3.74/3.92 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.74/3.92 inference(symmetry,[status(thm)],[8806])).
% 3.74/3.92 tff(11666,plain,
% 3.74/3.92 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 3.74/3.92 inference(monotonicity,[status(thm)],[3505])).
% 3.74/3.92 tff(11667,plain,
% 3.74/3.92 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 3.74/3.92 inference(transitivity,[status(thm)],[11666, 3881])).
% 3.74/3.92 tff(11668,plain,
% 3.74/3.92 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 3.74/3.92 inference(monotonicity,[status(thm)],[11667])).
% 3.74/3.92 tff(11669,plain,
% 3.74/3.92 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.74/3.92 inference(modus_ponens,[status(thm)],[8246, 11668])).
% 3.74/3.92 tff(11670,plain,
% 3.74/3.92 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[1649, 11669])).
% 3.74/3.92 tff(11671,plain,
% 3.74/3.92 (r(elem!1, s(s(elem!1)))),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[9352, 1324, 147])).
% 3.74/3.92 tff(11672,plain,
% 3.74/3.92 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[5845, 11664, 11671])).
% 3.74/3.92 tff(11673,plain,
% 3.74/3.92 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[3375, 11672, 11670])).
% 3.74/3.92 tff(11674,plain,
% 3.74/3.92 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.74/3.92 inference(modus_ponens,[status(thm)],[11673, 11665])).
% 3.74/3.92 tff(11675,plain,
% 3.74/3.92 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[5101, 147, 145, 5619])).
% 3.74/3.92 tff(11676,plain,
% 3.74/3.92 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[10755, 11675])).
% 3.74/3.92 tff(11677,plain,
% 3.74/3.92 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[3518, 178, 11631, 11673, 8176, 3510])).
% 3.74/3.92 tff(11678,plain,
% 3.74/3.92 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[5118, 11677, 3521])).
% 3.74/3.92 tff(11679,plain,
% 3.74/3.92 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[8721, 11678, 104, 8246, 223, 11676, 11630, 11674])).
% 3.74/3.92 tff(11680,plain,
% 3.74/3.92 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[11185, 11679])).
% 3.74/3.92 tff(11681,plain,
% 3.74/3.92 (r(s(s(s(s(z)))), s(elem!1))),
% 3.74/3.92 inference(modus_ponens,[status(thm)],[11680, 8580])).
% 3.74/3.92 tff(11682,plain,
% 3.74/3.92 (~r(elem!1, s(elem!1))),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[11326, 11681, 9349])).
% 3.74/3.92 tff(11683,plain,
% 3.74/3.92 (b(elem!1, s(elem!1))),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[756, 11682, 10913])).
% 3.74/3.92 tff(11684,plain,
% 3.74/3.92 (b(elem!1, z)),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[6641, 10916, 5618])).
% 3.74/3.92 tff(11685,plain,
% 3.74/3.92 (r(s(s(elem!1)), s(elem!1))),
% 3.74/3.92 inference(modus_ponens,[status(thm)],[11680, 8581])).
% 3.74/3.92 tff(11686,plain,
% 3.74/3.92 (~r(z, s(elem!1))),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[10967, 11685, 8134])).
% 3.74/3.92 tff(11687,plain,
% 3.74/3.92 (b(z, s(elem!1))),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[2351, 11686])).
% 3.74/3.92 tff(11688,plain,
% 3.74/3.92 (~b(s(elem!1), elem!1)),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[1396, 11687, 818, 11684, 11683])).
% 3.74/3.92 tff(11689,plain,
% 3.74/3.92 (r(s(elem!1), elem!1)),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[677, 11688, 10915])).
% 3.74/3.92 tff(11690,plain,
% 3.74/3.92 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 3.74/3.92 inference(transitivity,[status(thm)],[11667, 7104])).
% 3.74/3.92 tff(11691,plain,
% 3.74/3.92 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 3.74/3.92 inference(monotonicity,[status(thm)],[11690])).
% 3.74/3.92 tff(11692,plain,
% 3.74/3.92 (~(s(elem!1) = s(s(s(elem!1))))),
% 3.74/3.92 inference(modus_ponens,[status(thm)],[8246, 11691])).
% 3.74/3.92 tff(11693,plain,
% 3.74/3.92 (b(s(elem!1), s(s(s(s(z)))))),
% 3.74/3.92 inference(modus_ponens,[status(thm)],[11676, 8119])).
% 3.74/3.92 tff(11694,plain,
% 3.74/3.92 (b(s(elem!1), s(s(elem!1)))),
% 3.74/3.92 inference(modus_ponens,[status(thm)],[11693, 8488])).
% 3.74/3.92 tff(11695,plain,
% 3.74/3.92 (~r(z, s(s(s(elem!1))))),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[3533, 11673, 145, 3521, 203, 8176, 1324, 11631])).
% 3.74/3.92 tff(11696,plain,
% 3.74/3.92 (b(z, s(s(s(elem!1))))),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[2095, 11695])).
% 3.74/3.92 tff(11697,plain,
% 3.74/3.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.74/3.92 inference(rewrite,[status(thm)],[])).
% 3.74/3.92 tff(11698,plain,
% 3.74/3.92 (((~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(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, 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(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.74/3.92 inference(rewrite,[status(thm)],[])).
% 3.74/3.92 tff(11699,plain,
% 3.74/3.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 3.74/3.92 inference(monotonicity,[status(thm)],[11698])).
% 3.74/3.92 tff(11700,plain,
% 3.74/3.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.74/3.92 inference(transitivity,[status(thm)],[11699, 11697])).
% 3.74/3.92 tff(11701,plain,
% 3.74/3.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))))),
% 3.74/3.92 inference(quant_inst,[status(thm)],[])).
% 3.74/3.92 tff(11702,plain,
% 3.74/3.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 3.74/3.92 inference(modus_ponens,[status(thm)],[11701, 11700])).
% 3.74/3.92 tff(11703,plain,
% 3.74/3.92 ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[11702, 178, 11696, 11631, 11694])).
% 3.74/3.92 tff(11704,plain,
% 3.74/3.92 (~b(s(elem!1), s(s(s(elem!1))))),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[11703, 11687])).
% 3.74/3.92 tff(11705,plain,
% 3.74/3.92 (r(s(elem!1), s(s(s(elem!1))))),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[5432, 11704, 11692])).
% 3.74/3.92 tff(11706,plain,
% 3.74/3.92 ($false),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[9138, 11705, 11689, 11664])).
% 3.74/3.92 tff(11707,plain,((~(s(s(z)) = elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 3.74/3.92 tff(11708,plain,
% 3.74/3.92 (~(s(s(z)) = elem!1)),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[11707, 818, 104, 8246, 4254, 145, 4236, 273, 11615, 147, 5618])).
% 3.74/3.92 tff(11709,plain,
% 3.74/3.92 (r(s(s(z)), elem!1)),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[448, 11708, 11622])).
% 3.74/3.92 tff(11710,plain,
% 3.74/3.92 (~r(elem!1, s(s(s(s(z)))))),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[8763, 11709, 147])).
% 3.74/3.92 tff(11711,plain,
% 3.74/3.92 (r(s(s(s(s(z)))), elem!1)),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[8548, 11710, 104, 10813, 469, 11615])).
% 3.74/3.92 tff(11712,plain,
% 3.74/3.92 ($false),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[9469, 118, 11709, 11711, 147])).
% 3.74/3.92 tff(11713,plain,((~b(z, elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (elem!1 = s(s(s(s(z))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | r(s(s(z)), z) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | b(z, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.92 tff(11714,plain,
% 3.74/3.92 (~b(z, elem!1)),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[11713, 644, 104, 469, 11613, 47, 144, 10792, 166, 147, 4235])).
% 3.74/3.92 tff(11715,plain,
% 3.74/3.92 (r(z, elem!1)),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[585, 11714, 318])).
% 3.74/3.92 tff(11716,plain,
% 3.74/3.92 (~r(elem!1, s(s(s(s(z)))))),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[529, 521, 47])).
% 3.74/3.92 tff(11717,plain,
% 3.74/3.92 (b(elem!1, s(s(s(s(z)))))),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[483, 11716, 469])).
% 3.74/3.92 tff(11718,plain,
% 3.74/3.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.74/3.92 inference(rewrite,[status(thm)],[])).
% 3.74/3.92 tff(11719,plain,
% 3.74/3.92 (((~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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), elem!1))) <=> ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.74/3.92 inference(rewrite,[status(thm)],[])).
% 3.74/3.92 tff(11720,plain,
% 3.74/3.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.74/3.92 inference(monotonicity,[status(thm)],[11719])).
% 3.74/3.92 tff(11721,plain,
% 3.74/3.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.74/3.92 inference(transitivity,[status(thm)],[11720, 11718])).
% 3.74/3.92 tff(11722,plain,
% 3.74/3.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), elem!1)))),
% 3.74/3.92 inference(quant_inst,[status(thm)],[])).
% 3.74/3.92 tff(11723,plain,
% 3.74/3.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.74/3.92 inference(modus_ponens,[status(thm)],[11722, 11721])).
% 3.74/3.92 tff(11724,plain,
% 3.74/3.92 ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[11723, 178, 104, 166, 11717])).
% 3.74/3.92 tff(11725,plain,
% 3.74/3.92 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[11724, 817])).
% 3.74/3.92 tff(11726,plain,
% 3.74/3.92 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[691, 11725, 644])).
% 3.74/3.92 tff(11727,plain,
% 3.74/3.92 (b(elem!1, z) <=> b(s(s(s(s(s(s(s(z))))))), z)),
% 3.74/3.92 inference(monotonicity,[status(thm)],[11726])).
% 3.74/3.92 tff(11728,plain,
% 3.74/3.92 (b(elem!1, s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.74/3.92 inference(monotonicity,[status(thm)],[679])).
% 3.74/3.92 tff(11729,plain,
% 3.74/3.92 (b(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 3.74/3.92 inference(symmetry,[status(thm)],[11728])).
% 3.74/3.92 tff(11730,plain,
% 3.74/3.92 (s(s(s(s(s(s(s(s(z)))))))) = s(elem!1)),
% 3.74/3.92 inference(symmetry,[status(thm)],[2823])).
% 3.74/3.92 tff(11731,plain,
% 3.74/3.92 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.74/3.92 inference(monotonicity,[status(thm)],[11730])).
% 3.74/3.92 tff(11732,plain,
% 3.74/3.92 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))) <=> b(elem!1, s(elem!1))),
% 3.74/3.92 inference(transitivity,[status(thm)],[11731, 11729])).
% 3.74/3.92 tff(11733,plain,
% 3.74/3.92 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) <=> (~b(elem!1, s(elem!1)))),
% 3.74/3.92 inference(monotonicity,[status(thm)],[11732])).
% 3.74/3.92 tff(11734,plain,
% 3.74/3.92 (b(s(s(s(s(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))))))))),
% 3.74/3.92 inference(monotonicity,[status(thm)],[11730])).
% 3.74/3.92 tff(11735,plain,
% 3.74/3.92 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 3.74/3.92 inference(symmetry,[status(thm)],[11734])).
% 3.74/3.92 tff(11736,plain,
% 3.74/3.92 (~(s(elem!1) = elem!1)),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[2150, 10489])).
% 3.74/3.92 tff(11737,plain,
% 3.74/3.92 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 3.74/3.92 inference(monotonicity,[status(thm)],[2823])).
% 3.74/3.92 tff(11738,plain,
% 3.74/3.92 (r(s(s(z)), z) <=> r(s(elem!1), z)),
% 3.74/3.92 inference(monotonicity,[status(thm)],[1054])).
% 3.74/3.92 tff(11739,plain,
% 3.74/3.92 (r(s(elem!1), z) <=> r(s(s(z)), z)),
% 3.74/3.92 inference(symmetry,[status(thm)],[11738])).
% 3.74/3.92 tff(11740,plain,
% 3.74/3.92 (r(s(s(z)), z)),
% 3.74/3.92 inference(modus_ponens,[status(thm)],[844, 11739])).
% 3.74/3.92 tff(11741,plain,
% 3.74/3.92 ($false),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[5618, 11740])).
% 3.74/3.92 tff(11742,plain,((~(s(s(z)) = s(elem!1))) | r(s(s(z)), z) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.92 tff(11743,plain,
% 3.74/3.92 (~(s(s(z)) = s(elem!1))),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[11742, 844, 5618])).
% 3.74/3.92 tff(11744,plain,
% 3.74/3.92 (~r(s(elem!1), s(s(z)))),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[8621, 844, 3261])).
% 3.74/3.92 tff(11745,plain,
% 3.74/3.92 (s(elem!1) = s(s(z))),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[421, 11744, 305])).
% 3.74/3.92 tff(11746,plain,
% 3.74/3.92 ($false),
% 3.74/3.92 inference(unit_resolution,[status(thm)],[1362, 11745, 11743])).
% 3.74/3.92 tff(11747,plain,((~r(s(elem!1), z)) | b(s(elem!1), s(s(z))) | r(s(s(z)), z) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.93 tff(11748,plain,
% 3.74/3.93 (~r(s(elem!1), z)),
% 3.74/3.93 inference(unit_resolution,[status(thm)],[11747, 305, 5618, 3261])).
% 3.74/3.93 tff(11749,plain,
% 3.74/3.93 (b(s(elem!1), z)),
% 3.74/3.93 inference(unit_resolution,[status(thm)],[774, 11748])).
% 3.74/3.93 tff(11750,plain,
% 3.74/3.93 (~r(z, s(s(s(s(z)))))),
% 3.74/3.93 inference(unit_resolution,[status(thm)],[3269, 3261, 193])).
% 3.74/3.93 tff(11751,plain,
% 3.74/3.93 (b(z, s(s(s(s(z)))))),
% 3.74/3.93 inference(unit_resolution,[status(thm)],[46, 11750])).
% 3.74/3.93 tff(11752,plain,
% 3.74/3.93 (~r(s(s(s(s(z)))), z)),
% 3.74/3.93 inference(unit_resolution,[status(thm)],[9569, 3261, 193])).
% 3.74/3.93 tff(11753,plain,
% 3.74/3.93 (b(s(s(s(s(z)))), z)),
% 3.74/3.93 inference(unit_resolution,[status(thm)],[191, 11752])).
% 3.74/3.93 tff(11754,plain,
% 3.74/3.93 (r(s(elem!1), s(s(z)))),
% 3.74/3.93 inference(unit_resolution,[status(thm)],[421, 10483, 305])).
% 3.74/3.93 tff(11755,plain,
% 3.74/3.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z)))))),
% 3.74/3.93 inference(rewrite,[status(thm)],[])).
% 3.74/3.93 tff(11756,plain,
% 3.74/3.93 (((~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z)))))),
% 3.74/3.93 inference(rewrite,[status(thm)],[])).
% 3.74/3.93 tff(11757,plain,
% 3.74/3.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z))))))),
% 3.74/3.93 inference(monotonicity,[status(thm)],[11756])).
% 3.74/3.93 tff(11758,plain,
% 3.74/3.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z)))))),
% 3.74/3.93 inference(transitivity,[status(thm)],[11757, 11755])).
% 3.74/3.93 tff(11759,plain,
% 3.74/3.93 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(elem!1))))),
% 3.74/3.93 inference(quant_inst,[status(thm)],[])).
% 3.74/3.93 tff(11760,plain,
% 3.74/3.93 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z))))),
% 3.74/3.93 inference(modus_ponens,[status(thm)],[11759, 11758])).
% 3.74/3.93 tff(11761,plain,
% 3.74/3.93 ($false),
% 3.74/3.93 inference(unit_resolution,[status(thm)],[11760, 118, 2333, 3261, 363])).
% 3.74/3.93 tff(11762,plain,((~r(z, s(s(z)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.93 tff(11763,plain,
% 3.74/3.93 (~r(z, s(elem!1))),
% 3.74/3.93 inference(unit_resolution,[status(thm)],[11762, 363, 3261])).
% 3.74/3.93 tff(11764,plain,
% 3.74/3.93 (b(z, s(elem!1))),
% 3.74/3.93 inference(unit_resolution,[status(thm)],[2351, 11763])).
% 3.74/3.93 tff(11765,plain,
% 3.74/3.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 3.74/3.93 inference(rewrite,[status(thm)],[])).
% 3.74/3.93 tff(11766,plain,
% 3.74/3.93 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 3.74/3.93 inference(rewrite,[status(thm)],[])).
% 3.74/3.93 tff(11767,plain,
% 3.74/3.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))))),
% 3.74/3.93 inference(monotonicity,[status(thm)],[11766])).
% 3.74/3.93 tff(11768,plain,
% 3.74/3.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 3.74/3.93 inference(transitivity,[status(thm)],[11767, 11765])).
% 3.74/3.93 tff(11769,plain,
% 3.74/3.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(elem!1))))),
% 3.74/3.93 inference(quant_inst,[status(thm)],[])).
% 3.74/3.93 tff(11770,plain,
% 3.74/3.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))),
% 3.74/3.93 inference(modus_ponens,[status(thm)],[11769, 11768])).
% 3.74/3.93 tff(11771,plain,
% 3.74/3.93 ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 3.74/3.93 inference(unit_resolution,[status(thm)],[11770, 178, 853, 1687, 168])).
% 3.74/3.93 tff(11772,plain,
% 3.74/3.93 (~b(s(elem!1), s(s(s(s(z)))))),
% 3.74/3.93 inference(unit_resolution,[status(thm)],[11771, 11764])).
% 3.74/3.93 tff(11773,plain,
% 3.74/3.93 (r(s(elem!1), s(s(s(s(z)))))),
% 3.74/3.93 inference(unit_resolution,[status(thm)],[1084, 11772, 1369])).
% 3.74/3.93 tff(11774,plain,
% 3.74/3.93 ($false),
% 3.74/3.93 inference(unit_resolution,[status(thm)],[6774, 118, 363, 11773, 147])).
% 3.74/3.93 tff(11775,plain,((~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (s(elem!1) = s(s(s(s(z))))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.93 tff(11776,plain,
% 3.74/3.93 (s(elem!1) = s(s(s(s(z))))),
% 3.74/3.93 inference(unit_resolution,[status(thm)],[11775, 11754, 168, 853, 1687, 147, 3261])).
% 3.74/3.93 tff(11777,plain,
% 3.74/3.93 (s(s(s(s(z)))) = s(elem!1)),
% 3.74/3.93 inference(symmetry,[status(thm)],[11776])).
% 3.74/3.93 tff(11778,plain,
% 3.74/3.93 (s(s(s(s(z)))) = s(s(s(s(s(s(s(s(z))))))))),
% 3.74/3.93 inference(transitivity,[status(thm)],[11777, 2823])).
% 3.74/3.93 tff(11779,plain,
% 3.74/3.93 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(s(s(z)))))))))),
% 3.74/3.93 inference(monotonicity,[status(thm)],[11778])).
% 3.74/3.93 tff(11780,plain,
% 3.74/3.93 (inj_0(s(s(s(s(s(s(s(s(z))))))))) = inj_0(s(s(s(s(z)))))),
% 3.74/3.93 inference(symmetry,[status(thm)],[11779])).
% 3.74/3.93 tff(11781,plain,
% 3.74/3.93 (s(s(s(s(s(s(s(z))))))) = s(s(s(z)))),
% 3.74/3.93 inference(transitivity,[status(thm)],[2829, 11780, 11])).
% 3.74/3.93 tff(11782,plain,
% 3.74/3.93 ($false),
% 3.74/3.93 inference(unit_resolution,[status(thm)],[1104, 11781])).
% 3.74/3.93 tff(11783,plain,((~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | b(s(elem!1), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.93 tff(11784,plain,
% 3.74/3.93 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.74/3.93 inference(unit_resolution,[status(thm)],[11783, 11749, 11753, 11751, 147, 3261, 305])).
% 3.74/3.93 tff(11785,plain,
% 3.74/3.93 ((z = elem!1) <=> (z = s(s(s(z))))),
% 3.74/3.93 inference(monotonicity,[status(thm)],[1218])).
% 3.74/3.93 tff(11786,plain,
% 3.74/3.93 ((z = elem!1) <=> (s(s(s(z))) = z)),
% 3.74/3.93 inference(transitivity,[status(thm)],[11785, 4912])).
% 3.74/3.93 tff(11787,plain,
% 3.74/3.93 ((s(s(s(z))) = z) <=> (z = elem!1)),
% 3.74/3.93 inference(symmetry,[status(thm)],[11786])).
% 3.74/3.93 tff(11788,plain,
% 3.74/3.93 ((s(s(s(z))) = z) <=> (elem!1 = z)),
% 3.74/3.93 inference(transitivity,[status(thm)],[11787, 314])).
% 3.74/3.93 tff(11789,plain,
% 3.74/3.93 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = z))),
% 3.74/3.93 inference(monotonicity,[status(thm)],[11788])).
% 3.74/3.93 tff(11790,plain,
% 3.74/3.93 (~(elem!1 = z)),
% 3.74/3.93 inference(modus_ponens,[status(thm)],[77, 11789])).
% 3.74/3.93 tff(11791,plain,
% 3.74/3.93 (r(elem!1, z)),
% 3.74/3.93 inference(unit_resolution,[status(thm)],[498, 11790, 5723])).
% 3.74/3.93 tff(11792,plain,
% 3.74/3.93 ($false),
% 3.74/3.93 inference(unit_resolution,[status(thm)],[8416, 6643, 10801, 3261])).
% 3.74/3.93 tff(11793,plain,(b(elem!1, z) | (~r(z, s(s(z)))) | b(elem!1, s(s(z))) | (elem!1 = z) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 3.74/3.93 tff(11794,plain,
% 3.74/3.93 (b(elem!1, s(s(z)))),
% 3.74/3.93 inference(unit_resolution,[status(thm)],[11793, 11790, 3261, 5723, 5618])).
% 3.74/3.93 tff(11795,plain,
% 3.74/3.93 ((~(s(s(s(z))) = z)) <=> (~(z = elem!1))),
% 3.74/3.93 inference(monotonicity,[status(thm)],[11787])).
% 3.74/3.93 tff(11796,plain,
% 3.74/3.93 (~(z = elem!1)),
% 3.74/3.93 inference(modus_ponens,[status(thm)],[77, 11795])).
% 3.74/3.93 tff(11797,plain,
% 3.74/3.93 (~r(z, s(s(s(s(z)))))),
% 3.74/3.93 inference(unit_resolution,[status(thm)],[3478, 3261, 147])).
% 3.74/3.93 tff(11798,plain,
% 3.74/3.93 (b(z, s(s(s(s(z)))))),
% 3.74/3.93 inference(unit_resolution,[status(thm)],[46, 11797])).
% 3.74/3.93 tff(11799,plain,
% 3.74/3.93 (b(elem!1, s(s(z)))),
% 3.74/3.93 inference(unit_resolution,[status(thm)],[11793, 5723, 3261, 290, 5618])).
% 3.74/3.93 tff(11800,plain,
% 3.74/3.93 (~r(s(s(z)), elem!1)),
% 3.74/3.93 inference(unit_resolution,[status(thm)],[8412, 521, 3261])).
% 3.74/3.93 tff(11801,plain,
% 3.74/3.93 (b(s(s(z)), elem!1)),
% 3.74/3.93 inference(unit_resolution,[status(thm)],[448, 11800, 12])).
% 3.74/3.93 tff(11802,plain,
% 3.74/3.93 (~(s(s(s(s(s(s(s(z))))))) = s(s(z)))),
% 3.74/3.93 inference(modus_ponens,[status(thm)],[244, 2950])).
% 3.74/3.93 tff(11803,plain,
% 3.74/3.93 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.74/3.93 inference(unit_resolution,[status(thm)],[707, 41, 605, 4245])).
% 3.74/3.93 tff(11804,plain,
% 3.74/3.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.74/3.93 inference(rewrite,[status(thm)],[])).
% 3.74/3.93 tff(11805,plain,
% 3.74/3.93 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.74/3.93 inference(rewrite,[status(thm)],[])).
% 3.74/3.93 tff(11806,plain,
% 3.74/3.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.74/3.93 inference(monotonicity,[status(thm)],[11805])).
% 3.74/3.93 tff(11807,plain,
% 3.74/3.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.74/3.93 inference(transitivity,[status(thm)],[11806, 11804])).
% 3.74/3.93 tff(11808,plain,
% 3.74/3.93 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.74/3.93 inference(quant_inst,[status(thm)],[])).
% 3.74/3.93 tff(11809,plain,
% 3.74/3.93 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.74/3.93 inference(modus_ponens,[status(thm)],[11808, 11807])).
% 3.74/3.93 tff(11810,plain,
% 3.74/3.93 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.74/3.93 inference(unit_resolution,[status(thm)],[11809, 118, 437, 108])).
% 3.74/3.93 tff(11811,plain,
% 3.74/3.93 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.74/3.93 inference(unit_resolution,[status(thm)],[691, 11810, 701])).
% 3.74/3.93 tff(11812,plain,
% 3.74/3.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.74/3.93 inference(rewrite,[status(thm)],[])).
% 3.74/3.93 tff(11813,plain,
% 3.74/3.93 (((~b(s(s(z)), elem!1)) | (~b(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(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.74/3.93 inference(rewrite,[status(thm)],[])).
% 3.74/3.93 tff(11814,plain,
% 3.74/3.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(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(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.74/3.93 inference(monotonicity,[status(thm)],[11813])).
% 3.74/3.93 tff(11815,plain,
% 3.74/3.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(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(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.74/3.93 inference(transitivity,[status(thm)],[11814, 11812])).
% 3.74/3.93 tff(11816,plain,
% 3.74/3.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(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(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.74/3.93 inference(quant_inst,[status(thm)],[])).
% 3.74/3.93 tff(11817,plain,
% 3.74/3.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.74/3.93 inference(modus_ponens,[status(thm)],[11816, 11815])).
% 3.74/3.93 tff(11818,plain,
% 3.74/3.93 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.74/3.93 inference(unit_resolution,[status(thm)],[11817, 178, 817, 812, 11811, 11803])).
% 3.74/3.93 tff(11819,plain,
% 3.74/3.93 ((s(s(s(s(s(s(s(z))))))) = s(s(z))) | r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.74/3.93 inference(unit_resolution,[status(thm)],[2960, 41, 11818])).
% 3.74/3.93 tff(11820,plain,
% 3.74/3.93 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.74/3.93 inference(unit_resolution,[status(thm)],[11819, 11802])).
% 3.74/3.93 tff(11821,plain,
% 3.74/3.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 3.74/3.93 inference(rewrite,[status(thm)],[])).
% 3.74/3.93 tff(11822,plain,
% 3.74/3.93 (((~r(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))))))), z))) <=> ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 3.74/3.93 inference(rewrite,[status(thm)],[])).
% 3.74/3.93 tff(11823,plain,
% 3.74/3.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))))),
% 3.74/3.93 inference(monotonicity,[status(thm)],[11822])).
% 3.74/3.93 tff(11824,plain,
% 3.74/3.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 3.74/3.93 inference(transitivity,[status(thm)],[11823, 11821])).
% 3.74/3.93 tff(11825,plain,
% 3.74/3.93 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))))))), z)))),
% 3.74/3.93 inference(quant_inst,[status(thm)],[])).
% 3.74/3.93 tff(11826,plain,
% 3.74/3.93 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 3.74/3.93 inference(modus_ponens,[status(thm)],[11825, 11824])).
% 3.74/3.93 tff(11827,plain,
% 3.74/3.93 ($false),
% 3.74/3.93 inference(unit_resolution,[status(thm)],[11826, 118, 3261, 108, 11820])).
% 3.74/3.93 tff(11828,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.93 tff(11829,plain,
% 3.74/3.93 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.74/3.93 inference(unit_resolution,[status(thm)],[11828, 108, 817, 812, 3261, 701, 437])).
% 3.74/3.93 tff(11830,plain,
% 3.74/3.93 ($false),
% 3.74/3.93 inference(unit_resolution,[status(thm)],[11134, 118, 437, 108, 11829])).
% 3.74/3.93 tff(11831,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~r(z, s(s(z)))) | (elem!1 = s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.93 tff(11832,plain,
% 3.74/3.93 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.74/3.93 inference(unit_resolution,[status(thm)],[11831, 11801, 437, 812, 3261, 701])).
% 3.74/3.93 tff(11833,plain,
% 3.74/3.93 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.74/3.93 inference(unit_resolution,[status(thm)],[133, 11832])).
% 3.74/3.93 tff(11834,plain,
% 3.74/3.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.74/3.93 inference(rewrite,[status(thm)],[])).
% 3.74/3.93 tff(11835,plain,
% 3.74/3.93 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(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(z)), s(s(s(s(z)))))))),
% 3.74/3.93 inference(rewrite,[status(thm)],[])).
% 3.74/3.93 tff(11836,plain,
% 3.74/3.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(z)), s(s(s(s(z))))))))),
% 3.74/3.93 inference(monotonicity,[status(thm)],[11835])).
% 3.74/3.93 tff(11837,plain,
% 3.74/3.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(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(z)), s(s(s(s(z)))))))),
% 3.74/3.93 inference(transitivity,[status(thm)],[11836, 11834])).
% 3.74/3.93 tff(11838,plain,
% 3.74/3.93 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 3.74/3.93 inference(quant_inst,[status(thm)],[])).
% 3.74/3.93 tff(11839,plain,
% 3.74/3.93 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 3.74/3.93 inference(modus_ponens,[status(thm)],[11838, 11837])).
% 3.74/3.93 tff(11840,plain,
% 3.74/3.93 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.74/3.93 inference(unit_resolution,[status(thm)],[11839, 118, 1130, 147])).
% 3.74/3.93 tff(11841,plain,
% 3.74/3.93 ((s(s(s(s(s(s(s(z))))))) = s(s(z))) | b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.74/3.93 inference(unit_resolution,[status(thm)],[2960, 41, 11840])).
% 3.74/3.93 tff(11842,plain,
% 3.74/3.93 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.74/3.93 inference(unit_resolution,[status(thm)],[11841, 11802])).
% 3.74/3.93 tff(11843,plain,
% 3.74/3.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 3.74/3.93 inference(rewrite,[status(thm)],[])).
% 3.74/3.93 tff(11844,plain,
% 3.74/3.93 (((~b(elem!1, s(s(z)))) | (~b(elem!1, 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)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 3.74/3.93 inference(rewrite,[status(thm)],[])).
% 3.74/3.93 tff(11845,plain,
% 3.74/3.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, 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)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))))),
% 3.74/3.93 inference(monotonicity,[status(thm)],[11844])).
% 3.74/3.93 tff(11846,plain,
% 3.74/3.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, 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)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 3.74/3.94 inference(transitivity,[status(thm)],[11845, 11843])).
% 3.74/3.94 tff(11847,plain,
% 3.74/3.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, 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)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.74/3.94 inference(quant_inst,[status(thm)],[])).
% 3.74/3.94 tff(11848,plain,
% 3.74/3.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 3.74/3.94 inference(modus_ponens,[status(thm)],[11847, 11846])).
% 3.74/3.94 tff(11849,plain,
% 3.74/3.94 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.74/3.94 inference(unit_resolution,[status(thm)],[11848, 178, 817, 812, 3470, 11842])).
% 3.74/3.94 tff(11850,plain,
% 3.74/3.94 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.74/3.94 inference(unit_resolution,[status(thm)],[707, 41, 4245, 11849])).
% 3.74/3.94 tff(11851,plain,
% 3.74/3.94 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.74/3.94 inference(unit_resolution,[status(thm)],[11025, 118, 521, 11850])).
% 3.74/3.94 tff(11852,plain,
% 3.74/3.94 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.74/3.94 inference(unit_resolution,[status(thm)],[133, 11851])).
% 3.74/3.94 tff(11853,plain,
% 3.74/3.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.74/3.94 inference(rewrite,[status(thm)],[])).
% 3.74/3.94 tff(11854,plain,
% 3.74/3.94 (((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(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(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.74/3.94 inference(rewrite,[status(thm)],[])).
% 3.74/3.94 tff(11855,plain,
% 3.74/3.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.74/3.94 inference(monotonicity,[status(thm)],[11854])).
% 3.74/3.94 tff(11856,plain,
% 3.74/3.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.74/3.94 inference(transitivity,[status(thm)],[11855, 11853])).
% 3.74/3.94 tff(11857,plain,
% 3.74/3.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), elem!1)))),
% 3.74/3.94 inference(quant_inst,[status(thm)],[])).
% 3.74/3.94 tff(11858,plain,
% 3.74/3.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.74/3.94 inference(modus_ponens,[status(thm)],[11857, 11856])).
% 3.74/3.94 tff(11859,plain,
% 3.74/3.94 ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.74/3.94 inference(unit_resolution,[status(thm)],[11858, 178])).
% 3.74/3.94 tff(11860,plain,
% 3.74/3.94 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.74/3.94 inference(unit_resolution,[status(thm)],[11859, 11842, 817, 812, 3470])).
% 3.74/3.94 tff(11861,plain,
% 3.74/3.94 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.74/3.94 inference(unit_resolution,[status(thm)],[691, 11860, 701])).
% 3.74/3.94 tff(11862,plain,
% 3.74/3.94 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.74/3.94 inference(unit_resolution,[status(thm)],[3818, 11861, 521])).
% 3.74/3.94 tff(11863,plain,
% 3.74/3.94 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.74/3.94 inference(unit_resolution,[status(thm)],[271, 11862])).
% 3.74/3.94 tff(11864,plain,
% 3.74/3.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), 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))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), 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))))))), z)))),
% 3.74/3.94 inference(rewrite,[status(thm)],[])).
% 3.74/3.94 tff(11865,plain,
% 3.74/3.94 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), 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))))))), z)))),
% 3.74/3.94 inference(rewrite,[status(thm)],[])).
% 3.74/3.94 tff(11866,plain,
% 3.74/3.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), 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))))))), z))))),
% 3.74/3.94 inference(monotonicity,[status(thm)],[11865])).
% 3.74/3.94 tff(11867,plain,
% 3.74/3.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), 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))))))), z)))),
% 3.74/3.94 inference(transitivity,[status(thm)],[11866, 11864])).
% 3.74/3.94 tff(11868,plain,
% 3.74/3.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 3.74/3.94 inference(quant_inst,[status(thm)],[])).
% 3.74/3.94 tff(11869,plain,
% 3.74/3.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 3.74/3.94 inference(modus_ponens,[status(thm)],[11868, 11867])).
% 3.74/3.94 tff(11870,plain,
% 3.74/3.94 ($false),
% 3.74/3.94 inference(unit_resolution,[status(thm)],[11869, 178, 3461, 3470, 11863, 11852, 11842])).
% 3.74/3.94 tff(11871,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~r(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.94 tff(11872,plain,
% 3.74/3.94 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.74/3.94 inference(unit_resolution,[status(thm)],[11871, 521, 3461, 11801, 812, 701, 147])).
% 3.74/3.94 tff(11873,plain,
% 3.74/3.94 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.74/3.94 inference(unit_resolution,[status(thm)],[84, 11872])).
% 3.74/3.94 tff(11874,plain,
% 3.74/3.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 3.74/3.94 inference(rewrite,[status(thm)],[])).
% 3.74/3.94 tff(11875,plain,
% 3.74/3.94 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 3.74/3.94 inference(rewrite,[status(thm)],[])).
% 3.74/3.94 tff(11876,plain,
% 3.74/3.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z))))))))),
% 3.74/3.94 inference(monotonicity,[status(thm)],[11875])).
% 3.74/3.94 tff(11877,plain,
% 3.74/3.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 3.74/3.94 inference(transitivity,[status(thm)],[11876, 11874])).
% 3.74/3.94 tff(11878,plain,
% 3.74/3.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.74/3.94 inference(quant_inst,[status(thm)],[])).
% 3.74/3.94 tff(11879,plain,
% 3.74/3.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z))))))),
% 3.74/3.94 inference(modus_ponens,[status(thm)],[11878, 11877])).
% 3.74/3.94 tff(11880,plain,
% 3.74/3.94 ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 3.74/3.94 inference(unit_resolution,[status(thm)],[11879, 178, 3461, 11873, 1687])).
% 3.74/3.94 tff(11881,plain,
% 3.74/3.94 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.74/3.94 inference(unit_resolution,[status(thm)],[11880, 11833])).
% 3.74/3.94 tff(11882,plain,
% 3.74/3.94 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.74/3.94 inference(unit_resolution,[status(thm)],[249, 11881])).
% 3.74/3.94 tff(11883,plain,
% 3.74/3.94 (~r(s(s(s(s(z)))), z)),
% 3.74/3.94 inference(unit_resolution,[status(thm)],[9569, 193, 3261])).
% 3.74/3.94 tff(11884,plain,
% 3.74/3.94 (b(s(s(s(s(z)))), z)),
% 3.74/3.94 inference(unit_resolution,[status(thm)],[191, 11883])).
% 3.74/3.94 tff(11885,plain,
% 3.74/3.94 ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 3.74/3.94 inference(unit_resolution,[status(thm)],[11879, 178, 3461, 104, 1687])).
% 3.74/3.94 tff(11886,plain,
% 3.74/3.94 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.74/3.94 inference(unit_resolution,[status(thm)],[11885, 146])).
% 3.74/3.94 tff(11887,plain,
% 3.74/3.94 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.74/3.94 inference(unit_resolution,[status(thm)],[249, 11886])).
% 3.74/3.94 tff(11888,plain,
% 3.74/3.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 3.74/3.94 inference(rewrite,[status(thm)],[])).
% 3.74/3.94 tff(11889,plain,
% 3.74/3.94 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), 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(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 3.74/3.94 inference(rewrite,[status(thm)],[])).
% 3.74/3.94 tff(11890,plain,
% 3.74/3.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z))))))))),
% 3.74/3.94 inference(monotonicity,[status(thm)],[11889])).
% 3.74/3.94 tff(11891,plain,
% 3.74/3.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 3.74/3.94 inference(transitivity,[status(thm)],[11890, 11888])).
% 3.74/3.94 tff(11892,plain,
% 3.74/3.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.74/3.94 inference(quant_inst,[status(thm)],[])).
% 3.74/3.94 tff(11893,plain,
% 3.74/3.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z))))))),
% 3.74/3.94 inference(modus_ponens,[status(thm)],[11892, 11891])).
% 3.74/3.94 tff(11894,plain,
% 3.74/3.94 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 3.74/3.94 inference(unit_resolution,[status(thm)],[11893, 178, 104, 1687, 168])).
% 3.74/3.94 tff(11895,plain,
% 3.74/3.94 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.74/3.94 inference(unit_resolution,[status(thm)],[11894, 146])).
% 3.74/3.94 tff(11896,plain,
% 3.74/3.94 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.74/3.94 inference(unit_resolution,[status(thm)],[222, 11895])).
% 3.74/3.94 tff(11897,plain,
% 3.74/3.94 ($false),
% 3.74/3.94 inference(unit_resolution,[status(thm)],[3559, 11896, 11887, 193])).
% 3.74/3.94 tff(11898,plain,((~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.94 tff(11899,plain,
% 3.74/3.94 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.74/3.94 inference(unit_resolution,[status(thm)],[11898, 104, 193, 1687, 11884, 3461])).
% 3.74/3.94 tff(11900,plain,
% 3.74/3.94 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.74/3.94 inference(unit_resolution,[status(thm)],[133, 11899])).
% 3.74/3.94 tff(11901,plain,
% 3.74/3.94 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.74/3.94 inference(unit_resolution,[status(thm)],[11134, 118, 437, 11900])).
% 3.74/3.94 tff(11902,plain,
% 3.74/3.94 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.74/3.94 inference(unit_resolution,[status(thm)],[707, 41, 11901, 4245])).
% 3.74/3.94 tff(11903,plain,
% 3.74/3.94 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.74/3.94 inference(unit_resolution,[status(thm)],[11809, 118, 437, 11900])).
% 3.74/3.94 tff(11904,plain,
% 3.74/3.94 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.74/3.94 inference(unit_resolution,[status(thm)],[691, 11903, 701])).
% 3.74/3.94 tff(11905,plain,
% 3.74/3.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.74/3.94 inference(rewrite,[status(thm)],[])).
% 3.74/3.94 tff(11906,plain,
% 3.74/3.94 (((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z))))) <=> ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.74/3.94 inference(rewrite,[status(thm)],[])).
% 3.74/3.94 tff(11907,plain,
% 3.74/3.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.74/3.94 inference(monotonicity,[status(thm)],[11906])).
% 3.74/3.94 tff(11908,plain,
% 3.74/3.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.74/3.94 inference(transitivity,[status(thm)],[11907, 11905])).
% 3.74/3.94 tff(11909,plain,
% 3.74/3.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z)))))),
% 3.74/3.94 inference(quant_inst,[status(thm)],[])).
% 3.74/3.94 tff(11910,plain,
% 3.74/3.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.74/3.94 inference(modus_ponens,[status(thm)],[11909, 11908])).
% 3.74/3.94 tff(11911,plain,
% 3.74/3.94 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.74/3.94 inference(unit_resolution,[status(thm)],[11910, 178, 817, 812, 11904, 11902])).
% 3.74/3.94 tff(11912,plain,
% 3.74/3.94 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.74/3.94 inference(unit_resolution,[status(thm)],[249, 11911])).
% 3.74/3.94 tff(11913,plain,
% 3.74/3.94 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.74/3.94 inference(unit_resolution,[status(thm)],[3559, 11912, 193])).
% 3.74/3.94 tff(11914,plain,
% 3.74/3.94 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.74/3.94 inference(unit_resolution,[status(thm)],[222, 11913])).
% 3.74/3.95 tff(11915,plain,
% 3.74/3.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))))),
% 3.74/3.95 inference(rewrite,[status(thm)],[])).
% 3.74/3.95 tff(11916,plain,
% 3.74/3.95 (((~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(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(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(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))))),
% 3.74/3.95 inference(rewrite,[status(thm)],[])).
% 3.74/3.95 tff(11917,plain,
% 3.74/3.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z))))))))),
% 3.74/3.95 inference(monotonicity,[status(thm)],[11916])).
% 3.74/3.95 tff(11918,plain,
% 3.74/3.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))))),
% 3.74/3.95 inference(transitivity,[status(thm)],[11917, 11915])).
% 3.74/3.95 tff(11919,plain,
% 3.74/3.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)))),
% 3.74/3.95 inference(quant_inst,[status(thm)],[])).
% 3.74/3.95 tff(11920,plain,
% 3.74/3.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z))))))),
% 3.74/3.95 inference(modus_ponens,[status(thm)],[11919, 11918])).
% 3.74/3.95 tff(11921,plain,
% 3.74/3.95 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.74/3.95 inference(unit_resolution,[status(thm)],[11920, 178, 104, 1687, 11884, 11914])).
% 3.74/3.95 tff(11922,plain,
% 3.74/3.95 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.74/3.95 inference(unit_resolution,[status(thm)],[271, 11921])).
% 3.74/3.95 tff(11923,plain,
% 3.74/3.95 ($false),
% 3.74/3.95 inference(unit_resolution,[status(thm)],[4688, 118, 3261, 11912, 11922])).
% 3.74/3.95 tff(11924,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~r(elem!1, z)) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.95 tff(11925,plain,
% 3.74/3.95 (~r(s(s(s(s(z)))), s(s(z)))),
% 3.74/3.95 inference(unit_resolution,[status(thm)],[11924, 11873, 1687, 3261, 11801, 812, 701, 437, 3461])).
% 3.74/3.95 tff(11926,plain,
% 3.74/3.95 (b(s(s(s(s(z)))), s(s(z)))),
% 3.74/3.95 inference(unit_resolution,[status(thm)],[102, 11925])).
% 3.74/3.95 tff(11927,plain,
% 3.74/3.95 (~r(elem!1, s(s(s(s(z)))))),
% 3.74/3.95 inference(unit_resolution,[status(thm)],[9980, 194, 437])).
% 3.74/3.95 tff(11928,plain,
% 3.74/3.95 (b(elem!1, s(s(s(s(z)))))),
% 3.74/3.95 inference(unit_resolution,[status(thm)],[483, 11927, 469])).
% 3.74/3.95 tff(11929,plain,
% 3.74/3.95 (~r(s(s(s(s(z)))), elem!1)),
% 3.74/3.95 inference(unit_resolution,[status(thm)],[6033, 194, 437])).
% 3.74/3.95 tff(11930,plain,
% 3.74/3.95 (b(s(s(s(s(z)))), elem!1)),
% 3.74/3.95 inference(unit_resolution,[status(thm)],[3142, 11929, 323])).
% 3.74/3.95 tff(11931,plain,
% 3.74/3.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 3.74/3.95 inference(rewrite,[status(thm)],[])).
% 3.74/3.95 tff(11932,plain,
% 3.74/3.95 (((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 3.74/3.95 inference(rewrite,[status(thm)],[])).
% 3.74/3.95 tff(11933,plain,
% 3.74/3.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 3.74/3.95 inference(monotonicity,[status(thm)],[11932])).
% 3.74/3.95 tff(11934,plain,
% 3.74/3.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 3.74/3.95 inference(transitivity,[status(thm)],[11933, 11931])).
% 3.74/3.95 tff(11935,plain,
% 3.74/3.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))),
% 3.74/3.95 inference(quant_inst,[status(thm)],[])).
% 3.74/3.95 tff(11936,plain,
% 3.74/3.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z))))),
% 3.74/3.95 inference(modus_ponens,[status(thm)],[11935, 11934])).
% 3.74/3.95 tff(11937,plain,
% 3.74/3.95 ($false),
% 3.74/3.95 inference(unit_resolution,[status(thm)],[11936, 178, 817, 812, 11930, 11928, 202])).
% 3.74/3.95 tff(11938,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (elem!1 = s(s(s(s(z))))) | (s(s(s(s(z)))) = elem!1) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.95 tff(11939,plain,
% 3.74/3.95 (~r(s(s(s(s(z)))), z)),
% 3.74/3.95 inference(unit_resolution,[status(thm)],[11938, 11801, 812, 11926, 469, 323, 437])).
% 3.74/3.95 tff(11940,plain,
% 3.74/3.95 (b(s(s(s(s(z)))), z)),
% 3.74/3.95 inference(unit_resolution,[status(thm)],[191, 11939])).
% 3.74/3.95 tff(11941,plain,
% 3.74/3.95 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 3.74/3.95 inference(unit_resolution,[status(thm)],[11893, 178, 11873, 1687, 11940])).
% 3.74/3.95 tff(11942,plain,
% 3.74/3.95 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.74/3.95 inference(unit_resolution,[status(thm)],[11941, 11833])).
% 3.74/3.95 tff(11943,plain,
% 3.74/3.95 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.74/3.95 inference(unit_resolution,[status(thm)],[222, 11942])).
% 3.74/3.95 tff(11944,plain,
% 3.74/3.95 ($false),
% 3.74/3.95 inference(unit_resolution,[status(thm)],[5624, 11943, 11882, 147])).
% 3.74/3.95 tff(11945,plain,((~r(z, elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~r(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~r(z, s(s(z)))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (elem!1 = s(s(s(s(z))))) | (s(s(s(s(z)))) = elem!1) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.74/3.95 tff(11946,plain,
% 3.74/3.95 (~r(z, elem!1)),
% 3.74/3.95 inference(unit_resolution,[status(thm)],[11945, 10801, 147, 5619, 11798, 323, 3261, 701, 11799, 469, 12])).
% 3.74/3.95 tff(11947,plain,
% 3.74/3.95 (b(z, elem!1)),
% 3.74/3.95 inference(unit_resolution,[status(thm)],[585, 11946, 507])).
% 3.74/3.95 tff(11948,plain,
% 3.74/3.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 3.74/3.95 inference(rewrite,[status(thm)],[])).
% 3.74/3.95 tff(11949,plain,
% 3.74/3.95 (((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), z))) <=> ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 3.74/3.95 inference(rewrite,[status(thm)],[])).
% 3.74/3.95 tff(11950,plain,
% 3.74/3.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 3.74/3.95 inference(monotonicity,[status(thm)],[11949])).
% 3.74/3.95 tff(11951,plain,
% 3.74/3.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 3.74/3.95 inference(transitivity,[status(thm)],[11950, 11948])).
% 3.74/3.95 tff(11952,plain,
% 3.74/3.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), z)))),
% 3.74/3.95 inference(quant_inst,[status(thm)],[])).
% 3.74/3.95 tff(11953,plain,
% 3.74/3.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 3.74/3.95 inference(modus_ponens,[status(thm)],[11952, 11951])).
% 3.74/3.95 tff(11954,plain,
% 3.74/3.95 ($false),
% 3.74/3.95 inference(unit_resolution,[status(thm)],[11953, 178, 818, 817, 3461, 1687, 1301])).
% 3.74/3.95 tff(11955,plain,((~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.95 tff(11956,plain,
% 3.74/3.95 (~b(s(s(z)), elem!1)),
% 3.74/3.95 inference(unit_resolution,[status(thm)],[11955, 11947, 5619, 1301, 11798])).
% 3.74/3.95 tff(11957,plain,
% 3.74/3.95 (b(elem!1, s(s(s(s(z)))))),
% 3.74/3.95 inference(unit_resolution,[status(thm)],[483, 9308, 469])).
% 3.74/3.95 tff(11958,plain,
% 3.74/3.95 (~r(s(s(s(s(z)))), elem!1)),
% 3.74/3.95 inference(unit_resolution,[status(thm)],[3329, 193, 438])).
% 3.74/3.95 tff(11959,plain,
% 3.74/3.95 (b(s(s(s(s(z)))), elem!1)),
% 3.74/3.95 inference(unit_resolution,[status(thm)],[3142, 11958, 323])).
% 3.74/3.95 tff(11960,plain,
% 3.74/3.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 3.74/3.95 inference(rewrite,[status(thm)],[])).
% 3.74/3.95 tff(11961,plain,
% 3.74/3.95 (((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 3.74/3.95 inference(rewrite,[status(thm)],[])).
% 3.74/3.95 tff(11962,plain,
% 3.74/3.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z))))))))),
% 3.74/3.95 inference(monotonicity,[status(thm)],[11961])).
% 3.74/3.95 tff(11963,plain,
% 3.74/3.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 3.74/3.95 inference(transitivity,[status(thm)],[11962, 11960])).
% 3.74/3.95 tff(11964,plain,
% 3.74/3.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 3.74/3.95 inference(quant_inst,[status(thm)],[])).
% 3.74/3.95 tff(11965,plain,
% 3.74/3.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z))))))),
% 3.74/3.95 inference(modus_ponens,[status(thm)],[11964, 11963])).
% 3.74/3.95 tff(11966,plain,
% 3.74/3.95 ($false),
% 3.74/3.95 inference(unit_resolution,[status(thm)],[11965, 178, 818, 11959, 1687, 11884, 1301])).
% 3.74/3.95 tff(11967,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (s(s(s(s(z)))) = elem!1) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.95 tff(11968,plain,
% 3.74/3.95 (~r(s(s(s(s(z)))), s(s(z)))),
% 3.74/3.95 inference(unit_resolution,[status(thm)],[11967, 11957, 1687, 818, 323, 438, 3261])).
% 3.74/3.95 tff(11969,plain,
% 3.74/3.95 (b(s(s(s(s(z)))), s(s(z)))),
% 3.74/3.95 inference(unit_resolution,[status(thm)],[102, 11968])).
% 3.74/3.95 tff(11970,plain,
% 3.74/3.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 3.74/3.95 inference(rewrite,[status(thm)],[])).
% 3.74/3.95 tff(11971,plain,
% 3.74/3.95 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 3.74/3.95 inference(rewrite,[status(thm)],[])).
% 3.74/3.95 tff(11972,plain,
% 3.74/3.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))))),
% 3.74/3.95 inference(monotonicity,[status(thm)],[11971])).
% 3.74/3.95 tff(11973,plain,
% 3.74/3.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 3.74/3.95 inference(transitivity,[status(thm)],[11972, 11970])).
% 3.74/3.95 tff(11974,plain,
% 3.74/3.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)))),
% 3.74/3.95 inference(quant_inst,[status(thm)],[])).
% 3.74/3.95 tff(11975,plain,
% 3.74/3.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))),
% 3.74/3.95 inference(modus_ponens,[status(thm)],[11974, 11973])).
% 3.74/3.95 tff(11976,plain,
% 3.74/3.95 ($false),
% 3.74/3.95 inference(unit_resolution,[status(thm)],[11975, 178, 818, 812, 1687, 11957, 11969])).
% 3.74/3.95 tff(11977,plain,((~r(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (s(s(s(s(z)))) = elem!1) | (~r(z, s(s(z)))) | (elem!1 = s(s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.95 tff(11978,plain,
% 3.74/3.95 (~r(s(s(z)), elem!1)),
% 3.74/3.95 inference(unit_resolution,[status(thm)],[11977, 11947, 147, 11798, 323, 3261, 469, 11799])).
% 3.74/3.96 tff(11979,plain,
% 3.74/3.96 ($false),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[448, 11978, 11956, 12])).
% 3.74/3.96 tff(11980,plain,(b(elem!1, z) | (s(s(z)) = elem!1) | (~r(s(s(z)), s(s(s(s(z)))))) | (s(s(s(s(z)))) = elem!1) | (~r(z, s(s(z)))) | (elem!1 = s(s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (z = elem!1) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (elem!1 = z) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 3.74/3.96 tff(11981,plain,
% 3.74/3.96 (~b(elem!1, s(s(s(s(z)))))),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[11980, 11796, 147, 469, 3261, 701, 5723, 12, 551, 11790, 5618])).
% 3.74/3.96 tff(11982,plain,
% 3.74/3.96 (r(elem!1, s(s(s(s(z)))))),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[483, 11981, 469])).
% 3.74/3.96 tff(11983,plain,
% 3.74/3.96 (~r(s(s(z)), elem!1)),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[8763, 11982, 147])).
% 3.74/3.96 tff(11984,plain,
% 3.74/3.96 (b(s(s(z)), elem!1)),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[448, 11983, 12])).
% 3.74/3.96 tff(11985,plain,
% 3.74/3.96 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[11924, 11984, 11751, 3261, 193, 701, 11794, 11791, 5619])).
% 3.74/3.96 tff(11986,plain,
% 3.74/3.96 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.74/3.96 inference(rewrite,[status(thm)],[])).
% 3.74/3.96 tff(11987,plain,
% 3.74/3.96 (((~r(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(s(s(s(s(z))))))), elem!1))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.74/3.96 inference(rewrite,[status(thm)],[])).
% 3.74/3.96 tff(11988,plain,
% 3.74/3.96 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 3.74/3.96 inference(monotonicity,[status(thm)],[11987])).
% 3.74/3.96 tff(11989,plain,
% 3.74/3.96 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.74/3.96 inference(transitivity,[status(thm)],[11988, 11986])).
% 3.74/3.96 tff(11990,plain,
% 3.74/3.96 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.74/3.96 inference(quant_inst,[status(thm)],[])).
% 3.74/3.96 tff(11991,plain,
% 3.74/3.96 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 3.74/3.96 inference(modus_ponens,[status(thm)],[11990, 11989])).
% 3.74/3.96 tff(11992,plain,
% 3.74/3.96 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[11991, 118, 1130, 470])).
% 3.74/3.96 tff(11993,plain,
% 3.74/3.96 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[707, 41, 11992, 4245])).
% 3.74/3.96 tff(11994,plain,
% 3.74/3.96 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 3.74/3.96 inference(rewrite,[status(thm)],[])).
% 3.74/3.96 tff(11995,plain,
% 3.74/3.96 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 3.74/3.96 inference(rewrite,[status(thm)],[])).
% 3.74/3.96 tff(11996,plain,
% 3.74/3.96 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(z))))))))),
% 3.74/3.96 inference(monotonicity,[status(thm)],[11995])).
% 3.74/3.96 tff(11997,plain,
% 3.74/3.96 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 3.74/3.96 inference(transitivity,[status(thm)],[11996, 11994])).
% 3.74/3.96 tff(11998,plain,
% 3.74/3.96 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.74/3.96 inference(quant_inst,[status(thm)],[])).
% 3.74/3.96 tff(11999,plain,
% 3.74/3.96 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(z))))))),
% 3.74/3.96 inference(modus_ponens,[status(thm)],[11998, 11997])).
% 3.74/3.96 tff(12000,plain,
% 3.74/3.96 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[11999, 118, 1130, 470])).
% 3.74/3.96 tff(12001,plain,
% 3.74/3.96 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[691, 12000, 701])).
% 3.74/3.96 tff(12002,plain,
% 3.74/3.96 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[248, 3469, 2951])).
% 3.74/3.96 tff(12003,plain,
% 3.74/3.96 ($false),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[11910, 178, 817, 812, 12002, 12001, 11993])).
% 3.74/3.96 tff(12004,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (s(s(z)) = s(s(s(s(s(s(s(z)))))))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.96 tff(12005,plain,
% 3.74/3.96 ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[12004, 244])).
% 3.74/3.96 tff(12006,plain,
% 3.74/3.96 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[12005, 11984, 147, 701, 11794, 11982])).
% 3.74/3.96 tff(12007,plain,
% 3.74/3.96 ($false),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[84, 12006, 11985])).
% 3.74/3.96 tff(12008,plain,((~(s(elem!1) = s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (s(s(z)) = elem!1) | (elem!1 = s(s(s(s(z))))) | b(elem!1, z) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 3.74/3.96 tff(12009,plain,
% 3.74/3.96 (~(s(elem!1) = s(s(s(s(z)))))),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[12008, 11784, 147, 3261, 193, 12, 469, 5723, 5618])).
% 3.74/3.96 tff(12010,plain,
% 3.74/3.96 (~r(s(elem!1), s(s(z)))),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[11775, 12009, 11753, 11749, 11751, 147, 3261])).
% 3.74/3.96 tff(12011,plain,
% 3.74/3.96 (s(elem!1) = s(s(z))),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[421, 12010, 305])).
% 3.74/3.96 tff(12012,plain,
% 3.74/3.96 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 3.74/3.96 inference(monotonicity,[status(thm)],[12011])).
% 3.74/3.96 tff(12013,plain,
% 3.74/3.96 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 3.74/3.96 inference(symmetry,[status(thm)],[12012])).
% 3.74/3.96 tff(12014,plain,
% 3.74/3.96 (s(z) = elem!1),
% 3.74/3.96 inference(transitivity,[status(thm)],[71, 12013, 304])).
% 3.74/3.96 tff(12015,plain,
% 3.74/3.96 ((s(z) = z) <=> (elem!1 = z)),
% 3.74/3.96 inference(monotonicity,[status(thm)],[12014])).
% 3.74/3.96 tff(12016,plain,
% 3.74/3.96 ((s(z) = z) <=> (z = elem!1)),
% 3.74/3.96 inference(transitivity,[status(thm)],[12015, 313])).
% 3.74/3.96 tff(12017,plain,
% 3.74/3.96 ((s(z) = z) <=> (elem!1 = z)),
% 3.74/3.96 inference(transitivity,[status(thm)],[12016, 314])).
% 3.74/3.96 tff(12018,plain,
% 3.74/3.96 ((~(s(z) = z)) <=> (~(elem!1 = z))),
% 3.74/3.96 inference(monotonicity,[status(thm)],[12017])).
% 3.74/3.96 tff(12019,plain,
% 3.74/3.96 (~(elem!1 = z)),
% 3.74/3.96 inference(modus_ponens,[status(thm)],[1476, 12018])).
% 3.74/3.96 tff(12020,plain,
% 3.74/3.96 (r(elem!1, z)),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[498, 12019, 5723])).
% 3.74/3.96 tff(12021,plain,
% 3.74/3.96 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(z)))),
% 3.74/3.96 inference(monotonicity,[status(thm)],[12011])).
% 3.74/3.96 tff(12022,plain,
% 3.74/3.96 (b(elem!1, z) <=> b(s(elem!1), z)),
% 3.74/3.96 inference(monotonicity,[status(thm)],[745])).
% 3.74/3.96 tff(12023,plain,
% 3.74/3.96 (b(s(elem!1), z) <=> b(elem!1, z)),
% 3.74/3.96 inference(symmetry,[status(thm)],[12022])).
% 3.74/3.96 tff(12024,plain,
% 3.74/3.96 (b(elem!1, z)),
% 3.74/3.96 inference(modus_ponens,[status(thm)],[853, 12023])).
% 3.74/3.96 tff(12025,plain,
% 3.74/3.96 ($false),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[5723, 12024])).
% 3.74/3.96 tff(12026,plain,((~(elem!1 = s(elem!1))) | b(elem!1, z) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.96 tff(12027,plain,
% 3.74/3.96 (~(elem!1 = s(elem!1))),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[12026, 5723, 853])).
% 3.74/3.96 tff(12028,plain,
% 3.74/3.96 (r(elem!1, s(elem!1))),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[756, 12027, 751])).
% 3.74/3.96 tff(12029,plain,
% 3.74/3.96 (r(elem!1, s(s(elem!1))) <=> r(z, s(s(elem!1)))),
% 3.74/3.96 inference(monotonicity,[status(thm)],[928])).
% 3.74/3.96 tff(12030,plain,
% 3.74/3.96 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 3.74/3.96 inference(symmetry,[status(thm)],[12029])).
% 3.74/3.96 tff(12031,plain,
% 3.74/3.96 (r(z, s(s(z))) <=> r(elem!1, s(s(elem!1)))),
% 3.74/3.96 inference(transitivity,[status(thm)],[5224, 12030])).
% 3.74/3.96 tff(12032,plain,
% 3.74/3.96 (r(elem!1, s(s(elem!1)))),
% 3.74/3.96 inference(modus_ponens,[status(thm)],[3261, 12031])).
% 3.74/3.96 tff(12033,plain,
% 3.74/3.96 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 3.74/3.96 inference(symmetry,[status(thm)],[3400])).
% 3.74/3.96 tff(12034,plain,
% 3.74/3.96 (s(s(z)) = s(s(elem!1))),
% 3.74/3.96 inference(symmetry,[status(thm)],[930])).
% 3.74/3.96 tff(12035,plain,
% 3.74/3.96 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 3.74/3.96 inference(monotonicity,[status(thm)],[12034])).
% 3.74/3.96 tff(12036,plain,
% 3.74/3.96 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 3.74/3.96 inference(transitivity,[status(thm)],[12035, 12033])).
% 3.74/3.96 tff(12037,plain,
% 3.74/3.96 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 3.74/3.96 inference(monotonicity,[status(thm)],[12036])).
% 3.74/3.96 tff(12038,plain,
% 3.74/3.96 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 3.74/3.96 inference(modus_ponens,[status(thm)],[1683, 12037])).
% 3.74/3.96 tff(12039,plain,
% 3.74/3.96 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.74/3.96 inference(symmetry,[status(thm)],[5220])).
% 3.74/3.96 tff(12040,plain,
% 3.74/3.96 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.74/3.96 inference(transitivity,[status(thm)],[5218, 12039])).
% 3.74/3.96 tff(12041,plain,
% 3.74/3.96 ((~b(s(s(s(z))), s(s(z)))) <=> (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 3.74/3.96 inference(monotonicity,[status(thm)],[12040])).
% 3.74/3.96 tff(12042,plain,
% 3.74/3.96 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 3.74/3.96 inference(monotonicity,[status(thm)],[5207, 6683])).
% 3.74/3.96 tff(12043,plain,
% 3.74/3.96 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(z))),
% 3.74/3.96 inference(symmetry,[status(thm)],[12042])).
% 3.74/3.96 tff(12044,plain,
% 3.74/3.96 ((elem!1 = s(s(s(s(elem!1))))) <=> (z = s(s(s(s(elem!1)))))),
% 3.74/3.96 inference(monotonicity,[status(thm)],[928])).
% 3.74/3.96 tff(12045,plain,
% 3.74/3.96 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = z)),
% 3.74/3.96 inference(transitivity,[status(thm)],[12044, 4413])).
% 3.74/3.96 tff(12046,plain,
% 3.74/3.96 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 3.74/3.96 inference(symmetry,[status(thm)],[12045])).
% 3.74/3.96 tff(12047,plain,
% 3.74/3.96 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 3.74/3.96 inference(monotonicity,[status(thm)],[12046])).
% 3.74/3.96 tff(12048,plain,
% 3.74/3.96 (~(elem!1 = s(s(s(s(elem!1)))))),
% 3.74/3.96 inference(modus_ponens,[status(thm)],[1712, 12047])).
% 3.74/3.96 tff(12049,plain,
% 3.74/3.96 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[1509, 12048])).
% 3.74/3.96 tff(12050,plain,
% 3.74/3.96 (b(elem!1, s(elem!1)) <=> b(z, s(elem!1))),
% 3.74/3.96 inference(monotonicity,[status(thm)],[928])).
% 3.74/3.96 tff(12051,plain,
% 3.74/3.96 (b(z, s(elem!1)) <=> b(elem!1, s(elem!1))),
% 3.74/3.96 inference(symmetry,[status(thm)],[12050])).
% 3.74/3.96 tff(12052,plain,
% 3.74/3.96 (b(elem!1, s(elem!1))),
% 3.74/3.96 inference(modus_ponens,[status(thm)],[855, 12051])).
% 3.74/3.96 tff(12053,plain,
% 3.74/3.96 ($false),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[751, 12052])).
% 3.74/3.96 tff(12054,plain,((~(elem!1 = z)) | b(elem!1, s(elem!1)) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.96 tff(12055,plain,
% 3.74/3.96 (~b(z, s(elem!1))),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[12054, 928, 751])).
% 3.74/3.96 tff(12056,plain,
% 3.74/3.96 (r(z, s(elem!1))),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[2351, 12055])).
% 3.74/3.96 tff(12057,plain,
% 3.74/3.96 (~r(s(elem!1), s(s(z)))),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[11762, 12056, 3261])).
% 3.74/3.96 tff(12058,plain,
% 3.74/3.96 (~r(s(z), s(s(z)))),
% 3.74/3.96 inference(modus_ponens,[status(thm)],[12057, 1022])).
% 3.74/3.96 tff(12059,plain,
% 3.74/3.96 (~r(s(elem!1), s(s(elem!1)))),
% 3.74/3.96 inference(modus_ponens,[status(thm)],[12058, 1020])).
% 3.74/3.96 tff(12060,plain,
% 3.74/3.96 (b(s(elem!1), s(s(elem!1)))),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[1028, 12059, 980])).
% 3.74/3.96 tff(12061,plain,
% 3.74/3.96 (b(s(elem!1), elem!1) <=> b(s(elem!1), z)),
% 3.74/3.96 inference(monotonicity,[status(thm)],[928])).
% 3.74/3.96 tff(12062,plain,
% 3.74/3.96 (b(s(elem!1), z) <=> b(s(elem!1), elem!1)),
% 3.74/3.96 inference(symmetry,[status(thm)],[12061])).
% 3.74/3.96 tff(12063,plain,
% 3.74/3.96 (b(s(elem!1), elem!1)),
% 3.74/3.96 inference(modus_ponens,[status(thm)],[853, 12062])).
% 3.74/3.96 tff(12064,plain,
% 3.74/3.96 (z = elem!1),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[2808, 928])).
% 3.74/3.96 tff(12065,plain,
% 3.74/3.96 (b(s(s(elem!1)), elem!1)),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[5878, 12064, 3461])).
% 3.74/3.96 tff(12066,plain,
% 3.74/3.96 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 3.74/3.96 inference(symmetry,[status(thm)],[932])).
% 3.74/3.96 tff(12067,plain,
% 3.74/3.96 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(z)), s(s(s(s(elem!1)))))),
% 3.74/3.96 inference(monotonicity,[status(thm)],[12066])).
% 3.74/3.96 tff(12068,plain,
% 3.74/3.96 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 3.74/3.96 inference(modus_ponens,[status(thm)],[147, 12067])).
% 3.74/3.96 tff(12069,plain,
% 3.74/3.96 (r(s(s(s(s(elem!1)))), s(s(z))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 3.74/3.96 inference(monotonicity,[status(thm)],[932])).
% 3.74/3.96 tff(12070,plain,
% 3.74/3.96 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(s(z)))),
% 3.74/3.96 inference(symmetry,[status(thm)],[12069])).
% 3.74/3.96 tff(12071,plain,
% 3.74/3.96 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 3.74/3.96 inference(modus_ponens,[status(thm)],[193, 12070])).
% 3.74/3.96 tff(12072,plain,
% 3.74/3.96 ((s(elem!1) = s(s(s(s(elem!1))))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 3.74/3.96 inference(monotonicity,[status(thm)],[932])).
% 3.74/3.96 tff(12073,plain,
% 3.74/3.96 ((s(elem!1) = s(s(s(s(elem!1))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 3.74/3.96 inference(transitivity,[status(thm)],[12072, 2163])).
% 3.74/3.96 tff(12074,plain,
% 3.74/3.96 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 3.74/3.96 inference(symmetry,[status(thm)],[12073])).
% 3.74/3.96 tff(12075,plain,
% 3.74/3.96 ((~(s(s(s(s(z)))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(elem!1))))))),
% 3.74/3.96 inference(monotonicity,[status(thm)],[12074])).
% 3.74/3.96 tff(12076,plain,
% 3.74/3.96 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 3.74/3.96 inference(modus_ponens,[status(thm)],[2508, 12075])).
% 3.74/3.96 tff(12077,plain,
% 3.74/3.96 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[4343, 12076])).
% 3.74/3.96 tff(12078,plain,
% 3.74/3.96 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 3.74/3.96 inference(monotonicity,[status(thm)],[932, 931])).
% 3.74/3.96 tff(12079,plain,
% 3.74/3.96 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 3.74/3.96 inference(monotonicity,[status(thm)],[12035])).
% 3.74/3.96 tff(12080,plain,
% 3.74/3.96 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 3.74/3.96 inference(modus_ponens,[status(thm)],[1683, 12079])).
% 3.74/3.96 tff(12081,plain,
% 3.74/3.96 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[1657, 12080])).
% 3.74/3.96 tff(12082,plain,
% 3.74/3.96 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 3.74/3.96 inference(monotonicity,[status(thm)],[930])).
% 3.74/3.96 tff(12083,plain,
% 3.74/3.96 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 3.74/3.96 inference(transitivity,[status(thm)],[937, 2486])).
% 3.74/3.96 tff(12084,plain,
% 3.74/3.96 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 3.74/3.96 inference(monotonicity,[status(thm)],[12083])).
% 3.74/3.96 tff(12085,plain,
% 3.74/3.96 (~(elem!1 = s(s(s(elem!1))))),
% 3.74/3.96 inference(modus_ponens,[status(thm)],[940, 12084])).
% 3.74/3.96 tff(12086,plain,
% 3.74/3.96 (b(elem!1, s(s(s(elem!1))))),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[2054, 1592, 12085])).
% 3.74/3.96 tff(12087,plain,
% 3.74/3.96 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[5490, 12086, 5434, 683, 5391])).
% 3.74/3.96 tff(12088,plain,
% 3.74/3.96 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[3375, 12087, 12080])).
% 3.74/3.96 tff(12089,plain,
% 3.74/3.96 (r(s(s(z)), s(s(s(elem!1))))),
% 3.74/3.96 inference(modus_ponens,[status(thm)],[12088, 12082])).
% 3.74/3.96 tff(12090,plain,
% 3.74/3.96 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[3644, 12089, 3636])).
% 3.74/3.96 tff(12091,plain,
% 3.74/3.96 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[1988, 12090, 12081])).
% 3.74/3.96 tff(12092,plain,
% 3.74/3.96 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.74/3.96 inference(modus_ponens,[status(thm)],[12091, 12078])).
% 3.74/3.96 tff(12093,plain,
% 3.74/3.96 (b(z, s(s(s(z)))) <=> b(z, s(s(s(elem!1))))),
% 3.74/3.96 inference(monotonicity,[status(thm)],[5207])).
% 3.74/3.96 tff(12094,plain,
% 3.74/3.96 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(z))))),
% 3.74/3.96 inference(symmetry,[status(thm)],[12093])).
% 3.74/3.96 tff(12095,plain,
% 3.74/3.96 (b(z, s(s(s(z))))),
% 3.74/3.96 inference(modus_ponens,[status(thm)],[7340, 12094])).
% 3.74/3.96 tff(12096,plain,
% 3.74/3.96 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[4036, 12089, 1403])).
% 3.74/3.96 tff(12097,plain,
% 3.74/3.96 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[1750, 12096, 1858])).
% 3.74/3.96 tff(12098,plain,
% 3.74/3.96 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.74/3.96 inference(modus_ponens,[status(thm)],[12097, 5215])).
% 3.74/3.96 tff(12099,plain,
% 3.74/3.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 3.74/3.96 inference(rewrite,[status(thm)],[])).
% 3.74/3.96 tff(12100,plain,
% 3.74/3.96 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 3.74/3.96 inference(rewrite,[status(thm)],[])).
% 3.74/3.96 tff(12101,plain,
% 3.74/3.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))))),
% 3.74/3.96 inference(monotonicity,[status(thm)],[12100])).
% 3.74/3.96 tff(12102,plain,
% 3.74/3.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 3.74/3.96 inference(transitivity,[status(thm)],[12101, 12099])).
% 3.74/3.96 tff(12103,plain,
% 3.74/3.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 3.74/3.96 inference(quant_inst,[status(thm)],[])).
% 3.74/3.96 tff(12104,plain,
% 3.74/3.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))),
% 3.74/3.96 inference(modus_ponens,[status(thm)],[12103, 12102])).
% 3.74/3.96 tff(12105,plain,
% 3.74/3.96 ($false),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[12104, 178, 1687, 168, 12098, 12095, 12092])).
% 3.74/3.96 tff(12106,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~(elem!1 = z)) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(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)))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.96 tff(12107,plain,
% 3.74/3.96 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[12106, 928, 168, 1687, 12077, 12071, 12068, 12065, 12063, 12060, 12056, 1587])).
% 3.74/3.96 tff(12108,plain,
% 3.74/3.96 (b(s(s(s(elem!1))), s(elem!1))),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[373, 12107, 12049])).
% 3.74/3.96 tff(12109,plain,
% 3.74/3.96 (b(s(s(s(z))), s(z))),
% 3.74/3.96 inference(modus_ponens,[status(thm)],[12108, 12043])).
% 3.74/3.96 tff(12110,plain,
% 3.74/3.96 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(z)), s(elem!1))),
% 3.74/3.96 inference(monotonicity,[status(thm)],[930])).
% 3.74/3.96 tff(12111,plain,
% 3.74/3.96 (r(s(s(z)), s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 3.74/3.96 inference(symmetry,[status(thm)],[12110])).
% 3.74/3.96 tff(12112,plain,
% 3.74/3.96 ((~r(s(s(z)), s(elem!1))) <=> (~r(s(s(elem!1)), s(elem!1)))),
% 3.74/3.96 inference(monotonicity,[status(thm)],[12111])).
% 3.74/3.96 tff(12113,plain,
% 3.74/3.96 ($false),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[6220, 118, 2333, 3261, 1329])).
% 3.74/3.96 tff(12114,plain,((~r(z, s(elem!1))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.96 tff(12115,plain,
% 3.74/3.96 (~r(s(s(z)), s(elem!1))),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[12114, 12056, 3261])).
% 3.74/3.96 tff(12116,plain,
% 3.74/3.96 (~r(s(s(elem!1)), s(elem!1))),
% 3.74/3.96 inference(modus_ponens,[status(thm)],[12115, 12112])).
% 3.74/3.96 tff(12117,plain,
% 3.74/3.96 (b(s(s(elem!1)), s(elem!1))),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[1006, 987, 12116])).
% 3.74/3.96 tff(12118,plain,
% 3.74/3.96 (b(s(s(z)), s(z))),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[1015, 12117, 928])).
% 3.74/3.96 tff(12119,plain,
% 3.74/3.96 (b(s(z), z) <=> b(s(elem!1), z)),
% 3.74/3.96 inference(monotonicity,[status(thm)],[6683])).
% 3.74/3.96 tff(12120,plain,
% 3.74/3.96 (b(s(elem!1), z) <=> b(s(z), z)),
% 3.74/3.96 inference(symmetry,[status(thm)],[12119])).
% 3.74/3.96 tff(12121,plain,
% 3.74/3.96 (b(s(z), z)),
% 3.74/3.96 inference(modus_ponens,[status(thm)],[853, 12120])).
% 3.74/3.96 tff(12122,plain,
% 3.74/3.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 3.74/3.96 inference(rewrite,[status(thm)],[])).
% 3.74/3.96 tff(12123,plain,
% 3.74/3.96 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 3.74/3.96 inference(rewrite,[status(thm)],[])).
% 3.74/3.96 tff(12124,plain,
% 3.74/3.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))))),
% 3.74/3.96 inference(monotonicity,[status(thm)],[12123])).
% 3.74/3.96 tff(12125,plain,
% 3.74/3.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 3.74/3.96 inference(transitivity,[status(thm)],[12124, 12122])).
% 3.74/3.96 tff(12126,plain,
% 3.74/3.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 3.74/3.96 inference(quant_inst,[status(thm)],[])).
% 3.74/3.96 tff(12127,plain,
% 3.74/3.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))),
% 3.74/3.96 inference(modus_ponens,[status(thm)],[12126, 12125])).
% 3.74/3.96 tff(12128,plain,
% 3.74/3.96 ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[12127, 178, 3461, 12121, 12118])).
% 3.74/3.96 tff(12129,plain,
% 3.74/3.96 (~b(s(s(s(z))), s(s(z)))),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[12128, 12109])).
% 3.74/3.96 tff(12130,plain,
% 3.74/3.96 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.74/3.96 inference(modus_ponens,[status(thm)],[12129, 12041])).
% 3.74/3.96 tff(12131,plain,
% 3.74/3.96 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[3409, 12130, 12038])).
% 3.74/3.96 tff(12132,plain,
% 3.74/3.96 (~r(s(s(s(elem!1))), elem!1)),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[10206, 12131, 12032])).
% 3.74/3.96 tff(12133,plain,
% 3.74/3.96 (b(elem!1, s(s(s(s(elem!1))))) <=> b(z, s(s(s(s(elem!1)))))),
% 3.74/3.96 inference(monotonicity,[status(thm)],[928])).
% 3.74/3.96 tff(12134,plain,
% 3.74/3.96 (b(z, s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 3.74/3.96 inference(symmetry,[status(thm)],[12133])).
% 3.74/3.96 tff(12135,plain,
% 3.74/3.96 (b(z, s(s(s(s(elem!1))))) <=> b(z, s(s(s(s(z)))))),
% 3.74/3.96 inference(monotonicity,[status(thm)],[932])).
% 3.74/3.96 tff(12136,plain,
% 3.74/3.96 (b(z, s(s(s(s(z))))) <=> b(z, s(s(s(s(elem!1)))))),
% 3.74/3.96 inference(symmetry,[status(thm)],[12135])).
% 3.74/3.96 tff(12137,plain,
% 3.74/3.96 (b(z, s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 3.74/3.96 inference(transitivity,[status(thm)],[12136, 12134])).
% 3.74/3.96 tff(12138,plain,
% 3.74/3.96 (b(elem!1, s(s(s(s(elem!1)))))),
% 3.74/3.96 inference(modus_ponens,[status(thm)],[1687, 12137])).
% 3.74/3.96 tff(12139,plain,
% 3.74/3.96 (s(s(elem!1)) = s(s(z))),
% 3.74/3.96 inference(symmetry,[status(thm)],[15])).
% 3.74/3.96 tff(12140,plain,
% 3.74/3.96 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(s(s(s(elem!1)))), s(s(z)))),
% 3.74/3.96 inference(monotonicity,[status(thm)],[12139])).
% 3.74/3.96 tff(12141,plain,
% 3.74/3.96 (r(s(s(s(s(elem!1)))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.74/3.96 inference(symmetry,[status(thm)],[12140])).
% 3.74/3.96 tff(12142,plain,
% 3.74/3.96 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.74/3.96 inference(modus_ponens,[status(thm)],[3636, 12141])).
% 3.74/3.96 tff(12143,plain,
% 3.74/3.97 (~r(s(s(s(s(elem!1)))), z)),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[5194, 3636, 3261])).
% 3.74/3.97 tff(12144,plain,
% 3.74/3.97 (b(s(s(s(s(elem!1)))), z)),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[1716, 12143])).
% 3.74/3.97 tff(12145,plain,
% 3.74/3.97 (b(s(s(s(s(elem!1)))), elem!1)),
% 3.74/3.97 inference(modus_ponens,[status(thm)],[12144, 5176])).
% 3.74/3.97 tff(12146,plain,
% 3.74/3.97 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 3.74/3.97 inference(monotonicity,[status(thm)],[13])).
% 3.74/3.97 tff(12147,plain,
% 3.74/3.97 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 3.74/3.97 inference(transitivity,[status(thm)],[12146, 2486])).
% 3.74/3.97 tff(12148,plain,
% 3.74/3.97 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 3.74/3.97 inference(monotonicity,[status(thm)],[12147])).
% 3.74/3.97 tff(12149,plain,
% 3.74/3.97 (~(elem!1 = s(s(s(elem!1))))),
% 3.74/3.97 inference(modus_ponens,[status(thm)],[940, 12148])).
% 3.74/3.97 tff(12150,plain,
% 3.74/3.97 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(z)))),
% 3.74/3.97 inference(monotonicity,[status(thm)],[12139])).
% 3.74/3.97 tff(12151,plain,
% 3.74/3.97 (r(elem!1, s(s(z))) <=> r(elem!1, s(s(elem!1)))),
% 3.74/3.97 inference(symmetry,[status(thm)],[12150])).
% 3.74/3.97 tff(12152,plain,
% 3.74/3.97 (r(z, s(s(z))) <=> r(elem!1, s(s(z)))),
% 3.74/3.97 inference(monotonicity,[status(thm)],[13])).
% 3.74/3.97 tff(12153,plain,
% 3.74/3.97 (r(elem!1, s(s(z)))),
% 3.74/3.97 inference(modus_ponens,[status(thm)],[3261, 12152])).
% 3.74/3.97 tff(12154,plain,
% 3.74/3.97 (r(elem!1, s(s(elem!1)))),
% 3.74/3.97 inference(modus_ponens,[status(thm)],[12153, 12151])).
% 3.74/3.97 tff(12155,plain,
% 3.74/3.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.74/3.97 inference(rewrite,[status(thm)],[])).
% 3.74/3.97 tff(12156,plain,
% 3.74/3.97 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.74/3.97 inference(rewrite,[status(thm)],[])).
% 3.74/3.97 tff(12157,plain,
% 3.74/3.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))))),
% 3.74/3.97 inference(monotonicity,[status(thm)],[12156])).
% 3.74/3.97 tff(12158,plain,
% 3.74/3.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.74/3.97 inference(transitivity,[status(thm)],[12157, 12155])).
% 3.74/3.97 tff(12159,plain,
% 3.74/3.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))),
% 3.74/3.97 inference(quant_inst,[status(thm)],[])).
% 3.74/3.97 tff(12160,plain,
% 3.74/3.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 3.74/3.97 inference(modus_ponens,[status(thm)],[12159, 12158])).
% 3.74/3.97 tff(12161,plain,
% 3.74/3.97 (~r(elem!1, s(s(s(elem!1))))),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[12160, 118, 5227, 12154])).
% 3.74/3.97 tff(12162,plain,
% 3.74/3.97 (b(elem!1, s(s(s(elem!1))))),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[2054, 12161, 12149])).
% 3.74/3.97 tff(12163,plain,
% 3.74/3.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 3.74/3.97 inference(rewrite,[status(thm)],[])).
% 3.74/3.97 tff(12164,plain,
% 3.74/3.97 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 3.74/3.97 inference(rewrite,[status(thm)],[])).
% 3.74/3.97 tff(12165,plain,
% 3.74/3.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 3.74/3.97 inference(monotonicity,[status(thm)],[12164])).
% 3.74/3.97 tff(12166,plain,
% 3.74/3.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 3.74/3.97 inference(transitivity,[status(thm)],[12165, 12163])).
% 3.74/3.97 tff(12167,plain,
% 3.74/3.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 3.74/3.97 inference(quant_inst,[status(thm)],[])).
% 3.74/3.97 tff(12168,plain,
% 3.74/3.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 3.74/3.97 inference(modus_ponens,[status(thm)],[12167, 12166])).
% 3.74/3.97 tff(12169,plain,
% 3.74/3.97 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[12168, 178, 5818, 1597, 12162, 12145])).
% 3.74/3.97 tff(12170,plain,
% 3.74/3.97 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[1988, 12169, 1693])).
% 3.74/3.97 tff(12171,plain,
% 3.74/3.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 3.74/3.97 inference(rewrite,[status(thm)],[])).
% 3.74/3.97 tff(12172,plain,
% 3.74/3.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 3.74/3.97 inference(quant_inst,[status(thm)],[])).
% 3.74/3.97 tff(12173,plain,
% 3.74/3.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 3.74/3.97 inference(modus_ponens,[status(thm)],[12172, 12171])).
% 3.74/3.97 tff(12174,plain,
% 3.74/3.97 ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[12173, 118, 5227])).
% 3.74/3.97 tff(12175,plain,
% 3.74/3.97 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[12174, 12170])).
% 3.74/3.97 tff(12176,plain,
% 3.74/3.97 ($false),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[12175, 12142])).
% 3.74/3.97 tff(12177,plain,((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~(z = elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.97 tff(12178,plain,
% 3.74/3.97 (~b(s(s(s(elem!1))), elem!1)),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[12177, 12131, 12064, 12081, 12138, 12071, 3261])).
% 3.74/3.97 tff(12179,plain,
% 3.74/3.97 ($false),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[570, 12178, 12132, 941])).
% 3.74/3.97 tff(12180,plain,((~(elem!1 = z)) | (~r(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~r(elem!1, s(elem!1))) | (s(s(s(s(z)))) = s(elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), z)) | b(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.97 tff(12181,plain,
% 3.74/3.97 (~(elem!1 = z)),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[12180, 193, 3461, 168, 1687, 12028, 2169, 3261, 147, 853, 751])).
% 3.74/3.97 tff(12182,plain,
% 3.74/3.97 (r(elem!1, z)),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[498, 12181, 5723])).
% 3.74/3.97 tff(12183,plain,
% 3.74/3.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))),
% 3.74/3.97 inference(rewrite,[status(thm)],[])).
% 3.74/3.97 tff(12184,plain,
% 3.74/3.97 (((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z))) <=> ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))),
% 3.74/3.97 inference(rewrite,[status(thm)],[])).
% 3.74/3.97 tff(12185,plain,
% 3.74/3.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1)))))),
% 3.74/3.97 inference(monotonicity,[status(thm)],[12184])).
% 3.74/3.97 tff(12186,plain,
% 3.74/3.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))),
% 3.74/3.97 inference(transitivity,[status(thm)],[12185, 12183])).
% 3.74/3.97 tff(12187,plain,
% 3.74/3.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)))),
% 3.74/3.97 inference(quant_inst,[status(thm)],[])).
% 3.74/3.97 tff(12188,plain,
% 3.74/3.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1)))),
% 3.74/3.97 inference(modus_ponens,[status(thm)],[12187, 12186])).
% 3.74/3.97 tff(12189,plain,
% 3.74/3.97 ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1)))),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[12188, 118])).
% 3.74/3.97 tff(12190,plain,
% 3.74/3.97 (~r(z, s(elem!1))),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[12189, 12182, 12028])).
% 3.74/3.97 tff(12191,plain,
% 3.74/3.97 (b(z, s(elem!1))),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[2351, 12190])).
% 3.74/3.97 tff(12192,plain,
% 3.74/3.97 (~b(s(elem!1), s(s(s(s(z)))))),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[11771, 12191])).
% 3.74/3.97 tff(12193,plain,
% 3.74/3.97 (r(s(elem!1), s(s(s(s(z)))))),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[1084, 12192, 1369])).
% 3.74/3.97 tff(12194,plain,
% 3.74/3.97 (~r(s(elem!1), s(s(z)))),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[3949, 12193, 193])).
% 3.74/3.97 tff(12195,plain,
% 3.74/3.97 (~r(s(s(z)), s(elem!1))),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[5758, 12193, 147])).
% 3.74/3.97 tff(12196,plain,
% 3.74/3.97 (b(s(elem!1), s(s(z)))),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[421, 1056, 927])).
% 3.74/3.97 tff(12197,plain,
% 3.74/3.97 (b(s(s(z)), s(elem!1))),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[1067, 2311, 1062])).
% 3.74/3.97 tff(12198,plain,
% 3.74/3.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)))),
% 3.74/3.97 inference(rewrite,[status(thm)],[])).
% 3.74/3.97 tff(12199,plain,
% 3.74/3.97 (((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z))))) <=> ((~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)))),
% 3.74/3.97 inference(rewrite,[status(thm)],[])).
% 3.74/3.97 tff(12200,plain,
% 3.74/3.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z))))),
% 3.74/3.97 inference(monotonicity,[status(thm)],[12199])).
% 3.74/3.97 tff(12201,plain,
% 3.74/3.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)))),
% 3.74/3.97 inference(transitivity,[status(thm)],[12200, 12198])).
% 3.74/3.97 tff(12202,plain,
% 3.74/3.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))))),
% 3.74/3.97 inference(quant_inst,[status(thm)],[])).
% 3.74/3.97 tff(12203,plain,
% 3.74/3.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z))),
% 3.74/3.97 inference(modus_ponens,[status(thm)],[12202, 12201])).
% 3.74/3.97 tff(12204,plain,
% 3.74/3.97 ($false),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[12203, 178, 855, 853, 3461, 12197, 12196])).
% 3.74/3.97 tff(12205,plain,((s(elem!1) = s(s(z))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | r(s(s(z)), s(elem!1)) | r(s(elem!1), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.97 tff(12206,plain,
% 3.74/3.97 (s(elem!1) = s(s(z))),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[12205, 12191, 853, 3461, 12195, 12194])).
% 3.74/3.97 tff(12207,plain,
% 3.74/3.97 (r(z, s(elem!1)) <=> r(z, s(s(z)))),
% 3.74/3.97 inference(monotonicity,[status(thm)],[12206])).
% 3.74/3.97 tff(12208,plain,
% 3.74/3.97 (r(z, s(s(z))) <=> r(z, s(elem!1))),
% 3.74/3.97 inference(symmetry,[status(thm)],[12207])).
% 3.74/3.97 tff(12209,plain,
% 3.74/3.97 (r(z, s(elem!1))),
% 3.74/3.97 inference(modus_ponens,[status(thm)],[3261, 12208])).
% 3.74/3.97 tff(12210,plain,
% 3.74/3.97 ($false),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[12190, 12209])).
% 3.74/3.97 tff(12211,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (s(elem!1) = s(s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | b(elem!1, z) | b(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.97 tff(12212,plain,
% 3.74/3.97 (~r(s(s(s(s(z)))), s(s(z)))),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[12211, 5723, 853, 3461, 147, 1369, 1687, 168, 3261, 751])).
% 3.74/3.97 tff(12213,plain,
% 3.74/3.97 (~r(s(elem!1), s(s(z)))),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[11775, 168, 1369, 853, 1687, 147, 3261])).
% 3.74/3.97 tff(12214,plain,
% 3.74/3.97 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(elem!1))),
% 3.74/3.97 inference(monotonicity,[status(thm)],[745])).
% 3.74/3.97 tff(12215,plain,
% 3.74/3.97 ((s(s(z)) = elem!1) <=> (s(elem!1) = s(s(z)))),
% 3.74/3.97 inference(transitivity,[status(thm)],[12214, 1358])).
% 3.74/3.97 tff(12216,plain,
% 3.74/3.97 ((s(elem!1) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 3.74/3.97 inference(symmetry,[status(thm)],[12215])).
% 3.74/3.97 tff(12217,plain,
% 3.74/3.97 ((~(s(elem!1) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 3.74/3.97 inference(monotonicity,[status(thm)],[12216])).
% 3.74/3.97 tff(12218,plain,
% 3.74/3.97 (s(elem!1) = elem!1),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[748, 745])).
% 3.74/3.97 tff(12219,plain,
% 3.74/3.97 (s(s(elem!1)) = elem!1),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[672, 12218])).
% 3.74/3.97 tff(12220,plain,
% 3.74/3.97 (elem!1 = s(s(elem!1))),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[1546, 12219])).
% 3.74/3.97 tff(12221,plain,
% 3.74/3.97 (s(s(s(elem!1))) = s(elem!1)),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[1539, 12220])).
% 3.74/3.97 tff(12222,plain,
% 3.74/3.97 (elem!1 = s(s(s(s(elem!1))))),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[1509, 12221])).
% 3.74/3.97 tff(12223,plain,
% 3.74/3.97 (~(s(elem!1) = s(s(z)))),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[1422, 12222])).
% 3.74/3.97 tff(12224,plain,
% 3.74/3.97 (~(s(s(z)) = elem!1)),
% 3.74/3.97 inference(modus_ponens,[status(thm)],[12223, 12217])).
% 3.74/3.97 tff(12225,plain,
% 3.74/3.97 ((s(s(s(s(z)))) = elem!1) <=> (s(s(s(s(z)))) = s(elem!1))),
% 3.74/3.97 inference(monotonicity,[status(thm)],[745])).
% 3.74/3.97 tff(12226,plain,
% 3.74/3.97 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(s(s(z)))) = elem!1)),
% 3.74/3.97 inference(symmetry,[status(thm)],[12225])).
% 3.74/3.97 tff(12227,plain,
% 3.74/3.97 ((s(s(s(s(z)))) = s(elem!1)) <=> (elem!1 = s(s(s(s(z)))))),
% 3.74/3.97 inference(transitivity,[status(thm)],[12226, 501])).
% 3.74/3.97 tff(12228,plain,
% 3.74/3.97 ((~(s(s(s(s(z)))) = s(elem!1))) <=> (~(elem!1 = s(s(s(s(z))))))),
% 3.74/3.97 inference(monotonicity,[status(thm)],[12227])).
% 3.74/3.97 tff(12229,plain,
% 3.74/3.97 (~(elem!1 = s(s(s(s(z)))))),
% 3.74/3.97 inference(modus_ponens,[status(thm)],[2508, 12228])).
% 3.74/3.97 tff(12230,plain,
% 3.74/3.97 (b(elem!1, z)),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[12026, 745, 853])).
% 3.74/3.97 tff(12231,plain,
% 3.74/3.97 (~(z = elem!1)),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[6991, 12230])).
% 3.74/3.97 tff(12232,plain,
% 3.74/3.97 ((~(s(s(s(s(z)))) = s(elem!1))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 3.74/3.97 inference(monotonicity,[status(thm)],[12226])).
% 3.74/3.97 tff(12233,plain,
% 3.74/3.97 (~(s(s(s(s(z)))) = elem!1)),
% 3.74/3.97 inference(modus_ponens,[status(thm)],[2508, 12232])).
% 3.74/3.97 tff(12234,plain,
% 3.74/3.97 (~r(z, elem!1)),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[8412, 438, 3261])).
% 3.74/3.97 tff(12235,plain,
% 3.74/3.97 (b(z, elem!1)),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[585, 12234, 507])).
% 3.74/3.97 tff(12236,plain,
% 3.74/3.97 (~b(s(s(s(s(z)))), elem!1)),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[7020, 11957, 506, 12235, 1687])).
% 3.74/3.97 tff(12237,plain,
% 3.74/3.97 (r(s(s(s(s(z)))), elem!1)),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[3142, 12236, 323])).
% 3.74/3.97 tff(12238,plain,
% 3.74/3.97 ($false),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[9469, 118, 438, 12237, 147])).
% 3.74/3.97 tff(12239,plain,((~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (s(s(s(s(z)))) = elem!1) | (~b(elem!1, z)) | (~b(z, s(s(s(s(z)))))) | (z = elem!1) | (elem!1 = s(s(s(s(z))))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.97 tff(12240,plain,
% 3.74/3.97 (~r(s(s(z)), elem!1)),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[12239, 12233, 147, 12230, 1687, 12231, 12229, 3261])).
% 3.74/3.97 tff(12241,plain,
% 3.74/3.97 (b(s(s(z)), elem!1)),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[448, 12240, 12224])).
% 3.74/3.97 tff(12242,plain,
% 3.74/3.97 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[2510, 12219, 2508])).
% 3.74/3.97 tff(12243,plain,
% 3.74/3.97 (s(s(s(elem!1))) = elem!1),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[2150, 12218])).
% 3.74/3.97 tff(12244,plain,
% 3.74/3.97 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[3907, 12243, 927])).
% 3.74/3.97 tff(12245,plain,
% 3.74/3.97 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[1170, 12244])).
% 3.74/3.97 tff(12246,plain,
% 3.74/3.97 (b(elem!1, s(s(z)))),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[3901, 12222, 12245])).
% 3.74/3.97 tff(12247,plain,
% 3.74/3.97 ((s(elem!1) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 3.74/3.97 inference(transitivity,[status(thm)],[12216, 1666])).
% 3.74/3.97 tff(12248,plain,
% 3.74/3.97 ((~(s(elem!1) = s(s(z)))) <=> (~(elem!1 = s(s(z))))),
% 3.74/3.97 inference(monotonicity,[status(thm)],[12247])).
% 3.74/3.97 tff(12249,plain,
% 3.74/3.97 (~(elem!1 = s(s(z)))),
% 3.74/3.97 inference(modus_ponens,[status(thm)],[12223, 12248])).
% 3.74/3.97 tff(12250,plain,
% 3.74/3.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))),
% 3.74/3.97 inference(rewrite,[status(thm)],[])).
% 3.74/3.97 tff(12251,plain,
% 3.74/3.97 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z))))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))),
% 3.74/3.97 inference(rewrite,[status(thm)],[])).
% 3.74/3.97 tff(12252,plain,
% 3.74/3.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z))))),
% 3.74/3.97 inference(monotonicity,[status(thm)],[12251])).
% 3.74/3.97 tff(12253,plain,
% 3.74/3.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))),
% 3.74/3.97 inference(transitivity,[status(thm)],[12252, 12250])).
% 3.74/3.97 tff(12254,plain,
% 3.74/3.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))))),
% 3.74/3.97 inference(quant_inst,[status(thm)],[])).
% 3.74/3.97 tff(12255,plain,
% 3.74/3.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z))),
% 3.74/3.97 inference(modus_ponens,[status(thm)],[12254, 12253])).
% 3.74/3.97 tff(12256,plain,
% 3.74/3.97 ($false),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[12255, 178, 818, 506, 817, 3461, 812])).
% 3.74/3.97 tff(12257,plain,((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.97 tff(12258,plain,
% 3.74/3.97 (~b(elem!1, s(s(z)))),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[12257, 817, 3461, 506, 818])).
% 3.74/3.97 tff(12259,plain,
% 3.74/3.97 (r(elem!1, s(s(z)))),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[467, 12258, 462])).
% 3.74/3.97 tff(12260,plain,
% 3.74/3.97 (~r(elem!1, s(s(s(s(z)))))),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[5670, 12259, 147])).
% 3.74/3.97 tff(12261,plain,
% 3.74/3.97 (b(elem!1, s(s(s(s(z)))))),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[483, 12260, 469])).
% 3.74/3.97 tff(12262,plain,
% 3.74/3.97 ($false),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[11953, 178, 818, 817, 3461, 1687, 12261])).
% 3.74/3.97 tff(12263,plain,((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (elem!1 = s(s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (elem!1 = s(s(z))) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.97 tff(12264,plain,
% 3.74/3.97 (~b(z, elem!1)),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[12263, 12241, 3461, 1687, 12230, 147, 12229, 12249])).
% 3.74/3.97 tff(12265,plain,
% 3.74/3.97 (r(z, elem!1)),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[585, 12264, 12231])).
% 3.74/3.97 tff(12266,plain,
% 3.74/3.97 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[11871, 12265, 3461, 12246, 12242, 12241, 147])).
% 3.74/3.97 tff(12267,plain,
% 3.74/3.97 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[84, 12266])).
% 3.74/3.97 tff(12268,plain,
% 3.74/3.97 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[5624, 224, 147])).
% 3.74/3.97 tff(12269,plain,
% 3.74/3.97 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[222, 12268])).
% 3.74/3.97 tff(12270,plain,
% 3.74/3.97 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[11920, 178, 104, 1687, 168, 12269])).
% 3.74/3.97 tff(12271,plain,
% 3.74/3.97 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[271, 12270])).
% 3.74/3.97 tff(12272,plain,
% 3.74/3.97 ($false),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[4688, 118, 3261, 224, 12271])).
% 3.74/3.97 tff(12273,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.97 tff(12274,plain,
% 3.74/3.97 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[12273, 12267, 3261, 1687, 168, 147])).
% 3.74/3.97 tff(12275,plain,
% 3.74/3.97 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.74/3.97 inference(unit_resolution,[status(thm)],[249, 12274])).
% 3.74/3.97 tff(12276,plain,
% 3.74/3.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(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(z)), s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(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(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))))),
% 3.74/3.98 inference(rewrite,[status(thm)],[])).
% 3.74/3.98 tff(12277,plain,
% 3.74/3.98 (((~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(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), z)) | (~b(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(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))))),
% 3.74/3.98 inference(rewrite,[status(thm)],[])).
% 3.74/3.98 tff(12278,plain,
% 3.74/3.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(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(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z))))))))),
% 3.74/3.98 inference(monotonicity,[status(thm)],[12277])).
% 3.74/3.98 tff(12279,plain,
% 3.74/3.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(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(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))))),
% 3.74/3.98 inference(transitivity,[status(thm)],[12278, 12276])).
% 3.74/3.98 tff(12280,plain,
% 3.74/3.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)))),
% 3.74/3.98 inference(quant_inst,[status(thm)],[])).
% 3.74/3.98 tff(12281,plain,
% 3.74/3.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z))))))),
% 3.74/3.98 inference(modus_ponens,[status(thm)],[12280, 12279])).
% 3.74/3.98 tff(12282,plain,
% 3.74/3.98 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[12281, 178, 3461, 12267, 1687, 12275])).
% 3.74/3.98 tff(12283,plain,
% 3.74/3.98 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[271, 12282])).
% 3.74/3.98 tff(12284,plain,
% 3.74/3.98 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[3818, 12283, 12265])).
% 3.74/3.98 tff(12285,plain,
% 3.74/3.98 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[691, 12284, 12242])).
% 3.74/3.98 tff(12286,plain,
% 3.74/3.98 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[11859, 12285, 12246, 12241, 12275])).
% 3.74/3.98 tff(12287,plain,
% 3.74/3.98 ((s(s(s(s(s(s(s(z))))))) = s(s(z))) | r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[2960, 41, 12286])).
% 3.74/3.98 tff(12288,plain,
% 3.74/3.98 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[12287, 11802])).
% 3.74/3.98 tff(12289,plain,
% 3.74/3.98 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[11879, 178, 3461, 12267, 1687, 12275])).
% 3.74/3.98 tff(12290,plain,
% 3.74/3.98 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[133, 12289])).
% 3.74/3.98 tff(12291,plain,
% 3.74/3.98 ($false),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[11826, 118, 3261, 12290, 12288])).
% 3.74/3.98 tff(12292,plain,((~(elem!1 = s(elem!1))) | (~r(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(elem!1)) | r(s(elem!1), s(s(z))) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.98 tff(12293,plain,
% 3.74/3.98 (~(elem!1 = s(elem!1))),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[12292, 168, 3461, 1687, 3261, 147, 2169, 12213, 853])).
% 3.74/3.98 tff(12294,plain,
% 3.74/3.98 (r(elem!1, s(elem!1))),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[756, 12293, 751])).
% 3.74/3.98 tff(12295,plain,
% 3.74/3.98 ((~b(s(s(s(z))), s(z))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 3.74/3.98 inference(monotonicity,[status(thm)],[12042])).
% 3.74/3.98 tff(12296,plain,
% 3.74/3.98 (r(s(s(elem!1)), s(s(s(s(elem!1))))) <=> r(s(s(z)), s(s(s(s(elem!1)))))),
% 3.74/3.98 inference(monotonicity,[status(thm)],[930])).
% 3.74/3.98 tff(12297,plain,
% 3.74/3.98 (r(s(s(z)), s(s(s(s(elem!1))))) <=> r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 3.74/3.98 inference(symmetry,[status(thm)],[12296])).
% 3.74/3.98 tff(12298,plain,
% 3.74/3.98 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 3.74/3.98 inference(transitivity,[status(thm)],[12067, 12297])).
% 3.74/3.98 tff(12299,plain,
% 3.74/3.98 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 3.74/3.98 inference(modus_ponens,[status(thm)],[147, 12298])).
% 3.74/3.98 tff(12300,plain,
% 3.74/3.98 (b(z, s(s(s(s(elem!1)))))),
% 3.74/3.98 inference(modus_ponens,[status(thm)],[1687, 12136])).
% 3.74/3.98 tff(12301,plain,
% 3.74/3.98 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(z)))), z)),
% 3.74/3.98 inference(monotonicity,[status(thm)],[932])).
% 3.74/3.98 tff(12302,plain,
% 3.74/3.98 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(elem!1)))), z)),
% 3.74/3.98 inference(symmetry,[status(thm)],[12301])).
% 3.74/3.98 tff(12303,plain,
% 3.74/3.98 (b(s(s(s(s(elem!1)))), z)),
% 3.74/3.98 inference(modus_ponens,[status(thm)],[168, 12302])).
% 3.74/3.98 tff(12304,plain,
% 3.74/3.98 (~r(s(s(s(elem!1))), elem!1)),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[10206, 5227, 5816])).
% 3.74/3.98 tff(12305,plain,
% 3.74/3.98 (b(s(s(s(elem!1))), elem!1)),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[570, 12304, 941])).
% 3.74/3.98 tff(12306,plain,
% 3.74/3.98 (b(s(s(s(elem!1))), z)),
% 3.74/3.98 inference(modus_ponens,[status(thm)],[12305, 10092])).
% 3.74/3.98 tff(12307,assumption,(b(z, s(s(s(s(elem!1)))))), introduced(assumption)).
% 3.74/3.98 tff(12308,plain,
% 3.74/3.98 (~r(z, s(s(s(elem!1))))),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[5235, 5227, 5226])).
% 3.74/3.98 tff(12309,plain,
% 3.74/3.98 (b(z, s(s(s(elem!1))))),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[2095, 12308])).
% 3.74/3.98 tff(12310,assumption,(r(s(s(elem!1)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 3.74/3.98 tff(12311,plain,
% 3.74/3.98 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.74/3.98 inference(rewrite,[status(thm)],[])).
% 3.74/3.98 tff(12312,plain,
% 3.74/3.98 (((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.74/3.98 inference(rewrite,[status(thm)],[])).
% 3.74/3.98 tff(12313,plain,
% 3.74/3.98 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))))),
% 3.74/3.98 inference(monotonicity,[status(thm)],[12312])).
% 3.74/3.98 tff(12314,plain,
% 3.74/3.98 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.74/3.98 inference(transitivity,[status(thm)],[12313, 12311])).
% 3.74/3.98 tff(12315,plain,
% 3.74/3.98 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.74/3.98 inference(quant_inst,[status(thm)],[])).
% 3.74/3.98 tff(12316,plain,
% 3.74/3.98 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 3.74/3.98 inference(modus_ponens,[status(thm)],[12315, 12314])).
% 3.74/3.98 tff(12317,plain,
% 3.74/3.98 ($false),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[12316, 118, 5227, 1876, 12310])).
% 3.74/3.98 tff(12318,plain,((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.98 tff(12319,plain,
% 3.74/3.98 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[12318, 5227, 12310])).
% 3.74/3.98 tff(12320,plain,
% 3.74/3.98 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[1750, 12319, 1858])).
% 3.74/3.98 tff(12321,plain,
% 3.74/3.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 3.74/3.98 inference(rewrite,[status(thm)],[])).
% 3.74/3.98 tff(12322,plain,
% 3.74/3.98 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 3.74/3.98 inference(rewrite,[status(thm)],[])).
% 3.74/3.98 tff(12323,plain,
% 3.74/3.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))))),
% 3.74/3.98 inference(monotonicity,[status(thm)],[12322])).
% 3.74/3.98 tff(12324,plain,
% 3.74/3.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 3.74/3.98 inference(transitivity,[status(thm)],[12323, 12321])).
% 3.74/3.98 tff(12325,plain,
% 3.74/3.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))))),
% 3.74/3.98 inference(quant_inst,[status(thm)],[])).
% 3.74/3.98 tff(12326,plain,
% 3.74/3.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))),
% 3.74/3.98 inference(modus_ponens,[status(thm)],[12325, 12324])).
% 3.74/3.98 tff(12327,plain,
% 3.74/3.98 ($false),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[12326, 178, 2043, 7976, 5177, 4401, 12307])).
% 3.74/3.98 tff(12328,plain,((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.98 tff(12329,plain,
% 3.74/3.98 (~b(s(s(s(elem!1))), z)),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[12328, 12320, 5177, 12309, 12307])).
% 3.74/3.98 tff(12330,plain,
% 3.74/3.98 ($false),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[12329, 12306])).
% 3.74/3.98 tff(12331,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~(elem!1 = z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.98 tff(12332,plain,
% 3.74/3.98 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[12331, 928, 12303, 12300, 12077, 12299, 12032, 5225])).
% 3.74/3.98 tff(12333,plain,
% 3.74/3.98 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[3409, 12332, 12038])).
% 3.74/3.98 tff(12334,plain,
% 3.74/3.98 (b(s(s(s(z))), s(s(z)))),
% 3.74/3.98 inference(modus_ponens,[status(thm)],[12333, 5221])).
% 3.74/3.98 tff(12335,plain,
% 3.74/3.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 3.74/3.98 inference(rewrite,[status(thm)],[])).
% 3.74/3.98 tff(12336,plain,
% 3.74/3.98 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 3.74/3.98 inference(rewrite,[status(thm)],[])).
% 3.74/3.98 tff(12337,plain,
% 3.74/3.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))))),
% 3.74/3.98 inference(monotonicity,[status(thm)],[12336])).
% 3.74/3.98 tff(12338,plain,
% 3.74/3.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 3.74/3.98 inference(transitivity,[status(thm)],[12337, 12335])).
% 3.74/3.98 tff(12339,plain,
% 3.74/3.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 3.74/3.98 inference(quant_inst,[status(thm)],[])).
% 3.74/3.98 tff(12340,plain,
% 3.74/3.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))),
% 3.74/3.98 inference(modus_ponens,[status(thm)],[12339, 12338])).
% 3.74/3.98 tff(12341,plain,
% 3.74/3.98 (~b(s(s(s(z))), s(z))),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[12340, 178, 3461, 1030, 12121, 12334])).
% 3.74/3.98 tff(12342,plain,
% 3.74/3.98 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.74/3.98 inference(modus_ponens,[status(thm)],[12341, 12295])).
% 3.74/3.98 tff(12343,plain,
% 3.74/3.98 (r(s(s(s(elem!1))), s(elem!1))),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[373, 12342, 12049])).
% 3.74/3.98 tff(12344,plain,
% 3.74/3.98 (~r(elem!1, s(s(s(elem!1))))),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[1591, 12343, 1587])).
% 3.74/3.98 tff(12345,plain,
% 3.74/3.98 (b(elem!1, s(s(s(elem!1))))),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[2054, 12344, 12085])).
% 3.74/3.98 tff(12346,plain,
% 3.74/3.98 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[5490, 12345, 12065, 12063, 1029])).
% 3.74/3.98 tff(12347,plain,
% 3.74/3.98 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[3375, 12346, 12080])).
% 3.74/3.98 tff(12348,plain,
% 3.74/3.98 (r(s(s(z)), s(s(s(elem!1))))),
% 3.74/3.98 inference(modus_ponens,[status(thm)],[12347, 12082])).
% 3.74/3.98 tff(12349,plain,
% 3.74/3.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 3.74/3.98 inference(rewrite,[status(thm)],[])).
% 3.74/3.98 tff(12350,plain,
% 3.74/3.98 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), 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)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 3.74/3.98 inference(rewrite,[status(thm)],[])).
% 3.74/3.98 tff(12351,plain,
% 3.74/3.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z))))))),
% 3.74/3.98 inference(monotonicity,[status(thm)],[12350])).
% 3.74/3.98 tff(12352,plain,
% 3.74/3.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 3.74/3.98 inference(transitivity,[status(thm)],[12351, 12349])).
% 3.74/3.98 tff(12353,plain,
% 3.74/3.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 3.74/3.98 inference(quant_inst,[status(thm)],[])).
% 3.74/3.98 tff(12354,plain,
% 3.74/3.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z))))),
% 3.74/3.98 inference(modus_ponens,[status(thm)],[12353, 12352])).
% 3.74/3.98 tff(12355,plain,
% 3.74/3.98 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[12354, 178, 3461, 168, 202, 12334])).
% 3.74/3.98 tff(12356,plain,
% 3.74/3.98 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.74/3.98 inference(modus_ponens,[status(thm)],[12355, 5217])).
% 3.74/3.98 tff(12357,plain,
% 3.74/3.98 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[1750, 12356, 12077])).
% 3.74/3.98 tff(12358,plain,
% 3.74/3.98 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[4036, 12357, 12068])).
% 3.74/3.98 tff(12359,plain,
% 3.74/3.98 ($false),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[12358, 12348])).
% 3.74/3.98 tff(12360,plain,((~(elem!1 = z)) | (~r(elem!1, s(elem!1))) | (~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(s(s(z)))))) | (s(s(s(s(z)))) = s(elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | r(s(elem!1), s(s(z))) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.98 tff(12361,plain,
% 3.74/3.98 (~(elem!1 = z)),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[12360, 927, 3461, 168, 202, 1687, 2169, 147, 3261, 1587, 853])).
% 3.74/3.98 tff(12362,plain,
% 3.74/3.98 (r(elem!1, z)),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[498, 12361, 5723])).
% 3.74/3.98 tff(12363,plain,
% 3.74/3.98 (~r(z, s(elem!1))),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[12189, 12362, 1587])).
% 3.74/3.98 tff(12364,plain,
% 3.74/3.98 (b(z, s(elem!1))),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[2351, 12363])).
% 3.74/3.98 tff(12365,plain,
% 3.74/3.98 (~b(s(elem!1), s(s(s(s(z)))))),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[11771, 12364])).
% 3.74/3.98 tff(12366,plain,
% 3.74/3.98 (r(s(elem!1), s(s(s(s(z)))))),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[1084, 12365, 1369])).
% 3.74/3.98 tff(12367,plain,
% 3.74/3.98 (~r(s(s(z)), s(elem!1))),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[5758, 12366, 147])).
% 3.74/3.98 tff(12368,plain,
% 3.74/3.98 (s(elem!1) = s(s(z))),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[12205, 12367, 853, 3461, 12364, 927])).
% 3.74/3.98 tff(12369,plain,
% 3.74/3.98 (r(z, s(elem!1)) <=> r(z, s(s(z)))),
% 3.74/3.98 inference(monotonicity,[status(thm)],[12368])).
% 3.74/3.98 tff(12370,plain,
% 3.74/3.98 (r(z, s(s(z))) <=> r(z, s(elem!1))),
% 3.74/3.98 inference(symmetry,[status(thm)],[12369])).
% 3.74/3.98 tff(12371,plain,
% 3.74/3.98 (r(z, s(elem!1))),
% 3.74/3.98 inference(modus_ponens,[status(thm)],[3261, 12370])).
% 3.74/3.98 tff(12372,plain,
% 3.74/3.98 ($false),
% 3.74/3.98 inference(unit_resolution,[status(thm)],[12363, 12371])).
% 3.74/3.98 tff(12373,plain,(r(s(elem!1), s(s(z))) | (~r(z, s(s(z)))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (s(elem!1) = s(s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~r(elem!1, s(elem!1))) | b(elem!1, z) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.99 tff(12374,plain,
% 3.74/3.99 (~b(s(s(s(s(z)))), s(s(z)))),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[12373, 5723, 853, 3461, 147, 1369, 1687, 168, 3261, 12213, 12294])).
% 3.74/3.99 tff(12375,plain,
% 3.74/3.99 ($false),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[102, 12374, 12212])).
% 3.74/3.99 tff(12376,plain,(b(elem!1, z) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (s(elem!1) = s(s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))) | b(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.99 tff(12377,plain,
% 3.74/3.99 (b(elem!1, s(elem!1))),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[12376, 12009, 5619, 147, 11753, 11751, 11749, 3261, 5723])).
% 3.74/3.99 tff(12378,plain,
% 3.74/3.99 (b(elem!1, s(s(z)))),
% 3.74/3.99 inference(modus_ponens,[status(thm)],[12377, 12021])).
% 3.74/3.99 tff(12379,plain,
% 3.74/3.99 ((~(s(z) = z)) <=> (~(z = elem!1))),
% 3.74/3.99 inference(monotonicity,[status(thm)],[12016])).
% 3.74/3.99 tff(12380,plain,
% 3.74/3.99 (~(z = elem!1)),
% 3.74/3.99 inference(modus_ponens,[status(thm)],[1476, 12379])).
% 3.74/3.99 tff(12381,plain,
% 3.74/3.99 (~b(elem!1, s(s(s(s(z)))))),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[11980, 12380, 147, 469, 3261, 11784, 5723, 12, 551, 12019, 5618])).
% 3.74/3.99 tff(12382,plain,
% 3.74/3.99 (r(elem!1, s(s(s(s(z)))))),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[483, 12381, 469])).
% 3.74/3.99 tff(12383,plain,
% 3.74/3.99 (~r(s(s(z)), elem!1)),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[8763, 12382, 147])).
% 3.74/3.99 tff(12384,plain,
% 3.74/3.99 (b(s(s(z)), elem!1)),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[448, 12383, 12])).
% 3.74/3.99 tff(12385,plain,
% 3.74/3.99 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[11924, 12384, 11751, 3261, 193, 11784, 12378, 12020, 5619])).
% 3.74/3.99 tff(12386,plain,
% 3.74/3.99 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[12005, 12384, 147, 11784, 12378, 12382])).
% 3.74/3.99 tff(12387,plain,
% 3.74/3.99 ($false),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[84, 12386, 12385])).
% 3.74/3.99 tff(12388,plain,(b(s(elem!1), s(s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (s(s(z)) = elem!1) | (elem!1 = s(s(s(s(z))))) | b(elem!1, z) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 3.74/3.99 tff(12389,plain,
% 3.74/3.99 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[12388, 5723, 3261, 193, 12, 305, 469, 5618])).
% 3.74/3.99 tff(12390,plain,
% 3.74/3.99 (b(s(s(z)), s(s(s(s(z)))))),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[164, 12389])).
% 3.74/3.99 tff(12391,plain,
% 3.74/3.99 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 3.74/3.99 inference(monotonicity,[status(thm)],[518])).
% 3.74/3.99 tff(12392,plain,
% 3.74/3.99 (b(elem!1, s(s(z)))),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[11793, 1477, 3261, 5723, 5618])).
% 3.74/3.99 tff(12393,plain,
% 3.74/3.99 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[2832, 515])).
% 3.74/3.99 tff(12394,plain,
% 3.74/3.99 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[11826, 118, 3261, 107])).
% 3.74/3.99 tff(12395,plain,
% 3.74/3.99 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[133, 12394])).
% 3.74/3.99 tff(12396,plain,
% 3.74/3.99 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[3889, 118, 193, 107])).
% 3.74/3.99 tff(12397,plain,
% 3.74/3.99 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[84, 12396])).
% 3.74/3.99 tff(12398,plain,
% 3.74/3.99 ($false),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[11898, 12397, 12395, 193, 11751, 11753, 3461])).
% 3.74/3.99 tff(12399,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.99 tff(12400,plain,
% 3.74/3.99 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[12399, 3261, 5619, 193])).
% 3.74/3.99 tff(12401,plain,
% 3.74/3.99 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[2960, 41, 12400, 3574])).
% 3.74/3.99 tff(12402,plain,
% 3.74/3.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), 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))))))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), 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))))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 3.74/3.99 inference(rewrite,[status(thm)],[])).
% 3.74/3.99 tff(12403,plain,
% 3.74/3.99 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(z)), 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))))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 3.74/3.99 inference(rewrite,[status(thm)],[])).
% 3.74/3.99 tff(12404,plain,
% 3.74/3.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), 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))))))), z)) | (~b(z, s(s(s(s(z))))))))),
% 3.74/3.99 inference(monotonicity,[status(thm)],[12403])).
% 3.74/3.99 tff(12405,plain,
% 3.74/3.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), 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))))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 3.74/3.99 inference(transitivity,[status(thm)],[12404, 12402])).
% 3.74/3.99 tff(12406,plain,
% 3.74/3.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 3.74/3.99 inference(quant_inst,[status(thm)],[])).
% 3.74/3.99 tff(12407,plain,
% 3.74/3.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z))))))),
% 3.74/3.99 inference(modus_ponens,[status(thm)],[12406, 12405])).
% 3.74/3.99 tff(12408,plain,
% 3.74/3.99 ($false),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[12407, 178, 3461, 1687, 167, 146, 1146])).
% 3.74/3.99 tff(12409,plain,((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.99 tff(12410,plain,
% 3.74/3.99 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[12409, 167, 11751, 5619, 12401])).
% 3.74/3.99 tff(12411,plain,
% 3.74/3.99 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[133, 12410])).
% 3.74/3.99 tff(12412,plain,
% 3.74/3.99 (r(elem!1, z)),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[498, 1477, 5723])).
% 3.74/3.99 tff(12413,plain,
% 3.74/3.99 (~b(s(s(z)), elem!1)),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[11831, 12412, 12411, 12393, 3261, 12392])).
% 3.74/3.99 tff(12414,plain,
% 3.74/3.99 (r(s(s(z)), elem!1)),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[448, 12413, 12])).
% 3.74/3.99 tff(12415,plain,
% 3.74/3.99 (~r(s(s(s(s(z)))), elem!1)),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[3329, 12414, 193])).
% 3.74/3.99 tff(12416,plain,
% 3.74/3.99 (b(s(s(s(s(z)))), elem!1)),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[3142, 12415, 323])).
% 3.74/3.99 tff(12417,plain,
% 3.74/3.99 (b(s(s(s(s(z)))), s(z))),
% 3.74/3.99 inference(modus_ponens,[status(thm)],[12416, 12391])).
% 3.74/3.99 tff(12418,plain,
% 3.74/3.99 ((~(s(z) = z)) <=> (~(z = elem!1))),
% 3.74/3.99 inference(monotonicity,[status(thm)],[1472])).
% 3.74/3.99 tff(12419,plain,
% 3.74/3.99 (~(z = elem!1)),
% 3.74/3.99 inference(modus_ponens,[status(thm)],[1476, 12418])).
% 3.74/3.99 tff(12420,plain,
% 3.74/3.99 (~r(z, elem!1)),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[8412, 12414, 3261])).
% 3.74/3.99 tff(12421,plain,
% 3.74/3.99 (b(z, elem!1)),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[585, 12420, 12419])).
% 3.74/3.99 tff(12422,plain,
% 3.74/3.99 (b(z, s(z))),
% 3.74/3.99 inference(modus_ponens,[status(thm)],[12421, 519])).
% 3.74/3.99 tff(12423,plain,
% 3.74/3.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 3.74/3.99 inference(rewrite,[status(thm)],[])).
% 3.74/3.99 tff(12424,plain,
% 3.74/3.99 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 3.74/3.99 inference(rewrite,[status(thm)],[])).
% 3.74/3.99 tff(12425,plain,
% 3.74/3.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 3.74/3.99 inference(monotonicity,[status(thm)],[12424])).
% 3.74/3.99 tff(12426,plain,
% 3.74/3.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 3.74/3.99 inference(transitivity,[status(thm)],[12425, 12423])).
% 3.74/3.99 tff(12427,plain,
% 3.74/3.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 3.74/3.99 inference(quant_inst,[status(thm)],[])).
% 3.74/3.99 tff(12428,plain,
% 3.74/3.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 3.74/3.99 inference(modus_ponens,[status(thm)],[12427, 12426])).
% 3.74/3.99 tff(12429,plain,
% 3.74/3.99 ($false),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[12428, 178, 5619, 11751, 167, 12422, 12417])).
% 3.74/3.99 tff(12430,plain,((~(s(elem!1) = s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (s(s(s(s(z)))) = elem!1) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (s(s(z)) = elem!1) | b(elem!1, z) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 3.74/3.99 tff(12431,plain,
% 3.74/3.99 (~(s(elem!1) = s(s(z)))),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[12430, 12390, 551, 193, 3261, 12, 5723, 5618])).
% 3.74/3.99 tff(12432,plain,
% 3.74/3.99 (r(s(elem!1), s(s(z)))),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[421, 12431, 305])).
% 3.74/3.99 tff(12433,plain,
% 3.74/3.99 (~r(s(elem!1), s(s(s(s(z)))))),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[3949, 363, 193])).
% 3.74/3.99 tff(12434,plain,
% 3.74/3.99 (b(s(elem!1), s(s(s(s(z)))))),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[1084, 12433, 1369])).
% 3.74/3.99 tff(12435,plain,
% 3.74/3.99 ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[11770, 178, 853, 11751, 11753])).
% 3.74/3.99 tff(12436,plain,
% 3.74/3.99 ($false),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[12435, 11764, 12434])).
% 3.74/3.99 tff(12437,plain,((~r(s(elem!1), s(s(z)))) | (~b(s(elem!1), z)) | (s(elem!1) = s(s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.99 tff(12438,plain,
% 3.74/3.99 (s(elem!1) = s(s(s(s(z))))),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[12437, 12432, 11749, 3261, 193])).
% 3.74/3.99 tff(12439,plain,
% 3.74/3.99 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 3.74/3.99 inference(monotonicity,[status(thm)],[12438])).
% 3.74/3.99 tff(12440,plain,
% 3.74/3.99 (elem!1 = s(s(s(z)))),
% 3.74/3.99 inference(transitivity,[status(thm)],[517, 12439, 11])).
% 3.74/3.99 tff(12441,plain,
% 3.74/3.99 ((z = elem!1) <=> (z = s(s(s(z))))),
% 3.74/3.99 inference(monotonicity,[status(thm)],[12440])).
% 3.74/3.99 tff(12442,plain,
% 3.74/3.99 ((z = elem!1) <=> (s(s(s(z))) = z)),
% 3.74/3.99 inference(transitivity,[status(thm)],[12441, 4912])).
% 3.74/3.99 tff(12443,plain,
% 3.74/3.99 ((s(s(s(z))) = z) <=> (z = elem!1)),
% 3.74/3.99 inference(symmetry,[status(thm)],[12442])).
% 3.74/3.99 tff(12444,plain,
% 3.74/3.99 ((s(s(s(z))) = z) <=> (elem!1 = z)),
% 3.74/3.99 inference(transitivity,[status(thm)],[12443, 314])).
% 3.74/3.99 tff(12445,plain,
% 3.74/3.99 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = z))),
% 3.74/3.99 inference(monotonicity,[status(thm)],[12444])).
% 3.74/3.99 tff(12446,plain,
% 3.74/3.99 (~(elem!1 = z)),
% 3.74/3.99 inference(modus_ponens,[status(thm)],[77, 12445])).
% 3.74/3.99 tff(12447,plain,
% 3.74/3.99 (b(elem!1, s(s(z)))),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[11793, 12446, 3261, 5723, 5618])).
% 3.74/3.99 tff(12448,plain,
% 3.74/3.99 (b(s(s(s(s(z)))), elem!1)),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[3142, 8690, 323])).
% 3.74/3.99 tff(12449,plain,
% 3.74/3.99 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.74/3.99 inference(modus_ponens,[status(thm)],[12448, 1278])).
% 3.74/3.99 tff(12450,plain,
% 3.74/3.99 (b(z, elem!1)),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[585, 12234, 11796])).
% 3.74/3.99 tff(12451,plain,
% 3.74/3.99 (b(z, s(s(s(z))))),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[1238, 12450, 1117])).
% 3.74/3.99 tff(12452,plain,
% 3.74/3.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(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(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(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(z, s(s(s(z))))))),
% 3.74/3.99 inference(rewrite,[status(thm)],[])).
% 3.74/3.99 tff(12453,plain,
% 3.74/3.99 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), z)) | (~b(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(z, s(s(s(z))))))),
% 3.74/3.99 inference(rewrite,[status(thm)],[])).
% 3.74/3.99 tff(12454,plain,
% 3.74/3.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(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(z, s(s(s(z)))))))),
% 3.74/3.99 inference(monotonicity,[status(thm)],[12453])).
% 3.74/3.99 tff(12455,plain,
% 3.74/3.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(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(z, s(s(s(z))))))),
% 3.74/3.99 inference(transitivity,[status(thm)],[12454, 12452])).
% 3.74/3.99 tff(12456,plain,
% 3.74/3.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 3.74/3.99 inference(quant_inst,[status(thm)],[])).
% 3.74/3.99 tff(12457,plain,
% 3.74/3.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))),
% 3.74/3.99 inference(modus_ponens,[status(thm)],[12456, 12455])).
% 3.74/3.99 tff(12458,plain,
% 3.74/3.99 ($false),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[12457, 178, 3461, 11751, 167, 12451, 12449])).
% 3.74/3.99 tff(12459,plain,((~r(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~(s(elem!1) = s(s(s(s(z)))))) | (s(s(s(s(z)))) = elem!1) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.99 tff(12460,plain,
% 3.74/3.99 (~r(s(s(z)), elem!1)),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[12459, 12438, 12390, 5619, 551, 193, 3261])).
% 3.74/3.99 tff(12461,plain,
% 3.74/3.99 (b(s(s(z)), elem!1)),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[448, 12460, 12])).
% 3.74/3.99 tff(12462,plain,
% 3.74/3.99 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[12409, 12390, 11751, 5619, 12401])).
% 3.74/3.99 tff(12463,plain,
% 3.74/3.99 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[133, 12462])).
% 3.74/3.99 tff(12464,plain,
% 3.74/3.99 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 3.74/3.99 inference(symmetry,[status(thm)],[12439])).
% 3.74/3.99 tff(12465,plain,
% 3.74/3.99 (s(s(s(z))) = elem!1),
% 3.74/3.99 inference(transitivity,[status(thm)],[61, 12464, 304])).
% 3.74/3.99 tff(12466,plain,
% 3.74/3.99 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 3.74/3.99 inference(monotonicity,[status(thm)],[12465])).
% 3.74/3.99 tff(12467,plain,
% 3.74/3.99 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.74/3.99 inference(transitivity,[status(thm)],[12466, 836])).
% 3.74/3.99 tff(12468,plain,
% 3.74/3.99 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(s(s(s(s(z)))))))))),
% 3.74/3.99 inference(monotonicity,[status(thm)],[12467])).
% 3.74/3.99 tff(12469,plain,
% 3.74/3.99 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.74/3.99 inference(modus_ponens,[status(thm)],[1104, 12468])).
% 3.74/3.99 tff(12470,plain,
% 3.74/3.99 (r(elem!1, z)),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[498, 12446, 5723])).
% 3.74/3.99 tff(12471,plain,
% 3.74/3.99 ($false),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[11831, 12470, 12469, 12463, 12461, 3261, 12447])).
% 3.74/3.99 tff(12472,plain,(b(elem!1, z) | (~r(z, s(s(z)))) | r(s(s(z)), z) | (s(s(z)) = elem!1) | (~r(s(s(s(s(z)))), s(s(z)))) | b(s(elem!1), s(s(z))) | (elem!1 = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.99 tff(12473,plain,
% 3.74/3.99 (b(elem!1, z)),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[12472, 469, 5618, 12, 193, 305, 3261])).
% 3.74/3.99 tff(12474,plain,
% 3.74/3.99 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[11783, 147, 11753, 11751, 853, 3261, 305])).
% 3.74/3.99 tff(12475,plain,
% 3.74/3.99 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[703, 12474])).
% 3.74/3.99 tff(12476,plain,
% 3.74/3.99 (~r(s(s(z)), elem!1)),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[12239, 147, 506, 469, 11751, 551, 6992, 3261])).
% 3.74/3.99 tff(12477,plain,
% 3.74/3.99 (b(s(s(z)), elem!1)),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[448, 12476, 12])).
% 3.74/3.99 tff(12478,plain,
% 3.74/3.99 (~b(z, elem!1)),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[12263, 12477, 3461, 506, 11751, 469, 147, 312])).
% 3.74/3.99 tff(12479,plain,
% 3.74/3.99 (r(z, elem!1)),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[585, 12478, 6992])).
% 3.74/3.99 tff(12480,plain,
% 3.74/3.99 (~r(elem!1, s(s(z)))),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[4862, 12479, 3261])).
% 3.74/3.99 tff(12481,plain,
% 3.74/3.99 (b(elem!1, s(s(z)))),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[467, 12480, 312])).
% 3.74/3.99 tff(12482,plain,
% 3.74/3.99 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[12399, 3261, 3461, 193])).
% 3.74/3.99 tff(12483,plain,
% 3.74/3.99 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.74/3.99 inference(unit_resolution,[status(thm)],[2960, 41, 12482, 3574])).
% 3.74/3.99 tff(12484,plain,
% 3.74/3.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 3.74/3.99 inference(rewrite,[status(thm)],[])).
% 3.74/3.99 tff(12485,plain,
% 3.74/3.99 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 3.74/3.99 inference(rewrite,[status(thm)],[])).
% 3.74/3.99 tff(12486,plain,
% 3.74/3.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))))),
% 3.74/3.99 inference(monotonicity,[status(thm)],[12485])).
% 3.74/3.99 tff(12487,plain,
% 3.74/3.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 3.74/3.99 inference(transitivity,[status(thm)],[12486, 12484])).
% 3.74/3.99 tff(12488,plain,
% 3.74/3.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.74/3.99 inference(quant_inst,[status(thm)],[])).
% 3.74/3.99 tff(12489,plain,
% 3.74/4.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 3.74/4.00 inference(modus_ponens,[status(thm)],[12488, 12487])).
% 3.74/4.00 tff(12490,plain,
% 3.74/4.00 ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[12489, 178, 506, 3461, 12483])).
% 3.74/4.00 tff(12491,plain,
% 3.74/4.00 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[12490, 12481])).
% 3.74/4.00 tff(12492,plain,
% 3.74/4.00 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[3444, 12491, 12475])).
% 3.74/4.00 tff(12493,plain,
% 3.74/4.00 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[11871, 12481, 3461, 147, 12474, 12477, 12479])).
% 3.74/4.00 tff(12494,plain,
% 3.74/4.00 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[84, 12493])).
% 3.74/4.00 tff(12495,plain,
% 3.74/4.00 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[11898, 12494, 193, 11751, 11753, 3461])).
% 3.74/4.00 tff(12496,plain,
% 3.74/4.00 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[133, 12495])).
% 3.74/4.00 tff(12497,plain,
% 3.74/4.00 ($false),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[11025, 118, 12479, 12496, 12492])).
% 3.74/4.00 tff(12498,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~r(z, s(s(z)))) | (elem!1 = s(s(s(s(z))))) | (s(s(z)) = elem!1) | (~b(s(elem!1), z)) | b(s(elem!1), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.74/4.00 tff(12499,plain,
% 3.74/4.00 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[12498, 12473, 5619, 193, 3261, 469, 12, 11749, 305])).
% 3.74/4.00 tff(12500,plain,
% 3.74/4.00 (b(s(s(z)), s(s(s(s(z)))))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[164, 12499])).
% 3.74/4.00 tff(12501,plain,
% 3.74/4.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 3.74/4.00 inference(rewrite,[status(thm)],[])).
% 3.74/4.00 tff(12502,plain,
% 3.74/4.00 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z))))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 3.74/4.00 inference(rewrite,[status(thm)],[])).
% 3.74/4.00 tff(12503,plain,
% 3.74/4.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 3.74/4.00 inference(monotonicity,[status(thm)],[12502])).
% 3.74/4.00 tff(12504,plain,
% 3.74/4.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 3.74/4.00 inference(transitivity,[status(thm)],[12503, 12501])).
% 3.74/4.00 tff(12505,plain,
% 3.74/4.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))))),
% 3.74/4.00 inference(quant_inst,[status(thm)],[])).
% 3.74/4.00 tff(12506,plain,
% 3.74/4.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 3.74/4.00 inference(modus_ponens,[status(thm)],[12505, 12504])).
% 3.74/4.00 tff(12507,plain,
% 3.74/4.00 (~b(elem!1, s(s(z)))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[12506, 178, 12473, 5619, 11751, 12500])).
% 3.74/4.00 tff(12508,plain,
% 3.74/4.00 (r(elem!1, s(s(z)))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[467, 12507, 312])).
% 3.74/4.00 tff(12509,plain,
% 3.74/4.00 (~r(elem!1, s(s(s(s(z)))))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[3785, 12508, 193])).
% 3.74/4.00 tff(12510,plain,
% 3.74/4.00 (b(elem!1, s(s(s(s(z)))))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[483, 12509, 469])).
% 3.74/4.00 tff(12511,plain,
% 3.74/4.00 (~(z = elem!1)),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[6991, 12473])).
% 3.74/4.00 tff(12512,plain,
% 3.74/4.00 (~r(z, elem!1)),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[4862, 12508, 3261])).
% 3.74/4.00 tff(12513,plain,
% 3.74/4.00 (b(z, elem!1)),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[585, 12512, 12511])).
% 3.74/4.00 tff(12514,plain,
% 3.74/4.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 3.74/4.00 inference(rewrite,[status(thm)],[])).
% 3.74/4.00 tff(12515,plain,
% 3.74/4.00 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 3.74/4.00 inference(rewrite,[status(thm)],[])).
% 3.74/4.00 tff(12516,plain,
% 3.74/4.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))))),
% 3.74/4.00 inference(monotonicity,[status(thm)],[12515])).
% 3.74/4.00 tff(12517,plain,
% 3.74/4.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 3.74/4.00 inference(transitivity,[status(thm)],[12516, 12514])).
% 3.74/4.00 tff(12518,plain,
% 3.74/4.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)))),
% 3.74/4.00 inference(quant_inst,[status(thm)],[])).
% 3.74/4.00 tff(12519,plain,
% 3.74/4.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))),
% 3.74/4.00 inference(modus_ponens,[status(thm)],[12518, 12517])).
% 3.74/4.00 tff(12520,plain,
% 3.74/4.00 ((~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z))))))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[12519, 178, 12473, 11751, 11753])).
% 3.74/4.00 tff(12521,plain,
% 3.74/4.00 ($false),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[12520, 12513, 12510])).
% 3.74/4.00 tff(12522,plain,((elem!1 = s(s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (s(s(z)) = elem!1) | b(s(elem!1), s(s(z))) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 3.74/4.00 tff(12523,plain,
% 3.74/4.00 (elem!1 = s(s(s(s(z))))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[12522, 305, 193, 12, 3261, 5618])).
% 3.74/4.00 tff(12524,plain,
% 3.74/4.00 (s(elem!1) = s(s(s(s(s(z)))))),
% 3.74/4.00 inference(monotonicity,[status(thm)],[12523])).
% 3.74/4.00 tff(12525,plain,
% 3.74/4.00 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(s(s(z)))))),
% 3.74/4.00 inference(monotonicity,[status(thm)],[12523])).
% 3.74/4.00 tff(12526,plain,
% 3.74/4.00 ((s(elem!1) = elem!1) <=> (s(s(s(s(z)))) = s(elem!1))),
% 3.74/4.00 inference(transitivity,[status(thm)],[12525, 2163])).
% 3.74/4.00 tff(12527,plain,
% 3.74/4.00 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(s(s(z)))))),
% 3.74/4.00 inference(transitivity,[status(thm)],[12526, 2164])).
% 3.74/4.00 tff(12528,plain,
% 3.74/4.00 ((~(s(elem!1) = elem!1)) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 3.74/4.00 inference(monotonicity,[status(thm)],[12527])).
% 3.74/4.00 tff(12529,plain,
% 3.74/4.00 (s(s(s(s(z)))) = elem!1),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[325, 12523])).
% 3.74/4.00 tff(12530,plain,
% 3.74/4.00 (~(s(s(elem!1)) = elem!1)),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[338, 12529, 12])).
% 3.74/4.00 tff(12531,plain,
% 3.74/4.00 (~(s(elem!1) = elem!1)),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[672, 12530])).
% 3.74/4.00 tff(12532,plain,
% 3.74/4.00 (~(s(elem!1) = s(s(s(s(z)))))),
% 3.74/4.00 inference(modus_ponens,[status(thm)],[12531, 12528])).
% 3.74/4.00 tff(12533,plain,
% 3.74/4.00 (~r(s(elem!1), s(s(z)))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[12437, 12532, 11749, 3261, 193])).
% 3.74/4.00 tff(12534,plain,
% 3.74/4.00 (s(elem!1) = s(s(z))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[421, 12533, 305])).
% 3.74/4.00 tff(12535,plain,
% 3.74/4.00 (s(s(z)) = s(elem!1)),
% 3.74/4.00 inference(symmetry,[status(thm)],[12534])).
% 3.74/4.00 tff(12536,plain,
% 3.74/4.00 (s(s(z)) = s(s(s(s(s(z)))))),
% 3.74/4.00 inference(transitivity,[status(thm)],[12535, 12524])).
% 3.74/4.00 tff(12537,plain,
% 3.74/4.00 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(z))))))),
% 3.74/4.00 inference(monotonicity,[status(thm)],[12536])).
% 3.74/4.00 tff(12538,plain,
% 3.74/4.00 (s(z) = s(s(s(s(z))))),
% 3.74/4.00 inference(transitivity,[status(thm)],[71, 12537, 53])).
% 3.74/4.00 tff(12539,plain,
% 3.74/4.00 (inj_0(s(z)) = inj_0(s(s(s(s(z)))))),
% 3.74/4.00 inference(monotonicity,[status(thm)],[12538])).
% 3.74/4.00 tff(12540,plain,
% 3.74/4.00 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 3.74/4.00 inference(symmetry,[status(thm)],[12539])).
% 3.74/4.00 tff(12541,plain,
% 3.74/4.00 (s(s(s(z))) = s(s(s(s(s(s(z))))))),
% 3.74/4.00 inference(monotonicity,[status(thm)],[12536])).
% 3.74/4.00 tff(12542,plain,
% 3.74/4.00 (s(s(s(s(s(s(z)))))) = s(s(s(z)))),
% 3.74/4.00 inference(symmetry,[status(thm)],[12541])).
% 3.74/4.00 tff(12543,plain,
% 3.74/4.00 (s(s(s(s(s(s(z)))))) = z),
% 3.74/4.00 inference(transitivity,[status(thm)],[12542, 61, 12540, 51])).
% 3.74/4.00 tff(12544,plain,
% 3.74/4.00 ($false),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[433, 12543])).
% 3.74/4.00 tff(12545,plain,(b(s(elem!1), s(s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (s(s(z)) = elem!1) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 3.74/4.00 tff(12546,plain,
% 3.74/4.00 (b(s(elem!1), s(s(z)))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[12545, 3261, 103, 12, 5618])).
% 3.74/4.00 tff(12547,plain,
% 3.74/4.00 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 3.74/4.00 inference(monotonicity,[status(thm)],[1117])).
% 3.74/4.00 tff(12548,plain,
% 3.74/4.00 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(elem!1), s(s(z)))),
% 3.74/4.00 inference(symmetry,[status(thm)],[12547])).
% 3.74/4.00 tff(12549,plain,
% 3.74/4.00 ((~b(s(s(s(s(z)))), s(s(z)))) <=> (~b(s(elem!1), s(s(z))))),
% 3.74/4.00 inference(monotonicity,[status(thm)],[12548])).
% 3.74/4.00 tff(12550,plain,
% 3.74/4.00 (~b(s(elem!1), s(s(z)))),
% 3.74/4.00 inference(modus_ponens,[status(thm)],[86, 12549])).
% 3.74/4.00 tff(12551,plain,
% 3.74/4.00 ($false),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[1070, 12550])).
% 3.74/4.00 tff(12552,plain,((~(s(elem!1) = s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z)))) | b(s(s(s(s(z)))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.74/4.00 tff(12553,plain,
% 3.74/4.00 (~(s(elem!1) = s(s(s(s(z)))))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[12552, 12546, 86])).
% 3.74/4.00 tff(12554,plain,
% 3.74/4.00 ((~b(elem!1, z)) <=> (~b(s(s(s(s(z)))), z))),
% 3.74/4.00 inference(monotonicity,[status(thm)],[3168])).
% 3.74/4.00 tff(12555,plain,
% 3.74/4.00 (~b(s(s(s(s(z)))), z)),
% 3.74/4.00 inference(modus_ponens,[status(thm)],[5723, 12554])).
% 3.74/4.00 tff(12556,plain,
% 3.74/4.00 ($false),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[168, 12555])).
% 3.74/4.00 tff(12557,plain,((~(elem!1 = s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 3.74/4.00 tff(12558,plain,
% 3.74/4.00 (~(elem!1 = s(s(s(s(z)))))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[12557, 5723, 11753])).
% 3.74/4.00 tff(12559,plain,
% 3.74/4.00 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 3.74/4.00 inference(symmetry,[status(thm)],[2492])).
% 3.74/4.00 tff(12560,plain,
% 3.74/4.00 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[12008, 1117, 147, 3261, 193, 12, 469, 5723, 5618])).
% 3.74/4.00 tff(12561,plain,
% 3.74/4.00 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 3.74/4.00 inference(symmetry,[status(thm)],[12560])).
% 3.74/4.00 tff(12562,plain,
% 3.74/4.00 (s(s(s(s(s(s(s(z))))))) = s(s(s(z)))),
% 3.74/4.00 inference(transitivity,[status(thm)],[12561, 517, 12559, 11])).
% 3.74/4.00 tff(12563,plain,
% 3.74/4.00 ($false),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[1104, 12562])).
% 3.74/4.00 tff(12564,plain,((~(s(elem!1) = s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (s(s(z)) = elem!1) | (elem!1 = s(s(s(s(z))))) | b(elem!1, z) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 3.74/4.00 tff(12565,plain,
% 3.74/4.00 (~(s(elem!1) = s(s(s(s(z)))))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[12564, 5723, 3261, 193, 12, 469, 10794, 5618])).
% 3.74/4.00 tff(12566,plain,
% 3.74/4.00 (b(s(elem!1), s(s(z)))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[12545, 3261, 193, 12, 5618])).
% 3.74/4.00 tff(12567,plain,
% 3.74/4.00 (r(elem!1, z)),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[498, 2809, 5723])).
% 3.74/4.00 tff(12568,plain,
% 3.74/4.00 (~r(elem!1, s(elem!1))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[2711, 12567, 844])).
% 3.74/4.00 tff(12569,plain,
% 3.74/4.00 (r(s(elem!1), z)),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[774, 766])).
% 3.74/4.00 tff(12570,plain,
% 3.74/4.00 (~(s(s(z)) = s(elem!1))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[11742, 12569, 5618])).
% 3.74/4.00 tff(12571,plain,
% 3.74/4.00 (~(s(elem!1) = s(s(z)))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[1362, 12570])).
% 3.74/4.00 tff(12572,plain,
% 3.74/4.00 (r(s(elem!1), z) <=> r(elem!1, z)),
% 3.74/4.00 inference(monotonicity,[status(thm)],[668])).
% 3.74/4.00 tff(12573,plain,
% 3.74/4.00 (r(elem!1, z)),
% 3.74/4.00 inference(modus_ponens,[status(thm)],[844, 12572])).
% 3.74/4.00 tff(12574,plain,
% 3.74/4.00 (s(s(elem!1)) = elem!1),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[672, 668])).
% 3.74/4.00 tff(12575,plain,
% 3.74/4.00 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[2510, 12574, 2508])).
% 3.74/4.00 tff(12576,plain,
% 3.74/4.00 (elem!1 = s(s(elem!1))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[1546, 12574])).
% 3.74/4.00 tff(12577,plain,
% 3.74/4.00 (s(s(s(elem!1))) = s(elem!1)),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[1539, 12576])).
% 3.74/4.00 tff(12578,plain,
% 3.74/4.00 (elem!1 = s(s(s(s(elem!1))))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[1509, 12577])).
% 3.74/4.00 tff(12579,plain,
% 3.74/4.00 (s(s(s(s(elem!1)))) = elem!1),
% 3.74/4.00 inference(symmetry,[status(thm)],[12578])).
% 3.74/4.00 tff(12580,plain,
% 3.74/4.00 (r(s(s(s(s(elem!1)))), z) <=> r(elem!1, z)),
% 3.74/4.00 inference(monotonicity,[status(thm)],[12579])).
% 3.74/4.00 tff(12581,plain,
% 3.74/4.00 (r(elem!1, z) <=> r(s(s(s(s(elem!1)))), z)),
% 3.74/4.00 inference(symmetry,[status(thm)],[12580])).
% 3.74/4.00 tff(12582,plain,
% 3.74/4.00 (r(s(s(s(s(elem!1)))), z)),
% 3.74/4.00 inference(modus_ponens,[status(thm)],[12573, 12581])).
% 3.74/4.00 tff(12583,plain,
% 3.74/4.00 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[5194, 12582, 3261])).
% 3.74/4.00 tff(12584,plain,
% 3.74/4.00 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[1170, 12583])).
% 3.74/4.00 tff(12585,plain,
% 3.74/4.00 (b(elem!1, s(s(z)))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[3901, 12584, 12578])).
% 3.74/4.00 tff(12586,plain,
% 3.74/4.00 ((s(elem!1) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 3.74/4.00 inference(monotonicity,[status(thm)],[668])).
% 3.74/4.00 tff(12587,plain,
% 3.74/4.00 ((s(elem!1) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 3.74/4.00 inference(transitivity,[status(thm)],[12586, 1611])).
% 3.74/4.00 tff(12588,plain,
% 3.74/4.00 ((~(s(elem!1) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 3.74/4.00 inference(monotonicity,[status(thm)],[12587])).
% 3.74/4.00 tff(12589,plain,
% 3.74/4.00 (~(s(s(z)) = elem!1)),
% 3.74/4.00 inference(modus_ponens,[status(thm)],[1056, 12588])).
% 3.74/4.00 tff(12590,plain,
% 3.74/4.00 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(s(s(z)))) = elem!1)),
% 3.74/4.00 inference(monotonicity,[status(thm)],[668])).
% 3.74/4.00 tff(12591,plain,
% 3.74/4.00 ((s(s(s(s(z)))) = s(elem!1)) <=> (elem!1 = s(s(s(s(z)))))),
% 3.74/4.00 inference(transitivity,[status(thm)],[12590, 501])).
% 3.74/4.00 tff(12592,plain,
% 3.74/4.00 ((~(s(s(s(s(z)))) = s(elem!1))) <=> (~(elem!1 = s(s(s(s(z))))))),
% 3.74/4.00 inference(monotonicity,[status(thm)],[12591])).
% 3.74/4.00 tff(12593,plain,
% 3.74/4.00 (~(elem!1 = s(s(s(s(z)))))),
% 3.74/4.00 inference(modus_ponens,[status(thm)],[2508, 12592])).
% 3.74/4.00 tff(12594,plain,
% 3.74/4.00 ((~(s(s(s(s(z)))) = s(elem!1))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 3.74/4.00 inference(monotonicity,[status(thm)],[12590])).
% 3.74/4.00 tff(12595,plain,
% 3.74/4.00 (~(s(s(s(s(z)))) = elem!1)),
% 3.74/4.00 inference(modus_ponens,[status(thm)],[2508, 12594])).
% 3.74/4.00 tff(12596,plain,
% 3.74/4.00 ((s(elem!1) = z) <=> (elem!1 = z)),
% 3.74/4.00 inference(monotonicity,[status(thm)],[668])).
% 3.74/4.00 tff(12597,plain,
% 3.74/4.00 ((s(elem!1) = z) <=> (z = elem!1)),
% 3.74/4.00 inference(transitivity,[status(thm)],[12596, 313])).
% 3.74/4.00 tff(12598,plain,
% 3.74/4.00 ((~(s(elem!1) = z)) <=> (~(z = elem!1))),
% 3.74/4.00 inference(monotonicity,[status(thm)],[12597])).
% 3.74/4.00 tff(12599,plain,
% 3.74/4.00 (~(z = elem!1)),
% 3.74/4.00 inference(modus_ponens,[status(thm)],[769, 12598])).
% 3.74/4.00 tff(12600,plain,
% 3.74/4.00 (~r(z, elem!1)),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[11945, 12573, 1687, 3461, 147, 12585, 3261, 12575, 12593, 12595, 12589])).
% 3.74/4.00 tff(12601,plain,
% 3.74/4.00 (b(z, elem!1)),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[585, 12600, 12599])).
% 3.74/4.00 tff(12602,plain,
% 3.74/4.00 (~r(s(s(z)), elem!1)),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[11977, 12601, 12585, 1687, 12595, 3261, 12593, 147])).
% 3.74/4.00 tff(12603,plain,
% 3.74/4.00 (b(s(s(z)), elem!1)),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[448, 12602, 12589])).
% 3.74/4.00 tff(12604,plain,
% 3.74/4.00 (~b(elem!1, s(s(s(s(z)))))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[11955, 12601, 12603, 3461, 1687])).
% 3.74/4.00 tff(12605,plain,
% 3.74/4.00 (r(elem!1, s(s(s(s(z)))))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[483, 12604, 12593])).
% 3.74/4.00 tff(12606,plain,
% 3.74/4.00 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[12005, 12605, 147, 12575, 12585, 12603])).
% 3.74/4.00 tff(12607,plain,
% 3.74/4.00 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[84, 12606])).
% 3.74/4.00 tff(12608,plain,
% 3.74/4.00 (~r(s(s(s(s(z)))), s(s(z)))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[11924, 12607, 1687, 3261, 12603, 12585, 12575, 12573, 3461])).
% 3.74/4.00 tff(12609,plain,
% 3.74/4.00 (b(s(s(s(s(z)))), s(s(z)))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[102, 12608])).
% 3.74/4.00 tff(12610,plain,
% 3.74/4.00 (~r(s(s(s(s(z)))), z)),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[9980, 12605, 12573])).
% 3.74/4.00 tff(12611,plain,
% 3.74/4.00 (b(s(s(s(s(z)))), z)),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[191, 12610])).
% 3.74/4.00 tff(12612,plain,
% 3.74/4.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 3.74/4.00 inference(rewrite,[status(thm)],[])).
% 3.74/4.00 tff(12613,plain,
% 3.74/4.00 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 3.74/4.00 inference(rewrite,[status(thm)],[])).
% 3.74/4.00 tff(12614,plain,
% 3.74/4.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 3.74/4.00 inference(monotonicity,[status(thm)],[12613])).
% 3.74/4.00 tff(12615,plain,
% 3.74/4.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 3.74/4.00 inference(transitivity,[status(thm)],[12614, 12612])).
% 3.74/4.00 tff(12616,plain,
% 3.74/4.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 3.74/4.00 inference(quant_inst,[status(thm)],[])).
% 3.74/4.00 tff(12617,plain,
% 3.74/4.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))),
% 3.74/4.00 inference(modus_ponens,[status(thm)],[12616, 12615])).
% 3.74/4.00 tff(12618,plain,
% 3.74/4.00 ($false),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[12617, 178, 12601, 12603, 3461, 12611, 12609])).
% 3.74/4.00 tff(12619,plain,((~(s(elem!1) = elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(elem!1)) | (s(elem!1) = s(s(z))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 3.74/4.00 tff(12620,plain,
% 3.74/4.00 (~(s(elem!1) = elem!1)),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[12619, 12571, 1687, 3261, 10794, 2169, 5619, 12569])).
% 3.74/4.00 tff(12621,plain,
% 3.74/4.00 (~(elem!1 = s(elem!1))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[748, 12620])).
% 3.74/4.00 tff(12622,plain,
% 3.74/4.00 (r(elem!1, s(elem!1))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[756, 12621, 751])).
% 3.74/4.00 tff(12623,plain,
% 3.74/4.00 (~r(elem!1, z)),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[2711, 12622, 12569])).
% 3.74/4.00 tff(12624,plain,
% 3.74/4.00 (~r(s(elem!1), s(s(s(s(z)))))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[5758, 1329, 10794])).
% 3.74/4.00 tff(12625,plain,
% 3.74/4.00 (b(s(elem!1), s(s(s(s(z)))))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[1084, 12624, 1369])).
% 3.74/4.00 tff(12626,plain,
% 3.74/4.00 (~r(z, s(elem!1))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[12114, 1329, 3261])).
% 3.74/4.00 tff(12627,plain,
% 3.74/4.00 (b(z, s(elem!1))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[2351, 12626])).
% 3.74/4.00 tff(12628,plain,
% 3.74/4.00 (~(elem!1 = z)),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[12054, 12627, 751])).
% 3.74/4.00 tff(12629,plain,
% 3.74/4.00 (b(elem!1, z)),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[498, 12628, 1342])).
% 3.74/4.00 tff(12630,plain,
% 3.74/4.00 (~(s(elem!1) = elem!1)),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[790, 12629, 766])).
% 3.74/4.00 tff(12631,plain,
% 3.74/4.00 (~(elem!1 = s(elem!1))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[748, 12630])).
% 3.74/4.00 tff(12632,plain,
% 3.74/4.00 (r(elem!1, s(elem!1))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[756, 12631, 751])).
% 3.74/4.00 tff(12633,plain,
% 3.74/4.00 (r(s(s(z)), s(s(s(s(s(z)))))) <=> r(s(s(z)), s(elem!1))),
% 3.74/4.00 inference(monotonicity,[status(thm)],[350])).
% 3.74/4.00 tff(12634,plain,
% 3.74/4.00 (r(s(s(z)), s(elem!1)) <=> r(s(s(z)), s(s(s(s(s(z))))))),
% 3.74/4.00 inference(symmetry,[status(thm)],[12633])).
% 3.74/4.00 tff(12635,plain,
% 3.74/4.00 (r(s(s(z)), s(s(s(s(s(z))))))),
% 3.74/4.00 inference(modus_ponens,[status(thm)],[1329, 12634])).
% 3.74/4.00 tff(12636,plain,
% 3.74/4.00 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 3.74/4.00 inference(monotonicity,[status(thm)],[350])).
% 3.74/4.00 tff(12637,plain,
% 3.74/4.00 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.74/4.00 inference(symmetry,[status(thm)],[12636])).
% 3.74/4.00 tff(12638,plain,
% 3.74/4.00 (r(elem!1, s(elem!1)) <=> r(s(s(s(s(z)))), s(elem!1))),
% 3.74/4.00 inference(monotonicity,[status(thm)],[319])).
% 3.74/4.00 tff(12639,plain,
% 3.74/4.00 (r(s(s(s(s(z)))), s(elem!1))),
% 3.74/4.00 inference(modus_ponens,[status(thm)],[1587, 12638])).
% 3.74/4.00 tff(12640,plain,
% 3.74/4.00 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.74/4.00 inference(modus_ponens,[status(thm)],[12639, 12637])).
% 3.74/4.00 tff(12641,plain,
% 3.74/4.00 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.74/4.00 inference(rewrite,[status(thm)],[])).
% 3.74/4.00 tff(12642,plain,
% 3.74/4.00 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.74/4.00 inference(quant_inst,[status(thm)],[])).
% 3.74/4.00 tff(12643,plain,
% 3.74/4.00 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 3.74/4.00 inference(modus_ponens,[status(thm)],[12642, 12641])).
% 3.74/4.00 tff(12644,plain,
% 3.74/4.00 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[12643, 118, 147, 12640])).
% 3.74/4.00 tff(12645,plain,
% 3.74/4.00 ($false),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[12644, 12635])).
% 3.74/4.00 tff(12646,plain,((~(elem!1 = s(s(s(s(z)))))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.74/4.00 tff(12647,plain,
% 3.74/4.00 (~(elem!1 = s(s(s(s(z)))))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[12646, 1329, 10794, 12632])).
% 3.74/4.00 tff(12648,plain,
% 3.74/4.00 ((~(elem!1 = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 3.74/4.00 inference(monotonicity,[status(thm)],[321])).
% 3.74/4.00 tff(12649,plain,
% 3.74/4.00 (~(s(s(s(s(z)))) = elem!1)),
% 3.74/4.00 inference(modus_ponens,[status(thm)],[12647, 12648])).
% 3.74/4.00 tff(12650,plain,
% 3.74/4.00 (~r(elem!1, s(s(z)))),
% 3.74/4.00 inference(unit_resolution,[status(thm)],[3071, 118, 12632, 1329])).
% 3.74/4.00 tff(12651,plain,
% 3.74/4.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z)))))))),
% 3.74/4.00 inference(rewrite,[status(thm)],[])).
% 3.74/4.00 tff(12652,plain,
% 3.74/4.00 (((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, z))) <=> ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z)))))))),
% 3.74/4.00 inference(rewrite,[status(thm)],[])).
% 3.74/4.00 tff(12653,plain,
% 3.74/4.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z))))))))),
% 3.74/4.01 inference(monotonicity,[status(thm)],[12652])).
% 3.74/4.01 tff(12654,plain,
% 3.74/4.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z)))))))),
% 3.74/4.01 inference(transitivity,[status(thm)],[12653, 12651])).
% 3.74/4.01 tff(12655,plain,
% 3.74/4.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, z)))),
% 3.74/4.01 inference(quant_inst,[status(thm)],[])).
% 3.74/4.01 tff(12656,plain,
% 3.74/4.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z))))))),
% 3.74/4.01 inference(modus_ponens,[status(thm)],[12655, 12654])).
% 3.74/4.01 tff(12657,plain,
% 3.74/4.01 ($false),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[12656, 178, 506, 855, 1687, 8640, 1301])).
% 3.74/4.01 tff(12658,plain,((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.74/4.01 tff(12659,plain,
% 3.74/4.01 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[12658, 1301, 855, 1687, 506])).
% 3.74/4.01 tff(12660,plain,
% 3.74/4.01 (r(s(s(s(s(z)))), s(elem!1))),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[2173, 12659, 2508])).
% 3.74/4.01 tff(12661,plain,
% 3.74/4.01 (~r(s(s(s(s(z)))), elem!1)),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[10992, 12660, 1587])).
% 3.74/4.01 tff(12662,plain,
% 3.74/4.01 (b(s(s(s(s(z)))), elem!1)),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[3142, 12661, 323])).
% 3.74/4.01 tff(12663,plain,
% 3.74/4.01 ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1))),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[11389, 178, 506, 3461, 202])).
% 3.74/4.01 tff(12664,plain,
% 3.74/4.01 (~b(elem!1, s(s(z)))),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[12663, 12662])).
% 3.74/4.01 tff(12665,plain,
% 3.74/4.01 (elem!1 = s(s(z))),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[467, 12664, 460])).
% 3.74/4.01 tff(12666,plain,
% 3.74/4.01 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 3.74/4.01 inference(monotonicity,[status(thm)],[12665])).
% 3.74/4.01 tff(12667,plain,
% 3.74/4.01 (b(s(s(z)), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 3.74/4.01 inference(symmetry,[status(thm)],[12666])).
% 3.74/4.01 tff(12668,plain,
% 3.74/4.01 ((~b(s(s(z)), s(s(s(s(z)))))) <=> (~b(elem!1, s(s(s(s(z))))))),
% 3.74/4.01 inference(monotonicity,[status(thm)],[12667])).
% 3.74/4.01 tff(12669,plain,
% 3.74/4.01 (~b(elem!1, s(s(s(s(z)))))),
% 3.74/4.01 inference(modus_ponens,[status(thm)],[105, 12668])).
% 3.74/4.01 tff(12670,plain,
% 3.74/4.01 ($false),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[1301, 12669])).
% 3.74/4.01 tff(12671,plain,((~b(elem!1, s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(z))))) | r(elem!1, s(s(z))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (s(s(s(s(z)))) = elem!1) | (~r(elem!1, s(elem!1))) | (s(s(s(s(z)))) = s(elem!1)) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.74/4.01 tff(12672,plain,
% 3.74/4.01 (~b(elem!1, s(s(s(s(z)))))),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[12671, 12650, 105, 12629, 3461, 202, 12649, 12632, 2169, 12627, 1687])).
% 3.74/4.01 tff(12673,plain,
% 3.74/4.01 (r(elem!1, s(s(s(s(z)))))),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[483, 12672, 12647])).
% 3.74/4.01 tff(12674,plain,
% 3.74/4.01 (~r(s(s(s(s(z)))), s(elem!1))),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[11326, 12673, 12632])).
% 3.74/4.01 tff(12675,plain,
% 3.74/4.01 (b(s(s(s(s(z)))), s(elem!1))),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[2173, 12674, 2169])).
% 3.74/4.01 tff(12676,plain,
% 3.74/4.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z)))))))),
% 3.74/4.01 inference(rewrite,[status(thm)],[])).
% 3.74/4.01 tff(12677,plain,
% 3.74/4.01 (((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z)))))))),
% 3.74/4.01 inference(rewrite,[status(thm)],[])).
% 3.74/4.01 tff(12678,plain,
% 3.74/4.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z))))))))),
% 3.74/4.01 inference(monotonicity,[status(thm)],[12677])).
% 3.74/4.01 tff(12679,plain,
% 3.74/4.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z)))))))),
% 3.74/4.01 inference(transitivity,[status(thm)],[12678, 12676])).
% 3.74/4.01 tff(12680,plain,
% 3.74/4.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)))),
% 3.74/4.01 inference(quant_inst,[status(thm)],[])).
% 3.74/4.01 tff(12681,plain,
% 3.74/4.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z))))))),
% 3.74/4.01 inference(modus_ponens,[status(thm)],[12680, 12679])).
% 3.74/4.01 tff(12682,plain,
% 3.74/4.01 (~b(s(s(s(s(z)))), z)),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[12681, 178, 12627, 1687, 12675, 12625])).
% 3.74/4.01 tff(12683,plain,
% 3.74/4.01 (r(s(s(s(s(z)))), z)),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[191, 12682])).
% 3.74/4.01 tff(12684,plain,
% 3.74/4.01 (~r(s(elem!1), elem!1)),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[1284, 7054, 844])).
% 3.74/4.01 tff(12685,plain,
% 3.74/4.01 (b(s(elem!1), elem!1)),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[677, 12684, 725])).
% 3.74/4.01 tff(12686,plain,
% 3.74/4.01 (b(s(elem!1), s(s(z)))),
% 3.74/4.01 inference(modus_ponens,[status(thm)],[12685, 7046])).
% 3.74/4.01 tff(12687,plain,
% 3.74/4.01 (b(s(s(s(z))), s(s(z)))),
% 3.74/4.01 inference(modus_ponens,[status(thm)],[12686, 7045])).
% 3.74/4.01 tff(12688,plain,
% 3.74/4.01 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 3.74/4.01 inference(monotonicity,[status(thm)],[5636])).
% 3.74/4.01 tff(12689,plain,
% 3.74/4.01 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.74/4.01 inference(modus_ponens,[status(thm)],[8640, 12688])).
% 3.74/4.01 tff(12690,plain,
% 3.74/4.01 (b(z, s(s(s(z))))),
% 3.74/4.01 inference(modus_ponens,[status(thm)],[855, 7061])).
% 3.74/4.01 tff(12691,plain,
% 3.74/4.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 3.74/4.01 inference(rewrite,[status(thm)],[])).
% 3.74/4.01 tff(12692,plain,
% 3.74/4.01 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 3.74/4.01 inference(rewrite,[status(thm)],[])).
% 3.74/4.01 tff(12693,plain,
% 3.74/4.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))))),
% 3.74/4.01 inference(monotonicity,[status(thm)],[12692])).
% 3.74/4.01 tff(12694,plain,
% 3.74/4.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 3.74/4.01 inference(transitivity,[status(thm)],[12693, 12691])).
% 3.74/4.01 tff(12695,plain,
% 3.74/4.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 3.74/4.01 inference(quant_inst,[status(thm)],[])).
% 3.74/4.01 tff(12696,plain,
% 3.74/4.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 3.74/4.01 inference(modus_ponens,[status(thm)],[12695, 12694])).
% 3.74/4.01 tff(12697,plain,
% 3.74/4.01 ($false),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[12696, 178, 1687, 202, 12690, 12689, 12687])).
% 3.74/4.01 tff(12698,plain,((~(elem!1 = s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (s(elem!1) = elem!1) | (~r(s(elem!1), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.74/4.01 tff(12699,plain,
% 3.74/4.01 (~(elem!1 = s(s(z)))),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[12698, 12675, 202, 1687, 12627, 12630, 12569, 3261])).
% 3.74/4.01 tff(12700,plain,
% 3.74/4.01 (b(elem!1, s(s(z)))),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[467, 12699, 12650])).
% 3.74/4.01 tff(12701,plain,
% 3.74/4.01 ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1))),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[11389, 178, 12629, 3461, 202])).
% 3.74/4.01 tff(12702,plain,
% 3.74/4.01 (~b(s(s(s(s(z)))), elem!1)),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[12701, 12700])).
% 3.74/4.01 tff(12703,plain,
% 3.74/4.01 (r(s(s(s(s(z)))), elem!1)),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[3142, 12702, 12649])).
% 3.74/4.01 tff(12704,plain,
% 3.74/4.01 (~(z = elem!1)),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[317, 12628])).
% 3.74/4.01 tff(12705,plain,
% 3.74/4.01 (~r(s(s(z)), elem!1)),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[3063, 118, 12632, 1329])).
% 3.74/4.01 tff(12706,plain,
% 3.74/4.01 (~(s(s(z)) = elem!1)),
% 3.74/4.01 inference(modus_ponens,[status(thm)],[12699, 5676])).
% 3.74/4.01 tff(12707,plain,
% 3.74/4.01 (b(s(s(z)), elem!1)),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[448, 12706, 12705])).
% 3.74/4.01 tff(12708,plain,
% 3.74/4.01 (~b(z, elem!1)),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[12257, 12707, 3461, 12629, 12700])).
% 3.74/4.01 tff(12709,plain,
% 3.74/4.01 (r(z, elem!1)),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[585, 12708, 12704])).
% 3.74/4.01 tff(12710,plain,
% 3.74/4.01 ($false),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[3135, 118, 12709, 12703, 12683])).
% 3.74/4.01 tff(12711,plain,((~r(s(s(z)), s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))) | b(s(s(z)), s(s(s(s(z))))) | b(elem!1, s(elem!1)) | b(s(elem!1), z) | r(elem!1, z) | (s(elem!1) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.74/4.01 tff(12712,plain,
% 3.74/4.01 (~r(s(s(z)), s(elem!1))),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[12711, 202, 3461, 1687, 3261, 105, 751, 766, 1342, 1369])).
% 3.74/4.01 tff(12713,plain,
% 3.74/4.01 (b(s(s(z)), s(elem!1))),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[1067, 12712, 1060])).
% 3.74/4.01 tff(12714,plain,
% 3.74/4.01 (elem!1 = s(elem!1)),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[756, 744, 751])).
% 3.74/4.01 tff(12715,plain,
% 3.74/4.01 (s(elem!1) = elem!1),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[748, 12714])).
% 3.74/4.01 tff(12716,plain,
% 3.74/4.01 (~(elem!1 = z)),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[6201, 744, 2333])).
% 3.74/4.01 tff(12717,plain,
% 3.74/4.01 (b(elem!1, z)),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[498, 12716, 1342])).
% 3.74/4.01 tff(12718,plain,
% 3.74/4.01 ($false),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[790, 12717, 12715, 766])).
% 3.74/4.01 tff(12719,plain,(r(elem!1, s(elem!1)) | b(s(elem!1), z) | r(elem!1, z) | (~r(z, s(elem!1))) | b(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.74/4.01 tff(12720,plain,
% 3.74/4.01 (r(elem!1, s(elem!1))),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[12719, 2333, 1342, 766, 751])).
% 3.74/4.01 tff(12721,plain,
% 3.74/4.01 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))))),
% 3.74/4.01 inference(rewrite,[status(thm)],[])).
% 3.74/4.01 tff(12722,plain,
% 3.74/4.01 (((~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))))),
% 3.74/4.01 inference(rewrite,[status(thm)],[])).
% 3.74/4.01 tff(12723,plain,
% 3.74/4.01 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1)))))),
% 3.74/4.01 inference(monotonicity,[status(thm)],[12722])).
% 3.74/4.01 tff(12724,plain,
% 3.74/4.01 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))))),
% 3.74/4.01 inference(transitivity,[status(thm)],[12723, 12721])).
% 3.74/4.01 tff(12725,plain,
% 3.74/4.01 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1)))),
% 3.74/4.01 inference(quant_inst,[status(thm)],[])).
% 3.74/4.01 tff(12726,plain,
% 3.74/4.01 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1)))),
% 3.74/4.01 inference(modus_ponens,[status(thm)],[12725, 12724])).
% 3.74/4.01 tff(12727,plain,
% 3.74/4.01 (~r(z, elem!1)),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[12726, 118, 2333, 12720])).
% 3.74/4.01 tff(12728,plain,
% 3.74/4.01 (~(s(s(z)) = elem!1)),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[7053, 12727, 3261])).
% 3.74/4.01 tff(12729,plain,
% 3.74/4.01 (~r(s(elem!1), s(s(z)))),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[11762, 2333, 3261])).
% 3.74/4.01 tff(12730,plain,
% 3.74/4.01 (b(s(z), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 3.74/4.01 inference(monotonicity,[status(thm)],[6683])).
% 3.74/4.01 tff(12731,plain,
% 3.74/4.01 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(z), s(s(s(s(z)))))),
% 3.74/4.01 inference(symmetry,[status(thm)],[12730])).
% 3.74/4.01 tff(12732,plain,
% 3.74/4.01 (r(s(elem!1), elem!1) <=> r(s(elem!1), z)),
% 3.74/4.01 inference(monotonicity,[status(thm)],[928])).
% 3.74/4.01 tff(12733,plain,
% 3.74/4.01 (r(s(elem!1), z) <=> r(s(elem!1), elem!1)),
% 3.74/4.01 inference(symmetry,[status(thm)],[12732])).
% 3.74/4.01 tff(12734,plain,
% 3.74/4.01 (r(s(elem!1), elem!1)),
% 3.74/4.01 inference(modus_ponens,[status(thm)],[844, 12733])).
% 3.74/4.01 tff(12735,plain,
% 3.74/4.01 ((s(s(s(s(z)))) = elem!1) <=> (s(s(s(s(z)))) = z)),
% 3.74/4.01 inference(monotonicity,[status(thm)],[928])).
% 3.74/4.01 tff(12736,plain,
% 3.74/4.01 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 3.74/4.01 inference(symmetry,[status(thm)],[12735])).
% 3.74/4.01 tff(12737,plain,
% 3.74/4.01 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 3.74/4.01 inference(monotonicity,[status(thm)],[12736])).
% 3.74/4.01 tff(12738,plain,
% 3.74/4.01 (~(s(s(s(s(z)))) = elem!1)),
% 3.74/4.01 inference(modus_ponens,[status(thm)],[30, 12737])).
% 3.74/4.01 tff(12739,plain,
% 3.74/4.01 (b(s(s(s(z))), z) <=> b(s(s(s(elem!1))), z)),
% 3.74/4.01 inference(monotonicity,[status(thm)],[5207])).
% 3.74/4.01 tff(12740,plain,
% 3.74/4.01 (b(s(s(s(elem!1))), z) <=> b(s(s(s(z))), z)),
% 3.74/4.01 inference(symmetry,[status(thm)],[12739])).
% 3.74/4.01 tff(12741,plain,
% 3.74/4.01 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), z)),
% 3.74/4.01 inference(transitivity,[status(thm)],[10092, 12740])).
% 3.74/4.01 tff(12742,plain,
% 3.74/4.01 (b(s(s(s(elem!1))), s(elem!1))),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[373, 1700, 12049])).
% 3.74/4.01 tff(12743,plain,
% 3.74/4.01 (b(s(s(s(z))), s(z))),
% 3.74/4.01 inference(modus_ponens,[status(thm)],[12742, 12043])).
% 3.74/4.01 tff(12744,plain,
% 3.74/4.01 (b(s(z), s(s(s(z)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 3.74/4.01 inference(monotonicity,[status(thm)],[6683, 5207])).
% 3.74/4.01 tff(12745,plain,
% 3.74/4.01 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(z), s(s(s(z))))),
% 3.74/4.01 inference(symmetry,[status(thm)],[12744])).
% 3.74/4.01 tff(12746,plain,
% 3.74/4.01 (~(s(elem!1) = s(s(s(elem!1))))),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[5395, 12049])).
% 3.74/4.01 tff(12747,plain,
% 3.74/4.01 (~r(s(elem!1), s(s(s(elem!1))))),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[2110, 556, 1426])).
% 3.74/4.01 tff(12748,plain,
% 3.74/4.01 (b(s(elem!1), s(s(s(elem!1))))),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[5432, 12747, 12746])).
% 3.74/4.01 tff(12749,plain,
% 3.74/4.01 (b(s(z), s(s(s(z))))),
% 3.74/4.01 inference(modus_ponens,[status(thm)],[12748, 12745])).
% 3.74/4.01 tff(12750,assumption,(b(s(s(z)), s(z))), introduced(assumption)).
% 3.74/4.01 tff(12751,plain,
% 3.74/4.01 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[10206, 556, 5816])).
% 3.74/4.01 tff(12752,plain,
% 3.74/4.01 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[3409, 12751, 12038])).
% 3.74/4.01 tff(12753,plain,
% 3.74/4.01 (b(s(s(s(z))), s(s(z)))),
% 3.74/4.01 inference(modus_ponens,[status(thm)],[12752, 5221])).
% 3.74/4.01 tff(12754,plain,
% 3.74/4.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(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(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(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(s(z))), s(s(z)))))),
% 3.74/4.01 inference(rewrite,[status(thm)],[])).
% 3.74/4.01 tff(12755,plain,
% 3.74/4.01 (((~b(s(s(z)), 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(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(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(s(z))), s(s(z)))))),
% 3.74/4.01 inference(rewrite,[status(thm)],[])).
% 3.74/4.01 tff(12756,plain,
% 3.74/4.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), 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(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(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(s(z))), s(s(z))))))),
% 3.74/4.01 inference(monotonicity,[status(thm)],[12755])).
% 3.74/4.01 tff(12757,plain,
% 3.74/4.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), 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(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(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(s(z))), s(s(z)))))),
% 3.74/4.01 inference(transitivity,[status(thm)],[12756, 12754])).
% 3.74/4.01 tff(12758,plain,
% 3.74/4.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), 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(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 3.74/4.01 inference(quant_inst,[status(thm)],[])).
% 3.74/4.01 tff(12759,plain,
% 3.74/4.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))),
% 3.74/4.01 inference(modus_ponens,[status(thm)],[12758, 12757])).
% 3.74/4.01 tff(12760,plain,
% 3.74/4.01 ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[12759, 178, 10110, 12753, 12750])).
% 3.74/4.01 tff(12761,plain,
% 3.74/4.01 ($false),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[12760, 12749, 12743])).
% 3.74/4.01 tff(12762,plain,((~r(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~(elem!1 = z)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.74/4.01 tff(12763,plain,
% 3.74/4.01 (~r(s(s(s(elem!1))), elem!1)),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[12762, 1030, 10109, 928, 12734, 12032])).
% 3.74/4.01 tff(12764,plain,
% 3.74/4.01 (b(s(s(s(elem!1))), elem!1)),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[570, 12763, 941])).
% 3.74/4.01 tff(12765,plain,
% 3.74/4.01 (b(s(s(s(z))), z)),
% 3.74/4.01 inference(modus_ponens,[status(thm)],[12764, 12741])).
% 3.74/4.01 tff(12766,plain,
% 3.74/4.01 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 3.74/4.01 inference(modus_ponens,[status(thm)],[2169, 12075])).
% 3.74/4.01 tff(12767,plain,
% 3.74/4.01 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 3.74/4.01 inference(unit_resolution,[status(thm)],[4343, 12766])).
% 3.74/4.01 tff(12768,plain,
% 3.74/4.01 (b(s(s(s(elem!1))), z)),
% 3.74/4.01 inference(modus_ponens,[status(thm)],[12764, 10092])).
% 3.74/4.02 tff(12769,plain,
% 3.74/4.02 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), z)),
% 3.74/4.02 inference(monotonicity,[status(thm)],[928])).
% 3.74/4.02 tff(12770,plain,
% 3.74/4.02 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(elem!1)))), z)),
% 3.74/4.02 inference(transitivity,[status(thm)],[12769, 12302])).
% 3.74/4.02 tff(12771,plain,
% 3.74/4.02 (b(s(s(s(s(elem!1)))), z)),
% 3.74/4.02 inference(modus_ponens,[status(thm)],[3771, 12770])).
% 3.74/4.02 tff(12772,plain,
% 3.74/4.02 (b(s(s(s(s(z)))), z)),
% 3.74/4.02 inference(modus_ponens,[status(thm)],[3771, 12769])).
% 3.74/4.02 tff(12773,plain,
% 3.74/4.02 ((~b(s(z), s(s(s(z))))) <=> (~b(s(elem!1), s(s(s(elem!1)))))),
% 3.74/4.02 inference(monotonicity,[status(thm)],[12744])).
% 3.74/4.02 tff(12774,plain,
% 3.74/4.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 3.74/4.02 inference(rewrite,[status(thm)],[])).
% 3.74/4.02 tff(12775,plain,
% 3.74/4.02 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 3.74/4.02 inference(rewrite,[status(thm)],[])).
% 3.74/4.02 tff(12776,plain,
% 3.74/4.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))))),
% 3.74/4.02 inference(monotonicity,[status(thm)],[12775])).
% 3.74/4.02 tff(12777,plain,
% 3.74/4.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 3.74/4.02 inference(transitivity,[status(thm)],[12776, 12774])).
% 3.74/4.02 tff(12778,plain,
% 3.74/4.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 3.74/4.02 inference(quant_inst,[status(thm)],[])).
% 3.74/4.02 tff(12779,plain,
% 3.74/4.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))),
% 3.74/4.02 inference(modus_ponens,[status(thm)],[12778, 12777])).
% 3.74/4.02 tff(12780,plain,
% 3.74/4.02 ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 3.74/4.02 inference(unit_resolution,[status(thm)],[12779, 178, 3461, 10110, 1127])).
% 3.74/4.02 tff(12781,plain,
% 3.74/4.02 (~b(s(z), s(s(s(z))))),
% 3.74/4.02 inference(unit_resolution,[status(thm)],[12780, 4932])).
% 3.74/4.02 tff(12782,plain,
% 3.74/4.02 (~b(s(elem!1), s(s(s(elem!1))))),
% 3.74/4.02 inference(modus_ponens,[status(thm)],[12781, 12773])).
% 3.74/4.02 tff(12783,plain,
% 3.74/4.02 (r(s(elem!1), s(s(s(elem!1))))),
% 3.74/4.02 inference(unit_resolution,[status(thm)],[5432, 12782, 12746])).
% 3.74/4.02 tff(12784,plain,
% 3.74/4.02 (~r(elem!1, s(s(s(elem!1))))),
% 3.74/4.02 inference(unit_resolution,[status(thm)],[10317, 12783, 1587])).
% 3.74/4.02 tff(12785,plain,
% 3.74/4.02 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 3.74/4.02 inference(unit_resolution,[status(thm)],[12354, 178, 3461, 168, 202, 4932])).
% 3.74/4.02 tff(12786,plain,
% 3.74/4.02 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.74/4.02 inference(modus_ponens,[status(thm)],[12785, 5217])).
% 3.74/4.02 tff(12787,plain,
% 3.74/4.02 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.74/4.02 inference(unit_resolution,[status(thm)],[1750, 12786, 1858])).
% 3.74/4.02 tff(12788,plain,
% 3.74/4.02 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 3.74/4.02 inference(symmetry,[status(thm)],[7921])).
% 3.74/4.02 tff(12789,plain,
% 3.74/4.02 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(z))))),
% 3.74/4.02 inference(monotonicity,[status(thm)],[12788])).
% 3.74/4.02 tff(12790,plain,
% 3.74/4.02 (~(s(s(s(elem!1))) = s(s(z)))),
% 3.74/4.02 inference(modus_ponens,[status(thm)],[1683, 12789])).
% 3.74/4.02 tff(12791,plain,
% 3.74/4.02 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.74/4.02 inference(unit_resolution,[status(thm)],[4034, 118, 1403, 1876])).
% 3.74/4.02 tff(12792,plain,
% 3.74/4.02 (b(s(s(z)), s(s(s(elem!1))))),
% 3.74/4.02 inference(unit_resolution,[status(thm)],[4223, 12791])).
% 3.74/4.02 tff(12793,plain,
% 3.74/4.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 3.74/4.02 inference(rewrite,[status(thm)],[])).
% 3.74/4.02 tff(12794,plain,
% 3.74/4.02 (((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 3.74/4.02 inference(rewrite,[status(thm)],[])).
% 3.74/4.02 tff(12795,plain,
% 3.74/4.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 3.74/4.02 inference(monotonicity,[status(thm)],[12794])).
% 3.74/4.02 tff(12796,plain,
% 3.74/4.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 3.74/4.02 inference(transitivity,[status(thm)],[12795, 12793])).
% 3.74/4.02 tff(12797,plain,
% 3.74/4.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 3.74/4.02 inference(quant_inst,[status(thm)],[])).
% 3.74/4.02 tff(12798,plain,
% 3.74/4.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z))))),
% 3.74/4.02 inference(modus_ponens,[status(thm)],[12797, 12796])).
% 3.74/4.02 tff(12799,plain,
% 3.74/4.02 (~b(s(s(s(elem!1))), s(s(z)))),
% 3.74/4.02 inference(unit_resolution,[status(thm)],[12798, 178, 2043, 7976, 3461, 12792])).
% 3.74/4.02 tff(12800,plain,
% 3.74/4.02 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 3.74/4.02 inference(rewrite,[status(thm)],[])).
% 3.74/4.02 tff(12801,plain,
% 3.74/4.02 (((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(z))))) <=> ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 3.74/4.02 inference(rewrite,[status(thm)],[])).
% 3.74/4.02 tff(12802,plain,
% 3.74/4.02 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1))))))))),
% 3.74/4.02 inference(monotonicity,[status(thm)],[12801])).
% 3.74/4.02 tff(12803,plain,
% 3.74/4.02 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 3.74/4.02 inference(transitivity,[status(thm)],[12802, 12800])).
% 3.74/4.02 tff(12804,plain,
% 3.74/4.02 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 3.74/4.02 inference(quant_inst,[status(thm)],[])).
% 3.74/4.02 tff(12805,plain,
% 3.74/4.02 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1))))))),
% 3.74/4.02 inference(modus_ponens,[status(thm)],[12804, 12803])).
% 3.74/4.02 tff(12806,plain,
% 3.74/4.02 (~r(s(s(s(elem!1))), s(s(z)))),
% 3.74/4.02 inference(unit_resolution,[status(thm)],[12805, 118, 1403, 1876])).
% 3.74/4.02 tff(12807,plain,
% 3.74/4.02 ((s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z)))),
% 3.74/4.02 inference(unit_resolution,[status(thm)],[4209, 41, 12806])).
% 3.74/4.02 tff(12808,plain,
% 3.74/4.02 ($false),
% 3.74/4.02 inference(unit_resolution,[status(thm)],[12807, 12799, 12790])).
% 3.74/4.02 tff(12809,plain,((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 3.74/4.02 tff(12810,plain,
% 3.74/4.02 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 3.74/4.02 inference(unit_resolution,[status(thm)],[12809, 3461, 2043, 1876, 7976])).
% 3.74/4.02 tff(12811,plain,
% 3.74/4.02 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 3.74/4.02 inference(unit_resolution,[status(thm)],[2136, 12810])).
% 3.74/4.02 tff(12812,plain,
% 3.74/4.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 3.74/4.02 inference(rewrite,[status(thm)],[])).
% 3.74/4.02 tff(12813,plain,
% 3.74/4.02 (((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 3.74/4.02 inference(rewrite,[status(thm)],[])).
% 3.74/4.02 tff(12814,plain,
% 3.74/4.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1))))))))),
% 3.74/4.02 inference(monotonicity,[status(thm)],[12813])).
% 3.74/4.02 tff(12815,plain,
% 3.74/4.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 3.74/4.02 inference(transitivity,[status(thm)],[12814, 12812])).
% 3.74/4.02 tff(12816,plain,
% 3.74/4.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 3.74/4.02 inference(quant_inst,[status(thm)],[])).
% 3.74/4.02 tff(12817,plain,
% 3.74/4.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1))))))),
% 3.74/4.02 inference(modus_ponens,[status(thm)],[12816, 12815])).
% 3.74/4.02 tff(12818,plain,
% 3.74/4.02 (~b(s(s(s(elem!1))), s(s(z)))),
% 3.74/4.02 inference(unit_resolution,[status(thm)],[12817, 178, 7976, 12811, 3461, 12307])).
% 3.74/4.02 tff(12819,plain,
% 3.74/4.02 ((s(s(s(elem!1))) = s(s(z))) | r(s(s(s(elem!1))), s(s(z)))),
% 3.74/4.02 inference(unit_resolution,[status(thm)],[4209, 41, 12818])).
% 3.74/4.02 tff(12820,plain,
% 3.74/4.02 (r(s(s(s(elem!1))), s(s(z)))),
% 3.74/4.02 inference(unit_resolution,[status(thm)],[12819, 12790])).
% 3.74/4.02 tff(12821,plain,
% 3.74/4.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 3.74/4.02 inference(rewrite,[status(thm)],[])).
% 3.74/4.02 tff(12822,plain,
% 3.74/4.02 (((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 3.74/4.02 inference(rewrite,[status(thm)],[])).
% 3.74/4.02 tff(12823,plain,
% 3.74/4.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1))))))))),
% 3.74/4.02 inference(monotonicity,[status(thm)],[12822])).
% 3.74/4.02 tff(12824,plain,
% 3.74/4.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 3.74/4.02 inference(transitivity,[status(thm)],[12823, 12821])).
% 3.74/4.02 tff(12825,plain,
% 3.74/4.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 3.74/4.02 inference(quant_inst,[status(thm)],[])).
% 3.74/4.02 tff(12826,plain,
% 3.74/4.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1))))))),
% 3.74/4.02 inference(modus_ponens,[status(thm)],[12825, 12824])).
% 3.74/4.02 tff(12827,plain,
% 3.74/4.02 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 3.74/4.02 inference(unit_resolution,[status(thm)],[12826, 178, 12811, 3461, 5177, 12307])).
% 3.74/4.02 tff(12828,plain,
% 3.74/4.02 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 3.74/4.02 inference(unit_resolution,[status(thm)],[1170, 12827])).
% 3.74/4.02 tff(12829,plain,
% 3.74/4.02 ($false),
% 3.74/4.02 inference(unit_resolution,[status(thm)],[3958, 118, 12828, 12820, 1876])).
% 3.74/4.02 tff(12830,plain,((~b(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.74/4.02 tff(12831,plain,
% 3.74/4.02 (~b(z, s(s(s(elem!1))))),
% 3.74/4.02 inference(unit_resolution,[status(thm)],[12830, 12787, 12307, 7976, 3461, 5177])).
% 3.74/4.02 tff(12832,plain,
% 3.74/4.02 (r(z, s(s(s(elem!1))))),
% 3.74/4.02 inference(unit_resolution,[status(thm)],[2095, 12831])).
% 3.74/4.02 tff(12833,plain,
% 3.74/4.02 ($false),
% 3.74/4.02 inference(unit_resolution,[status(thm)],[4850, 12832, 12784, 928])).
% 3.74/4.02 tff(12834,plain,((~b(s(s(s(z))), s(s(z)))) | (~(elem!1 = z)) | (~r(elem!1, s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.74/4.02 tff(12835,plain,
% 3.74/4.02 (~b(s(s(s(z))), s(s(z)))),
% 3.74/4.02 inference(unit_resolution,[status(thm)],[12834, 12771, 1587, 12307, 7976, 3461, 928, 1858, 10110, 1127, 12772, 202])).
% 3.74/4.02 tff(12836,plain,
% 3.74/4.02 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.74/4.02 inference(modus_ponens,[status(thm)],[12835, 12041])).
% 3.87/4.03 tff(12837,plain,
% 3.87/4.03 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[3409, 12836, 12038])).
% 3.87/4.03 tff(12838,plain,
% 3.87/4.03 (~r(z, s(s(s(elem!1))))),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[5235, 12837, 5226])).
% 3.87/4.03 tff(12839,plain,
% 3.87/4.03 (b(z, s(s(s(elem!1))))),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[2095, 12838])).
% 3.87/4.03 tff(12840,plain,
% 3.87/4.03 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[12318, 12837, 12310])).
% 3.87/4.03 tff(12841,plain,
% 3.87/4.03 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[1750, 12840, 1858])).
% 3.87/4.03 tff(12842,plain,
% 3.87/4.03 ($false),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[12328, 12841, 12839, 7976, 12771, 12307])).
% 3.87/4.03 tff(12843,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(elem!1)))) | (~(elem!1 = z)) | (~r(elem!1, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.03 tff(12844,plain,
% 3.87/4.03 (~b(s(s(s(s(z)))), elem!1)),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[12843, 12768, 12300, 12767, 12299, 5225, 928, 1587, 3461, 1030, 12765, 202])).
% 3.87/4.03 tff(12845,plain,
% 3.87/4.03 (r(s(s(s(s(z)))), elem!1)),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[3142, 12844, 12738])).
% 3.87/4.03 tff(12846,plain,
% 3.87/4.03 (~r(s(elem!1), s(s(s(s(z)))))),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[7010, 12845, 12734])).
% 3.87/4.03 tff(12847,plain,
% 3.87/4.03 (b(s(elem!1), s(s(s(s(z)))))),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[1084, 12846, 1369])).
% 3.87/4.03 tff(12848,plain,
% 3.87/4.03 (b(s(z), s(s(s(s(z)))))),
% 3.87/4.03 inference(modus_ponens,[status(thm)],[12847, 12731])).
% 3.87/4.03 tff(12849,plain,
% 3.87/4.03 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(z))),
% 3.87/4.03 inference(monotonicity,[status(thm)],[929])).
% 3.87/4.03 tff(12850,plain,
% 3.87/4.03 (~r(s(s(s(s(z)))), s(elem!1))),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[10992, 12845, 1587])).
% 3.87/4.03 tff(12851,plain,
% 3.87/4.03 (b(s(s(s(s(z)))), s(elem!1))),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[2173, 12850, 2169])).
% 3.87/4.03 tff(12852,plain,
% 3.87/4.03 (b(s(s(s(s(z)))), s(z))),
% 3.87/4.03 inference(modus_ponens,[status(thm)],[12851, 12849])).
% 3.87/4.03 tff(12853,plain,
% 3.87/4.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 3.87/4.03 inference(rewrite,[status(thm)],[])).
% 3.87/4.03 tff(12854,plain,
% 3.87/4.03 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 3.87/4.03 inference(rewrite,[status(thm)],[])).
% 3.87/4.03 tff(12855,plain,
% 3.87/4.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))))),
% 3.87/4.03 inference(monotonicity,[status(thm)],[12854])).
% 3.87/4.03 tff(12856,plain,
% 3.87/4.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 3.87/4.03 inference(transitivity,[status(thm)],[12855, 12853])).
% 3.87/4.03 tff(12857,plain,
% 3.87/4.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 3.87/4.03 inference(quant_inst,[status(thm)],[])).
% 3.87/4.03 tff(12858,plain,
% 3.87/4.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))),
% 3.87/4.03 inference(modus_ponens,[status(thm)],[12857, 12856])).
% 3.87/4.03 tff(12859,plain,
% 3.87/4.03 ($false),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[12858, 178, 1030, 202, 12852, 10109, 12848])).
% 3.87/4.03 tff(12860,plain,((~(elem!1 = z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (s(elem!1) = s(s(s(s(z))))) | (~r(elem!1, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | r(s(elem!1), s(s(z))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.03 tff(12861,plain,
% 3.87/4.03 (~(elem!1 = z)),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[12860, 12720, 1369, 202, 3461, 1071, 1687, 147, 3261, 12729, 12569])).
% 3.87/4.03 tff(12862,plain,
% 3.87/4.03 (b(elem!1, z)),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[498, 12861, 1342])).
% 3.87/4.03 tff(12863,plain,
% 3.87/4.03 (~(s(elem!1) = elem!1)),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[790, 12862, 766])).
% 3.87/4.03 tff(12864,plain,
% 3.87/4.03 (~(z = elem!1)),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[317, 12861])).
% 3.87/4.03 tff(12865,plain,
% 3.87/4.03 (b(z, elem!1)),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[585, 12864, 12727])).
% 3.87/4.03 tff(12866,plain,
% 3.87/4.03 (s(s(s(s(s(z))))) = s(elem!1)),
% 3.87/4.03 inference(monotonicity,[status(thm)],[331])).
% 3.87/4.03 tff(12867,plain,
% 3.87/4.03 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 3.87/4.03 inference(monotonicity,[status(thm)],[12866])).
% 3.87/4.03 tff(12868,plain,
% 3.87/4.03 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 3.87/4.03 inference(monotonicity,[status(thm)],[12867])).
% 3.87/4.03 tff(12869,plain,
% 3.87/4.03 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 3.87/4.03 inference(symmetry,[status(thm)],[12868])).
% 3.87/4.03 tff(12870,plain,
% 3.87/4.03 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 3.87/4.03 inference(monotonicity,[status(thm)],[12869])).
% 3.87/4.03 tff(12871,plain,
% 3.87/4.03 ((s(s(s(elem!1))) = elem!1) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.87/4.03 inference(transitivity,[status(thm)],[12870, 836])).
% 3.87/4.03 tff(12872,plain,
% 3.87/4.03 ((elem!1 = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(elem!1))) = elem!1)),
% 3.87/4.03 inference(symmetry,[status(thm)],[12871])).
% 3.87/4.03 tff(12873,plain,
% 3.87/4.03 ((~(elem!1 = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 3.87/4.03 inference(monotonicity,[status(thm)],[12872])).
% 3.87/4.03 tff(12874,plain,
% 3.87/4.03 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 3.87/4.03 inference(monotonicity,[status(thm)],[331])).
% 3.87/4.03 tff(12875,plain,
% 3.87/4.03 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.87/4.03 inference(transitivity,[status(thm)],[12874, 836])).
% 3.87/4.03 tff(12876,plain,
% 3.87/4.03 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(s(s(s(s(s(z)))))))))),
% 3.87/4.03 inference(monotonicity,[status(thm)],[12875])).
% 3.87/4.03 tff(12877,plain,
% 3.87/4.03 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.87/4.03 inference(modus_ponens,[status(thm)],[79, 12876])).
% 3.87/4.03 tff(12878,plain,
% 3.87/4.03 (~(s(s(s(elem!1))) = elem!1)),
% 3.87/4.03 inference(modus_ponens,[status(thm)],[12877, 12873])).
% 3.87/4.03 tff(12879,plain,
% 3.87/4.03 (~(s(s(elem!1)) = elem!1)),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[338, 331, 12])).
% 3.87/4.03 tff(12880,plain,
% 3.87/4.03 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[348, 12879])).
% 3.87/4.03 tff(12881,plain,
% 3.87/4.03 (b(elem!1, s(s(z)))),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[4509, 331, 202])).
% 3.87/4.03 tff(12882,plain,
% 3.87/4.03 (~b(s(s(z)), elem!1)),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[12257, 12881, 3461, 506, 818])).
% 3.87/4.03 tff(12883,plain,
% 3.87/4.03 (r(s(s(z)), elem!1)),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[448, 12882, 12])).
% 3.87/4.03 tff(12884,plain,
% 3.87/4.03 ((elem!1 = s(s(s(s(s(s(s(z)))))))) <=> (elem!1 = s(s(s(elem!1))))),
% 3.87/4.03 inference(transitivity,[status(thm)],[12872, 2486])).
% 3.87/4.03 tff(12885,plain,
% 3.87/4.03 ((~(elem!1 = s(s(s(s(s(s(s(z))))))))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 3.87/4.03 inference(monotonicity,[status(thm)],[12884])).
% 3.87/4.03 tff(12886,plain,
% 3.87/4.03 (~(elem!1 = s(s(s(elem!1))))),
% 3.87/4.03 inference(modus_ponens,[status(thm)],[12877, 12885])).
% 3.87/4.03 tff(12887,plain,
% 3.87/4.03 ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 3.87/4.03 inference(monotonicity,[status(thm)],[12868])).
% 3.87/4.03 tff(12888,plain,
% 3.87/4.03 ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 3.87/4.03 inference(transitivity,[status(thm)],[12887, 3881])).
% 3.87/4.03 tff(12889,plain,
% 3.87/4.03 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.87/4.03 inference(symmetry,[status(thm)],[12888])).
% 3.87/4.03 tff(12890,plain,
% 3.87/4.03 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 3.87/4.03 inference(monotonicity,[status(thm)],[12889])).
% 3.87/4.03 tff(12891,plain,
% 3.87/4.03 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.87/4.03 inference(modus_ponens,[status(thm)],[356, 12890])).
% 3.87/4.03 tff(12892,plain,
% 3.87/4.03 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 3.87/4.03 inference(monotonicity,[status(thm)],[12868])).
% 3.87/4.03 tff(12893,plain,
% 3.87/4.03 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.03 inference(symmetry,[status(thm)],[12892])).
% 3.87/4.03 tff(12894,plain,
% 3.87/4.03 ((~r(s(elem!1), s(s(s(elem!1))))) <=> (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 3.87/4.03 inference(monotonicity,[status(thm)],[12893])).
% 3.87/4.03 tff(12895,plain,
% 3.87/4.03 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))),
% 3.87/4.03 inference(rewrite,[status(thm)],[])).
% 3.87/4.03 tff(12896,plain,
% 3.87/4.03 (((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))),
% 3.87/4.03 inference(rewrite,[status(thm)],[])).
% 3.87/4.03 tff(12897,plain,
% 3.87/4.03 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z))))),
% 3.87/4.03 inference(monotonicity,[status(thm)],[12896])).
% 3.87/4.03 tff(12898,plain,
% 3.87/4.03 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))),
% 3.87/4.03 inference(transitivity,[status(thm)],[12897, 12895])).
% 3.87/4.03 tff(12899,plain,
% 3.87/4.03 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 3.87/4.03 inference(quant_inst,[status(thm)],[])).
% 3.87/4.03 tff(12900,plain,
% 3.87/4.03 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z))),
% 3.87/4.03 inference(modus_ponens,[status(thm)],[12899, 12898])).
% 3.87/4.03 tff(12901,plain,
% 3.87/4.03 (~r(s(elem!1), s(s(s(elem!1))))),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[12900, 118, 844, 1552])).
% 3.87/4.03 tff(12902,plain,
% 3.87/4.03 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.03 inference(modus_ponens,[status(thm)],[12901, 12894])).
% 3.87/4.03 tff(12903,plain,
% 3.87/4.03 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[395, 12902, 12891])).
% 3.87/4.03 tff(12904,plain,
% 3.87/4.03 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 3.87/4.03 inference(monotonicity,[status(thm)],[12868])).
% 3.87/4.03 tff(12905,plain,
% 3.87/4.03 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.87/4.03 inference(symmetry,[status(thm)],[12904])).
% 3.87/4.03 tff(12906,plain,
% 3.87/4.03 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[1557, 1552, 844])).
% 3.87/4.03 tff(12907,plain,
% 3.87/4.03 (b(s(s(s(elem!1))), s(elem!1))),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[373, 12906, 356])).
% 3.87/4.03 tff(12908,plain,
% 3.87/4.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(elem!1))), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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(elem!1))), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 3.87/4.03 inference(rewrite,[status(thm)],[])).
% 3.87/4.03 tff(12909,plain,
% 3.87/4.03 (((~b(s(elem!1), 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(z)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(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(elem!1))), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 3.87/4.03 inference(rewrite,[status(thm)],[])).
% 3.87/4.03 tff(12910,plain,
% 3.87/4.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(elem!1))), elem!1)) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 3.87/4.03 inference(monotonicity,[status(thm)],[12909])).
% 3.87/4.03 tff(12911,plain,
% 3.87/4.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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(elem!1))), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 3.87/4.03 inference(transitivity,[status(thm)],[12910, 12908])).
% 3.87/4.03 tff(12912,plain,
% 3.87/4.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 3.87/4.03 inference(quant_inst,[status(thm)],[])).
% 3.87/4.03 tff(12913,plain,
% 3.87/4.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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(elem!1))), elem!1)) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 3.87/4.03 inference(modus_ponens,[status(thm)],[12912, 12911])).
% 3.87/4.03 tff(12914,plain,
% 3.87/4.03 (~b(s(s(z)), s(s(s(elem!1))))),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[12913, 178, 2044, 683, 1597, 1071])).
% 3.87/4.03 tff(12915,plain,
% 3.87/4.03 (r(s(s(z)), s(s(s(elem!1))))),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[4223, 12914])).
% 3.87/4.03 tff(12916,plain,
% 3.87/4.03 (~r(z, s(s(s(elem!1))))),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[4808, 12915, 3261])).
% 3.87/4.03 tff(12917,plain,
% 3.87/4.03 (b(z, s(s(s(elem!1))))),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[2095, 12916])).
% 3.87/4.03 tff(12918,plain,
% 3.87/4.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 3.87/4.03 inference(rewrite,[status(thm)],[])).
% 3.87/4.03 tff(12919,plain,
% 3.87/4.03 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z))) <=> ((~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 3.87/4.03 inference(rewrite,[status(thm)],[])).
% 3.87/4.03 tff(12920,plain,
% 3.87/4.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))))),
% 3.87/4.03 inference(monotonicity,[status(thm)],[12919])).
% 3.87/4.03 tff(12921,plain,
% 3.87/4.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 3.87/4.03 inference(transitivity,[status(thm)],[12920, 12918])).
% 3.87/4.03 tff(12922,plain,
% 3.87/4.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)))),
% 3.87/4.03 inference(quant_inst,[status(thm)],[])).
% 3.87/4.03 tff(12923,plain,
% 3.87/4.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))),
% 3.87/4.03 inference(modus_ponens,[status(thm)],[12922, 12921])).
% 3.87/4.03 tff(12924,plain,
% 3.87/4.03 ($false),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[12923, 178, 818, 506, 2043, 1597, 2042])).
% 3.87/4.03 tff(12925,plain,((~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.03 tff(12926,plain,
% 3.87/4.03 (~b(elem!1, s(s(s(elem!1))))),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[12925, 12917, 506, 818, 1597])).
% 3.87/4.03 tff(12927,plain,
% 3.87/4.03 (r(elem!1, s(s(s(elem!1))))),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[2054, 12926, 1586])).
% 3.87/4.03 tff(12928,plain,
% 3.87/4.03 ($false),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[5684, 118, 12927, 438, 12915])).
% 3.87/4.03 tff(12929,plain,((~b(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (elem!1 = s(s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~r(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.03 tff(12930,plain,
% 3.87/4.03 (~b(s(s(s(elem!1))), elem!1)),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[12929, 12907, 12886, 506, 818, 3261, 438, 683, 1071])).
% 3.87/4.03 tff(12931,plain,
% 3.87/4.03 (r(s(s(s(elem!1))), elem!1)),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[570, 12930, 12878])).
% 3.87/4.03 tff(12932,plain,
% 3.87/4.03 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.87/4.03 inference(modus_ponens,[status(thm)],[12931, 12905])).
% 3.87/4.03 tff(12933,plain,
% 3.87/4.03 (~b(s(elem!1), s(s(z)))),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[2979, 12932, 438, 12903, 1071])).
% 3.87/4.03 tff(12934,plain,
% 3.87/4.03 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[4216, 118, 12931, 438])).
% 3.87/4.03 tff(12935,plain,
% 3.87/4.03 (~(s(elem!1) = s(s(z)))),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[1838, 12934, 147])).
% 3.87/4.03 tff(12936,plain,
% 3.87/4.03 ($false),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[421, 12935, 12933, 927])).
% 3.87/4.03 tff(12937,plain,((~r(s(s(s(elem!1))), z)) | r(s(elem!1), s(s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~(s(s(s(s(z)))) = elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~r(z, s(s(z)))) | (~b(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.03 tff(12938,plain,
% 3.87/4.03 (~r(s(s(s(elem!1))), z)),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[12937, 683, 147, 438, 1071, 331, 506, 818, 3261, 927, 844, 356])).
% 3.87/4.03 tff(12939,plain,
% 3.87/4.03 (b(s(s(s(elem!1))), z)),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[1565, 12938])).
% 3.87/4.03 tff(12940,plain,
% 3.87/4.03 (~(s(elem!1) = s(s(z)))),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[1838, 5343, 147])).
% 3.87/4.03 tff(12941,plain,
% 3.87/4.03 (b(s(elem!1), s(s(z)))),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[421, 12940, 927])).
% 3.87/4.03 tff(12942,plain,
% 3.87/4.03 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(elem!1))))),
% 3.87/4.03 inference(monotonicity,[status(thm)],[12868])).
% 3.87/4.03 tff(12943,plain,
% 3.87/4.03 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.87/4.03 inference(modus_ponens,[status(thm)],[556, 12905])).
% 3.87/4.03 tff(12944,plain,
% 3.87/4.03 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[2979, 12941, 438, 12943, 1071])).
% 3.87/4.03 tff(12945,plain,
% 3.87/4.03 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[395, 12944, 2286])).
% 3.87/4.03 tff(12946,plain,
% 3.87/4.03 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[2935, 12945, 1587])).
% 3.87/4.03 tff(12947,plain,
% 3.87/4.03 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.87/4.03 inference(unit_resolution,[status(thm)],[691, 12946, 12877])).
% 3.87/4.03 tff(12948,plain,
% 3.87/4.03 (b(elem!1, s(s(s(elem!1))))),
% 3.87/4.03 inference(modus_ponens,[status(thm)],[12947, 12942])).
% 3.87/4.03 tff(12949,plain,
% 3.87/4.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))),
% 3.87/4.03 inference(rewrite,[status(thm)],[])).
% 3.87/4.03 tff(12950,plain,
% 3.87/4.03 (((~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))),
% 3.87/4.04 inference(rewrite,[status(thm)],[])).
% 3.87/4.04 tff(12951,plain,
% 3.87/4.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z))))),
% 3.87/4.04 inference(monotonicity,[status(thm)],[12950])).
% 3.87/4.04 tff(12952,plain,
% 3.87/4.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))),
% 3.87/4.04 inference(transitivity,[status(thm)],[12951, 12949])).
% 3.87/4.04 tff(12953,plain,
% 3.87/4.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))),
% 3.87/4.04 inference(quant_inst,[status(thm)],[])).
% 3.87/4.04 tff(12954,plain,
% 3.87/4.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z))),
% 3.87/4.04 inference(modus_ponens,[status(thm)],[12953, 12952])).
% 3.87/4.04 tff(12955,plain,
% 3.87/4.04 ($false),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[12954, 178, 506, 683, 7976, 3461, 812, 12948, 12941])).
% 3.87/4.04 tff(12956,plain,((~r(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~(s(s(s(s(z)))) = elem!1)) | (~r(elem!1, s(elem!1))) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))) | r(s(elem!1), s(s(z))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.04 tff(12957,plain,
% 3.87/4.04 (~r(s(s(s(elem!1))), elem!1)),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[12956, 683, 506, 12939, 3461, 812, 331, 1587, 12891, 438, 1071, 927, 147])).
% 3.87/4.04 tff(12958,plain,
% 3.87/4.04 (b(s(s(s(elem!1))), elem!1)),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[570, 12957, 12878])).
% 3.87/4.04 tff(12959,plain,
% 3.87/4.04 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[1607, 12958, 1587, 844, 818, 506, 12886])).
% 3.87/4.04 tff(12960,plain,
% 3.87/4.04 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[12929, 12958, 12886, 506, 818, 3261, 438, 683, 1071])).
% 3.87/4.04 tff(12961,plain,
% 3.87/4.04 ($false),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[373, 12960, 12959, 356])).
% 3.87/4.04 tff(12962,plain,((~b(s(elem!1), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~r(z, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~(s(s(s(s(z)))) = elem!1)) | r(s(elem!1), s(s(z))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.04 tff(12963,plain,
% 3.87/4.04 (~b(s(elem!1), elem!1)),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[12962, 12880, 506, 818, 3261, 12883, 1071, 1587, 844, 3461, 12881, 331, 927, 147])).
% 3.87/4.04 tff(12964,plain,
% 3.87/4.04 (r(s(elem!1), elem!1)),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[677, 12963, 725])).
% 3.87/4.04 tff(12965,plain,
% 3.87/4.04 (b(s(elem!1), s(s(s(elem!1))))),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[5432, 12747, 5396])).
% 3.87/4.04 tff(12966,plain,
% 3.87/4.04 ((~(s(elem!1) = s(s(z)))) <=> (~(s(s(z)) = s(elem!1)))),
% 3.87/4.04 inference(monotonicity,[status(thm)],[1359])).
% 3.87/4.04 tff(12967,plain,
% 3.87/4.04 (~(s(s(z)) = s(elem!1))),
% 3.87/4.04 inference(modus_ponens,[status(thm)],[1056, 12966])).
% 3.87/4.04 tff(12968,plain,
% 3.87/4.04 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1))))),
% 3.87/4.04 inference(rewrite,[status(thm)],[])).
% 3.87/4.04 tff(12969,plain,
% 3.87/4.04 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1))))),
% 3.87/4.04 inference(quant_inst,[status(thm)],[])).
% 3.87/4.04 tff(12970,plain,
% 3.87/4.04 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1)))),
% 3.87/4.04 inference(modus_ponens,[status(thm)],[12969, 12968])).
% 3.87/4.04 tff(12971,plain,
% 3.87/4.04 (~r(s(s(z)), s(elem!1))),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[12970, 118, 1426, 438])).
% 3.87/4.04 tff(12972,plain,
% 3.87/4.04 ((s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1))),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[1065, 41, 12971])).
% 3.87/4.04 tff(12973,plain,
% 3.87/4.04 (b(s(s(z)), s(elem!1))),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[12972, 12967])).
% 3.87/4.04 tff(12974,plain,
% 3.87/4.04 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 3.87/4.04 inference(rewrite,[status(thm)],[])).
% 3.87/4.04 tff(12975,plain,
% 3.87/4.04 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 3.87/4.04 inference(quant_inst,[status(thm)],[])).
% 3.87/4.04 tff(12976,plain,
% 3.87/4.04 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(z))))),
% 3.87/4.04 inference(modus_ponens,[status(thm)],[12975, 12974])).
% 3.87/4.04 tff(12977,plain,
% 3.87/4.04 (~r(s(s(s(elem!1))), s(s(z)))),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[12976, 118, 556, 438])).
% 3.87/4.04 tff(12978,plain,
% 3.87/4.04 ((s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z)))),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[4209, 41, 12977])).
% 3.87/4.04 tff(12979,plain,
% 3.87/4.04 (b(s(s(s(elem!1))), s(s(z)))),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[12978, 12790])).
% 3.87/4.04 tff(12980,plain,
% 3.87/4.04 (b(s(s(z)), s(s(s(elem!1))))),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[4221, 41, 1683, 1836])).
% 3.87/4.04 tff(12981,plain,
% 3.87/4.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 3.87/4.04 inference(rewrite,[status(thm)],[])).
% 3.87/4.04 tff(12982,plain,
% 3.87/4.04 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(z)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 3.87/4.04 inference(rewrite,[status(thm)],[])).
% 3.87/4.04 tff(12983,plain,
% 3.87/4.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(z)), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 3.87/4.04 inference(monotonicity,[status(thm)],[12982])).
% 3.87/4.04 tff(12984,plain,
% 3.87/4.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(z)), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 3.87/4.04 inference(transitivity,[status(thm)],[12983, 12981])).
% 3.87/4.04 tff(12985,plain,
% 3.87/4.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 3.87/4.04 inference(quant_inst,[status(thm)],[])).
% 3.87/4.04 tff(12986,plain,
% 3.87/4.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 3.87/4.04 inference(modus_ponens,[status(thm)],[12985, 12984])).
% 3.87/4.04 tff(12987,plain,
% 3.87/4.04 ((~b(s(s(z)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[12986, 178, 2044, 5888, 12980])).
% 3.87/4.04 tff(12988,plain,
% 3.87/4.04 ($false),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[12987, 12979, 12973])).
% 3.87/4.04 tff(12989,plain,((~r(s(s(z)), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (s(elem!1) = s(s(z))) | r(s(s(z)), s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.04 tff(12990,plain,
% 3.87/4.04 ($false),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[12989, 12940, 5343, 438, 1426, 556, 1701, 12965])).
% 3.87/4.04 tff(12991,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.04 tff(12992,plain,
% 3.87/4.04 (~r(s(s(s(elem!1))), elem!1)),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[12991, 12883, 12964, 147, 12880])).
% 3.87/4.04 tff(12993,plain,
% 3.87/4.04 (b(s(s(s(elem!1))), elem!1)),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[570, 12992, 12878])).
% 3.87/4.04 tff(12994,plain,
% 3.87/4.04 (~r(z, s(s(s(elem!1))))),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[4808, 1823, 3261])).
% 3.87/4.04 tff(12995,plain,
% 3.87/4.04 (b(z, s(s(s(elem!1))))),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[2095, 12994])).
% 3.87/4.04 tff(12996,plain,
% 3.87/4.04 (~b(elem!1, s(s(s(elem!1))))),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[12925, 12995, 506, 818, 1597])).
% 3.87/4.04 tff(12997,plain,
% 3.87/4.04 (r(elem!1, s(s(s(elem!1))))),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[2054, 12996, 1586])).
% 3.87/4.04 tff(12998,plain,
% 3.87/4.04 ($false),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[5684, 118, 12997, 438, 1823])).
% 3.87/4.04 tff(12999,plain,((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), elem!1)) | (elem!1 = s(s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.04 tff(13000,plain,
% 3.87/4.04 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[12999, 12883, 12886, 506, 818, 12993, 3261])).
% 3.87/4.04 tff(13001,plain,
% 3.87/4.04 (~(s(elem!1) = s(s(z)))),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[1838, 13000, 147])).
% 3.87/4.04 tff(13002,plain,
% 3.87/4.04 (b(s(elem!1), s(s(z)))),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[421, 13001, 927])).
% 3.87/4.04 tff(13003,plain,
% 3.87/4.04 (b(s(s(z)), s(s(s(elem!1))))),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[4223, 13000])).
% 3.87/4.04 tff(13004,plain,
% 3.87/4.04 (~(s(elem!1) = s(s(s(elem!1))))),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[5395, 12880])).
% 3.87/4.04 tff(13005,plain,
% 3.87/4.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)))),
% 3.87/4.04 inference(rewrite,[status(thm)],[])).
% 3.87/4.04 tff(13006,plain,
% 3.87/4.04 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)))),
% 3.87/4.04 inference(rewrite,[status(thm)],[])).
% 3.87/4.04 tff(13007,plain,
% 3.87/4.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z))))),
% 3.87/4.04 inference(monotonicity,[status(thm)],[13006])).
% 3.87/4.04 tff(13008,plain,
% 3.87/4.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)))),
% 3.87/4.04 inference(transitivity,[status(thm)],[13007, 13005])).
% 3.87/4.04 tff(13009,plain,
% 3.87/4.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 3.87/4.04 inference(quant_inst,[status(thm)],[])).
% 3.87/4.04 tff(13010,plain,
% 3.87/4.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z))),
% 3.87/4.04 inference(modus_ponens,[status(thm)],[13009, 13008])).
% 3.87/4.04 tff(13011,plain,
% 3.87/4.04 ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[13010, 178, 818, 12993, 3461])).
% 3.87/4.04 tff(13012,plain,
% 3.87/4.04 (~b(s(s(s(elem!1))), z)),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[13011, 13003])).
% 3.87/4.04 tff(13013,plain,
% 3.87/4.04 (r(s(s(s(elem!1))), z)),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[1565, 13012])).
% 3.87/4.04 tff(13014,plain,
% 3.87/4.04 (~r(s(elem!1), s(s(s(elem!1))))),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[12900, 118, 844, 13013])).
% 3.87/4.04 tff(13015,plain,
% 3.87/4.04 (b(s(elem!1), s(s(s(elem!1))))),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[5432, 13014, 13004])).
% 3.87/4.04 tff(13016,plain,
% 3.87/4.04 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[1607, 12993, 1587, 844, 818, 506, 12886])).
% 3.87/4.04 tff(13017,plain,
% 3.87/4.04 (b(s(s(s(elem!1))), s(elem!1))),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[373, 13016, 12880])).
% 3.87/4.04 tff(13018,plain,
% 3.87/4.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 3.87/4.04 inference(rewrite,[status(thm)],[])).
% 3.87/4.04 tff(13019,plain,
% 3.87/4.04 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(z))))) <=> ((~b(s(s(z)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 3.87/4.04 inference(rewrite,[status(thm)],[])).
% 3.87/4.04 tff(13020,plain,
% 3.87/4.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 3.87/4.04 inference(monotonicity,[status(thm)],[13019])).
% 3.87/4.04 tff(13021,plain,
% 3.87/4.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 3.87/4.04 inference(transitivity,[status(thm)],[13020, 13018])).
% 3.87/4.04 tff(13022,plain,
% 3.87/4.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(z)))))),
% 3.87/4.04 inference(quant_inst,[status(thm)],[])).
% 3.87/4.04 tff(13023,plain,
% 3.87/4.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 3.87/4.04 inference(modus_ponens,[status(thm)],[13022, 13021])).
% 3.87/4.04 tff(13024,plain,
% 3.87/4.04 ($false),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[13023, 178, 13017, 1071, 13015, 13003, 13002])).
% 3.87/4.04 tff(13025,plain,((~(s(s(s(s(z)))) = elem!1)) | (~b(s(s(z)), s(elem!1))) | (~r(s(elem!1), z)) | r(s(elem!1), s(s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, z)) | (~r(z, s(s(z)))) | (~r(elem!1, s(elem!1))) | (s(elem!1) = elem!1) | (s(s(z)) = elem!1) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.04 tff(13026,plain,
% 3.87/4.04 (~(s(s(s(s(z)))) = elem!1)),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[13025, 12729, 12569, 1071, 12865, 3461, 147, 12862, 3261, 12720, 12863, 12728, 202])).
% 3.87/4.04 tff(13027,plain,
% 3.87/4.04 (~(elem!1 = s(s(s(s(z)))))),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[325, 13026])).
% 3.87/4.04 tff(13028,plain,
% 3.87/4.04 (~(elem!1 = s(s(z)))),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[311, 12728])).
% 3.87/4.04 tff(13029,plain,
% 3.87/4.04 (~b(s(s(z)), elem!1)),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[12263, 12865, 3461, 1687, 13027, 147, 13028, 12862])).
% 3.87/4.04 tff(13030,plain,
% 3.87/4.04 (r(s(s(z)), elem!1)),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[448, 13029, 12728])).
% 3.87/4.04 tff(13031,plain,
% 3.87/4.04 (~r(elem!1, s(s(s(s(z)))))),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[8763, 13030, 147])).
% 3.87/4.04 tff(13032,plain,
% 3.87/4.04 (b(elem!1, s(s(s(s(z)))))),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[483, 13031, 13027])).
% 3.87/4.04 tff(13033,plain,
% 3.87/4.04 (~b(s(s(s(s(z)))), elem!1)),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[7020, 13032, 12862, 12865, 1687])).
% 3.87/4.04 tff(13034,plain,
% 3.87/4.04 (r(s(s(s(s(z)))), elem!1)),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[3142, 13033, 13026])).
% 3.87/4.04 tff(13035,plain,
% 3.87/4.04 ($false),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[9469, 118, 13030, 13034, 147])).
% 3.87/4.04 tff(13036,plain,((~r(z, s(elem!1))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))) | (~r(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | b(s(elem!1), z) | r(elem!1, z) | (s(elem!1) = s(s(s(s(z))))) | b(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.04 tff(13037,plain,
% 3.87/4.04 (~r(z, s(elem!1))),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[13036, 12713, 1687, 3461, 10794, 3261, 202, 766, 1342, 1369, 751])).
% 3.87/4.04 tff(13038,plain,
% 3.87/4.04 (b(z, s(elem!1))),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[2351, 13037])).
% 3.87/4.04 tff(13039,plain,
% 3.87/4.04 (~(elem!1 = z)),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[12054, 13038, 751])).
% 3.87/4.04 tff(13040,plain,
% 3.87/4.04 (b(elem!1, z)),
% 3.87/4.04 inference(unit_resolution,[status(thm)],[498, 13039, 1342])).
% 3.87/4.04 tff(13041,plain,
% 3.87/4.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))),
% 3.87/4.04 inference(rewrite,[status(thm)],[])).
% 3.87/4.04 tff(13042,plain,
% 3.87/4.04 (((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z))))) <=> ((~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))),
% 3.87/4.05 inference(rewrite,[status(thm)],[])).
% 3.87/4.05 tff(13043,plain,
% 3.87/4.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z))))),
% 3.87/4.05 inference(monotonicity,[status(thm)],[13042])).
% 3.87/4.05 tff(13044,plain,
% 3.87/4.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))),
% 3.87/4.05 inference(transitivity,[status(thm)],[13043, 13041])).
% 3.87/4.05 tff(13045,plain,
% 3.87/4.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))))),
% 3.87/4.05 inference(quant_inst,[status(thm)],[])).
% 3.87/4.05 tff(13046,plain,
% 3.87/4.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z))),
% 3.87/4.05 inference(modus_ponens,[status(thm)],[13045, 13044])).
% 3.87/4.05 tff(13047,plain,
% 3.87/4.05 (~b(elem!1, s(s(z)))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[13046, 178, 13040, 13038, 3461, 12713])).
% 3.87/4.05 tff(13048,plain,
% 3.87/4.05 (~(s(elem!1) = elem!1)),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[790, 13040, 766])).
% 3.87/4.05 tff(13049,plain,
% 3.87/4.05 (~(elem!1 = s(elem!1))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[748, 13048])).
% 3.87/4.05 tff(13050,plain,
% 3.87/4.05 (r(elem!1, s(elem!1))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[756, 13049, 751])).
% 3.87/4.05 tff(13051,plain,
% 3.87/4.05 (~(z = elem!1)),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[317, 13039])).
% 3.87/4.05 tff(13052,plain,
% 3.87/4.05 (elem!1 = s(s(z))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[467, 460, 461])).
% 3.87/4.05 tff(13053,plain,
% 3.87/4.05 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[12698, 13052, 202, 1687, 855, 725, 844, 3261])).
% 3.87/4.05 tff(13054,plain,
% 3.87/4.05 (~(s(s(s(s(z)))) = elem!1)),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[4509, 461, 202])).
% 3.87/4.05 tff(13055,plain,
% 3.87/4.05 (~(elem!1 = s(s(s(s(z)))))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[325, 13054])).
% 3.87/4.05 tff(13056,plain,
% 3.87/4.05 (~b(elem!1, s(s(s(s(z)))))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[12671, 460, 105, 855, 3461, 202, 506, 1587, 2508, 13054, 1687])).
% 3.87/4.05 tff(13057,plain,
% 3.87/4.05 (r(elem!1, s(s(s(s(z)))))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[483, 13056, 13055])).
% 3.87/4.05 tff(13058,plain,
% 3.87/4.05 (~r(s(s(s(s(z)))), s(elem!1))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[11326, 13057, 1587])).
% 3.87/4.05 tff(13059,plain,
% 3.87/4.05 ($false),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[2173, 13058, 13053, 2508])).
% 3.87/4.05 tff(13060,plain,(r(elem!1, s(s(z))) | (s(s(s(s(z)))) = s(elem!1)) | (~r(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(elem!1))) | (s(elem!1) = elem!1) | (~r(s(elem!1), z)) | (~r(z, s(s(z)))) | b(elem!1, s(s(z))) | b(s(s(z)), s(s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.05 tff(13061,plain,
% 3.87/4.05 (r(elem!1, s(s(z)))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[13060, 13050, 2169, 202, 1687, 13038, 13048, 12569, 3261, 13047, 105, 3461, 13040])).
% 3.87/4.05 tff(13062,plain,
% 3.87/4.05 (~r(z, elem!1)),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[4862, 13061, 3261])).
% 3.87/4.05 tff(13063,plain,
% 3.87/4.05 (b(z, elem!1)),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[585, 13062, 13051])).
% 3.87/4.05 tff(13064,plain,
% 3.87/4.05 (~(s(s(z)) = elem!1)),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[7053, 13062, 3261])).
% 3.87/4.05 tff(13065,plain,
% 3.87/4.05 (~(elem!1 = s(s(z)))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[311, 13064])).
% 3.87/4.05 tff(13066,plain,
% 3.87/4.05 (r(elem!1, s(s(z)))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[467, 461, 462])).
% 3.87/4.05 tff(13067,plain,
% 3.87/4.05 (~r(elem!1, s(s(s(s(z)))))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[5670, 13066, 147])).
% 3.87/4.05 tff(13068,plain,
% 3.87/4.05 (b(elem!1, s(s(s(s(z)))))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[483, 13067, 13055])).
% 3.87/4.05 tff(13069,plain,
% 3.87/4.05 (~b(s(s(s(s(z)))), elem!1)),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[7020, 13068, 506, 818, 1687])).
% 3.87/4.05 tff(13070,plain,
% 3.87/4.05 (r(s(s(s(s(z)))), elem!1)),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[3142, 13069, 13054])).
% 3.87/4.05 tff(13071,plain,
% 3.87/4.05 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[12658, 13068, 855, 1687, 506])).
% 3.87/4.05 tff(13072,plain,
% 3.87/4.05 (r(s(s(s(s(z)))), s(elem!1))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[2173, 13071, 2508])).
% 3.87/4.05 tff(13073,plain,
% 3.87/4.05 ($false),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[10992, 13072, 13070, 1587])).
% 3.87/4.05 tff(13074,plain,(b(elem!1, s(s(z))) | (~r(elem!1, s(elem!1))) | (s(s(s(s(z)))) = s(elem!1)) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (elem!1 = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.05 tff(13075,plain,
% 3.87/4.05 ($false),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[13074, 13065, 13063, 2169, 13038, 1687, 13040, 13050, 10794, 202, 13047])).
% 3.87/4.05 tff(13076,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))) | b(s(s(z)), s(s(s(s(z))))) | (~b(s(s(z)), z)) | b(elem!1, s(elem!1)) | b(s(elem!1), z) | r(elem!1, z) | (s(elem!1) = s(s(s(s(z))))) | (s(s(z)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.05 tff(13077,plain,
% 3.87/4.05 (~b(s(s(s(s(z)))), s(s(z)))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[13076, 12623, 3261, 105, 5619, 751, 766, 1687, 1369, 12570])).
% 3.87/4.05 tff(13078,plain,
% 3.87/4.05 (r(s(s(s(s(z)))), s(s(z)))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[102, 13077])).
% 3.87/4.05 tff(13079,plain,
% 3.87/4.05 (~r(s(s(s(s(z)))), z)),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[9569, 13078, 3261])).
% 3.87/4.05 tff(13080,plain,
% 3.87/4.05 (b(s(s(s(s(z)))), z)),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[191, 13079])).
% 3.87/4.05 tff(13081,plain,
% 3.87/4.05 (~r(s(elem!1), s(s(z)))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[8621, 12569, 3261])).
% 3.87/4.05 tff(13082,plain,
% 3.87/4.05 (b(s(elem!1), s(s(z)))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[421, 13081, 12571])).
% 3.87/4.05 tff(13083,plain,
% 3.87/4.05 (r(s(elem!1), elem!1)),
% 3.87/4.05 inference(modus_ponens,[status(thm)],[12569, 12733])).
% 3.87/4.05 tff(13084,plain,
% 3.87/4.05 (b(s(s(z)), s(elem!1)) <=> b(s(s(z)), s(z))),
% 3.87/4.05 inference(monotonicity,[status(thm)],[929])).
% 3.87/4.05 tff(13085,plain,
% 3.87/4.05 (b(s(s(z)), s(elem!1))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[1067, 12115, 1060])).
% 3.87/4.05 tff(13086,plain,
% 3.87/4.05 (b(s(s(z)), s(z))),
% 3.87/4.05 inference(modus_ponens,[status(thm)],[13085, 13084])).
% 3.87/4.05 tff(13087,plain,
% 3.87/4.05 (b(s(z), s(s(z)))),
% 3.87/4.05 inference(modus_ponens,[status(thm)],[12060, 1017])).
% 3.87/4.05 tff(13088,plain,
% 3.87/4.05 (~r(s(s(s(elem!1))), elem!1)),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[12762, 13087, 13086, 928, 13083, 12032])).
% 3.87/4.05 tff(13089,plain,
% 3.87/4.05 (b(s(s(s(elem!1))), elem!1)),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[570, 13088, 941])).
% 3.87/4.05 tff(13090,plain,
% 3.87/4.05 (b(s(s(s(elem!1))), z)),
% 3.87/4.05 inference(modus_ponens,[status(thm)],[13089, 10092])).
% 3.87/4.05 tff(13091,plain,
% 3.87/4.05 (r(elem!1, s(elem!1))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[12719, 12056, 1342, 766, 751])).
% 3.87/4.05 tff(13092,plain,
% 3.87/4.05 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[12177, 13089, 12064, 12081, 12138, 12071, 3261])).
% 3.87/4.05 tff(13093,plain,
% 3.87/4.05 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[3409, 13092, 12038])).
% 3.87/4.05 tff(13094,plain,
% 3.87/4.05 (b(s(s(s(z))), s(s(z)))),
% 3.87/4.05 inference(modus_ponens,[status(thm)],[13093, 5221])).
% 3.87/4.05 tff(13095,plain,
% 3.87/4.05 (b(s(s(s(z))), z)),
% 3.87/4.05 inference(modus_ponens,[status(thm)],[13089, 12741])).
% 3.87/4.05 tff(13096,plain,
% 3.87/4.05 (~b(s(z), s(s(s(z))))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[12779, 178, 3461, 13087, 13095, 13094])).
% 3.87/4.05 tff(13097,plain,
% 3.87/4.05 (~b(s(elem!1), s(s(s(elem!1))))),
% 3.87/4.05 inference(modus_ponens,[status(thm)],[13096, 12773])).
% 3.87/4.05 tff(13098,plain,
% 3.87/4.05 (r(s(elem!1), s(s(s(elem!1))))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[5432, 13097, 12746])).
% 3.87/4.05 tff(13099,plain,
% 3.87/4.05 (~r(elem!1, s(s(s(elem!1))))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[10317, 13098, 13091])).
% 3.87/4.05 tff(13100,plain,
% 3.87/4.05 (~r(z, s(s(s(elem!1))))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[4850, 13099, 928])).
% 3.87/4.05 tff(13101,plain,
% 3.87/4.05 (b(z, s(s(s(elem!1))))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[2095, 13100])).
% 3.87/4.05 tff(13102,plain,
% 3.87/4.05 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[12809, 13101, 3461, 12068, 13090])).
% 3.87/4.05 tff(13103,plain,
% 3.87/4.05 (b(s(s(s(s(elem!1)))), z)),
% 3.87/4.05 inference(modus_ponens,[status(thm)],[11884, 12302])).
% 3.87/4.05 tff(13104,plain,
% 3.87/4.05 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[12328, 13101, 13090, 13103, 12300])).
% 3.87/4.05 tff(13105,plain,
% 3.87/4.05 ($false),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[1750, 13104, 13102, 12077])).
% 3.87/4.05 tff(13106,plain,((~(elem!1 = z)) | (~b(s(s(z)), z)) | (~r(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (s(s(z)) = s(elem!1)) | r(elem!1, z) | b(s(elem!1), z) | b(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.05 tff(13107,plain,
% 3.87/4.05 (~(elem!1 = z)),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[13106, 13078, 3261, 1687, 2169, 5619, 10794, 12570, 12623, 766, 751])).
% 3.87/4.05 tff(13108,plain,
% 3.87/4.05 (b(elem!1, z)),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[498, 13107, 12623])).
% 3.87/4.05 tff(13109,plain,
% 3.87/4.05 (~r(s(elem!1), s(s(s(s(z)))))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[5758, 1329, 147])).
% 3.87/4.05 tff(13110,plain,
% 3.87/4.05 (b(s(elem!1), s(s(s(s(z)))))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[1084, 13109, 1369])).
% 3.87/4.05 tff(13111,plain,
% 3.87/4.05 (~(elem!1 = s(s(s(s(z)))))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[12646, 1329, 147, 1587])).
% 3.87/4.05 tff(13112,plain,
% 3.87/4.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 3.87/4.05 inference(rewrite,[status(thm)],[])).
% 3.87/4.05 tff(13113,plain,
% 3.87/4.05 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 3.87/4.05 inference(rewrite,[status(thm)],[])).
% 3.87/4.05 tff(13114,plain,
% 3.87/4.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 3.87/4.05 inference(monotonicity,[status(thm)],[13113])).
% 3.87/4.05 tff(13115,plain,
% 3.87/4.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 3.87/4.05 inference(transitivity,[status(thm)],[13114, 13112])).
% 3.87/4.05 tff(13116,plain,
% 3.87/4.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)))),
% 3.87/4.05 inference(quant_inst,[status(thm)],[])).
% 3.87/4.05 tff(13117,plain,
% 3.87/4.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 3.87/4.05 inference(modus_ponens,[status(thm)],[13116, 13115])).
% 3.87/4.05 tff(13118,plain,
% 3.87/4.05 (~b(elem!1, s(s(s(s(z)))))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[13117, 178, 506, 683, 168, 13110])).
% 3.87/4.05 tff(13119,plain,
% 3.87/4.05 (r(elem!1, s(s(s(s(z)))))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[483, 13118, 13111])).
% 3.87/4.05 tff(13120,plain,
% 3.87/4.05 (~r(s(s(s(s(z)))), s(elem!1))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[11326, 13119, 1587])).
% 3.87/4.05 tff(13121,plain,
% 3.87/4.05 (b(s(s(s(s(z)))), s(elem!1))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[2173, 13120, 2169])).
% 3.87/4.05 tff(13122,plain,
% 3.87/4.05 ($false),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[12681, 178, 12627, 1687, 168, 13121, 13110])).
% 3.87/4.05 tff(13123,plain,((~r(s(s(z)), s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~r(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (s(elem!1) = s(s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.05 tff(13124,plain,
% 3.87/4.05 (~r(s(s(z)), s(elem!1))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[13123, 1286, 168, 1587, 506, 1687, 1369, 147, 3261])).
% 3.87/4.05 tff(13125,plain,
% 3.87/4.05 (r(s(s(z)), s(elem!1))),
% 3.87/4.05 inference(modus_ponens,[status(thm)],[1587, 1326])).
% 3.87/4.05 tff(13126,plain,
% 3.87/4.05 ($false),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[1062, 13125])).
% 3.87/4.05 tff(13127,plain,((~(s(s(z)) = elem!1)) | r(s(s(z)), s(elem!1)) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.05 tff(13128,plain,
% 3.87/4.05 (~(s(s(z)) = elem!1)),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[13127, 13124, 1587])).
% 3.87/4.05 tff(13129,plain,
% 3.87/4.05 (~r(elem!1, s(s(z)))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[4862, 521, 3261])).
% 3.87/4.05 tff(13130,plain,
% 3.87/4.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))),
% 3.87/4.05 inference(rewrite,[status(thm)],[])).
% 3.87/4.05 tff(13131,plain,
% 3.87/4.05 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))),
% 3.87/4.05 inference(rewrite,[status(thm)],[])).
% 3.87/4.05 tff(13132,plain,
% 3.87/4.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z))))),
% 3.87/4.05 inference(monotonicity,[status(thm)],[13131])).
% 3.87/4.05 tff(13133,plain,
% 3.87/4.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))),
% 3.87/4.05 inference(transitivity,[status(thm)],[13132, 13130])).
% 3.87/4.05 tff(13134,plain,
% 3.87/4.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), elem!1)))),
% 3.87/4.05 inference(quant_inst,[status(thm)],[])).
% 3.87/4.05 tff(13135,plain,
% 3.87/4.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z))),
% 3.87/4.05 inference(modus_ponens,[status(thm)],[13134, 13133])).
% 3.87/4.05 tff(13136,plain,
% 3.87/4.05 ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(z))))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[13135, 178, 506, 3461, 1070])).
% 3.87/4.05 tff(13137,plain,
% 3.87/4.05 (~b(elem!1, s(s(z)))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[13136, 1286])).
% 3.87/4.05 tff(13138,plain,
% 3.87/4.05 (elem!1 = s(s(z))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[467, 13137, 13129])).
% 3.87/4.05 tff(13139,plain,
% 3.87/4.05 ($false),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[311, 13138, 13128])).
% 3.87/4.05 tff(13140,plain,((~r(z, elem!1)) | (~r(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (s(elem!1) = s(s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (s(elem!1) = elem!1) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.05 tff(13141,plain,
% 3.87/4.05 (~r(z, elem!1)),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[13140, 12622, 13108, 5619, 13082, 13080, 1687, 1369, 10794, 3261, 12620, 12569])).
% 3.87/4.05 tff(13142,plain,
% 3.87/4.05 (~(s(s(z)) = elem!1)),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[7053, 13141, 3261])).
% 3.87/4.05 tff(13143,plain,
% 3.87/4.05 (~(elem!1 = s(s(z)))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[311, 13142])).
% 3.87/4.05 tff(13144,plain,
% 3.87/4.05 (~(z = elem!1)),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[317, 13107])).
% 3.87/4.05 tff(13145,plain,
% 3.87/4.05 (~(s(elem!1) = s(s(z)))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[1362, 1060])).
% 3.87/4.05 tff(13146,plain,
% 3.87/4.05 (~(s(elem!1) = elem!1)),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[12619, 13145, 1687, 3261, 147, 2169, 3461, 844])).
% 3.87/4.05 tff(13147,plain,
% 3.87/4.05 (s(s(z)) = elem!1),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[448, 11800, 3241])).
% 3.87/4.05 tff(13148,plain,
% 3.87/4.05 ($false),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[13127, 13124, 13147, 1587])).
% 3.87/4.05 tff(13149,plain,((~r(z, elem!1)) | (~r(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(z)))))) | (s(elem!1) = s(s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | b(s(s(z)), elem!1) | (s(elem!1) = elem!1) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.05 tff(13150,plain,
% 3.87/4.05 (~r(z, elem!1)),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[13149, 3241, 11884, 506, 1687, 1369, 147, 3261, 1587, 13146, 844])).
% 3.87/4.05 tff(13151,plain,
% 3.87/4.05 (b(z, elem!1)),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[585, 13150, 507])).
% 3.87/4.05 tff(13152,plain,
% 3.87/4.05 ((~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z))))))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[12519, 178, 506, 1687, 11884])).
% 3.87/4.05 tff(13153,plain,
% 3.87/4.05 (~b(elem!1, s(s(s(s(z)))))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[13152, 13151])).
% 3.87/4.05 tff(13154,plain,
% 3.87/4.05 (~(s(s(z)) = elem!1)),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[7053, 13150, 3261])).
% 3.87/4.05 tff(13155,plain,
% 3.87/4.05 (r(s(s(z)), elem!1)),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[448, 13154, 3241])).
% 3.87/4.05 tff(13156,plain,
% 3.87/4.05 (~r(elem!1, s(s(s(s(z)))))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[8763, 13155, 147])).
% 3.87/4.05 tff(13157,plain,
% 3.87/4.05 (elem!1 = s(s(s(s(z))))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[483, 13156, 13153])).
% 3.87/4.05 tff(13158,plain,
% 3.87/4.05 (s(elem!1) = s(s(s(s(s(z)))))),
% 3.87/4.05 inference(monotonicity,[status(thm)],[13157])).
% 3.87/4.05 tff(13159,plain,
% 3.87/4.05 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 3.87/4.05 inference(monotonicity,[status(thm)],[13158])).
% 3.87/4.05 tff(13160,plain,
% 3.87/4.05 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 3.87/4.05 inference(monotonicity,[status(thm)],[13159])).
% 3.87/4.05 tff(13161,plain,
% 3.87/4.05 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(s(s(s(z))))))), z)),
% 3.87/4.05 inference(monotonicity,[status(thm)],[13160])).
% 3.87/4.05 tff(13162,plain,
% 3.87/4.05 (s(s(s(s(z)))) = elem!1),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[325, 13157])).
% 3.87/4.05 tff(13163,plain,
% 3.87/4.05 (~(s(s(elem!1)) = elem!1)),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[338, 13162, 13154])).
% 3.87/4.05 tff(13164,plain,
% 3.87/4.05 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[348, 13163])).
% 3.87/4.05 tff(13165,plain,
% 3.87/4.05 (b(s(s(z)), s(elem!1)) <=> b(s(s(z)), s(s(s(s(s(z))))))),
% 3.87/4.05 inference(monotonicity,[status(thm)],[13158])).
% 3.87/4.05 tff(13166,plain,
% 3.87/4.05 (~r(s(s(z)), s(elem!1))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[12646, 13157, 147, 1587])).
% 3.87/4.05 tff(13167,plain,
% 3.87/4.05 (b(s(s(z)), s(elem!1))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[1067, 13166, 1060])).
% 3.87/4.05 tff(13168,plain,
% 3.87/4.05 (b(s(s(z)), s(s(s(s(s(z))))))),
% 3.87/4.05 inference(modus_ponens,[status(thm)],[13167, 13165])).
% 3.87/4.05 tff(13169,plain,
% 3.87/4.05 (~b(elem!1, s(s(s(s(z)))))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[13152, 818])).
% 3.87/4.05 tff(13170,plain,
% 3.87/4.05 (elem!1 = s(s(s(s(z))))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[483, 9308, 13169])).
% 3.87/4.05 tff(13171,plain,
% 3.87/4.05 (s(elem!1) = s(s(s(s(s(z)))))),
% 3.87/4.05 inference(monotonicity,[status(thm)],[13170])).
% 3.87/4.05 tff(13172,plain,
% 3.87/4.05 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 3.87/4.05 inference(monotonicity,[status(thm)],[13171])).
% 3.87/4.05 tff(13173,plain,
% 3.87/4.05 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 3.87/4.05 inference(monotonicity,[status(thm)],[13172])).
% 3.87/4.05 tff(13174,plain,
% 3.87/4.05 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.05 inference(monotonicity,[status(thm)],[13173])).
% 3.87/4.05 tff(13175,plain,
% 3.87/4.05 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 3.87/4.05 inference(symmetry,[status(thm)],[13174])).
% 3.87/4.05 tff(13176,plain,
% 3.87/4.05 ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(s(z)), s(s(s(elem!1)))))),
% 3.87/4.05 inference(monotonicity,[status(thm)],[13175])).
% 3.87/4.05 tff(13177,plain,
% 3.87/4.05 (s(s(s(s(s(z))))) = s(elem!1)),
% 3.87/4.05 inference(symmetry,[status(thm)],[13171])).
% 3.87/4.05 tff(13178,plain,
% 3.87/4.05 (b(s(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))))))))),
% 3.87/4.05 inference(monotonicity,[status(thm)],[13177])).
% 3.87/4.05 tff(13179,plain,
% 3.87/4.05 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.05 inference(symmetry,[status(thm)],[13178])).
% 3.87/4.05 tff(13180,plain,
% 3.87/4.05 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.87/4.05 inference(monotonicity,[status(thm)],[13173])).
% 3.87/4.05 tff(13181,plain,
% 3.87/4.05 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.87/4.05 inference(transitivity,[status(thm)],[13180, 377])).
% 3.87/4.05 tff(13182,plain,
% 3.87/4.05 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 3.87/4.05 inference(monotonicity,[status(thm)],[13181])).
% 3.87/4.05 tff(13183,plain,
% 3.87/4.05 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.87/4.05 inference(modus_ponens,[status(thm)],[356, 13182])).
% 3.87/4.05 tff(13184,plain,
% 3.87/4.05 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.05 inference(monotonicity,[status(thm)],[13177])).
% 3.87/4.05 tff(13185,plain,
% 3.87/4.05 ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) <=> (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 3.87/4.05 inference(monotonicity,[status(thm)],[13184])).
% 3.87/4.05 tff(13186,plain,
% 3.87/4.05 (r(s(elem!1), z) <=> r(s(s(s(s(s(z))))), z)),
% 3.87/4.05 inference(monotonicity,[status(thm)],[13171])).
% 3.87/4.05 tff(13187,plain,
% 3.87/4.05 (r(s(s(s(s(s(z))))), z)),
% 3.87/4.05 inference(modus_ponens,[status(thm)],[844, 13186])).
% 3.87/4.05 tff(13188,plain,
% 3.87/4.05 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.87/4.05 inference(monotonicity,[status(thm)],[13173, 13170])).
% 3.87/4.05 tff(13189,plain,
% 3.87/4.05 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.87/4.05 inference(monotonicity,[status(thm)],[13170])).
% 3.87/4.05 tff(13190,plain,
% 3.87/4.05 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = elem!1)),
% 3.87/4.05 inference(symmetry,[status(thm)],[13189])).
% 3.87/4.05 tff(13191,plain,
% 3.87/4.05 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 3.87/4.05 inference(monotonicity,[status(thm)],[13190])).
% 3.87/4.05 tff(13192,plain,
% 3.87/4.05 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[2840, 1056])).
% 3.87/4.05 tff(13193,plain,
% 3.87/4.05 (~(s(s(s(elem!1))) = elem!1)),
% 3.87/4.05 inference(modus_ponens,[status(thm)],[13192, 13191])).
% 3.87/4.05 tff(13194,plain,
% 3.87/4.05 (~r(s(s(s(elem!1))), elem!1)),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[12991, 1426, 438, 147, 356])).
% 3.87/4.05 tff(13195,plain,
% 3.87/4.05 (b(s(s(s(elem!1))), elem!1)),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[570, 13194, 13193])).
% 3.87/4.05 tff(13196,plain,
% 3.87/4.05 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.87/4.05 inference(modus_ponens,[status(thm)],[13195, 13188])).
% 3.87/4.05 tff(13197,plain,
% 3.87/4.05 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[11898, 13196, 193, 1687, 11884, 3461])).
% 3.87/4.05 tff(13198,plain,
% 3.87/4.05 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.87/4.05 inference(unit_resolution,[status(thm)],[133, 13197])).
% 3.87/4.05 tff(13199,plain,
% 3.87/4.05 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 3.87/4.05 inference(rewrite,[status(thm)],[])).
% 3.87/4.05 tff(13200,plain,
% 3.87/4.05 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 3.87/4.05 inference(rewrite,[status(thm)],[])).
% 3.87/4.05 tff(13201,plain,
% 3.87/4.05 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))))),
% 3.87/4.05 inference(monotonicity,[status(thm)],[13200])).
% 3.87/4.05 tff(13202,plain,
% 3.87/4.05 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 3.87/4.05 inference(transitivity,[status(thm)],[13201, 13199])).
% 3.87/4.05 tff(13203,plain,
% 3.87/4.05 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 3.87/4.05 inference(quant_inst,[status(thm)],[])).
% 3.87/4.05 tff(13204,plain,
% 3.87/4.05 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 3.87/4.06 inference(modus_ponens,[status(thm)],[13203, 13202])).
% 3.87/4.06 tff(13205,plain,
% 3.87/4.06 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.06 inference(unit_resolution,[status(thm)],[13204, 118, 13198, 13187])).
% 3.87/4.06 tff(13206,plain,
% 3.87/4.06 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.06 inference(modus_ponens,[status(thm)],[13205, 13185])).
% 3.87/4.06 tff(13207,plain,
% 3.87/4.06 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.06 inference(unit_resolution,[status(thm)],[395, 13206, 13183])).
% 3.87/4.06 tff(13208,plain,
% 3.87/4.06 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.06 inference(modus_ponens,[status(thm)],[13207, 13179])).
% 3.87/4.06 tff(13209,plain,
% 3.87/4.06 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 3.87/4.06 inference(symmetry,[status(thm)],[13173])).
% 3.87/4.06 tff(13210,plain,
% 3.87/4.06 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 3.87/4.06 inference(monotonicity,[status(thm)],[13209, 13177])).
% 3.87/4.06 tff(13211,plain,
% 3.87/4.06 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.87/4.06 inference(symmetry,[status(thm)],[13210])).
% 3.87/4.06 tff(13212,plain,
% 3.87/4.06 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(elem!1))))),
% 3.87/4.06 inference(transitivity,[status(thm)],[13190, 2486])).
% 3.87/4.06 tff(13213,plain,
% 3.87/4.06 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 3.87/4.06 inference(monotonicity,[status(thm)],[13212])).
% 3.87/4.06 tff(13214,plain,
% 3.87/4.06 (~(elem!1 = s(s(s(elem!1))))),
% 3.87/4.06 inference(modus_ponens,[status(thm)],[13192, 13213])).
% 3.87/4.06 tff(13215,plain,
% 3.87/4.06 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.87/4.06 inference(unit_resolution,[status(thm)],[1607, 13195, 1587, 844, 818, 506, 13214])).
% 3.87/4.06 tff(13216,plain,
% 3.87/4.06 (b(s(s(s(elem!1))), s(elem!1))),
% 3.87/4.06 inference(unit_resolution,[status(thm)],[373, 13215, 356])).
% 3.87/4.06 tff(13217,plain,
% 3.87/4.06 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.87/4.06 inference(modus_ponens,[status(thm)],[13216, 13211])).
% 3.87/4.06 tff(13218,plain,
% 3.87/4.06 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 3.87/4.06 inference(monotonicity,[status(thm)],[13171])).
% 3.87/4.06 tff(13219,plain,
% 3.87/4.06 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(s(s(z)))))),
% 3.87/4.06 inference(monotonicity,[status(thm)],[13170])).
% 3.87/4.06 tff(13220,plain,
% 3.87/4.06 (r(s(elem!1), s(s(s(s(z)))))),
% 3.87/4.06 inference(modus_ponens,[status(thm)],[1426, 13219])).
% 3.87/4.06 tff(13221,plain,
% 3.87/4.06 (~r(s(elem!1), s(s(z)))),
% 3.87/4.06 inference(unit_resolution,[status(thm)],[3949, 13220, 193])).
% 3.87/4.06 tff(13222,plain,
% 3.87/4.06 (b(s(elem!1), s(s(z)))),
% 3.87/4.06 inference(unit_resolution,[status(thm)],[421, 13221, 1056])).
% 3.87/4.06 tff(13223,plain,
% 3.87/4.06 (b(s(s(s(s(s(z))))), s(s(z)))),
% 3.87/4.06 inference(modus_ponens,[status(thm)],[13222, 13218])).
% 3.87/4.06 tff(13224,plain,
% 3.87/4.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 3.87/4.06 inference(rewrite,[status(thm)],[])).
% 3.87/4.06 tff(13225,plain,
% 3.87/4.06 (((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 3.87/4.06 inference(rewrite,[status(thm)],[])).
% 3.87/4.06 tff(13226,plain,
% 3.87/4.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 3.87/4.06 inference(monotonicity,[status(thm)],[13225])).
% 3.87/4.06 tff(13227,plain,
% 3.87/4.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 3.87/4.06 inference(transitivity,[status(thm)],[13226, 13224])).
% 3.87/4.06 tff(13228,plain,
% 3.87/4.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 3.87/4.06 inference(quant_inst,[status(thm)],[])).
% 3.87/4.06 tff(13229,plain,
% 3.87/4.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 3.87/4.06 inference(modus_ponens,[status(thm)],[13228, 13227])).
% 3.87/4.06 tff(13230,plain,
% 3.87/4.06 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
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% 3.87/4.06 tff(13231,plain,
% 3.87/4.06 (~b(s(s(z)), s(s(s(elem!1))))),
% 3.87/4.06 inference(modus_ponens,[status(thm)],[13230, 13176])).
% 3.87/4.06 tff(13232,plain,
% 3.87/4.06 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.87/4.06 inference(unit_resolution,[status(thm)],[12999, 13195, 438, 506, 818, 13214, 3261])).
% 3.87/4.06 tff(13233,plain,
% 3.87/4.06 (b(s(s(z)), s(s(s(elem!1))))),
% 3.87/4.06 inference(unit_resolution,[status(thm)],[4223, 13232])).
% 3.87/4.06 tff(13234,plain,
% 3.87/4.06 ($false),
% 3.87/4.06 inference(unit_resolution,[status(thm)],[13233, 13231])).
% 3.87/4.06 tff(13235,plain,((~r(s(elem!1), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (s(elem!1) = s(s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~r(z, s(s(z)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.06 tff(13236,plain,
% 3.87/4.06 (~r(s(elem!1), elem!1)),
% 3.87/4.06 inference(unit_resolution,[status(thm)],[13235, 13168, 13145, 193, 1687, 3461, 13164, 13155, 506, 13151, 3261, 1587, 844, 147])).
% 3.87/4.06 tff(13237,plain,
% 3.87/4.06 (b(s(elem!1), elem!1)),
% 3.87/4.06 inference(unit_resolution,[status(thm)],[677, 13236, 13146])).
% 3.87/4.06 tff(13238,plain,
% 3.87/4.06 (b(z, s(elem!1)) <=> b(z, s(s(s(s(s(z))))))),
% 3.87/4.06 inference(monotonicity,[status(thm)],[13158])).
% 3.87/4.06 tff(13239,plain,
% 3.87/4.06 (b(z, s(s(s(s(s(z)))))) <=> b(z, s(elem!1))),
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% 3.87/4.06 tff(13240,plain,
% 3.87/4.06 ((~b(z, s(s(s(s(s(z))))))) <=> (~b(z, s(elem!1)))),
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% 3.87/4.06 tff(13241,plain,
% 3.87/4.06 (s(s(s(s(s(z))))) = s(elem!1)),
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% 3.87/4.06 tff(13242,plain,
% 3.87/4.06 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
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% 3.87/4.06 tff(13243,plain,
% 3.87/4.06 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
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% 3.87/4.06 tff(13244,plain,
% 3.87/4.06 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(s(z)))))),
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% 3.87/4.06 tff(13245,plain,
% 3.87/4.06 (b(s(elem!1), elem!1) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
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% 3.87/4.06 tff(13246,plain,
% 3.87/4.06 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
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% 3.87/4.06 tff(13247,plain,
% 3.87/4.06 (~b(z, s(s(s(s(s(z))))))),
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% 3.87/4.06 tff(13248,plain,
% 3.87/4.06 (~b(z, s(elem!1))),
% 3.87/4.06 inference(modus_ponens,[status(thm)],[13247, 13240])).
% 3.87/4.06 tff(13249,plain,
% 3.87/4.06 (r(z, s(elem!1))),
% 3.87/4.06 inference(unit_resolution,[status(thm)],[2351, 13248])).
% 3.87/4.06 tff(13250,plain,
% 3.87/4.06 (~r(s(elem!1), s(s(z)))),
% 3.87/4.06 inference(unit_resolution,[status(thm)],[11762, 13249, 3261])).
% 3.87/4.06 tff(13251,plain,
% 3.87/4.06 (~r(s(s(s(elem!1))), z)),
% 3.87/4.06 inference(unit_resolution,[status(thm)],[12937, 13250, 147, 13155, 13167, 13162, 506, 13151, 3261, 13237, 844, 13164])).
% 3.87/4.06 tff(13252,plain,
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% 3.87/4.06 tff(13253,plain,
% 3.87/4.06 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.87/4.06 inference(modus_ponens,[status(thm)],[13252, 13161])).
% 3.87/4.06 tff(13254,plain,
% 3.87/4.06 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(s(s(s(s(z))))))))),
% 3.87/4.06 inference(monotonicity,[status(thm)],[13160])).
% 3.87/4.06 tff(13255,plain,
% 3.87/4.06 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 3.87/4.06 inference(symmetry,[status(thm)],[13160])).
% 3.87/4.06 tff(13256,plain,
% 3.87/4.06 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 3.87/4.06 inference(monotonicity,[status(thm)],[13255, 13241])).
% 3.87/4.06 tff(13257,plain,
% 3.87/4.06 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 3.87/4.06 inference(monotonicity,[status(thm)],[13256])).
% 3.87/4.06 tff(13258,plain,
% 3.87/4.06 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.87/4.06 inference(unit_resolution,[status(thm)],[11898, 13253, 193, 1687, 11884, 3461])).
% 3.87/4.06 tff(13259,plain,
% 3.87/4.06 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.87/4.06 inference(unit_resolution,[status(thm)],[84, 13258])).
% 3.87/4.06 tff(13260,plain,
% 3.87/4.06 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.87/4.06 inference(unit_resolution,[status(thm)],[11839, 118, 13259, 147])).
% 3.87/4.06 tff(13261,plain,
% 3.87/4.06 ((s(s(s(s(s(s(s(z))))))) = s(s(z))) | b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.87/4.06 inference(unit_resolution,[status(thm)],[2960, 41, 13260])).
% 3.87/4.06 tff(13262,plain,
% 3.87/4.06 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.87/4.06 inference(unit_resolution,[status(thm)],[13261, 11802])).
% 3.87/4.06 tff(13263,plain,
% 3.87/4.06 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 3.87/4.06 inference(monotonicity,[status(thm)],[13158])).
% 3.87/4.06 tff(13264,plain,
% 3.87/4.06 (b(s(elem!1), s(s(z)))),
% 3.87/4.06 inference(unit_resolution,[status(thm)],[421, 13250, 13145])).
% 3.87/4.06 tff(13265,plain,
% 3.87/4.06 (b(s(s(s(s(s(z))))), s(s(z)))),
% 3.87/4.06 inference(modus_ponens,[status(thm)],[13264, 13263])).
% 3.87/4.06 tff(13266,plain,
% 3.87/4.06 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.06 inference(unit_resolution,[status(thm)],[3468, 118, 13259, 147])).
% 3.87/4.06 tff(13267,plain,
% 3.87/4.06 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.06 inference(unit_resolution,[status(thm)],[249, 13266])).
% 3.87/4.06 tff(13268,plain,
% 3.87/4.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), 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(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), 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(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 3.87/4.06 inference(rewrite,[status(thm)],[])).
% 3.87/4.06 tff(13269,plain,
% 3.87/4.06 (((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(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(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), 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(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 3.87/4.06 inference(rewrite,[status(thm)],[])).
% 3.87/4.06 tff(13270,plain,
% 3.87/4.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(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(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), 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(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 3.87/4.06 inference(monotonicity,[status(thm)],[13269])).
% 3.87/4.06 tff(13271,plain,
% 3.87/4.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(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(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), 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(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 3.87/4.06 inference(transitivity,[status(thm)],[13270, 13268])).
% 3.87/4.06 tff(13272,plain,
% 3.87/4.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(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(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.87/4.06 inference(quant_inst,[status(thm)],[])).
% 3.87/4.06 tff(13273,plain,
% 3.87/4.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), 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(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 3.87/4.06 inference(modus_ponens,[status(thm)],[13272, 13271])).
% 3.87/4.06 tff(13274,plain,
% 3.87/4.06 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.87/4.06 inference(unit_resolution,[status(thm)],[13273, 178, 13267, 13265, 13168, 13262])).
% 3.87/4.06 tff(13275,plain,
% 3.87/4.06 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.87/4.06 inference(modus_ponens,[status(thm)],[13274, 13257])).
% 3.87/4.06 tff(13276,plain,
% 3.87/4.06 (r(s(s(s(elem!1))), s(elem!1))),
% 3.87/4.06 inference(unit_resolution,[status(thm)],[373, 13275, 13164])).
% 3.87/4.06 tff(13277,plain,
% 3.87/4.06 (~r(z, s(s(s(elem!1))))),
% 3.87/4.06 inference(unit_resolution,[status(thm)],[5447, 13276, 13249])).
% 3.87/4.06 tff(13278,plain,
% 3.87/4.06 (b(z, s(s(s(elem!1))))),
% 3.87/4.06 inference(unit_resolution,[status(thm)],[2095, 13277])).
% 3.87/4.06 tff(13279,plain,
% 3.87/4.06 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.87/4.06 inference(modus_ponens,[status(thm)],[13278, 13254])).
% 3.87/4.06 tff(13280,plain,
% 3.87/4.06 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.06 inference(monotonicity,[status(thm)],[13157])).
% 3.87/4.06 tff(13281,plain,
% 3.87/4.06 ((elem!1 = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))),
% 3.87/4.06 inference(monotonicity,[status(thm)],[13157])).
% 3.87/4.06 tff(13282,plain,
% 3.87/4.06 ((elem!1 = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(z)))))),
% 3.87/4.06 inference(transitivity,[status(thm)],[13281, 214])).
% 3.87/4.06 tff(13283,plain,
% 3.87/4.06 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.87/4.06 inference(symmetry,[status(thm)],[13282])).
% 3.87/4.06 tff(13284,plain,
% 3.87/4.06 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(s(s(s(s(s(z)))))))))),
% 3.87/4.06 inference(monotonicity,[status(thm)],[13283])).
% 3.87/4.06 tff(13285,plain,
% 3.87/4.06 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.87/4.06 inference(modus_ponens,[status(thm)],[79, 13284])).
% 3.87/4.06 tff(13286,plain,
% 3.87/4.06 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.87/4.06 inference(monotonicity,[status(thm)],[13160])).
% 3.87/4.06 tff(13287,plain,
% 3.87/4.06 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.87/4.06 inference(transitivity,[status(thm)],[13286, 377])).
% 3.87/4.06 tff(13288,plain,
% 3.87/4.06 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 3.87/4.06 inference(monotonicity,[status(thm)],[13287])).
% 3.87/4.06 tff(13289,plain,
% 3.87/4.06 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.87/4.06 inference(modus_ponens,[status(thm)],[13164, 13288])).
% 3.87/4.06 tff(13290,plain,
% 3.87/4.06 (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)))))),
% 3.87/4.06 inference(monotonicity,[status(thm)],[13157])).
% 3.87/4.06 tff(13291,plain,
% 3.87/4.06 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.87/4.06 inference(symmetry,[status(thm)],[13290])).
% 3.87/4.06 tff(13292,plain,
% 3.87/4.06 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.87/4.06 inference(modus_ponens,[status(thm)],[13259, 13291])).
% 3.87/4.06 tff(13293,plain,
% 3.87/4.06 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.06 inference(unit_resolution,[status(thm)],[2979, 13292, 13264, 13155, 13167])).
% 3.87/4.06 tff(13294,plain,
% 3.87/4.06 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.06 inference(unit_resolution,[status(thm)],[395, 13293, 13289])).
% 3.87/4.06 tff(13295,plain,
% 3.87/4.06 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.87/4.06 inference(unit_resolution,[status(thm)],[2935, 13294, 1587])).
% 3.87/4.06 tff(13296,plain,
% 3.87/4.06 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.87/4.06 inference(unit_resolution,[status(thm)],[691, 13295, 13285])).
% 3.87/4.06 tff(13297,plain,
% 3.87/4.06 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.06 inference(modus_ponens,[status(thm)],[13296, 13280])).
% 3.87/4.06 tff(13298,plain,
% 3.87/4.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 3.87/4.06 inference(rewrite,[status(thm)],[])).
% 3.87/4.06 tff(13299,plain,
% 3.87/4.06 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(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(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 3.87/4.06 inference(rewrite,[status(thm)],[])).
% 3.87/4.06 tff(13300,plain,
% 3.87/4.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z))))))))),
% 3.87/4.06 inference(monotonicity,[status(thm)],[13299])).
% 3.87/4.06 tff(13301,plain,
% 3.87/4.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 3.87/4.06 inference(transitivity,[status(thm)],[13300, 13298])).
% 3.87/4.06 tff(13302,plain,
% 3.87/4.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))))),
% 3.87/4.06 inference(quant_inst,[status(thm)],[])).
% 3.87/4.06 tff(13303,plain,
% 3.87/4.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z))))))),
% 3.87/4.06 inference(modus_ponens,[status(thm)],[13302, 13301])).
% 3.87/4.06 tff(13304,plain,
% 3.87/4.06 ($false),
% 3.87/4.06 inference(unit_resolution,[status(thm)],[13303, 178, 1687, 11884, 13297, 13279, 13253])).
% 3.87/4.06 tff(13305,plain,(b(s(s(z)), elem!1) | (~b(z, s(s(s(s(z)))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(elem!1), z)) | (s(s(z)) = s(elem!1)) | (z = elem!1) | (s(elem!1) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.06 tff(13306,plain,
% 3.87/4.06 (b(s(s(z)), elem!1)),
% 3.87/4.06 inference(unit_resolution,[status(thm)],[13305, 12622, 1687, 10794, 13078, 5619, 13108, 3261, 12569, 12570, 13144, 1369])).
% 3.87/4.06 tff(13307,plain,
% 3.87/4.06 (b(z, elem!1)),
% 3.87/4.06 inference(unit_resolution,[status(thm)],[585, 13141, 13144])).
% 3.87/4.06 tff(13308,plain,
% 3.87/4.06 (elem!1 = s(s(s(s(z))))),
% 3.87/4.06 inference(unit_resolution,[status(thm)],[12263, 13307, 5619, 1687, 13108, 10794, 13306, 13143])).
% 3.87/4.06 tff(13309,plain,
% 3.87/4.06 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(s(z)))))),
% 3.87/4.06 inference(monotonicity,[status(thm)],[13308])).
% 3.87/4.06 tff(13310,plain,
% 3.87/4.06 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), elem!1)),
% 3.87/4.06 inference(symmetry,[status(thm)],[13309])).
% 3.87/4.06 tff(13311,plain,
% 3.87/4.06 ((~b(s(s(z)), s(s(s(s(z)))))) <=> (~b(s(s(z)), elem!1))),
% 3.87/4.06 inference(monotonicity,[status(thm)],[13310])).
% 3.87/4.06 tff(13312,plain,
% 3.87/4.06 (~b(s(s(z)), elem!1)),
% 3.87/4.06 inference(modus_ponens,[status(thm)],[105, 13311])).
% 3.87/4.06 tff(13313,plain,
% 3.87/4.06 ($false),
% 3.87/4.06 inference(unit_resolution,[status(thm)],[13306, 13312])).
% 3.87/4.06 tff(13314,plain,(b(s(elem!1), z) | b(s(s(z)), s(s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (s(elem!1) = s(s(s(s(z))))) | b(elem!1, s(elem!1)) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 3.87/4.06 tff(13315,plain,
% 3.87/4.06 (b(s(elem!1), z)),
% 3.87/4.06 inference(unit_resolution,[status(thm)],[13314, 105, 1687, 3261, 1369, 751, 5618])).
% 3.87/4.07 tff(13316,plain,
% 3.87/4.07 (~r(s(elem!1), s(s(z)))),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[11775, 168, 1369, 853, 1687, 10794, 3261])).
% 3.87/4.07 tff(13317,plain,
% 3.87/4.07 (~(elem!1 = s(elem!1))),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[12292, 168, 3461, 1687, 3261, 10794, 2169, 13316, 853])).
% 3.87/4.07 tff(13318,plain,
% 3.87/4.07 (r(elem!1, s(elem!1))),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[756, 13317, 751])).
% 3.87/4.07 tff(13319,plain,
% 3.87/4.07 (b(elem!1, z)),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[12376, 168, 3461, 10794, 1369, 1687, 853, 3261, 751])).
% 3.87/4.07 tff(13320,plain,
% 3.87/4.07 ((~(elem!1 = s(elem!1))) <=> (~(s(elem!1) = elem!1))),
% 3.87/4.07 inference(monotonicity,[status(thm)],[3190])).
% 3.87/4.07 tff(13321,plain,
% 3.87/4.07 (~(s(elem!1) = elem!1)),
% 3.87/4.07 inference(modus_ponens,[status(thm)],[13317, 13320])).
% 3.87/4.07 tff(13322,plain,
% 3.87/4.07 (~r(z, elem!1)),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[12726, 118, 2333, 1587])).
% 3.87/4.07 tff(13323,plain,
% 3.87/4.07 (b(z, elem!1)),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[585, 13322, 6992])).
% 3.87/4.07 tff(13324,plain,
% 3.87/4.07 ((~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z))))))),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[12519, 178, 506, 1687, 168])).
% 3.87/4.07 tff(13325,plain,
% 3.87/4.07 (~b(elem!1, s(s(s(s(z)))))),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[13324, 13323])).
% 3.87/4.07 tff(13326,plain,
% 3.87/4.07 (~r(s(s(z)), s(elem!1))),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[12114, 2333, 3261])).
% 3.87/4.07 tff(13327,plain,
% 3.87/4.07 (~(s(s(z)) = elem!1)),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[13127, 13326, 1587])).
% 3.87/4.07 tff(13328,assumption,(~b(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 3.87/4.07 tff(13329,plain,
% 3.87/4.07 (r(elem!1, s(s(s(s(z)))))),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[483, 469, 13328])).
% 3.87/4.07 tff(13330,plain,
% 3.87/4.07 (~b(s(s(z)), elem!1)),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[12263, 469, 3461, 1687, 506, 147, 818, 312])).
% 3.87/4.07 tff(13331,plain,
% 3.87/4.07 (r(s(s(z)), elem!1)),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[448, 13330, 12])).
% 3.87/4.07 tff(13332,plain,
% 3.87/4.07 ($false),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[8763, 13331, 13329, 147])).
% 3.87/4.07 tff(13333,plain,((elem!1 = s(s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (s(s(z)) = elem!1) | b(elem!1, s(s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.07 tff(13334,plain,
% 3.87/4.07 (elem!1 = s(s(s(s(z))))),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[13333, 13327, 10794, 13325, 3461, 1687, 506, 13323])).
% 3.87/4.07 tff(13335,plain,
% 3.87/4.07 (s(elem!1) = s(s(s(s(s(z)))))),
% 3.87/4.07 inference(monotonicity,[status(thm)],[13334])).
% 3.87/4.07 tff(13336,plain,
% 3.87/4.07 (s(s(s(s(z)))) = elem!1),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[325, 13334])).
% 3.87/4.07 tff(13337,plain,
% 3.87/4.07 (~(s(s(elem!1)) = elem!1)),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[338, 13336, 13327])).
% 3.87/4.07 tff(13338,plain,
% 3.87/4.07 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[348, 13337])).
% 3.87/4.07 tff(13339,plain,
% 3.87/4.07 (b(s(elem!1), z) <=> b(s(s(s(s(s(z))))), z)),
% 3.87/4.07 inference(monotonicity,[status(thm)],[13335])).
% 3.87/4.07 tff(13340,plain,
% 3.87/4.07 (b(s(s(s(s(s(z))))), z)),
% 3.87/4.07 inference(modus_ponens,[status(thm)],[853, 13339])).
% 3.87/4.07 tff(13341,plain,
% 3.87/4.07 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(s(s(s(z))))))))),
% 3.87/4.07 inference(monotonicity,[status(thm)],[352])).
% 3.87/4.07 tff(13342,plain,
% 3.87/4.07 (r(z, s(s(s(s(s(s(s(z)))))))) <=> r(z, s(s(s(elem!1))))),
% 3.87/4.07 inference(symmetry,[status(thm)],[13341])).
% 3.87/4.07 tff(13343,plain,
% 3.87/4.07 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.87/4.07 inference(monotonicity,[status(thm)],[352, 319])).
% 3.87/4.07 tff(13344,plain,
% 3.87/4.07 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.87/4.07 inference(monotonicity,[status(thm)],[319])).
% 3.87/4.07 tff(13345,plain,
% 3.87/4.07 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = elem!1)),
% 3.87/4.07 inference(symmetry,[status(thm)],[13344])).
% 3.87/4.07 tff(13346,plain,
% 3.87/4.07 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(z)))))),
% 3.87/4.07 inference(monotonicity,[status(thm)],[352])).
% 3.87/4.07 tff(13347,plain,
% 3.87/4.07 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.87/4.07 inference(symmetry,[status(thm)],[13346])).
% 3.87/4.07 tff(13348,plain,
% 3.87/4.07 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = elem!1)),
% 3.87/4.07 inference(transitivity,[status(thm)],[13347, 13345])).
% 3.87/4.07 tff(13349,plain,
% 3.87/4.07 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 3.87/4.07 inference(monotonicity,[status(thm)],[13348])).
% 3.87/4.07 tff(13350,plain,
% 3.87/4.07 (~(s(s(s(elem!1))) = elem!1)),
% 3.87/4.07 inference(modus_ponens,[status(thm)],[79, 13349])).
% 3.87/4.07 tff(13351,plain,
% 3.87/4.07 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(s(s(z)))))),
% 3.87/4.07 inference(monotonicity,[status(thm)],[319])).
% 3.87/4.07 tff(13352,plain,
% 3.87/4.07 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(z)), elem!1)),
% 3.87/4.07 inference(symmetry,[status(thm)],[13351])).
% 3.87/4.07 tff(13353,plain,
% 3.87/4.07 (r(s(s(z)), elem!1)),
% 3.87/4.07 inference(modus_ponens,[status(thm)],[147, 13352])).
% 3.87/4.07 tff(13354,plain,
% 3.87/4.07 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(s(z)))))),
% 3.87/4.07 inference(monotonicity,[status(thm)],[319])).
% 3.87/4.07 tff(13355,plain,
% 3.87/4.07 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), elem!1)),
% 3.87/4.07 inference(symmetry,[status(thm)],[13354])).
% 3.87/4.07 tff(13356,plain,
% 3.87/4.07 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(elem!1), elem!1)),
% 3.87/4.07 inference(transitivity,[status(thm)],[2692, 13355])).
% 3.87/4.07 tff(13357,plain,
% 3.87/4.07 ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) <=> (~b(s(elem!1), elem!1))),
% 3.87/4.07 inference(monotonicity,[status(thm)],[13356])).
% 3.87/4.07 tff(13358,plain,
% 3.87/4.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))),
% 3.87/4.07 inference(rewrite,[status(thm)],[])).
% 3.87/4.07 tff(13359,plain,
% 3.87/4.07 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))),
% 3.87/4.07 inference(rewrite,[status(thm)],[])).
% 3.87/4.07 tff(13360,plain,
% 3.87/4.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z))))))))),
% 3.87/4.07 inference(monotonicity,[status(thm)],[13359])).
% 3.87/4.07 tff(13361,plain,
% 3.87/4.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))),
% 3.87/4.07 inference(transitivity,[status(thm)],[13360, 13358])).
% 3.87/4.07 tff(13362,plain,
% 3.87/4.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 3.87/4.07 inference(quant_inst,[status(thm)],[])).
% 3.87/4.07 tff(13363,plain,
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% 3.87/4.07 inference(monotonicity,[status(thm)],[13381])).
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% 3.87/4.07 inference(unit_resolution,[status(thm)],[677, 13426, 725])).
% 3.87/4.07 tff(13428,plain,
% 3.87/4.07 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.87/4.07 inference(modus_ponens,[status(thm)],[13427, 13407])).
% 3.87/4.07 tff(13429,plain,
% 3.87/4.07 (b(s(s(z)), s(s(s(s(z)))))),
% 3.87/4.07 inference(modus_ponens,[status(thm)],[13428, 13402])).
% 3.87/4.07 tff(13430,plain,
% 3.87/4.07 ($false),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[105, 13429])).
% 3.87/4.07 tff(13431,plain,((~r(z, s(elem!1))) | b(s(s(z)), s(s(s(s(z))))) | (s(elem!1) = elem!1) | (~b(elem!1, z)) | (~r(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.07 tff(13432,plain,
% 3.87/4.07 (~r(z, s(elem!1))),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[13431, 13321, 105, 13319, 3261, 3461, 1687, 168, 853, 13318])).
% 3.87/4.07 tff(13433,plain,
% 3.87/4.07 (b(z, s(elem!1))),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[2351, 13432])).
% 3.87/4.07 tff(13434,plain,
% 3.87/4.07 (~b(s(elem!1), s(s(s(s(z)))))),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[11771, 13433])).
% 3.87/4.07 tff(13435,plain,
% 3.87/4.07 (r(s(elem!1), s(s(s(s(z)))))),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[1084, 13434, 1369])).
% 3.87/4.07 tff(13436,plain,
% 3.87/4.07 (~r(s(s(z)), s(elem!1))),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[5758, 13435, 10794])).
% 3.87/4.07 tff(13437,plain,
% 3.87/4.07 (s(elem!1) = s(s(z))),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[12205, 13436, 853, 3461, 13316, 13433])).
% 3.87/4.07 tff(13438,plain,
% 3.87/4.07 (r(z, s(elem!1)) <=> r(z, s(s(z)))),
% 3.87/4.07 inference(monotonicity,[status(thm)],[13437])).
% 3.87/4.07 tff(13439,plain,
% 3.87/4.07 (r(z, s(s(z))) <=> r(z, s(elem!1))),
% 3.87/4.07 inference(symmetry,[status(thm)],[13438])).
% 3.87/4.07 tff(13440,plain,
% 3.87/4.07 (r(z, s(elem!1))),
% 3.87/4.07 inference(modus_ponens,[status(thm)],[3261, 13439])).
% 3.87/4.07 tff(13441,plain,
% 3.87/4.07 ($false),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[13432, 13440])).
% 3.87/4.07 tff(13442,plain,((~b(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (s(elem!1) = s(s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(z))))) | b(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.07 tff(13443,plain,
% 3.87/4.07 (~b(s(s(s(s(z)))), z)),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[13442, 13315, 3261, 5619, 1369, 1687, 105, 751])).
% 3.87/4.07 tff(13444,plain,
% 3.87/4.07 (r(s(s(s(s(z)))), z)),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[191, 13443])).
% 3.87/4.07 tff(13445,plain,
% 3.87/4.07 ((s(elem!1) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 3.87/4.07 inference(transitivity,[status(thm)],[12587, 1666])).
% 3.87/4.07 tff(13446,plain,
% 3.87/4.07 ((~(s(elem!1) = s(s(z)))) <=> (~(elem!1 = s(s(z))))),
% 3.87/4.07 inference(monotonicity,[status(thm)],[13445])).
% 3.87/4.07 tff(13447,plain,
% 3.87/4.07 (~(s(elem!1) = s(s(z)))),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[1422, 12578])).
% 3.87/4.07 tff(13448,plain,
% 3.87/4.07 (~(elem!1 = s(s(z)))),
% 3.87/4.07 inference(modus_ponens,[status(thm)],[13447, 13446])).
% 3.87/4.07 tff(13449,plain,
% 3.87/4.07 (s(s(s(elem!1))) = elem!1),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[2150, 668])).
% 3.87/4.07 tff(13450,plain,
% 3.87/4.07 (elem!1 = s(s(s(elem!1)))),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[2489, 13449])).
% 3.87/4.07 tff(13451,plain,
% 3.87/4.07 (~r(s(s(s(s(elem!1)))), z)),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[3991, 13450, 767])).
% 3.87/4.07 tff(13452,plain,
% 3.87/4.07 (b(s(s(s(s(elem!1)))), z)),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[1716, 13451])).
% 3.87/4.07 tff(13453,plain,
% 3.87/4.07 (~(z = elem!1)),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[5184, 13452, 3170])).
% 3.87/4.07 tff(13454,plain,
% 3.87/4.07 (b(elem!1, z)),
% 3.87/4.07 inference(modus_ponens,[status(thm)],[853, 786])).
% 3.87/4.07 tff(13455,plain,
% 3.87/4.07 (~(s(s(z)) = elem!1)),
% 3.87/4.07 inference(modus_ponens,[status(thm)],[13447, 12588])).
% 3.87/4.07 tff(13456,plain,
% 3.87/4.07 (~r(s(s(z)), elem!1)),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[12239, 12595, 147, 13454, 1687, 13453, 12593, 3261])).
% 3.87/4.07 tff(13457,plain,
% 3.87/4.07 (b(s(s(z)), elem!1)),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[448, 13456, 13455])).
% 3.87/4.07 tff(13458,plain,
% 3.87/4.07 (~b(z, elem!1)),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[12263, 13457, 3461, 1687, 13454, 147, 12593, 13448])).
% 3.87/4.07 tff(13459,plain,
% 3.87/4.07 (r(z, elem!1)),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[585, 13458, 13453])).
% 3.87/4.07 tff(13460,plain,
% 3.87/4.07 (~r(elem!1, s(s(z)))),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[4862, 13459, 3261])).
% 3.87/4.07 tff(13461,plain,
% 3.87/4.07 (b(elem!1, s(s(z)))),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[467, 13460, 13448])).
% 3.87/4.07 tff(13462,plain,
% 3.87/4.07 (~r(s(s(s(s(z)))), s(s(z)))),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[9569, 3244, 3261])).
% 3.87/4.07 tff(13463,plain,
% 3.87/4.07 (b(s(s(s(s(z)))), s(s(z)))),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[102, 13462])).
% 3.87/4.07 tff(13464,plain,
% 3.87/4.07 ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1))),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[11389, 178, 13454, 3461, 13463])).
% 3.87/4.07 tff(13465,plain,
% 3.87/4.07 (~b(s(s(s(s(z)))), elem!1)),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[13464, 13461])).
% 3.87/4.07 tff(13466,plain,
% 3.87/4.07 (r(s(s(s(s(z)))), elem!1)),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[3142, 13465, 12595])).
% 3.87/4.07 tff(13467,plain,
% 3.87/4.07 ($false),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[3135, 118, 13459, 13466, 3244])).
% 3.87/4.07 tff(13468,plain,((~(s(elem!1) = elem!1)) | (~b(s(s(z)), z)) | (~r(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(elem!1)) | (~b(s(elem!1), z)) | b(s(s(s(s(z)))), z) | r(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 3.87/4.07 tff(13469,plain,
% 3.87/4.07 (~(s(elem!1) = elem!1)),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[13468, 3170, 3261, 1687, 10794, 2169, 13315, 5619, 767])).
% 3.87/4.07 tff(13470,plain,
% 3.87/4.07 (~(elem!1 = s(elem!1))),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[748, 13469])).
% 3.87/4.07 tff(13471,plain,
% 3.87/4.07 (r(elem!1, s(elem!1))),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[756, 13470, 751])).
% 3.87/4.07 tff(13472,plain,
% 3.87/4.07 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(z)))),
% 3.87/4.07 inference(monotonicity,[status(thm)],[12139])).
% 3.87/4.07 tff(13473,plain,
% 3.87/4.07 (r(s(elem!1), s(s(elem!1))) <=> r(s(elem!1), s(s(z)))),
% 3.87/4.07 inference(monotonicity,[status(thm)],[12139])).
% 3.87/4.07 tff(13474,plain,
% 3.87/4.07 (r(s(elem!1), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 3.87/4.07 inference(symmetry,[status(thm)],[13473])).
% 3.87/4.07 tff(13475,plain,
% 3.87/4.07 ((~r(s(elem!1), s(s(z)))) <=> (~r(s(elem!1), s(s(elem!1))))),
% 3.87/4.07 inference(monotonicity,[status(thm)],[13474])).
% 3.87/4.07 tff(13476,plain,
% 3.87/4.07 (~b(z, s(elem!1))),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[12054, 5198, 751])).
% 3.87/4.07 tff(13477,plain,
% 3.87/4.07 (r(z, s(elem!1))),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[2351, 13476])).
% 3.87/4.07 tff(13478,plain,
% 3.87/4.07 (~r(s(elem!1), s(s(z)))),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[11762, 13477, 3261])).
% 3.87/4.07 tff(13479,plain,
% 3.87/4.07 (~r(s(elem!1), s(s(elem!1)))),
% 3.87/4.07 inference(modus_ponens,[status(thm)],[13478, 13475])).
% 3.87/4.07 tff(13480,plain,
% 3.87/4.07 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 3.87/4.07 inference(monotonicity,[status(thm)],[13])).
% 3.87/4.07 tff(13481,plain,
% 3.87/4.07 ((~(s(s(elem!1)) = z)) <=> (~(s(s(elem!1)) = elem!1))),
% 3.87/4.07 inference(monotonicity,[status(thm)],[13480])).
% 3.87/4.07 tff(13482,plain,
% 3.87/4.07 (~(s(s(elem!1)) = elem!1)),
% 3.87/4.07 inference(modus_ponens,[status(thm)],[970, 13481])).
% 3.87/4.07 tff(13483,plain,
% 3.87/4.07 (~(s(elem!1) = s(s(elem!1)))),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[979, 13482])).
% 3.87/4.07 tff(13484,plain,
% 3.87/4.07 (b(s(elem!1), s(s(elem!1)))),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[1028, 13483, 13479])).
% 3.87/4.07 tff(13485,plain,
% 3.87/4.07 (b(s(elem!1), s(s(z)))),
% 3.87/4.07 inference(modus_ponens,[status(thm)],[13484, 13472])).
% 3.87/4.07 tff(13486,plain,
% 3.87/4.07 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(z)))), elem!1)),
% 3.87/4.07 inference(monotonicity,[status(thm)],[13])).
% 3.87/4.07 tff(13487,plain,
% 3.87/4.07 (r(s(s(s(s(z)))), elem!1)),
% 3.87/4.07 inference(modus_ponens,[status(thm)],[194, 13486])).
% 3.87/4.07 tff(13488,plain,
% 3.87/4.07 (~r(s(s(s(s(z)))), s(elem!1))),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[10992, 13487, 1587])).
% 3.87/4.07 tff(13489,plain,
% 3.87/4.07 (b(s(s(s(s(z)))), s(elem!1))),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[2173, 13488, 2508])).
% 3.87/4.07 tff(13490,plain,
% 3.87/4.07 (~r(s(s(s(s(z)))), s(s(z)))),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[9569, 194, 3261])).
% 3.87/4.07 tff(13491,plain,
% 3.87/4.07 (b(s(s(s(s(z)))), s(s(z)))),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[102, 13490])).
% 3.87/4.07 tff(13492,plain,
% 3.87/4.07 ((~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[10001, 178, 853, 3461, 13491])).
% 3.87/4.07 tff(13493,plain,
% 3.87/4.07 (~b(s(elem!1), s(s(z)))),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[13492, 13489])).
% 3.87/4.07 tff(13494,plain,
% 3.87/4.07 ($false),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[13493, 13485])).
% 3.87/4.07 tff(13495,plain,((~(z = elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (s(s(s(s(z)))) = s(elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))) | b(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.07 tff(13496,plain,
% 3.87/4.07 (~(z = elem!1)),
% 3.87/4.07 inference(unit_resolution,[status(thm)],[13495, 1587, 5619, 2169, 853, 194, 3261, 751])).
% 3.87/4.08 tff(13497,plain,
% 3.87/4.08 (~(elem!1 = z)),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[2808, 13496])).
% 3.87/4.08 tff(13498,plain,
% 3.87/4.08 (r(elem!1, z)),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[498, 5723, 13497])).
% 3.87/4.08 tff(13499,plain,
% 3.87/4.08 (~r(elem!1, s(s(s(s(z)))))),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[9980, 13498, 194])).
% 3.87/4.08 tff(13500,plain,
% 3.87/4.08 (~r(elem!1, s(s(z)))),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[8416, 13498, 3261])).
% 3.87/4.08 tff(13501,plain,
% 3.87/4.08 (b(elem!1, s(s(z)))),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[467, 13500, 6642])).
% 3.87/4.08 tff(13502,plain,
% 3.87/4.08 (r(s(s(z)), s(elem!1))),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[13127, 1324, 1587])).
% 3.87/4.08 tff(13503,plain,
% 3.87/4.08 (~r(z, s(elem!1))),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[12114, 13502, 3261])).
% 3.87/4.08 tff(13504,plain,
% 3.87/4.08 (~r(elem!1, z)),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[6206, 1324, 5618])).
% 3.87/4.08 tff(13505,plain,
% 3.87/4.08 (elem!1 = z),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[498, 13504, 5723])).
% 3.87/4.08 tff(13506,plain,
% 3.87/4.08 (~b(z, s(elem!1))),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[12054, 13505, 751])).
% 3.87/4.08 tff(13507,plain,
% 3.87/4.08 ($false),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[2351, 13506, 13503])).
% 3.87/4.08 tff(13508,plain,((~(s(s(z)) = elem!1)) | b(elem!1, s(elem!1)) | (~r(z, s(s(z)))) | b(elem!1, z) | (~r(elem!1, s(elem!1))) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 3.87/4.08 tff(13509,plain,
% 3.87/4.08 (~(s(s(z)) = elem!1)),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[13508, 5723, 3261, 751, 1587, 5618])).
% 3.87/4.08 tff(13510,plain,
% 3.87/4.08 (r(z, elem!1)),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[585, 5786, 507])).
% 3.87/4.08 tff(13511,plain,
% 3.87/4.08 (~r(s(s(z)), elem!1)),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[8412, 13510, 3261])).
% 3.87/4.08 tff(13512,plain,
% 3.87/4.08 (b(s(s(z)), elem!1)),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[448, 13511, 12])).
% 3.87/4.08 tff(13513,plain,
% 3.87/4.08 (~r(elem!1, s(s(z)))),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[4862, 13510, 3261])).
% 3.87/4.08 tff(13514,plain,
% 3.87/4.08 (b(elem!1, s(s(z)))),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[467, 13513, 462])).
% 3.87/4.08 tff(13515,plain,
% 3.87/4.08 (s(s(s(s(z)))) = elem!1),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[11938, 469, 194, 202, 437, 812, 817])).
% 3.87/4.08 tff(13516,plain,
% 3.87/4.08 (elem!1 = s(s(s(s(z))))),
% 3.87/4.08 inference(modus_ponens,[status(thm)],[13515, 501])).
% 3.87/4.08 tff(13517,plain,
% 3.87/4.08 ($false),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[469, 13516])).
% 3.87/4.08 tff(13518,plain,((elem!1 = s(s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.08 tff(13519,plain,
% 3.87/4.08 (elem!1 = s(s(s(s(z))))),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[13518, 13514, 13491, 437, 194, 13512])).
% 3.87/4.08 tff(13520,plain,
% 3.87/4.08 (b(z, elem!1) <=> b(z, s(s(s(s(z)))))),
% 3.87/4.08 inference(monotonicity,[status(thm)],[13519])).
% 3.87/4.08 tff(13521,plain,
% 3.87/4.08 (b(z, s(s(s(s(z))))) <=> b(z, elem!1)),
% 3.87/4.08 inference(symmetry,[status(thm)],[13520])).
% 3.87/4.08 tff(13522,plain,
% 3.87/4.08 (b(z, elem!1)),
% 3.87/4.08 inference(modus_ponens,[status(thm)],[1687, 13521])).
% 3.87/4.08 tff(13523,plain,
% 3.87/4.08 ($false),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[5786, 13522])).
% 3.87/4.08 tff(13524,plain,(b(z, elem!1) | (~b(z, s(s(s(s(z)))))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (s(s(z)) = elem!1) | (elem!1 = s(s(z))) | (~r(z, s(s(z)))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.87/4.08 tff(13525,plain,
% 3.87/4.08 (b(z, elem!1)),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[13524, 13498, 1687, 194, 13509, 6642, 3261, 13496])).
% 3.87/4.08 tff(13526,plain,
% 3.87/4.08 (~b(elem!1, s(s(s(s(z)))))),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[11975, 178, 13525, 13501, 1687, 13491])).
% 3.87/4.08 tff(13527,plain,
% 3.87/4.08 (elem!1 = s(s(s(s(z))))),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[483, 13526, 13499])).
% 3.87/4.08 tff(13528,plain,
% 3.87/4.08 (s(elem!1) = s(s(s(s(s(z)))))),
% 3.87/4.08 inference(monotonicity,[status(thm)],[13527])).
% 3.87/4.08 tff(13529,plain,
% 3.87/4.08 (s(s(s(s(s(z))))) = s(elem!1)),
% 3.87/4.08 inference(symmetry,[status(thm)],[13528])).
% 3.87/4.08 tff(13530,plain,
% 3.87/4.08 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 3.87/4.08 inference(monotonicity,[status(thm)],[13529])).
% 3.87/4.08 tff(13531,plain,
% 3.87/4.08 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.87/4.08 inference(symmetry,[status(thm)],[13530])).
% 3.87/4.08 tff(13532,plain,
% 3.87/4.08 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 3.87/4.08 inference(monotonicity,[status(thm)],[13529])).
% 3.87/4.08 tff(13533,plain,
% 3.87/4.08 ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) <=> (~b(s(elem!1), s(s(s(s(z))))))),
% 3.87/4.08 inference(monotonicity,[status(thm)],[13532])).
% 3.87/4.08 tff(13534,plain,
% 3.87/4.08 (b(s(elem!1), z) <=> b(s(s(s(s(s(z))))), z)),
% 3.87/4.08 inference(monotonicity,[status(thm)],[13528])).
% 3.87/4.08 tff(13535,plain,
% 3.87/4.08 (b(s(s(s(s(s(z))))), z)),
% 3.87/4.08 inference(modus_ponens,[status(thm)],[853, 13534])).
% 3.87/4.08 tff(13536,plain,
% 3.87/4.08 (~r(s(s(z)), s(elem!1))),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[12646, 13527, 147, 1587])).
% 3.87/4.08 tff(13537,plain,
% 3.87/4.08 (r(z, s(elem!1)) <=> r(z, s(s(s(s(s(z))))))),
% 3.87/4.08 inference(monotonicity,[status(thm)],[13528])).
% 3.87/4.08 tff(13538,plain,
% 3.87/4.08 ((~r(z, s(elem!1))) <=> (~r(z, s(s(s(s(s(z)))))))),
% 3.87/4.08 inference(monotonicity,[status(thm)],[13537])).
% 3.87/4.08 tff(13539,plain,
% 3.87/4.08 (~r(z, s(elem!1))),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[12189, 13498, 1587])).
% 3.87/4.08 tff(13540,plain,
% 3.87/4.08 (~r(z, s(s(s(s(s(z))))))),
% 3.87/4.08 inference(modus_ponens,[status(thm)],[13539, 13538])).
% 3.87/4.08 tff(13541,plain,
% 3.87/4.08 (r(z, s(s(z))) <=> r(z, s(s(s(s(s(z))))))),
% 3.87/4.08 inference(monotonicity,[status(thm)],[2290])).
% 3.87/4.08 tff(13542,plain,
% 3.87/4.08 (r(z, s(s(s(s(s(z)))))) <=> r(z, s(s(z)))),
% 3.87/4.08 inference(symmetry,[status(thm)],[13541])).
% 3.87/4.08 tff(13543,plain,
% 3.87/4.08 ((~r(z, s(s(s(s(s(z))))))) <=> (~r(z, s(s(z))))),
% 3.87/4.08 inference(monotonicity,[status(thm)],[13542])).
% 3.87/4.08 tff(13544,assumption,(~r(z, s(s(s(s(s(z))))))), introduced(assumption)).
% 3.87/4.08 tff(13545,plain,
% 3.87/4.08 (~r(z, s(s(z)))),
% 3.87/4.08 inference(modus_ponens,[status(thm)],[13544, 13543])).
% 3.87/4.08 tff(13546,plain,
% 3.87/4.08 ($false),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[3261, 13545])).
% 3.87/4.08 tff(13547,plain,((~(s(elem!1) = s(s(z)))) | (~r(z, s(s(z)))) | r(z, s(s(s(s(s(z)))))) | (~(elem!1 = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.08 tff(13548,plain,
% 3.87/4.08 (~(s(elem!1) = s(s(z)))),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[13547, 13540, 3261, 13527])).
% 3.87/4.08 tff(13549,plain,
% 3.87/4.08 (~(s(s(z)) = s(elem!1))),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[1058, 13548])).
% 3.87/4.08 tff(13550,plain,
% 3.87/4.08 (b(s(s(z)), s(elem!1))),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[1067, 13549, 13536])).
% 3.87/4.08 tff(13551,plain,
% 3.87/4.08 (b(s(s(z)), s(s(s(s(s(z))))))),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[2330, 13550, 13527])).
% 3.87/4.08 tff(13552,plain,
% 3.87/4.08 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[13365, 13551, 1687, 5619, 13535])).
% 3.87/4.08 tff(13553,plain,
% 3.87/4.08 (~b(s(elem!1), s(s(s(s(z)))))),
% 3.87/4.08 inference(modus_ponens,[status(thm)],[13552, 13533])).
% 3.87/4.08 tff(13554,plain,
% 3.87/4.08 (r(s(elem!1), s(s(s(s(z)))))),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[1084, 13553, 1369])).
% 3.87/4.08 tff(13555,plain,
% 3.87/4.08 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.87/4.08 inference(modus_ponens,[status(thm)],[13554, 13531])).
% 3.87/4.08 tff(13556,plain,
% 3.87/4.08 (r(s(elem!1), s(s(z))) <=> r(s(s(s(s(s(z))))), s(s(z)))),
% 3.87/4.08 inference(monotonicity,[status(thm)],[13528])).
% 3.87/4.08 tff(13557,plain,
% 3.87/4.08 (b(z, s(elem!1)) <=> b(z, s(s(s(s(s(z))))))),
% 3.87/4.08 inference(monotonicity,[status(thm)],[13528])).
% 3.87/4.08 tff(13558,plain,
% 3.87/4.08 (b(z, s(elem!1))),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[2351, 13539])).
% 3.87/4.08 tff(13559,plain,
% 3.87/4.08 (b(z, s(s(s(s(s(z))))))),
% 3.87/4.08 inference(modus_ponens,[status(thm)],[13558, 13557])).
% 3.87/4.08 tff(13560,assumption,(b(z, s(s(s(s(s(z))))))), introduced(assumption)).
% 3.87/4.08 tff(13561,plain,
% 3.87/4.08 ((s(s(z)) = s(s(s(s(s(z)))))) <=> (s(s(z)) = s(elem!1))),
% 3.87/4.08 inference(monotonicity,[status(thm)],[350])).
% 3.87/4.08 tff(13562,plain,
% 3.87/4.08 ((s(s(z)) = s(s(s(s(s(z)))))) <=> (s(elem!1) = s(s(z)))),
% 3.87/4.08 inference(transitivity,[status(thm)],[13561, 1358])).
% 3.87/4.08 tff(13563,plain,
% 3.87/4.08 ((s(elem!1) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(z))))))),
% 3.87/4.08 inference(symmetry,[status(thm)],[13562])).
% 3.87/4.08 tff(13564,plain,
% 3.87/4.08 ((~(s(elem!1) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(s(z)))))))),
% 3.87/4.08 inference(monotonicity,[status(thm)],[13563])).
% 3.87/4.08 tff(13565,plain,
% 3.87/4.08 (~(s(s(z)) = s(s(s(s(s(z))))))),
% 3.87/4.08 inference(modus_ponens,[status(thm)],[1056, 13564])).
% 3.87/4.08 tff(13566,plain,
% 3.87/4.08 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 3.87/4.08 inference(monotonicity,[status(thm)],[350])).
% 3.87/4.08 tff(13567,plain,
% 3.87/4.08 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.87/4.08 inference(symmetry,[status(thm)],[13566])).
% 3.87/4.08 tff(13568,plain,
% 3.87/4.08 ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) <=> (~b(s(elem!1), s(s(s(s(z))))))),
% 3.87/4.08 inference(monotonicity,[status(thm)],[2692])).
% 3.87/4.08 tff(13569,plain,
% 3.87/4.08 (b(s(s(s(s(s(z))))), s(s(z)))),
% 3.87/4.08 inference(modus_ponens,[status(thm)],[12196, 2747])).
% 3.87/4.08 tff(13570,plain,
% 3.87/4.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 3.87/4.08 inference(rewrite,[status(thm)],[])).
% 3.87/4.08 tff(13571,plain,
% 3.87/4.08 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 3.87/4.08 inference(rewrite,[status(thm)],[])).
% 3.87/4.08 tff(13572,plain,
% 3.87/4.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))))),
% 3.87/4.08 inference(monotonicity,[status(thm)],[13571])).
% 3.87/4.08 tff(13573,plain,
% 3.87/4.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 3.87/4.08 inference(transitivity,[status(thm)],[13572, 13570])).
% 3.87/4.08 tff(13574,plain,
% 3.87/4.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))))),
% 3.87/4.08 inference(quant_inst,[status(thm)],[])).
% 3.87/4.08 tff(13575,plain,
% 3.87/4.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))),
% 3.87/4.08 inference(modus_ponens,[status(thm)],[13574, 13573])).
% 3.87/4.08 tff(13576,plain,
% 3.87/4.08 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[13575, 178, 1687, 202, 13569, 13560])).
% 3.87/4.08 tff(13577,plain,
% 3.87/4.08 (~b(s(elem!1), s(s(s(s(z)))))),
% 3.87/4.08 inference(modus_ponens,[status(thm)],[13576, 13568])).
% 3.87/4.08 tff(13578,plain,
% 3.87/4.08 (r(s(elem!1), s(s(s(s(z)))))),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[1084, 13577, 1369])).
% 3.87/4.08 tff(13579,plain,
% 3.87/4.08 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.87/4.08 inference(modus_ponens,[status(thm)],[13578, 13567])).
% 3.87/4.08 tff(13580,plain,
% 3.87/4.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.87/4.08 inference(rewrite,[status(thm)],[])).
% 3.87/4.08 tff(13581,plain,
% 3.87/4.08 (((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.87/4.08 inference(rewrite,[status(thm)],[])).
% 3.87/4.08 tff(13582,plain,
% 3.87/4.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 3.87/4.08 inference(monotonicity,[status(thm)],[13581])).
% 3.87/4.08 tff(13583,plain,
% 3.87/4.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.87/4.08 inference(transitivity,[status(thm)],[13582, 13580])).
% 3.87/4.08 tff(13584,plain,
% 3.87/4.08 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 3.87/4.08 inference(quant_inst,[status(thm)],[])).
% 3.87/4.08 tff(13585,plain,
% 3.87/4.08 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 3.87/4.08 inference(modus_ponens,[status(thm)],[13584, 13583])).
% 3.87/4.08 tff(13586,plain,
% 3.87/4.08 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[13585, 118, 147, 13579])).
% 3.87/4.08 tff(13587,plain,
% 3.87/4.08 ((s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z))))))),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[2781, 41, 13586])).
% 3.87/4.08 tff(13588,plain,
% 3.87/4.08 (b(s(s(z)), s(s(s(s(s(z))))))),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[13587, 13565])).
% 3.87/4.08 tff(13589,plain,
% 3.87/4.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 3.87/4.08 inference(rewrite,[status(thm)],[])).
% 3.87/4.08 tff(13590,plain,
% 3.87/4.08 (((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 3.87/4.08 inference(rewrite,[status(thm)],[])).
% 3.87/4.08 tff(13591,plain,
% 3.87/4.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 3.87/4.08 inference(monotonicity,[status(thm)],[13590])).
% 3.87/4.08 tff(13592,plain,
% 3.87/4.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 3.87/4.08 inference(transitivity,[status(thm)],[13591, 13589])).
% 3.87/4.08 tff(13593,plain,
% 3.87/4.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 3.87/4.08 inference(quant_inst,[status(thm)],[])).
% 3.87/4.08 tff(13594,plain,
% 3.87/4.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 3.87/4.08 inference(modus_ponens,[status(thm)],[13593, 13592])).
% 3.87/4.08 tff(13595,plain,
% 3.87/4.08 ($false),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[13594, 178, 3461, 13569, 13588, 1916, 13560])).
% 3.87/4.08 tff(13596,plain,((s(elem!1) = s(s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~(elem!1 = s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (s(elem!1) = s(s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | r(s(elem!1), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.08 tff(13597,plain,
% 3.87/4.08 (r(s(elem!1), s(s(z)))),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[13596, 13548, 13535, 13559, 13527, 147, 1369, 1687, 13491, 5619])).
% 3.87/4.08 tff(13598,plain,
% 3.87/4.08 (r(s(s(s(s(s(z))))), s(s(z)))),
% 3.87/4.08 inference(modus_ponens,[status(thm)],[13597, 13556])).
% 3.87/4.08 tff(13599,plain,
% 3.87/4.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 3.87/4.08 inference(rewrite,[status(thm)],[])).
% 3.87/4.08 tff(13600,plain,
% 3.87/4.08 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z))))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 3.87/4.08 inference(rewrite,[status(thm)],[])).
% 3.87/4.08 tff(13601,plain,
% 3.87/4.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 3.87/4.08 inference(monotonicity,[status(thm)],[13600])).
% 3.87/4.08 tff(13602,plain,
% 3.87/4.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 3.87/4.08 inference(transitivity,[status(thm)],[13601, 13599])).
% 3.87/4.08 tff(13603,plain,
% 3.87/4.08 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 3.87/4.08 inference(quant_inst,[status(thm)],[])).
% 3.87/4.08 tff(13604,plain,
% 3.87/4.08 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 3.87/4.08 inference(modus_ponens,[status(thm)],[13603, 13602])).
% 3.87/4.08 tff(13605,plain,
% 3.87/4.08 ($false),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[13604, 118, 147, 13598, 13555])).
% 3.87/4.08 tff(13606,plain,(b(elem!1, z) | (~r(s(s(z)), s(s(s(s(z)))))) | (s(elem!1) = s(s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~b(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | b(elem!1, s(elem!1)) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 3.87/4.08 tff(13607,plain,
% 3.87/4.08 (b(elem!1, z)),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[13606, 13471, 1369, 1687, 3261, 13315, 10794, 3244, 751, 5618])).
% 3.87/4.08 tff(13608,plain,
% 3.87/4.08 (~(elem!1 = s(s(s(s(z)))))),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[3172, 13607, 3170])).
% 3.87/4.08 tff(13609,plain,
% 3.87/4.08 (~(s(s(s(s(z)))) = elem!1)),
% 3.87/4.08 inference(modus_ponens,[status(thm)],[13608, 12648])).
% 3.87/4.08 tff(13610,plain,
% 3.87/4.08 (~(z = elem!1)),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[13495, 13471, 5619, 2169, 13315, 3244, 3261, 751])).
% 3.87/4.08 tff(13611,plain,
% 3.87/4.08 (elem!1 = s(s(z))),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[467, 461, 460])).
% 3.87/4.08 tff(13612,plain,
% 3.87/4.08 (s(s(z)) = elem!1),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[311, 13611])).
% 3.87/4.08 tff(13613,plain,
% 3.87/4.08 (s(s(s(z))) = s(elem!1)),
% 3.87/4.08 inference(monotonicity,[status(thm)],[13612])).
% 3.87/4.08 tff(13614,plain,
% 3.87/4.08 (s(s(s(s(z)))) = s(s(elem!1))),
% 3.87/4.08 inference(monotonicity,[status(thm)],[13613])).
% 3.87/4.08 tff(13615,plain,
% 3.87/4.08 (s(s(elem!1)) = s(s(s(s(z))))),
% 3.87/4.08 inference(symmetry,[status(thm)],[13614])).
% 3.87/4.08 tff(13616,plain,
% 3.87/4.08 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 3.87/4.08 inference(monotonicity,[status(thm)],[13615])).
% 3.87/4.08 tff(13617,plain,
% 3.87/4.08 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), s(s(elem!1)))),
% 3.87/4.08 inference(symmetry,[status(thm)],[13616])).
% 3.87/4.08 tff(13618,plain,
% 3.87/4.08 (r(s(s(z)), s(elem!1))),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[13127, 13612, 1587])).
% 3.87/4.08 tff(13619,plain,
% 3.87/4.08 (~r(s(elem!1), s(s(s(s(z)))))),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[5758, 13618, 10794])).
% 3.87/4.08 tff(13620,plain,
% 3.87/4.08 (b(s(elem!1), s(s(s(s(z)))))),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[1084, 13619, 1369])).
% 3.87/4.08 tff(13621,plain,
% 3.87/4.08 (b(s(elem!1), s(s(elem!1)))),
% 3.87/4.08 inference(modus_ponens,[status(thm)],[13620, 13617])).
% 3.87/4.08 tff(13622,plain,
% 3.87/4.08 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 3.87/4.08 inference(monotonicity,[status(thm)],[13615])).
% 3.87/4.08 tff(13623,plain,
% 3.87/4.08 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 3.87/4.08 inference(symmetry,[status(thm)],[13622])).
% 3.87/4.08 tff(13624,plain,
% 3.87/4.08 (~r(z, s(elem!1))),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[12114, 13618, 3261])).
% 3.87/4.08 tff(13625,plain,
% 3.87/4.08 (b(z, s(elem!1))),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[2351, 13624])).
% 3.87/4.08 tff(13626,plain,
% 3.87/4.08 (~b(elem!1, s(s(s(s(z)))))),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[12671, 13625, 105, 202, 3461, 506, 460, 1587, 2169, 13054, 1687])).
% 3.87/4.08 tff(13627,plain,
% 3.87/4.08 (r(elem!1, s(s(s(s(z)))))),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[483, 13626, 469])).
% 3.87/4.08 tff(13628,plain,
% 3.87/4.08 (~r(s(s(s(s(z)))), s(elem!1))),
% 3.87/4.08 inference(unit_resolution,[status(thm)],[11326, 13627, 1587])).
% 3.87/4.08 tff(13629,plain,
% 3.87/4.08 (b(s(s(s(s(z)))), s(elem!1))),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[2173, 13628, 2169])).
% 3.87/4.09 tff(13630,plain,
% 3.87/4.09 (b(s(s(elem!1)), s(elem!1))),
% 3.87/4.09 inference(modus_ponens,[status(thm)],[13629, 13623])).
% 3.87/4.09 tff(13631,plain,
% 3.87/4.09 (b(z, s(s(s(s(z))))) <=> b(z, s(s(elem!1)))),
% 3.87/4.09 inference(monotonicity,[status(thm)],[13614])).
% 3.87/4.09 tff(13632,plain,
% 3.87/4.09 (b(z, s(s(elem!1)))),
% 3.87/4.09 inference(modus_ponens,[status(thm)],[1687, 13631])).
% 3.87/4.09 tff(13633,plain,
% 3.87/4.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 3.87/4.09 inference(rewrite,[status(thm)],[])).
% 3.87/4.09 tff(13634,plain,
% 3.87/4.09 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 3.87/4.09 inference(rewrite,[status(thm)],[])).
% 3.87/4.09 tff(13635,plain,
% 3.87/4.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1))))))),
% 3.87/4.09 inference(monotonicity,[status(thm)],[13634])).
% 3.87/4.09 tff(13636,plain,
% 3.87/4.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 3.87/4.09 inference(transitivity,[status(thm)],[13635, 13633])).
% 3.87/4.09 tff(13637,plain,
% 3.87/4.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 3.87/4.09 inference(quant_inst,[status(thm)],[])).
% 3.87/4.09 tff(13638,plain,
% 3.87/4.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1))))),
% 3.87/4.09 inference(modus_ponens,[status(thm)],[13637, 13636])).
% 3.87/4.09 tff(13639,plain,
% 3.87/4.09 ($false),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[13638, 178, 13625, 853, 13632, 13630, 13621])).
% 3.87/4.09 tff(13640,plain,(b(elem!1, s(s(z))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(z)))))) | (~r(elem!1, s(elem!1))) | (elem!1 = 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(z)), z)) | (~b(elem!1, z)) | r(elem!1, s(s(z))) | (s(elem!1) = s(s(s(s(z))))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.09 tff(13641,plain,
% 3.87/4.09 (b(elem!1, s(s(z)))),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[13640, 13129, 1687, 1587, 469, 105, 13491, 3461, 506, 853, 1369, 3261])).
% 3.87/4.09 tff(13642,plain,
% 3.87/4.09 ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1))),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[11389, 178, 506, 3461, 13491])).
% 3.87/4.09 tff(13643,plain,
% 3.87/4.09 (~b(s(s(s(s(z)))), elem!1)),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[13642, 13641])).
% 3.87/4.09 tff(13644,plain,
% 3.87/4.09 (~(s(s(s(s(z)))) = elem!1)),
% 3.87/4.09 inference(modus_ponens,[status(thm)],[469, 12648])).
% 3.87/4.09 tff(13645,plain,
% 3.87/4.09 (r(s(s(s(s(z)))), elem!1)),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[3142, 13644, 13643])).
% 3.87/4.09 tff(13646,plain,
% 3.87/4.09 ($false),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[3135, 118, 521, 13645, 194])).
% 3.87/4.09 tff(13647,plain,((~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (elem!1 = s(s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~r(elem!1, s(elem!1))) | b(s(s(z)), s(s(s(s(z))))) | (~b(s(elem!1), z)) | (s(elem!1) = s(s(s(s(z))))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.09 tff(13648,plain,
% 3.87/4.09 (~r(z, elem!1)),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[13647, 3244, 13608, 13607, 5619, 1687, 13471, 105, 13315, 1369, 3261])).
% 3.87/4.09 tff(13649,plain,
% 3.87/4.09 (~(s(s(z)) = elem!1)),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[7053, 13648, 3261])).
% 3.87/4.09 tff(13650,plain,
% 3.87/4.09 (~(elem!1 = s(s(z)))),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[311, 13649])).
% 3.87/4.09 tff(13651,plain,
% 3.87/4.09 (b(z, elem!1)),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[585, 13648, 13610])).
% 3.87/4.09 tff(13652,plain,
% 3.87/4.09 (~b(s(s(z)), elem!1)),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[12263, 13651, 5619, 1687, 13607, 10794, 13608, 13650])).
% 3.87/4.09 tff(13653,plain,
% 3.87/4.09 (r(s(s(z)), elem!1)),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[448, 13652, 13649])).
% 3.87/4.09 tff(13654,plain,
% 3.87/4.09 (s(s(s(s(z)))) = elem!1),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[12239, 13653, 10794, 13607, 1687, 13610, 13608, 3261])).
% 3.87/4.09 tff(13655,plain,
% 3.87/4.09 ($false),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[13654, 13609])).
% 3.87/4.09 tff(13656,plain,(b(s(s(s(s(z)))), z) | (~b(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))) | b(s(s(z)), s(s(s(s(z))))) | (s(elem!1) = s(s(s(s(z))))) | b(elem!1, s(elem!1)) | r(s(s(z)), z) | r(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 3.87/4.09 tff(13657,plain,
% 3.87/4.09 (r(s(elem!1), z)),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[13656, 13443, 3261, 105, 1369, 751, 5618, 1687])).
% 3.87/4.09 tff(13658,plain,
% 3.87/4.09 (~(s(s(z)) = s(elem!1))),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[11742, 13657, 5618])).
% 3.87/4.09 tff(13659,plain,
% 3.87/4.09 (~(s(elem!1) = s(s(z)))),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[1362, 13658])).
% 3.87/4.09 tff(13660,plain,
% 3.87/4.09 (~(s(elem!1) = elem!1)),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[12619, 13659, 1687, 3261, 10794, 2169, 5619, 13657])).
% 3.87/4.09 tff(13661,plain,
% 3.87/4.09 (~(elem!1 = s(elem!1))),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[748, 13660])).
% 3.87/4.09 tff(13662,plain,
% 3.87/4.09 (r(elem!1, s(elem!1))),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[756, 13661, 751])).
% 3.87/4.09 tff(13663,plain,
% 3.87/4.09 (b(elem!1, z)),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[13606, 13662, 1369, 1687, 3261, 13315, 10794, 13444, 751, 5618])).
% 3.87/4.09 tff(13664,plain,
% 3.87/4.09 (~(elem!1 = s(s(s(s(z)))))),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[3172, 13663, 13443])).
% 3.87/4.09 tff(13665,plain,
% 3.87/4.09 (~(z = elem!1)),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[13495, 13662, 5619, 2169, 13315, 13444, 3261, 751])).
% 3.87/4.09 tff(13666,plain,
% 3.87/4.09 (~r(z, elem!1)),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[13647, 13664, 13444, 13662, 5619, 1687, 13663, 105, 13315, 1369, 3261])).
% 3.87/4.09 tff(13667,plain,
% 3.87/4.09 (~(s(s(z)) = elem!1)),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[7053, 13666, 3261])).
% 3.87/4.09 tff(13668,plain,
% 3.87/4.09 (~(elem!1 = s(s(z)))),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[311, 13667])).
% 3.87/4.09 tff(13669,plain,
% 3.87/4.09 (b(z, elem!1)),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[585, 13666, 13665])).
% 3.87/4.09 tff(13670,plain,
% 3.87/4.09 (~b(s(s(z)), elem!1)),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[12263, 13669, 5619, 1687, 13663, 10794, 13664, 13668])).
% 3.87/4.09 tff(13671,plain,
% 3.87/4.09 (r(s(s(z)), elem!1)),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[448, 13670, 13667])).
% 3.87/4.09 tff(13672,plain,
% 3.87/4.09 (s(s(s(s(z)))) = elem!1),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[12239, 13671, 10794, 13663, 1687, 13665, 13664, 3261])).
% 3.87/4.09 tff(13673,plain,
% 3.87/4.09 (elem!1 = s(s(s(s(z))))),
% 3.87/4.09 inference(modus_ponens,[status(thm)],[13672, 501])).
% 3.87/4.09 tff(13674,plain,
% 3.87/4.09 ($false),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[13664, 13673])).
% 3.87/4.09 tff(13675,plain,(b(s(s(z)), s(s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (s(elem!1) = s(s(s(s(z))))) | b(elem!1, s(elem!1)) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 3.87/4.09 tff(13676,plain,
% 3.87/4.09 (b(elem!1, s(elem!1))),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[13675, 1369, 105, 3261, 1687, 5618])).
% 3.87/4.09 tff(13677,plain,
% 3.87/4.09 (~(s(elem!1) = s(s(z)))),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[1362, 11743])).
% 3.87/4.09 tff(13678,plain,
% 3.87/4.09 (~(s(elem!1) = elem!1)),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[12619, 2169, 10794, 3261, 1687, 844, 5619, 13677])).
% 3.87/4.09 tff(13679,plain,
% 3.87/4.09 (~(elem!1 = s(s(s(s(z)))))),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[12557, 5723, 168])).
% 3.87/4.09 tff(13680,plain,
% 3.87/4.09 (~(s(s(s(s(z)))) = elem!1)),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[504, 13679])).
% 3.87/4.09 tff(13681,plain,
% 3.87/4.09 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[12273, 224, 3261, 11798, 168, 147])).
% 3.87/4.09 tff(13682,plain,
% 3.87/4.09 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[84, 13681])).
% 3.87/4.09 tff(13683,plain,
% 3.87/4.09 ($false),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[3468, 118, 13682, 224, 147])).
% 3.87/4.09 tff(13684,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.09 tff(13685,plain,
% 3.87/4.09 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[13684, 168, 3261, 147])).
% 3.87/4.09 tff(13686,plain,
% 3.87/4.09 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[249, 13685])).
% 3.87/4.09 tff(13687,plain,
% 3.87/4.09 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 3.87/4.09 inference(rewrite,[status(thm)],[])).
% 3.87/4.09 tff(13688,plain,
% 3.87/4.09 (((~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 3.87/4.09 inference(rewrite,[status(thm)],[])).
% 3.87/4.09 tff(13689,plain,
% 3.87/4.09 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))))),
% 3.87/4.09 inference(monotonicity,[status(thm)],[13688])).
% 3.87/4.09 tff(13690,plain,
% 3.87/4.09 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 3.87/4.09 inference(transitivity,[status(thm)],[13689, 13687])).
% 3.87/4.09 tff(13691,plain,
% 3.87/4.09 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))),
% 3.87/4.09 inference(quant_inst,[status(thm)],[])).
% 3.87/4.09 tff(13692,plain,
% 3.87/4.09 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))),
% 3.87/4.09 inference(modus_ponens,[status(thm)],[13691, 13690])).
% 3.87/4.09 tff(13693,plain,
% 3.87/4.09 ($false),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[13692, 118, 437, 1426, 844])).
% 3.87/4.09 tff(13694,plain,((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.09 tff(13695,plain,
% 3.87/4.09 (~r(s(elem!1), elem!1)),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[13694, 10801, 844])).
% 3.87/4.09 tff(13696,plain,
% 3.87/4.09 (b(s(elem!1), elem!1)),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[677, 13695, 725])).
% 3.87/4.09 tff(13697,plain,
% 3.87/4.09 ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[2976, 178, 1070, 166, 1146])).
% 3.87/4.09 tff(13698,plain,
% 3.87/4.09 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[13697, 1071])).
% 3.87/4.09 tff(13699,plain,
% 3.87/4.09 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[686, 13698, 683])).
% 3.87/4.09 tff(13700,plain,
% 3.87/4.09 (~r(z, elem!1)),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[11945, 13699, 147, 3461, 11798, 551, 3261, 437, 812, 469, 12])).
% 3.87/4.09 tff(13701,plain,
% 3.87/4.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))))),
% 3.87/4.09 inference(rewrite,[status(thm)],[])).
% 3.87/4.09 tff(13702,plain,
% 3.87/4.09 (((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))))),
% 3.87/4.09 inference(rewrite,[status(thm)],[])).
% 3.87/4.09 tff(13703,plain,
% 3.87/4.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z))))))),
% 3.87/4.09 inference(monotonicity,[status(thm)],[13702])).
% 3.87/4.09 tff(13704,plain,
% 3.87/4.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))))),
% 3.87/4.09 inference(transitivity,[status(thm)],[13703, 13701])).
% 3.87/4.09 tff(13705,plain,
% 3.87/4.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))))),
% 3.87/4.09 inference(quant_inst,[status(thm)],[])).
% 3.87/4.09 tff(13706,plain,
% 3.87/4.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z))))),
% 3.87/4.09 inference(modus_ponens,[status(thm)],[13705, 13704])).
% 3.87/4.09 tff(13707,plain,
% 3.87/4.09 ($false),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[13706, 178, 683, 817, 812, 1071, 1070])).
% 3.87/4.09 tff(13708,plain,((~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.09 tff(13709,plain,
% 3.87/4.09 (~b(s(s(z)), elem!1)),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[13708, 1071, 812, 683, 1070])).
% 3.87/4.09 tff(13710,plain,
% 3.87/4.09 (r(s(s(z)), elem!1)),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[448, 13709, 12])).
% 3.87/4.09 tff(13711,plain,
% 3.87/4.09 (~b(z, elem!1)),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[11977, 13710, 147, 11798, 551, 3261, 469, 812])).
% 3.87/4.09 tff(13712,plain,
% 3.87/4.09 ($false),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[585, 13711, 13700, 507])).
% 3.87/4.09 tff(13713,plain,((~b(s(s(z)), s(elem!1))) | (z = elem!1) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (elem!1 = s(s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~r(elem!1, z)) | (s(s(z)) = elem!1) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.09 tff(13714,plain,
% 3.87/4.09 (~b(s(s(z)), s(elem!1))),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[13713, 13679, 147, 3261, 318, 812, 3461, 10801, 12, 13696, 1070, 13686, 1146])).
% 3.87/4.09 tff(13715,plain,
% 3.87/4.09 (r(s(s(z)), s(elem!1))),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[1067, 13714, 1060])).
% 3.87/4.09 tff(13716,plain,
% 3.87/4.09 (~r(z, s(elem!1))),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[12114, 13715, 3261])).
% 3.87/4.09 tff(13717,plain,
% 3.87/4.09 (b(z, s(elem!1))),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[2351, 13716])).
% 3.87/4.09 tff(13718,plain,
% 3.87/4.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 3.87/4.09 inference(rewrite,[status(thm)],[])).
% 3.87/4.09 tff(13719,plain,
% 3.87/4.09 (((~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 3.87/4.09 inference(rewrite,[status(thm)],[])).
% 3.87/4.09 tff(13720,plain,
% 3.87/4.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z))))))),
% 3.87/4.09 inference(monotonicity,[status(thm)],[13719])).
% 3.87/4.09 tff(13721,plain,
% 3.87/4.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 3.87/4.09 inference(transitivity,[status(thm)],[13720, 13718])).
% 3.87/4.09 tff(13722,plain,
% 3.87/4.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)))),
% 3.87/4.09 inference(quant_inst,[status(thm)],[])).
% 3.87/4.09 tff(13723,plain,
% 3.87/4.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z))))),
% 3.87/4.09 inference(modus_ponens,[status(thm)],[13722, 13721])).
% 3.87/4.09 tff(13724,plain,
% 3.87/4.09 (~b(z, elem!1)),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[13723, 178, 13717, 854, 812, 1070])).
% 3.87/4.09 tff(13725,plain,
% 3.87/4.09 (r(z, elem!1)),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[585, 13724, 318])).
% 3.87/4.09 tff(13726,plain,
% 3.87/4.09 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[11945, 13725, 147, 3461, 11798, 13680, 3261, 10801, 812, 13679, 12])).
% 3.87/4.09 tff(13727,plain,
% 3.87/4.09 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 3.87/4.09 inference(monotonicity,[status(thm)],[13726])).
% 3.87/4.09 tff(13728,plain,
% 3.87/4.09 (s(s(s(s(s(s(s(s(z)))))))) = s(elem!1)),
% 3.87/4.09 inference(symmetry,[status(thm)],[13727])).
% 3.87/4.09 tff(13729,plain,
% 3.87/4.09 (b(s(s(s(s(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))))))))),
% 3.87/4.09 inference(monotonicity,[status(thm)],[13728])).
% 3.87/4.09 tff(13730,plain,
% 3.87/4.09 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.09 inference(symmetry,[status(thm)],[13729])).
% 3.87/4.09 tff(13731,plain,
% 3.87/4.09 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[686, 13726, 13696])).
% 3.87/4.09 tff(13732,plain,
% 3.87/4.09 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.09 inference(modus_ponens,[status(thm)],[13731, 13730])).
% 3.87/4.09 tff(13733,plain,
% 3.87/4.09 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(z))) <=> b(s(elem!1), s(s(z)))),
% 3.87/4.09 inference(monotonicity,[status(thm)],[13728])).
% 3.87/4.09 tff(13734,plain,
% 3.87/4.09 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 3.87/4.09 inference(symmetry,[status(thm)],[13733])).
% 3.87/4.09 tff(13735,plain,
% 3.87/4.09 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 3.87/4.09 inference(modus_ponens,[status(thm)],[1070, 13734])).
% 3.87/4.09 tff(13736,plain,
% 3.87/4.09 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.87/4.09 inference(monotonicity,[status(thm)],[13728])).
% 3.87/4.09 tff(13737,plain,
% 3.87/4.09 (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(s(s(s(s(z)))))))))),
% 3.87/4.09 inference(symmetry,[status(thm)],[13736])).
% 3.87/4.09 tff(13738,plain,
% 3.87/4.09 (b(elem!1, s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.87/4.09 inference(monotonicity,[status(thm)],[13726])).
% 3.87/4.09 tff(13739,plain,
% 3.87/4.09 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.87/4.09 inference(modus_ponens,[status(thm)],[854, 13738])).
% 3.87/4.09 tff(13740,plain,
% 3.87/4.09 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 3.87/4.09 inference(modus_ponens,[status(thm)],[13739, 13737])).
% 3.87/4.09 tff(13741,plain,
% 3.87/4.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), 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(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), 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(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 3.87/4.09 inference(rewrite,[status(thm)],[])).
% 3.87/4.09 tff(13742,plain,
% 3.87/4.09 (((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(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(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~b(s(s(z)), 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(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 3.87/4.09 inference(rewrite,[status(thm)],[])).
% 3.87/4.09 tff(13743,plain,
% 3.87/4.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(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(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), 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(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))))),
% 3.87/4.09 inference(monotonicity,[status(thm)],[13742])).
% 3.87/4.09 tff(13744,plain,
% 3.87/4.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(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(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), 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(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 3.87/4.09 inference(transitivity,[status(thm)],[13743, 13741])).
% 3.87/4.09 tff(13745,plain,
% 3.87/4.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(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(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 3.87/4.09 inference(quant_inst,[status(thm)],[])).
% 3.87/4.09 tff(13746,plain,
% 3.87/4.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))),
% 3.87/4.09 inference(modus_ponens,[status(thm)],[13745, 13744])).
% 3.87/4.09 tff(13747,plain,
% 3.87/4.09 ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[13746, 178, 13686, 1146])).
% 3.87/4.09 tff(13748,plain,
% 3.87/4.09 ($false),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[13747, 13740, 13735, 13732])).
% 3.87/4.09 tff(13749,plain,(b(elem!1, z) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(elem!1))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~r(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (s(s(z)) = elem!1) | (s(s(z)) = s(elem!1)) | (s(elem!1) = elem!1) | (~r(s(elem!1), z)) | (elem!1 = z) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.09 tff(13750,plain,
% 3.87/4.09 ($false),
% 3.87/4.09 inference(unit_resolution,[status(thm)],[13749, 11799, 5723, 1070, 854, 147, 5619, 3261, 1146, 12, 1060, 725, 844, 290, 168])).
% 3.87/4.09 tff(13751,plain,(b(elem!1, z) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(elem!1))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (s(s(z)) = elem!1) | (s(s(z)) = s(elem!1)) | (s(elem!1) = elem!1) | (~r(s(elem!1), z)) | (elem!1 = z) | (~b(s(s(s(s(z)))), z)) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 3.87/4.10 tff(13752,plain,
% 3.87/4.10 ($false),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[13751, 13678, 13676, 12, 1146, 3261, 10794, 1070, 5723, 11743, 844, 290, 168, 5618])).
% 3.87/4.10 tff(13753,plain,((s(elem!1) = s(s(s(s(z))))) | (s(s(z)) = elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | b(elem!1, z) | (~r(s(elem!1), z)) | (elem!1 = z) | (~b(s(s(s(s(z)))), z)) | r(s(s(z)), z) | (~b(z, s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.10 tff(13754,plain,
% 3.87/4.10 (s(elem!1) = s(s(s(s(z))))),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[13753, 2809, 1146, 3261, 1070, 5723, 844, 12, 168, 5618, 1687, 105])).
% 3.87/4.10 tff(13755,plain,
% 3.87/4.10 (~(elem!1 = s(s(s(elem!1))))),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[2498, 13754, 2387])).
% 3.87/4.10 tff(13756,plain,
% 3.87/4.10 (~(s(s(s(elem!1))) = elem!1)),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[2489, 13755])).
% 3.87/4.10 tff(13757,plain,
% 3.87/4.10 (~(s(elem!1) = elem!1)),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[2150, 13756])).
% 3.87/4.10 tff(13758,plain,
% 3.87/4.10 (~(elem!1 = s(elem!1))),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[748, 13757])).
% 3.87/4.10 tff(13759,plain,
% 3.87/4.10 (b(elem!1, s(s(z)))),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[11793, 2809, 3261, 5723, 5618])).
% 3.87/4.10 tff(13760,plain,
% 3.87/4.10 (~b(elem!1, s(elem!1))),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[13749, 13757, 1146, 10794, 1070, 5619, 3261, 5723, 12, 11743, 13759, 844, 2809, 168])).
% 3.87/4.10 tff(13761,plain,
% 3.87/4.10 ($false),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[756, 13760, 13758, 12568])).
% 3.87/4.10 tff(13762,plain,((z = elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~r(z, s(s(z)))) | b(elem!1, z) | (s(s(z)) = elem!1) | (~r(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | r(s(s(z)), z) | (~b(z, s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.10 tff(13763,plain,
% 3.87/4.10 (z = elem!1),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[13762, 844, 12566, 3261, 5723, 12, 12401, 11753, 5618, 11751, 105])).
% 3.87/4.10 tff(13764,plain,
% 3.87/4.10 (s(z) = s(elem!1)),
% 3.87/4.10 inference(monotonicity,[status(thm)],[13763])).
% 3.87/4.10 tff(13765,plain,
% 3.87/4.10 ((s(s(s(s(s(s(s(z))))))) = s(z)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.87/4.10 inference(monotonicity,[status(thm)],[13764])).
% 3.87/4.10 tff(13766,plain,
% 3.87/4.10 ((s(s(s(s(s(s(s(z))))))) = s(z)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.87/4.10 inference(transitivity,[status(thm)],[13765, 377])).
% 3.87/4.10 tff(13767,plain,
% 3.87/4.10 ((s(s(s(s(s(s(s(z))))))) = s(z)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.87/4.10 inference(transitivity,[status(thm)],[13766, 655])).
% 3.87/4.10 tff(13768,plain,
% 3.87/4.10 ((~(s(s(s(s(s(s(s(z))))))) = s(z))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 3.87/4.10 inference(monotonicity,[status(thm)],[13767])).
% 3.87/4.10 tff(13769,plain,
% 3.87/4.10 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.87/4.10 inference(modus_ponens,[status(thm)],[612, 13768])).
% 3.87/4.10 tff(13770,plain,
% 3.87/4.10 (r(s(s(s(s(s(s(s(z))))))), z) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.87/4.10 inference(monotonicity,[status(thm)],[13763])).
% 3.87/4.10 tff(13771,plain,
% 3.87/4.10 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[2960, 41, 3575, 3574])).
% 3.87/4.10 tff(13772,plain,
% 3.87/4.10 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[13684, 11884, 3261, 10794])).
% 3.87/4.10 tff(13773,plain,
% 3.87/4.10 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[249, 13772])).
% 3.87/4.10 tff(13774,plain,
% 3.87/4.10 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[133, 126])).
% 3.87/4.10 tff(13775,plain,
% 3.87/4.10 ($false),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[11869, 178, 3461, 166, 595, 146, 1146])).
% 3.87/4.10 tff(13776,plain,((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.10 tff(13777,plain,
% 3.87/4.10 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[13776, 13774, 13773, 5619, 13771])).
% 3.87/4.10 tff(13778,plain,
% 3.87/4.10 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[271, 13777])).
% 3.87/4.10 tff(13779,plain,
% 3.87/4.10 (~r(z, s(s(s(s(z)))))),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[3478, 3261, 10794])).
% 3.87/4.10 tff(13780,plain,
% 3.87/4.10 (b(z, s(s(s(s(z)))))),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[46, 13779])).
% 3.87/4.10 tff(13781,plain,
% 3.87/4.10 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[11898, 146, 193, 13780, 11884, 5619])).
% 3.87/4.10 tff(13782,plain,
% 3.87/4.10 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[84, 13781])).
% 3.87/4.10 tff(13783,plain,
% 3.87/4.10 (~r(s(elem!1), s(s(z)))),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[11775, 1369, 11884, 853, 13780, 10794, 3261])).
% 3.87/4.10 tff(13784,plain,
% 3.87/4.10 (b(s(elem!1), s(s(z)))),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[421, 13783, 1056])).
% 3.87/4.10 tff(13785,plain,
% 3.87/4.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 3.87/4.10 inference(rewrite,[status(thm)],[])).
% 3.87/4.10 tff(13786,plain,
% 3.87/4.10 (((~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(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 3.87/4.10 inference(rewrite,[status(thm)],[])).
% 3.87/4.10 tff(13787,plain,
% 3.87/4.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 3.87/4.10 inference(monotonicity,[status(thm)],[13786])).
% 3.87/4.10 tff(13788,plain,
% 3.87/4.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 3.87/4.10 inference(transitivity,[status(thm)],[13787, 13785])).
% 3.87/4.10 tff(13789,plain,
% 3.87/4.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), s(elem!1))))),
% 3.87/4.10 inference(quant_inst,[status(thm)],[])).
% 3.87/4.10 tff(13790,plain,
% 3.87/4.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 3.87/4.10 inference(modus_ponens,[status(thm)],[13789, 13788])).
% 3.87/4.10 tff(13791,plain,
% 3.87/4.10 ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), z))),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[13790, 178, 3461, 1687, 1069])).
% 3.87/4.10 tff(13792,plain,
% 3.87/4.10 (~b(s(s(z)), s(elem!1))),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[13791, 853])).
% 3.87/4.10 tff(13793,plain,
% 3.87/4.10 (r(s(s(z)), s(elem!1))),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[1067, 13792, 1060])).
% 3.87/4.10 tff(13794,plain,
% 3.87/4.10 (~r(z, s(elem!1))),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[12114, 13793, 3261])).
% 3.87/4.10 tff(13795,plain,
% 3.87/4.10 (b(z, s(elem!1))),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[2351, 13794])).
% 3.87/4.10 tff(13796,plain,
% 3.87/4.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 3.87/4.10 inference(rewrite,[status(thm)],[])).
% 3.87/4.10 tff(13797,plain,
% 3.87/4.10 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 3.87/4.10 inference(rewrite,[status(thm)],[])).
% 3.87/4.10 tff(13798,plain,
% 3.87/4.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))))),
% 3.87/4.10 inference(monotonicity,[status(thm)],[13797])).
% 3.87/4.10 tff(13799,plain,
% 3.87/4.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 3.87/4.10 inference(transitivity,[status(thm)],[13798, 13796])).
% 3.87/4.10 tff(13800,plain,
% 3.87/4.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))))),
% 3.87/4.10 inference(quant_inst,[status(thm)],[])).
% 3.87/4.10 tff(13801,plain,
% 3.87/4.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))),
% 3.87/4.10 inference(modus_ponens,[status(thm)],[13800, 13799])).
% 3.87/4.10 tff(13802,plain,
% 3.87/4.10 ($false),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[13801, 178, 13795, 853, 3461, 1070, 1687, 168, 1069])).
% 3.87/4.10 tff(13803,plain,((~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (s(s(z)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.10 tff(13804,plain,
% 3.87/4.10 (~b(s(elem!1), s(s(s(s(z)))))),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[13803, 13784, 853, 13780, 11884, 5619, 3261, 2311])).
% 3.87/4.10 tff(13805,plain,
% 3.87/4.10 (r(s(elem!1), s(s(s(s(z)))))),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[1084, 13804, 1369])).
% 3.87/4.10 tff(13806,plain,
% 3.87/4.10 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[5568, 13805, 13782])).
% 3.87/4.10 tff(13807,plain,
% 3.87/4.10 (~r(s(s(z)), s(elem!1))),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[5758, 13805, 10794])).
% 3.87/4.10 tff(13808,plain,
% 3.87/4.10 (b(s(s(z)), s(elem!1))),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[1067, 13807, 2311])).
% 3.87/4.10 tff(13809,plain,
% 3.87/4.10 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[2976, 178, 13808, 13784, 13773, 1146])).
% 3.87/4.10 tff(13810,plain,
% 3.87/4.10 (s(elem!1) = s(s(s(s(s(s(s(z)))))))),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[395, 13809, 13806])).
% 3.87/4.10 tff(13811,plain,
% 3.87/4.10 (inj_0(s(elem!1)) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 3.87/4.10 inference(monotonicity,[status(thm)],[13810])).
% 3.87/4.10 tff(13812,plain,
% 3.87/4.10 (elem!1 = s(s(s(s(s(s(z))))))),
% 3.87/4.10 inference(transitivity,[status(thm)],[517, 13811, 57])).
% 3.87/4.10 tff(13813,plain,
% 3.87/4.10 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 3.87/4.10 inference(monotonicity,[status(thm)],[13812])).
% 3.87/4.10 tff(13814,plain,
% 3.87/4.10 (b(s(s(z)), s(s(s(s(s(s(z))))))) <=> b(s(s(z)), elem!1)),
% 3.87/4.10 inference(symmetry,[status(thm)],[13813])).
% 3.87/4.10 tff(13815,plain,
% 3.87/4.10 ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) <=> (~b(s(s(z)), elem!1))),
% 3.87/4.10 inference(monotonicity,[status(thm)],[13814])).
% 3.87/4.10 tff(13816,plain,
% 3.87/4.10 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(elem!1))),
% 3.87/4.10 inference(symmetry,[status(thm)],[13811])).
% 3.87/4.10 tff(13817,plain,
% 3.87/4.10 (s(s(s(s(s(s(z)))))) = elem!1),
% 3.87/4.10 inference(transitivity,[status(thm)],[609, 13816, 304])).
% 3.87/4.10 tff(13818,plain,
% 3.87/4.10 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.87/4.10 inference(monotonicity,[status(thm)],[13817])).
% 3.87/4.10 tff(13819,plain,
% 3.87/4.10 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.10 inference(symmetry,[status(thm)],[13818])).
% 3.87/4.10 tff(13820,plain,
% 3.87/4.10 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.87/4.10 inference(monotonicity,[status(thm)],[13810])).
% 3.87/4.10 tff(13821,plain,
% 3.87/4.10 (b(elem!1, s(elem!1))),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[13675, 1369, 105, 3261, 13780, 5618])).
% 3.87/4.10 tff(13822,plain,
% 3.87/4.10 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.87/4.10 inference(modus_ponens,[status(thm)],[13821, 13820])).
% 3.87/4.10 tff(13823,plain,
% 3.87/4.10 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.10 inference(modus_ponens,[status(thm)],[13822, 13819])).
% 3.87/4.10 tff(13824,plain,
% 3.87/4.10 (b(elem!1, z) <=> b(s(s(s(s(s(s(z)))))), z)),
% 3.87/4.10 inference(monotonicity,[status(thm)],[13812])).
% 3.87/4.10 tff(13825,plain,
% 3.87/4.10 (~b(z, s(elem!1))),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[12205, 13807, 853, 5619, 13783, 1056])).
% 3.87/4.10 tff(13826,plain,
% 3.87/4.10 (r(z, s(elem!1))),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[2351, 13825])).
% 3.87/4.10 tff(13827,plain,
% 3.87/4.10 (~(elem!1 = z)),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[6201, 13826, 744])).
% 3.87/4.10 tff(13828,plain,
% 3.87/4.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))),
% 3.87/4.10 inference(rewrite,[status(thm)],[])).
% 3.87/4.10 tff(13829,plain,
% 3.87/4.10 (((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(s(z))))) <=> ((~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))),
% 3.87/4.10 inference(rewrite,[status(thm)],[])).
% 3.87/4.10 tff(13830,plain,
% 3.87/4.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z))))),
% 3.87/4.10 inference(monotonicity,[status(thm)],[13829])).
% 3.87/4.10 tff(13831,plain,
% 3.87/4.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))),
% 3.87/4.10 inference(transitivity,[status(thm)],[13830, 13828])).
% 3.87/4.10 tff(13832,plain,
% 3.87/4.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(s(z)))))),
% 3.87/4.10 inference(quant_inst,[status(thm)],[])).
% 3.87/4.10 tff(13833,plain,
% 3.87/4.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z))),
% 3.87/4.10 inference(modus_ponens,[status(thm)],[13832, 13831])).
% 3.87/4.10 tff(13834,plain,
% 3.87/4.10 (~b(elem!1, s(s(z)))),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[13833, 178, 13821, 853, 5619, 13808])).
% 3.87/4.10 tff(13835,plain,
% 3.87/4.10 (b(elem!1, z)),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[11793, 13834, 3261, 13827, 5618])).
% 3.87/4.10 tff(13836,plain,
% 3.87/4.10 (b(s(s(s(s(s(s(z)))))), z)),
% 3.87/4.10 inference(modus_ponens,[status(thm)],[13835, 13824])).
% 3.87/4.10 tff(13837,plain,
% 3.87/4.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 3.87/4.10 inference(rewrite,[status(thm)],[])).
% 3.87/4.10 tff(13838,plain,
% 3.87/4.10 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 3.87/4.10 inference(rewrite,[status(thm)],[])).
% 3.87/4.10 tff(13839,plain,
% 3.87/4.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 3.87/4.10 inference(monotonicity,[status(thm)],[13838])).
% 3.87/4.10 tff(13840,plain,
% 3.87/4.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 3.87/4.10 inference(transitivity,[status(thm)],[13839, 13837])).
% 3.87/4.10 tff(13841,plain,
% 3.87/4.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 3.87/4.10 inference(quant_inst,[status(thm)],[])).
% 3.87/4.10 tff(13842,plain,
% 3.87/4.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 3.87/4.10 inference(modus_ponens,[status(thm)],[13841, 13840])).
% 3.87/4.10 tff(13843,plain,
% 3.87/4.10 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[13842, 178, 13773, 146, 13836, 13823])).
% 3.87/4.10 tff(13844,plain,
% 3.87/4.10 (~b(s(s(z)), elem!1)),
% 3.87/4.10 inference(modus_ponens,[status(thm)],[13843, 13815])).
% 3.87/4.10 tff(13845,plain,
% 3.87/4.10 (~(s(s(z)) = elem!1)),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[5361, 13810])).
% 3.87/4.10 tff(13846,plain,
% 3.87/4.10 (r(s(s(z)), elem!1)),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[448, 13845, 13844])).
% 3.87/4.10 tff(13847,plain,
% 3.87/4.10 (~r(s(s(s(s(z)))), elem!1)),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[3329, 13846, 193])).
% 3.87/4.10 tff(13848,plain,
% 3.87/4.10 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 3.87/4.10 inference(monotonicity,[status(thm)],[13812])).
% 3.87/4.10 tff(13849,plain,
% 3.87/4.10 (b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) <=> b(s(s(s(s(z)))), elem!1)),
% 3.87/4.10 inference(symmetry,[status(thm)],[13848])).
% 3.87/4.10 tff(13850,plain,
% 3.87/4.10 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) <=> (~b(s(s(s(s(z)))), elem!1))),
% 3.87/4.10 inference(monotonicity,[status(thm)],[13849])).
% 3.87/4.10 tff(13851,plain,
% 3.87/4.10 (b(z, elem!1) <=> b(z, s(s(s(s(s(s(z)))))))),
% 3.87/4.10 inference(monotonicity,[status(thm)],[13812])).
% 3.87/4.10 tff(13852,plain,
% 3.87/4.10 (~(z = elem!1)),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[317, 13827])).
% 3.87/4.10 tff(13853,plain,
% 3.87/4.10 (~r(z, elem!1)),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[8412, 13846, 3261])).
% 3.87/4.10 tff(13854,plain,
% 3.87/4.10 (b(z, elem!1)),
% 3.87/4.10 inference(unit_resolution,[status(thm)],[585, 13853, 13852])).
% 3.87/4.10 tff(13855,plain,
% 3.87/4.10 (b(z, s(s(s(s(s(s(z)))))))),
% 3.87/4.10 inference(modus_ponens,[status(thm)],[13854, 13851])).
% 3.87/4.10 tff(13856,plain,
% 3.87/4.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 3.87/4.11 inference(rewrite,[status(thm)],[])).
% 3.87/4.11 tff(13857,plain,
% 3.87/4.11 (((~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(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(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(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 3.87/4.11 inference(rewrite,[status(thm)],[])).
% 3.87/4.11 tff(13858,plain,
% 3.87/4.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 3.87/4.11 inference(monotonicity,[status(thm)],[13857])).
% 3.87/4.11 tff(13859,plain,
% 3.87/4.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 3.87/4.11 inference(transitivity,[status(thm)],[13858, 13856])).
% 3.87/4.11 tff(13860,plain,
% 3.87/4.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(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)))))))),
% 3.87/4.11 inference(quant_inst,[status(thm)],[])).
% 3.87/4.11 tff(13861,plain,
% 3.87/4.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 3.87/4.11 inference(modus_ponens,[status(thm)],[13860, 13859])).
% 3.87/4.11 tff(13862,plain,
% 3.87/4.11 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[13861, 178, 13780, 11884, 13855, 13836])).
% 3.87/4.11 tff(13863,plain,
% 3.87/4.11 (~b(s(s(s(s(z)))), elem!1)),
% 3.87/4.11 inference(modus_ponens,[status(thm)],[13862, 13850])).
% 3.87/4.11 tff(13864,plain,
% 3.87/4.11 (s(s(s(s(z)))) = elem!1),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[3142, 13863, 13847])).
% 3.87/4.11 tff(13865,plain,
% 3.87/4.11 (s(s(s(s(z)))) = s(s(s(s(s(s(z))))))),
% 3.87/4.11 inference(transitivity,[status(thm)],[13864, 517, 13811, 57])).
% 3.87/4.11 tff(13866,plain,
% 3.87/4.11 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 3.87/4.11 inference(monotonicity,[status(thm)],[13865])).
% 3.87/4.11 tff(13867,plain,
% 3.87/4.11 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(s(s(z)))))),
% 3.87/4.11 inference(symmetry,[status(thm)],[13866])).
% 3.87/4.11 tff(13868,plain,
% 3.87/4.11 (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))),
% 3.87/4.11 inference(monotonicity,[status(thm)],[13865])).
% 3.87/4.11 tff(13869,plain,
% 3.87/4.11 (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))),
% 3.87/4.11 inference(symmetry,[status(thm)],[13868])).
% 3.87/4.11 tff(13870,plain,
% 3.87/4.11 (s(s(s(s(s(s(s(z))))))) = s(s(s(z)))),
% 3.87/4.11 inference(transitivity,[status(thm)],[13869, 239, 13867, 11])).
% 3.87/4.11 tff(13871,plain,
% 3.87/4.11 ($false),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[1104, 13870])).
% 3.87/4.11 tff(13872,plain,((s(elem!1) = s(s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | r(s(s(z)), z) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(elem!1), z)) | r(elem!1, s(elem!1)) | (s(elem!1) = s(s(z))) | b(s(s(z)), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.11 tff(13873,plain,
% 3.87/4.11 (s(elem!1) = s(s(s(s(z))))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[13872, 744, 3261, 146, 5618, 1146, 853, 193, 1056, 105])).
% 3.87/4.11 tff(13874,plain,
% 3.87/4.11 ((s(elem!1) = elem!1) <=> (s(s(s(s(z)))) = elem!1)),
% 3.87/4.11 inference(monotonicity,[status(thm)],[13873])).
% 3.87/4.11 tff(13875,plain,
% 3.87/4.11 ((~(s(elem!1) = elem!1)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 3.87/4.11 inference(monotonicity,[status(thm)],[13874])).
% 3.87/4.11 tff(13876,plain,
% 3.87/4.11 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 3.87/4.11 inference(symmetry,[status(thm)],[341])).
% 3.87/4.11 tff(13877,plain,
% 3.87/4.11 (s(s(s(z))) = s(s(elem!1))),
% 3.87/4.11 inference(transitivity,[status(thm)],[61, 2492, 13876, 343])).
% 3.87/4.11 tff(13878,plain,
% 3.87/4.11 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 3.87/4.11 inference(monotonicity,[status(thm)],[13877])).
% 3.87/4.11 tff(13879,plain,
% 3.87/4.11 (inj_0(s(s(elem!1))) = inj_0(s(s(s(z))))),
% 3.87/4.11 inference(symmetry,[status(thm)],[13878])).
% 3.87/4.11 tff(13880,plain,
% 3.87/4.11 (s(elem!1) = s(s(z))),
% 3.87/4.11 inference(transitivity,[status(thm)],[975, 13879, 65])).
% 3.87/4.11 tff(13881,plain,
% 3.87/4.11 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(elem!1))),
% 3.87/4.11 inference(monotonicity,[status(thm)],[340])).
% 3.87/4.11 tff(13882,plain,
% 3.87/4.11 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(z)))),
% 3.87/4.11 inference(transitivity,[status(thm)],[13881, 1358])).
% 3.87/4.11 tff(13883,plain,
% 3.87/4.11 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(elem!1) = s(s(z))))),
% 3.87/4.11 inference(monotonicity,[status(thm)],[13882])).
% 3.87/4.11 tff(13884,plain,
% 3.87/4.11 (~(s(elem!1) = s(s(z)))),
% 3.87/4.11 inference(modus_ponens,[status(thm)],[1683, 13883])).
% 3.87/4.11 tff(13885,plain,
% 3.87/4.11 ($false),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[13884, 13880])).
% 3.87/4.11 tff(13886,plain,((~(s(elem!1) = s(s(s(s(z)))))) | (~(s(s(s(elem!1))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.11 tff(13887,plain,
% 3.87/4.11 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[13886, 13873])).
% 3.87/4.11 tff(13888,plain,
% 3.87/4.11 (~(elem!1 = s(s(elem!1)))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[1539, 13887])).
% 3.87/4.11 tff(13889,plain,
% 3.87/4.11 (~(s(s(elem!1)) = elem!1)),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[1546, 13888])).
% 3.87/4.11 tff(13890,plain,
% 3.87/4.11 (~(s(elem!1) = elem!1)),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[672, 13889])).
% 3.87/4.11 tff(13891,plain,
% 3.87/4.11 (~(s(s(s(s(z)))) = elem!1)),
% 3.87/4.11 inference(modus_ponens,[status(thm)],[13890, 13875])).
% 3.87/4.11 tff(13892,plain,
% 3.87/4.11 (~(elem!1 = s(s(z)))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[1353, 13891, 13873])).
% 3.87/4.11 tff(13893,plain,
% 3.87/4.11 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 3.87/4.11 inference(monotonicity,[status(thm)],[13873])).
% 3.87/4.11 tff(13894,plain,
% 3.87/4.11 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 3.87/4.11 inference(symmetry,[status(thm)],[13893])).
% 3.87/4.11 tff(13895,plain,
% 3.87/4.11 (s(s(s(z))) = elem!1),
% 3.87/4.11 inference(transitivity,[status(thm)],[61, 13894, 304])).
% 3.87/4.11 tff(13896,plain,
% 3.87/4.11 ((s(s(s(z))) = z) <=> (elem!1 = z)),
% 3.87/4.11 inference(monotonicity,[status(thm)],[13895])).
% 3.87/4.11 tff(13897,plain,
% 3.87/4.11 ((s(s(s(z))) = z) <=> (z = elem!1)),
% 3.87/4.11 inference(transitivity,[status(thm)],[13896, 313])).
% 3.87/4.11 tff(13898,plain,
% 3.87/4.11 ((~(s(s(s(z))) = z)) <=> (~(z = elem!1))),
% 3.87/4.11 inference(monotonicity,[status(thm)],[13897])).
% 3.87/4.11 tff(13899,plain,
% 3.87/4.11 (~(z = elem!1)),
% 3.87/4.11 inference(modus_ponens,[status(thm)],[77, 13898])).
% 3.87/4.11 tff(13900,plain,
% 3.87/4.11 (b(z, s(elem!1)) <=> b(z, s(s(s(s(z)))))),
% 3.87/4.11 inference(monotonicity,[status(thm)],[13873])).
% 3.87/4.11 tff(13901,plain,
% 3.87/4.11 (b(z, s(s(s(s(z))))) <=> b(z, s(elem!1))),
% 3.87/4.11 inference(symmetry,[status(thm)],[13900])).
% 3.87/4.11 tff(13902,plain,
% 3.87/4.11 (b(z, s(elem!1))),
% 3.87/4.11 inference(modus_ponens,[status(thm)],[13780, 13901])).
% 3.87/4.11 tff(13903,plain,
% 3.87/4.11 (~(elem!1 = s(elem!1))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[748, 13890])).
% 3.87/4.11 tff(13904,plain,
% 3.87/4.11 (b(elem!1, s(elem!1))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[756, 13903, 744])).
% 3.87/4.11 tff(13905,plain,
% 3.87/4.11 ((s(s(s(z))) = z) <=> (elem!1 = z)),
% 3.87/4.11 inference(transitivity,[status(thm)],[13897, 314])).
% 3.87/4.11 tff(13906,plain,
% 3.87/4.11 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = z))),
% 3.87/4.11 inference(monotonicity,[status(thm)],[13905])).
% 3.87/4.11 tff(13907,plain,
% 3.87/4.11 (~(elem!1 = z)),
% 3.87/4.11 inference(modus_ponens,[status(thm)],[77, 13906])).
% 3.87/4.11 tff(13908,plain,
% 3.87/4.11 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 3.87/4.11 inference(monotonicity,[status(thm)],[13895])).
% 3.87/4.11 tff(13909,plain,
% 3.87/4.11 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.87/4.11 inference(transitivity,[status(thm)],[13908, 836])).
% 3.87/4.11 tff(13910,plain,
% 3.87/4.11 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(s(s(s(s(z)))))))))),
% 3.87/4.11 inference(monotonicity,[status(thm)],[13909])).
% 3.87/4.11 tff(13911,plain,
% 3.87/4.11 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.87/4.11 inference(modus_ponens,[status(thm)],[1104, 13910])).
% 3.87/4.11 tff(13912,plain,
% 3.87/4.11 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(s(z)))))),
% 3.87/4.11 inference(monotonicity,[status(thm)],[13873])).
% 3.87/4.11 tff(13913,plain,
% 3.87/4.11 (b(elem!1, s(s(s(s(z)))))),
% 3.87/4.11 inference(modus_ponens,[status(thm)],[13904, 13912])).
% 3.87/4.11 tff(13914,plain,
% 3.87/4.11 ((s(elem!1) = elem!1) <=> (elem!1 = s(s(s(s(z)))))),
% 3.87/4.11 inference(transitivity,[status(thm)],[13874, 501])).
% 3.87/4.11 tff(13915,plain,
% 3.87/4.11 ((~(s(elem!1) = elem!1)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 3.87/4.11 inference(monotonicity,[status(thm)],[13914])).
% 3.87/4.11 tff(13916,plain,
% 3.87/4.11 (~(elem!1 = s(s(s(s(z)))))),
% 3.87/4.11 inference(modus_ponens,[status(thm)],[13890, 13915])).
% 3.87/4.11 tff(13917,plain,
% 3.87/4.11 (r(s(s(z)), s(elem!1)) <=> r(s(s(z)), s(s(s(s(z)))))),
% 3.87/4.11 inference(monotonicity,[status(thm)],[13873])).
% 3.87/4.11 tff(13918,plain,
% 3.87/4.11 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(z)), s(elem!1))),
% 3.87/4.11 inference(symmetry,[status(thm)],[13917])).
% 3.87/4.11 tff(13919,plain,
% 3.87/4.11 (r(s(s(z)), s(elem!1))),
% 3.87/4.11 inference(modus_ponens,[status(thm)],[10794, 13918])).
% 3.87/4.11 tff(13920,plain,
% 3.87/4.11 (~(s(s(z)) = elem!1)),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[1331, 13919, 744])).
% 3.87/4.11 tff(13921,plain,
% 3.87/4.11 (b(elem!1, z)),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[11980, 13920, 10794, 13891, 3261, 13916, 13913, 13899, 13911, 13907, 5618])).
% 3.87/4.11 tff(13922,plain,
% 3.87/4.11 (~b(z, elem!1)),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[863, 13921, 13904, 853, 13902])).
% 3.87/4.11 tff(13923,plain,
% 3.87/4.11 (r(z, elem!1)),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[585, 13922, 13899])).
% 3.87/4.11 tff(13924,plain,
% 3.87/4.11 (~r(elem!1, s(s(z)))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[4862, 13923, 3261])).
% 3.87/4.11 tff(13925,plain,
% 3.87/4.11 (~r(s(s(z)), elem!1)),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[12239, 13921, 10794, 13891, 13780, 13899, 13916, 3261])).
% 3.87/4.11 tff(13926,plain,
% 3.87/4.11 (b(s(s(z)), elem!1)),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[448, 13925, 13920])).
% 3.87/4.11 tff(13927,plain,
% 3.87/4.11 (~b(elem!1, s(s(z)))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[11871, 13923, 5619, 10794, 13911, 13926, 13782])).
% 3.87/4.11 tff(13928,plain,
% 3.87/4.11 ($false),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[467, 13927, 13924, 13892])).
% 3.87/4.11 tff(13929,plain,(r(elem!1, s(elem!1)) | (~r(z, s(s(z)))) | (~b(s(elem!1), z)) | r(s(s(z)), z) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (s(elem!1) = s(s(z))) | b(s(s(z)), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.11 tff(13930,plain,
% 3.87/4.11 (r(elem!1, s(elem!1))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[13929, 853, 3261, 5618, 146, 1146, 193, 1056, 105])).
% 3.87/4.11 tff(13931,plain,
% 3.87/4.11 (z = elem!1),
% 3.87/4.11 inference(symmetry,[status(thm)],[928])).
% 3.87/4.11 tff(13932,plain,
% 3.87/4.11 (s(z) = s(elem!1)),
% 3.87/4.11 inference(monotonicity,[status(thm)],[13931])).
% 3.87/4.11 tff(13933,plain,
% 3.87/4.11 (s(elem!1) = s(z)),
% 3.87/4.11 inference(symmetry,[status(thm)],[13932])).
% 3.87/4.11 tff(13934,plain,
% 3.87/4.11 (s(s(elem!1)) = s(s(z))),
% 3.87/4.11 inference(monotonicity,[status(thm)],[13933])).
% 3.87/4.11 tff(13935,plain,
% 3.87/4.11 (s(s(s(elem!1))) = s(s(s(z)))),
% 3.87/4.11 inference(monotonicity,[status(thm)],[13934])).
% 3.87/4.11 tff(13936,plain,
% 3.87/4.11 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 3.87/4.11 inference(monotonicity,[status(thm)],[13935])).
% 3.87/4.11 tff(13937,plain,
% 3.87/4.11 ((s(elem!1) = s(s(s(s(elem!1))))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 3.87/4.11 inference(monotonicity,[status(thm)],[13936])).
% 3.87/4.11 tff(13938,plain,
% 3.87/4.11 ((s(elem!1) = s(s(s(s(elem!1))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 3.87/4.11 inference(transitivity,[status(thm)],[13937, 2163])).
% 3.87/4.11 tff(13939,plain,
% 3.87/4.11 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 3.87/4.11 inference(symmetry,[status(thm)],[13938])).
% 3.87/4.11 tff(13940,plain,
% 3.87/4.11 (r(z, s(elem!1))),
% 3.87/4.11 inference(modus_ponens,[status(thm)],[1587, 6197])).
% 3.87/4.11 tff(13941,plain,
% 3.87/4.11 (~r(s(elem!1), s(s(z)))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[11762, 13940, 3261])).
% 3.87/4.11 tff(13942,plain,
% 3.87/4.11 (b(s(elem!1), s(s(z)))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[421, 13941, 1056])).
% 3.87/4.11 tff(13943,plain,
% 3.87/4.11 (~b(s(elem!1), s(s(s(s(z)))))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[13803, 13942, 853, 1687, 168, 3461, 3261, 2311])).
% 3.87/4.11 tff(13944,plain,
% 3.87/4.11 ((s(s(s(s(s(s(s(z))))))) = s(z)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.87/4.11 inference(monotonicity,[status(thm)],[13932])).
% 3.87/4.11 tff(13945,plain,
% 3.87/4.11 ((s(s(s(s(s(s(s(z))))))) = s(z)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.87/4.11 inference(transitivity,[status(thm)],[13944, 377])).
% 3.87/4.11 tff(13946,plain,
% 3.87/4.11 ((~(s(s(s(s(s(s(s(z))))))) = s(z))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 3.87/4.11 inference(monotonicity,[status(thm)],[13945])).
% 3.87/4.11 tff(13947,plain,
% 3.87/4.11 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.87/4.11 inference(modus_ponens,[status(thm)],[612, 13946])).
% 3.87/4.11 tff(13948,plain,
% 3.87/4.11 (~r(s(s(z)), s(elem!1))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[12114, 13940, 3261])).
% 3.87/4.11 tff(13949,plain,
% 3.87/4.11 (b(s(s(z)), s(elem!1))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[1067, 13948, 2311])).
% 3.87/4.11 tff(13950,plain,
% 3.87/4.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.87/4.11 inference(rewrite,[status(thm)],[])).
% 3.87/4.11 tff(13951,plain,
% 3.87/4.11 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(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(z)), s(elem!1)))) <=> ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.87/4.11 inference(rewrite,[status(thm)],[])).
% 3.87/4.11 tff(13952,plain,
% 3.87/4.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(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(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 3.87/4.11 inference(monotonicity,[status(thm)],[13951])).
% 3.87/4.11 tff(13953,plain,
% 3.87/4.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(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(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.87/4.11 inference(transitivity,[status(thm)],[13952, 13950])).
% 3.87/4.11 tff(13954,plain,
% 3.87/4.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(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(z)), s(elem!1))))),
% 3.87/4.11 inference(quant_inst,[status(thm)],[])).
% 3.87/4.11 tff(13955,plain,
% 3.87/4.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 3.87/4.11 inference(modus_ponens,[status(thm)],[13954, 13953])).
% 3.87/4.11 tff(13956,plain,
% 3.87/4.11 ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[13955, 178, 853, 166, 146])).
% 3.87/4.11 tff(13957,plain,
% 3.87/4.11 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[13956, 13949])).
% 3.87/4.11 tff(13958,plain,
% 3.87/4.11 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[395, 13957, 13947])).
% 3.87/4.11 tff(13959,plain,
% 3.87/4.11 (~r(s(elem!1), s(s(s(s(z)))))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[5568, 13958, 1130])).
% 3.87/4.11 tff(13960,plain,
% 3.87/4.11 (s(elem!1) = s(s(s(s(z))))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[1084, 13959, 13943])).
% 3.87/4.11 tff(13961,plain,
% 3.87/4.11 (s(s(s(s(z)))) = s(elem!1)),
% 3.87/4.11 inference(modus_ponens,[status(thm)],[1117, 2163])).
% 3.87/4.11 tff(13962,plain,
% 3.87/4.11 ($false),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[2508, 13961])).
% 3.87/4.11 tff(13963,plain,((~(s(elem!1) = s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.11 tff(13964,plain,
% 3.87/4.11 (s(s(s(s(z)))) = s(elem!1)),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[13963, 13960])).
% 3.87/4.11 tff(13965,plain,
% 3.87/4.11 (s(elem!1) = s(s(s(s(elem!1))))),
% 3.87/4.11 inference(modus_ponens,[status(thm)],[13964, 13939])).
% 3.87/4.11 tff(13966,plain,
% 3.87/4.11 ($false),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[952, 13965])).
% 3.87/4.11 tff(13967,plain,((~(elem!1 = z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(elem!1), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~r(z, s(s(z)))) | (s(elem!1) = s(s(z))) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.11 tff(13968,plain,
% 3.87/4.11 (~(elem!1 = z)),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[13967, 853, 13782, 13773, 146, 13780, 11884, 5619, 3261, 1056, 13930])).
% 3.87/4.11 tff(13969,plain,
% 3.87/4.11 ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[11770, 178, 853, 11798, 168])).
% 3.87/4.11 tff(13970,plain,
% 3.87/4.11 (~b(s(elem!1), s(s(s(s(z)))))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[13969, 855])).
% 3.87/4.11 tff(13971,plain,
% 3.87/4.11 (r(s(elem!1), s(s(s(s(z)))))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[1084, 1369, 13970])).
% 3.87/4.11 tff(13972,plain,
% 3.87/4.11 (~r(s(elem!1), s(s(z)))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[11775, 1369, 168, 853, 11798, 147, 3261])).
% 3.87/4.11 tff(13973,plain,
% 3.87/4.11 (r(s(s(z)), s(elem!1))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[12205, 13972, 853, 3461, 855, 1056])).
% 3.87/4.11 tff(13974,plain,
% 3.87/4.11 ($false),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[5758, 13973, 13971, 147])).
% 3.87/4.11 tff(13975,plain,((s(elem!1) = s(s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(z, s(elem!1))) | (s(elem!1) = s(s(z))) | (~b(s(s(s(s(z)))), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.11 tff(13976,plain,
% 3.87/4.11 (~b(z, s(elem!1))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[13975, 1369, 853, 3461, 10794, 1056, 168, 3261])).
% 3.87/4.11 tff(13977,plain,
% 3.87/4.11 (r(z, s(elem!1))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[2351, 13976])).
% 3.87/4.11 tff(13978,plain,
% 3.87/4.11 (~r(s(s(z)), s(elem!1))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[12114, 13977, 3261])).
% 3.87/4.11 tff(13979,plain,
% 3.87/4.11 (~(s(s(z)) = elem!1)),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[13127, 13978, 1587])).
% 3.87/4.11 tff(13980,plain,
% 3.87/4.11 (~(elem!1 = s(s(z)))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[311, 13979])).
% 3.87/4.11 tff(13981,plain,
% 3.87/4.11 (~r(elem!1, z)),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[12189, 13977, 1587])).
% 3.87/4.11 tff(13982,plain,
% 3.87/4.11 (b(elem!1, z)),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[498, 13981, 290])).
% 3.87/4.11 tff(13983,plain,
% 3.87/4.11 (s(elem!1) = elem!1),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[13431, 13982, 105, 168, 3261, 3461, 13780, 1587, 853, 13977])).
% 3.87/4.11 tff(13984,plain,
% 3.87/4.11 (s(s(elem!1)) = elem!1),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[672, 13983])).
% 3.87/4.11 tff(13985,plain,
% 3.87/4.11 (~(s(s(s(s(z)))) = elem!1)),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[338, 13984, 13979])).
% 3.87/4.11 tff(13986,plain,
% 3.87/4.11 (~(elem!1 = s(s(s(s(z)))))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[325, 13985])).
% 3.87/4.11 tff(13987,plain,
% 3.87/4.11 (~r(s(s(z)), elem!1)),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[12239, 13985, 10794, 13982, 13780, 318, 13986, 3261])).
% 3.87/4.11 tff(13988,plain,
% 3.87/4.11 (b(s(s(z)), elem!1)),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[448, 13987, 13979])).
% 3.87/4.11 tff(13989,plain,
% 3.87/4.11 (~b(z, elem!1)),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[12263, 13988, 3461, 10794, 13780, 13982, 13986, 13980])).
% 3.87/4.11 tff(13990,plain,
% 3.87/4.11 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[2510, 13984, 2169])).
% 3.87/4.11 tff(13991,plain,
% 3.87/4.11 (~r(s(elem!1), s(s(z)))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[11775, 1369, 168, 853, 13780, 10794, 3261])).
% 3.87/4.11 tff(13992,plain,
% 3.87/4.11 (s(s(s(elem!1))) = elem!1),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[2150, 13983])).
% 3.87/4.11 tff(13993,plain,
% 3.87/4.11 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[3907, 13992, 13991])).
% 3.87/4.11 tff(13994,plain,
% 3.87/4.11 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[1170, 13993])).
% 3.87/4.11 tff(13995,plain,
% 3.87/4.11 (elem!1 = s(s(elem!1))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[1546, 13984])).
% 3.87/4.11 tff(13996,plain,
% 3.87/4.11 (s(s(s(elem!1))) = s(elem!1)),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[1539, 13995])).
% 3.87/4.11 tff(13997,plain,
% 3.87/4.11 (elem!1 = s(s(s(s(elem!1))))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[1509, 13996])).
% 3.87/4.11 tff(13998,plain,
% 3.87/4.11 (b(elem!1, s(s(z)))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[3901, 13997, 13994])).
% 3.87/4.11 tff(13999,plain,
% 3.87/4.11 (~r(z, elem!1)),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[11871, 13998, 3461, 10794, 13990, 13988, 1130])).
% 3.87/4.11 tff(14000,plain,
% 3.87/4.11 ($false),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[585, 13999, 13989, 318])).
% 3.87/4.11 tff(14001,plain,((s(elem!1) = s(s(s(s(z))))) | (~b(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | b(s(s(z)), s(s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~r(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (elem!1 = z) | (s(elem!1) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.11 tff(14002,plain,
% 3.87/4.11 (s(elem!1) = s(s(s(s(z))))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[14001, 13930, 13782, 3261, 105, 11884, 5619, 853, 13968, 1056])).
% 3.87/4.11 tff(14003,plain,
% 3.87/4.11 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 3.87/4.11 inference(monotonicity,[status(thm)],[14002])).
% 3.87/4.11 tff(14004,plain,
% 3.87/4.11 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 3.87/4.11 inference(symmetry,[status(thm)],[14003])).
% 3.87/4.11 tff(14005,plain,
% 3.87/4.11 (s(s(s(z))) = elem!1),
% 3.87/4.11 inference(transitivity,[status(thm)],[61, 14004, 304])).
% 3.87/4.11 tff(14006,plain,
% 3.87/4.11 ((s(s(z)) = s(s(s(z)))) <=> (s(s(z)) = elem!1)),
% 3.87/4.11 inference(monotonicity,[status(thm)],[14005])).
% 3.87/4.11 tff(14007,plain,
% 3.87/4.11 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(z))))),
% 3.87/4.11 inference(symmetry,[status(thm)],[14006])).
% 3.87/4.11 tff(14008,plain,
% 3.87/4.11 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(s(z)))))),
% 3.87/4.11 inference(monotonicity,[status(thm)],[14002])).
% 3.87/4.11 tff(14009,plain,
% 3.87/4.11 (r(elem!1, s(s(s(s(z)))))),
% 3.87/4.11 inference(modus_ponens,[status(thm)],[13930, 14008])).
% 3.87/4.11 tff(14010,plain,
% 3.87/4.11 (~r(s(s(z)), elem!1)),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[8763, 14009, 10794])).
% 3.87/4.11 tff(14011,plain,
% 3.87/4.11 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 3.87/4.11 inference(monotonicity,[status(thm)],[14005])).
% 3.87/4.11 tff(14012,plain,
% 3.87/4.11 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.87/4.11 inference(transitivity,[status(thm)],[14011, 836])).
% 3.87/4.11 tff(14013,plain,
% 3.87/4.11 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(s(s(s(s(z)))))))))),
% 3.87/4.11 inference(monotonicity,[status(thm)],[14012])).
% 3.87/4.11 tff(14014,plain,
% 3.87/4.11 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.87/4.11 inference(modus_ponens,[status(thm)],[1104, 14013])).
% 3.87/4.11 tff(14015,plain,
% 3.87/4.11 ((s(elem!1) = elem!1) <=> (s(s(s(s(z)))) = elem!1)),
% 3.87/4.11 inference(monotonicity,[status(thm)],[14002])).
% 3.87/4.11 tff(14016,plain,
% 3.87/4.11 ((~(s(elem!1) = elem!1)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 3.87/4.11 inference(monotonicity,[status(thm)],[14015])).
% 3.87/4.11 tff(14017,plain,
% 3.87/4.11 (~(z = elem!1)),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[317, 13968])).
% 3.87/4.11 tff(14018,plain,
% 3.87/4.11 (~(s(s(elem!1)) = s(s(z)))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[2386, 14017])).
% 3.87/4.11 tff(14019,plain,
% 3.87/4.11 (~(elem!1 = s(s(s(elem!1))))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[2498, 14002, 14018])).
% 3.87/4.11 tff(14020,plain,
% 3.87/4.11 (~(s(s(s(elem!1))) = elem!1)),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[2489, 14019])).
% 3.87/4.11 tff(14021,plain,
% 3.87/4.11 (~(s(elem!1) = elem!1)),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[2150, 14020])).
% 3.87/4.11 tff(14022,plain,
% 3.87/4.11 (~(s(s(s(s(z)))) = elem!1)),
% 3.87/4.11 inference(modus_ponens,[status(thm)],[14021, 14016])).
% 3.87/4.11 tff(14023,plain,
% 3.87/4.11 (~(elem!1 = s(s(z)))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[1353, 14022, 14002])).
% 3.87/4.11 tff(14024,plain,
% 3.87/4.11 (~r(elem!1, s(s(z)))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[3785, 14009, 193])).
% 3.87/4.11 tff(14025,plain,
% 3.87/4.11 (b(elem!1, s(s(z)))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[467, 14024, 14023])).
% 3.87/4.11 tff(14026,plain,
% 3.87/4.11 (~b(s(s(z)), elem!1)),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[12005, 14025, 10794, 13782, 14014, 14009])).
% 3.87/4.11 tff(14027,plain,
% 3.87/4.11 (s(s(z)) = elem!1),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[448, 14026, 14010])).
% 3.87/4.11 tff(14028,plain,
% 3.87/4.11 (s(s(z)) = s(s(s(z)))),
% 3.87/4.11 inference(modus_ponens,[status(thm)],[14027, 14007])).
% 3.87/4.11 tff(14029,plain,
% 3.87/4.11 (~(s(s(z)) = s(s(s(z))))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[2196, 14023, 14002])).
% 3.87/4.11 tff(14030,plain,
% 3.87/4.11 ($false),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[14029, 14028])).
% 3.87/4.11 tff(14031,plain,((~b(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | b(s(s(z)), s(s(s(s(z))))) | (s(elem!1) = s(s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | r(s(s(z)), z) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.11 tff(14032,plain,
% 3.87/4.11 (~b(s(elem!1), z)),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[14031, 13774, 3261, 105, 1056, 193, 5618, 13771])).
% 3.87/4.11 tff(14033,plain,
% 3.87/4.11 (r(s(elem!1), z)),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[774, 14032])).
% 3.87/4.11 tff(14034,plain,
% 3.87/4.11 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[847, 14033, 126])).
% 3.87/4.11 tff(14035,plain,
% 3.87/4.11 (~r(s(elem!1), s(s(z)))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[8621, 14033, 3261])).
% 3.87/4.11 tff(14036,plain,
% 3.87/4.11 (b(s(elem!1), s(s(z)))),
% 3.87/4.11 inference(unit_resolution,[status(thm)],[421, 14035, 1056])).
% 3.87/4.11 tff(14037,plain,
% 3.87/4.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)) | (~b(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))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)) | (~b(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))))))), z)))),
% 3.87/4.12 inference(rewrite,[status(thm)],[])).
% 3.87/4.12 tff(14038,plain,
% 3.87/4.12 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)) | (~b(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))))))), z)))),
% 3.87/4.12 inference(rewrite,[status(thm)],[])).
% 3.87/4.12 tff(14039,plain,
% 3.87/4.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)) | (~b(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))))))), z))))),
% 3.87/4.12 inference(monotonicity,[status(thm)],[14038])).
% 3.87/4.12 tff(14040,plain,
% 3.87/4.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)) | (~b(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))))))), z)))),
% 3.87/4.12 inference(transitivity,[status(thm)],[14039, 14037])).
% 3.87/4.12 tff(14041,plain,
% 3.87/4.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 3.87/4.12 inference(quant_inst,[status(thm)],[])).
% 3.87/4.12 tff(14042,plain,
% 3.87/4.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 3.87/4.12 inference(modus_ponens,[status(thm)],[14041, 14040])).
% 3.87/4.12 tff(14043,plain,
% 3.87/4.12 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[14042, 178, 5619, 14036, 13774, 13771])).
% 3.87/4.12 tff(14044,plain,
% 3.87/4.12 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[395, 14043, 14034])).
% 3.87/4.12 tff(14045,plain,
% 3.87/4.12 ($false),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[10943, 118, 14033, 14044, 13778])).
% 3.87/4.12 tff(14046,plain,(r(s(s(s(s(s(s(s(z))))))), z) | (s(elem!1) = s(s(z))) | (~r(z, s(s(z)))) | b(s(s(z)), s(s(s(s(z))))) | (~r(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)))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.12 tff(14047,plain,
% 3.87/4.12 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[14046, 13677, 3261, 12400, 193, 5618, 105])).
% 3.87/4.12 tff(14048,plain,
% 3.87/4.12 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.87/4.12 inference(modus_ponens,[status(thm)],[14047, 13770])).
% 3.87/4.12 tff(14049,plain,
% 3.87/4.12 (r(s(elem!1), z) <=> r(s(elem!1), elem!1)),
% 3.87/4.12 inference(monotonicity,[status(thm)],[13763])).
% 3.87/4.12 tff(14050,plain,
% 3.87/4.12 (r(s(elem!1), elem!1)),
% 3.87/4.12 inference(modus_ponens,[status(thm)],[844, 14049])).
% 3.87/4.12 tff(14051,plain,
% 3.87/4.12 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 3.87/4.12 inference(rewrite,[status(thm)],[])).
% 3.87/4.12 tff(14052,plain,
% 3.87/4.12 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 3.87/4.12 inference(quant_inst,[status(thm)],[])).
% 3.87/4.12 tff(14053,plain,
% 3.87/4.12 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 3.87/4.12 inference(modus_ponens,[status(thm)],[14052, 14051])).
% 3.87/4.12 tff(14054,plain,
% 3.87/4.12 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[14053, 118, 14050, 14048])).
% 3.87/4.12 tff(14055,plain,
% 3.87/4.12 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[806, 41, 14054, 13769])).
% 3.87/4.12 tff(14056,plain,
% 3.87/4.12 (s(s(z)) = s(s(elem!1))),
% 3.87/4.12 inference(monotonicity,[status(thm)],[13764])).
% 3.87/4.12 tff(14057,plain,
% 3.87/4.12 (s(s(elem!1)) = s(s(z))),
% 3.87/4.12 inference(symmetry,[status(thm)],[14056])).
% 3.87/4.12 tff(14058,plain,
% 3.87/4.12 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.87/4.12 inference(monotonicity,[status(thm)],[14057])).
% 3.87/4.12 tff(14059,plain,
% 3.87/4.12 (b(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.87/4.12 inference(symmetry,[status(thm)],[14058])).
% 3.87/4.12 tff(14060,plain,
% 3.87/4.12 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.87/4.12 inference(modus_ponens,[status(thm)],[12401, 14059])).
% 3.87/4.12 tff(14061,plain,
% 3.87/4.12 (b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.12 inference(monotonicity,[status(thm)],[14057])).
% 3.87/4.12 tff(14062,plain,
% 3.87/4.12 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.12 inference(symmetry,[status(thm)],[14061])).
% 3.87/4.12 tff(14063,plain,
% 3.87/4.12 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[13684, 10794, 3261, 11753])).
% 3.87/4.12 tff(14064,plain,
% 3.87/4.12 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[249, 14063])).
% 3.87/4.12 tff(14065,plain,
% 3.87/4.12 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.12 inference(modus_ponens,[status(thm)],[14064, 14062])).
% 3.87/4.12 tff(14066,plain,
% 3.87/4.12 ((~(s(s(s(s(s(s(s(z))))))) = s(z))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 3.87/4.12 inference(monotonicity,[status(thm)],[13766])).
% 3.87/4.12 tff(14067,plain,
% 3.87/4.12 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.87/4.12 inference(modus_ponens,[status(thm)],[612, 14066])).
% 3.87/4.12 tff(14068,plain,
% 3.87/4.12 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[8168, 118, 14050, 14048])).
% 3.87/4.12 tff(14069,plain,
% 3.87/4.12 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[395, 14068, 14067])).
% 3.87/4.12 tff(14070,plain,
% 3.87/4.12 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(z)))),
% 3.87/4.12 inference(monotonicity,[status(thm)],[14057])).
% 3.87/4.12 tff(14071,plain,
% 3.87/4.12 (b(s(elem!1), s(s(z))) <=> b(s(elem!1), s(s(elem!1)))),
% 3.87/4.12 inference(symmetry,[status(thm)],[14070])).
% 3.87/4.12 tff(14072,plain,
% 3.87/4.12 (b(s(elem!1), s(s(elem!1)))),
% 3.87/4.12 inference(modus_ponens,[status(thm)],[12566, 14071])).
% 3.87/4.12 tff(14073,plain,
% 3.87/4.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), 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(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), 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(elem!1)))))),
% 3.87/4.12 inference(rewrite,[status(thm)],[])).
% 3.87/4.12 tff(14074,plain,
% 3.87/4.12 (((~b(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(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~b(s(elem!1), 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))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 3.87/4.12 inference(rewrite,[status(thm)],[])).
% 3.87/4.12 tff(14075,plain,
% 3.87/4.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), 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(elem!1))))))),
% 3.87/4.12 inference(monotonicity,[status(thm)],[14074])).
% 3.87/4.12 tff(14076,plain,
% 3.87/4.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), 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(elem!1)))))),
% 3.87/4.12 inference(transitivity,[status(thm)],[14075, 14073])).
% 3.87/4.12 tff(14077,plain,
% 3.87/4.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 3.87/4.12 inference(quant_inst,[status(thm)],[])).
% 3.87/4.12 tff(14078,plain,
% 3.87/4.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 3.87/4.12 inference(modus_ponens,[status(thm)],[14077, 14076])).
% 3.87/4.12 tff(14079,plain,
% 3.87/4.12 ($false),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[14078, 178, 14072, 14069, 14065, 14060, 14055])).
% 3.87/4.12 tff(14080,plain,((~r(s(elem!1), z)) | (~r(z, s(s(z)))) | b(elem!1, z) | (s(s(z)) = elem!1) | r(s(s(z)), z) | b(s(s(z)), s(s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.12 tff(14081,plain,
% 3.87/4.12 (~r(s(elem!1), z)),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[14080, 5723, 3261, 12, 5618, 105, 193])).
% 3.87/4.12 tff(14082,plain,
% 3.87/4.12 (b(s(elem!1), z)),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[774, 14081])).
% 3.87/4.12 tff(14083,plain,
% 3.87/4.12 ($false),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[13833, 178, 854, 853, 3461, 812, 1071])).
% 3.87/4.12 tff(14084,plain,((~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.12 tff(14085,plain,
% 3.87/4.12 (~b(s(s(z)), s(elem!1))),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[14084, 13676, 853, 5619, 812])).
% 3.87/4.12 tff(14086,plain,
% 3.87/4.12 (r(s(s(z)), s(elem!1))),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[2879, 14085, 1070])).
% 3.87/4.12 tff(14087,plain,
% 3.87/4.12 (~r(z, s(elem!1))),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[12114, 14086, 3261])).
% 3.87/4.12 tff(14088,plain,
% 3.87/4.12 (b(z, s(elem!1))),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[2351, 14087])).
% 3.87/4.12 tff(14089,plain,
% 3.87/4.12 (~r(s(elem!1), s(s(s(s(z)))))),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[5758, 14086, 10794])).
% 3.87/4.12 tff(14090,plain,
% 3.87/4.12 (b(s(elem!1), s(s(s(s(z)))))),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[1084, 14089, 1369])).
% 3.87/4.12 tff(14091,plain,
% 3.87/4.12 ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[13801, 178, 853, 5619, 1070, 1687, 168])).
% 3.87/4.12 tff(14092,plain,
% 3.87/4.12 ($false),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[14091, 14090, 14088])).
% 3.87/4.12 tff(14093,plain,((s(elem!1) = s(s(s(s(z))))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 3.87/4.12 tff(14094,plain,
% 3.87/4.12 (~b(elem!1, s(s(z)))),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[14093, 12565, 12566, 11751, 11753, 3261, 14082, 105, 5618])).
% 3.87/4.12 tff(14095,plain,
% 3.87/4.12 (elem!1 = z),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[11793, 14094, 3261, 5723, 5618])).
% 3.87/4.12 tff(14096,plain,
% 3.87/4.12 (b(elem!1, s(elem!1)) <=> b(z, s(elem!1))),
% 3.87/4.12 inference(monotonicity,[status(thm)],[14095])).
% 3.87/4.12 tff(14097,plain,
% 3.87/4.12 (b(elem!1, s(elem!1))),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[13675, 12565, 105, 3261, 11751, 5618])).
% 3.87/4.12 tff(14098,plain,
% 3.87/4.12 (b(z, s(elem!1))),
% 3.87/4.12 inference(modus_ponens,[status(thm)],[14097, 14096])).
% 3.87/4.12 tff(14099,plain,
% 3.87/4.12 ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[13801, 178, 14082, 5619, 12566, 11751, 11753])).
% 3.87/4.12 tff(14100,plain,
% 3.87/4.12 (~b(s(elem!1), s(s(s(s(z)))))),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[14099, 14098])).
% 3.87/4.12 tff(14101,plain,
% 3.87/4.12 (r(s(elem!1), s(s(s(s(z)))))),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[1084, 14100, 12565])).
% 3.87/4.12 tff(14102,plain,
% 3.87/4.12 (s(elem!1) = s(z)),
% 3.87/4.12 inference(monotonicity,[status(thm)],[14095])).
% 3.87/4.12 tff(14103,plain,
% 3.87/4.12 (s(z) = s(elem!1)),
% 3.87/4.12 inference(symmetry,[status(thm)],[14102])).
% 3.87/4.12 tff(14104,plain,
% 3.87/4.12 (b(z, s(z)) <=> b(z, s(elem!1))),
% 3.87/4.12 inference(monotonicity,[status(thm)],[14103])).
% 3.87/4.12 tff(14105,plain,
% 3.87/4.12 (b(z, s(elem!1)) <=> b(z, s(z))),
% 3.87/4.12 inference(symmetry,[status(thm)],[14104])).
% 3.87/4.12 tff(14106,plain,
% 3.87/4.12 (b(z, s(z))),
% 3.87/4.12 inference(modus_ponens,[status(thm)],[14098, 14105])).
% 3.87/4.12 tff(14107,plain,
% 3.87/4.12 (b(s(elem!1), s(s(z))) <=> b(s(z), s(s(z)))),
% 3.87/4.12 inference(monotonicity,[status(thm)],[14102])).
% 3.87/4.12 tff(14108,plain,
% 3.87/4.12 (b(s(z), s(s(z)))),
% 3.87/4.12 inference(modus_ponens,[status(thm)],[12566, 14107])).
% 3.87/4.12 tff(14109,plain,
% 3.87/4.12 (b(s(z), z) <=> b(s(elem!1), z)),
% 3.87/4.12 inference(monotonicity,[status(thm)],[14103])).
% 3.87/4.12 tff(14110,plain,
% 3.87/4.12 (b(s(elem!1), z) <=> b(s(z), z)),
% 3.87/4.12 inference(symmetry,[status(thm)],[14109])).
% 3.87/4.12 tff(14111,plain,
% 3.87/4.12 (b(s(z), z)),
% 3.87/4.12 inference(modus_ponens,[status(thm)],[14082, 14110])).
% 3.87/4.12 tff(14112,plain,
% 3.87/4.12 (~b(s(s(z)), s(elem!1))),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[10112, 14111, 5619, 14108, 14106, 14095])).
% 3.87/4.12 tff(14113,plain,
% 3.87/4.12 (r(s(s(z)), s(elem!1))),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[2879, 14112, 12566])).
% 3.87/4.12 tff(14114,plain,
% 3.87/4.12 ($false),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[5758, 14113, 14101, 10794])).
% 3.87/4.12 tff(14115,plain,(b(elem!1, z) | (~r(z, s(s(z)))) | r(s(s(z)), z) | b(s(s(z)), s(s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (s(s(z)) = elem!1) | (elem!1 = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.12 tff(14116,plain,
% 3.87/4.12 (b(s(s(z)), s(s(s(s(z)))))),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[14115, 5723, 5618, 3261, 193, 12, 12558])).
% 3.87/4.12 tff(14117,plain,
% 3.87/4.12 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[12409, 14116, 11751, 5619, 12401])).
% 3.87/4.12 tff(14118,plain,
% 3.87/4.12 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[133, 14117])).
% 3.87/4.12 tff(14119,plain,
% 3.87/4.12 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[4690, 224, 3261])).
% 3.87/4.12 tff(14120,plain,
% 3.87/4.12 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[271, 14119])).
% 3.87/4.12 tff(14121,plain,
% 3.87/4.12 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[3559, 224, 193])).
% 3.87/4.12 tff(14122,plain,
% 3.87/4.12 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[222, 14121])).
% 3.87/4.12 tff(14123,plain,
% 3.87/4.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.87/4.12 inference(rewrite,[status(thm)],[])).
% 3.87/4.12 tff(14124,plain,
% 3.87/4.12 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, 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)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.87/4.12 inference(rewrite,[status(thm)],[])).
% 3.87/4.12 tff(14125,plain,
% 3.87/4.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 3.87/4.12 inference(monotonicity,[status(thm)],[14124])).
% 3.87/4.12 tff(14126,plain,
% 3.87/4.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.87/4.12 inference(transitivity,[status(thm)],[14125, 14123])).
% 3.87/4.12 tff(14127,plain,
% 3.87/4.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 3.87/4.12 inference(quant_inst,[status(thm)],[])).
% 3.87/4.12 tff(14128,plain,
% 3.87/4.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 3.87/4.12 inference(modus_ponens,[status(thm)],[14127, 14126])).
% 3.87/4.12 tff(14129,plain,
% 3.87/4.12 ($false),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[14128, 178, 3461, 11753, 167, 14122, 14120])).
% 3.87/4.12 tff(14130,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.87/4.12 tff(14131,plain,
% 3.87/4.12 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[14130, 14116, 5619, 3261, 193])).
% 3.87/4.12 tff(14132,plain,
% 3.87/4.12 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[249, 14131])).
% 3.87/4.12 tff(14133,plain,
% 3.87/4.12 (r(s(z), z) <=> r(s(elem!1), z)),
% 3.87/4.12 inference(monotonicity,[status(thm)],[6683])).
% 3.87/4.12 tff(14134,plain,
% 3.87/4.12 (r(s(elem!1), z) <=> r(s(z), z)),
% 3.87/4.12 inference(symmetry,[status(thm)],[14133])).
% 3.87/4.12 tff(14135,plain,
% 3.87/4.12 (r(s(z), z)),
% 3.87/4.12 inference(modus_ponens,[status(thm)],[844, 14134])).
% 3.87/4.12 tff(14136,plain,
% 3.87/4.12 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.87/4.12 inference(rewrite,[status(thm)],[])).
% 3.87/4.12 tff(14137,plain,
% 3.87/4.12 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.87/4.12 inference(quant_inst,[status(thm)],[])).
% 3.87/4.12 tff(14138,plain,
% 3.87/4.12 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 3.87/4.12 inference(modus_ponens,[status(thm)],[14137, 14136])).
% 3.87/4.12 tff(14139,plain,
% 3.87/4.12 ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[14138, 118, 108])).
% 3.87/4.12 tff(14140,plain,
% 3.87/4.12 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[14139, 14135])).
% 3.87/4.12 tff(14141,plain,
% 3.87/4.12 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.87/4.12 inference(unit_resolution,[status(thm)],[615, 41, 612, 14140])).
% 3.87/4.12 tff(14142,plain,
% 3.87/4.12 (b(s(z), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.12 inference(monotonicity,[status(thm)],[6683])).
% 3.87/4.12 tff(14143,plain,
% 3.87/4.12 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.12 inference(symmetry,[status(thm)],[14142])).
% 3.87/4.12 tff(14144,plain,
% 3.87/4.12 ((s(s(s(s(s(s(s(z))))))) = s(z)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.87/4.12 inference(monotonicity,[status(thm)],[6683])).
% 3.87/4.12 tff(14145,plain,
% 3.87/4.12 ((s(s(s(s(s(s(s(z))))))) = s(z)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.87/4.12 inference(transitivity,[status(thm)],[14144, 377])).
% 3.87/4.12 tff(14146,plain,
% 3.87/4.12 ((~(s(s(s(s(s(s(s(z))))))) = s(z))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 3.87/4.12 inference(monotonicity,[status(thm)],[14145])).
% 3.87/4.12 tff(14147,plain,
% 3.87/4.12 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.87/4.12 inference(modus_ponens,[status(thm)],[612, 14146])).
% 3.87/4.12 tff(14148,plain,
% 3.87/4.12 (r(s(z), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.87/4.12 inference(monotonicity,[status(thm)],[6683])).
% 3.87/4.12 tff(14149,plain,
% 3.87/4.12 ((~r(s(z), s(s(s(s(s(s(s(z))))))))) <=> (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 3.87/4.12 inference(monotonicity,[status(thm)],[14148])).
% 3.87/4.12 tff(14150,plain,
% 3.87/4.12 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 3.87/4.12 inference(rewrite,[status(thm)],[])).
% 3.97/4.12 tff(14151,plain,
% 3.97/4.12 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 3.97/4.12 inference(rewrite,[status(thm)],[])).
% 3.97/4.12 tff(14152,plain,
% 3.97/4.12 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))))),
% 3.97/4.12 inference(monotonicity,[status(thm)],[14151])).
% 3.97/4.12 tff(14153,plain,
% 3.97/4.12 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 3.97/4.12 inference(transitivity,[status(thm)],[14152, 14150])).
% 3.97/4.12 tff(14154,plain,
% 3.97/4.12 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.97/4.12 inference(quant_inst,[status(thm)],[])).
% 3.97/4.12 tff(14155,plain,
% 3.97/4.12 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 3.97/4.12 inference(modus_ponens,[status(thm)],[14154, 14153])).
% 3.97/4.12 tff(14156,plain,
% 3.97/4.12 ((~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.97/4.12 inference(unit_resolution,[status(thm)],[14155, 118, 108])).
% 3.97/4.12 tff(14157,plain,
% 3.97/4.12 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.12 inference(unit_resolution,[status(thm)],[14156, 14135])).
% 3.97/4.12 tff(14158,plain,
% 3.97/4.12 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.12 inference(modus_ponens,[status(thm)],[14157, 14149])).
% 3.97/4.12 tff(14159,plain,
% 3.97/4.12 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.12 inference(unit_resolution,[status(thm)],[395, 14158, 14147])).
% 3.97/4.12 tff(14160,plain,
% 3.97/4.12 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.12 inference(modus_ponens,[status(thm)],[14159, 14143])).
% 3.97/4.12 tff(14161,plain,
% 3.97/4.12 (b(s(elem!1), s(s(z))) <=> b(s(z), s(s(z)))),
% 3.97/4.12 inference(monotonicity,[status(thm)],[929])).
% 3.97/4.12 tff(14162,plain,
% 3.97/4.12 (b(s(z), s(s(z)))),
% 3.97/4.12 inference(modus_ponens,[status(thm)],[1070, 14161])).
% 3.97/4.12 tff(14163,plain,
% 3.97/4.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), 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))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), 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))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.97/4.12 inference(rewrite,[status(thm)],[])).
% 3.97/4.12 tff(14164,plain,
% 3.97/4.12 (((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), 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))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.97/4.12 inference(rewrite,[status(thm)],[])).
% 3.97/4.12 tff(14165,plain,
% 3.97/4.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), 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))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.97/4.13 inference(monotonicity,[status(thm)],[14164])).
% 3.97/4.13 tff(14166,plain,
% 3.97/4.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), 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))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.97/4.13 inference(transitivity,[status(thm)],[14165, 14163])).
% 3.97/4.13 tff(14167,plain,
% 3.97/4.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.97/4.13 inference(quant_inst,[status(thm)],[])).
% 3.97/4.13 tff(14168,plain,
% 3.97/4.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.97/4.13 inference(modus_ponens,[status(thm)],[14167, 14166])).
% 3.97/4.13 tff(14169,plain,
% 3.97/4.13 ($false),
% 3.97/4.13 inference(unit_resolution,[status(thm)],[14168, 178, 14162, 166, 1146, 14160, 14141])).
% 3.97/4.13 tff(14170,plain,((~(elem!1 = z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), z)) | (~b(s(elem!1), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.97/4.13 tff(14171,plain,
% 3.97/4.13 (~(elem!1 = z)),
% 3.97/4.13 inference(unit_resolution,[status(thm)],[14170, 12569, 1146, 108, 166, 1070])).
% 3.97/4.13 tff(14172,plain,
% 3.97/4.13 (r(elem!1, z)),
% 3.97/4.13 inference(unit_resolution,[status(thm)],[498, 14171, 5723])).
% 3.97/4.13 tff(14173,plain,
% 3.97/4.13 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.97/4.13 inference(unit_resolution,[status(thm)],[11809, 118, 14172, 108])).
% 3.97/4.13 tff(14174,plain,
% 3.97/4.13 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.97/4.13 inference(unit_resolution,[status(thm)],[11134, 118, 14172, 108])).
% 3.97/4.13 tff(14175,plain,
% 3.97/4.13 (b(elem!1, s(s(z)))),
% 3.97/4.13 inference(unit_resolution,[status(thm)],[11793, 14171, 3261, 5723, 5618])).
% 3.97/4.13 tff(14176,plain,
% 3.97/4.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.97/4.13 inference(rewrite,[status(thm)],[])).
% 3.97/4.13 tff(14177,plain,
% 3.97/4.13 (((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.97/4.13 inference(rewrite,[status(thm)],[])).
% 3.97/4.13 tff(14178,plain,
% 3.97/4.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.97/4.13 inference(monotonicity,[status(thm)],[14177])).
% 3.97/4.13 tff(14179,plain,
% 3.97/4.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.97/4.13 inference(transitivity,[status(thm)],[14178, 14176])).
% 3.97/4.13 tff(14180,plain,
% 3.97/4.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.97/4.13 inference(quant_inst,[status(thm)],[])).
% 3.97/4.13 tff(14181,plain,
% 3.97/4.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.97/4.13 inference(modus_ponens,[status(thm)],[14180, 14179])).
% 3.97/4.13 tff(14182,plain,
% 3.97/4.13 ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.97/4.13 inference(unit_resolution,[status(thm)],[14181, 178])).
% 3.97/4.13 tff(14183,plain,
% 3.97/4.13 ($false),
% 3.97/4.13 inference(unit_resolution,[status(thm)],[14182, 11096, 11095, 1146, 166, 812])).
% 3.97/4.13 tff(14184,plain,((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(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z)))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.97/4.13 tff(14185,plain,
% 3.97/4.13 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 3.97/4.13 inference(unit_resolution,[status(thm)],[14184, 14175, 166, 1146, 14174, 14173])).
% 3.97/4.13 tff(14186,plain,
% 3.97/4.13 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 3.97/4.13 inference(monotonicity,[status(thm)],[14185])).
% 3.97/4.13 tff(14187,plain,
% 3.97/4.13 (s(s(s(s(s(s(s(s(z)))))))) = s(elem!1)),
% 3.97/4.13 inference(symmetry,[status(thm)],[14186])).
% 3.97/4.13 tff(14188,plain,
% 3.97/4.13 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(z))) <=> b(s(elem!1), s(s(z)))),
% 3.97/4.13 inference(monotonicity,[status(thm)],[14187])).
% 3.97/4.13 tff(14189,plain,
% 3.97/4.13 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 3.97/4.13 inference(symmetry,[status(thm)],[14188])).
% 3.97/4.13 tff(14190,plain,
% 3.97/4.13 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 3.97/4.13 inference(modus_ponens,[status(thm)],[1070, 14189])).
% 3.97/4.13 tff(14191,plain,
% 3.97/4.13 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.97/4.13 inference(monotonicity,[status(thm)],[14187])).
% 3.97/4.13 tff(14192,plain,
% 3.97/4.13 (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(s(s(s(s(z)))))))))),
% 3.97/4.13 inference(symmetry,[status(thm)],[14191])).
% 3.97/4.13 tff(14193,plain,
% 3.97/4.13 (b(elem!1, s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.97/4.13 inference(monotonicity,[status(thm)],[14185])).
% 3.97/4.13 tff(14194,plain,
% 3.97/4.13 (b(s(s(z)), s(s(s(s(z)))))),
% 3.97/4.13 inference(unit_resolution,[status(thm)],[13675, 751, 3261, 1369, 1687, 5618])).
% 3.97/4.13 tff(14195,plain,
% 3.97/4.13 (~r(s(elem!1), s(s(s(s(z)))))),
% 3.97/4.13 inference(unit_resolution,[status(thm)],[916, 194, 844])).
% 3.97/4.13 tff(14196,plain,
% 3.97/4.13 (b(s(elem!1), s(s(s(s(z)))))),
% 3.97/4.13 inference(unit_resolution,[status(thm)],[1084, 14195, 1369])).
% 3.97/4.13 tff(14197,plain,
% 3.97/4.13 (b(s(elem!1), s(s(z)))),
% 3.97/4.13 inference(unit_resolution,[status(thm)],[421, 13145, 11744])).
% 3.97/4.13 tff(14198,plain,
% 3.97/4.13 (~b(s(s(z)), s(elem!1))),
% 3.97/4.13 inference(unit_resolution,[status(thm)],[1079, 14196, 167, 14197, 13491])).
% 3.97/4.13 tff(14199,plain,
% 3.97/4.13 (r(s(s(z)), s(elem!1))),
% 3.97/4.13 inference(unit_resolution,[status(thm)],[1067, 14198, 1060])).
% 3.97/4.13 tff(14200,plain,
% 3.97/4.13 (~r(z, s(elem!1))),
% 3.97/4.13 inference(unit_resolution,[status(thm)],[12114, 14199, 3261])).
% 3.97/4.13 tff(14201,plain,
% 3.97/4.13 (b(z, s(elem!1))),
% 3.97/4.13 inference(unit_resolution,[status(thm)],[2351, 14200])).
% 3.97/4.13 tff(14202,plain,
% 3.97/4.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 3.97/4.13 inference(rewrite,[status(thm)],[])).
% 3.97/4.13 tff(14203,plain,
% 3.97/4.13 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 3.97/4.13 inference(rewrite,[status(thm)],[])).
% 3.97/4.13 tff(14204,plain,
% 3.97/4.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))))),
% 3.97/4.13 inference(monotonicity,[status(thm)],[14203])).
% 3.97/4.13 tff(14205,plain,
% 3.97/4.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 3.97/4.13 inference(transitivity,[status(thm)],[14204, 14202])).
% 3.97/4.13 tff(14206,plain,
% 3.97/4.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(elem!1))))),
% 3.97/4.13 inference(quant_inst,[status(thm)],[])).
% 3.97/4.13 tff(14207,plain,
% 3.97/4.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))),
% 3.97/4.13 inference(modus_ponens,[status(thm)],[14206, 14205])).
% 3.97/4.13 tff(14208,plain,
% 3.97/4.13 ($false),
% 3.97/4.13 inference(unit_resolution,[status(thm)],[14207, 178, 14201, 14197, 1687, 14196, 13491])).
% 3.97/4.13 tff(14209,plain,((~r(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (s(s(z)) = s(elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (s(elem!1) = s(s(s(s(z))))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 3.97/4.13 tff(14210,plain,
% 3.97/4.13 (~r(s(s(s(s(z)))), z)),
% 3.97/4.13 inference(unit_resolution,[status(thm)],[14209, 12570, 3261, 1687, 14194, 1369, 12569])).
% 3.97/4.13 tff(14211,plain,
% 3.97/4.13 (b(s(s(s(s(z)))), z)),
% 3.97/4.13 inference(unit_resolution,[status(thm)],[191, 14210])).
% 3.97/4.13 tff(14212,plain,
% 3.97/4.13 ((elem!1 = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.97/4.13 inference(monotonicity,[status(thm)],[745])).
% 3.97/4.13 tff(14213,plain,
% 3.97/4.13 ((elem!1 = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.97/4.13 inference(transitivity,[status(thm)],[14212, 655])).
% 3.97/4.13 tff(14214,plain,
% 3.97/4.13 ((~(elem!1 = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 3.97/4.13 inference(monotonicity,[status(thm)],[14213])).
% 3.97/4.13 tff(14215,plain,
% 3.97/4.13 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.97/4.13 inference(modus_ponens,[status(thm)],[12242, 14214])).
% 3.97/4.13 tff(14216,plain,
% 3.97/4.13 (r(elem!1, s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 3.97/4.13 inference(monotonicity,[status(thm)],[745])).
% 3.97/4.13 tff(14217,plain,
% 3.97/4.13 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 3.97/4.13 inference(unit_resolution,[status(thm)],[3907, 12243, 11744])).
% 3.97/4.13 tff(14218,plain,
% 3.97/4.13 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 3.97/4.13 inference(unit_resolution,[status(thm)],[1170, 14217])).
% 3.97/4.13 tff(14219,plain,
% 3.97/4.13 (b(elem!1, s(s(z)))),
% 3.97/4.13 inference(unit_resolution,[status(thm)],[3901, 12222, 14218])).
% 3.97/4.13 tff(14220,plain,
% 3.97/4.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 3.97/4.13 inference(rewrite,[status(thm)],[])).
% 3.97/4.13 tff(14221,plain,
% 3.97/4.13 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z))))) <=> ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 3.97/4.13 inference(rewrite,[status(thm)],[])).
% 3.97/4.13 tff(14222,plain,
% 3.97/4.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 3.97/4.13 inference(monotonicity,[status(thm)],[14221])).
% 3.97/4.13 tff(14223,plain,
% 3.97/4.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 3.97/4.13 inference(transitivity,[status(thm)],[14222, 14220])).
% 3.97/4.13 tff(14224,plain,
% 3.97/4.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))))),
% 3.97/4.13 inference(quant_inst,[status(thm)],[])).
% 3.97/4.13 tff(14225,plain,
% 3.97/4.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 3.97/4.13 inference(modus_ponens,[status(thm)],[14224, 14223])).
% 3.97/4.13 tff(14226,plain,
% 3.97/4.13 ($false),
% 3.97/4.13 inference(unit_resolution,[status(thm)],[14225, 178, 3461, 812, 168, 1301, 167])).
% 3.97/4.13 tff(14227,plain,((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.97/4.13 tff(14228,plain,
% 3.97/4.13 (~b(elem!1, s(s(s(s(z)))))),
% 3.97/4.13 inference(unit_resolution,[status(thm)],[14227, 14219, 3461, 167, 168])).
% 3.97/4.13 tff(14229,plain,
% 3.97/4.13 (r(elem!1, s(s(s(s(z)))))),
% 3.97/4.13 inference(unit_resolution,[status(thm)],[483, 14228, 469])).
% 3.97/4.13 tff(14230,plain,
% 3.97/4.13 (r(s(elem!1), s(s(s(s(z)))))),
% 3.97/4.13 inference(modus_ponens,[status(thm)],[14229, 14216])).
% 3.97/4.13 tff(14231,plain,
% 3.97/4.13 (r(elem!1, z) <=> r(s(elem!1), z)),
% 3.97/4.13 inference(monotonicity,[status(thm)],[745])).
% 3.97/4.13 tff(14232,plain,
% 3.97/4.13 (r(s(elem!1), z) <=> r(elem!1, z)),
% 3.97/4.13 inference(symmetry,[status(thm)],[14231])).
% 3.97/4.13 tff(14233,plain,
% 3.97/4.13 (r(elem!1, z)),
% 3.97/4.13 inference(modus_ponens,[status(thm)],[844, 14232])).
% 3.97/4.13 tff(14234,plain,
% 3.97/4.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 3.97/4.13 inference(rewrite,[status(thm)],[])).
% 3.97/4.13 tff(14235,plain,
% 3.97/4.13 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(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)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 3.97/4.13 inference(rewrite,[status(thm)],[])).
% 3.97/4.13 tff(14236,plain,
% 3.97/4.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))))),
% 3.97/4.13 inference(monotonicity,[status(thm)],[14235])).
% 3.97/4.13 tff(14237,plain,
% 3.97/4.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 3.97/4.14 inference(transitivity,[status(thm)],[14236, 14234])).
% 3.97/4.14 tff(14238,plain,
% 3.97/4.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 3.97/4.14 inference(quant_inst,[status(thm)],[])).
% 3.97/4.14 tff(14239,plain,
% 3.97/4.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))),
% 3.97/4.14 inference(modus_ponens,[status(thm)],[14238, 14237])).
% 3.97/4.14 tff(14240,plain,
% 3.97/4.14 (~b(s(s(s(s(z)))), s(s(z)))),
% 3.97/4.14 inference(unit_resolution,[status(thm)],[14239, 178, 3461, 1687, 168, 167])).
% 3.97/4.14 tff(14241,plain,
% 3.97/4.14 (r(s(s(s(s(z)))), s(s(z)))),
% 3.97/4.14 inference(unit_resolution,[status(thm)],[102, 14240])).
% 3.97/4.14 tff(14242,plain,
% 3.97/4.14 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(elem!1))),
% 3.97/4.14 inference(monotonicity,[status(thm)],[745])).
% 3.97/4.14 tff(14243,plain,
% 3.97/4.14 (b(s(s(z)), s(elem!1)) <=> b(s(s(z)), elem!1)),
% 3.97/4.14 inference(symmetry,[status(thm)],[14242])).
% 3.97/4.14 tff(14244,plain,
% 3.97/4.14 (~(s(s(z)) = elem!1)),
% 3.97/4.14 inference(modus_ponens,[status(thm)],[13145, 12217])).
% 3.97/4.14 tff(14245,plain,
% 3.97/4.14 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(elem!1))),
% 3.97/4.14 inference(monotonicity,[status(thm)],[745])).
% 3.97/4.14 tff(14246,plain,
% 3.97/4.14 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.97/4.14 inference(modus_ponens,[status(thm)],[701, 14214])).
% 3.97/4.14 tff(14247,plain,
% 3.97/4.14 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.97/4.14 inference(unit_resolution,[status(thm)],[11924, 817, 1687, 3261, 193, 812, 701, 437, 3461])).
% 3.97/4.14 tff(14248,plain,
% 3.97/4.14 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.97/4.14 inference(unit_resolution,[status(thm)],[84, 14247])).
% 3.97/4.14 tff(14249,plain,
% 3.97/4.14 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.97/4.14 inference(unit_resolution,[status(thm)],[5558, 118, 14248, 908])).
% 3.97/4.14 tff(14250,plain,
% 3.97/4.14 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.97/4.14 inference(unit_resolution,[status(thm)],[806, 41, 14249, 4017])).
% 3.97/4.14 tff(14251,plain,
% 3.97/4.14 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.97/4.14 inference(unit_resolution,[status(thm)],[11831, 817, 437, 812, 3261, 701])).
% 3.97/4.14 tff(14252,plain,
% 3.97/4.14 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.97/4.14 inference(unit_resolution,[status(thm)],[133, 14251])).
% 3.97/4.14 tff(14253,plain,
% 3.97/4.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 3.97/4.14 inference(rewrite,[status(thm)],[])).
% 3.97/4.14 tff(14254,plain,
% 3.97/4.14 (((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 3.97/4.14 inference(rewrite,[status(thm)],[])).
% 3.97/4.14 tff(14255,plain,
% 3.97/4.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 3.97/4.14 inference(monotonicity,[status(thm)],[14254])).
% 3.97/4.14 tff(14256,plain,
% 3.97/4.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 3.97/4.14 inference(transitivity,[status(thm)],[14255, 14253])).
% 3.97/4.14 tff(14257,plain,
% 3.97/4.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.97/4.14 inference(quant_inst,[status(thm)],[])).
% 3.97/4.14 tff(14258,plain,
% 3.97/4.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 3.97/4.14 inference(modus_ponens,[status(thm)],[14257, 14256])).
% 3.97/4.14 tff(14259,plain,
% 3.97/4.14 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.14 inference(unit_resolution,[status(thm)],[14258, 178, 855, 3461, 14252, 14250])).
% 3.97/4.14 tff(14260,plain,
% 3.97/4.14 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.14 inference(unit_resolution,[status(thm)],[249, 14259])).
% 3.97/4.14 tff(14261,plain,
% 3.97/4.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 3.97/4.14 inference(rewrite,[status(thm)],[])).
% 3.97/4.14 tff(14262,plain,
% 3.97/4.14 (((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 3.97/4.14 inference(rewrite,[status(thm)],[])).
% 3.97/4.14 tff(14263,plain,
% 3.97/4.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 3.97/4.14 inference(monotonicity,[status(thm)],[14262])).
% 3.97/4.14 tff(14264,plain,
% 3.97/4.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 3.97/4.14 inference(transitivity,[status(thm)],[14263, 14261])).
% 3.97/4.14 tff(14265,plain,
% 3.97/4.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.97/4.14 inference(quant_inst,[status(thm)],[])).
% 3.97/4.14 tff(14266,plain,
% 3.97/4.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 3.97/4.14 inference(modus_ponens,[status(thm)],[14265, 14264])).
% 3.97/4.14 tff(14267,plain,
% 3.97/4.14 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.14 inference(unit_resolution,[status(thm)],[14266, 178, 855, 168, 14252, 14250])).
% 3.97/4.14 tff(14268,plain,
% 3.97/4.14 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.14 inference(unit_resolution,[status(thm)],[222, 14267])).
% 3.97/4.14 tff(14269,plain,
% 3.97/4.14 ($false),
% 3.97/4.14 inference(unit_resolution,[status(thm)],[3559, 14268, 14260, 193])).
% 3.97/4.14 tff(14270,plain,((~b(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~r(z, s(s(z)))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.97/4.14 tff(14271,plain,
% 3.97/4.14 (~b(s(s(z)), elem!1)),
% 3.97/4.14 inference(unit_resolution,[status(thm)],[14270, 855, 14241, 168, 3461, 14246, 908, 437, 812, 3261, 701, 1687])).
% 3.97/4.14 tff(14272,plain,
% 3.97/4.14 (r(s(s(z)), elem!1)),
% 3.97/4.14 inference(unit_resolution,[status(thm)],[448, 14271, 12])).
% 3.97/4.14 tff(14273,plain,
% 3.97/4.14 (~r(s(s(s(s(z)))), elem!1)),
% 3.97/4.14 inference(unit_resolution,[status(thm)],[3329, 14272, 14241])).
% 3.97/4.14 tff(14274,plain,
% 3.97/4.14 (b(s(s(s(s(z)))), elem!1)),
% 3.97/4.14 inference(unit_resolution,[status(thm)],[3142, 14273, 323])).
% 3.97/4.14 tff(14275,plain,
% 3.97/4.14 (b(s(s(s(s(z)))), s(elem!1))),
% 3.97/4.14 inference(modus_ponens,[status(thm)],[14274, 14245])).
% 3.97/4.14 tff(14276,plain,
% 3.97/4.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 3.97/4.14 inference(rewrite,[status(thm)],[])).
% 3.97/4.14 tff(14277,plain,
% 3.97/4.14 (((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 3.97/4.14 inference(rewrite,[status(thm)],[])).
% 3.97/4.14 tff(14278,plain,
% 3.97/4.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 3.97/4.14 inference(monotonicity,[status(thm)],[14277])).
% 3.97/4.14 tff(14279,plain,
% 3.97/4.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 3.97/4.14 inference(transitivity,[status(thm)],[14278, 14276])).
% 3.97/4.14 tff(14280,plain,
% 3.97/4.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 3.97/4.14 inference(quant_inst,[status(thm)],[])).
% 3.97/4.14 tff(14281,plain,
% 3.97/4.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 3.97/4.14 inference(modus_ponens,[status(thm)],[14280, 14279])).
% 3.97/4.14 tff(14282,plain,
% 3.97/4.14 ($false),
% 3.97/4.14 inference(unit_resolution,[status(thm)],[14281, 178, 855, 3461, 168, 14275, 167])).
% 3.97/4.14 tff(14283,plain,((~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~(elem!1 = s(elem!1))) | (s(s(s(s(z)))) = elem!1) | (s(s(z)) = elem!1) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~r(z, s(s(z)))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.97/4.14 tff(14284,plain,
% 3.97/4.14 (~b(z, s(elem!1))),
% 3.97/4.14 inference(unit_resolution,[status(thm)],[14283, 745, 168, 167, 3461, 12233, 14244, 14230, 14233, 14219, 3261, 12242, 1687])).
% 3.97/4.14 tff(14285,plain,
% 3.97/4.14 (r(z, s(elem!1))),
% 3.97/4.14 inference(unit_resolution,[status(thm)],[2351, 14284])).
% 3.97/4.14 tff(14286,plain,
% 3.97/4.14 (~r(s(s(z)), s(elem!1))),
% 3.97/4.14 inference(unit_resolution,[status(thm)],[12114, 14285, 3261])).
% 3.97/4.14 tff(14287,plain,
% 3.97/4.14 (b(s(s(z)), s(elem!1))),
% 3.97/4.14 inference(unit_resolution,[status(thm)],[1067, 14286, 1060])).
% 3.97/4.14 tff(14288,plain,
% 3.97/4.14 (b(s(s(z)), elem!1)),
% 3.97/4.14 inference(modus_ponens,[status(thm)],[14287, 14243])).
% 3.97/4.14 tff(14289,plain,
% 3.97/4.14 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.97/4.14 inference(unit_resolution,[status(thm)],[11924, 14288, 1687, 3261, 14241, 14219, 12242, 14233, 3461])).
% 3.97/4.14 tff(14290,plain,
% 3.97/4.14 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.97/4.14 inference(unit_resolution,[status(thm)],[84, 14289])).
% 3.97/4.14 tff(14291,plain,
% 3.97/4.14 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.97/4.14 inference(unit_resolution,[status(thm)],[5558, 118, 14290, 14230])).
% 3.97/4.14 tff(14292,plain,
% 3.97/4.14 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.97/4.14 inference(unit_resolution,[status(thm)],[806, 41, 14291, 14215])).
% 3.97/4.14 tff(14293,plain,
% 3.97/4.14 ((~(elem!1 = s(s(s(s(s(s(s(z))))))))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 3.97/4.14 inference(monotonicity,[status(thm)],[14212])).
% 3.97/4.14 tff(14294,plain,
% 3.97/4.14 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.97/4.14 inference(modus_ponens,[status(thm)],[12242, 14293])).
% 3.97/4.14 tff(14295,plain,
% 3.97/4.14 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.14 inference(unit_resolution,[status(thm)],[5568, 14290, 14230])).
% 3.97/4.14 tff(14296,plain,
% 3.97/4.14 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.14 inference(unit_resolution,[status(thm)],[395, 14295, 14294])).
% 3.97/4.14 tff(14297,plain,
% 3.97/4.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), 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(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), 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(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 3.97/4.14 inference(rewrite,[status(thm)],[])).
% 3.97/4.14 tff(14298,plain,
% 3.97/4.14 (((~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), 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(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), 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(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 3.97/4.14 inference(rewrite,[status(thm)],[])).
% 3.97/4.14 tff(14299,plain,
% 3.97/4.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), 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(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), 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(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 3.97/4.14 inference(monotonicity,[status(thm)],[14298])).
% 3.97/4.14 tff(14300,plain,
% 3.97/4.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), 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(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), 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(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 3.97/4.14 inference(transitivity,[status(thm)],[14299, 14297])).
% 3.97/4.14 tff(14301,plain,
% 3.97/4.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), 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(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 3.97/4.14 inference(quant_inst,[status(thm)],[])).
% 3.97/4.14 tff(14302,plain,
% 3.97/4.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 3.97/4.14 inference(modus_ponens,[status(thm)],[14301, 14300])).
% 3.97/4.14 tff(14303,plain,
% 3.97/4.14 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.97/4.14 inference(unit_resolution,[status(thm)],[14302, 178, 14287, 14197, 14296, 14292])).
% 3.97/4.14 tff(14304,plain,
% 3.97/4.14 ((s(s(s(s(s(s(s(z))))))) = s(s(z))) | r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.97/4.14 inference(unit_resolution,[status(thm)],[2960, 41, 14303])).
% 3.97/4.14 tff(14305,plain,
% 3.97/4.14 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.97/4.14 inference(unit_resolution,[status(thm)],[14304, 11802])).
% 3.97/4.14 tff(14306,plain,
% 3.97/4.14 ($false),
% 3.97/4.14 inference(unit_resolution,[status(thm)],[3889, 118, 14290, 14241, 14305])).
% 3.97/4.14 tff(14307,plain,((~(elem!1 = s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~b(s(s(z)), z)) | (s(s(z)) = s(elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(elem!1)) | (~r(s(elem!1), z)) | (elem!1 = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.97/4.14 tff(14308,plain,
% 3.97/4.14 (~(elem!1 = s(elem!1))),
% 3.97/4.14 inference(unit_resolution,[status(thm)],[14307, 13679, 3261, 3461, 1060, 168, 167, 2508, 844, 1687])).
% 3.97/4.14 tff(14309,plain,
% 3.97/4.14 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 3.97/4.14 inference(monotonicity,[status(thm)],[12066])).
% 3.97/4.14 tff(14310,plain,
% 3.97/4.14 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 3.97/4.14 inference(transitivity,[status(thm)],[14309, 1690])).
% 3.97/4.14 tff(14311,plain,
% 3.97/4.14 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(elem!1)))))),
% 3.97/4.14 inference(monotonicity,[status(thm)],[14310])).
% 3.97/4.14 tff(14312,plain,
% 3.97/4.14 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 3.97/4.14 inference(modus_ponens,[status(thm)],[13192, 14311])).
% 3.97/4.14 tff(14313,plain,
% 3.97/4.14 (b(s(elem!1), s(s(z)))),
% 3.97/4.14 inference(unit_resolution,[status(thm)],[421, 1056, 11744])).
% 3.97/4.14 tff(14314,plain,
% 3.97/4.14 (b(s(z), s(s(z)))),
% 3.97/4.14 inference(modus_ponens,[status(thm)],[14313, 14161])).
% 3.97/4.14 tff(14315,plain,
% 3.97/4.14 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(z)) = s(elem!1))),
% 3.97/4.14 inference(monotonicity,[status(thm)],[12139])).
% 3.97/4.14 tff(14316,plain,
% 3.97/4.14 ((s(s(elem!1)) = s(elem!1)) <=> (s(elem!1) = s(s(z)))),
% 3.97/4.14 inference(transitivity,[status(thm)],[14315, 1358])).
% 3.97/4.14 tff(14317,plain,
% 3.97/4.14 ((s(elem!1) = s(s(z))) <=> (s(s(elem!1)) = s(elem!1))),
% 3.97/4.14 inference(symmetry,[status(thm)],[14316])).
% 3.97/4.14 tff(14318,plain,
% 3.97/4.14 ((~(s(elem!1) = s(s(z)))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 3.97/4.14 inference(monotonicity,[status(thm)],[14317])).
% 3.97/4.14 tff(14319,plain,
% 3.97/4.14 (~(s(s(elem!1)) = s(elem!1))),
% 3.97/4.14 inference(modus_ponens,[status(thm)],[1056, 14318])).
% 3.97/4.14 tff(14320,plain,
% 3.97/4.14 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(z)), s(elem!1))),
% 3.97/4.14 inference(monotonicity,[status(thm)],[12139])).
% 3.97/4.14 tff(14321,plain,
% 3.97/4.14 (r(s(s(z)), s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 3.97/4.14 inference(symmetry,[status(thm)],[14320])).
% 3.97/4.14 tff(14322,plain,
% 3.97/4.14 ((~r(s(s(z)), s(elem!1))) <=> (~r(s(s(elem!1)), s(elem!1)))),
% 3.97/4.14 inference(monotonicity,[status(thm)],[14321])).
% 3.97/4.14 tff(14323,plain,
% 3.97/4.14 (~r(s(s(elem!1)), s(elem!1))),
% 3.97/4.14 inference(modus_ponens,[status(thm)],[1062, 14322])).
% 3.97/4.14 tff(14324,plain,
% 3.97/4.14 ((s(s(elem!1)) = s(elem!1)) | r(s(s(elem!1)), s(elem!1))),
% 3.97/4.14 inference(unit_resolution,[status(thm)],[1004, 41, 1001])).
% 3.97/4.14 tff(14325,plain,
% 3.97/4.14 ($false),
% 3.97/4.14 inference(unit_resolution,[status(thm)],[14324, 14323, 14319])).
% 3.97/4.14 tff(14326,plain,(b(s(s(elem!1)), s(elem!1)) | r(s(s(z)), s(elem!1)) | (~(z = elem!1)) | (s(elem!1) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.97/4.14 tff(14327,plain,
% 3.97/4.14 (b(s(s(elem!1)), s(elem!1))),
% 3.97/4.14 inference(unit_resolution,[status(thm)],[14326, 12115, 1056, 12064])).
% 3.97/4.14 tff(14328,plain,
% 3.97/4.14 (b(s(s(z)), s(z))),
% 3.97/4.14 inference(unit_resolution,[status(thm)],[1015, 14327, 928])).
% 3.97/4.14 tff(14329,plain,
% 3.97/4.14 (~r(s(s(s(elem!1))), elem!1)),
% 3.97/4.14 inference(unit_resolution,[status(thm)],[12762, 12032, 14328, 928, 12734, 14314])).
% 3.97/4.15 tff(14330,plain,
% 3.97/4.15 (b(s(s(s(elem!1))), elem!1)),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[570, 14329, 941])).
% 3.97/4.15 tff(14331,plain,
% 3.97/4.15 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[12177, 14330, 12064, 14312, 12138, 12071, 3261])).
% 3.97/4.15 tff(14332,plain,
% 3.97/4.15 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[3409, 14331, 12038])).
% 3.97/4.15 tff(14333,plain,
% 3.97/4.15 (b(s(s(s(z))), s(s(z)))),
% 3.97/4.15 inference(modus_ponens,[status(thm)],[14332, 5221])).
% 3.97/4.15 tff(14334,plain,
% 3.97/4.15 (b(s(s(s(z))), z)),
% 3.97/4.15 inference(modus_ponens,[status(thm)],[14330, 12741])).
% 3.97/4.15 tff(14335,plain,
% 3.97/4.15 ($false),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[5967, 178, 3461, 1687, 167, 14334, 14333])).
% 3.97/4.15 tff(14336,plain,((~(elem!1 = z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(elem!1), z)) | (s(elem!1) = s(s(z))) | b(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.97/4.15 tff(14337,plain,
% 3.97/4.15 (~(elem!1 = z)),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[14336, 14241, 1687, 167, 3261, 3461, 844, 13145, 751])).
% 3.97/4.15 tff(14338,plain,
% 3.97/4.15 (r(elem!1, z)),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[498, 5723, 14337])).
% 3.97/4.15 tff(14339,plain,
% 3.97/4.15 (~r(elem!1, s(elem!1))),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[2711, 14338, 844])).
% 3.97/4.15 tff(14340,plain,
% 3.97/4.15 ($false),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[756, 14339, 14308, 751])).
% 3.97/4.15 tff(14341,plain,(b(elem!1, z) | b(elem!1, s(elem!1)) | (~r(s(elem!1), z)) | (~r(z, s(s(z)))) | (~b(s(s(z)), z)) | (s(s(z)) = s(elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(elem!1)) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.97/4.15 tff(14342,plain,
% 3.97/4.15 (b(elem!1, z)),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[14341, 12569, 751, 3261, 5619, 12570, 14211, 14194, 2169, 1687])).
% 3.97/4.15 tff(14343,plain,
% 3.97/4.15 (~(s(elem!1) = elem!1)),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[790, 14342, 766])).
% 3.97/4.15 tff(14344,plain,
% 3.97/4.15 (~(elem!1 = s(elem!1))),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[748, 14343])).
% 3.97/4.15 tff(14345,plain,
% 3.97/4.15 (r(elem!1, s(elem!1))),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[756, 14344, 751])).
% 3.97/4.15 tff(14346,plain,
% 3.97/4.15 (b(s(elem!1), s(s(z)))),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[421, 12571, 13081])).
% 3.97/4.15 tff(14347,plain,
% 3.97/4.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 3.97/4.15 inference(rewrite,[status(thm)],[])).
% 3.97/4.15 tff(14348,plain,
% 3.97/4.15 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z))))) <=> ((~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 3.97/4.15 inference(rewrite,[status(thm)],[])).
% 3.97/4.15 tff(14349,plain,
% 3.97/4.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 3.97/4.15 inference(monotonicity,[status(thm)],[14348])).
% 3.97/4.15 tff(14350,plain,
% 3.97/4.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 3.97/4.15 inference(transitivity,[status(thm)],[14349, 14347])).
% 3.97/4.15 tff(14351,plain,
% 3.97/4.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z)))))),
% 3.97/4.15 inference(quant_inst,[status(thm)],[])).
% 3.97/4.15 tff(14352,plain,
% 3.97/4.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 3.97/4.15 inference(modus_ponens,[status(thm)],[14351, 14350])).
% 3.97/4.15 tff(14353,plain,
% 3.97/4.15 ($false),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[14352, 178, 3461, 1070, 168, 1069, 167])).
% 3.97/4.15 tff(14354,plain,((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.97/4.15 tff(14355,plain,
% 3.97/4.15 (~b(s(elem!1), s(s(s(s(z)))))),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[14354, 14346, 5619, 14211, 14194])).
% 3.97/4.15 tff(14356,plain,
% 3.97/4.15 (r(s(elem!1), s(s(s(s(z)))))),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[1084, 14355, 1369])).
% 3.97/4.15 tff(14357,plain,
% 3.97/4.15 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 3.97/4.15 inference(rewrite,[status(thm)],[])).
% 3.97/4.15 tff(14358,plain,
% 3.97/4.15 (((~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 3.97/4.15 inference(rewrite,[status(thm)],[])).
% 3.97/4.15 tff(14359,plain,
% 3.97/4.15 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 3.97/4.15 inference(monotonicity,[status(thm)],[14358])).
% 3.97/4.15 tff(14360,plain,
% 3.97/4.15 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 3.97/4.15 inference(transitivity,[status(thm)],[14359, 14357])).
% 3.97/4.15 tff(14361,plain,
% 3.97/4.15 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(elem!1))))),
% 3.97/4.15 inference(quant_inst,[status(thm)],[])).
% 3.97/4.15 tff(14362,plain,
% 3.97/4.15 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 3.97/4.15 inference(modus_ponens,[status(thm)],[14361, 14360])).
% 3.97/4.15 tff(14363,plain,
% 3.97/4.15 ($false),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[14362, 118, 1587, 470, 908])).
% 3.97/4.15 tff(14364,plain,((~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.97/4.15 tff(14365,plain,
% 3.97/4.15 (~r(elem!1, s(s(s(s(z)))))),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[14364, 14356, 14345])).
% 3.97/4.15 tff(14366,plain,
% 3.97/4.15 (~b(s(s(s(s(z)))), s(s(z)))),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[14239, 178, 5619, 1687, 14211, 14194])).
% 3.97/4.15 tff(14367,plain,
% 3.97/4.15 (r(s(s(s(s(z)))), s(s(z)))),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[102, 14366])).
% 3.97/4.15 tff(14368,plain,
% 3.97/4.15 (~(elem!1 = z)),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[14336, 14367, 1687, 14194, 3261, 5619, 12569, 12571, 751])).
% 3.97/4.15 tff(14369,plain,
% 3.97/4.15 (~(z = elem!1)),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[317, 14368])).
% 3.97/4.15 tff(14370,plain,
% 3.97/4.15 (~b(elem!1, s(s(z)))),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[12506, 178, 506, 3461, 1687, 167])).
% 3.97/4.15 tff(14371,plain,
% 3.97/4.15 (~(s(s(z)) = elem!1)),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[13127, 1062, 1587])).
% 3.97/4.15 tff(14372,plain,
% 3.97/4.15 (~(elem!1 = s(s(z)))),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[311, 14371])).
% 3.97/4.15 tff(14373,plain,
% 3.97/4.15 (r(elem!1, s(s(z)))),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[467, 14372, 14370])).
% 3.97/4.15 tff(14374,plain,
% 3.97/4.15 (~r(elem!1, s(s(s(s(z)))))),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[3785, 14373, 14241])).
% 3.97/4.15 tff(14375,plain,
% 3.97/4.15 (~r(z, elem!1)),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[4862, 14373, 3261])).
% 3.97/4.15 tff(14376,plain,
% 3.97/4.15 (b(z, elem!1)),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[585, 14375, 507])).
% 3.97/4.15 tff(14377,plain,
% 3.97/4.15 (~b(elem!1, s(s(s(s(z)))))),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[13324, 14376])).
% 3.97/4.15 tff(14378,plain,
% 3.97/4.15 (elem!1 = s(s(s(s(z))))),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[483, 14377, 14374])).
% 3.97/4.15 tff(14379,plain,
% 3.97/4.15 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.97/4.15 inference(monotonicity,[status(thm)],[14378])).
% 3.97/4.15 tff(14380,plain,
% 3.97/4.15 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = elem!1)),
% 3.97/4.15 inference(symmetry,[status(thm)],[14379])).
% 3.97/4.15 tff(14381,plain,
% 3.97/4.15 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 3.97/4.15 inference(monotonicity,[status(thm)],[14380])).
% 3.97/4.15 tff(14382,plain,
% 3.97/4.15 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[2840, 13145])).
% 3.97/4.15 tff(14383,plain,
% 3.97/4.15 (~(s(s(s(elem!1))) = elem!1)),
% 3.97/4.15 inference(modus_ponens,[status(thm)],[14382, 14381])).
% 3.97/4.15 tff(14384,plain,
% 3.97/4.15 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.15 inference(monotonicity,[status(thm)],[352])).
% 3.97/4.15 tff(14385,plain,
% 3.97/4.15 (r(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 3.97/4.15 inference(symmetry,[status(thm)],[14384])).
% 3.97/4.15 tff(14386,plain,
% 3.97/4.15 (r(s(s(z)), s(s(s(elem!1))))),
% 3.97/4.15 inference(modus_ponens,[status(thm)],[224, 14385])).
% 3.97/4.15 tff(14387,plain,
% 3.97/4.15 (~r(z, s(s(s(elem!1))))),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[4808, 14386, 3261])).
% 3.97/4.15 tff(14388,plain,
% 3.97/4.15 (b(z, s(s(s(elem!1))))),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[2095, 14387])).
% 3.97/4.15 tff(14389,plain,
% 3.97/4.15 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.97/4.15 inference(modus_ponens,[status(thm)],[14388, 11472])).
% 3.97/4.15 tff(14390,plain,
% 3.97/4.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(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(s(z))))))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(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(s(z))))))))) | (~b(z, s(s(s(s(z)))))))),
% 3.97/4.15 inference(rewrite,[status(thm)],[])).
% 3.97/4.15 tff(14391,plain,
% 3.97/4.15 (((~b(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))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), z)) | (~b(z, s(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(s(z))))))))) | (~b(z, s(s(s(s(z)))))))),
% 3.97/4.15 inference(rewrite,[status(thm)],[])).
% 3.97/4.15 tff(14392,plain,
% 3.97/4.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(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(s(z))))))))) | (~b(z, s(s(s(s(z))))))))),
% 3.97/4.15 inference(monotonicity,[status(thm)],[14391])).
% 3.97/4.15 tff(14393,plain,
% 3.97/4.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(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(s(z))))))))) | (~b(z, s(s(s(s(z)))))))),
% 3.97/4.15 inference(transitivity,[status(thm)],[14392, 14390])).
% 3.97/4.15 tff(14394,plain,
% 3.97/4.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 3.97/4.15 inference(quant_inst,[status(thm)],[])).
% 3.97/4.15 tff(14395,plain,
% 3.97/4.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z))))))),
% 3.97/4.15 inference(modus_ponens,[status(thm)],[14394, 14393])).
% 3.97/4.15 tff(14396,plain,
% 3.97/4.15 ($false),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[14395, 178, 3461, 1687, 167, 14122, 14389])).
% 3.97/4.15 tff(14397,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~(elem!1 = s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.97/4.15 tff(14398,plain,
% 3.97/4.15 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[14397, 14378, 1687, 167, 3461, 3261, 14241])).
% 3.97/4.15 tff(14399,plain,
% 3.97/4.15 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[249, 14398])).
% 3.97/4.15 tff(14400,plain,
% 3.97/4.15 (r(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 3.97/4.15 inference(monotonicity,[status(thm)],[353])).
% 3.97/4.15 tff(14401,plain,
% 3.97/4.15 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.97/4.15 inference(symmetry,[status(thm)],[14400])).
% 3.97/4.15 tff(14402,plain,
% 3.97/4.15 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.97/4.15 inference(modus_ponens,[status(thm)],[3859, 14401])).
% 3.97/4.15 tff(14403,plain,
% 3.97/4.15 (~r(s(s(s(elem!1))), elem!1)),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[4205, 3859, 450])).
% 3.97/4.15 tff(14404,plain,
% 3.97/4.15 (b(s(s(s(elem!1))), elem!1)),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[570, 14403, 949])).
% 3.97/4.15 tff(14405,plain,
% 3.97/4.15 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.97/4.15 inference(modus_ponens,[status(thm)],[14404, 13343])).
% 3.97/4.15 tff(14406,plain,
% 3.97/4.15 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[11879, 178, 3461, 14405, 1687, 166])).
% 3.97/4.15 tff(14407,plain,
% 3.97/4.15 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[133, 14406])).
% 3.97/4.15 tff(14408,plain,
% 3.97/4.15 ($false),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[11826, 118, 3261, 14407, 14402])).
% 3.97/4.15 tff(14409,plain,((~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~(elem!1 = s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (s(s(s(elem!1))) = elem!1) | (~r(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.97/4.15 tff(14410,plain,
% 3.97/4.15 (~r(s(s(s(elem!1))), s(s(z)))),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[14409, 14378, 3261, 3461, 1687, 14399, 14383, 14373])).
% 3.97/4.15 tff(14411,plain,
% 3.97/4.15 ((~r(s(s(s(elem!1))), s(s(z)))) <=> (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 3.97/4.15 inference(monotonicity,[status(thm)],[14401])).
% 3.97/4.15 tff(14412,plain,
% 3.97/4.15 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.97/4.15 inference(modus_ponens,[status(thm)],[5810, 14411])).
% 3.97/4.15 tff(14413,plain,
% 3.97/4.15 ((s(s(s(s(s(s(s(z))))))) = s(s(z))) | r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[2960, 41, 3576])).
% 3.97/4.15 tff(14414,plain,
% 3.97/4.15 ($false),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[14413, 14412, 11802])).
% 3.97/4.15 tff(14415,plain,(b(s(s(s(s(s(s(s(z))))))), s(s(z))) | r(s(s(s(elem!1))), s(s(z))) | (~(elem!1 = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.97/4.15 tff(14416,plain,
% 3.97/4.15 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[14415, 14410, 14378])).
% 3.97/4.15 tff(14417,plain,
% 3.97/4.15 (s(elem!1) = s(s(s(s(s(z)))))),
% 3.97/4.15 inference(monotonicity,[status(thm)],[14378])).
% 3.97/4.15 tff(14418,plain,
% 3.97/4.15 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 3.97/4.15 inference(monotonicity,[status(thm)],[14417])).
% 3.97/4.15 tff(14419,plain,
% 3.97/4.15 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 3.97/4.15 inference(monotonicity,[status(thm)],[14418])).
% 3.97/4.15 tff(14420,plain,
% 3.97/4.15 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.15 inference(monotonicity,[status(thm)],[14419])).
% 3.97/4.15 tff(14421,plain,
% 3.97/4.15 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.97/4.15 inference(monotonicity,[status(thm)],[14378])).
% 3.97/4.15 tff(14422,plain,
% 3.97/4.15 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.15 inference(transitivity,[status(thm)],[14421, 14420])).
% 3.97/4.15 tff(14423,plain,
% 3.97/4.15 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(elem!1))))),
% 3.97/4.15 inference(transitivity,[status(thm)],[14380, 2486])).
% 3.97/4.15 tff(14424,plain,
% 3.97/4.15 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 3.97/4.15 inference(monotonicity,[status(thm)],[14423])).
% 3.97/4.15 tff(14425,plain,
% 3.97/4.15 (~(elem!1 = s(s(s(elem!1))))),
% 3.97/4.15 inference(modus_ponens,[status(thm)],[14382, 14424])).
% 3.97/4.15 tff(14426,plain,
% 3.97/4.15 (s(s(s(s(z)))) = elem!1),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[325, 14378])).
% 3.97/4.15 tff(14427,plain,
% 3.97/4.15 (~(s(s(elem!1)) = elem!1)),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[338, 14426, 14371])).
% 3.97/4.15 tff(14428,plain,
% 3.97/4.15 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[348, 14427])).
% 3.97/4.15 tff(14429,plain,
% 3.97/4.15 (~(s(elem!1) = s(s(s(elem!1))))),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[5395, 14428])).
% 3.97/4.15 tff(14430,plain,
% 3.97/4.15 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.15 inference(monotonicity,[status(thm)],[14419])).
% 3.97/4.15 tff(14431,plain,
% 3.97/4.15 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 3.97/4.15 inference(symmetry,[status(thm)],[14430])).
% 3.97/4.15 tff(14432,plain,
% 3.97/4.15 (s(s(s(s(s(z))))) = s(elem!1)),
% 3.97/4.15 inference(symmetry,[status(thm)],[14417])).
% 3.97/4.15 tff(14433,plain,
% 3.97/4.15 (b(s(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))))))))),
% 3.97/4.15 inference(monotonicity,[status(thm)],[14432])).
% 3.97/4.15 tff(14434,plain,
% 3.97/4.15 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 3.97/4.15 inference(transitivity,[status(thm)],[14433, 14431])).
% 3.97/4.15 tff(14435,plain,
% 3.97/4.15 ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(elem!1), s(s(s(elem!1)))))),
% 3.97/4.15 inference(monotonicity,[status(thm)],[14434])).
% 3.97/4.15 tff(14436,plain,
% 3.97/4.15 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 3.97/4.15 inference(monotonicity,[status(thm)],[14417])).
% 3.97/4.15 tff(14437,plain,
% 3.97/4.15 (b(s(s(s(s(s(z))))), s(s(z)))),
% 3.97/4.15 inference(modus_ponens,[status(thm)],[1070, 14436])).
% 3.97/4.15 tff(14438,plain,
% 3.97/4.15 (b(s(s(z)), s(elem!1))),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[1067, 1062, 1060])).
% 3.97/4.15 tff(14439,plain,
% 3.97/4.15 (b(s(s(z)), s(s(s(s(s(z))))))),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[2330, 14378, 14438])).
% 3.97/4.15 tff(14440,assumption,(b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 3.97/4.15 tff(14441,plain,
% 3.97/4.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), 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(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), 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(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 3.97/4.15 inference(rewrite,[status(thm)],[])).
% 3.97/4.15 tff(14442,plain,
% 3.97/4.15 (((~b(s(s(s(s(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(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~b(s(s(z)), 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(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 3.97/4.15 inference(rewrite,[status(thm)],[])).
% 3.97/4.15 tff(14443,plain,
% 3.97/4.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(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(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), 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(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 3.97/4.15 inference(monotonicity,[status(thm)],[14442])).
% 3.97/4.15 tff(14444,plain,
% 3.97/4.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(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(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), 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(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 3.97/4.15 inference(transitivity,[status(thm)],[14443, 14441])).
% 3.97/4.15 tff(14445,plain,
% 3.97/4.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(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(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 3.97/4.15 inference(quant_inst,[status(thm)],[])).
% 3.97/4.15 tff(14446,plain,
% 3.97/4.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 3.97/4.15 inference(modus_ponens,[status(thm)],[14445, 14444])).
% 3.97/4.15 tff(14447,plain,
% 3.97/4.15 ($false),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[14446, 178, 166, 1851, 1665, 1146, 14440])).
% 3.97/4.15 tff(14448,plain,((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.97/4.15 tff(14449,plain,
% 3.97/4.15 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[14448, 14416, 14439, 14399, 14437])).
% 3.97/4.15 tff(14450,plain,
% 3.97/4.15 (~b(s(elem!1), s(s(s(elem!1))))),
% 3.97/4.15 inference(modus_ponens,[status(thm)],[14449, 14435])).
% 3.97/4.15 tff(14451,plain,
% 3.97/4.15 (r(s(elem!1), s(s(s(elem!1))))),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[5432, 14450, 14429])).
% 3.97/4.15 tff(14452,plain,
% 3.97/4.15 (~r(elem!1, s(s(s(elem!1))))),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[10317, 14451, 1587])).
% 3.97/4.15 tff(14453,plain,
% 3.97/4.15 (b(elem!1, s(s(s(elem!1))))),
% 3.97/4.15 inference(unit_resolution,[status(thm)],[2054, 14452, 14425])).
% 3.97/4.15 tff(14454,plain,
% 3.97/4.15 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.15 inference(modus_ponens,[status(thm)],[14453, 14422])).
% 3.97/4.15 tff(14455,plain,
% 3.97/4.15 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 3.97/4.15 inference(monotonicity,[status(thm)],[14432])).
% 3.97/4.15 tff(14456,plain,
% 3.97/4.15 ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) <=> (~b(s(elem!1), s(s(s(s(z))))))),
% 3.97/4.15 inference(monotonicity,[status(thm)],[14455])).
% 3.97/4.15 tff(14457,plain,
% 3.97/4.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 3.97/4.15 inference(rewrite,[status(thm)],[])).
% 3.97/4.15 tff(14458,plain,
% 3.97/4.15 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(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(z))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 3.97/4.15 inference(rewrite,[status(thm)],[])).
% 3.97/4.15 tff(14459,plain,
% 3.97/4.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 3.97/4.15 inference(monotonicity,[status(thm)],[14458])).
% 3.97/4.15 tff(14460,plain,
% 3.97/4.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 3.97/4.16 inference(transitivity,[status(thm)],[14459, 14457])).
% 3.97/4.16 tff(14461,plain,
% 3.97/4.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 3.97/4.16 inference(quant_inst,[status(thm)],[])).
% 3.97/4.16 tff(14462,plain,
% 3.97/4.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 3.97/4.16 inference(modus_ponens,[status(thm)],[14461, 14460])).
% 3.97/4.16 tff(14463,plain,
% 3.97/4.16 ($false),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[14462, 178, 3461, 168, 167, 1851, 1664])).
% 3.97/4.16 tff(14464,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.97/4.16 tff(14465,plain,
% 3.97/4.16 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[14464, 14437, 168, 167, 3461])).
% 3.97/4.16 tff(14466,plain,
% 3.97/4.16 (~b(s(elem!1), s(s(s(s(z)))))),
% 3.97/4.16 inference(modus_ponens,[status(thm)],[14465, 14456])).
% 3.97/4.16 tff(14467,plain,
% 3.97/4.16 (r(s(elem!1), s(s(s(s(z)))))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[1084, 14466, 1369])).
% 3.97/4.16 tff(14468,plain,
% 3.97/4.16 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.97/4.16 inference(monotonicity,[status(thm)],[14419])).
% 3.97/4.16 tff(14469,plain,
% 3.97/4.16 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.97/4.16 inference(transitivity,[status(thm)],[14468, 377])).
% 3.97/4.16 tff(14470,plain,
% 3.97/4.16 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 3.97/4.16 inference(monotonicity,[status(thm)],[14469])).
% 3.97/4.16 tff(14471,plain,
% 3.97/4.16 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.97/4.16 inference(modus_ponens,[status(thm)],[14428, 14470])).
% 3.97/4.16 tff(14472,plain,
% 3.97/4.16 ((~b(s(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)))))))))),
% 3.97/4.16 inference(monotonicity,[status(thm)],[14433])).
% 3.97/4.16 tff(14473,plain,
% 3.97/4.16 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.16 inference(modus_ponens,[status(thm)],[14449, 14472])).
% 3.97/4.16 tff(14474,plain,
% 3.97/4.16 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[395, 14473, 14471])).
% 3.97/4.16 tff(14475,plain,
% 3.97/4.16 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[5568, 14474, 14467])).
% 3.97/4.16 tff(14476,plain,
% 3.97/4.16 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[84, 14475])).
% 3.97/4.16 tff(14477,plain,
% 3.97/4.16 ($false),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[9047, 178, 14476, 14399, 167, 14454, 14416])).
% 3.97/4.16 tff(14478,plain,(r(s(s(z)), s(elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(elem!1))) | (~r(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (s(elem!1) = s(s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, z)) | (z = elem!1) | (s(s(z)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.97/4.16 tff(14479,plain,
% 3.97/4.16 (r(s(s(z)), s(elem!1))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[14478, 14345, 14194, 3261, 5619, 1687, 1369, 14211, 14346, 14342, 14369, 12570])).
% 3.97/4.16 tff(14480,plain,
% 3.97/4.16 (~r(z, s(elem!1))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[12114, 14479, 3261])).
% 3.97/4.16 tff(14481,plain,
% 3.97/4.16 (b(z, s(elem!1))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[2351, 14480])).
% 3.97/4.16 tff(14482,plain,
% 3.97/4.16 (~b(elem!1, s(s(z)))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[12506, 178, 14342, 5619, 1687, 14194])).
% 3.97/4.16 tff(14483,plain,
% 3.97/4.16 (~b(z, elem!1)),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[13324, 1301])).
% 3.97/4.16 tff(14484,plain,
% 3.97/4.16 (r(z, elem!1)),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[585, 14483, 507])).
% 3.97/4.16 tff(14485,plain,
% 3.97/4.16 (~r(elem!1, s(s(z)))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[4862, 14484, 3261])).
% 3.97/4.16 tff(14486,plain,
% 3.97/4.16 (elem!1 = s(s(z))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[467, 14485, 461])).
% 3.97/4.16 tff(14487,plain,
% 3.97/4.16 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(z)))),
% 3.97/4.16 inference(monotonicity,[status(thm)],[14486])).
% 3.97/4.16 tff(14488,plain,
% 3.97/4.16 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(z)))), elem!1)),
% 3.97/4.16 inference(symmetry,[status(thm)],[14487])).
% 3.97/4.16 tff(14489,plain,
% 3.97/4.16 (r(s(s(s(s(z)))), elem!1)),
% 3.97/4.16 inference(modus_ponens,[status(thm)],[193, 14488])).
% 3.97/4.16 tff(14490,plain,
% 3.97/4.16 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[12658, 1301, 506, 1687, 855])).
% 3.97/4.16 tff(14491,plain,
% 3.97/4.16 (r(s(s(s(s(z)))), s(elem!1))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[2173, 14490, 2508])).
% 3.97/4.16 tff(14492,plain,
% 3.97/4.16 (~r(s(s(s(s(z)))), elem!1)),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[10992, 14491, 1587])).
% 3.97/4.16 tff(14493,plain,
% 3.97/4.16 ($false),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[14492, 14489])).
% 3.97/4.16 tff(14494,plain,((~b(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | b(elem!1, s(s(z))) | (~r(elem!1, s(elem!1))) | (~r(z, s(s(z)))) | (s(s(s(s(z)))) = s(elem!1)) | (z = elem!1) | (~b(elem!1, z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 3.97/4.16 tff(14495,plain,
% 3.97/4.16 (~b(elem!1, s(s(s(s(z)))))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[14494, 14367, 14482, 14345, 3261, 2169, 14369, 14342, 1687, 14481, 14211])).
% 3.97/4.16 tff(14496,plain,
% 3.97/4.16 (elem!1 = s(s(s(s(z))))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[483, 14495, 14365])).
% 3.97/4.16 tff(14497,plain,
% 3.97/4.16 (s(elem!1) = s(s(s(s(s(z)))))),
% 3.97/4.16 inference(monotonicity,[status(thm)],[14496])).
% 3.97/4.16 tff(14498,plain,
% 3.97/4.16 (s(s(s(s(s(z))))) = s(elem!1)),
% 3.97/4.16 inference(symmetry,[status(thm)],[14497])).
% 3.97/4.16 tff(14499,plain,
% 3.97/4.16 (r(s(s(z)), s(s(s(s(s(z)))))) <=> r(s(s(z)), s(elem!1))),
% 3.97/4.16 inference(monotonicity,[status(thm)],[14498])).
% 3.97/4.16 tff(14500,plain,
% 3.97/4.16 (r(s(s(z)), s(elem!1)) <=> r(s(s(z)), s(s(s(s(s(z))))))),
% 3.97/4.16 inference(symmetry,[status(thm)],[14499])).
% 3.97/4.16 tff(14501,plain,
% 3.97/4.16 (r(s(s(z)), s(s(s(s(s(z))))))),
% 3.97/4.16 inference(modus_ponens,[status(thm)],[14479, 14500])).
% 3.97/4.16 tff(14502,plain,
% 3.97/4.16 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 3.97/4.16 inference(monotonicity,[status(thm)],[14498])).
% 3.97/4.16 tff(14503,plain,
% 3.97/4.16 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.97/4.16 inference(symmetry,[status(thm)],[14502])).
% 3.97/4.16 tff(14504,plain,
% 3.97/4.16 (r(elem!1, s(elem!1)) <=> r(s(s(s(s(z)))), s(elem!1))),
% 3.97/4.16 inference(monotonicity,[status(thm)],[14496])).
% 3.97/4.16 tff(14505,plain,
% 3.97/4.16 (r(s(s(s(s(z)))), s(elem!1))),
% 3.97/4.16 inference(modus_ponens,[status(thm)],[14345, 14504])).
% 3.97/4.16 tff(14506,plain,
% 3.97/4.16 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.97/4.16 inference(modus_ponens,[status(thm)],[14505, 14503])).
% 3.97/4.16 tff(14507,assumption,(r(s(s(z)), s(s(s(s(s(z))))))), introduced(assumption)).
% 3.97/4.16 tff(14508,plain,
% 3.97/4.16 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 3.97/4.16 inference(rewrite,[status(thm)],[])).
% 3.97/4.16 tff(14509,plain,
% 3.97/4.16 (((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 3.97/4.16 inference(rewrite,[status(thm)],[])).
% 3.97/4.16 tff(14510,plain,
% 3.97/4.16 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 3.97/4.16 inference(monotonicity,[status(thm)],[14509])).
% 3.97/4.16 tff(14511,plain,
% 3.97/4.16 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 3.97/4.16 inference(transitivity,[status(thm)],[14510, 14508])).
% 3.97/4.16 tff(14512,plain,
% 3.97/4.16 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 3.97/4.16 inference(quant_inst,[status(thm)],[])).
% 3.97/4.16 tff(14513,plain,
% 3.97/4.16 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 3.97/4.16 inference(modus_ponens,[status(thm)],[14512, 14511])).
% 3.97/4.16 tff(14514,plain,
% 3.97/4.16 ($false),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[14513, 118, 193, 7139, 14507])).
% 3.97/4.16 tff(14515,plain,((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 3.97/4.16 tff(14516,plain,
% 3.97/4.16 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[14515, 14367, 14506])).
% 3.97/4.16 tff(14517,plain,
% 3.97/4.16 ($false),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[14516, 14501])).
% 3.97/4.16 tff(14518,plain,(b(s(elem!1), z) | (~r(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (s(elem!1) = s(s(s(s(z))))) | b(elem!1, s(elem!1)) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 3.97/4.16 tff(14519,plain,
% 3.97/4.16 (b(elem!1, s(elem!1))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[14518, 766, 1687, 1369, 3261, 5618])).
% 3.97/4.16 tff(14520,plain,
% 3.97/4.16 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.97/4.16 inference(modus_ponens,[status(thm)],[14519, 14193])).
% 3.97/4.16 tff(14521,plain,
% 3.97/4.16 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 3.97/4.16 inference(modus_ponens,[status(thm)],[14520, 14192])).
% 3.97/4.16 tff(14522,plain,
% 3.97/4.16 (b(s(s(s(s(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))))))))),
% 3.97/4.16 inference(monotonicity,[status(thm)],[14187])).
% 3.97/4.16 tff(14523,plain,
% 3.97/4.16 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.16 inference(symmetry,[status(thm)],[14522])).
% 3.97/4.16 tff(14524,plain,
% 3.97/4.16 (~r(s(elem!1), elem!1)),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[13694, 14172, 12569])).
% 3.97/4.16 tff(14525,plain,
% 3.97/4.16 (~(s(s(elem!1)) = elem!1)),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[2510, 14185, 2169])).
% 3.97/4.16 tff(14526,plain,
% 3.97/4.16 (~(s(elem!1) = elem!1)),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[672, 14525])).
% 3.97/4.16 tff(14527,plain,
% 3.97/4.16 (b(s(elem!1), elem!1)),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[677, 14526, 14524])).
% 3.97/4.16 tff(14528,plain,
% 3.97/4.16 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[686, 14527, 14185])).
% 3.97/4.16 tff(14529,plain,
% 3.97/4.16 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.16 inference(modus_ponens,[status(thm)],[14528, 14523])).
% 3.97/4.16 tff(14530,plain,
% 3.97/4.16 ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[13746, 178, 166, 1146])).
% 3.97/4.16 tff(14531,plain,
% 3.97/4.16 ($false),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[14530, 14529, 14521, 14190])).
% 3.97/4.16 tff(14532,plain,(b(s(elem!1), z) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(z)))) | b(elem!1, z) | r(s(s(z)), z) | (~b(z, s(s(s(s(z)))))) | (s(elem!1) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.97/4.16 tff(14533,plain,
% 3.97/4.16 (b(s(elem!1), z)),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[14532, 14132, 12401, 12566, 14118, 3261, 5723, 5618, 11751, 1369])).
% 3.97/4.16 tff(14534,plain,
% 3.97/4.16 ($false),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[6706, 178, 14533, 5619, 12566, 11751, 14116])).
% 3.97/4.16 tff(14535,plain,(b(elem!1, z) | (~r(z, s(s(z)))) | r(s(s(z)), z) | (s(elem!1) = s(s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.97/4.16 tff(14536,plain,
% 3.97/4.16 (b(elem!1, z)),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[14535, 3261, 5618, 12553, 103, 12])).
% 3.97/4.16 tff(14537,plain,
% 3.97/4.16 (~(s(elem!1) = elem!1)),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[790, 766, 14536])).
% 3.97/4.16 tff(14538,plain,
% 3.97/4.16 (~r(z, s(s(s(s(z)))))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[3269, 3261, 103])).
% 3.97/4.16 tff(14539,plain,
% 3.97/4.16 (b(z, s(s(s(s(z)))))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[46, 14538])).
% 3.97/4.16 tff(14540,plain,
% 3.97/4.16 (b(elem!1, s(elem!1))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[14518, 766, 14539, 12553, 3261, 5618])).
% 3.97/4.16 tff(14541,plain,
% 3.97/4.16 (~(z = elem!1)),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[6991, 14536])).
% 3.97/4.16 tff(14542,plain,
% 3.97/4.16 (~(elem!1 = z)),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[2808, 14541])).
% 3.97/4.16 tff(14543,plain,
% 3.97/4.16 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[12399, 3261, 5619, 103])).
% 3.97/4.16 tff(14544,plain,
% 3.97/4.16 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[14046, 105, 3261, 14543, 103, 5618, 13677])).
% 3.97/4.16 tff(14545,plain,
% 3.97/4.16 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[2960, 41, 14543, 3574])).
% 3.97/4.16 tff(14546,plain,
% 3.97/4.16 (~r(s(s(s(s(z)))), z)),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[9569, 103, 3261])).
% 3.97/4.16 tff(14547,plain,
% 3.97/4.16 (b(s(s(s(s(z)))), z)),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[191, 14546])).
% 3.97/4.16 tff(14548,plain,
% 3.97/4.16 (r(elem!1, s(s(z)))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[467, 461, 312])).
% 3.97/4.16 tff(14549,plain,
% 3.97/4.16 (~r(elem!1, s(s(s(s(z)))))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[5670, 14548, 147])).
% 3.97/4.16 tff(14550,plain,
% 3.97/4.16 (b(elem!1, z)),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[11793, 461, 3261, 290, 5618])).
% 3.97/4.16 tff(14551,plain,
% 3.97/4.16 (~r(z, elem!1)),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[4862, 14548, 3261])).
% 3.97/4.16 tff(14552,plain,
% 3.97/4.16 (b(z, elem!1)),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[585, 14551, 318])).
% 3.97/4.16 tff(14553,plain,
% 3.97/4.16 (~b(elem!1, s(s(s(s(z)))))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[12519, 178, 14552, 14550, 11798, 168])).
% 3.97/4.16 tff(14554,plain,
% 3.97/4.16 (elem!1 = s(s(s(s(z))))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[483, 14553, 14549])).
% 3.97/4.16 tff(14555,plain,
% 3.97/4.16 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(s(z)))))),
% 3.97/4.16 inference(monotonicity,[status(thm)],[14554])).
% 3.97/4.16 tff(14556,plain,
% 3.97/4.16 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), elem!1)),
% 3.97/4.16 inference(symmetry,[status(thm)],[14555])).
% 3.97/4.16 tff(14557,plain,
% 3.97/4.16 (s(elem!1) = s(s(s(s(s(z)))))),
% 3.97/4.16 inference(monotonicity,[status(thm)],[14554])).
% 3.97/4.16 tff(14558,plain,
% 3.97/4.16 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 3.97/4.16 inference(monotonicity,[status(thm)],[14557])).
% 3.97/4.16 tff(14559,plain,
% 3.97/4.16 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 3.97/4.16 inference(monotonicity,[status(thm)],[14558])).
% 3.97/4.16 tff(14560,plain,
% 3.97/4.16 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.97/4.16 inference(monotonicity,[status(thm)],[14559])).
% 3.97/4.16 tff(14561,plain,
% 3.97/4.16 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.97/4.16 inference(transitivity,[status(thm)],[14560, 377])).
% 3.97/4.16 tff(14562,plain,
% 3.97/4.16 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 3.97/4.16 inference(monotonicity,[status(thm)],[14561])).
% 3.97/4.16 tff(14563,plain,
% 3.97/4.16 (s(s(s(s(z)))) = elem!1),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[325, 14554])).
% 3.97/4.16 tff(14564,plain,
% 3.97/4.16 (~(s(s(elem!1)) = elem!1)),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[338, 14563, 12])).
% 3.97/4.16 tff(14565,plain,
% 3.97/4.16 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[348, 14564])).
% 3.97/4.16 tff(14566,plain,
% 3.97/4.16 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.97/4.16 inference(modus_ponens,[status(thm)],[14565, 14562])).
% 3.97/4.16 tff(14567,plain,
% 3.97/4.16 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(s(s(s(z))))))))),
% 3.97/4.16 inference(monotonicity,[status(thm)],[14559])).
% 3.97/4.16 tff(14568,plain,
% 3.97/4.16 (r(z, s(s(s(s(s(s(s(z)))))))) <=> r(z, s(s(s(elem!1))))),
% 3.97/4.16 inference(symmetry,[status(thm)],[14567])).
% 3.97/4.16 tff(14569,plain,
% 3.97/4.16 (r(z, s(s(s(elem!1))))),
% 3.97/4.16 inference(modus_ponens,[status(thm)],[203, 14568])).
% 3.97/4.16 tff(14570,plain,
% 3.97/4.16 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.97/4.16 inference(monotonicity,[status(thm)],[14554])).
% 3.97/4.16 tff(14571,plain,
% 3.97/4.16 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 3.97/4.16 inference(symmetry,[status(thm)],[14570])).
% 3.97/4.16 tff(14572,plain,
% 3.97/4.16 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.16 inference(monotonicity,[status(thm)],[14559])).
% 3.97/4.16 tff(14573,plain,
% 3.97/4.16 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.97/4.16 inference(symmetry,[status(thm)],[14572])).
% 3.97/4.16 tff(14574,plain,
% 3.97/4.16 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(elem!1))))),
% 3.97/4.16 inference(transitivity,[status(thm)],[14573, 14571])).
% 3.97/4.16 tff(14575,plain,
% 3.97/4.16 (s(s(s(s(s(z))))) = s(elem!1)),
% 3.97/4.16 inference(symmetry,[status(thm)],[14557])).
% 3.97/4.16 tff(14576,plain,
% 3.97/4.16 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.97/4.16 inference(monotonicity,[status(thm)],[14575])).
% 3.97/4.16 tff(14577,plain,
% 3.97/4.16 (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(s(z))))))),
% 3.97/4.16 inference(symmetry,[status(thm)],[14576])).
% 3.97/4.16 tff(14578,plain,
% 3.97/4.16 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.97/4.16 inference(monotonicity,[status(thm)],[14559])).
% 3.97/4.16 tff(14579,plain,
% 3.97/4.16 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(s(s(s(z))))))), z)),
% 3.97/4.16 inference(monotonicity,[status(thm)],[14559])).
% 3.97/4.16 tff(14580,plain,
% 3.97/4.16 (r(s(s(s(s(s(s(s(z))))))), z) <=> r(s(s(s(elem!1))), z)),
% 3.97/4.16 inference(symmetry,[status(thm)],[14579])).
% 3.97/4.16 tff(14581,plain,
% 3.97/4.16 (r(s(s(s(elem!1))), z)),
% 3.97/4.16 inference(modus_ponens,[status(thm)],[108, 14580])).
% 3.97/4.16 tff(14582,plain,
% 3.97/4.16 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[1557, 14581, 844])).
% 3.97/4.16 tff(14583,plain,
% 3.97/4.16 (b(s(s(s(elem!1))), s(elem!1))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[373, 14582, 14565])).
% 3.97/4.16 tff(14584,plain,
% 3.97/4.16 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.97/4.16 inference(modus_ponens,[status(thm)],[14583, 14578])).
% 3.97/4.16 tff(14585,plain,
% 3.97/4.16 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.97/4.16 inference(modus_ponens,[status(thm)],[14584, 14577])).
% 3.97/4.16 tff(14586,plain,
% 3.97/4.16 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 3.97/4.16 inference(monotonicity,[status(thm)],[14575])).
% 3.97/4.16 tff(14587,plain,
% 3.97/4.16 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.97/4.16 inference(symmetry,[status(thm)],[14586])).
% 3.97/4.16 tff(14588,plain,
% 3.97/4.16 (b(elem!1, s(elem!1)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 3.97/4.16 inference(monotonicity,[status(thm)],[14554])).
% 3.97/4.16 tff(14589,plain,
% 3.97/4.16 (b(s(s(s(s(z)))), s(elem!1))),
% 3.97/4.16 inference(modus_ponens,[status(thm)],[854, 14588])).
% 3.97/4.16 tff(14590,plain,
% 3.97/4.16 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.97/4.16 inference(modus_ponens,[status(thm)],[14589, 14587])).
% 3.97/4.16 tff(14591,plain,
% 3.97/4.16 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 3.97/4.16 inference(monotonicity,[status(thm)],[14557])).
% 3.97/4.16 tff(14592,plain,
% 3.97/4.16 (b(s(s(s(s(s(z))))), s(s(z)))),
% 3.97/4.16 inference(modus_ponens,[status(thm)],[1070, 14591])).
% 3.97/4.16 tff(14593,plain,
% 3.97/4.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 3.97/4.16 inference(rewrite,[status(thm)],[])).
% 3.97/4.16 tff(14594,plain,
% 3.97/4.16 (((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(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(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 3.97/4.16 inference(rewrite,[status(thm)],[])).
% 3.97/4.16 tff(14595,plain,
% 3.97/4.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(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(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 3.97/4.16 inference(monotonicity,[status(thm)],[14594])).
% 3.97/4.16 tff(14596,plain,
% 3.97/4.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(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(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 3.97/4.16 inference(transitivity,[status(thm)],[14595, 14593])).
% 3.97/4.16 tff(14597,plain,
% 3.97/4.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(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(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.97/4.16 inference(quant_inst,[status(thm)],[])).
% 3.97/4.16 tff(14598,plain,
% 3.97/4.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 3.97/4.16 inference(modus_ponens,[status(thm)],[14597, 14596])).
% 3.97/4.16 tff(14599,plain,
% 3.97/4.16 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[14598, 178, 14592, 14590, 1146])).
% 3.97/4.16 tff(14600,plain,
% 3.97/4.16 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[14599, 14585])).
% 3.97/4.16 tff(14601,plain,
% 3.97/4.16 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[222, 14600])).
% 3.97/4.16 tff(14602,plain,
% 3.97/4.16 (r(elem!1, s(s(s(elem!1))))),
% 3.97/4.16 inference(modus_ponens,[status(thm)],[14601, 14574])).
% 3.97/4.16 tff(14603,plain,
% 3.97/4.16 (~r(s(elem!1), s(s(s(elem!1))))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[5423, 14602, 14552, 725, 14569, 14550])).
% 3.97/4.16 tff(14604,plain,
% 3.97/4.16 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.16 inference(monotonicity,[status(thm)],[352])).
% 3.97/4.16 tff(14605,plain,
% 3.97/4.16 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 3.97/4.16 inference(symmetry,[status(thm)],[14604])).
% 3.97/4.16 tff(14606,plain,
% 3.97/4.16 (r(s(elem!1), s(s(s(elem!1))))),
% 3.97/4.16 inference(modus_ponens,[status(thm)],[382, 14605])).
% 3.97/4.16 tff(14607,plain,
% 3.97/4.16 ($false),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[5426, 14606])).
% 3.97/4.16 tff(14608,plain,((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | r(s(elem!1), s(s(s(elem!1)))) | (~(elem!1 = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.97/4.16 tff(14609,plain,
% 3.97/4.16 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[14608, 14603, 14554])).
% 3.97/4.16 tff(14610,plain,
% 3.97/4.16 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[395, 14609, 14566])).
% 3.97/4.16 tff(14611,plain,
% 3.97/4.16 ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[2976, 178, 1070, 13686, 1146])).
% 3.97/4.16 tff(14612,plain,
% 3.97/4.16 (~b(s(s(z)), s(elem!1))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[14611, 14610])).
% 3.97/4.16 tff(14613,plain,
% 3.97/4.16 (r(s(s(z)), s(elem!1))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[1067, 14612, 1060])).
% 3.97/4.16 tff(14614,plain,
% 3.97/4.16 (~r(s(elem!1), s(s(s(s(z)))))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[5758, 14613, 147])).
% 3.97/4.16 tff(14615,plain,
% 3.97/4.16 (b(s(elem!1), s(s(s(s(z)))))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[1084, 14614, 1369])).
% 3.97/4.16 tff(14616,plain,
% 3.97/4.16 (b(s(elem!1), elem!1)),
% 3.97/4.16 inference(modus_ponens,[status(thm)],[14615, 14556])).
% 3.97/4.16 tff(14617,plain,
% 3.97/4.16 (~r(z, s(elem!1))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[12114, 14613, 3261])).
% 3.97/4.16 tff(14618,plain,
% 3.97/4.16 (b(z, s(elem!1))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[2351, 14617])).
% 3.97/4.16 tff(14619,plain,
% 3.97/4.16 (~b(s(elem!1), elem!1)),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[1396, 14618, 854, 14552, 14550])).
% 3.97/4.16 tff(14620,plain,
% 3.97/4.16 ($false),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[14619, 14616])).
% 3.97/4.16 tff(14621,plain,(b(elem!1, s(s(z))) | (~b(elem!1, s(elem!1))) | (s(elem!1) = s(s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (s(s(z)) = s(elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (s(elem!1) = elem!1) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (s(s(z)) = elem!1) | (~b(s(s(s(s(z)))), z)) | (elem!1 = z) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 3.97/4.16 tff(14622,plain,
% 3.97/4.16 (b(elem!1, s(s(z)))),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[14621, 12, 1369, 3261, 147, 1060, 1070, 1146, 725, 844, 203, 108, 854, 14547, 290, 5618])).
% 3.97/4.16 tff(14623,plain,
% 3.97/4.16 (b(elem!1, z)),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[13749, 14622, 1070, 854, 147, 5619, 3261, 1146, 12, 1060, 725, 844, 290, 14547])).
% 3.97/4.16 tff(14624,plain,
% 3.97/4.16 (~b(s(elem!1), elem!1)),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[13135, 178, 14623, 5619, 14622, 1070])).
% 3.97/4.16 tff(14625,plain,
% 3.97/4.16 (r(s(elem!1), elem!1)),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[677, 14624, 725])).
% 3.97/4.16 tff(14626,plain,
% 3.97/4.16 (~r(z, elem!1)),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[1284, 14625, 844])).
% 3.97/4.16 tff(14627,plain,
% 3.97/4.16 (b(z, elem!1)),
% 3.97/4.16 inference(unit_resolution,[status(thm)],[585, 14626, 318])).
% 3.97/4.16 tff(14628,plain,
% 3.97/4.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 3.97/4.16 inference(rewrite,[status(thm)],[])).
% 3.97/4.16 tff(14629,plain,
% 3.97/4.16 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 3.97/4.17 inference(rewrite,[status(thm)],[])).
% 3.97/4.17 tff(14630,plain,
% 3.97/4.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))))),
% 3.97/4.17 inference(monotonicity,[status(thm)],[14629])).
% 3.97/4.17 tff(14631,plain,
% 3.97/4.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 3.97/4.17 inference(transitivity,[status(thm)],[14630, 14628])).
% 3.97/4.17 tff(14632,plain,
% 3.97/4.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)))),
% 3.97/4.17 inference(quant_inst,[status(thm)],[])).
% 3.97/4.17 tff(14633,plain,
% 3.97/4.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))),
% 3.97/4.17 inference(modus_ponens,[status(thm)],[14632, 14631])).
% 3.97/4.17 tff(14634,plain,
% 3.97/4.17 ((~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z))))))),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[14633, 178, 14623, 5619, 14622, 11798, 14547])).
% 3.97/4.17 tff(14635,plain,
% 3.97/4.17 (~b(elem!1, s(s(s(s(z)))))),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[14634, 14627])).
% 3.97/4.17 tff(14636,plain,
% 3.97/4.17 (elem!1 = s(s(s(s(z))))),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[13333, 14635, 147, 14623, 5619, 11798, 12, 14627])).
% 3.97/4.17 tff(14637,plain,
% 3.97/4.17 (b(elem!1, s(s(z))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 3.97/4.17 inference(monotonicity,[status(thm)],[14636])).
% 3.97/4.17 tff(14638,plain,
% 3.97/4.17 (b(s(s(s(s(z)))), s(s(z))) <=> b(elem!1, s(s(z)))),
% 3.97/4.17 inference(symmetry,[status(thm)],[14637])).
% 3.97/4.17 tff(14639,plain,
% 3.97/4.17 ((~b(s(s(s(s(z)))), s(s(z)))) <=> (~b(elem!1, s(s(z))))),
% 3.97/4.17 inference(monotonicity,[status(thm)],[14638])).
% 3.97/4.17 tff(14640,plain,
% 3.97/4.17 (~b(elem!1, s(s(z)))),
% 3.97/4.17 inference(modus_ponens,[status(thm)],[86, 14639])).
% 3.97/4.17 tff(14641,plain,
% 3.97/4.17 ($false),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[14622, 14640])).
% 3.97/4.17 tff(14642,plain,((s(s(z)) = elem!1) | b(s(s(s(s(z)))), s(s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(elem!1), z)) | (s(elem!1) = elem!1) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(elem!1))) | (~r(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (s(s(z)) = s(elem!1)) | (elem!1 = z) | (s(elem!1) = s(s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 3.97/4.17 tff(14643,plain,
% 3.97/4.17 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[14642, 10794, 12, 14545, 12546, 14544, 14542, 3261, 725, 11743, 854, 12553, 86, 844, 5618])).
% 3.97/4.17 tff(14644,plain,
% 3.97/4.17 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[271, 14643])).
% 3.97/4.17 tff(14645,plain,
% 3.97/4.17 (~r(s(s(s(s(z)))), z)),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[9569, 3261, 103])).
% 3.97/4.17 tff(14646,plain,
% 3.97/4.17 (b(s(s(s(s(z)))), z)),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[191, 14645])).
% 3.97/4.17 tff(14647,plain,
% 3.97/4.17 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[13684, 10794, 3261, 14646])).
% 3.97/4.17 tff(14648,plain,
% 3.97/4.17 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[249, 14647])).
% 3.97/4.17 tff(14649,plain,
% 3.97/4.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.97/4.17 inference(rewrite,[status(thm)],[])).
% 3.97/4.17 tff(14650,plain,
% 3.97/4.17 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z))))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.97/4.17 inference(rewrite,[status(thm)],[])).
% 3.97/4.17 tff(14651,plain,
% 3.97/4.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 3.97/4.17 inference(monotonicity,[status(thm)],[14650])).
% 3.97/4.17 tff(14652,plain,
% 3.97/4.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.97/4.17 inference(transitivity,[status(thm)],[14651, 14649])).
% 3.97/4.17 tff(14653,plain,
% 3.97/4.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))))),
% 3.97/4.17 inference(quant_inst,[status(thm)],[])).
% 3.97/4.17 tff(14654,plain,
% 3.97/4.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 3.97/4.17 inference(modus_ponens,[status(thm)],[14653, 14652])).
% 3.97/4.17 tff(14655,plain,
% 3.97/4.17 (~b(elem!1, s(s(z)))),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[14654, 178, 14536, 5619, 14648, 14644])).
% 3.97/4.17 tff(14656,plain,
% 3.97/4.17 (r(elem!1, s(s(z)))),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[467, 14655, 312])).
% 3.97/4.17 tff(14657,plain,
% 3.97/4.17 (~r(z, elem!1)),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[4862, 14656, 3261])).
% 3.97/4.17 tff(14658,plain,
% 3.97/4.17 (b(z, elem!1)),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[585, 14657, 14541])).
% 3.97/4.17 tff(14659,plain,
% 3.97/4.17 (~r(elem!1, s(s(s(s(z)))))),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[3785, 14656, 103])).
% 3.97/4.17 tff(14660,plain,
% 3.97/4.17 ((~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z))))))),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[12519, 178, 14536, 14539, 14646])).
% 3.97/4.17 tff(14661,plain,
% 3.97/4.17 (~b(elem!1, s(s(s(s(z)))))),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[14660, 14658])).
% 3.97/4.17 tff(14662,plain,
% 3.97/4.17 (elem!1 = s(s(s(s(z))))),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[483, 14661, 14659])).
% 3.97/4.17 tff(14663,plain,
% 3.97/4.17 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(s(z)))))),
% 3.97/4.17 inference(monotonicity,[status(thm)],[14662])).
% 3.97/4.17 tff(14664,plain,
% 3.97/4.17 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), elem!1)),
% 3.97/4.17 inference(symmetry,[status(thm)],[14663])).
% 3.97/4.17 tff(14665,plain,
% 3.97/4.17 (~b(s(s(z)), s(elem!1))),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[13697, 727])).
% 3.97/4.17 tff(14666,plain,
% 3.97/4.17 (r(s(s(z)), s(elem!1))),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[1067, 14665, 1060])).
% 3.97/4.17 tff(14667,plain,
% 3.97/4.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), 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))))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), 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))))))), s(s(z)))))),
% 3.97/4.17 inference(rewrite,[status(thm)],[])).
% 3.97/4.17 tff(14668,plain,
% 3.97/4.17 (((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), 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(z, s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), 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))))))), s(s(z)))))),
% 3.97/4.17 inference(rewrite,[status(thm)],[])).
% 3.97/4.17 tff(14669,plain,
% 3.97/4.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), 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(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), 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))))))), s(s(z))))))),
% 3.97/4.17 inference(monotonicity,[status(thm)],[14668])).
% 3.97/4.17 tff(14670,plain,
% 3.97/4.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), 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(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), 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))))))), s(s(z)))))),
% 3.97/4.17 inference(transitivity,[status(thm)],[14669, 14667])).
% 3.97/4.17 tff(14671,plain,
% 3.97/4.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), 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(z, s(elem!1))))),
% 3.97/4.17 inference(quant_inst,[status(thm)],[])).
% 3.97/4.17 tff(14672,plain,
% 3.97/4.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 3.97/4.17 inference(modus_ponens,[status(thm)],[14671, 14670])).
% 3.97/4.17 tff(14673,plain,
% 3.97/4.17 ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[14672, 178, 1070, 595, 1146])).
% 3.97/4.17 tff(14674,plain,
% 3.97/4.17 (~b(z, s(elem!1))),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[14673, 727])).
% 3.97/4.17 tff(14675,plain,
% 3.97/4.17 (r(z, s(elem!1))),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[2351, 14674])).
% 3.97/4.17 tff(14676,plain,
% 3.97/4.17 ($false),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[12114, 14675, 14666, 3261])).
% 3.97/4.17 tff(14677,plain,((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (s(s(z)) = s(elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.97/4.17 tff(14678,plain,
% 3.97/4.17 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[14677, 14644, 3261, 12546, 11743, 14545, 14648])).
% 3.97/4.17 tff(14679,plain,
% 3.97/4.17 (s(elem!1) = s(s(s(s(s(z)))))),
% 3.97/4.17 inference(monotonicity,[status(thm)],[14662])).
% 3.97/4.17 tff(14680,plain,
% 3.97/4.17 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 3.97/4.17 inference(monotonicity,[status(thm)],[14679])).
% 3.97/4.17 tff(14681,plain,
% 3.97/4.17 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 3.97/4.17 inference(monotonicity,[status(thm)],[14680])).
% 3.97/4.17 tff(14682,plain,
% 3.97/4.17 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.97/4.17 inference(monotonicity,[status(thm)],[14681])).
% 3.97/4.17 tff(14683,plain,
% 3.97/4.17 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.97/4.17 inference(transitivity,[status(thm)],[14682, 377])).
% 3.97/4.17 tff(14684,plain,
% 3.97/4.17 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 3.97/4.17 inference(monotonicity,[status(thm)],[14683])).
% 3.97/4.17 tff(14685,plain,
% 3.97/4.17 (s(s(s(s(z)))) = elem!1),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[325, 14662])).
% 3.97/4.17 tff(14686,plain,
% 3.97/4.17 (~(s(s(elem!1)) = elem!1)),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[338, 14685, 12])).
% 3.97/4.17 tff(14687,plain,
% 3.97/4.17 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[348, 14686])).
% 3.97/4.17 tff(14688,plain,
% 3.97/4.17 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.97/4.17 inference(modus_ponens,[status(thm)],[14687, 14684])).
% 3.97/4.17 tff(14689,plain,
% 3.97/4.17 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[395, 14688, 14678])).
% 3.97/4.17 tff(14690,plain,
% 3.97/4.17 (s(s(s(s(s(z))))) = s(elem!1)),
% 3.97/4.17 inference(symmetry,[status(thm)],[14679])).
% 3.97/4.17 tff(14691,plain,
% 3.97/4.17 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 3.97/4.17 inference(symmetry,[status(thm)],[14681])).
% 3.97/4.17 tff(14692,plain,
% 3.97/4.17 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 3.97/4.17 inference(monotonicity,[status(thm)],[14691, 14690])).
% 3.97/4.17 tff(14693,plain,
% 3.97/4.17 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.97/4.17 inference(symmetry,[status(thm)],[14692])).
% 3.97/4.17 tff(14694,plain,
% 3.97/4.17 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(s(s(s(z))))))), z)),
% 3.97/4.17 inference(monotonicity,[status(thm)],[14681])).
% 3.97/4.17 tff(14695,plain,
% 3.97/4.17 (r(s(s(s(s(s(s(s(z))))))), z) <=> r(s(s(s(elem!1))), z)),
% 3.97/4.17 inference(symmetry,[status(thm)],[14694])).
% 3.97/4.17 tff(14696,plain,
% 3.97/4.17 (r(s(s(s(elem!1))), z)),
% 3.97/4.17 inference(modus_ponens,[status(thm)],[14544, 14695])).
% 3.97/4.17 tff(14697,plain,
% 3.97/4.17 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[1557, 14696, 844])).
% 3.97/4.17 tff(14698,plain,
% 3.97/4.17 (b(s(s(s(elem!1))), s(elem!1))),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[373, 14697, 14687])).
% 3.97/4.17 tff(14699,plain,
% 3.97/4.17 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.97/4.17 inference(modus_ponens,[status(thm)],[14698, 14693])).
% 3.97/4.17 tff(14700,plain,
% 3.97/4.17 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 3.97/4.17 inference(monotonicity,[status(thm)],[14690])).
% 3.97/4.17 tff(14701,plain,
% 3.97/4.17 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.97/4.17 inference(symmetry,[status(thm)],[14700])).
% 3.97/4.17 tff(14702,plain,
% 3.97/4.17 (b(elem!1, s(elem!1)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 3.97/4.17 inference(monotonicity,[status(thm)],[14662])).
% 3.97/4.17 tff(14703,plain,
% 3.97/4.17 (b(s(s(s(s(z)))), s(elem!1))),
% 3.97/4.17 inference(modus_ponens,[status(thm)],[854, 14702])).
% 3.97/4.17 tff(14704,plain,
% 3.97/4.17 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.97/4.17 inference(modus_ponens,[status(thm)],[14703, 14701])).
% 3.97/4.17 tff(14705,plain,
% 3.97/4.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 3.97/4.17 inference(rewrite,[status(thm)],[])).
% 3.97/4.17 tff(14706,plain,
% 3.97/4.17 (((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 3.97/4.17 inference(rewrite,[status(thm)],[])).
% 3.97/4.17 tff(14707,plain,
% 3.97/4.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 3.97/4.17 inference(monotonicity,[status(thm)],[14706])).
% 3.97/4.17 tff(14708,plain,
% 3.97/4.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 3.97/4.17 inference(transitivity,[status(thm)],[14707, 14705])).
% 3.97/4.17 tff(14709,plain,
% 3.97/4.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.97/4.17 inference(quant_inst,[status(thm)],[])).
% 3.97/4.17 tff(14710,plain,
% 3.97/4.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 3.97/4.17 inference(modus_ponens,[status(thm)],[14709, 14708])).
% 3.97/4.17 tff(14711,plain,
% 3.97/4.17 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[14710, 178, 14539, 14644, 14704])).
% 3.97/4.17 tff(14712,plain,
% 3.97/4.17 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[14711, 14699])).
% 3.97/4.17 tff(14713,plain,
% 3.97/4.17 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[84, 14712])).
% 3.97/4.17 tff(14714,plain,
% 3.97/4.17 (~r(s(elem!1), s(s(s(s(z)))))),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[5568, 14713, 14689])).
% 3.97/4.17 tff(14715,plain,
% 3.97/4.17 (b(s(elem!1), s(s(s(s(z)))))),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[1084, 14714, 12553])).
% 3.97/4.17 tff(14716,plain,
% 3.97/4.17 (b(s(elem!1), elem!1)),
% 3.97/4.17 inference(modus_ponens,[status(thm)],[14715, 14664])).
% 3.97/4.17 tff(14717,plain,
% 3.97/4.17 (~b(z, s(elem!1))),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[1396, 14716, 14536, 854, 14658])).
% 3.97/4.17 tff(14718,plain,
% 3.97/4.17 (r(z, s(elem!1))),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[2351, 14717])).
% 3.97/4.17 tff(14719,plain,
% 3.97/4.17 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(s(s(z)))))),
% 3.97/4.17 inference(monotonicity,[status(thm)],[14662])).
% 3.97/4.17 tff(14720,plain,
% 3.97/4.17 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(z)), elem!1)),
% 3.97/4.17 inference(symmetry,[status(thm)],[14719])).
% 3.97/4.17 tff(14721,plain,
% 3.97/4.17 (r(s(s(z)), elem!1)),
% 3.97/4.17 inference(modus_ponens,[status(thm)],[10794, 14720])).
% 3.97/4.17 tff(14722,plain,
% 3.97/4.17 (~b(s(s(z)), s(elem!1))),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[12937, 14716, 14536, 11744, 10794, 14721, 14696, 14658, 3261, 14685, 844, 14687])).
% 3.97/4.17 tff(14723,plain,
% 3.97/4.17 (r(s(s(z)), s(elem!1))),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[2879, 14722, 12546])).
% 3.97/4.17 tff(14724,plain,
% 3.97/4.17 ($false),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[12114, 14723, 14718, 3261])).
% 3.97/4.17 tff(14725,plain,(b(s(s(z)), s(s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (s(s(z)) = elem!1) | (s(elem!1) = elem!1) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 3.97/4.17 tff(14726,plain,
% 3.97/4.17 (b(s(s(z)), s(s(s(s(z)))))),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[14725, 12569, 3261, 14540, 12, 14537, 86, 5618])).
% 3.97/4.17 tff(14727,plain,
% 3.97/4.17 (~b(elem!1, s(s(z)))),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[12506, 178, 14536, 5619, 14539, 14726])).
% 3.97/4.17 tff(14728,plain,
% 3.97/4.17 (r(elem!1, s(s(z)))),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[467, 14727, 312])).
% 3.97/4.17 tff(14729,plain,
% 3.97/4.17 (~r(elem!1, s(s(s(s(z)))))),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[3785, 14728, 103])).
% 3.97/4.17 tff(14730,plain,
% 3.97/4.17 (~r(z, elem!1)),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[4862, 14728, 3261])).
% 3.97/4.17 tff(14731,plain,
% 3.97/4.17 (b(z, elem!1)),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[585, 14730, 14541])).
% 3.97/4.17 tff(14732,plain,
% 3.97/4.17 (~b(elem!1, s(s(s(s(z)))))),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[14660, 14731])).
% 3.97/4.17 tff(14733,plain,
% 3.97/4.17 (elem!1 = s(s(s(s(z))))),
% 3.97/4.17 inference(unit_resolution,[status(thm)],[483, 14732, 14729])).
% 3.97/4.17 tff(14734,plain,
% 3.97/4.17 (s(elem!1) = s(s(s(s(s(z)))))),
% 3.97/4.17 inference(monotonicity,[status(thm)],[14733])).
% 3.97/4.17 tff(14735,plain,
% 3.97/4.17 (s(s(s(s(s(z))))) = s(elem!1)),
% 3.97/4.17 inference(symmetry,[status(thm)],[14734])).
% 3.97/4.17 tff(14736,plain,
% 3.97/4.17 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.97/4.17 inference(monotonicity,[status(thm)],[14735])).
% 3.97/4.17 tff(14737,plain,
% 3.97/4.17 (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(s(z))))))),
% 3.97/4.18 inference(symmetry,[status(thm)],[14736])).
% 3.97/4.18 tff(14738,plain,
% 3.97/4.18 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 3.97/4.18 inference(monotonicity,[status(thm)],[14734])).
% 3.97/4.18 tff(14739,plain,
% 3.97/4.18 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 3.97/4.18 inference(monotonicity,[status(thm)],[14738])).
% 3.97/4.18 tff(14740,plain,
% 3.97/4.18 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.97/4.18 inference(monotonicity,[status(thm)],[14739])).
% 3.97/4.18 tff(14741,plain,
% 3.97/4.18 (s(s(s(s(z)))) = elem!1),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[325, 14733])).
% 3.97/4.18 tff(14742,plain,
% 3.97/4.18 (~(s(s(elem!1)) = elem!1)),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[338, 14741, 12])).
% 3.97/4.18 tff(14743,plain,
% 3.97/4.18 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[348, 14742])).
% 3.97/4.18 tff(14744,plain,
% 3.97/4.18 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(s(s(s(z))))))), z)),
% 3.97/4.18 inference(monotonicity,[status(thm)],[14739])).
% 3.97/4.18 tff(14745,plain,
% 3.97/4.18 (r(s(s(s(s(s(s(s(z))))))), z) <=> r(s(s(s(elem!1))), z)),
% 3.97/4.18 inference(symmetry,[status(thm)],[14744])).
% 3.97/4.18 tff(14746,plain,
% 3.97/4.18 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[12409, 14726, 14539, 5619, 14545])).
% 3.97/4.18 tff(14747,plain,
% 3.97/4.18 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[133, 14746])).
% 3.97/4.18 tff(14748,plain,
% 3.97/4.18 (r(s(s(s(elem!1))), z)),
% 3.97/4.18 inference(modus_ponens,[status(thm)],[14747, 14745])).
% 3.97/4.18 tff(14749,plain,
% 3.97/4.18 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[1557, 14748, 12569])).
% 3.97/4.18 tff(14750,plain,
% 3.97/4.18 (b(s(s(s(elem!1))), s(elem!1))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[373, 14749, 14743])).
% 3.97/4.18 tff(14751,plain,
% 3.97/4.18 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.97/4.18 inference(modus_ponens,[status(thm)],[14750, 14740])).
% 3.97/4.18 tff(14752,plain,
% 3.97/4.18 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.97/4.18 inference(modus_ponens,[status(thm)],[14751, 14737])).
% 3.97/4.18 tff(14753,plain,
% 3.97/4.18 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.18 inference(monotonicity,[status(thm)],[14734])).
% 3.97/4.18 tff(14754,plain,
% 3.97/4.18 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.97/4.18 inference(monotonicity,[status(thm)],[14739])).
% 3.97/4.18 tff(14755,plain,
% 3.97/4.18 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.97/4.18 inference(transitivity,[status(thm)],[14754, 377])).
% 3.97/4.18 tff(14756,plain,
% 3.97/4.18 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 3.97/4.18 inference(monotonicity,[status(thm)],[14755])).
% 3.97/4.18 tff(14757,plain,
% 3.97/4.18 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.97/4.18 inference(modus_ponens,[status(thm)],[14743, 14756])).
% 3.97/4.18 tff(14758,plain,
% 3.97/4.18 (~b(s(elem!1), s(s(s(s(z)))))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[14354, 14726, 5619, 14646, 12546])).
% 3.97/4.18 tff(14759,plain,
% 3.97/4.18 (r(s(elem!1), s(s(s(s(z)))))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[1084, 14758, 12553])).
% 3.97/4.18 tff(14760,plain,
% 3.97/4.18 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 3.97/4.18 inference(monotonicity,[status(thm)],[14735])).
% 3.97/4.18 tff(14761,plain,
% 3.97/4.18 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.97/4.18 inference(symmetry,[status(thm)],[14760])).
% 3.97/4.18 tff(14762,plain,
% 3.97/4.18 (b(elem!1, s(elem!1)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 3.97/4.18 inference(monotonicity,[status(thm)],[14733])).
% 3.97/4.18 tff(14763,plain,
% 3.97/4.18 (b(s(s(s(s(z)))), s(elem!1))),
% 3.97/4.18 inference(modus_ponens,[status(thm)],[14540, 14762])).
% 3.97/4.18 tff(14764,plain,
% 3.97/4.18 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.97/4.18 inference(modus_ponens,[status(thm)],[14763, 14761])).
% 3.97/4.18 tff(14765,plain,
% 3.97/4.18 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[14130, 14726, 5619, 3261, 103])).
% 3.97/4.18 tff(14766,plain,
% 3.97/4.18 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[249, 14765])).
% 3.97/4.18 tff(14767,plain,
% 3.97/4.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.97/4.18 inference(rewrite,[status(thm)],[])).
% 3.97/4.18 tff(14768,plain,
% 3.97/4.18 (((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(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(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.97/4.18 inference(rewrite,[status(thm)],[])).
% 3.97/4.18 tff(14769,plain,
% 3.97/4.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 3.97/4.18 inference(monotonicity,[status(thm)],[14768])).
% 3.97/4.18 tff(14770,plain,
% 3.97/4.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.97/4.18 inference(transitivity,[status(thm)],[14769, 14767])).
% 3.97/4.18 tff(14771,plain,
% 3.97/4.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.97/4.18 inference(quant_inst,[status(thm)],[])).
% 3.97/4.18 tff(14772,plain,
% 3.97/4.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 3.97/4.18 inference(modus_ponens,[status(thm)],[14771, 14770])).
% 3.97/4.18 tff(14773,plain,
% 3.97/4.18 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[14772, 178, 14766, 14726, 14764, 14752])).
% 3.97/4.18 tff(14774,plain,
% 3.97/4.18 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[84, 14773])).
% 3.97/4.18 tff(14775,plain,
% 3.97/4.18 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[5568, 14774, 14759])).
% 3.97/4.18 tff(14776,plain,
% 3.97/4.18 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[395, 14775, 14757])).
% 3.97/4.18 tff(14777,plain,
% 3.97/4.18 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.18 inference(modus_ponens,[status(thm)],[14776, 14753])).
% 3.97/4.18 tff(14778,plain,
% 3.97/4.18 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 3.97/4.18 inference(monotonicity,[status(thm)],[14734])).
% 3.97/4.18 tff(14779,plain,
% 3.97/4.18 (b(s(s(s(s(s(z))))), s(s(z)))),
% 3.97/4.18 inference(modus_ponens,[status(thm)],[12546, 14778])).
% 3.97/4.18 tff(14780,plain,
% 3.97/4.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), 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(z))))), s(s(z)))) | (~b(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), 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(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 3.97/4.18 inference(rewrite,[status(thm)],[])).
% 3.97/4.18 tff(14781,plain,
% 3.97/4.18 (((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), 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(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 3.97/4.18 inference(rewrite,[status(thm)],[])).
% 3.97/4.18 tff(14782,plain,
% 3.97/4.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), 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(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 3.97/4.18 inference(monotonicity,[status(thm)],[14781])).
% 3.97/4.18 tff(14783,plain,
% 3.97/4.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), 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(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 3.97/4.18 inference(transitivity,[status(thm)],[14782, 14780])).
% 3.97/4.18 tff(14784,plain,
% 3.97/4.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 3.97/4.18 inference(quant_inst,[status(thm)],[])).
% 3.97/4.18 tff(14785,plain,
% 3.97/4.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 3.97/4.18 inference(modus_ponens,[status(thm)],[14784, 14783])).
% 3.97/4.18 tff(14786,plain,
% 3.97/4.18 ($false),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[14785, 178, 14766, 14779, 14545, 14777, 14752])).
% 3.97/4.18 tff(14787,plain,(b(s(elem!1), z) | (s(s(z)) = elem!1) | (~r(z, s(s(z)))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 3.97/4.18 tff(14788,plain,
% 3.97/4.18 (b(s(elem!1), z)),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[14787, 3261, 12, 86, 5618])).
% 3.97/4.18 tff(14789,plain,
% 3.97/4.18 (~b(elem!1, s(s(z)))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[14093, 105, 12566, 11751, 11753, 3261, 1369, 853, 5618])).
% 3.97/4.18 tff(14790,plain,
% 3.97/4.18 (r(elem!1, s(s(z)))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[467, 14789, 312])).
% 3.97/4.18 tff(14791,plain,
% 3.97/4.18 (~r(elem!1, s(s(s(s(z)))))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[3785, 14790, 193])).
% 3.97/4.18 tff(14792,plain,
% 3.97/4.18 (b(elem!1, z)),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[14535, 3261, 5618, 1369, 193, 12])).
% 3.97/4.18 tff(14793,plain,
% 3.97/4.18 (~(z = elem!1)),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[6991, 14792])).
% 3.97/4.18 tff(14794,plain,
% 3.97/4.18 (~r(z, elem!1)),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[4862, 14790, 3261])).
% 3.97/4.18 tff(14795,plain,
% 3.97/4.18 (b(z, elem!1)),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[585, 14794, 14793])).
% 3.97/4.18 tff(14796,plain,
% 3.97/4.18 ((~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z))))))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[12519, 178, 14792, 11751, 11753])).
% 3.97/4.18 tff(14797,plain,
% 3.97/4.18 (~b(elem!1, s(s(s(s(z)))))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[14796, 14795])).
% 3.97/4.18 tff(14798,plain,
% 3.97/4.18 (elem!1 = s(s(s(s(z))))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[483, 14797, 14791])).
% 3.97/4.18 tff(14799,plain,
% 3.97/4.18 (s(elem!1) = s(s(s(s(s(z)))))),
% 3.97/4.18 inference(monotonicity,[status(thm)],[14798])).
% 3.97/4.18 tff(14800,plain,
% 3.97/4.18 (b(s(elem!1), z) <=> b(s(s(s(s(s(z))))), z)),
% 3.97/4.18 inference(monotonicity,[status(thm)],[14799])).
% 3.97/4.18 tff(14801,plain,
% 3.97/4.18 (b(s(s(s(s(s(z))))), z) <=> b(s(elem!1), z)),
% 3.97/4.18 inference(symmetry,[status(thm)],[14800])).
% 3.97/4.18 tff(14802,plain,
% 3.97/4.18 ((~b(s(s(s(s(s(z))))), z)) <=> (~b(s(elem!1), z))),
% 3.97/4.18 inference(monotonicity,[status(thm)],[14801])).
% 3.97/4.18 tff(14803,plain,
% 3.97/4.18 (s(s(s(s(z)))) = elem!1),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[325, 14798])).
% 3.97/4.18 tff(14804,plain,
% 3.97/4.18 (~(s(s(elem!1)) = elem!1)),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[338, 14803, 12])).
% 3.97/4.18 tff(14805,plain,
% 3.97/4.18 (~(s(elem!1) = elem!1)),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[672, 14804])).
% 3.97/4.18 tff(14806,plain,
% 3.97/4.18 (b(elem!1, s(elem!1))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[13675, 105, 1369, 3261, 11751, 5618])).
% 3.97/4.18 tff(14807,plain,
% 3.97/4.18 (~b(z, s(elem!1))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[863, 14795, 14792, 853, 14806])).
% 3.97/4.18 tff(14808,plain,
% 3.97/4.18 (r(z, s(elem!1))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[2351, 14807])).
% 3.97/4.18 tff(14809,plain,
% 3.97/4.18 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[348, 14804])).
% 3.97/4.18 tff(14810,plain,
% 3.97/4.18 (~r(s(s(z)), s(elem!1))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[12114, 14808, 3261])).
% 3.97/4.18 tff(14811,plain,
% 3.97/4.18 (b(s(s(z)), s(elem!1))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[2879, 14810, 12566])).
% 3.97/4.18 tff(14812,plain,
% 3.97/4.18 (b(s(s(z)), s(s(s(s(s(z))))))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[2330, 14811, 14798])).
% 3.97/4.18 tff(14813,plain,
% 3.97/4.18 (~b(s(s(s(s(s(z))))), z)),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[13394, 14812, 5619, 10794, 3261, 14809, 14808, 11751, 11753, 14798, 14805])).
% 3.97/4.18 tff(14814,plain,
% 3.97/4.18 (~b(s(elem!1), z)),
% 3.97/4.18 inference(modus_ponens,[status(thm)],[14813, 14802])).
% 3.97/4.18 tff(14815,plain,
% 3.97/4.18 ($false),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[853, 14814])).
% 3.97/4.18 tff(14816,plain,(b(s(s(z)), s(s(s(s(z))))) | (~b(s(elem!1), z)) | (~r(z, s(s(z)))) | (s(s(z)) = elem!1) | (~r(s(s(s(s(z)))), s(s(z)))) | (s(elem!1) = s(s(s(s(z))))) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 3.97/4.18 tff(14817,plain,
% 3.97/4.18 (b(s(s(z)), s(s(s(s(z)))))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[14816, 14788, 3261, 12, 103, 12553, 5618])).
% 3.97/4.18 tff(14818,plain,
% 3.97/4.18 (~b(elem!1, s(s(z)))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[12506, 178, 14536, 5619, 14539, 14817])).
% 3.97/4.18 tff(14819,plain,
% 3.97/4.18 (r(elem!1, s(s(z)))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[467, 14818, 312])).
% 3.97/4.18 tff(14820,plain,
% 3.97/4.18 (~r(elem!1, s(s(s(s(z)))))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[3785, 14819, 103])).
% 3.97/4.18 tff(14821,plain,
% 3.97/4.18 (~r(z, elem!1)),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[4862, 14819, 3261])).
% 3.97/4.18 tff(14822,plain,
% 3.97/4.18 (b(z, elem!1)),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[585, 14821, 14541])).
% 3.97/4.18 tff(14823,plain,
% 3.97/4.18 (~b(elem!1, s(s(s(s(z)))))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[14660, 14822])).
% 3.97/4.18 tff(14824,plain,
% 3.97/4.18 (elem!1 = s(s(s(s(z))))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[483, 14823, 14820])).
% 3.97/4.18 tff(14825,plain,
% 3.97/4.18 (s(elem!1) = s(s(s(s(s(z)))))),
% 3.97/4.18 inference(monotonicity,[status(thm)],[14824])).
% 3.97/4.18 tff(14826,plain,
% 3.97/4.18 (s(s(s(s(s(z))))) = s(elem!1)),
% 3.97/4.18 inference(symmetry,[status(thm)],[14825])).
% 3.97/4.18 tff(14827,plain,
% 3.97/4.18 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 3.97/4.18 inference(monotonicity,[status(thm)],[14825])).
% 3.97/4.18 tff(14828,plain,
% 3.97/4.18 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 3.97/4.18 inference(monotonicity,[status(thm)],[14827])).
% 3.97/4.18 tff(14829,plain,
% 3.97/4.18 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 3.97/4.18 inference(symmetry,[status(thm)],[14828])).
% 3.97/4.18 tff(14830,plain,
% 3.97/4.18 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 3.97/4.18 inference(monotonicity,[status(thm)],[14829, 14826])).
% 3.97/4.18 tff(14831,plain,
% 3.97/4.18 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.97/4.18 inference(symmetry,[status(thm)],[14830])).
% 3.97/4.18 tff(14832,plain,
% 3.97/4.18 (s(s(s(s(z)))) = elem!1),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[325, 14824])).
% 3.97/4.18 tff(14833,plain,
% 3.97/4.18 (~(s(s(elem!1)) = elem!1)),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[338, 14832, 12])).
% 3.97/4.18 tff(14834,plain,
% 3.97/4.18 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[348, 14833])).
% 3.97/4.18 tff(14835,plain,
% 3.97/4.18 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(s(s(z)))))),
% 3.97/4.18 inference(monotonicity,[status(thm)],[14824])).
% 3.97/4.18 tff(14836,plain,
% 3.97/4.18 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(elem!1), elem!1)),
% 3.97/4.18 inference(symmetry,[status(thm)],[14835])).
% 3.97/4.18 tff(14837,plain,
% 3.97/4.18 (~b(s(elem!1), s(s(s(s(z)))))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[14354, 14817, 5619, 14646, 12546])).
% 3.97/4.18 tff(14838,plain,
% 3.97/4.18 (r(s(elem!1), s(s(s(s(z)))))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[1084, 14837, 12553])).
% 3.97/4.18 tff(14839,plain,
% 3.97/4.18 (r(s(elem!1), elem!1)),
% 3.97/4.18 inference(modus_ponens,[status(thm)],[14838, 14836])).
% 3.97/4.18 tff(14840,plain,
% 3.97/4.18 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.97/4.18 inference(monotonicity,[status(thm)],[14824])).
% 3.97/4.18 tff(14841,plain,
% 3.97/4.18 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), elem!1)),
% 3.97/4.18 inference(symmetry,[status(thm)],[14840])).
% 3.97/4.18 tff(14842,plain,
% 3.97/4.18 (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)))))),
% 3.97/4.18 inference(monotonicity,[status(thm)],[14828])).
% 3.97/4.18 tff(14843,plain,
% 3.97/4.18 (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)))))),
% 3.97/4.18 inference(symmetry,[status(thm)],[14842])).
% 3.97/4.18 tff(14844,plain,
% 3.97/4.18 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), elem!1)),
% 3.97/4.18 inference(transitivity,[status(thm)],[14843, 14841])).
% 3.97/4.18 tff(14845,plain,
% 3.97/4.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(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)))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(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)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 3.97/4.18 inference(rewrite,[status(thm)],[])).
% 3.97/4.18 tff(14846,plain,
% 3.97/4.18 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(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(s(z))))))), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(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)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 3.97/4.18 inference(rewrite,[status(thm)],[])).
% 3.97/4.18 tff(14847,plain,
% 3.97/4.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(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(z)), s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(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)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))))),
% 3.97/4.18 inference(monotonicity,[status(thm)],[14846])).
% 3.97/4.18 tff(14848,plain,
% 3.97/4.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(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(z)), s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(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)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 3.97/4.18 inference(transitivity,[status(thm)],[14847, 14845])).
% 3.97/4.18 tff(14849,plain,
% 3.97/4.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 3.97/4.18 inference(quant_inst,[status(thm)],[])).
% 3.97/4.18 tff(14850,plain,
% 3.97/4.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 3.97/4.18 inference(modus_ponens,[status(thm)],[14849, 14848])).
% 3.97/4.18 tff(14851,plain,
% 3.97/4.18 ($false),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[14850, 178, 3461, 104, 168, 167, 1146])).
% 3.97/4.18 tff(14852,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.97/4.18 tff(14853,plain,
% 3.97/4.18 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[14852, 14646, 5619, 14817, 14545])).
% 3.97/4.18 tff(14854,plain,
% 3.97/4.18 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[84, 14853])).
% 3.97/4.18 tff(14855,plain,
% 3.97/4.18 (r(s(s(s(elem!1))), elem!1)),
% 3.97/4.18 inference(modus_ponens,[status(thm)],[14854, 14844])).
% 3.97/4.18 tff(14856,plain,
% 3.97/4.18 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[1576, 14855, 14839])).
% 3.97/4.18 tff(14857,plain,
% 3.97/4.18 (b(s(s(s(elem!1))), s(elem!1))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[373, 14856, 14834])).
% 3.97/4.18 tff(14858,plain,
% 3.97/4.18 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.97/4.18 inference(modus_ponens,[status(thm)],[14857, 14831])).
% 3.97/4.18 tff(14859,plain,
% 3.97/4.18 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.18 inference(monotonicity,[status(thm)],[14825])).
% 3.97/4.18 tff(14860,plain,
% 3.97/4.18 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.97/4.18 inference(monotonicity,[status(thm)],[14828])).
% 3.97/4.18 tff(14861,plain,
% 3.97/4.18 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.97/4.18 inference(transitivity,[status(thm)],[14860, 377])).
% 3.97/4.18 tff(14862,plain,
% 3.97/4.18 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 3.97/4.18 inference(monotonicity,[status(thm)],[14861])).
% 3.97/4.18 tff(14863,plain,
% 3.97/4.18 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.97/4.18 inference(modus_ponens,[status(thm)],[14834, 14862])).
% 3.97/4.18 tff(14864,plain,
% 3.97/4.18 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[5568, 14854, 14838])).
% 3.97/4.18 tff(14865,plain,
% 3.97/4.18 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[395, 14864, 14863])).
% 3.97/4.18 tff(14866,plain,
% 3.97/4.18 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.18 inference(modus_ponens,[status(thm)],[14865, 14859])).
% 3.97/4.18 tff(14867,plain,
% 3.97/4.18 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 3.97/4.18 inference(monotonicity,[status(thm)],[14825])).
% 3.97/4.18 tff(14868,plain,
% 3.97/4.18 (b(s(s(s(s(s(z))))), s(s(z)))),
% 3.97/4.18 inference(modus_ponens,[status(thm)],[12546, 14867])).
% 3.97/4.18 tff(14869,plain,
% 3.97/4.18 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[14130, 14817, 5619, 3261, 103])).
% 3.97/4.18 tff(14870,plain,
% 3.97/4.18 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[249, 14869])).
% 3.97/4.18 tff(14871,plain,
% 3.97/4.18 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[14785, 178, 14870, 14868, 14545, 14866])).
% 3.97/4.18 tff(14872,plain,
% 3.97/4.18 ($false),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[14871, 14858])).
% 3.97/4.18 tff(14873,plain,((~r(z, s(s(z)))) | (s(s(z)) = elem!1) | r(s(s(z)), z) | b(s(s(s(s(z)))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.97/4.18 tff(14874,plain,
% 3.97/4.18 (~r(z, s(s(z)))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[14873, 86, 5618, 12])).
% 3.97/4.18 tff(14875,plain,
% 3.97/4.18 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[3488, 47, 5619, 147])).
% 3.97/4.18 tff(14876,plain,
% 3.97/4.18 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[84, 14875])).
% 3.97/4.18 tff(14877,plain,
% 3.97/4.18 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[2840, 13677])).
% 3.97/4.18 tff(14878,plain,
% 3.97/4.18 (r(s(elem!1), s(s(z)))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[421, 13677, 305])).
% 3.97/4.18 tff(14879,plain,
% 3.97/4.18 (~r(s(elem!1), s(s(s(s(z)))))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[3949, 14878, 103])).
% 3.97/4.18 tff(14880,plain,
% 3.97/4.18 (b(s(elem!1), s(s(s(s(z)))))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[1084, 14879, 1369])).
% 3.97/4.18 tff(14881,plain,
% 3.97/4.18 (b(z, s(s(z)))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[143, 14874])).
% 3.97/4.18 tff(14882,plain,
% 3.97/4.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 3.97/4.18 inference(rewrite,[status(thm)],[])).
% 3.97/4.18 tff(14883,plain,
% 3.97/4.18 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 3.97/4.18 inference(quant_inst,[status(thm)],[])).
% 3.97/4.18 tff(14884,plain,
% 3.97/4.18 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 3.97/4.18 inference(modus_ponens,[status(thm)],[14883, 14882])).
% 3.97/4.18 tff(14885,plain,
% 3.97/4.18 (~r(s(s(s(s(z)))), s(elem!1))),
% 3.97/4.18 inference(unit_resolution,[status(thm)],[14884, 118, 363, 103])).
% 3.97/4.19 tff(14886,plain,
% 3.97/4.19 (b(s(s(s(s(z)))), s(elem!1))),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[2173, 14885, 2508])).
% 3.97/4.19 tff(14887,plain,
% 3.97/4.19 (r(s(z), s(s(z)))),
% 3.97/4.19 inference(modus_ponens,[status(thm)],[363, 1021])).
% 3.97/4.19 tff(14888,plain,
% 3.97/4.19 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(z), s(s(s(s(z)))))),
% 3.97/4.19 inference(monotonicity,[status(thm)],[929])).
% 3.97/4.19 tff(14889,plain,
% 3.97/4.19 (b(s(z), s(s(s(s(z)))))),
% 3.97/4.19 inference(modus_ponens,[status(thm)],[1069, 14888])).
% 3.97/4.19 tff(14890,plain,
% 3.97/4.19 (b(s(s(s(s(z)))), s(z))),
% 3.97/4.19 inference(modus_ponens,[status(thm)],[8640, 12849])).
% 3.97/4.19 tff(14891,assumption,(b(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 3.97/4.19 tff(14892,plain,
% 3.97/4.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.97/4.19 inference(rewrite,[status(thm)],[])).
% 3.97/4.19 tff(14893,plain,
% 3.97/4.19 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(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(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.97/4.19 inference(rewrite,[status(thm)],[])).
% 3.97/4.19 tff(14894,plain,
% 3.97/4.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 3.97/4.19 inference(monotonicity,[status(thm)],[14893])).
% 3.97/4.19 tff(14895,plain,
% 3.97/4.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.97/4.19 inference(transitivity,[status(thm)],[14894, 14892])).
% 3.97/4.19 tff(14896,plain,
% 3.97/4.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.97/4.19 inference(quant_inst,[status(thm)],[])).
% 3.97/4.19 tff(14897,plain,
% 3.97/4.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 3.97/4.19 inference(modus_ponens,[status(thm)],[14896, 14895])).
% 3.97/4.19 tff(14898,plain,
% 3.97/4.19 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[14897, 178, 104, 1789, 14891])).
% 3.97/4.19 tff(14899,plain,
% 3.97/4.19 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[14898, 3922])).
% 3.97/4.19 tff(14900,plain,
% 3.97/4.19 ($false),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[615, 41, 612, 2641, 14899])).
% 3.97/4.19 tff(14901,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.97/4.19 tff(14902,plain,
% 3.97/4.19 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[14901, 14890, 104, 14889, 193, 14887])).
% 3.97/4.19 tff(14903,plain,
% 3.97/4.19 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[3578, 14902])).
% 3.97/4.19 tff(14904,plain,
% 3.97/4.19 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[390, 224, 363])).
% 3.97/4.19 tff(14905,plain,
% 3.97/4.19 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[395, 14904, 2286])).
% 3.97/4.19 tff(14906,plain,
% 3.97/4.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 3.97/4.19 inference(rewrite,[status(thm)],[])).
% 3.97/4.19 tff(14907,plain,
% 3.97/4.19 (((~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(elem!1), 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(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(elem!1)))) <=> ((~b(s(s(s(s(s(s(s(z))))))), 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(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 3.97/4.19 inference(rewrite,[status(thm)],[])).
% 3.97/4.19 tff(14908,plain,
% 3.97/4.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~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(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(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 3.97/4.19 inference(monotonicity,[status(thm)],[14907])).
% 3.97/4.19 tff(14909,plain,
% 3.97/4.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~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(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(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 3.97/4.19 inference(transitivity,[status(thm)],[14908, 14906])).
% 3.97/4.19 tff(14910,plain,
% 3.97/4.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~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(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(z)))), s(elem!1))))),
% 3.97/4.19 inference(quant_inst,[status(thm)],[])).
% 3.97/4.19 tff(14911,plain,
% 3.97/4.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 3.97/4.19 inference(modus_ponens,[status(thm)],[14910, 14909])).
% 3.97/4.19 tff(14912,plain,
% 3.97/4.19 ($false),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[14911, 178, 104, 8640, 1069, 14905, 14122])).
% 3.97/4.19 tff(14913,plain,((~r(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(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.97/4.19 tff(14914,plain,
% 3.97/4.19 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[14913, 14147, 8640, 1069, 104, 363, 193])).
% 3.97/4.19 tff(14915,plain,
% 3.97/4.19 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[249, 14914])).
% 3.97/4.19 tff(14916,plain,
% 3.97/4.19 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[4055, 178, 3461, 273, 14915, 14903])).
% 3.97/4.19 tff(14917,plain,
% 3.97/4.19 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[133, 14916])).
% 3.97/4.19 tff(14918,plain,
% 3.97/4.19 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.97/4.19 inference(rewrite,[status(thm)],[])).
% 3.97/4.19 tff(14919,plain,
% 3.97/4.19 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.97/4.19 inference(rewrite,[status(thm)],[])).
% 3.97/4.19 tff(14920,plain,
% 3.97/4.19 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 3.97/4.19 inference(monotonicity,[status(thm)],[14919])).
% 3.97/4.19 tff(14921,plain,
% 3.97/4.19 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.97/4.19 inference(transitivity,[status(thm)],[14920, 14918])).
% 3.97/4.19 tff(14922,plain,
% 3.97/4.19 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 3.97/4.19 inference(quant_inst,[status(thm)],[])).
% 3.97/4.19 tff(14923,plain,
% 3.97/4.19 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 3.97/4.19 inference(modus_ponens,[status(thm)],[14922, 14921])).
% 3.97/4.19 tff(14924,plain,
% 3.97/4.19 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[14923, 118, 194, 14917])).
% 3.97/4.19 tff(14925,plain,
% 3.97/4.19 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[222, 14924])).
% 3.97/4.19 tff(14926,plain,
% 3.97/4.19 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[14897, 178, 104, 14890, 14889])).
% 3.97/4.19 tff(14927,plain,
% 3.97/4.19 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[14926, 14925])).
% 3.97/4.19 tff(14928,plain,
% 3.97/4.19 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[615, 41, 612, 14927])).
% 3.97/4.19 tff(14929,plain,
% 3.97/4.19 ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[14138, 118, 14917])).
% 3.97/4.19 tff(14930,plain,
% 3.97/4.19 ($false),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[14929, 14928, 14135])).
% 3.97/4.19 tff(14931,plain,((~(elem!1 = z)) | (~r(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.97/4.19 tff(14932,plain,
% 3.97/4.19 (~(elem!1 = z)),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[14931, 194, 104, 844, 3461, 273, 103, 14886, 1069, 363])).
% 3.97/4.19 tff(14933,plain,
% 3.97/4.19 (r(elem!1, z)),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[498, 14932, 5723])).
% 3.97/4.19 tff(14934,plain,
% 3.97/4.19 (~r(s(s(s(s(z)))), elem!1)),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[6033, 437, 194])).
% 3.97/4.19 tff(14935,plain,
% 3.97/4.19 (~r(s(elem!1), elem!1)),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[13694, 437, 844])).
% 3.97/4.19 tff(14936,plain,
% 3.97/4.19 (~r(elem!1, s(elem!1))),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[2711, 437, 844])).
% 3.97/4.19 tff(14937,plain,
% 3.97/4.19 (~r(s(s(s(s(z)))), s(elem!1))),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[14884, 118, 363, 193])).
% 3.97/4.19 tff(14938,plain,
% 3.97/4.19 (b(s(s(s(s(z)))), s(elem!1))),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[2173, 14937, 2508])).
% 3.97/4.19 tff(14939,plain,
% 3.97/4.19 (~b(elem!1, s(elem!1))),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[8646, 178, 8546, 14938, 8545, 1069])).
% 3.97/4.19 tff(14940,plain,
% 3.97/4.19 (elem!1 = s(elem!1)),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[756, 14939, 744])).
% 3.97/4.19 tff(14941,plain,
% 3.97/4.19 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.97/4.19 inference(monotonicity,[status(thm)],[14940])).
% 3.97/4.19 tff(14942,plain,
% 3.97/4.19 (r(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.97/4.19 inference(symmetry,[status(thm)],[14941])).
% 3.97/4.19 tff(14943,plain,
% 3.97/4.19 ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) <=> (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 3.97/4.19 inference(monotonicity,[status(thm)],[14942])).
% 3.97/4.19 tff(14944,plain,
% 3.97/4.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 3.97/4.19 inference(rewrite,[status(thm)],[])).
% 3.97/4.19 tff(14945,plain,
% 3.97/4.19 (((~b(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(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 3.97/4.19 inference(rewrite,[status(thm)],[])).
% 3.97/4.19 tff(14946,plain,
% 3.97/4.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 3.97/4.19 inference(monotonicity,[status(thm)],[14945])).
% 3.97/4.19 tff(14947,plain,
% 3.97/4.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 3.97/4.19 inference(transitivity,[status(thm)],[14946, 14944])).
% 3.97/4.19 tff(14948,plain,
% 3.97/4.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 3.97/4.19 inference(quant_inst,[status(thm)],[])).
% 3.97/4.19 tff(14949,plain,
% 3.97/4.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 3.97/4.19 inference(modus_ponens,[status(thm)],[14948, 14947])).
% 3.97/4.19 tff(14950,plain,
% 3.97/4.19 (~b(s(elem!1), elem!1)),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[14949, 178, 8546, 14938, 8545, 1069])).
% 3.97/4.19 tff(14951,plain,
% 3.97/4.19 (s(elem!1) = elem!1),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[677, 14950, 724])).
% 3.97/4.19 tff(14952,plain,
% 3.97/4.19 (s(s(elem!1)) = elem!1),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[672, 14951])).
% 3.97/4.19 tff(14953,plain,
% 3.97/4.19 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[2510, 14952, 2508])).
% 3.97/4.19 tff(14954,plain,
% 3.97/4.19 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[703, 14953])).
% 3.97/4.19 tff(14955,plain,
% 3.97/4.19 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[3933, 14940, 14954, 104, 8546, 8545, 193, 363])).
% 3.97/4.19 tff(14956,plain,
% 3.97/4.19 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[3578, 14955])).
% 3.97/4.19 tff(14957,plain,
% 3.97/4.19 ((elem!1 = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.97/4.19 inference(monotonicity,[status(thm)],[14940])).
% 3.97/4.19 tff(14958,plain,
% 3.97/4.19 ((~(elem!1 = s(s(s(s(s(s(s(z))))))))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 3.97/4.19 inference(monotonicity,[status(thm)],[14957])).
% 3.97/4.19 tff(14959,plain,
% 3.97/4.19 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.97/4.19 inference(modus_ponens,[status(thm)],[14953, 14958])).
% 3.97/4.19 tff(14960,plain,
% 3.97/4.19 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[14913, 14959, 14938, 1069, 104, 363, 193])).
% 3.97/4.19 tff(14961,plain,
% 3.97/4.19 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[249, 14960])).
% 3.97/4.19 tff(14962,plain,
% 3.97/4.19 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[4055, 178, 3461, 273, 14961, 14956])).
% 3.97/4.19 tff(14963,plain,
% 3.97/4.19 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[133, 14962])).
% 3.97/4.19 tff(14964,plain,
% 3.97/4.19 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 3.97/4.19 inference(rewrite,[status(thm)],[])).
% 3.97/4.19 tff(14965,plain,
% 3.97/4.19 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 3.97/4.19 inference(quant_inst,[status(thm)],[])).
% 3.97/4.19 tff(14966,plain,
% 3.97/4.19 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 3.97/4.19 inference(modus_ponens,[status(thm)],[14965, 14964])).
% 3.97/4.19 tff(14967,plain,
% 3.97/4.19 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[14966, 118, 844, 14963])).
% 3.97/4.19 tff(14968,plain,
% 3.97/4.19 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.97/4.19 inference(modus_ponens,[status(thm)],[14967, 14943])).
% 3.97/4.19 tff(14969,plain,
% 3.97/4.19 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[14923, 118, 194, 14963])).
% 3.97/4.19 tff(14970,plain,
% 3.97/4.19 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[222, 14969])).
% 3.97/4.19 tff(14971,plain,
% 3.97/4.19 ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[3928, 178, 104, 8546, 8545])).
% 3.97/4.19 tff(14972,plain,
% 3.97/4.19 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[14971, 14970])).
% 3.97/4.19 tff(14973,plain,
% 3.97/4.19 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[3444, 14972, 14954])).
% 3.97/4.19 tff(14974,plain,
% 3.97/4.19 ($false),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[14973, 14968])).
% 3.97/4.19 tff(14975,plain,((elem!1 = s(s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(elem!1)) | r(s(elem!1), elem!1) | r(elem!1, s(elem!1)) | r(s(s(s(s(z)))), elem!1) | r(elem!1, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.97/4.19 tff(14976,plain,
% 3.97/4.19 ($false),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[14975, 14936, 14935, 194, 844, 3461, 273, 193, 363, 1069, 2508, 104, 469, 14934, 479])).
% 3.97/4.19 tff(14977,plain,((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (elem!1 = s(s(s(s(z))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.97/4.19 tff(14978,plain,
% 3.97/4.19 (elem!1 = s(s(s(s(z))))),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[14977, 14933, 844, 3461, 273, 103, 363, 1069, 2508, 104, 194, 47])).
% 3.97/4.19 tff(14979,plain,
% 3.97/4.19 (b(elem!1, s(s(z))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 3.97/4.19 inference(monotonicity,[status(thm)],[14978])).
% 3.97/4.19 tff(14980,plain,
% 3.97/4.19 (b(s(s(s(s(z)))), s(s(z))) <=> b(elem!1, s(s(z)))),
% 3.97/4.19 inference(symmetry,[status(thm)],[14979])).
% 3.97/4.19 tff(14981,plain,
% 3.97/4.19 ((~b(s(s(s(s(z)))), s(s(z)))) <=> (~b(elem!1, s(s(z))))),
% 3.97/4.19 inference(monotonicity,[status(thm)],[14980])).
% 3.97/4.19 tff(14982,plain,
% 3.97/4.19 (~b(elem!1, s(s(z)))),
% 3.97/4.19 inference(modus_ponens,[status(thm)],[86, 14981])).
% 3.97/4.19 tff(14983,plain,
% 3.97/4.19 (~r(elem!1, s(s(s(s(z)))))),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[3785, 14548, 193])).
% 3.97/4.19 tff(14984,plain,
% 3.97/4.19 (~(elem!1 = z)),
% 3.97/4.19 inference(unit_resolution,[status(thm)],[3276, 461, 273])).
% 3.97/4.20 tff(14985,plain,
% 3.97/4.20 (r(elem!1, z)),
% 3.97/4.20 inference(unit_resolution,[status(thm)],[498, 14984, 5723])).
% 3.97/4.20 tff(14986,plain,
% 3.97/4.20 (~r(s(s(s(s(z)))), elem!1)),
% 3.97/4.20 inference(unit_resolution,[status(thm)],[6033, 14985, 194])).
% 3.97/4.20 tff(14987,plain,
% 3.97/4.20 (~r(elem!1, s(elem!1))),
% 3.97/4.20 inference(unit_resolution,[status(thm)],[2711, 14985, 844])).
% 3.97/4.20 tff(14988,plain,
% 3.97/4.20 (~r(s(elem!1), elem!1)),
% 3.97/4.20 inference(unit_resolution,[status(thm)],[13694, 14985, 844])).
% 3.97/4.20 tff(14989,plain,
% 3.97/4.20 (elem!1 = s(s(s(s(z))))),
% 3.97/4.20 inference(unit_resolution,[status(thm)],[14975, 14988, 194, 844, 3461, 273, 193, 363, 1069, 2508, 104, 14987, 14986, 14983])).
% 3.97/4.20 tff(14990,plain,
% 3.97/4.20 (s(elem!1) = s(s(s(s(s(z)))))),
% 3.97/4.20 inference(monotonicity,[status(thm)],[14989])).
% 3.97/4.20 tff(14991,plain,
% 3.97/4.20 (s(s(s(s(s(z))))) = s(elem!1)),
% 3.97/4.20 inference(symmetry,[status(thm)],[14990])).
% 3.97/4.20 tff(14992,plain,
% 3.97/4.20 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.20 inference(monotonicity,[status(thm)],[14991])).
% 3.97/4.20 tff(14993,plain,
% 3.97/4.20 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.20 inference(symmetry,[status(thm)],[14992])).
% 3.97/4.20 tff(14994,plain,
% 3.97/4.20 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 3.97/4.20 inference(monotonicity,[status(thm)],[14990])).
% 3.97/4.20 tff(14995,plain,
% 3.97/4.20 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 3.97/4.20 inference(monotonicity,[status(thm)],[14994])).
% 3.97/4.20 tff(14996,plain,
% 3.97/4.20 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 3.97/4.20 inference(monotonicity,[status(thm)],[14995])).
% 3.97/4.20 tff(14997,plain,
% 3.97/4.20 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.97/4.20 inference(transitivity,[status(thm)],[14996, 377])).
% 3.97/4.20 tff(14998,plain,
% 3.97/4.20 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 3.97/4.20 inference(monotonicity,[status(thm)],[14997])).
% 3.97/4.20 tff(14999,plain,
% 3.97/4.20 (s(s(s(s(z)))) = elem!1),
% 3.97/4.20 inference(unit_resolution,[status(thm)],[325, 14989])).
% 3.97/4.20 tff(15000,plain,
% 3.97/4.20 (~(s(s(elem!1)) = elem!1)),
% 3.97/4.20 inference(unit_resolution,[status(thm)],[338, 14999, 12])).
% 3.97/4.20 tff(15001,plain,
% 3.97/4.20 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.97/4.20 inference(unit_resolution,[status(thm)],[348, 15000])).
% 3.97/4.20 tff(15002,plain,
% 3.97/4.20 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 3.97/4.20 inference(modus_ponens,[status(thm)],[15001, 14998])).
% 3.97/4.20 tff(15003,plain,
% 3.97/4.20 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.20 inference(monotonicity,[status(thm)],[14990])).
% 3.97/4.20 tff(15004,plain,
% 3.97/4.20 (b(s(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))))))))),
% 3.97/4.20 inference(symmetry,[status(thm)],[15003])).
% 3.97/4.20 tff(15005,plain,
% 3.97/4.20 ((~b(s(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)))))))))),
% 3.97/4.20 inference(monotonicity,[status(thm)],[15004])).
% 3.97/4.20 tff(15006,plain,
% 3.97/4.20 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 3.97/4.20 inference(monotonicity,[status(thm)],[14991])).
% 3.97/4.20 tff(15007,plain,
% 3.97/4.20 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.97/4.20 inference(symmetry,[status(thm)],[15006])).
% 3.97/4.20 tff(15008,plain,
% 3.97/4.20 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.97/4.20 inference(modus_ponens,[status(thm)],[14938, 15007])).
% 3.97/4.20 tff(15009,plain,
% 3.97/4.20 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 3.97/4.20 inference(monotonicity,[status(thm)],[14991])).
% 3.97/4.20 tff(15010,plain,
% 3.97/4.20 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.97/4.20 inference(symmetry,[status(thm)],[15009])).
% 3.97/4.20 tff(15011,plain,
% 3.97/4.20 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.97/4.20 inference(modus_ponens,[status(thm)],[1069, 15010])).
% 3.97/4.20 tff(15012,plain,
% 3.97/4.20 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.20 inference(monotonicity,[status(thm)],[14995])).
% 3.97/4.20 tff(15013,plain,
% 3.97/4.20 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.97/4.20 inference(monotonicity,[status(thm)],[14989])).
% 3.97/4.20 tff(15014,plain,
% 3.97/4.20 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 3.97/4.20 inference(transitivity,[status(thm)],[15013, 15012])).
% 3.97/4.20 tff(15015,plain,
% 3.97/4.20 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.04/4.20 inference(monotonicity,[status(thm)],[14989])).
% 4.04/4.20 tff(15016,plain,
% 4.04/4.20 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = elem!1)),
% 4.04/4.20 inference(symmetry,[status(thm)],[15015])).
% 4.04/4.20 tff(15017,plain,
% 4.04/4.20 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(elem!1))))),
% 4.04/4.20 inference(transitivity,[status(thm)],[15016, 2486])).
% 4.04/4.20 tff(15018,plain,
% 4.04/4.20 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 4.04/4.20 inference(monotonicity,[status(thm)],[15017])).
% 4.04/4.20 tff(15019,plain,
% 4.04/4.20 (~(elem!1 = s(s(s(elem!1))))),
% 4.04/4.20 inference(modus_ponens,[status(thm)],[2857, 15018])).
% 4.04/4.20 tff(15020,plain,
% 4.04/4.20 (~(z = elem!1)),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[317, 14984])).
% 4.04/4.20 tff(15021,plain,
% 4.04/4.20 (~b(z, elem!1)),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[1846, 14989, 1])).
% 4.04/4.20 tff(15022,plain,
% 4.04/4.20 (r(z, elem!1)),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[585, 15021, 15020])).
% 4.04/4.20 tff(15023,plain,
% 4.04/4.20 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[14913, 15002, 14938, 1069, 104, 363, 193])).
% 4.04/4.20 tff(15024,plain,
% 4.04/4.20 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[249, 15023])).
% 4.04/4.20 tff(15025,plain,
% 4.04/4.20 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(s(s(s(z))))))), z)),
% 4.04/4.20 inference(monotonicity,[status(thm)],[352])).
% 4.04/4.20 tff(15026,plain,
% 4.04/4.20 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.04/4.20 inference(modus_ponens,[status(thm)],[6073, 15025])).
% 4.04/4.20 tff(15027,plain,
% 4.04/4.20 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.04/4.20 inference(modus_ponens,[status(thm)],[10843, 11472])).
% 4.04/4.20 tff(15028,plain,
% 4.04/4.20 ($false),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[3486, 178, 3461, 273, 166, 15027, 15026])).
% 4.04/4.20 tff(15029,plain,((~r(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(s(s(s(z)))))) | (~r(z, elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 4.04/4.20 tff(15030,plain,
% 4.04/4.20 (~r(elem!1, s(s(s(elem!1))))),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[15029, 15024, 273, 3461, 14989, 15022, 14985])).
% 4.04/4.20 tff(15031,plain,
% 4.04/4.20 (b(elem!1, s(s(s(elem!1))))),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[2054, 15030, 15019])).
% 4.04/4.20 tff(15032,plain,
% 4.04/4.20 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.20 inference(modus_ponens,[status(thm)],[15031, 15014])).
% 4.04/4.20 tff(15033,plain,
% 4.04/4.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 4.04/4.20 inference(rewrite,[status(thm)],[])).
% 4.04/4.20 tff(15034,plain,
% 4.04/4.20 (((~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(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(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(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 4.04/4.20 inference(rewrite,[status(thm)],[])).
% 4.04/4.20 tff(15035,plain,
% 4.04/4.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), 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(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 4.04/4.20 inference(monotonicity,[status(thm)],[15034])).
% 4.04/4.20 tff(15036,plain,
% 4.04/4.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), 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(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 4.04/4.20 inference(transitivity,[status(thm)],[15035, 15033])).
% 4.04/4.20 tff(15037,plain,
% 4.04/4.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), 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(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 4.04/4.20 inference(quant_inst,[status(thm)],[])).
% 4.04/4.20 tff(15038,plain,
% 4.04/4.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 4.04/4.20 inference(modus_ponens,[status(thm)],[15037, 15036])).
% 4.04/4.20 tff(15039,plain,
% 4.04/4.20 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[15038, 178, 104, 15032, 15011, 15008])).
% 4.04/4.20 tff(15040,plain,
% 4.04/4.20 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.20 inference(modus_ponens,[status(thm)],[15039, 15005])).
% 4.04/4.20 tff(15041,plain,
% 4.04/4.20 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[395, 15040, 15002])).
% 4.04/4.20 tff(15042,plain,
% 4.04/4.20 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.20 inference(modus_ponens,[status(thm)],[15041, 14993])).
% 4.04/4.20 tff(15043,plain,
% 4.04/4.20 (r(s(elem!1), z) <=> r(s(s(s(s(s(z))))), z)),
% 4.04/4.20 inference(monotonicity,[status(thm)],[14990])).
% 4.04/4.20 tff(15044,plain,
% 4.04/4.20 (r(s(s(s(s(s(z))))), z)),
% 4.04/4.20 inference(modus_ponens,[status(thm)],[844, 15043])).
% 4.04/4.20 tff(15045,plain,
% 4.04/4.20 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[2307, 15040, 305, 14989, 15024, 15002])).
% 4.04/4.20 tff(15046,plain,
% 4.04/4.20 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[3578, 15045])).
% 4.04/4.20 tff(15047,plain,
% 4.04/4.20 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(s(s(s(z))))))), z)),
% 4.04/4.20 inference(monotonicity,[status(thm)],[14995])).
% 4.04/4.20 tff(15048,plain,
% 4.04/4.20 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.04/4.20 inference(monotonicity,[status(thm)],[14995])).
% 4.04/4.20 tff(15049,plain,
% 4.04/4.20 (b(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 4.04/4.20 inference(symmetry,[status(thm)],[15048])).
% 4.04/4.20 tff(15050,plain,
% 4.04/4.20 ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 4.04/4.20 inference(monotonicity,[status(thm)],[15049])).
% 4.04/4.20 tff(15051,plain,
% 4.04/4.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(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(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(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(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 4.04/4.20 inference(rewrite,[status(thm)],[])).
% 4.04/4.20 tff(15052,plain,
% 4.04/4.20 (((~b(s(elem!1), 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(s(s(s(z)))), s(elem!1))) | (~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(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(z)))), 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(elem!1))))),
% 4.04/4.20 inference(rewrite,[status(thm)],[])).
% 4.04/4.20 tff(15053,plain,
% 4.04/4.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(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(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 4.04/4.20 inference(monotonicity,[status(thm)],[15052])).
% 4.04/4.20 tff(15054,plain,
% 4.04/4.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(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(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 4.04/4.20 inference(transitivity,[status(thm)],[15053, 15051])).
% 4.04/4.20 tff(15055,plain,
% 4.04/4.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~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))))))))))),
% 4.04/4.20 inference(quant_inst,[status(thm)],[])).
% 4.04/4.20 tff(15056,plain,
% 4.04/4.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(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(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 4.04/4.20 inference(modus_ponens,[status(thm)],[15055, 15054])).
% 4.04/4.20 tff(15057,plain,
% 4.04/4.20 ((~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)))),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[15056, 178, 104, 14938, 1069])).
% 4.04/4.20 tff(15058,plain,
% 4.04/4.20 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[15057, 15032])).
% 4.04/4.20 tff(15059,plain,
% 4.04/4.20 (~b(s(s(s(elem!1))), s(elem!1))),
% 4.04/4.20 inference(modus_ponens,[status(thm)],[15058, 15050])).
% 4.04/4.20 tff(15060,plain,
% 4.04/4.20 (r(s(s(s(elem!1))), s(elem!1))),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[373, 15059, 15001])).
% 4.04/4.20 tff(15061,plain,
% 4.04/4.20 (~r(s(s(s(elem!1))), z)),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[1557, 15060, 844])).
% 4.04/4.20 tff(15062,plain,
% 4.04/4.20 (b(s(s(s(elem!1))), z)),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[1565, 15061])).
% 4.04/4.20 tff(15063,plain,
% 4.04/4.20 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.04/4.20 inference(modus_ponens,[status(thm)],[15062, 15047])).
% 4.04/4.20 tff(15064,plain,
% 4.04/4.20 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[4091, 178, 3461, 273, 15063, 15046])).
% 4.04/4.20 tff(15065,plain,
% 4.04/4.20 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[271, 15064])).
% 4.04/4.20 tff(15066,plain,
% 4.04/4.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 4.04/4.20 inference(rewrite,[status(thm)],[])).
% 4.04/4.20 tff(15067,plain,
% 4.04/4.20 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 4.04/4.20 inference(rewrite,[status(thm)],[])).
% 4.04/4.20 tff(15068,plain,
% 4.04/4.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 4.04/4.20 inference(monotonicity,[status(thm)],[15067])).
% 4.04/4.20 tff(15069,plain,
% 4.04/4.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 4.04/4.20 inference(transitivity,[status(thm)],[15068, 15066])).
% 4.04/4.20 tff(15070,plain,
% 4.04/4.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), z)))),
% 4.04/4.20 inference(quant_inst,[status(thm)],[])).
% 4.04/4.20 tff(15071,plain,
% 4.04/4.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 4.04/4.20 inference(modus_ponens,[status(thm)],[15070, 15069])).
% 4.04/4.20 tff(15072,plain,
% 4.04/4.20 ($false),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[15071, 118, 15065, 15044, 15042])).
% 4.04/4.20 tff(15073,plain,(b(elem!1, s(s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(s(elem!1), z)) | b(s(elem!1), s(s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (s(s(z)) = elem!1) | b(z, s(s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (s(s(s(s(z)))) = s(elem!1)) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 4.04/4.20 tff(15074,plain,
% 4.04/4.20 (b(elem!1, s(s(z)))),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[15073, 194, 273, 844, 305, 104, 1069, 363, 103, 2857, 12, 1, 3461, 2508, 5723])).
% 4.04/4.20 tff(15075,plain,
% 4.04/4.20 ($false),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[15074, 14982])).
% 4.04/4.20 tff(15076,plain,((~r(s(s(s(s(z)))), z)) | b(s(s(s(s(z)))), s(s(z))) | (~r(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | b(elem!1, z) | b(s(elem!1), s(s(z))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (s(s(z)) = elem!1) | b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.04/4.20 tff(15077,plain,
% 4.04/4.20 (~r(s(s(s(s(z)))), z)),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[15076, 844, 86, 5619, 14881, 14878, 14880, 2169, 104, 5723, 305, 14877, 12, 1])).
% 4.04/4.20 tff(15078,plain,
% 4.04/4.20 (b(s(s(s(s(z)))), z)),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[191, 15077])).
% 4.04/4.20 tff(15079,plain,
% 4.04/4.20 (~(elem!1 = s(s(s(s(z)))))),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[12557, 15078, 5723])).
% 4.04/4.20 tff(15080,plain,
% 4.04/4.20 (~r(s(s(s(s(z)))), s(elem!1))),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[14884, 118, 14878, 103])).
% 4.04/4.20 tff(15081,plain,
% 4.04/4.20 (b(s(s(s(s(z)))), s(elem!1))),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[2173, 15080, 2169])).
% 4.04/4.20 tff(15082,plain,
% 4.04/4.20 (s(s(s(s(s(s(z)))))) = elem!1),
% 4.04/4.20 inference(transitivity,[status(thm)],[609, 658, 304])).
% 4.04/4.20 tff(15083,plain,
% 4.04/4.20 ((s(s(s(s(s(s(z)))))) = z) <=> (elem!1 = z)),
% 4.04/4.20 inference(monotonicity,[status(thm)],[15082])).
% 4.04/4.20 tff(15084,plain,
% 4.04/4.20 ((s(s(s(s(s(s(z)))))) = z) <=> (z = elem!1)),
% 4.04/4.20 inference(transitivity,[status(thm)],[15083, 313])).
% 4.04/4.20 tff(15085,plain,
% 4.04/4.20 ((s(s(s(s(s(s(z)))))) = z) <=> (elem!1 = z)),
% 4.04/4.20 inference(transitivity,[status(thm)],[15084, 314])).
% 4.04/4.20 tff(15086,plain,
% 4.04/4.20 ((~(s(s(s(s(s(s(z)))))) = z)) <=> (~(elem!1 = z))),
% 4.04/4.20 inference(monotonicity,[status(thm)],[15085])).
% 4.04/4.20 tff(15087,plain,
% 4.04/4.20 (~(elem!1 = z)),
% 4.04/4.20 inference(modus_ponens,[status(thm)],[433, 15086])).
% 4.04/4.20 tff(15088,plain,
% 4.04/4.20 (r(elem!1, z)),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[498, 15087, 5723])).
% 4.04/4.20 tff(15089,plain,
% 4.04/4.20 (~r(elem!1, s(s(s(s(z)))))),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[478, 15088, 145])).
% 4.04/4.20 tff(15090,plain,
% 4.04/4.20 (b(elem!1, s(s(s(s(z)))))),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[483, 15089, 469])).
% 4.04/4.20 tff(15091,plain,
% 4.04/4.20 (~(s(s(elem!1)) = elem!1)),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[666, 657, 551])).
% 4.04/4.20 tff(15092,plain,
% 4.04/4.20 (~(s(elem!1) = elem!1)),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[672, 15091])).
% 4.04/4.20 tff(15093,plain,
% 4.04/4.20 (~(elem!1 = s(elem!1))),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[748, 15092])).
% 4.04/4.20 tff(15094,plain,
% 4.04/4.20 (~r(elem!1, s(elem!1))),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[2711, 15088, 844])).
% 4.04/4.20 tff(15095,plain,
% 4.04/4.20 (b(elem!1, s(elem!1))),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[756, 15094, 15093])).
% 4.04/4.20 tff(15096,plain,
% 4.04/4.20 (~r(s(elem!1), elem!1)),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[13694, 15088, 844])).
% 4.04/4.20 tff(15097,plain,
% 4.04/4.20 (b(s(elem!1), elem!1)),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[677, 15096, 15092])).
% 4.04/4.20 tff(15098,plain,
% 4.04/4.20 ($false),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[2180, 178, 15097, 15095, 8640, 15090, 1069])).
% 4.04/4.20 tff(15099,plain,((~(s(s(s(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(z)))))) | (elem!1 = s(s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), z)) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 4.04/4.20 tff(15100,plain,
% 4.04/4.20 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[15099, 15081, 14880, 15079, 47, 844, 5723])).
% 4.04/4.20 tff(15101,plain,
% 4.04/4.20 ((~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)))),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[15056, 178, 104, 8640, 1069])).
% 4.04/4.20 tff(15102,plain,
% 4.04/4.20 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[15101, 3922])).
% 4.04/4.20 tff(15103,plain,
% 4.04/4.20 ($false),
% 4.04/4.20 inference(unit_resolution,[status(thm)],[806, 41, 3912, 4017, 15102])).
% 4.04/4.20 tff(15104,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (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(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(elem!1), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.04/4.20 tff(15105,plain,
% 4.04/4.20 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[15104, 15100, 104, 15081, 14880, 103, 14878])).
% 4.04/4.21 tff(15106,plain,
% 4.04/4.21 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[3578, 15105])).
% 4.04/4.21 tff(15107,plain,
% 4.04/4.21 ((~(s(s(s(s(s(s(s(z))))))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 4.04/4.21 inference(monotonicity,[status(thm)],[377])).
% 4.04/4.21 tff(15108,plain,
% 4.04/4.21 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.04/4.21 inference(modus_ponens,[status(thm)],[15100, 15107])).
% 4.04/4.21 tff(15109,plain,
% 4.04/4.21 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[14913, 15108, 15081, 14880, 104, 14878, 103])).
% 4.04/4.21 tff(15110,plain,
% 4.04/4.21 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[249, 15109])).
% 4.04/4.21 tff(15111,plain,
% 4.04/4.21 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[4055, 178, 5619, 14881, 15110, 15106])).
% 4.04/4.21 tff(15112,plain,
% 4.04/4.21 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[133, 15111])).
% 4.04/4.21 tff(15113,plain,
% 4.04/4.21 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[14966, 118, 844, 15112])).
% 4.04/4.21 tff(15114,plain,
% 4.04/4.21 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[806, 41, 15113, 15100])).
% 4.04/4.21 tff(15115,plain,
% 4.04/4.21 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 4.04/4.21 inference(rewrite,[status(thm)],[])).
% 4.04/4.21 tff(15116,plain,
% 4.04/4.21 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 4.04/4.21 inference(rewrite,[status(thm)],[])).
% 4.04/4.21 tff(15117,plain,
% 4.04/4.21 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))))),
% 4.04/4.21 inference(monotonicity,[status(thm)],[15116])).
% 4.04/4.21 tff(15118,plain,
% 4.04/4.21 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 4.04/4.21 inference(transitivity,[status(thm)],[15117, 15115])).
% 4.04/4.21 tff(15119,plain,
% 4.04/4.21 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 4.04/4.21 inference(quant_inst,[status(thm)],[])).
% 4.04/4.21 tff(15120,plain,
% 4.04/4.21 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 4.04/4.21 inference(modus_ponens,[status(thm)],[15119, 15118])).
% 4.04/4.21 tff(15121,plain,
% 4.04/4.21 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[15120, 118, 844, 15112])).
% 4.04/4.21 tff(15122,plain,
% 4.04/4.21 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[395, 15121, 15108])).
% 4.04/4.21 tff(15123,plain,
% 4.04/4.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(elem!1), 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(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(elem!1), 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(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 4.04/4.21 inference(rewrite,[status(thm)],[])).
% 4.04/4.21 tff(15124,plain,
% 4.04/4.21 (((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), 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(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(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(elem!1), 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(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 4.04/4.21 inference(rewrite,[status(thm)],[])).
% 4.04/4.21 tff(15125,plain,
% 4.04/4.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), 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(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(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(elem!1), 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(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 4.04/4.21 inference(monotonicity,[status(thm)],[15124])).
% 4.04/4.21 tff(15126,plain,
% 4.04/4.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), 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(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(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(elem!1), 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(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 4.04/4.21 inference(transitivity,[status(thm)],[15125, 15123])).
% 4.04/4.21 tff(15127,plain,
% 4.04/4.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), 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(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(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 4.04/4.21 inference(quant_inst,[status(thm)],[])).
% 4.04/4.21 tff(15128,plain,
% 4.04/4.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 4.04/4.21 inference(modus_ponens,[status(thm)],[15127, 15126])).
% 4.04/4.21 tff(15129,plain,
% 4.04/4.21 ($false),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[15128, 178, 104, 15081, 14880, 15122, 15114])).
% 4.04/4.21 tff(15130,plain,((~r(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | b(elem!1, z) | b(s(s(s(s(z)))), s(s(z))) | b(s(elem!1), s(s(z))) | (s(s(z)) = elem!1) | b(z, s(s(s(s(z))))) | (s(elem!1) = s(s(s(s(z))))) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 4.04/4.21 tff(15131,plain,
% 4.04/4.21 (~r(s(elem!1), z)),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[15130, 1369, 5723, 86, 305, 12, 1, 14876, 5618])).
% 4.04/4.21 tff(15132,plain,
% 4.04/4.21 (~r(elem!1, s(s(s(s(z)))))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[478, 12412, 145])).
% 4.04/4.21 tff(15133,plain,
% 4.04/4.21 (b(elem!1, s(s(s(s(z)))))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[483, 15132, 469])).
% 4.04/4.21 tff(15134,plain,
% 4.04/4.21 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[3488, 145, 3461, 147])).
% 4.04/4.21 tff(15135,plain,
% 4.04/4.21 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[84, 15134])).
% 4.04/4.21 tff(15136,plain,
% 4.04/4.21 (r(s(s(z)), s(s(s(elem!1))))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[1838, 515, 147])).
% 4.04/4.21 tff(15137,plain,
% 4.04/4.21 (r(s(elem!1), s(s(s(elem!1))))),
% 4.04/4.21 inference(modus_ponens,[status(thm)],[15136, 2099])).
% 4.04/4.21 tff(15138,plain,
% 4.04/4.21 (~(elem!1 = s(s(elem!1)))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[1539, 1510])).
% 4.04/4.21 tff(15139,plain,
% 4.04/4.21 (~(s(s(elem!1)) = elem!1)),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[1546, 15138])).
% 4.04/4.21 tff(15140,plain,
% 4.04/4.21 (~(s(elem!1) = s(s(elem!1)))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[979, 15139])).
% 4.04/4.21 tff(15141,plain,
% 4.04/4.21 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[11597, 555, 15140, 15137])).
% 4.04/4.21 tff(15142,plain,
% 4.04/4.21 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[3375, 15141, 4681])).
% 4.04/4.21 tff(15143,plain,
% 4.04/4.21 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(s(s(elem!1))))),
% 4.04/4.21 inference(transitivity,[status(thm)],[549, 2486])).
% 4.04/4.21 tff(15144,plain,
% 4.04/4.21 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 4.04/4.21 inference(monotonicity,[status(thm)],[15143])).
% 4.04/4.21 tff(15145,plain,
% 4.04/4.21 (~(elem!1 = s(s(s(elem!1))))),
% 4.04/4.21 inference(modus_ponens,[status(thm)],[551, 15144])).
% 4.04/4.21 tff(15146,plain,
% 4.04/4.21 (~r(elem!1, s(s(s(elem!1))))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[3421, 555, 12412])).
% 4.04/4.21 tff(15147,plain,
% 4.04/4.21 (b(elem!1, s(s(s(elem!1))))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[2054, 15146, 15145])).
% 4.04/4.21 tff(15148,plain,
% 4.04/4.21 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 4.04/4.21 inference(symmetry,[status(thm)],[547])).
% 4.04/4.21 tff(15149,plain,
% 4.04/4.21 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 4.04/4.21 inference(transitivity,[status(thm)],[12391, 15148])).
% 4.04/4.21 tff(15150,plain,
% 4.04/4.21 ((~b(s(s(s(s(z)))), elem!1)) <=> (~b(s(s(s(elem!1))), elem!1))),
% 4.04/4.21 inference(monotonicity,[status(thm)],[15149])).
% 4.04/4.21 tff(15151,plain,
% 4.04/4.21 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[3404, 4681])).
% 4.04/4.21 tff(15152,plain,
% 4.04/4.21 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 4.04/4.21 inference(monotonicity,[status(thm)],[546])).
% 4.04/4.21 tff(15153,plain,
% 4.04/4.21 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 4.04/4.21 inference(symmetry,[status(thm)],[15152])).
% 4.04/4.21 tff(15154,plain,
% 4.04/4.21 (r(s(s(s(elem!1))), s(s(z)))),
% 4.04/4.21 inference(modus_ponens,[status(thm)],[193, 15153])).
% 4.04/4.21 tff(15155,plain,
% 4.04/4.21 ((s(elem!1) = s(s(elem!1))) <=> (s(s(z)) = s(s(elem!1)))),
% 4.04/4.21 inference(monotonicity,[status(thm)],[515])).
% 4.04/4.21 tff(15156,plain,
% 4.04/4.21 ((s(elem!1) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(z)))),
% 4.04/4.21 inference(transitivity,[status(thm)],[15155, 6456])).
% 4.04/4.21 tff(15157,plain,
% 4.04/4.21 ((~(s(elem!1) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(s(z))))),
% 4.04/4.21 inference(monotonicity,[status(thm)],[15156])).
% 4.04/4.21 tff(15158,plain,
% 4.04/4.21 (~(s(s(elem!1)) = s(s(z)))),
% 4.04/4.21 inference(modus_ponens,[status(thm)],[15140, 15157])).
% 4.04/4.21 tff(15159,plain,
% 4.04/4.21 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[6503, 557, 3461, 273, 15158, 15154])).
% 4.04/4.21 tff(15160,plain,
% 4.04/4.21 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[3409, 15159, 15151])).
% 4.04/4.21 tff(15161,plain,
% 4.04/4.21 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 4.04/4.21 inference(monotonicity,[status(thm)],[546, 545])).
% 4.04/4.21 tff(15162,plain,
% 4.04/4.21 (b(s(s(s(s(z)))), s(s(s(z))))),
% 4.04/4.21 inference(modus_ponens,[status(thm)],[3512, 15161])).
% 4.04/4.21 tff(15163,plain,
% 4.04/4.21 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 4.04/4.21 inference(monotonicity,[status(thm)],[545, 546])).
% 4.04/4.21 tff(15164,plain,
% 4.04/4.21 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.04/4.21 inference(modus_ponens,[status(thm)],[3511, 15163])).
% 4.04/4.21 tff(15165,plain,
% 4.04/4.21 ((~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(z)))))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[7596, 178, 104, 15164, 15162])).
% 4.04/4.21 tff(15166,plain,
% 4.04/4.21 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[15165, 251])).
% 4.04/4.21 tff(15167,plain,
% 4.04/4.21 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 15166])).
% 4.04/4.21 tff(15168,plain,
% 4.04/4.21 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[703, 12393])).
% 4.04/4.21 tff(15169,plain,
% 4.04/4.21 (b(s(s(s(s(s(s(s(z))))))), s(z)) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.04/4.21 inference(monotonicity,[status(thm)],[534])).
% 4.04/4.21 tff(15170,plain,
% 4.04/4.21 ((~b(s(s(s(s(s(s(s(z))))))), s(z))) <=> (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 4.04/4.21 inference(monotonicity,[status(thm)],[15169])).
% 4.04/4.21 tff(15171,plain,
% 4.04/4.21 (b(elem!1, s(s(s(elem!1)))) <=> b(s(z), s(s(s(s(z)))))),
% 4.04/4.21 inference(monotonicity,[status(thm)],[518, 546])).
% 4.04/4.21 tff(15172,plain,
% 4.04/4.21 (b(s(z), s(s(s(s(z)))))),
% 4.04/4.21 inference(modus_ponens,[status(thm)],[2042, 15171])).
% 4.04/4.21 tff(15173,plain,
% 4.04/4.21 (b(s(s(s(s(z)))), s(z))),
% 4.04/4.21 inference(modus_ponens,[status(thm)],[3771, 12391])).
% 4.04/4.21 tff(15174,plain,
% 4.04/4.21 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[14897, 178, 104, 251, 15173, 15172])).
% 4.04/4.21 tff(15175,plain,
% 4.04/4.21 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.04/4.21 inference(modus_ponens,[status(thm)],[15174, 15170])).
% 4.04/4.21 tff(15176,plain,
% 4.04/4.21 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[3444, 15175, 15168])).
% 4.04/4.21 tff(15177,plain,
% 4.04/4.21 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.04/4.21 inference(modus_ponens,[status(thm)],[15176, 603])).
% 4.04/4.21 tff(15178,plain,
% 4.04/4.21 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(z))), s(z))),
% 4.04/4.21 inference(monotonicity,[status(thm)],[545, 518])).
% 4.04/4.21 tff(15179,plain,
% 4.04/4.21 (b(s(s(s(elem!1))), elem!1)),
% 4.04/4.21 inference(modus_ponens,[status(thm)],[3771, 15149])).
% 4.04/4.21 tff(15180,plain,
% 4.04/4.21 (~b(s(s(elem!1)), elem!1)),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[5500, 15179, 2042, 3512, 3511])).
% 4.04/4.21 tff(15181,plain,
% 4.04/4.21 (r(s(s(elem!1)), elem!1)),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[3362, 15180, 15139])).
% 4.04/4.21 tff(15182,plain,
% 4.04/4.21 (r(s(s(s(z))), s(z))),
% 4.04/4.21 inference(modus_ponens,[status(thm)],[15181, 15178])).
% 4.04/4.21 tff(15183,plain,
% 4.04/4.21 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 4.04/4.21 inference(rewrite,[status(thm)],[])).
% 4.04/4.21 tff(15184,plain,
% 4.04/4.21 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 4.04/4.21 inference(quant_inst,[status(thm)],[])).
% 4.04/4.21 tff(15185,plain,
% 4.04/4.21 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 4.04/4.21 inference(modus_ponens,[status(thm)],[15184, 15183])).
% 4.04/4.21 tff(15186,plain,
% 4.04/4.21 ($false),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[15185, 118, 15182, 15177, 15167])).
% 4.04/4.21 tff(15187,plain,((~b(s(s(s(s(z)))), elem!1)) | (~(s(elem!1) = s(s(z)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~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)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.04/4.21 tff(15188,plain,
% 4.04/4.21 (~b(s(s(s(s(z)))), elem!1)),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[15187, 3922, 2042, 15160, 3511, 104, 515])).
% 4.04/4.21 tff(15189,plain,
% 4.04/4.21 (~b(s(s(s(elem!1))), elem!1)),
% 4.04/4.21 inference(modus_ponens,[status(thm)],[15188, 15150])).
% 4.04/4.21 tff(15190,plain,
% 4.04/4.21 (~(s(s(s(elem!1))) = elem!1)),
% 4.04/4.21 inference(modus_ponens,[status(thm)],[323, 550])).
% 4.04/4.21 tff(15191,plain,
% 4.04/4.21 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(z)))),
% 4.04/4.21 inference(monotonicity,[status(thm)],[515])).
% 4.04/4.21 tff(15192,plain,
% 4.04/4.21 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 4.04/4.21 inference(symmetry,[status(thm)],[15191])).
% 4.04/4.21 tff(15193,plain,
% 4.04/4.21 (r(s(s(s(s(z)))), s(elem!1))),
% 4.04/4.21 inference(modus_ponens,[status(thm)],[193, 15192])).
% 4.04/4.21 tff(15194,plain,
% 4.04/4.21 (r(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.04/4.21 inference(monotonicity,[status(thm)],[515])).
% 4.04/4.21 tff(15195,plain,
% 4.04/4.21 (r(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.04/4.21 inference(symmetry,[status(thm)],[15194])).
% 4.04/4.21 tff(15196,plain,
% 4.04/4.21 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.04/4.21 inference(modus_ponens,[status(thm)],[107, 15195])).
% 4.04/4.21 tff(15197,plain,
% 4.04/4.21 (~r(s(s(s(s(z)))), elem!1)),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[10992, 1587, 6400])).
% 4.04/4.21 tff(15198,assumption,(r(s(s(s(s(s(s(s(z))))))), s(elem!1))), introduced(assumption)).
% 4.04/4.21 tff(15199,plain,
% 4.04/4.21 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 4.04/4.21 inference(rewrite,[status(thm)],[])).
% 4.04/4.21 tff(15200,plain,
% 4.04/4.21 (((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 4.04/4.21 inference(rewrite,[status(thm)],[])).
% 4.04/4.21 tff(15201,plain,
% 4.04/4.21 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1)))))),
% 4.04/4.21 inference(monotonicity,[status(thm)],[15200])).
% 4.04/4.21 tff(15202,plain,
% 4.04/4.21 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 4.04/4.21 inference(transitivity,[status(thm)],[15201, 15199])).
% 4.04/4.21 tff(15203,plain,
% 4.04/4.21 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.04/4.21 inference(quant_inst,[status(thm)],[])).
% 4.04/4.21 tff(15204,plain,
% 4.04/4.21 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 4.04/4.21 inference(modus_ponens,[status(thm)],[15203, 15202])).
% 4.04/4.21 tff(15205,plain,
% 4.04/4.21 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[15204, 118, 6400, 15198])).
% 4.04/4.21 tff(15206,plain,
% 4.04/4.21 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[222, 15205])).
% 4.04/4.21 tff(15207,plain,
% 4.04/4.21 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[3929, 15206])).
% 4.04/4.21 tff(15208,plain,
% 4.04/4.21 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 4.04/4.21 inference(rewrite,[status(thm)],[])).
% 4.04/4.21 tff(15209,plain,
% 4.04/4.21 (((~r(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))))))), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 4.04/4.21 inference(rewrite,[status(thm)],[])).
% 4.04/4.21 tff(15210,plain,
% 4.04/4.21 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 4.04/4.21 inference(monotonicity,[status(thm)],[15209])).
% 4.04/4.21 tff(15211,plain,
% 4.04/4.21 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 4.04/4.21 inference(transitivity,[status(thm)],[15210, 15208])).
% 4.04/4.21 tff(15212,plain,
% 4.04/4.21 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))))))), elem!1)))),
% 4.04/4.21 inference(quant_inst,[status(thm)],[])).
% 4.04/4.21 tff(15213,plain,
% 4.04/4.21 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 4.04/4.21 inference(modus_ponens,[status(thm)],[15212, 15211])).
% 4.04/4.21 tff(15214,plain,
% 4.04/4.21 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[15213, 118, 1587, 15198])).
% 4.04/4.21 tff(15215,plain,
% 4.04/4.21 ($false),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[707, 41, 15214, 3914, 15207])).
% 4.04/4.21 tff(15216,plain,((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (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(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 4.04/4.21 tff(15217,plain,
% 4.04/4.21 (~b(s(s(s(s(z)))), elem!1)),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[15216, 1587, 104, 6400, 1301, 3914, 15198])).
% 4.04/4.21 tff(15218,plain,
% 4.04/4.21 ($false),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[3142, 15217, 15197, 323])).
% 4.04/4.21 tff(15219,plain,((~r(elem!1, s(elem!1))) | (s(s(s(s(z)))) = elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 4.04/4.21 tff(15220,plain,
% 4.04/4.21 (~r(elem!1, s(elem!1))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[15219, 15196, 104, 15193, 1301, 15168, 323])).
% 4.04/4.21 tff(15221,plain,
% 4.04/4.21 (~r(elem!1, s(s(z)))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[1047, 15220, 515])).
% 4.04/4.21 tff(15222,plain,
% 4.04/4.21 (b(elem!1, s(s(z)))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[467, 15221, 312])).
% 4.04/4.21 tff(15223,plain,
% 4.04/4.21 (r(s(s(s(s(z)))), elem!1)),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[3142, 15188, 323])).
% 4.04/4.21 tff(15224,plain,
% 4.04/4.21 (~r(s(s(z)), elem!1)),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[3329, 15223, 193])).
% 4.04/4.21 tff(15225,plain,
% 4.04/4.21 (b(s(s(z)), elem!1)),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[448, 15224, 12])).
% 4.04/4.21 tff(15226,plain,
% 4.04/4.21 (~b(z, elem!1)),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[10893, 15225, 3461, 273, 15222])).
% 4.04/4.21 tff(15227,plain,
% 4.04/4.21 (r(z, elem!1)),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[585, 15226, 12419])).
% 4.04/4.21 tff(15228,plain,
% 4.04/4.21 (~r(s(s(s(elem!1))), elem!1)),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[565, 15227, 557])).
% 4.04/4.21 tff(15229,plain,
% 4.04/4.21 (b(s(s(s(elem!1))), elem!1)),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[570, 15228, 15190])).
% 4.04/4.21 tff(15230,plain,
% 4.04/4.21 ($false),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[15229, 15189])).
% 4.04/4.21 tff(15231,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~(s(elem!1) = s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (s(s(z)) = elem!1) | (~r(s(s(s(s(z)))), s(s(z)))) | (s(s(s(s(z)))) = elem!1) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.04/4.21 tff(15232,plain,
% 4.04/4.21 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[15231, 515, 555, 3461, 273, 12, 193, 551, 15147, 15142, 15135, 15133])).
% 4.04/4.21 tff(15233,plain,
% 4.04/4.21 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[3578, 15232])).
% 4.04/4.21 tff(15234,plain,
% 4.04/4.21 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[6503, 555, 3461, 273, 15158, 15154])).
% 4.04/4.21 tff(15235,plain,
% 4.04/4.21 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[3409, 15234, 15151])).
% 4.04/4.21 tff(15236,plain,
% 4.04/4.21 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(z)))), s(z))),
% 4.04/4.21 inference(monotonicity,[status(thm)],[546, 518])).
% 4.04/4.21 tff(15237,plain,
% 4.04/4.21 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 4.04/4.21 inference(symmetry,[status(thm)],[15236])).
% 4.04/4.21 tff(15238,plain,
% 4.04/4.21 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(z))),
% 4.04/4.21 inference(monotonicity,[status(thm)],[518])).
% 4.04/4.21 tff(15239,plain,
% 4.04/4.21 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 4.04/4.21 inference(transitivity,[status(thm)],[15238, 15237])).
% 4.04/4.21 tff(15240,plain,
% 4.04/4.21 (r(s(s(s(elem!1))), elem!1)),
% 4.04/4.21 inference(modus_ponens,[status(thm)],[3132, 15239])).
% 4.04/4.21 tff(15241,plain,
% 4.04/4.21 (~r(s(s(z)), elem!1)),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[3329, 3132, 193])).
% 4.04/4.21 tff(15242,plain,
% 4.04/4.21 (b(s(s(z)), elem!1)),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[448, 15241, 12])).
% 4.04/4.21 tff(15243,plain,
% 4.04/4.21 (~r(elem!1, s(elem!1))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[10992, 3132, 15193])).
% 4.04/4.21 tff(15244,plain,
% 4.04/4.21 (~r(elem!1, s(s(z)))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[1047, 15243, 515])).
% 4.04/4.21 tff(15245,plain,
% 4.04/4.21 (b(elem!1, s(s(z)))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[467, 15244, 312])).
% 4.04/4.21 tff(15246,plain,
% 4.04/4.21 (~b(z, elem!1)),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[10893, 15245, 3461, 273, 15242])).
% 4.04/4.21 tff(15247,plain,
% 4.04/4.21 (r(z, elem!1)),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[585, 15246, 12419])).
% 4.04/4.21 tff(15248,plain,
% 4.04/4.21 (~r(s(s(s(elem!1))), elem!1)),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[565, 15247, 557])).
% 4.04/4.21 tff(15249,plain,
% 4.04/4.21 ($false),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[15248, 15240])).
% 4.04/4.21 tff(15250,plain,((~r(s(s(s(s(z)))), elem!1)) | (~(s(elem!1) = s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (s(s(z)) = elem!1) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.04/4.21 tff(15251,plain,
% 4.04/4.21 (~r(s(s(s(s(z)))), elem!1)),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[15250, 515, 555, 3461, 273, 12, 193])).
% 4.04/4.21 tff(15252,plain,
% 4.04/4.21 (b(s(s(s(s(z)))), elem!1)),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[3142, 15251, 551])).
% 4.04/4.21 tff(15253,plain,
% 4.04/4.21 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[15187, 15252, 15147, 15235, 15142, 15135, 515])).
% 4.04/4.21 tff(15254,plain,
% 4.04/4.21 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[222, 15253])).
% 4.04/4.21 tff(15255,plain,
% 4.04/4.21 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[3559, 15254, 193])).
% 4.04/4.21 tff(15256,plain,
% 4.04/4.21 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[249, 15255])).
% 4.04/4.21 tff(15257,plain,
% 4.04/4.21 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[3567, 178, 3461, 273, 15256, 15233])).
% 4.04/4.21 tff(15258,plain,
% 4.04/4.21 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[271, 15257])).
% 4.04/4.21 tff(15259,plain,
% 4.04/4.21 ($false),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[210, 118, 145, 15254, 15258])).
% 4.04/4.21 tff(15260,plain,((~(s(elem!1) = s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (s(s(z)) = elem!1) | (elem!1 = s(s(s(s(z))))) | b(elem!1, z) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.04/4.21 tff(15261,plain,
% 4.04/4.21 (~(s(elem!1) = s(s(z)))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[15260, 469, 3461, 144, 193, 12, 145, 5723, 147])).
% 4.04/4.21 tff(15262,plain,
% 4.04/4.21 (r(s(elem!1), s(s(z)))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[421, 15261, 305])).
% 4.04/4.21 tff(15263,plain,
% 4.04/4.21 (~r(s(elem!1), s(s(s(s(z)))))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[6776, 15261, 3461, 144, 147, 10020])).
% 4.04/4.21 tff(15264,plain,
% 4.04/4.21 (b(s(elem!1), s(s(s(s(z)))))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[1084, 15263, 1369])).
% 4.04/4.21 tff(15265,plain,
% 4.04/4.21 (~r(s(s(s(s(z)))), s(elem!1))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[14884, 118, 15262, 193])).
% 4.04/4.21 tff(15266,plain,
% 4.04/4.21 (b(s(s(s(s(z)))), s(elem!1))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[2173, 15265, 2169])).
% 4.04/4.21 tff(15267,plain,
% 4.04/4.21 (~(s(s(z)) = s(elem!1))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[1058, 15261])).
% 4.04/4.21 tff(15268,plain,
% 4.04/4.21 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[2840, 15261])).
% 4.04/4.21 tff(15269,plain,
% 4.04/4.21 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.04/4.21 inference(unit_resolution,[status(thm)],[3578, 3575])).
% 4.04/4.22 tff(15270,plain,
% 4.04/4.22 (r(s(elem!1), s(s(z))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.04/4.22 inference(monotonicity,[status(thm)],[645])).
% 4.04/4.22 tff(15271,plain,
% 4.04/4.22 (r(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 4.04/4.22 inference(symmetry,[status(thm)],[15270])).
% 4.04/4.22 tff(15272,plain,
% 4.04/4.22 ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) <=> (~r(s(elem!1), s(s(z))))),
% 4.04/4.22 inference(monotonicity,[status(thm)],[15271])).
% 4.04/4.22 tff(15273,plain,
% 4.04/4.22 (~r(s(elem!1), s(s(z)))),
% 4.04/4.22 inference(modus_ponens,[status(thm)],[3575, 15272])).
% 4.04/4.22 tff(15274,plain,
% 4.04/4.22 ($false),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[363, 15273])).
% 4.04/4.22 tff(15275,plain,((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(z)))) | r(s(s(s(s(s(s(s(z))))))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.04/4.22 tff(15276,plain,
% 4.04/4.22 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[15275, 3575, 363])).
% 4.04/4.22 tff(15277,plain,
% 4.04/4.22 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[14913, 15276, 14938, 1069, 15135, 363, 193])).
% 4.04/4.22 tff(15278,plain,
% 4.04/4.22 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[249, 15277])).
% 4.04/4.22 tff(15279,plain,
% 4.04/4.22 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[3567, 178, 3461, 144, 15278, 15269])).
% 4.04/4.22 tff(15280,plain,
% 4.04/4.22 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[271, 15279])).
% 4.04/4.22 tff(15281,plain,
% 4.04/4.22 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[212, 15280, 145])).
% 4.04/4.22 tff(15282,plain,
% 4.04/4.22 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[222, 15281])).
% 4.04/4.22 tff(15283,plain,
% 4.04/4.22 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[14911, 178, 15135, 14938, 1069, 15282])).
% 4.04/4.22 tff(15284,plain,
% 4.04/4.22 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[395, 15283, 15276])).
% 4.04/4.22 tff(15285,plain,
% 4.04/4.22 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 4.04/4.22 inference(rewrite,[status(thm)],[])).
% 4.04/4.22 tff(15286,plain,
% 4.04/4.22 (((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 4.04/4.22 inference(rewrite,[status(thm)],[])).
% 4.04/4.22 tff(15287,plain,
% 4.04/4.22 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 4.04/4.22 inference(monotonicity,[status(thm)],[15286])).
% 4.04/4.22 tff(15288,plain,
% 4.04/4.22 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 4.04/4.22 inference(transitivity,[status(thm)],[15287, 15285])).
% 4.04/4.22 tff(15289,plain,
% 4.04/4.22 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(elem!1))))),
% 4.04/4.22 inference(quant_inst,[status(thm)],[])).
% 4.04/4.22 tff(15290,plain,
% 4.04/4.22 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 4.04/4.22 inference(modus_ponens,[status(thm)],[15289, 15288])).
% 4.04/4.22 tff(15291,plain,
% 4.04/4.22 (~r(z, s(elem!1))),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[15290, 118, 15284, 15280])).
% 4.04/4.22 tff(15292,plain,
% 4.04/4.22 (b(z, s(elem!1))),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[2351, 15291])).
% 4.04/4.22 tff(15293,plain,
% 4.04/4.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 4.04/4.22 inference(rewrite,[status(thm)],[])).
% 4.04/4.22 tff(15294,plain,
% 4.04/4.22 (((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 4.04/4.22 inference(rewrite,[status(thm)],[])).
% 4.04/4.22 tff(15295,plain,
% 4.04/4.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 4.04/4.22 inference(monotonicity,[status(thm)],[15294])).
% 4.04/4.22 tff(15296,plain,
% 4.04/4.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 4.04/4.22 inference(transitivity,[status(thm)],[15295, 15293])).
% 4.04/4.22 tff(15297,plain,
% 4.04/4.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 4.04/4.22 inference(quant_inst,[status(thm)],[])).
% 4.04/4.22 tff(15298,plain,
% 4.04/4.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 4.04/4.22 inference(modus_ponens,[status(thm)],[15297, 15296])).
% 4.04/4.22 tff(15299,plain,
% 4.04/4.22 (~b(s(s(s(s(z)))), z)),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[15298, 178, 15292, 10020, 14938, 1069])).
% 4.04/4.22 tff(15300,plain,
% 4.04/4.22 (r(s(s(s(s(z)))), z)),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[191, 15299])).
% 4.04/4.22 tff(15301,plain,
% 4.04/4.22 (~b(s(s(z)), s(elem!1))),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[6788, 178, 15292, 10020, 3461, 144])).
% 4.04/4.22 tff(15302,plain,
% 4.04/4.22 (r(s(s(z)), s(elem!1))),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[1067, 15301, 1060])).
% 4.04/4.22 tff(15303,plain,
% 4.04/4.22 (r(s(elem!1), s(s(elem!1)))),
% 4.04/4.22 inference(modus_ponens,[status(thm)],[14887, 1019])).
% 4.04/4.22 tff(15304,plain,
% 4.04/4.22 (~b(s(s(s(s(elem!1)))), z)),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[5184, 12064, 3170])).
% 4.04/4.22 tff(15305,plain,
% 4.04/4.22 (r(s(s(s(s(elem!1)))), z)),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[1716, 15304])).
% 4.04/4.22 tff(15306,plain,
% 4.04/4.22 (~(elem!1 = s(s(s(elem!1))))),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[3991, 15305, 767])).
% 4.04/4.22 tff(15307,plain,
% 4.04/4.22 (~(s(s(s(elem!1))) = elem!1)),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[2489, 15306])).
% 4.04/4.22 tff(15308,plain,
% 4.04/4.22 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[951, 15307])).
% 4.04/4.22 tff(15309,plain,
% 4.04/4.22 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[4343, 15308])).
% 4.04/4.22 tff(15310,plain,
% 4.04/4.22 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(s(z)))))),
% 4.04/4.22 inference(monotonicity,[status(thm)],[10728])).
% 4.04/4.22 tff(15311,plain,
% 4.04/4.22 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 4.04/4.22 inference(modus_ponens,[status(thm)],[2857, 15310])).
% 4.04/4.22 tff(15312,plain,
% 4.04/4.22 (~r(s(s(s(elem!1))), s(elem!1))),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[5980, 5227, 5972])).
% 4.04/4.22 tff(15313,plain,
% 4.04/4.22 (b(s(s(s(elem!1))), s(elem!1))),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[373, 15312, 12049])).
% 4.04/4.22 tff(15314,plain,
% 4.04/4.22 (b(s(s(s(z))), s(z))),
% 4.04/4.22 inference(modus_ponens,[status(thm)],[15313, 12043])).
% 4.04/4.22 tff(15315,assumption,(~(s(s(s(s(z)))) = s(s(s(z))))), introduced(assumption)).
% 4.04/4.22 tff(15316,plain,
% 4.04/4.22 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(z))), s(s(z)))),
% 4.04/4.22 inference(symmetry,[status(thm)],[10746])).
% 4.04/4.22 tff(15317,plain,
% 4.04/4.22 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 4.04/4.22 inference(monotonicity,[status(thm)],[930])).
% 4.04/4.22 tff(15318,plain,
% 4.04/4.22 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(z)))),
% 4.04/4.22 inference(transitivity,[status(thm)],[15317, 15316])).
% 4.04/4.22 tff(15319,plain,
% 4.04/4.22 (r(s(s(s(z))), s(s(z)))),
% 4.04/4.22 inference(modus_ponens,[status(thm)],[5227, 15318])).
% 4.04/4.22 tff(15320,plain,
% 4.04/4.22 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[8696, 118, 193, 15319])).
% 4.04/4.22 tff(15321,plain,
% 4.04/4.22 (b(s(s(s(s(z)))), s(s(s(z))))),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[4950, 15320, 15315])).
% 4.04/4.22 tff(15322,plain,
% 4.04/4.22 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.04/4.22 inference(modus_ponens,[status(thm)],[12320, 5215])).
% 4.04/4.22 tff(15323,plain,
% 4.04/4.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(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(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(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(s(s(z))), s(z))))),
% 4.04/4.22 inference(rewrite,[status(thm)],[])).
% 4.04/4.22 tff(15324,plain,
% 4.04/4.22 (((~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(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(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(s(s(z))), s(z))))),
% 4.04/4.22 inference(rewrite,[status(thm)],[])).
% 4.04/4.22 tff(15325,plain,
% 4.04/4.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(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(s(s(z))), s(z)))))),
% 4.04/4.22 inference(monotonicity,[status(thm)],[15324])).
% 4.04/4.22 tff(15326,plain,
% 4.04/4.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(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(s(s(z))), s(z))))),
% 4.04/4.22 inference(transitivity,[status(thm)],[15325, 15323])).
% 4.04/4.22 tff(15327,plain,
% 4.04/4.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 4.04/4.22 inference(quant_inst,[status(thm)],[])).
% 4.04/4.22 tff(15328,plain,
% 4.04/4.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))),
% 4.04/4.22 inference(modus_ponens,[status(thm)],[15327, 15326])).
% 4.04/4.22 tff(15329,plain,
% 4.04/4.22 ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[15328, 178, 1789, 15322, 14891])).
% 4.04/4.22 tff(15330,plain,
% 4.04/4.22 (~b(s(s(s(z))), s(z))),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[15329, 15321])).
% 4.04/4.22 tff(15331,plain,
% 4.04/4.22 ($false),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[15330, 15314])).
% 4.04/4.22 tff(15332,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~(elem!1 = z)) | (~b(s(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(s(z)))), s(s(z)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 4.04/4.22 tff(15333,plain,
% 4.04/4.22 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[15332, 928, 14890, 14889, 15311, 193, 15309, 12299, 15303])).
% 4.04/4.22 tff(15334,plain,
% 4.04/4.22 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[3409, 15333, 12038])).
% 4.04/4.22 tff(15335,plain,
% 4.04/4.22 (b(s(s(s(z))), s(s(z)))),
% 4.04/4.22 inference(modus_ponens,[status(thm)],[15334, 5221])).
% 4.04/4.22 tff(15336,plain,
% 4.04/4.22 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 4.04/4.22 inference(monotonicity,[status(thm)],[930])).
% 4.04/4.22 tff(15337,plain,
% 4.04/4.22 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(z))))),
% 4.04/4.22 inference(transitivity,[status(thm)],[15336, 5240])).
% 4.04/4.22 tff(15338,plain,
% 4.04/4.22 (r(s(s(elem!1)), s(elem!1))),
% 4.04/4.22 inference(modus_ponens,[status(thm)],[1329, 12111])).
% 4.04/4.22 tff(15339,plain,
% 4.04/4.22 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 4.04/4.22 inference(monotonicity,[status(thm)],[932, 931])).
% 4.04/4.22 tff(15340,plain,
% 4.04/4.22 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 4.04/4.22 inference(symmetry,[status(thm)],[15339])).
% 4.04/4.22 tff(15341,plain,
% 4.04/4.22 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(elem!1)))))),
% 4.04/4.22 inference(monotonicity,[status(thm)],[15340])).
% 4.04/4.22 tff(15342,plain,
% 4.04/4.22 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 4.04/4.22 inference(modus_ponens,[status(thm)],[15311, 15341])).
% 4.04/4.22 tff(15343,plain,
% 4.04/4.22 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 4.04/4.22 inference(rewrite,[status(thm)],[])).
% 4.04/4.22 tff(15344,plain,
% 4.04/4.22 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 4.04/4.22 inference(rewrite,[status(thm)],[])).
% 4.04/4.22 tff(15345,plain,
% 4.04/4.22 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1)))))),
% 4.04/4.22 inference(monotonicity,[status(thm)],[15344])).
% 4.04/4.22 tff(15346,plain,
% 4.04/4.22 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 4.04/4.22 inference(transitivity,[status(thm)],[15345, 15343])).
% 4.04/4.22 tff(15347,plain,
% 4.04/4.22 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 4.04/4.22 inference(quant_inst,[status(thm)],[])).
% 4.04/4.22 tff(15348,plain,
% 4.04/4.22 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1)))),
% 4.04/4.22 inference(modus_ponens,[status(thm)],[15347, 15346])).
% 4.04/4.22 tff(15349,plain,
% 4.04/4.22 ($false),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[15348, 118, 1551, 3364, 992])).
% 4.04/4.22 tff(15350,plain,((~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)))))), inference(lemma,lemma(discharge,[]))).
% 4.04/4.22 tff(15351,plain,
% 4.04/4.22 (~r(s(s(s(elem!1))), s(elem!1))),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[15350, 3364, 992])).
% 4.04/4.22 tff(15352,plain,
% 4.04/4.22 (b(s(s(s(elem!1))), s(elem!1))),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[373, 15351, 12049])).
% 4.04/4.22 tff(15353,plain,
% 4.04/4.22 (b(s(s(s(z))), s(z))),
% 4.04/4.22 inference(modus_ponens,[status(thm)],[15352, 12043])).
% 4.04/4.22 tff(15354,plain,
% 4.04/4.22 (r(s(s(z)), s(s(s(elem!1))))),
% 4.04/4.22 inference(modus_ponens,[status(thm)],[3364, 12082])).
% 4.04/4.22 tff(15355,plain,
% 4.04/4.22 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[3644, 15354, 3636])).
% 4.04/4.22 tff(15356,plain,
% 4.04/4.22 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[1988, 15355, 1693])).
% 4.04/4.22 tff(15357,plain,
% 4.04/4.22 (b(s(s(s(s(z)))), s(s(s(z))))),
% 4.04/4.22 inference(modus_ponens,[status(thm)],[15356, 12078])).
% 4.04/4.22 tff(15358,plain,
% 4.04/4.22 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[4036, 15354, 1403])).
% 4.04/4.22 tff(15359,plain,
% 4.04/4.22 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[1750, 15358, 1858])).
% 4.04/4.22 tff(15360,plain,
% 4.04/4.22 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.04/4.22 inference(modus_ponens,[status(thm)],[15359, 5215])).
% 4.04/4.22 tff(15361,plain,
% 4.04/4.22 ($false),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[15328, 178, 1789, 15360, 15357, 14891, 15353])).
% 4.04/4.22 tff(15362,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~(elem!1 = z)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 4.04/4.22 tff(15363,plain,
% 4.04/4.22 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[15362, 14890, 14889, 928, 15342, 15309, 12071, 12068, 15338])).
% 4.04/4.22 tff(15364,plain,
% 4.04/4.22 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[3375, 15363, 12080])).
% 4.04/4.22 tff(15365,plain,
% 4.04/4.22 (b(s(s(z)), s(s(s(z))))),
% 4.04/4.22 inference(modus_ponens,[status(thm)],[15364, 15337])).
% 4.04/4.22 tff(15366,plain,
% 4.04/4.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), 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))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), 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))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.04/4.22 inference(rewrite,[status(thm)],[])).
% 4.04/4.22 tff(15367,plain,
% 4.04/4.22 (((~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(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(z)), 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))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.04/4.22 inference(rewrite,[status(thm)],[])).
% 4.04/4.22 tff(15368,plain,
% 4.04/4.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), 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))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))))),
% 4.04/4.22 inference(monotonicity,[status(thm)],[15367])).
% 4.04/4.22 tff(15369,plain,
% 4.04/4.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), 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))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.04/4.22 inference(transitivity,[status(thm)],[15368, 15366])).
% 4.04/4.22 tff(15370,plain,
% 4.04/4.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 4.04/4.22 inference(quant_inst,[status(thm)],[])).
% 4.04/4.22 tff(15371,plain,
% 4.04/4.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), 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))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 4.04/4.22 inference(modus_ponens,[status(thm)],[15370, 15369])).
% 4.04/4.22 tff(15372,plain,
% 4.04/4.22 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[15371, 178, 166, 15365, 15335, 1146])).
% 4.04/4.22 tff(15373,plain,
% 4.04/4.22 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 15372])).
% 4.04/4.22 tff(15374,plain,
% 4.04/4.22 (r(elem!1, s(s(s(elem!1)))) <=> r(z, s(s(s(z))))),
% 4.04/4.22 inference(transitivity,[status(thm)],[4846, 10722])).
% 4.04/4.22 tff(15375,plain,
% 4.04/4.22 ((s(s(elem!1)) = z) <=> (elem!1 = s(s(elem!1)))),
% 4.04/4.22 inference(transitivity,[status(thm)],[967, 1542])).
% 4.04/4.22 tff(15376,plain,
% 4.04/4.22 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = s(s(elem!1))))),
% 4.04/4.22 inference(monotonicity,[status(thm)],[15375])).
% 4.04/4.22 tff(15377,plain,
% 4.04/4.22 (~(elem!1 = s(s(elem!1)))),
% 4.04/4.22 inference(modus_ponens,[status(thm)],[970, 15376])).
% 4.04/4.22 tff(15378,plain,
% 4.04/4.22 ((~r(z, s(s(z)))) <=> (~r(elem!1, s(s(elem!1))))),
% 4.04/4.22 inference(monotonicity,[status(thm)],[12031])).
% 4.04/4.22 tff(15379,plain,
% 4.04/4.22 (~r(elem!1, s(s(elem!1)))),
% 4.04/4.22 inference(modus_ponens,[status(thm)],[48, 15378])).
% 4.04/4.22 tff(15380,plain,
% 4.04/4.22 (~b(elem!1, s(s(s(elem!1))))),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[5479, 15364, 12065, 15379, 15377, 15334])).
% 4.04/4.22 tff(15381,plain,
% 4.04/4.22 (r(elem!1, s(s(s(elem!1))))),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[2054, 15380, 15306])).
% 4.04/4.22 tff(15382,plain,
% 4.04/4.22 (r(z, s(s(s(z))))),
% 4.04/4.22 inference(modus_ponens,[status(thm)],[15381, 15374])).
% 4.04/4.22 tff(15383,plain,
% 4.04/4.22 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[4055, 178, 3461, 144, 166, 1146])).
% 4.04/4.22 tff(15384,plain,
% 4.04/4.22 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.04/4.22 inference(unit_resolution,[status(thm)],[133, 15383])).
% 4.04/4.22 tff(15385,plain,
% 4.04/4.22 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 4.04/4.22 inference(rewrite,[status(thm)],[])).
% 4.04/4.22 tff(15386,plain,
% 4.04/4.22 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z))) <=> ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 4.04/4.22 inference(rewrite,[status(thm)],[])).
% 4.04/4.22 tff(15387,plain,
% 4.04/4.22 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(z)))))))),
% 4.04/4.22 inference(monotonicity,[status(thm)],[15386])).
% 4.04/4.22 tff(15388,plain,
% 4.04/4.22 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 4.04/4.22 inference(transitivity,[status(thm)],[15387, 15385])).
% 4.04/4.22 tff(15389,plain,
% 4.04/4.22 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 4.04/4.22 inference(quant_inst,[status(thm)],[])).
% 4.04/4.22 tff(15390,plain,
% 4.04/4.22 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(z)))))),
% 4.04/4.23 inference(modus_ponens,[status(thm)],[15389, 15388])).
% 4.04/4.23 tff(15391,plain,
% 4.04/4.23 ($false),
% 4.04/4.23 inference(unit_resolution,[status(thm)],[15390, 118, 15384, 15382, 15373])).
% 4.04/4.23 tff(15392,plain,((~(elem!1 = z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | r(z, s(s(z))) | (~r(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(z)))) | r(s(elem!1), z) | b(s(s(s(s(z)))), z) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 4.04/4.23 tff(15393,plain,
% 4.04/4.23 (~(elem!1 = z)),
% 4.04/4.23 inference(unit_resolution,[status(thm)],[15392, 15278, 15269, 193, 147, 2857, 48, 15302, 1069, 14938, 363, 767, 15299, 3461])).
% 4.04/4.23 tff(15394,plain,
% 4.04/4.23 (r(elem!1, z)),
% 4.04/4.23 inference(unit_resolution,[status(thm)],[498, 15393, 5723])).
% 4.04/4.23 tff(15395,plain,
% 4.04/4.23 (~r(s(s(s(s(z)))), elem!1)),
% 4.04/4.23 inference(unit_resolution,[status(thm)],[6033, 15394, 15300])).
% 4.04/4.23 tff(15396,plain,
% 4.04/4.23 (b(s(s(s(s(z)))), elem!1)),
% 4.04/4.23 inference(unit_resolution,[status(thm)],[3142, 15395, 551])).
% 4.04/4.23 tff(15397,plain,
% 4.04/4.23 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.04/4.23 inference(unit_resolution,[status(thm)],[4055, 178, 3461, 144, 15278, 15269])).
% 4.04/4.23 tff(15398,plain,
% 4.04/4.23 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.04/4.23 inference(unit_resolution,[status(thm)],[133, 15397])).
% 4.04/4.23 tff(15399,plain,
% 4.04/4.23 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.04/4.23 inference(unit_resolution,[status(thm)],[11809, 118, 14985, 108])).
% 4.04/4.23 tff(15400,plain,
% 4.04/4.23 (~r(elem!1, s(s(s(s(z)))))),
% 4.04/4.23 inference(unit_resolution,[status(thm)],[3785, 13066, 193])).
% 4.04/4.23 tff(15401,plain,
% 4.04/4.23 (b(elem!1, s(s(s(s(z)))))),
% 4.04/4.23 inference(unit_resolution,[status(thm)],[483, 15400, 469])).
% 4.04/4.23 tff(15402,plain,
% 4.04/4.23 (b(s(s(s(s(z)))), elem!1)),
% 4.04/4.23 inference(unit_resolution,[status(thm)],[3142, 14986, 551])).
% 4.04/4.23 tff(15403,plain,
% 4.04/4.23 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.04/4.23 inference(unit_resolution,[status(thm)],[4266, 178, 104, 15402, 15401, 251])).
% 4.04/4.23 tff(15404,plain,
% 4.04/4.23 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 4.04/4.23 inference(unit_resolution,[status(thm)],[691, 15403, 15399])).
% 4.04/4.23 tff(15405,plain,
% 4.04/4.23 (b(elem!1, s(s(z))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.04/4.23 inference(monotonicity,[status(thm)],[15404])).
% 4.04/4.23 tff(15406,plain,
% 4.04/4.23 (b(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> b(elem!1, s(s(z)))),
% 4.04/4.23 inference(symmetry,[status(thm)],[15405])).
% 4.04/4.23 tff(15407,plain,
% 4.04/4.23 (b(elem!1, s(s(z)))),
% 4.04/4.23 inference(modus_ponens,[status(thm)],[1146, 15406])).
% 4.04/4.23 tff(15408,plain,
% 4.04/4.23 ($false),
% 4.04/4.23 inference(unit_resolution,[status(thm)],[461, 15407])).
% 4.04/4.23 tff(15409,plain,(b(elem!1, 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(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), z)) | (elem!1 = s(s(s(s(z))))) | b(elem!1, z) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (elem!1 = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.04/4.23 tff(15410,plain,
% 4.04/4.23 (b(elem!1, s(s(z)))),
% 4.04/4.23 inference(unit_resolution,[status(thm)],[15409, 15269, 15135, 15282, 15398, 15300, 469, 5723, 193, 144, 462])).
% 4.04/4.23 tff(15411,plain,
% 4.04/4.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.04/4.23 inference(rewrite,[status(thm)],[])).
% 4.04/4.23 tff(15412,plain,
% 4.04/4.23 (((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.04/4.23 inference(rewrite,[status(thm)],[])).
% 4.04/4.23 tff(15413,plain,
% 4.04/4.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 4.04/4.23 inference(monotonicity,[status(thm)],[15412])).
% 4.04/4.23 tff(15414,plain,
% 4.04/4.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.04/4.23 inference(transitivity,[status(thm)],[15413, 15411])).
% 4.04/4.23 tff(15415,plain,
% 4.04/4.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 4.04/4.23 inference(quant_inst,[status(thm)],[])).
% 4.04/4.23 tff(15416,plain,
% 4.04/4.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 4.04/4.23 inference(modus_ponens,[status(thm)],[15415, 15414])).
% 4.04/4.23 tff(15417,plain,
% 4.04/4.23 ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 4.04/4.23 inference(unit_resolution,[status(thm)],[15416, 178, 15410, 15282, 15269])).
% 4.04/4.23 tff(15418,plain,
% 4.04/4.23 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.04/4.23 inference(unit_resolution,[status(thm)],[15417, 15396])).
% 4.04/4.23 tff(15419,plain,
% 4.04/4.23 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.04/4.23 inference(unit_resolution,[status(thm)],[11809, 118, 15394, 15398])).
% 4.04/4.23 tff(15420,plain,
% 4.04/4.23 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 4.04/4.23 inference(unit_resolution,[status(thm)],[691, 15419, 15418])).
% 4.04/4.23 tff(15421,plain,
% 4.04/4.23 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 4.04/4.23 inference(monotonicity,[status(thm)],[15420])).
% 4.04/4.23 tff(15422,plain,
% 4.04/4.23 (s(s(elem!1)) = s(s(s(s(s(s(s(s(s(z)))))))))),
% 4.04/4.23 inference(monotonicity,[status(thm)],[15421])).
% 4.04/4.23 tff(15423,plain,
% 4.04/4.23 (s(s(s(elem!1))) = s(s(s(s(s(s(s(s(s(s(z))))))))))),
% 4.04/4.23 inference(monotonicity,[status(thm)],[15422])).
% 4.04/4.23 tff(15424,plain,
% 4.04/4.23 (s(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(s(elem!1)))),
% 4.04/4.23 inference(symmetry,[status(thm)],[15423])).
% 4.04/4.23 tff(15425,plain,
% 4.04/4.23 (r(s(s(z)), s(s(s(s(s(s(s(s(s(s(z))))))))))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 4.04/4.23 inference(monotonicity,[status(thm)],[15424])).
% 4.04/4.23 tff(15426,plain,
% 4.04/4.23 ((~r(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) <=> (~r(s(s(z)), s(s(s(elem!1)))))),
% 4.04/4.23 inference(monotonicity,[status(thm)],[15425])).
% 4.04/4.23 tff(15427,plain,
% 4.04/4.23 (s(s(s(s(s(s(s(s(z)))))))) = s(elem!1)),
% 4.04/4.23 inference(symmetry,[status(thm)],[15421])).
% 4.04/4.23 tff(15428,plain,
% 4.04/4.23 (r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z))))))))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 4.04/4.23 inference(monotonicity,[status(thm)],[15424, 15427])).
% 4.04/4.23 tff(15429,plain,
% 4.04/4.23 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.04/4.23 inference(symmetry,[status(thm)],[15428])).
% 4.04/4.23 tff(15430,plain,
% 4.04/4.23 (~(s(s(elem!1)) = elem!1)),
% 4.04/4.23 inference(unit_resolution,[status(thm)],[2510, 15420, 2508])).
% 4.04/4.23 tff(15431,plain,
% 4.04/4.23 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.04/4.23 inference(unit_resolution,[status(thm)],[348, 15430])).
% 4.04/4.23 tff(15432,plain,
% 4.04/4.23 (b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z))))))))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 4.04/4.23 inference(monotonicity,[status(thm)],[15424, 15427])).
% 4.04/4.23 tff(15433,plain,
% 4.04/4.23 ((~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z)))))))))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 4.04/4.23 inference(monotonicity,[status(thm)],[15432])).
% 4.04/4.23 tff(15434,plain,
% 4.04/4.23 (~(s(elem!1) = s(s(s(elem!1))))),
% 4.04/4.23 inference(unit_resolution,[status(thm)],[5395, 15431])).
% 4.04/4.23 tff(15435,plain,
% 4.04/4.23 (~r(elem!1, s(s(s(elem!1))))),
% 4.04/4.23 inference(unit_resolution,[status(thm)],[6352, 15434, 3461, 144, 10020, 15394, 15292, 15302])).
% 4.04/4.23 tff(15436,plain,
% 4.04/4.23 (~(elem!1 = s(s(s(elem!1))))),
% 4.04/4.23 inference(unit_resolution,[status(thm)],[2859, 15420, 2857])).
% 4.04/4.23 tff(15437,plain,
% 4.04/4.23 (b(elem!1, s(s(s(elem!1))))),
% 4.04/4.23 inference(unit_resolution,[status(thm)],[2054, 15436, 15435])).
% 4.04/4.23 tff(15438,plain,
% 4.04/4.23 (b(s(s(s(s(s(s(s(s(z)))))))), z) <=> b(s(elem!1), z)),
% 4.04/4.23 inference(monotonicity,[status(thm)],[11730])).
% 4.04/4.23 tff(15439,plain,
% 4.04/4.23 (b(s(elem!1), z) <=> b(s(s(s(s(s(s(s(s(z)))))))), z)),
% 4.04/4.23 inference(symmetry,[status(thm)],[15438])).
% 4.04/4.23 tff(15440,plain,
% 4.04/4.23 (b(s(s(s(s(s(s(s(s(z)))))))), z)),
% 4.04/4.23 inference(modus_ponens,[status(thm)],[853, 15439])).
% 4.04/4.23 tff(15441,plain,
% 4.04/4.23 (b(s(s(s(s(s(s(s(s(s(s(z)))))))))), z) <=> b(s(s(s(elem!1))), z)),
% 4.04/4.23 inference(monotonicity,[status(thm)],[4345])).
% 4.04/4.23 tff(15442,plain,
% 4.04/4.23 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)),
% 4.04/4.23 inference(symmetry,[status(thm)],[15441])).
% 4.04/4.23 tff(15443,plain,
% 4.04/4.23 ((~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) <=> (~r(s(s(s(elem!1))), z))),
% 4.04/4.23 inference(monotonicity,[status(thm)],[10552])).
% 4.04/4.23 tff(15444,plain,
% 4.04/4.23 ((s(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.04/4.23 inference(monotonicity,[status(thm)],[4345])).
% 4.04/4.23 tff(15445,plain,
% 4.04/4.23 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(s(s(z)))))),
% 4.04/4.23 inference(symmetry,[status(thm)],[15444])).
% 4.04/4.23 tff(15446,plain,
% 4.04/4.23 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(s(s(z))))))),
% 4.04/4.23 inference(monotonicity,[status(thm)],[15445])).
% 4.04/4.23 tff(15447,plain,
% 4.04/4.23 (~(s(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(s(s(z)))))),
% 4.04/4.23 inference(modus_ponens,[status(thm)],[2857, 15446])).
% 4.04/4.23 tff(15448,plain,
% 4.04/4.23 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z))))))))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 4.04/4.23 inference(monotonicity,[status(thm)],[11730])).
% 4.04/4.23 tff(15449,plain,
% 4.04/4.23 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.04/4.23 inference(symmetry,[status(thm)],[15448])).
% 4.04/4.23 tff(15450,plain,
% 4.04/4.23 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.04/4.23 inference(modus_ponens,[status(thm)],[8640, 15449])).
% 4.04/4.23 tff(15451,assumption,(b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z)))))))))), introduced(assumption)).
% 4.04/4.23 tff(15452,plain,
% 4.04/4.23 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z))))))))))) <=> b(elem!1, s(s(s(elem!1))))),
% 4.04/4.23 inference(monotonicity,[status(thm)],[680, 4345])).
% 4.04/4.23 tff(15453,plain,
% 4.04/4.23 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 4.04/4.23 inference(symmetry,[status(thm)],[15452])).
% 4.04/4.23 tff(15454,plain,
% 4.04/4.23 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 4.04/4.23 inference(modus_ponens,[status(thm)],[2042, 15453])).
% 4.04/4.23 tff(15455,plain,
% 4.04/4.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))))),
% 4.04/4.23 inference(rewrite,[status(thm)],[])).
% 4.04/4.23 tff(15456,plain,
% 4.04/4.23 (((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(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(s(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(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(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))))),
% 4.04/4.23 inference(rewrite,[status(thm)],[])).
% 4.04/4.23 tff(15457,plain,
% 4.04/4.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(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(s(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(s(s(s(s(s(s(z)))))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z))))))))))))),
% 4.04/4.23 inference(monotonicity,[status(thm)],[15456])).
% 4.04/4.23 tff(15458,plain,
% 4.04/4.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(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(s(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(s(s(s(s(s(s(z)))))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))))),
% 4.04/4.23 inference(transitivity,[status(thm)],[15457, 15455])).
% 4.04/4.23 tff(15459,plain,
% 4.04/4.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(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(s(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(s(s(s(s(s(s(z)))))))))))))),
% 4.04/4.23 inference(quant_inst,[status(thm)],[])).
% 4.04/4.23 tff(15460,plain,
% 4.04/4.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z))))))))))),
% 4.04/4.23 inference(modus_ponens,[status(thm)],[15459, 15458])).
% 4.04/4.23 tff(15461,plain,
% 4.04/4.23 ((~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z))))))))))),
% 4.04/4.23 inference(unit_resolution,[status(thm)],[15460, 178, 15135])).
% 4.04/4.23 tff(15462,plain,
% 4.04/4.23 (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))),
% 4.04/4.23 inference(unit_resolution,[status(thm)],[15461, 15454, 15451, 15450])).
% 4.04/4.23 tff(15463,plain,
% 4.04/4.23 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z))))) | r(s(s(s(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(s(s(s(z)))))))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z))))))),
% 4.04/4.23 inference(rewrite,[status(thm)],[])).
% 4.04/4.23 tff(15464,plain,
% 4.04/4.23 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z))))))),
% 4.04/4.23 inference(quant_inst,[status(thm)],[])).
% 4.04/4.23 tff(15465,plain,
% 4.04/4.23 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))),
% 4.04/4.23 inference(modus_ponens,[status(thm)],[15464, 15463])).
% 4.04/4.23 tff(15466,plain,
% 4.04/4.23 ((s(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(s(s(z))))) | r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))),
% 4.04/4.23 inference(unit_resolution,[status(thm)],[15465, 41, 15462])).
% 4.04/4.23 tff(15467,plain,
% 4.04/4.23 (r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))),
% 4.04/4.23 inference(unit_resolution,[status(thm)],[15466, 15447])).
% 4.04/4.23 tff(15468,plain,
% 4.04/4.23 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)))),
% 4.04/4.23 inference(rewrite,[status(thm)],[])).
% 4.04/4.23 tff(15469,plain,
% 4.04/4.23 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)))),
% 4.04/4.23 inference(quant_inst,[status(thm)],[])).
% 4.04/4.23 tff(15470,plain,
% 4.04/4.23 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), z))),
% 4.04/4.23 inference(modus_ponens,[status(thm)],[15469, 15468])).
% 4.04/4.23 tff(15471,plain,
% 4.04/4.23 (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)),
% 4.04/4.23 inference(unit_resolution,[status(thm)],[15470, 118, 145, 15467])).
% 4.04/4.23 tff(15472,plain,
% 4.04/4.23 (~r(s(s(s(elem!1))), z)),
% 4.04/4.23 inference(modus_ponens,[status(thm)],[15471, 15443])).
% 4.04/4.23 tff(15473,plain,
% 4.04/4.23 (b(s(s(s(elem!1))), z)),
% 4.04/4.23 inference(unit_resolution,[status(thm)],[1565, 15472])).
% 4.04/4.23 tff(15474,plain,
% 4.04/4.23 (b(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)),
% 4.04/4.23 inference(modus_ponens,[status(thm)],[15473, 15442])).
% 4.04/4.23 tff(15475,plain,
% 4.04/4.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))))),
% 4.04/4.23 inference(rewrite,[status(thm)],[])).
% 4.04/4.23 tff(15476,plain,
% 4.04/4.23 (((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~b(s(s(s(s(s(s(s(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(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z))))))))))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))))),
% 4.04/4.23 inference(rewrite,[status(thm)],[])).
% 4.04/4.23 tff(15477,plain,
% 4.04/4.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~b(s(s(s(s(s(s(s(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(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z))))))),
% 4.04/4.23 inference(monotonicity,[status(thm)],[15476])).
% 4.04/4.23 tff(15478,plain,
% 4.04/4.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~b(s(s(s(s(s(s(s(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(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))))),
% 4.04/4.23 inference(transitivity,[status(thm)],[15477, 15475])).
% 4.04/4.23 tff(15479,plain,
% 4.04/4.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~b(s(s(s(s(s(s(s(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(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 4.04/4.24 inference(quant_inst,[status(thm)],[])).
% 4.04/4.24 tff(15480,plain,
% 4.04/4.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z))))),
% 4.04/4.24 inference(modus_ponens,[status(thm)],[15479, 15478])).
% 4.04/4.24 tff(15481,plain,
% 4.04/4.24 (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[15480, 178, 3461, 1146, 15451, 15454, 15474, 15440])).
% 4.04/4.24 tff(15482,plain,
% 4.04/4.24 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))))),
% 4.04/4.24 inference(rewrite,[status(thm)],[])).
% 4.04/4.24 tff(15483,plain,
% 4.04/4.24 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))))),
% 4.04/4.24 inference(quant_inst,[status(thm)],[])).
% 4.04/4.24 tff(15484,plain,
% 4.04/4.24 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z))))),
% 4.04/4.24 inference(modus_ponens,[status(thm)],[15483, 15482])).
% 4.04/4.24 tff(15485,plain,
% 4.04/4.24 (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[15484, 118, 147, 15467])).
% 4.04/4.24 tff(15486,plain,
% 4.04/4.24 ((s(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(z))) | b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[7943, 41, 15485])).
% 4.04/4.24 tff(15487,plain,
% 4.04/4.24 ($false),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[15486, 15481, 10502])).
% 4.04/4.24 tff(15488,plain,((~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 4.04/4.24 tff(15489,plain,
% 4.04/4.24 (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[15488, 15269, 3461, 15420, 147, 145, 2857, 10020, 14938, 15437])).
% 4.04/4.24 tff(15490,plain,
% 4.04/4.24 (~b(s(s(s(elem!1))), s(elem!1))),
% 4.04/4.24 inference(modus_ponens,[status(thm)],[15489, 15433])).
% 4.04/4.24 tff(15491,plain,
% 4.04/4.24 (r(s(s(s(elem!1))), s(elem!1))),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[373, 15490, 15431])).
% 4.04/4.24 tff(15492,plain,
% 4.04/4.24 (r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.04/4.24 inference(modus_ponens,[status(thm)],[15491, 15429])).
% 4.04/4.24 tff(15493,plain,
% 4.04/4.24 (r(s(s(z)), s(s(s(s(s(s(s(s(z))))))))) <=> r(s(s(z)), s(elem!1))),
% 4.04/4.24 inference(monotonicity,[status(thm)],[15427])).
% 4.04/4.24 tff(15494,plain,
% 4.04/4.24 (r(s(s(z)), s(elem!1)) <=> r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 4.04/4.24 inference(symmetry,[status(thm)],[15493])).
% 4.04/4.24 tff(15495,plain,
% 4.04/4.24 (r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 4.04/4.24 inference(modus_ponens,[status(thm)],[15302, 15494])).
% 4.04/4.24 tff(15496,plain,
% 4.04/4.24 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 4.04/4.24 inference(rewrite,[status(thm)],[])).
% 4.04/4.24 tff(15497,plain,
% 4.04/4.24 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 4.04/4.24 inference(quant_inst,[status(thm)],[])).
% 4.04/4.24 tff(15498,plain,
% 4.04/4.24 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(s(s(z))))))))))))),
% 4.04/4.24 inference(modus_ponens,[status(thm)],[15497, 15496])).
% 4.04/4.24 tff(15499,plain,
% 4.04/4.24 ((~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(s(s(z))))))))))))),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[15498, 118])).
% 4.04/4.24 tff(15500,plain,
% 4.04/4.24 (~r(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[15499, 15495, 15492])).
% 4.04/4.24 tff(15501,plain,
% 4.04/4.24 (~r(s(s(z)), s(s(s(elem!1))))),
% 4.04/4.24 inference(modus_ponens,[status(thm)],[15500, 15426])).
% 4.04/4.24 tff(15502,plain,
% 4.04/4.24 (b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z))))))))))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 4.04/4.24 inference(monotonicity,[status(thm)],[15424])).
% 4.04/4.24 tff(15503,plain,
% 4.04/4.24 ((~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) <=> (~b(s(s(z)), s(s(s(elem!1)))))),
% 4.04/4.24 inference(monotonicity,[status(thm)],[15502])).
% 4.04/4.24 tff(15504,plain,
% 4.04/4.24 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 4.04/4.24 inference(symmetry,[status(thm)],[15420])).
% 4.04/4.24 tff(15505,plain,
% 4.04/4.24 (b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(elem!1))), elem!1)),
% 4.04/4.24 inference(monotonicity,[status(thm)],[15424, 15504])).
% 4.04/4.24 tff(15506,plain,
% 4.04/4.24 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.24 inference(symmetry,[status(thm)],[15505])).
% 4.04/4.24 tff(15507,plain,
% 4.04/4.24 (~(s(s(s(elem!1))) = elem!1)),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[2489, 15436])).
% 4.04/4.24 tff(15508,plain,
% 4.04/4.24 (~r(elem!1, s(s(s(s(z)))))),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[478, 15394, 145])).
% 4.04/4.24 tff(15509,plain,
% 4.04/4.24 (b(elem!1, s(s(s(s(z)))))),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[483, 15508, 469])).
% 4.04/4.24 tff(15510,plain,
% 4.04/4.24 (~b(s(elem!1), elem!1)),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[14949, 178, 15396, 14938, 15509, 1069])).
% 4.04/4.24 tff(15511,plain,
% 4.04/4.24 (~(s(elem!1) = elem!1)),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[672, 15430])).
% 4.04/4.24 tff(15512,plain,
% 4.04/4.24 (r(s(elem!1), elem!1)),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[677, 15511, 15510])).
% 4.04/4.24 tff(15513,plain,
% 4.04/4.24 (~r(s(s(s(elem!1))), elem!1)),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[1576, 15491, 15512])).
% 4.04/4.24 tff(15514,plain,
% 4.04/4.24 (b(s(s(s(elem!1))), elem!1)),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[570, 15513, 15507])).
% 4.04/4.24 tff(15515,plain,
% 4.04/4.24 (b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.24 inference(modus_ponens,[status(thm)],[15514, 15506])).
% 4.04/4.24 tff(15516,plain,
% 4.04/4.24 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z))))))))))) <=> b(elem!1, s(s(s(elem!1))))),
% 4.04/4.24 inference(monotonicity,[status(thm)],[15504, 15424])).
% 4.04/4.24 tff(15517,plain,
% 4.04/4.24 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 4.04/4.24 inference(symmetry,[status(thm)],[15516])).
% 4.04/4.24 tff(15518,plain,
% 4.04/4.24 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 4.04/4.24 inference(modus_ponens,[status(thm)],[15437, 15517])).
% 4.04/4.24 tff(15519,plain,
% 4.04/4.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(z)), 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))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(z)), 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))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))))),
% 4.04/4.24 inference(rewrite,[status(thm)],[])).
% 4.04/4.24 tff(15520,plain,
% 4.04/4.24 (((~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(z)), 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))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))))),
% 4.04/4.24 inference(rewrite,[status(thm)],[])).
% 4.04/4.24 tff(15521,plain,
% 4.04/4.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(z)), 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))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z)))))))))))),
% 4.04/4.24 inference(monotonicity,[status(thm)],[15520])).
% 4.04/4.24 tff(15522,plain,
% 4.04/4.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(z)), 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))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))))),
% 4.04/4.24 inference(transitivity,[status(thm)],[15521, 15519])).
% 4.04/4.24 tff(15523,plain,
% 4.04/4.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 4.04/4.24 inference(quant_inst,[status(thm)],[])).
% 4.04/4.24 tff(15524,plain,
% 4.04/4.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z)))))))))),
% 4.04/4.24 inference(modus_ponens,[status(thm)],[15523, 15522])).
% 4.04/4.24 tff(15525,plain,
% 4.04/4.24 ((~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z)))))))))),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[15524, 178, 15278, 15269])).
% 4.04/4.24 tff(15526,plain,
% 4.04/4.24 (~b(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[15525, 15518, 15515])).
% 4.04/4.24 tff(15527,plain,
% 4.04/4.24 (~b(s(s(z)), s(s(s(elem!1))))),
% 4.04/4.24 inference(modus_ponens,[status(thm)],[15526, 15503])).
% 4.04/4.24 tff(15528,plain,
% 4.04/4.24 ($false),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[4223, 15527, 15501])).
% 4.04/4.24 tff(15529,plain,(r(s(s(s(s(s(s(s(z))))))), s(s(z))) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (s(s(s(s(z)))) = s(elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (elem!1 = s(s(s(s(z))))) | b(elem!1, z) | (~r(s(s(s(s(z)))), s(s(z)))) | r(z, s(s(z))) | (~r(s(elem!1), s(s(z)))) | r(s(elem!1), z) | (elem!1 = s(s(z))) | (s(s(z)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.04/4.24 tff(15530,plain,
% 4.04/4.24 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[15529, 15268, 147, 145, 3461, 2169, 15264, 469, 5723, 193, 48, 15262, 767, 312, 15267])).
% 4.04/4.24 tff(15531,plain,
% 4.04/4.24 (s(s(s(s(s(s(s(z))))))) = s(elem!1)),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[15104, 15530, 15135, 15266, 15264, 193, 15262])).
% 4.04/4.24 tff(15532,plain,
% 4.04/4.24 (~(elem!1 = s(s(s(elem!1))))),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[4015, 15531, 2169])).
% 4.04/4.24 tff(15533,plain,
% 4.04/4.24 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(elem!1))),
% 4.04/4.24 inference(monotonicity,[status(thm)],[15531])).
% 4.04/4.24 tff(15534,plain,
% 4.04/4.24 (s(s(s(s(s(s(z)))))) = elem!1),
% 4.04/4.24 inference(transitivity,[status(thm)],[609, 15533, 304])).
% 4.04/4.24 tff(15535,plain,
% 4.04/4.24 ((s(s(s(s(s(s(z)))))) = z) <=> (elem!1 = z)),
% 4.04/4.24 inference(monotonicity,[status(thm)],[15534])).
% 4.04/4.24 tff(15536,plain,
% 4.04/4.24 ((s(s(s(s(s(s(z)))))) = z) <=> (z = elem!1)),
% 4.04/4.24 inference(transitivity,[status(thm)],[15535, 313])).
% 4.04/4.24 tff(15537,plain,
% 4.04/4.24 ((s(s(s(s(s(s(z)))))) = z) <=> (elem!1 = z)),
% 4.04/4.24 inference(transitivity,[status(thm)],[15536, 314])).
% 4.04/4.24 tff(15538,plain,
% 4.04/4.24 ((~(s(s(s(s(s(s(z)))))) = z)) <=> (~(elem!1 = z))),
% 4.04/4.24 inference(monotonicity,[status(thm)],[15537])).
% 4.04/4.24 tff(15539,plain,
% 4.04/4.24 (~(elem!1 = z)),
% 4.04/4.24 inference(modus_ponens,[status(thm)],[433, 15538])).
% 4.04/4.24 tff(15540,plain,
% 4.04/4.24 (r(elem!1, z)),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[498, 15539, 5723])).
% 4.04/4.24 tff(15541,plain,
% 4.04/4.24 (~(elem!1 = s(elem!1))),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[12026, 10020, 5723])).
% 4.04/4.24 tff(15542,plain,
% 4.04/4.24 (~r(elem!1, s(s(s(s(z)))))),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[478, 15540, 145])).
% 4.04/4.24 tff(15543,plain,
% 4.04/4.24 (b(elem!1, s(s(s(s(z)))))),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[483, 15542, 469])).
% 4.04/4.24 tff(15544,plain,
% 4.04/4.24 (~b(elem!1, s(elem!1))),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[8659, 15543, 10020, 15264, 15540, 551, 15266])).
% 4.04/4.24 tff(15545,plain,
% 4.04/4.24 (r(elem!1, s(elem!1))),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[756, 15544, 15541])).
% 4.04/4.24 tff(15546,plain,
% 4.04/4.24 (~r(z, s(elem!1))),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[12189, 15545, 15540])).
% 4.04/4.24 tff(15547,plain,
% 4.04/4.24 (b(z, s(elem!1))),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[2351, 15546])).
% 4.04/4.24 tff(15548,plain,
% 4.04/4.24 (~(s(s(elem!1)) = elem!1)),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[666, 15531, 551])).
% 4.04/4.24 tff(15549,plain,
% 4.04/4.24 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[348, 15548])).
% 4.04/4.24 tff(15550,plain,
% 4.04/4.24 (~(s(elem!1) = s(s(s(elem!1))))),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[5395, 15549])).
% 4.04/4.24 tff(15551,plain,
% 4.04/4.24 (~b(s(s(z)), s(elem!1))),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[6788, 178, 15547, 10020, 3461, 144])).
% 4.04/4.24 tff(15552,plain,
% 4.04/4.24 (r(s(s(z)), s(elem!1))),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[1067, 15551, 15267])).
% 4.04/4.24 tff(15553,plain,
% 4.04/4.24 (~r(elem!1, s(s(s(elem!1))))),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[6352, 15552, 3461, 144, 10020, 15550, 15540, 15547])).
% 4.04/4.24 tff(15554,plain,
% 4.04/4.24 (b(elem!1, s(s(s(elem!1))))),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[2054, 15553, 15532])).
% 4.04/4.24 tff(15555,plain,
% 4.04/4.24 (~r(elem!1, s(s(z)))),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[3071, 118, 15545, 15552])).
% 4.04/4.24 tff(15556,plain,
% 4.04/4.24 (b(elem!1, s(s(z)))),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[467, 15555, 312])).
% 4.04/4.24 tff(15557,plain,
% 4.04/4.24 (~(s(elem!1) = elem!1)),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[672, 15548])).
% 4.04/4.24 tff(15558,plain,
% 4.04/4.24 (~r(s(elem!1), z)),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[2711, 437, 1587])).
% 4.04/4.24 tff(15559,plain,
% 4.04/4.24 (b(s(elem!1), z)),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[774, 15558])).
% 4.04/4.24 tff(15560,plain,
% 4.04/4.24 (~r(z, s(elem!1))),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[12189, 437, 1587])).
% 4.04/4.24 tff(15561,plain,
% 4.04/4.24 (b(z, s(elem!1))),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[2351, 15560])).
% 4.04/4.24 tff(15562,plain,
% 4.04/4.24 ($false),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[15298, 178, 15561, 15559, 168, 8640, 1069])).
% 4.04/4.24 tff(15563,plain,((~r(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 4.04/4.24 tff(15564,plain,
% 4.04/4.24 (~b(s(s(s(s(z)))), z)),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[15563, 15545, 15264, 15266, 15540])).
% 4.04/4.24 tff(15565,plain,
% 4.04/4.24 (r(s(s(s(s(z)))), z)),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[191, 15564])).
% 4.04/4.24 tff(15566,plain,
% 4.04/4.24 (~r(s(s(s(s(z)))), elem!1)),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[6033, 15565, 15540])).
% 4.04/4.24 tff(15567,plain,
% 4.04/4.24 (b(s(s(s(s(z)))), elem!1)),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[3142, 15566, 551])).
% 4.04/4.24 tff(15568,plain,
% 4.04/4.24 (~b(s(elem!1), elem!1)),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[14949, 178, 15567, 15266, 15543, 15264])).
% 4.04/4.24 tff(15569,plain,
% 4.04/4.24 (r(s(elem!1), elem!1)),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[677, 15568, 15557])).
% 4.04/4.24 tff(15570,plain,
% 4.04/4.24 (~r(s(s(z)), elem!1)),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[2249, 15569, 15262])).
% 4.04/4.24 tff(15571,plain,
% 4.04/4.24 (b(s(s(z)), elem!1)),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[448, 15570, 12])).
% 4.04/4.24 tff(15572,plain,
% 4.04/4.24 (~(s(s(s(elem!1))) = elem!1)),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[2489, 15532])).
% 4.04/4.24 tff(15573,plain,
% 4.04/4.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(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)))))))),
% 4.04/4.24 inference(rewrite,[status(thm)],[])).
% 4.04/4.24 tff(15574,plain,
% 4.04/4.24 (((~b(s(s(s(s(z)))), s(elem!1))) | (~b(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(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 4.04/4.24 inference(rewrite,[status(thm)],[])).
% 4.04/4.24 tff(15575,plain,
% 4.04/4.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(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(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(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))))))))),
% 4.04/4.24 inference(monotonicity,[status(thm)],[15574])).
% 4.04/4.24 tff(15576,plain,
% 4.04/4.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(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(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(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)))))))),
% 4.04/4.24 inference(transitivity,[status(thm)],[15575, 15573])).
% 4.04/4.24 tff(15577,plain,
% 4.04/4.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(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(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 4.04/4.24 inference(quant_inst,[status(thm)],[])).
% 4.04/4.24 tff(15578,plain,
% 4.04/4.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(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))))))),
% 4.04/4.24 inference(modus_ponens,[status(thm)],[15577, 15576])).
% 4.04/4.24 tff(15579,plain,
% 4.04/4.24 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[15578, 178, 2044, 2042, 8640, 1301])).
% 4.04/4.24 tff(15580,plain,
% 4.04/4.24 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[3825, 41, 2857, 15579])).
% 4.04/4.24 tff(15581,plain,
% 4.04/4.24 (~r(s(s(s(elem!1))), z)),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[8018, 118, 145, 15580])).
% 4.04/4.24 tff(15582,plain,
% 4.04/4.24 (b(s(s(s(elem!1))), z)),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[1565, 15581])).
% 4.04/4.24 tff(15583,plain,
% 4.04/4.24 (~r(s(s(z)), s(s(s(elem!1))))),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[8079, 118, 147, 15580])).
% 4.04/4.24 tff(15584,plain,
% 4.04/4.24 (b(s(s(z)), s(s(s(elem!1))))),
% 4.04/4.24 inference(unit_resolution,[status(thm)],[4223, 15583])).
% 4.04/4.24 tff(15585,plain,
% 4.04/4.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)))),
% 4.04/4.24 inference(rewrite,[status(thm)],[])).
% 4.04/4.24 tff(15586,plain,
% 4.04/4.24 (((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)))),
% 4.04/4.24 inference(rewrite,[status(thm)],[])).
% 4.04/4.24 tff(15587,plain,
% 4.04/4.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z))))),
% 4.04/4.25 inference(monotonicity,[status(thm)],[15586])).
% 4.04/4.25 tff(15588,plain,
% 4.04/4.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)))),
% 4.04/4.25 inference(transitivity,[status(thm)],[15587, 15585])).
% 4.04/4.25 tff(15589,plain,
% 4.04/4.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 4.04/4.25 inference(quant_inst,[status(thm)],[])).
% 4.04/4.25 tff(15590,plain,
% 4.04/4.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z))),
% 4.04/4.25 inference(modus_ponens,[status(thm)],[15589, 15588])).
% 4.04/4.25 tff(15591,plain,
% 4.04/4.25 ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[15590, 178, 2044, 855, 3461])).
% 4.04/4.25 tff(15592,plain,
% 4.04/4.25 ($false),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[15591, 15584, 15582])).
% 4.04/4.25 tff(15593,plain,((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.04/4.25 tff(15594,plain,
% 4.04/4.25 (~b(s(s(s(elem!1))), s(elem!1))),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[15593, 15547, 3461, 147, 145, 15268, 15554, 15266, 15543])).
% 4.04/4.25 tff(15595,plain,
% 4.04/4.25 (r(s(s(s(elem!1))), s(elem!1))),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[373, 15594, 15549])).
% 4.04/4.25 tff(15596,plain,
% 4.04/4.25 (~r(s(s(s(elem!1))), elem!1)),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[1576, 15595, 15569])).
% 4.04/4.25 tff(15597,plain,
% 4.04/4.25 (b(s(s(s(elem!1))), elem!1)),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[570, 15596, 15572])).
% 4.04/4.25 tff(15598,plain,
% 4.04/4.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 4.04/4.25 inference(rewrite,[status(thm)],[])).
% 4.04/4.25 tff(15599,plain,
% 4.04/4.25 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(elem!1, s(s(z))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 4.04/4.25 inference(rewrite,[status(thm)],[])).
% 4.04/4.25 tff(15600,plain,
% 4.04/4.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 4.04/4.25 inference(monotonicity,[status(thm)],[15599])).
% 4.04/4.25 tff(15601,plain,
% 4.04/4.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 4.04/4.25 inference(transitivity,[status(thm)],[15600, 15598])).
% 4.04/4.25 tff(15602,plain,
% 4.04/4.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))))),
% 4.04/4.25 inference(quant_inst,[status(thm)],[])).
% 4.04/4.25 tff(15603,plain,
% 4.04/4.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 4.04/4.25 inference(modus_ponens,[status(thm)],[15602, 15601])).
% 4.04/4.25 tff(15604,plain,
% 4.04/4.25 (~b(s(s(z)), s(s(s(elem!1))))),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[15603, 178, 15597, 15571, 15556, 15554])).
% 4.04/4.25 tff(15605,plain,
% 4.04/4.25 (~r(s(s(z)), s(s(s(elem!1))))),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[6276, 118, 15595, 15552])).
% 4.04/4.25 tff(15606,plain,
% 4.04/4.25 ($false),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[4223, 15605, 15604])).
% 4.04/4.25 tff(15607,plain,((elem!1 = s(s(s(s(z))))) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (s(s(z)) = elem!1) | b(elem!1, z) | (~r(s(s(s(s(z)))), s(s(z)))) | r(z, s(s(z))) | r(s(elem!1), z) | (s(elem!1) = s(s(s(s(z))))) | b(s(elem!1), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.04/4.25 tff(15608,plain,
% 4.04/4.25 (elem!1 = s(s(s(s(z))))),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[15607, 15131, 147, 47, 12, 5723, 103, 14874, 5619, 1369, 305])).
% 4.04/4.25 tff(15609,plain,
% 4.04/4.25 (s(s(s(s(z)))) = elem!1),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[325, 15608])).
% 4.04/4.25 tff(15610,plain,
% 4.04/4.25 (~(s(s(elem!1)) = elem!1)),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[338, 15609, 12])).
% 4.04/4.25 tff(15611,plain,
% 4.04/4.25 (~(s(elem!1) = s(s(elem!1)))),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[979, 15610])).
% 4.04/4.25 tff(15612,plain,
% 4.04/4.25 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[348, 15610])).
% 4.04/4.25 tff(15613,plain,
% 4.04/4.25 (s(elem!1) = s(s(s(s(s(z)))))),
% 4.04/4.25 inference(monotonicity,[status(thm)],[15608])).
% 4.04/4.25 tff(15614,plain,
% 4.04/4.25 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 4.04/4.25 inference(monotonicity,[status(thm)],[15613])).
% 4.04/4.25 tff(15615,plain,
% 4.04/4.25 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 4.04/4.25 inference(monotonicity,[status(thm)],[15614])).
% 4.04/4.25 tff(15616,plain,
% 4.04/4.25 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.04/4.25 inference(monotonicity,[status(thm)],[15615])).
% 4.04/4.25 tff(15617,plain,
% 4.04/4.25 (b(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 4.04/4.25 inference(symmetry,[status(thm)],[15616])).
% 4.04/4.25 tff(15618,plain,
% 4.04/4.25 (s(s(s(s(s(z))))) = s(elem!1)),
% 4.04/4.25 inference(symmetry,[status(thm)],[15613])).
% 4.04/4.25 tff(15619,plain,
% 4.04/4.25 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.04/4.25 inference(monotonicity,[status(thm)],[15618])).
% 4.04/4.25 tff(15620,plain,
% 4.04/4.25 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 4.04/4.25 inference(transitivity,[status(thm)],[15619, 15617])).
% 4.04/4.25 tff(15621,plain,
% 4.04/4.25 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 4.04/4.25 inference(monotonicity,[status(thm)],[15620])).
% 4.04/4.25 tff(15622,plain,
% 4.04/4.25 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 4.04/4.25 inference(monotonicity,[status(thm)],[15618])).
% 4.04/4.25 tff(15623,plain,
% 4.04/4.25 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 4.04/4.25 inference(symmetry,[status(thm)],[15622])).
% 4.04/4.25 tff(15624,plain,
% 4.04/4.25 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 4.04/4.25 inference(monotonicity,[status(thm)],[15618])).
% 4.04/4.25 tff(15625,plain,
% 4.04/4.25 ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) <=> (~r(s(s(s(s(z)))), s(elem!1)))),
% 4.04/4.25 inference(monotonicity,[status(thm)],[15624])).
% 4.04/4.25 tff(15626,plain,
% 4.04/4.25 (r(s(elem!1), s(s(z))) <=> r(s(s(s(s(s(z))))), s(s(z)))),
% 4.04/4.25 inference(monotonicity,[status(thm)],[15613])).
% 4.04/4.25 tff(15627,plain,
% 4.04/4.25 (~(s(elem!1) = s(s(z)))),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[11438, 15608])).
% 4.04/4.25 tff(15628,plain,
% 4.04/4.25 (r(s(elem!1), s(s(z)))),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[421, 15627, 305])).
% 4.04/4.25 tff(15629,plain,
% 4.04/4.25 (r(s(s(s(s(s(z))))), s(s(z)))),
% 4.04/4.25 inference(modus_ponens,[status(thm)],[15628, 15626])).
% 4.04/4.25 tff(15630,plain,
% 4.04/4.25 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 4.04/4.25 inference(rewrite,[status(thm)],[])).
% 4.04/4.25 tff(15631,plain,
% 4.04/4.25 (((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 4.04/4.25 inference(rewrite,[status(thm)],[])).
% 4.04/4.25 tff(15632,plain,
% 4.04/4.25 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 4.04/4.25 inference(monotonicity,[status(thm)],[15631])).
% 4.04/4.25 tff(15633,plain,
% 4.04/4.25 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 4.04/4.25 inference(transitivity,[status(thm)],[15632, 15630])).
% 4.04/4.25 tff(15634,plain,
% 4.04/4.25 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 4.04/4.25 inference(quant_inst,[status(thm)],[])).
% 4.04/4.25 tff(15635,plain,
% 4.04/4.25 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 4.04/4.25 inference(modus_ponens,[status(thm)],[15634, 15633])).
% 4.04/4.25 tff(15636,plain,
% 4.04/4.25 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[15635, 118, 103, 15629])).
% 4.04/4.25 tff(15637,plain,
% 4.04/4.25 (~r(s(s(s(s(z)))), s(elem!1))),
% 4.04/4.25 inference(modus_ponens,[status(thm)],[15636, 15625])).
% 4.04/4.25 tff(15638,plain,
% 4.04/4.25 (b(s(s(s(s(z)))), s(elem!1))),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[2173, 15637, 2169])).
% 4.04/4.25 tff(15639,plain,
% 4.04/4.25 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 4.04/4.25 inference(modus_ponens,[status(thm)],[15638, 15623])).
% 4.04/4.25 tff(15640,plain,
% 4.04/4.25 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 4.04/4.25 inference(monotonicity,[status(thm)],[15618])).
% 4.04/4.25 tff(15641,plain,
% 4.04/4.25 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 4.04/4.25 inference(symmetry,[status(thm)],[15640])).
% 4.04/4.25 tff(15642,plain,
% 4.04/4.25 (b(s(elem!1), z)),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[774, 15131])).
% 4.04/4.25 tff(15643,plain,
% 4.04/4.25 (~r(s(elem!1), s(s(s(s(z)))))),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[6776, 15627, 5619, 14881, 147, 15642])).
% 4.04/4.25 tff(15644,plain,
% 4.04/4.25 (b(s(elem!1), s(s(s(s(z)))))),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[1084, 15643, 1369])).
% 4.04/4.25 tff(15645,plain,
% 4.04/4.25 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 4.04/4.25 inference(modus_ponens,[status(thm)],[15644, 15641])).
% 4.04/4.25 tff(15646,plain,
% 4.04/4.25 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.25 inference(monotonicity,[status(thm)],[15615])).
% 4.04/4.25 tff(15647,plain,
% 4.04/4.25 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.04/4.25 inference(monotonicity,[status(thm)],[15608])).
% 4.04/4.25 tff(15648,plain,
% 4.04/4.25 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.25 inference(transitivity,[status(thm)],[15647, 15646])).
% 4.04/4.25 tff(15649,plain,
% 4.04/4.25 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.04/4.25 inference(monotonicity,[status(thm)],[15608])).
% 4.04/4.25 tff(15650,plain,
% 4.04/4.25 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = elem!1)),
% 4.04/4.25 inference(symmetry,[status(thm)],[15649])).
% 4.04/4.25 tff(15651,plain,
% 4.04/4.25 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(z)))))),
% 4.04/4.25 inference(monotonicity,[status(thm)],[15615])).
% 4.04/4.25 tff(15652,plain,
% 4.04/4.25 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.04/4.25 inference(symmetry,[status(thm)],[15651])).
% 4.04/4.25 tff(15653,plain,
% 4.04/4.25 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(elem!1))))),
% 4.04/4.25 inference(transitivity,[status(thm)],[15652, 15650, 2486])).
% 4.04/4.25 tff(15654,plain,
% 4.04/4.25 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 4.04/4.25 inference(monotonicity,[status(thm)],[15653])).
% 4.04/4.25 tff(15655,plain,
% 4.04/4.25 (~(elem!1 = s(s(s(elem!1))))),
% 4.04/4.25 inference(modus_ponens,[status(thm)],[79, 15654])).
% 4.04/4.25 tff(15656,plain,
% 4.04/4.25 (r(elem!1, z) <=> r(s(s(s(s(z)))), z)),
% 4.04/4.25 inference(monotonicity,[status(thm)],[15608])).
% 4.04/4.25 tff(15657,plain,
% 4.04/4.25 (r(s(s(s(s(z)))), z) <=> r(elem!1, z)),
% 4.04/4.25 inference(symmetry,[status(thm)],[15656])).
% 4.04/4.25 tff(15658,plain,
% 4.04/4.25 (~b(s(s(s(s(z)))), z)),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[12557, 15608, 5723])).
% 4.04/4.25 tff(15659,plain,
% 4.04/4.25 (r(s(s(s(s(z)))), z)),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[191, 15658])).
% 4.04/4.25 tff(15660,plain,
% 4.04/4.25 (r(elem!1, z)),
% 4.04/4.25 inference(modus_ponens,[status(thm)],[15659, 15657])).
% 4.04/4.25 tff(15661,plain,
% 4.04/4.25 (r(z, elem!1) <=> r(z, s(s(s(s(z)))))),
% 4.04/4.25 inference(monotonicity,[status(thm)],[15608])).
% 4.04/4.25 tff(15662,plain,
% 4.04/4.25 (r(z, s(s(s(s(z))))) <=> r(z, elem!1)),
% 4.04/4.25 inference(symmetry,[status(thm)],[15661])).
% 4.04/4.25 tff(15663,plain,
% 4.04/4.25 (r(z, elem!1)),
% 4.04/4.25 inference(modus_ponens,[status(thm)],[47, 15662])).
% 4.04/4.25 tff(15664,plain,
% 4.04/4.25 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 4.04/4.25 inference(monotonicity,[status(thm)],[15615])).
% 4.04/4.25 tff(15665,plain,
% 4.04/4.25 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.04/4.25 inference(transitivity,[status(thm)],[15664, 377])).
% 4.04/4.25 tff(15666,plain,
% 4.04/4.25 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 4.04/4.25 inference(monotonicity,[status(thm)],[15665])).
% 4.04/4.25 tff(15667,plain,
% 4.04/4.25 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.04/4.25 inference(modus_ponens,[status(thm)],[15612, 15666])).
% 4.04/4.25 tff(15668,plain,
% 4.04/4.25 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[14913, 15638, 15667, 15644, 14876, 15628, 103])).
% 4.04/4.25 tff(15669,plain,
% 4.04/4.25 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[249, 15668])).
% 4.04/4.25 tff(15670,plain,
% 4.04/4.25 (~r(elem!1, s(s(s(elem!1))))),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[15029, 15669, 14881, 5619, 15608, 15663, 15660])).
% 4.04/4.25 tff(15671,plain,
% 4.04/4.25 (b(elem!1, s(s(s(elem!1))))),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[2054, 15670, 15655])).
% 4.04/4.25 tff(15672,plain,
% 4.04/4.25 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.25 inference(modus_ponens,[status(thm)],[15671, 15648])).
% 4.04/4.25 tff(15673,plain,
% 4.04/4.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.04/4.25 inference(rewrite,[status(thm)],[])).
% 4.04/4.25 tff(15674,plain,
% 4.04/4.25 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.04/4.25 inference(rewrite,[status(thm)],[])).
% 4.04/4.25 tff(15675,plain,
% 4.04/4.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 4.04/4.25 inference(monotonicity,[status(thm)],[15674])).
% 4.04/4.25 tff(15676,plain,
% 4.04/4.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.04/4.25 inference(transitivity,[status(thm)],[15675, 15673])).
% 4.04/4.25 tff(15677,plain,
% 4.04/4.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.04/4.25 inference(quant_inst,[status(thm)],[])).
% 4.04/4.25 tff(15678,plain,
% 4.04/4.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 4.04/4.25 inference(modus_ponens,[status(thm)],[15677, 15676])).
% 4.04/4.25 tff(15679,plain,
% 4.04/4.25 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[15678, 178, 14876, 15672, 15645, 15639])).
% 4.04/4.25 tff(15680,plain,
% 4.04/4.25 (~b(s(s(s(elem!1))), s(elem!1))),
% 4.04/4.25 inference(modus_ponens,[status(thm)],[15679, 15621])).
% 4.04/4.25 tff(15681,plain,
% 4.04/4.25 (r(s(s(s(elem!1))), s(elem!1))),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[373, 15680, 15612])).
% 4.04/4.25 tff(15682,plain,
% 4.04/4.25 (~(s(elem!1) = s(s(s(elem!1))))),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[5395, 15612])).
% 4.04/4.25 tff(15683,plain,
% 4.04/4.25 (~(elem!1 = s(elem!1))),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[12026, 15642, 5723])).
% 4.04/4.25 tff(15684,plain,
% 4.04/4.25 (r(elem!1, s(elem!1)) <=> r(s(s(s(s(z)))), s(elem!1))),
% 4.04/4.25 inference(monotonicity,[status(thm)],[15608])).
% 4.04/4.25 tff(15685,plain,
% 4.04/4.25 (r(s(s(s(s(z)))), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 4.04/4.25 inference(symmetry,[status(thm)],[15684])).
% 4.04/4.25 tff(15686,plain,
% 4.04/4.25 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(elem!1, s(elem!1))),
% 4.04/4.25 inference(transitivity,[status(thm)],[15624, 15685])).
% 4.04/4.25 tff(15687,plain,
% 4.04/4.25 ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) <=> (~r(elem!1, s(elem!1)))),
% 4.04/4.25 inference(monotonicity,[status(thm)],[15686])).
% 4.04/4.25 tff(15688,plain,
% 4.04/4.25 (~r(elem!1, s(elem!1))),
% 4.04/4.25 inference(modus_ponens,[status(thm)],[15636, 15687])).
% 4.04/4.25 tff(15689,plain,
% 4.04/4.25 (b(elem!1, s(elem!1))),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[756, 15688, 15683])).
% 4.04/4.25 tff(15690,plain,
% 4.04/4.25 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 4.04/4.25 inference(monotonicity,[status(thm)],[15615, 15608])).
% 4.04/4.25 tff(15691,plain,
% 4.04/4.25 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), elem!1)),
% 4.04/4.25 inference(symmetry,[status(thm)],[15690])).
% 4.04/4.25 tff(15692,plain,
% 4.04/4.25 (b(s(s(s(elem!1))), elem!1)),
% 4.04/4.25 inference(modus_ponens,[status(thm)],[14876, 15691])).
% 4.04/4.25 tff(15693,plain,
% 4.04/4.25 (~(s(elem!1) = elem!1)),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[672, 15610])).
% 4.04/4.25 tff(15694,plain,
% 4.04/4.25 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(s(s(z)))))),
% 4.04/4.25 inference(monotonicity,[status(thm)],[15608])).
% 4.04/4.25 tff(15695,plain,
% 4.04/4.25 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(z)), elem!1)),
% 4.04/4.25 inference(symmetry,[status(thm)],[15694])).
% 4.04/4.25 tff(15696,plain,
% 4.04/4.25 (r(s(s(z)), elem!1)),
% 4.04/4.25 inference(modus_ponens,[status(thm)],[147, 15695])).
% 4.04/4.25 tff(15697,plain,
% 4.04/4.25 (~r(s(elem!1), elem!1)),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[2249, 15628, 15696])).
% 4.04/4.25 tff(15698,plain,
% 4.04/4.25 (b(s(elem!1), elem!1)),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[677, 15697, 15693])).
% 4.04/4.25 tff(15699,plain,
% 4.04/4.25 (~b(s(elem!1), s(s(s(elem!1))))),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[6834, 15671, 15698, 15692, 15689])).
% 4.04/4.25 tff(15700,plain,
% 4.04/4.25 (r(s(elem!1), s(s(s(elem!1))))),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[5432, 15699, 15682])).
% 4.04/4.25 tff(15701,plain,
% 4.04/4.25 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[3356, 15611])).
% 4.04/4.25 tff(15702,plain,
% 4.04/4.25 (s(s(s(s(z)))) = elem!1),
% 4.04/4.25 inference(symmetry,[status(thm)],[15608])).
% 4.04/4.25 tff(15703,plain,
% 4.04/4.25 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 4.04/4.25 inference(symmetry,[status(thm)],[15614])).
% 4.04/4.25 tff(15704,plain,
% 4.04/4.25 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> r(s(s(elem!1)), elem!1)),
% 4.04/4.25 inference(monotonicity,[status(thm)],[15703, 15702])).
% 4.04/4.25 tff(15705,plain,
% 4.04/4.25 ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) <=> (~r(s(s(elem!1)), elem!1))),
% 4.04/4.25 inference(monotonicity,[status(thm)],[15704])).
% 4.04/4.25 tff(15706,plain,
% 4.04/4.25 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[11534, 15608, 5619, 14881, 147, 47])).
% 4.04/4.25 tff(15707,plain,
% 4.04/4.25 (~r(s(s(elem!1)), elem!1)),
% 4.04/4.25 inference(modus_ponens,[status(thm)],[15706, 15705])).
% 4.04/4.25 tff(15708,plain,
% 4.04/4.25 (b(s(s(elem!1)), elem!1)),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[3362, 15707, 15610])).
% 4.04/4.25 tff(15709,plain,
% 4.04/4.25 (~r(s(elem!1), s(s(elem!1)))),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[10103, 15708, 15671, 15692, 15701, 15700, 15681])).
% 4.04/4.25 tff(15710,plain,
% 4.04/4.25 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(s(s(s(z))))))))),
% 4.04/4.25 inference(monotonicity,[status(thm)],[15615])).
% 4.04/4.25 tff(15711,plain,
% 4.04/4.25 (r(z, s(s(s(s(s(s(s(z)))))))) <=> r(z, s(s(s(elem!1))))),
% 4.04/4.25 inference(symmetry,[status(thm)],[15710])).
% 4.04/4.25 tff(15712,plain,
% 4.04/4.25 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 4.04/4.25 inference(transitivity,[status(thm)],[15665, 655])).
% 4.04/4.25 tff(15713,plain,
% 4.04/4.25 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 4.04/4.25 inference(monotonicity,[status(thm)],[15712])).
% 4.04/4.25 tff(15714,plain,
% 4.04/4.25 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 4.04/4.25 inference(modus_ponens,[status(thm)],[15612, 15713])).
% 4.04/4.25 tff(15715,plain,
% 4.04/4.25 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[15104, 15638, 14876, 15714, 15644, 103, 15628])).
% 4.04/4.25 tff(15716,plain,
% 4.04/4.25 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[3578, 15715])).
% 4.04/4.25 tff(15717,plain,
% 4.04/4.25 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[3567, 178, 5619, 14881, 15669, 15716])).
% 4.04/4.25 tff(15718,plain,
% 4.04/4.25 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[271, 15717])).
% 4.04/4.25 tff(15719,plain,
% 4.04/4.25 (r(z, s(s(s(elem!1))))),
% 4.04/4.25 inference(modus_ponens,[status(thm)],[15718, 15711])).
% 4.04/4.25 tff(15720,plain,
% 4.04/4.25 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[11597, 15719, 15611, 15700])).
% 4.04/4.25 tff(15721,plain,
% 4.04/4.25 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[3375, 15720, 15701])).
% 4.04/4.25 tff(15722,plain,
% 4.04/4.25 (~b(s(elem!1), s(s(elem!1)))),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[5490, 15708, 15721, 15671, 15698])).
% 4.04/4.25 tff(15723,plain,
% 4.04/4.25 ($false),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[1028, 15722, 15709, 15611])).
% 4.04/4.25 tff(15724,plain,((s(elem!1) = s(s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | b(s(elem!1), s(s(z))) | (s(s(z)) = elem!1) | b(elem!1, z) | b(s(s(s(s(z)))), s(s(z))) | b(z, s(s(s(s(z))))) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 4.04/4.25 tff(15725,plain,
% 4.04/4.25 (s(elem!1) = s(s(s(s(z))))),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[15724, 1, 305, 12, 5723, 86, 147, 5618])).
% 4.04/4.25 tff(15726,plain,
% 4.04/4.25 (~(s(s(z)) = s(s(s(z))))),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[2196, 15725, 312])).
% 4.04/4.25 tff(15727,plain,
% 4.04/4.25 (~(s(s(s(z))) = s(s(z)))),
% 4.04/4.25 inference(modus_ponens,[status(thm)],[15726, 3005])).
% 4.04/4.25 tff(15728,plain,
% 4.04/4.25 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 4.04/4.25 inference(monotonicity,[status(thm)],[15725])).
% 4.04/4.25 tff(15729,plain,
% 4.04/4.25 (elem!1 = s(s(s(z)))),
% 4.04/4.25 inference(transitivity,[status(thm)],[517, 15728, 11])).
% 4.04/4.25 tff(15730,plain,
% 4.04/4.25 (b(elem!1, s(s(z))) <=> b(s(s(s(z))), s(s(z)))),
% 4.04/4.25 inference(monotonicity,[status(thm)],[15729])).
% 4.04/4.25 tff(15731,plain,
% 4.04/4.25 ((~b(elem!1, s(s(z)))) <=> (~b(s(s(s(z))), s(s(z))))),
% 4.04/4.25 inference(monotonicity,[status(thm)],[15730])).
% 4.04/4.25 tff(15732,plain,
% 4.04/4.25 ((s(elem!1) = elem!1) <=> (s(s(s(s(z)))) = elem!1)),
% 4.04/4.25 inference(monotonicity,[status(thm)],[15725])).
% 4.04/4.25 tff(15733,plain,
% 4.04/4.25 ((~(s(elem!1) = elem!1)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 4.04/4.25 inference(monotonicity,[status(thm)],[15732])).
% 4.04/4.25 tff(15734,plain,
% 4.04/4.25 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[13886, 15725])).
% 4.04/4.25 tff(15735,plain,
% 4.04/4.25 (~(elem!1 = s(s(elem!1)))),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[1539, 15734])).
% 4.04/4.25 tff(15736,plain,
% 4.04/4.25 (~(s(s(elem!1)) = elem!1)),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[1546, 15735])).
% 4.04/4.25 tff(15737,plain,
% 4.04/4.25 (~(s(elem!1) = elem!1)),
% 4.04/4.25 inference(unit_resolution,[status(thm)],[672, 15736])).
% 4.04/4.25 tff(15738,plain,
% 4.04/4.25 (~(s(s(s(s(z)))) = elem!1)),
% 4.04/4.25 inference(modus_ponens,[status(thm)],[15737, 15733])).
% 4.04/4.25 tff(15739,plain,
% 4.04/4.26 ((z = elem!1) <=> (z = s(s(s(z))))),
% 4.04/4.26 inference(monotonicity,[status(thm)],[15729])).
% 4.04/4.26 tff(15740,plain,
% 4.04/4.26 ((z = elem!1) <=> (s(s(s(z))) = z)),
% 4.04/4.26 inference(transitivity,[status(thm)],[15739, 4912])).
% 4.04/4.26 tff(15741,plain,
% 4.04/4.26 ((s(s(s(z))) = z) <=> (z = elem!1)),
% 4.04/4.26 inference(symmetry,[status(thm)],[15740])).
% 4.04/4.26 tff(15742,plain,
% 4.04/4.26 ((s(s(s(z))) = z) <=> (elem!1 = z)),
% 4.04/4.26 inference(transitivity,[status(thm)],[15741, 314])).
% 4.04/4.26 tff(15743,plain,
% 4.04/4.26 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = z))),
% 4.04/4.26 inference(monotonicity,[status(thm)],[15742])).
% 4.04/4.26 tff(15744,plain,
% 4.04/4.26 (~(elem!1 = z)),
% 4.04/4.26 inference(modus_ponens,[status(thm)],[77, 15743])).
% 4.04/4.26 tff(15745,plain,
% 4.04/4.26 (r(elem!1, z)),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[498, 15744, 5723])).
% 4.04/4.26 tff(15746,plain,
% 4.04/4.26 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.04/4.26 inference(monotonicity,[status(thm)],[1183])).
% 4.04/4.26 tff(15747,plain,
% 4.04/4.26 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.04/4.26 inference(symmetry,[status(thm)],[15746])).
% 4.04/4.26 tff(15748,plain,
% 4.04/4.26 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 4.04/4.26 inference(transitivity,[status(thm)],[1187, 3660])).
% 4.04/4.26 tff(15749,plain,
% 4.04/4.26 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(s(s(s(s(s(s(s(z))))))) = elem!1))),
% 4.04/4.26 inference(monotonicity,[status(thm)],[15748])).
% 4.04/4.26 tff(15750,plain,
% 4.04/4.26 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 4.04/4.26 inference(modus_ponens,[status(thm)],[1104, 15749])).
% 4.04/4.26 tff(15751,plain,
% 4.04/4.26 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.04/4.26 inference(monotonicity,[status(thm)],[1183])).
% 4.04/4.26 tff(15752,plain,
% 4.04/4.26 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) <=> (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 4.04/4.26 inference(monotonicity,[status(thm)],[15751])).
% 4.04/4.26 tff(15753,plain,
% 4.04/4.26 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[13886, 1117])).
% 4.04/4.26 tff(15754,plain,
% 4.04/4.26 (~(elem!1 = s(s(elem!1)))),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[1539, 15753])).
% 4.04/4.26 tff(15755,plain,
% 4.04/4.26 (~(s(s(elem!1)) = elem!1)),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[1546, 15754])).
% 4.04/4.26 tff(15756,plain,
% 4.04/4.26 (~(s(elem!1) = elem!1)),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[672, 15755])).
% 4.04/4.26 tff(15757,plain,
% 4.04/4.26 (~(s(s(s(s(z)))) = elem!1)),
% 4.04/4.26 inference(modus_ponens,[status(thm)],[15756, 9678])).
% 4.04/4.26 tff(15758,plain,
% 4.04/4.26 ((s(elem!1) = elem!1) <=> (elem!1 = s(s(s(s(z)))))),
% 4.04/4.26 inference(transitivity,[status(thm)],[9677, 501])).
% 4.04/4.26 tff(15759,plain,
% 4.04/4.26 ((~(s(elem!1) = elem!1)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 4.04/4.26 inference(monotonicity,[status(thm)],[15758])).
% 4.04/4.26 tff(15760,plain,
% 4.04/4.26 (~(elem!1 = s(s(s(s(z)))))),
% 4.04/4.26 inference(modus_ponens,[status(thm)],[15756, 15759])).
% 4.04/4.26 tff(15761,plain,
% 4.04/4.26 (b(elem!1, s(s(s(s(z)))))),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[483, 479, 15760])).
% 4.04/4.26 tff(15762,plain,
% 4.04/4.26 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.04/4.26 inference(modus_ponens,[status(thm)],[15761, 6046])).
% 4.04/4.26 tff(15763,plain,
% 4.04/4.26 (b(s(s(s(elem!1))), s(elem!1))),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[373, 7546, 15753])).
% 4.04/4.26 tff(15764,plain,
% 4.04/4.26 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 4.04/4.26 inference(modus_ponens,[status(thm)],[15763, 6039])).
% 4.04/4.26 tff(15765,plain,
% 4.04/4.26 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[3578, 3576])).
% 4.04/4.26 tff(15766,plain,
% 4.04/4.26 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 4.04/4.26 inference(monotonicity,[status(thm)],[6036, 7553])).
% 4.04/4.26 tff(15767,plain,
% 4.04/4.26 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.26 inference(symmetry,[status(thm)],[15766])).
% 4.04/4.26 tff(15768,plain,
% 4.04/4.26 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[1649, 15753])).
% 4.04/4.26 tff(15769,plain,
% 4.04/4.26 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[1657, 15768])).
% 4.04/4.26 tff(15770,plain,
% 4.04/4.26 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[1695, 15769])).
% 4.04/4.26 tff(15771,plain,
% 4.04/4.26 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 4.04/4.26 inference(monotonicity,[status(thm)],[6036, 7553])).
% 4.04/4.26 tff(15772,plain,
% 4.04/4.26 ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) <=> (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 4.04/4.26 inference(monotonicity,[status(thm)],[15771])).
% 4.04/4.26 tff(15773,plain,
% 4.04/4.26 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 4.04/4.26 inference(modus_ponens,[status(thm)],[2419, 15772])).
% 4.04/4.26 tff(15774,plain,
% 4.04/4.26 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[1750, 15773, 15770])).
% 4.04/4.26 tff(15775,plain,
% 4.04/4.26 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.26 inference(modus_ponens,[status(thm)],[15774, 15767])).
% 4.04/4.26 tff(15776,plain,
% 4.04/4.26 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[7299, 41, 9657, 3698])).
% 4.04/4.26 tff(15777,plain,
% 4.04/4.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(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(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(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(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 4.04/4.26 inference(rewrite,[status(thm)],[])).
% 4.04/4.26 tff(15778,plain,
% 4.04/4.26 (((~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(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(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))))))))) | (~b(s(s(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(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(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(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 4.04/4.26 inference(rewrite,[status(thm)],[])).
% 4.04/4.26 tff(15779,plain,
% 4.04/4.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(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(z)))))), s(s(s(s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(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(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))))),
% 4.04/4.26 inference(monotonicity,[status(thm)],[15778])).
% 4.04/4.26 tff(15780,plain,
% 4.04/4.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(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(z)))))), s(s(s(s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(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(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 4.04/4.26 inference(transitivity,[status(thm)],[15779, 15777])).
% 4.04/4.26 tff(15781,plain,
% 4.04/4.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(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(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 4.04/4.26 inference(quant_inst,[status(thm)],[])).
% 4.04/4.26 tff(15782,plain,
% 4.04/4.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))),
% 4.04/4.26 inference(modus_ponens,[status(thm)],[15781, 15780])).
% 4.04/4.26 tff(15783,plain,
% 4.04/4.26 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[15782, 178, 104, 3922, 6154])).
% 4.04/4.26 tff(15784,plain,
% 4.04/4.26 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[15783, 15776])).
% 4.04/4.26 tff(15785,plain,
% 4.04/4.26 ($false),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[15784, 15775])).
% 4.04/4.26 tff(15786,plain,((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~(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(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.04/4.26 tff(15787,plain,
% 4.04/4.26 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[15786, 15765, 15135, 15764, 193, 1117])).
% 4.04/4.26 tff(15788,plain,
% 4.04/4.26 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[6139, 15787, 6059])).
% 4.04/4.26 tff(15789,plain,
% 4.04/4.26 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 4.04/4.26 inference(modus_ponens,[status(thm)],[3576, 1129])).
% 4.04/4.26 tff(15790,plain,
% 4.04/4.26 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[1170, 15789])).
% 4.04/4.26 tff(15791,plain,
% 4.04/4.26 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[3920, 118, 193, 15765])).
% 4.04/4.26 tff(15792,plain,
% 4.04/4.26 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[222, 15791])).
% 4.04/4.26 tff(15793,plain,
% 4.04/4.26 (r(s(s(z)), s(s(s(s(elem!1))))) <=> r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.26 inference(monotonicity,[status(thm)],[1120])).
% 4.04/4.26 tff(15794,plain,
% 4.04/4.26 (r(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(z)), s(s(s(s(elem!1)))))),
% 4.04/4.26 inference(symmetry,[status(thm)],[15793])).
% 4.04/4.26 tff(15795,plain,
% 4.04/4.26 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 4.04/4.26 inference(modus_ponens,[status(thm)],[224, 15794])).
% 4.04/4.26 tff(15796,plain,
% 4.04/4.26 (~(s(s(elem!1)) = s(s(z)))),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[2386, 11796])).
% 4.04/4.26 tff(15797,plain,
% 4.04/4.26 (~(elem!1 = s(s(s(elem!1))))),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[2498, 15796, 1117])).
% 4.04/4.26 tff(15798,plain,
% 4.04/4.26 (~(s(s(s(elem!1))) = elem!1)),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[2489, 15797])).
% 4.04/4.26 tff(15799,plain,
% 4.04/4.26 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 4.04/4.26 inference(monotonicity,[status(thm)],[1119, 1218])).
% 4.04/4.26 tff(15800,plain,
% 4.04/4.26 (r(s(s(s(s(s(s(z)))))), s(s(s(z)))) <=> r(s(s(s(elem!1))), elem!1)),
% 4.04/4.26 inference(symmetry,[status(thm)],[15799])).
% 4.04/4.26 tff(15801,plain,
% 4.04/4.26 ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) <=> (~r(s(s(s(elem!1))), elem!1))),
% 4.04/4.26 inference(monotonicity,[status(thm)],[15800])).
% 4.04/4.26 tff(15802,plain,
% 4.04/4.26 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(s(s(z)))))), z)),
% 4.04/4.26 inference(monotonicity,[status(thm)],[1119])).
% 4.04/4.26 tff(15803,plain,
% 4.04/4.26 (b(s(s(s(s(s(s(z)))))), z) <=> b(s(s(s(elem!1))), z)),
% 4.04/4.26 inference(symmetry,[status(thm)],[15802])).
% 4.04/4.26 tff(15804,plain,
% 4.04/4.26 ((~b(s(s(s(s(s(s(z)))))), z)) <=> (~b(s(s(s(elem!1))), z))),
% 4.04/4.26 inference(monotonicity,[status(thm)],[15803])).
% 4.04/4.26 tff(15805,plain,
% 4.04/4.26 (~(elem!1 = s(elem!1))),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[748, 15756])).
% 4.04/4.26 tff(15806,plain,
% 4.04/4.26 (~r(elem!1, s(elem!1))),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[12189, 437, 2333])).
% 4.04/4.26 tff(15807,plain,
% 4.04/4.26 (b(elem!1, s(elem!1))),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[756, 15806, 15805])).
% 4.04/4.26 tff(15808,plain,
% 4.04/4.26 (~r(elem!1, s(s(s(elem!1))))),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[6086, 6067, 1117, 273, 437, 3461])).
% 4.04/4.26 tff(15809,plain,
% 4.04/4.26 (b(elem!1, s(s(s(elem!1))))),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[2054, 15808, 15797])).
% 4.04/4.26 tff(15810,plain,
% 4.04/4.26 (~r(s(s(s(elem!1))), s(elem!1))),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[6297, 1329, 3461, 273, 2333])).
% 4.04/4.26 tff(15811,plain,
% 4.04/4.26 (b(s(s(s(elem!1))), s(elem!1))),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[373, 15810, 15753])).
% 4.04/4.26 tff(15812,plain,
% 4.04/4.26 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 4.04/4.26 inference(modus_ponens,[status(thm)],[15811, 6039])).
% 4.04/4.26 tff(15813,plain,
% 4.04/4.26 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.26 inference(monotonicity,[status(thm)],[1218])).
% 4.04/4.26 tff(15814,plain,
% 4.04/4.26 (b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.04/4.26 inference(symmetry,[status(thm)],[15813])).
% 4.04/4.26 tff(15815,plain,
% 4.04/4.26 ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) <=> (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 4.04/4.26 inference(monotonicity,[status(thm)],[15814])).
% 4.04/4.26 tff(15816,plain,
% 4.04/4.26 ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[11182, 178, 104, 251, 1126])).
% 4.04/4.26 tff(15817,plain,
% 4.04/4.26 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[15816, 6042])).
% 4.04/4.26 tff(15818,plain,
% 4.04/4.26 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.04/4.26 inference(modus_ponens,[status(thm)],[15817, 15815])).
% 4.04/4.26 tff(15819,plain,
% 4.04/4.26 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[691, 15818, 1189])).
% 4.04/4.26 tff(15820,plain,
% 4.04/4.26 (~r(s(s(z)), elem!1)),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[2803, 15819, 224])).
% 4.04/4.26 tff(15821,plain,
% 4.04/4.26 (b(s(s(z)), elem!1)),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[448, 15820, 12])).
% 4.04/4.26 tff(15822,plain,
% 4.04/4.26 (b(elem!1, s(s(z))) <=> b(s(s(s(z))), s(s(z)))),
% 4.04/4.26 inference(monotonicity,[status(thm)],[1218])).
% 4.04/4.26 tff(15823,plain,
% 4.04/4.26 (b(s(s(s(z))), s(s(z))) <=> b(elem!1, s(s(z)))),
% 4.04/4.26 inference(symmetry,[status(thm)],[15822])).
% 4.04/4.26 tff(15824,plain,
% 4.04/4.26 (~(s(s(z)) = s(s(s(z))))),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[2196, 1117, 312])).
% 4.04/4.26 tff(15825,plain,
% 4.04/4.26 (~(s(s(s(z))) = s(s(z)))),
% 4.04/4.26 inference(modus_ponens,[status(thm)],[15824, 3005])).
% 4.04/4.26 tff(15826,plain,
% 4.04/4.26 (~r(s(s(s(z))), s(s(z)))),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[1272, 15819, 1117, 224])).
% 4.04/4.26 tff(15827,plain,
% 4.04/4.26 (b(s(s(s(z))), s(s(z)))),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[4965, 15826, 15825])).
% 4.04/4.26 tff(15828,plain,
% 4.04/4.26 (b(elem!1, s(s(z)))),
% 4.04/4.26 inference(modus_ponens,[status(thm)],[15827, 15823])).
% 4.04/4.26 tff(15829,plain,
% 4.04/4.26 (~b(z, elem!1)),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[10893, 15828, 3461, 273, 15821])).
% 4.04/4.26 tff(15830,plain,
% 4.04/4.26 (r(z, elem!1)),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[585, 15829, 11796])).
% 4.04/4.26 tff(15831,plain,
% 4.04/4.26 (~r(s(s(s(elem!1))), elem!1)),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[9701, 15830, 273, 1117, 6067, 3461])).
% 4.04/4.26 tff(15832,plain,
% 4.04/4.26 (b(s(s(s(elem!1))), elem!1)),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[570, 15831, 15798])).
% 4.04/4.26 tff(15833,plain,
% 4.04/4.26 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 4.04/4.26 inference(modus_ponens,[status(thm)],[15832, 7527])).
% 4.04/4.26 tff(15834,plain,
% 4.04/4.26 (~(s(elem!1) = s(s(s(elem!1))))),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[5395, 15753])).
% 4.04/4.26 tff(15835,plain,
% 4.04/4.26 (~b(s(elem!1), s(s(s(elem!1))))),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[6834, 15832, 2042, 6797, 854])).
% 4.04/4.26 tff(15836,plain,
% 4.04/4.26 (b(s(s(z)), s(s(s(elem!1))))),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[6127, 15835, 1329, 15834])).
% 4.04/4.26 tff(15837,plain,
% 4.04/4.26 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[7268, 15836, 1117])).
% 4.04/4.26 tff(15838,plain,
% 4.04/4.26 (b(s(s(z)), s(s(s(z))))),
% 4.04/4.26 inference(modus_ponens,[status(thm)],[15821, 1219])).
% 4.04/4.26 tff(15839,plain,
% 4.04/4.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 4.04/4.26 inference(rewrite,[status(thm)],[])).
% 4.04/4.26 tff(15840,plain,
% 4.04/4.26 (((~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(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(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(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 4.04/4.26 inference(rewrite,[status(thm)],[])).
% 4.04/4.26 tff(15841,plain,
% 4.04/4.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 4.04/4.26 inference(monotonicity,[status(thm)],[15840])).
% 4.04/4.26 tff(15842,plain,
% 4.04/4.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 4.04/4.26 inference(transitivity,[status(thm)],[15841, 15839])).
% 4.04/4.26 tff(15843,plain,
% 4.04/4.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 4.04/4.26 inference(quant_inst,[status(thm)],[])).
% 4.04/4.26 tff(15844,plain,
% 4.04/4.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 4.04/4.26 inference(modus_ponens,[status(thm)],[15843, 15842])).
% 4.04/4.26 tff(15845,plain,
% 4.04/4.26 ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[15844, 178, 6154, 1126, 15838])).
% 4.04/4.26 tff(15846,plain,
% 4.04/4.26 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[15845, 15837])).
% 4.04/4.26 tff(15847,plain,
% 4.04/4.26 ($false),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[15846, 15833])).
% 4.04/4.26 tff(15848,plain,((~b(s(s(s(s(z)))), elem!1)) | (~(s(elem!1) = s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), z)) | (s(s(z)) = elem!1) | (~r(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(s(s(z)))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.04/4.26 tff(15849,plain,
% 4.04/4.26 (~b(s(s(s(s(z)))), elem!1)),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[15848, 224, 15812, 1126, 1329, 15809, 15807, 273, 6067, 3461, 12, 1117, 104, 251])).
% 4.04/4.26 tff(15850,plain,
% 4.04/4.26 (r(s(s(s(s(z)))), elem!1)),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[3142, 15849, 15757])).
% 4.04/4.26 tff(15851,plain,
% 4.04/4.26 (~r(s(s(z)), elem!1)),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[3329, 15850, 193])).
% 4.04/4.26 tff(15852,plain,
% 4.04/4.26 (b(s(s(z)), elem!1)),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[448, 15851, 12])).
% 4.04/4.26 tff(15853,plain,
% 4.04/4.26 (b(s(s(z)), s(s(s(z))))),
% 4.04/4.26 inference(modus_ponens,[status(thm)],[15852, 1219])).
% 4.04/4.26 tff(15854,plain,
% 4.04/4.26 (r(s(s(s(s(z)))), elem!1) <=> r(s(elem!1), elem!1)),
% 4.04/4.26 inference(symmetry,[status(thm)],[7213])).
% 4.04/4.26 tff(15855,plain,
% 4.04/4.26 (r(s(elem!1), elem!1)),
% 4.04/4.26 inference(modus_ponens,[status(thm)],[15850, 15854])).
% 4.04/4.26 tff(15856,plain,
% 4.04/4.26 (~r(z, elem!1)),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[7070, 15855, 2333])).
% 4.04/4.26 tff(15857,plain,
% 4.04/4.26 (b(z, elem!1)),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[585, 15856, 11796])).
% 4.04/4.26 tff(15858,plain,
% 4.04/4.26 (b(z, s(s(s(z))))),
% 4.04/4.26 inference(unit_resolution,[status(thm)],[1238, 15857, 1117])).
% 4.04/4.26 tff(15859,plain,
% 4.04/4.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 4.04/4.26 inference(rewrite,[status(thm)],[])).
% 4.04/4.26 tff(15860,plain,
% 4.04/4.26 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 4.04/4.26 inference(rewrite,[status(thm)],[])).
% 4.04/4.26 tff(15861,plain,
% 4.04/4.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 4.04/4.26 inference(monotonicity,[status(thm)],[15860])).
% 4.04/4.26 tff(15862,plain,
% 4.04/4.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 4.04/4.27 inference(transitivity,[status(thm)],[15861, 15859])).
% 4.04/4.27 tff(15863,plain,
% 4.04/4.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 4.04/4.27 inference(quant_inst,[status(thm)],[])).
% 4.04/4.27 tff(15864,plain,
% 4.04/4.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))),
% 4.04/4.27 inference(modus_ponens,[status(thm)],[15863, 15862])).
% 4.04/4.27 tff(15865,plain,
% 4.04/4.27 (~b(s(s(s(s(s(s(z)))))), z)),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[15864, 178, 273, 15858, 6067, 15853])).
% 4.04/4.27 tff(15866,plain,
% 4.04/4.27 (~b(s(s(s(elem!1))), z)),
% 4.04/4.27 inference(modus_ponens,[status(thm)],[15865, 15804])).
% 4.04/4.27 tff(15867,plain,
% 4.04/4.27 (r(s(s(s(elem!1))), z)),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[1565, 15866])).
% 4.04/4.27 tff(15868,plain,
% 4.04/4.27 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[9761, 15867, 1117, 437])).
% 4.04/4.27 tff(15869,plain,
% 4.04/4.27 (~r(s(s(s(elem!1))), elem!1)),
% 4.04/4.27 inference(modus_ponens,[status(thm)],[15868, 15801])).
% 4.04/4.27 tff(15870,plain,
% 4.04/4.27 (b(s(s(s(elem!1))), elem!1)),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[570, 15869, 15798])).
% 4.04/4.27 tff(15871,plain,
% 4.04/4.27 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 4.04/4.27 inference(modus_ponens,[status(thm)],[15870, 7527])).
% 4.04/4.27 tff(15872,plain,
% 4.04/4.27 ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[15844, 178, 15812, 1126, 15853])).
% 4.04/4.27 tff(15873,plain,
% 4.04/4.27 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[15872, 15871])).
% 4.04/4.27 tff(15874,plain,
% 4.04/4.27 (~b(s(s(z)), s(s(s(elem!1))))),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[7268, 15873, 1117])).
% 4.04/4.27 tff(15875,plain,
% 4.04/4.27 (r(s(s(z)), s(s(s(elem!1))))),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[4223, 15874])).
% 4.04/4.27 tff(15876,plain,
% 4.04/4.27 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[4036, 15875, 15795])).
% 4.04/4.27 tff(15877,plain,
% 4.04/4.27 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[1750, 15876, 15770])).
% 4.04/4.27 tff(15878,plain,
% 4.04/4.27 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.27 inference(modus_ponens,[status(thm)],[15877, 15767])).
% 4.04/4.27 tff(15879,plain,
% 4.04/4.27 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[3644, 15875, 3636])).
% 4.04/4.27 tff(15880,plain,
% 4.04/4.27 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[1988, 15879, 15769])).
% 4.04/4.27 tff(15881,plain,
% 4.04/4.27 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 4.04/4.27 inference(modus_ponens,[status(thm)],[15880, 7556])).
% 4.04/4.27 tff(15882,plain,
% 4.04/4.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(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(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(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(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 4.04/4.27 inference(rewrite,[status(thm)],[])).
% 4.04/4.27 tff(15883,plain,
% 4.04/4.27 (((~b(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))))))))) | (~b(s(s(s(s(s(s(z)))))), s(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(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(s(z))))))), 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))))))))) | (~b(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(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 4.04/4.27 inference(rewrite,[status(thm)],[])).
% 4.04/4.27 tff(15884,plain,
% 4.04/4.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(s(s(s(s(z)))))), s(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(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(s(z))))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(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(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))))),
% 4.04/4.27 inference(monotonicity,[status(thm)],[15883])).
% 4.04/4.27 tff(15885,plain,
% 4.04/4.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(s(s(s(s(z)))))), s(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(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(s(z))))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(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(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 4.04/4.27 inference(transitivity,[status(thm)],[15884, 15882])).
% 4.04/4.27 tff(15886,plain,
% 4.04/4.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(s(s(s(s(z)))))), s(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(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(s(z))))))), s(s(s(s(s(s(z)))))))))),
% 4.04/4.27 inference(quant_inst,[status(thm)],[])).
% 4.04/4.27 tff(15887,plain,
% 4.04/4.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))),
% 4.04/4.27 inference(modus_ponens,[status(thm)],[15886, 15885])).
% 4.04/4.27 tff(15888,plain,
% 4.04/4.27 ($false),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[15887, 178, 104, 251, 15881, 15812, 15878])).
% 4.04/4.27 tff(15889,plain,((~r(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(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~(s(elem!1) = s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(z, s(elem!1))) | (s(s(z)) = elem!1) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(elem!1))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 4.04/4.27 tff(15890,plain,
% 4.04/4.27 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[15889, 15792, 15135, 1117, 15790, 15762, 437, 273, 15788, 7529, 12, 193, 7540, 3461])).
% 4.04/4.27 tff(15891,plain,
% 4.04/4.27 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[249, 15890])).
% 4.04/4.27 tff(15892,plain,
% 4.04/4.27 (r(elem!1, s(s(z))) <=> r(s(s(s(z))), s(s(z)))),
% 4.04/4.27 inference(monotonicity,[status(thm)],[1218])).
% 4.04/4.27 tff(15893,plain,
% 4.04/4.27 (r(s(elem!1), elem!1)),
% 4.04/4.27 inference(modus_ponens,[status(thm)],[3132, 15854])).
% 4.04/4.27 tff(15894,plain,
% 4.04/4.27 (~r(z, elem!1)),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[7070, 15893, 2333])).
% 4.04/4.27 tff(15895,plain,
% 4.04/4.27 (b(z, elem!1)),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[585, 15894, 11796])).
% 4.04/4.27 tff(15896,plain,
% 4.04/4.27 (~b(elem!1, s(s(z)))),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[10893, 15895, 3461, 273, 15242])).
% 4.04/4.27 tff(15897,plain,
% 4.04/4.27 (r(elem!1, s(s(z)))),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[467, 15896, 312])).
% 4.04/4.27 tff(15898,plain,
% 4.04/4.27 (r(s(s(s(z))), s(s(z)))),
% 4.04/4.27 inference(modus_ponens,[status(thm)],[15897, 15892])).
% 4.04/4.27 tff(15899,plain,
% 4.04/4.27 (r(elem!1, s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.27 inference(monotonicity,[status(thm)],[1218, 1120])).
% 4.04/4.27 tff(15900,plain,
% 4.04/4.27 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(z))) = s(s(s(s(s(s(s(z))))))))),
% 4.04/4.27 inference(monotonicity,[status(thm)],[1218, 1120])).
% 4.04/4.27 tff(15901,plain,
% 4.04/4.27 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(z))))),
% 4.04/4.27 inference(transitivity,[status(thm)],[15900, 5018])).
% 4.04/4.27 tff(15902,plain,
% 4.04/4.27 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 4.04/4.27 inference(symmetry,[status(thm)],[15901])).
% 4.04/4.27 tff(15903,plain,
% 4.04/4.27 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 4.04/4.27 inference(monotonicity,[status(thm)],[15902])).
% 4.04/4.27 tff(15904,plain,
% 4.04/4.27 (~(elem!1 = s(s(s(s(elem!1)))))),
% 4.04/4.27 inference(modus_ponens,[status(thm)],[1104, 15903])).
% 4.04/4.27 tff(15905,plain,
% 4.04/4.27 (b(elem!1, s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.27 inference(monotonicity,[status(thm)],[1218, 1120])).
% 4.04/4.27 tff(15906,plain,
% 4.04/4.27 (b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 4.04/4.27 inference(symmetry,[status(thm)],[15905])).
% 4.04/4.27 tff(15907,plain,
% 4.04/4.27 ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) <=> (~b(elem!1, s(s(s(s(elem!1))))))),
% 4.04/4.27 inference(monotonicity,[status(thm)],[15906])).
% 4.04/4.27 tff(15908,plain,
% 4.04/4.27 (b(s(s(z)), s(s(s(z))))),
% 4.04/4.27 inference(modus_ponens,[status(thm)],[15242, 1219])).
% 4.04/4.27 tff(15909,plain,
% 4.04/4.27 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[1228, 15908])).
% 4.04/4.27 tff(15910,plain,
% 4.04/4.27 (~b(elem!1, s(s(s(s(elem!1)))))),
% 4.04/4.27 inference(modus_ponens,[status(thm)],[15909, 15907])).
% 4.04/4.27 tff(15911,plain,
% 4.04/4.27 (r(elem!1, s(s(s(s(elem!1)))))),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[1465, 15910, 15904])).
% 4.04/4.27 tff(15912,plain,
% 4.04/4.27 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.27 inference(modus_ponens,[status(thm)],[15911, 15899])).
% 4.04/4.27 tff(15913,plain,
% 4.04/4.27 (~r(s(s(s(z))), s(s(z)))),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[8218, 15912, 107])).
% 4.04/4.27 tff(15914,plain,
% 4.04/4.27 ($false),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[15913, 15898])).
% 4.04/4.27 tff(15915,plain,((~r(s(s(s(s(z)))), elem!1)) | (~(s(elem!1) = s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(elem!1))) | (s(s(z)) = elem!1) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.04/4.27 tff(15916,plain,
% 4.04/4.27 (~r(s(s(s(s(z)))), elem!1)),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[15915, 15765, 1117, 3461, 273, 15135, 15891, 15762, 7529, 12, 193])).
% 4.04/4.27 tff(15917,plain,
% 4.04/4.27 (b(s(s(s(s(z)))), elem!1)),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[3142, 15916, 15757])).
% 4.04/4.27 tff(15918,plain,
% 4.04/4.27 (b(s(s(s(s(z)))), s(s(s(z))))),
% 4.04/4.27 inference(modus_ponens,[status(thm)],[15917, 1278])).
% 4.04/4.27 tff(15919,plain,
% 4.04/4.27 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[7596, 178, 15135, 15792, 15762, 15918])).
% 4.04/4.27 tff(15920,plain,
% 4.04/4.27 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.04/4.27 inference(modus_ponens,[status(thm)],[15919, 15752])).
% 4.04/4.27 tff(15921,plain,
% 4.04/4.27 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[3444, 15920, 15750])).
% 4.04/4.27 tff(15922,plain,
% 4.04/4.27 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.04/4.27 inference(modus_ponens,[status(thm)],[15921, 15747])).
% 4.04/4.27 tff(15923,plain,
% 4.04/4.27 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(s(z))))),
% 4.04/4.27 inference(monotonicity,[status(thm)],[1218])).
% 4.04/4.27 tff(15924,plain,
% 4.04/4.27 ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[11182, 178, 15135, 15792, 15762])).
% 4.04/4.27 tff(15925,plain,
% 4.04/4.27 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[15924, 15918])).
% 4.04/4.27 tff(15926,plain,
% 4.04/4.27 (~b(elem!1, s(s(s(s(elem!1)))))),
% 4.04/4.27 inference(modus_ponens,[status(thm)],[15925, 15907])).
% 4.04/4.27 tff(15927,plain,
% 4.04/4.27 (r(elem!1, s(s(s(s(elem!1)))))),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[1465, 15926, 15904])).
% 4.04/4.27 tff(15928,plain,
% 4.04/4.27 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.27 inference(modus_ponens,[status(thm)],[15927, 15899])).
% 4.04/4.27 tff(15929,plain,
% 4.04/4.27 (~r(s(s(s(z))), s(s(z)))),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[8218, 15928, 15765])).
% 4.04/4.27 tff(15930,plain,
% 4.04/4.27 (b(s(s(s(z))), s(s(z)))),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[4965, 15929, 15825])).
% 4.04/4.27 tff(15931,plain,
% 4.04/4.27 (b(elem!1, s(s(z)))),
% 4.04/4.27 inference(modus_ponens,[status(thm)],[15930, 15823])).
% 4.04/4.27 tff(15932,plain,
% 4.04/4.27 (~r(elem!1, s(elem!1))),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[12189, 437, 7529])).
% 4.04/4.27 tff(15933,plain,
% 4.04/4.27 (r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 4.04/4.27 inference(symmetry,[status(thm)],[15899])).
% 4.04/4.27 tff(15934,plain,
% 4.04/4.27 ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) <=> (~r(elem!1, s(s(s(s(elem!1))))))),
% 4.04/4.27 inference(monotonicity,[status(thm)],[15933])).
% 4.04/4.27 tff(15935,plain,
% 4.04/4.27 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[6086, 3311, 1117, 273, 437, 3461])).
% 4.04/4.27 tff(15936,plain,
% 4.04/4.27 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[6139, 15935, 6059])).
% 4.04/4.27 tff(15937,plain,
% 4.04/4.27 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[15786, 15936, 104, 6154, 193, 1117])).
% 4.04/4.27 tff(15938,plain,
% 4.04/4.27 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[3578, 15937])).
% 4.04/4.27 tff(15939,plain,
% 4.04/4.27 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[3569, 15938, 273, 3461, 145, 193])).
% 4.04/4.27 tff(15940,plain,
% 4.04/4.27 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[222, 15939])).
% 4.04/4.27 tff(15941,plain,
% 4.04/4.27 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[9656, 118, 193, 15936])).
% 4.04/4.27 tff(15942,plain,
% 4.04/4.27 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[7299, 41, 15941, 3698])).
% 4.04/4.27 tff(15943,plain,
% 4.04/4.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(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(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(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(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))),
% 4.04/4.27 inference(rewrite,[status(thm)],[])).
% 4.04/4.27 tff(15944,plain,
% 4.04/4.27 (((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), 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(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(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(s(z))))))), s(s(s(s(s(s(z)))))))))),
% 4.04/4.27 inference(rewrite,[status(thm)],[])).
% 4.04/4.27 tff(15945,plain,
% 4.04/4.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(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(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))))))),
% 4.04/4.27 inference(monotonicity,[status(thm)],[15944])).
% 4.04/4.27 tff(15946,plain,
% 4.04/4.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(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(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))),
% 4.04/4.27 inference(transitivity,[status(thm)],[15945, 15943])).
% 4.04/4.27 tff(15947,plain,
% 4.04/4.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.04/4.27 inference(quant_inst,[status(thm)],[])).
% 4.04/4.27 tff(15948,plain,
% 4.04/4.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(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(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))))),
% 4.04/4.27 inference(modus_ponens,[status(thm)],[15947, 15946])).
% 4.04/4.27 tff(15949,plain,
% 4.04/4.27 ((~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(s(s(z))))))))),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[15948, 178, 104, 6154, 15942])).
% 4.04/4.27 tff(15950,plain,
% 4.04/4.27 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[15949, 15940])).
% 4.04/4.27 tff(15951,plain,
% 4.04/4.27 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 4.04/4.27 inference(modus_ponens,[status(thm)],[15950, 7558])).
% 4.04/4.27 tff(15952,plain,
% 4.04/4.27 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[1988, 15951, 15769])).
% 4.04/4.27 tff(15953,plain,
% 4.04/4.27 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 4.04/4.27 inference(modus_ponens,[status(thm)],[15952, 7555])).
% 4.04/4.27 tff(15954,plain,
% 4.04/4.27 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[7770, 3311, 1117])).
% 4.04/4.27 tff(15955,plain,
% 4.04/4.27 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[7713, 118, 15954, 15953])).
% 4.04/4.27 tff(15956,plain,
% 4.04/4.27 (~r(elem!1, s(s(s(s(elem!1)))))),
% 4.04/4.27 inference(modus_ponens,[status(thm)],[15955, 15934])).
% 4.04/4.27 tff(15957,plain,
% 4.04/4.27 (~(s(s(z)) = s(s(s(s(s(s(z)))))))),
% 4.04/4.27 inference(modus_ponens,[status(thm)],[6059, 9709])).
% 4.04/4.27 tff(15958,plain,
% 4.04/4.27 (b(s(s(s(s(s(s(z)))))), z)),
% 4.04/4.27 inference(modus_ponens,[status(thm)],[6073, 15802])).
% 4.04/4.27 tff(15959,plain,
% 4.04/4.27 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[6334, 178, 3461, 273, 6078, 15958])).
% 4.04/4.27 tff(15960,plain,
% 4.04/4.27 ((s(s(z)) = s(s(s(s(s(s(z))))))) | r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[9714, 41, 15959])).
% 4.04/4.27 tff(15961,plain,
% 4.04/4.27 (r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[15960, 15957])).
% 4.04/4.27 tff(15962,plain,
% 4.04/4.27 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(z)))))),
% 4.04/4.27 inference(rewrite,[status(thm)],[])).
% 4.04/4.27 tff(15963,plain,
% 4.04/4.27 (((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), 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)))))))) | (~r(s(s(s(z))), s(s(z)))))),
% 4.04/4.27 inference(rewrite,[status(thm)],[])).
% 4.04/4.27 tff(15964,plain,
% 4.04/4.27 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(z))))))),
% 4.04/4.27 inference(monotonicity,[status(thm)],[15963])).
% 4.04/4.27 tff(15965,plain,
% 4.04/4.27 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(z)))))),
% 4.04/4.27 inference(transitivity,[status(thm)],[15964, 15962])).
% 4.04/4.27 tff(15966,plain,
% 4.04/4.27 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(z)))))),
% 4.04/4.27 inference(quant_inst,[status(thm)],[])).
% 4.04/4.27 tff(15967,plain,
% 4.04/4.27 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(z))))),
% 4.04/4.27 inference(modus_ponens,[status(thm)],[15966, 15965])).
% 4.04/4.27 tff(15968,plain,
% 4.04/4.27 (~r(s(s(s(z))), s(s(z)))),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[15967, 118, 15961, 15954])).
% 4.04/4.27 tff(15969,plain,
% 4.04/4.27 (b(s(s(s(z))), s(s(z)))),
% 4.04/4.27 inference(unit_resolution,[status(thm)],[4965, 15968, 11274])).
% 4.04/4.27 tff(15970,plain,
% 4.04/4.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 4.04/4.27 inference(rewrite,[status(thm)],[])).
% 4.04/4.27 tff(15971,plain,
% 4.04/4.27 (((~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(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(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 4.04/4.28 inference(rewrite,[status(thm)],[])).
% 4.04/4.28 tff(15972,plain,
% 4.04/4.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(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(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 4.04/4.28 inference(monotonicity,[status(thm)],[15971])).
% 4.04/4.28 tff(15973,plain,
% 4.04/4.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(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(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 4.04/4.28 inference(transitivity,[status(thm)],[15972, 15970])).
% 4.04/4.28 tff(15974,plain,
% 4.04/4.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(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(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 4.04/4.28 inference(quant_inst,[status(thm)],[])).
% 4.04/4.28 tff(15975,plain,
% 4.04/4.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 4.04/4.28 inference(modus_ponens,[status(thm)],[15974, 15973])).
% 4.04/4.28 tff(15976,plain,
% 4.04/4.28 (~b(s(s(s(s(z)))), z)),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[15975, 178, 6078, 6154, 15958, 15942])).
% 4.04/4.28 tff(15977,plain,
% 4.04/4.28 (r(s(s(s(s(z)))), z)),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[191, 15976])).
% 4.04/4.28 tff(15978,plain,
% 4.04/4.28 (~r(s(s(s(s(z)))), elem!1)),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[6033, 15977, 437])).
% 4.04/4.28 tff(15979,plain,
% 4.04/4.28 (b(s(s(s(s(z)))), elem!1)),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[3142, 15978, 15757])).
% 4.04/4.28 tff(15980,plain,
% 4.04/4.28 (b(s(s(s(s(z)))), s(s(s(z))))),
% 4.04/4.28 inference(modus_ponens,[status(thm)],[15979, 1278])).
% 4.04/4.28 tff(15981,plain,
% 4.04/4.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.04/4.28 inference(rewrite,[status(thm)],[])).
% 4.04/4.28 tff(15982,plain,
% 4.04/4.28 (((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(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(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.04/4.28 inference(rewrite,[status(thm)],[])).
% 4.04/4.28 tff(15983,plain,
% 4.04/4.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(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(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z))))))),
% 4.04/4.28 inference(monotonicity,[status(thm)],[15982])).
% 4.04/4.28 tff(15984,plain,
% 4.04/4.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(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(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.04/4.28 inference(transitivity,[status(thm)],[15983, 15981])).
% 4.04/4.28 tff(15985,plain,
% 4.04/4.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(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(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 4.04/4.28 inference(quant_inst,[status(thm)],[])).
% 4.04/4.28 tff(15986,plain,
% 4.04/4.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z))))),
% 4.04/4.28 inference(modus_ponens,[status(thm)],[15985, 15984])).
% 4.04/4.28 tff(15987,plain,
% 4.04/4.28 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[15986, 178, 15940, 15980, 15969, 15938])).
% 4.04/4.28 tff(15988,plain,
% 4.04/4.28 (~b(elem!1, s(s(s(s(elem!1)))))),
% 4.04/4.28 inference(modus_ponens,[status(thm)],[15987, 15907])).
% 4.04/4.28 tff(15989,plain,
% 4.04/4.28 (r(elem!1, s(s(s(s(elem!1)))))),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[1465, 15988, 15904])).
% 4.04/4.28 tff(15990,plain,
% 4.04/4.28 ($false),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[15989, 15956])).
% 4.04/4.28 tff(15991,plain,((~r(elem!1, s(s(s(elem!1))))) | (~(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(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, z)) | (s(s(s(z))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.04/4.28 tff(15992,plain,
% 4.04/4.28 (~r(elem!1, s(s(s(elem!1))))),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[15991, 1117, 15135, 15764, 273, 3461, 145, 193, 437, 15825])).
% 4.04/4.28 tff(15993,plain,
% 4.04/4.28 (b(elem!1, s(s(s(elem!1))))),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[2054, 15992, 15797])).
% 4.04/4.28 tff(15994,plain,
% 4.04/4.28 (b(s(elem!1), elem!1)),
% 4.04/4.28 inference(modus_ponens,[status(thm)],[15917, 6796])).
% 4.04/4.28 tff(15995,plain,
% 4.04/4.28 (~r(s(s(s(elem!1))), elem!1)),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[9701, 521, 273, 1117, 6067, 3461])).
% 4.04/4.28 tff(15996,plain,
% 4.04/4.28 (b(s(s(s(elem!1))), elem!1)),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[570, 15995, 15798])).
% 4.04/4.28 tff(15997,plain,
% 4.04/4.28 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 4.04/4.28 inference(modus_ponens,[status(thm)],[15996, 7527])).
% 4.04/4.28 tff(15998,plain,
% 4.04/4.28 (b(elem!1, s(elem!1))),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[756, 744, 15805])).
% 4.04/4.28 tff(15999,plain,
% 4.04/4.28 (~b(s(elem!1), s(s(s(elem!1))))),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[6834, 15996, 2042, 683, 15998])).
% 4.04/4.28 tff(16000,plain,
% 4.04/4.28 (b(s(s(z)), s(s(s(elem!1))))),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[6127, 15999, 7540, 15834])).
% 4.04/4.28 tff(16001,plain,
% 4.04/4.28 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[7268, 16000, 1117])).
% 4.04/4.28 tff(16002,plain,
% 4.04/4.28 (b(s(s(z)), elem!1)),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[7607, 521, 147, 145, 3461, 1117, 273, 15753, 15797, 744, 1126])).
% 4.04/4.28 tff(16003,plain,
% 4.04/4.28 (b(s(s(z)), s(s(s(z))))),
% 4.04/4.28 inference(modus_ponens,[status(thm)],[16002, 1219])).
% 4.04/4.28 tff(16004,plain,
% 4.04/4.28 ($false),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[15844, 178, 15764, 1126, 16003, 16001, 15997])).
% 4.04/4.28 tff(16005,plain,((~r(z, elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~(s(elem!1) = s(s(s(s(z)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | r(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.04/4.28 tff(16006,plain,
% 4.04/4.28 (~r(z, elem!1)),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[16005, 15994, 1117, 15993, 15762, 273, 15788, 3461, 147, 145, 15932])).
% 4.04/4.28 tff(16007,plain,
% 4.04/4.28 (b(z, elem!1)),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[585, 16006, 11796])).
% 4.04/4.28 tff(16008,plain,
% 4.04/4.28 (~b(s(s(z)), elem!1)),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[10893, 16007, 3461, 273, 15931])).
% 4.04/4.28 tff(16009,plain,
% 4.04/4.28 (r(s(s(z)), elem!1)),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[448, 16008, 12])).
% 4.04/4.28 tff(16010,plain,
% 4.04/4.28 (r(s(s(z)), s(s(s(z))))),
% 4.04/4.28 inference(modus_ponens,[status(thm)],[16009, 15923])).
% 4.04/4.28 tff(16011,plain,
% 4.04/4.28 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 4.04/4.28 inference(rewrite,[status(thm)],[])).
% 4.04/4.28 tff(16012,plain,
% 4.04/4.28 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 4.04/4.28 inference(rewrite,[status(thm)],[])).
% 4.04/4.28 tff(16013,plain,
% 4.04/4.28 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))))),
% 4.04/4.28 inference(monotonicity,[status(thm)],[16012])).
% 4.04/4.28 tff(16014,plain,
% 4.04/4.28 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 4.04/4.28 inference(transitivity,[status(thm)],[16013, 16011])).
% 4.04/4.28 tff(16015,plain,
% 4.04/4.28 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 4.04/4.28 inference(quant_inst,[status(thm)],[])).
% 4.04/4.28 tff(16016,plain,
% 4.04/4.28 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 4.04/4.28 inference(modus_ponens,[status(thm)],[16015, 16014])).
% 4.04/4.28 tff(16017,plain,
% 4.04/4.28 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[16016, 118, 16010, 15765])).
% 4.04/4.28 tff(16018,plain,
% 4.04/4.28 ($false),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[16017, 15922])).
% 4.04/4.28 tff(16019,plain,(b(s(s(s(s(s(s(s(z))))))), s(s(z))) | (~(s(elem!1) = s(s(s(s(z)))))) | (s(s(z)) = elem!1) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 4.04/4.28 tff(16020,plain,
% 4.04/4.28 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[16019, 15725, 12, 5619, 14881, 147, 47, 103, 15745])).
% 4.04/4.28 tff(16021,plain,
% 4.04/4.28 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[3569, 16020, 14881, 5619, 47, 103])).
% 4.04/4.28 tff(16022,plain,
% 4.04/4.28 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[222, 16021])).
% 4.04/4.28 tff(16023,plain,
% 4.04/4.28 ((~(s(s(s(z))) = z)) <=> (~(z = elem!1))),
% 4.04/4.28 inference(monotonicity,[status(thm)],[15741])).
% 4.04/4.28 tff(16024,plain,
% 4.04/4.28 (~(z = elem!1)),
% 4.04/4.28 inference(modus_ponens,[status(thm)],[77, 16023])).
% 4.04/4.28 tff(16025,plain,
% 4.04/4.28 (~(s(s(elem!1)) = s(s(z)))),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[2386, 16024])).
% 4.04/4.28 tff(16026,plain,
% 4.04/4.28 (~(elem!1 = s(s(s(elem!1))))),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[2498, 16025, 15725])).
% 4.04/4.28 tff(16027,plain,
% 4.04/4.28 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 4.04/4.28 inference(monotonicity,[status(thm)],[15725])).
% 4.04/4.28 tff(16028,plain,
% 4.04/4.28 (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))),
% 4.04/4.28 inference(monotonicity,[status(thm)],[16027])).
% 4.04/4.28 tff(16029,plain,
% 4.04/4.28 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 4.04/4.28 inference(monotonicity,[status(thm)],[16028, 15725])).
% 4.04/4.28 tff(16030,plain,
% 4.04/4.28 (r(z, s(elem!1)) <=> r(z, s(s(s(s(z)))))),
% 4.04/4.28 inference(monotonicity,[status(thm)],[15725])).
% 4.04/4.28 tff(16031,plain,
% 4.04/4.28 (r(z, s(s(s(s(z))))) <=> r(z, s(elem!1))),
% 4.04/4.28 inference(symmetry,[status(thm)],[16030])).
% 4.04/4.28 tff(16032,plain,
% 4.04/4.28 (r(z, s(elem!1))),
% 4.04/4.28 inference(modus_ponens,[status(thm)],[47, 16031])).
% 4.04/4.28 tff(16033,plain,
% 4.04/4.28 (r(s(s(z)), s(elem!1)) <=> r(s(s(z)), s(s(s(s(z)))))),
% 4.04/4.28 inference(monotonicity,[status(thm)],[15725])).
% 4.04/4.28 tff(16034,plain,
% 4.04/4.28 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(z)), s(elem!1))),
% 4.04/4.28 inference(symmetry,[status(thm)],[16033])).
% 4.04/4.28 tff(16035,plain,
% 4.04/4.28 (r(s(s(z)), s(elem!1))),
% 4.04/4.28 inference(modus_ponens,[status(thm)],[147, 16034])).
% 4.04/4.28 tff(16036,plain,
% 4.04/4.28 (~r(s(s(s(elem!1))), s(elem!1))),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[6297, 16035, 5619, 14881, 16032])).
% 4.04/4.28 tff(16037,plain,
% 4.04/4.28 (b(s(s(s(elem!1))), s(elem!1))),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[373, 16036, 15734])).
% 4.04/4.28 tff(16038,plain,
% 4.04/4.28 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 4.04/4.28 inference(modus_ponens,[status(thm)],[16037, 16029])).
% 4.04/4.28 tff(16039,plain,
% 4.04/4.28 (~r(elem!1, s(s(s(elem!1))))),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[15991, 15725, 14876, 16038, 14881, 5619, 47, 103, 15745, 15727])).
% 4.04/4.28 tff(16040,plain,
% 4.04/4.28 (b(elem!1, s(s(s(elem!1))))),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[2054, 16039, 16026])).
% 4.04/4.28 tff(16041,plain,
% 4.04/4.28 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 4.04/4.28 inference(symmetry,[status(thm)],[15728])).
% 4.04/4.28 tff(16042,plain,
% 4.04/4.28 (s(s(s(z))) = elem!1),
% 4.04/4.28 inference(transitivity,[status(thm)],[61, 16041, 304])).
% 4.04/4.28 tff(16043,plain,
% 4.04/4.28 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 4.04/4.28 inference(monotonicity,[status(thm)],[16042])).
% 4.04/4.28 tff(16044,plain,
% 4.04/4.28 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 4.04/4.28 inference(symmetry,[status(thm)],[16043])).
% 4.04/4.28 tff(16045,plain,
% 4.04/4.28 ((s(elem!1) = elem!1) <=> (elem!1 = s(s(s(s(z)))))),
% 4.04/4.28 inference(transitivity,[status(thm)],[15732, 501])).
% 4.04/4.28 tff(16046,plain,
% 4.04/4.28 ((~(s(elem!1) = elem!1)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 4.04/4.28 inference(monotonicity,[status(thm)],[16045])).
% 4.04/4.28 tff(16047,plain,
% 4.04/4.28 (~(elem!1 = s(s(s(s(z)))))),
% 4.04/4.28 inference(modus_ponens,[status(thm)],[15737, 16046])).
% 4.04/4.28 tff(16048,plain,
% 4.04/4.28 (~r(elem!1, s(s(s(s(z)))))),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[478, 15745, 47])).
% 4.04/4.28 tff(16049,plain,
% 4.04/4.28 (b(elem!1, s(s(s(s(z)))))),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[483, 16048, 16047])).
% 4.04/4.28 tff(16050,plain,
% 4.04/4.28 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.04/4.28 inference(modus_ponens,[status(thm)],[16049, 16044])).
% 4.04/4.28 tff(16051,plain,
% 4.04/4.28 (~(elem!1 = s(elem!1))),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[748, 15737])).
% 4.04/4.28 tff(16052,plain,
% 4.04/4.28 (~r(elem!1, s(elem!1))),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[12189, 15745, 16032])).
% 4.04/4.28 tff(16053,plain,
% 4.04/4.28 (b(elem!1, s(elem!1))),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[756, 16052, 16051])).
% 4.04/4.28 tff(16054,plain,
% 4.04/4.28 (b(elem!1, z) <=> b(s(s(s(z))), z)),
% 4.04/4.28 inference(monotonicity,[status(thm)],[15729])).
% 4.04/4.28 tff(16055,plain,
% 4.04/4.28 ((~b(elem!1, z)) <=> (~b(s(s(s(z))), z))),
% 4.04/4.28 inference(monotonicity,[status(thm)],[16054])).
% 4.04/4.28 tff(16056,plain,
% 4.04/4.28 (~b(s(s(s(z))), z)),
% 4.04/4.28 inference(modus_ponens,[status(thm)],[5723, 16055])).
% 4.04/4.28 tff(16057,plain,
% 4.04/4.28 (r(s(s(s(z))), z)),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[4903, 41, 77, 16056])).
% 4.04/4.28 tff(16058,plain,
% 4.04/4.28 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[7596, 178, 104, 251, 1126, 6042])).
% 4.04/4.28 tff(16059,plain,
% 4.04/4.28 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.04/4.28 inference(modus_ponens,[status(thm)],[16058, 15752])).
% 4.04/4.28 tff(16060,plain,
% 4.04/4.28 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[3444, 16059, 15750])).
% 4.04/4.28 tff(16061,plain,
% 4.04/4.28 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.04/4.28 inference(modus_ponens,[status(thm)],[16060, 15747])).
% 4.04/4.28 tff(16062,assumption,(r(s(s(s(z))), z)), introduced(assumption)).
% 4.04/4.28 tff(16063,assumption,(r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))), introduced(assumption)).
% 4.04/4.28 tff(16064,plain,
% 4.04/4.28 (r(z, elem!1) <=> r(z, s(s(s(z))))),
% 4.04/4.28 inference(monotonicity,[status(thm)],[1218])).
% 4.04/4.28 tff(16065,plain,
% 4.04/4.28 (r(z, s(s(s(z))))),
% 4.04/4.28 inference(modus_ponens,[status(thm)],[521, 16064])).
% 4.04/4.28 tff(16066,plain,
% 4.04/4.28 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[15390, 118, 16065, 16063])).
% 4.04/4.28 tff(16067,plain,
% 4.04/4.28 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[133, 16066])).
% 4.04/4.28 tff(16068,plain,
% 4.04/4.28 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[3818, 521, 1265])).
% 4.04/4.28 tff(16069,plain,
% 4.04/4.28 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[271, 16068])).
% 4.04/4.28 tff(16070,plain,
% 4.04/4.28 ($false),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[4091, 178, 3461, 273, 16069, 16067, 1146])).
% 4.04/4.28 tff(16071,plain,((~r(z, elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~(s(elem!1) = s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.04/4.28 tff(16072,plain,
% 4.04/4.28 (~r(z, elem!1)),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[16071, 16061, 273, 1146, 3461, 1117, 15819])).
% 4.04/4.28 tff(16073,plain,
% 4.04/4.28 (b(z, elem!1)),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[585, 16072, 11796])).
% 4.04/4.28 tff(16074,plain,
% 4.04/4.28 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[15848, 224, 6154, 1126, 1329, 2042, 854, 273, 3771, 3461, 12, 1117, 104, 251])).
% 4.04/4.28 tff(16075,plain,
% 4.04/4.28 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[6139, 16074, 6059])).
% 4.04/4.28 tff(16076,plain,
% 4.04/4.28 (~r(elem!1, s(s(z)))),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[9668, 16075, 193, 1117, 854, 15797, 15834, 6797])).
% 4.04/4.28 tff(16077,plain,
% 4.04/4.28 (~r(s(s(z)), elem!1)),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[2803, 224, 15819])).
% 4.04/4.28 tff(16078,plain,
% 4.04/4.28 (b(s(s(z)), elem!1)),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[448, 16077, 12])).
% 4.04/4.28 tff(16079,plain,
% 4.04/4.28 (~b(elem!1, s(s(z)))),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[10893, 16078, 3461, 273, 818])).
% 4.04/4.28 tff(16080,plain,
% 4.04/4.28 ($false),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[467, 16079, 16076, 312])).
% 4.04/4.28 tff(16081,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(z, elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~(s(elem!1) = s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))) | (s(s(z)) = elem!1) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.04/4.28 tff(16082,plain,
% 4.04/4.28 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[16081, 16073, 273, 3461, 193, 1117, 854, 12, 6154, 1126, 1329, 2042, 3771, 104, 251])).
% 4.04/4.28 tff(16083,plain,
% 4.04/4.28 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[249, 16082])).
% 4.04/4.28 tff(16084,plain,
% 4.04/4.28 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[4057, 16083, 273, 3461, 1146])).
% 4.04/4.28 tff(16085,plain,
% 4.04/4.28 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[133, 16084])).
% 4.04/4.28 tff(16086,plain,
% 4.04/4.28 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 4.04/4.28 inference(rewrite,[status(thm)],[])).
% 4.04/4.28 tff(16087,plain,
% 4.04/4.28 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 4.04/4.28 inference(quant_inst,[status(thm)],[])).
% 4.04/4.28 tff(16088,plain,
% 4.04/4.28 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 4.04/4.28 inference(modus_ponens,[status(thm)],[16087, 16086])).
% 4.04/4.28 tff(16089,plain,
% 4.04/4.28 ($false),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[16088, 118, 16085, 16062, 16061])).
% 4.04/4.28 tff(16090,plain,((~b(s(s(s(s(z)))), elem!1)) | (~r(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(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~(s(elem!1) = s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))) | (s(s(z)) = elem!1) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(elem!1))) | (~b(elem!1, s(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)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.04/4.28 tff(16091,plain,
% 4.04/4.28 (~b(s(s(s(s(z)))), elem!1)),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[16090, 16057, 14881, 5619, 16020, 103, 15725, 16053, 12, 16038, 16050, 16035, 16040, 14876, 16022])).
% 4.04/4.28 tff(16092,plain,
% 4.04/4.28 (r(s(s(s(s(z)))), elem!1)),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[3142, 16091, 15738])).
% 4.04/4.28 tff(16093,plain,
% 4.04/4.28 (~r(s(s(z)), elem!1)),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[3329, 16092, 103])).
% 4.04/4.28 tff(16094,plain,
% 4.04/4.28 (b(s(s(z)), elem!1)),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[448, 16093, 12])).
% 4.04/4.28 tff(16095,plain,
% 4.04/4.28 (r(s(elem!1), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 4.04/4.28 inference(monotonicity,[status(thm)],[15725])).
% 4.04/4.28 tff(16096,plain,
% 4.04/4.28 (r(s(s(s(s(z)))), elem!1) <=> r(s(elem!1), elem!1)),
% 4.04/4.28 inference(symmetry,[status(thm)],[16095])).
% 4.04/4.28 tff(16097,plain,
% 4.04/4.28 (r(s(elem!1), elem!1)),
% 4.04/4.28 inference(modus_ponens,[status(thm)],[16092, 16096])).
% 4.04/4.28 tff(16098,plain,
% 4.04/4.28 (~r(z, elem!1)),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[7070, 16097, 16032])).
% 4.04/4.28 tff(16099,plain,
% 4.04/4.28 (b(z, elem!1)),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[585, 16098, 16024])).
% 4.04/4.28 tff(16100,plain,
% 4.04/4.28 (~b(elem!1, s(s(z)))),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[10893, 16099, 5619, 14881, 16094])).
% 4.04/4.28 tff(16101,plain,
% 4.04/4.28 (~b(s(s(s(z))), s(s(z)))),
% 4.04/4.28 inference(modus_ponens,[status(thm)],[16100, 15731])).
% 4.04/4.28 tff(16102,plain,
% 4.04/4.28 (r(s(s(s(z))), s(s(z)))),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[4965, 16101, 15727])).
% 4.04/4.28 tff(16103,plain,
% 4.04/4.28 (r(s(s(s(s(z)))), s(s(s(z))))),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[7220, 16092, 15725])).
% 4.04/4.28 tff(16104,plain,
% 4.04/4.28 ($false),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[8696, 118, 103, 16103, 16102])).
% 4.04/4.28 tff(16105,plain,(b(z, s(s(s(s(z))))) | (s(s(z)) = elem!1) | (~r(s(s(z)), s(s(s(s(z)))))) | b(elem!1, z) | b(s(elem!1), s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 4.04/4.28 tff(16106,plain,
% 4.04/4.28 (b(s(elem!1), s(s(z)))),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[16105, 86, 1, 147, 5723, 12, 5618])).
% 4.04/4.28 tff(16107,plain,
% 4.04/4.28 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 4.04/4.28 inference(modus_ponens,[status(thm)],[16106, 11737])).
% 4.04/4.28 tff(16108,plain,
% 4.04/4.28 (b(z, s(s(s(s(s(s(s(s(z))))))))) <=> b(z, s(elem!1))),
% 4.04/4.28 inference(monotonicity,[status(thm)],[11730])).
% 4.04/4.28 tff(16109,plain,
% 4.04/4.28 (b(z, s(elem!1)) <=> b(z, s(s(s(s(s(s(s(s(z)))))))))),
% 4.04/4.28 inference(symmetry,[status(thm)],[16108])).
% 4.04/4.28 tff(16110,plain,
% 4.04/4.28 (~r(z, s(elem!1))),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[7070, 1426, 521])).
% 4.04/4.28 tff(16111,plain,
% 4.04/4.28 (b(z, s(elem!1))),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[2351, 16110])).
% 4.04/4.28 tff(16112,plain,
% 4.04/4.28 (b(z, s(s(s(s(s(s(s(s(z)))))))))),
% 4.04/4.28 inference(modus_ponens,[status(thm)],[16111, 16109])).
% 4.04/4.28 tff(16113,plain,
% 4.04/4.28 (r(s(s(s(s(s(s(s(s(z)))))))), z) <=> r(s(elem!1), z)),
% 4.04/4.28 inference(monotonicity,[status(thm)],[11730])).
% 4.04/4.28 tff(16114,plain,
% 4.04/4.28 (r(s(elem!1), z) <=> r(s(s(s(s(s(s(s(s(z)))))))), z)),
% 4.04/4.28 inference(symmetry,[status(thm)],[16113])).
% 4.04/4.28 tff(16115,plain,
% 4.04/4.28 ((~r(s(elem!1), z)) <=> (~r(s(s(s(s(s(s(s(s(z)))))))), z))),
% 4.04/4.28 inference(monotonicity,[status(thm)],[16114])).
% 4.04/4.28 tff(16116,plain,
% 4.04/4.28 (~r(s(s(s(s(s(s(s(s(z)))))))), z)),
% 4.04/4.28 inference(modus_ponens,[status(thm)],[11440, 16115])).
% 4.04/4.28 tff(16117,plain,
% 4.04/4.28 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(s(s(z)))))))) = z))),
% 4.04/4.28 inference(quant_inst,[status(thm)],[])).
% 4.04/4.28 tff(16118,plain,
% 4.04/4.28 (~(s(s(s(s(s(s(s(s(z)))))))) = z)),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[16117, 28])).
% 4.04/4.28 tff(16119,plain,
% 4.04/4.28 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(z)))))))) = z) | b(s(s(s(s(s(s(s(s(z)))))))), z) | r(s(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(s(z)))))))) = z) | b(s(s(s(s(s(s(s(s(z)))))))), z) | r(s(s(s(s(s(s(s(s(z)))))))), z))),
% 4.04/4.28 inference(rewrite,[status(thm)],[])).
% 4.04/4.28 tff(16120,plain,
% 4.04/4.28 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(z)))))))) = z) | b(s(s(s(s(s(s(s(s(z)))))))), z) | r(s(s(s(s(s(s(s(s(z)))))))), z))),
% 4.04/4.28 inference(quant_inst,[status(thm)],[])).
% 4.04/4.28 tff(16121,plain,
% 4.04/4.28 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(s(z)))))))) = z) | b(s(s(s(s(s(s(s(s(z)))))))), z) | r(s(s(s(s(s(s(s(s(z)))))))), z)),
% 4.04/4.28 inference(modus_ponens,[status(thm)],[16120, 16119])).
% 4.04/4.28 tff(16122,plain,
% 4.04/4.28 (b(s(s(s(s(s(s(s(s(z)))))))), z) | r(s(s(s(s(s(s(s(s(z)))))))), z)),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[16121, 41, 16118])).
% 4.04/4.28 tff(16123,plain,
% 4.04/4.28 (b(s(s(s(s(s(s(s(s(z)))))))), z)),
% 4.04/4.28 inference(unit_resolution,[status(thm)],[16122, 16116])).
% 4.04/4.28 tff(16124,assumption,(b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))), introduced(assumption)).
% 4.04/4.28 tff(16125,plain,
% 4.04/4.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))))),
% 4.04/4.29 inference(rewrite,[status(thm)],[])).
% 4.04/4.29 tff(16126,plain,
% 4.04/4.29 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(s(z))))))))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))))),
% 4.04/4.29 inference(rewrite,[status(thm)],[])).
% 4.04/4.29 tff(16127,plain,
% 4.04/4.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(z, s(s(s(s(s(s(s(s(z))))))))))))),
% 4.04/4.29 inference(monotonicity,[status(thm)],[16126])).
% 4.04/4.29 tff(16128,plain,
% 4.04/4.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))))),
% 4.04/4.29 inference(transitivity,[status(thm)],[16127, 16125])).
% 4.04/4.29 tff(16129,plain,
% 4.04/4.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))))),
% 4.04/4.29 inference(quant_inst,[status(thm)],[])).
% 4.04/4.29 tff(16130,plain,
% 4.04/4.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(z, s(s(s(s(s(s(s(s(z))))))))))),
% 4.04/4.29 inference(modus_ponens,[status(thm)],[16129, 16128])).
% 4.04/4.29 tff(16131,plain,
% 4.04/4.29 ($false),
% 4.04/4.29 inference(unit_resolution,[status(thm)],[16130, 178, 3461, 273, 16124, 16123, 16112])).
% 4.04/4.29 tff(16132,plain,((~r(s(elem!1), elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.04/4.29 tff(16133,plain,
% 4.04/4.29 (~r(s(elem!1), elem!1)),
% 4.04/4.29 inference(unit_resolution,[status(thm)],[16132, 16107, 273, 5619, 679, 521])).
% 4.04/4.29 tff(16134,plain,
% 4.04/4.29 (b(s(elem!1), elem!1)),
% 4.04/4.29 inference(unit_resolution,[status(thm)],[677, 16133, 11736])).
% 4.04/4.29 tff(16135,plain,
% 4.04/4.29 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.29 inference(unit_resolution,[status(thm)],[686, 16134, 679])).
% 4.04/4.29 tff(16136,plain,
% 4.04/4.29 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.29 inference(modus_ponens,[status(thm)],[16135, 11735])).
% 4.04/4.29 tff(16137,plain,
% 4.04/4.29 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 4.04/4.29 inference(monotonicity,[status(thm)],[11730])).
% 4.04/4.29 tff(16138,plain,
% 4.04/4.29 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 4.04/4.29 inference(symmetry,[status(thm)],[16137])).
% 4.04/4.29 tff(16139,plain,
% 4.04/4.29 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.04/4.29 inference(unit_resolution,[status(thm)],[12552, 16106, 86])).
% 4.04/4.29 tff(16140,plain,
% 4.04/4.29 ((~b(z, s(s(s(s(s(s(s(s(z)))))))))) <=> (~b(z, s(elem!1)))),
% 4.04/4.29 inference(monotonicity,[status(thm)],[16108])).
% 4.04/4.29 tff(16141,plain,
% 4.04/4.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 4.04/4.29 inference(rewrite,[status(thm)],[])).
% 4.04/4.29 tff(16142,plain,
% 4.04/4.29 (((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(s(z))))))))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 4.04/4.29 inference(rewrite,[status(thm)],[])).
% 4.04/4.29 tff(16143,plain,
% 4.04/4.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))))),
% 4.04/4.29 inference(monotonicity,[status(thm)],[16142])).
% 4.04/4.29 tff(16144,plain,
% 4.04/4.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 4.04/4.29 inference(transitivity,[status(thm)],[16143, 16141])).
% 4.04/4.29 tff(16145,plain,
% 4.04/4.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))))),
% 4.04/4.29 inference(quant_inst,[status(thm)],[])).
% 4.04/4.29 tff(16146,plain,
% 4.04/4.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))),
% 4.04/4.29 inference(modus_ponens,[status(thm)],[16145, 16144])).
% 4.04/4.29 tff(16147,plain,
% 4.04/4.29 ((~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))),
% 4.04/4.29 inference(unit_resolution,[status(thm)],[16146, 178, 273, 166, 16107])).
% 4.04/4.29 tff(16148,plain,
% 4.04/4.29 (~b(z, s(s(s(s(s(s(s(s(z)))))))))),
% 4.04/4.29 inference(unit_resolution,[status(thm)],[16147, 16136])).
% 4.04/4.29 tff(16149,plain,
% 4.04/4.29 (~b(z, s(elem!1))),
% 4.04/4.29 inference(modus_ponens,[status(thm)],[16148, 16140])).
% 4.04/4.29 tff(16150,plain,
% 4.04/4.29 (r(z, s(elem!1))),
% 4.04/4.29 inference(unit_resolution,[status(thm)],[2351, 16149])).
% 4.04/4.29 tff(16151,plain,
% 4.04/4.29 (~r(s(elem!1), s(s(s(s(z)))))),
% 4.04/4.29 inference(unit_resolution,[status(thm)],[2766, 16150, 47])).
% 4.04/4.29 tff(16152,plain,
% 4.04/4.29 (b(s(elem!1), s(s(s(s(z)))))),
% 4.04/4.29 inference(unit_resolution,[status(thm)],[1084, 16151, 16139])).
% 4.04/4.29 tff(16153,plain,
% 4.04/4.29 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 4.04/4.29 inference(modus_ponens,[status(thm)],[16152, 16138])).
% 4.04/4.29 tff(16154,plain,
% 4.04/4.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(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))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(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))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 4.04/4.29 inference(rewrite,[status(thm)],[])).
% 4.04/4.29 tff(16155,plain,
% 4.04/4.29 (((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(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(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(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(z)), 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(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 4.04/4.29 inference(rewrite,[status(thm)],[])).
% 4.04/4.29 tff(16156,plain,
% 4.04/4.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(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(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(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))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))))),
% 4.04/4.29 inference(monotonicity,[status(thm)],[16155])).
% 4.04/4.29 tff(16157,plain,
% 4.04/4.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(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(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(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))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 4.04/4.29 inference(transitivity,[status(thm)],[16156, 16154])).
% 4.04/4.29 tff(16158,plain,
% 4.04/4.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(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(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 4.04/4.29 inference(quant_inst,[status(thm)],[])).
% 4.04/4.29 tff(16159,plain,
% 4.04/4.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))),
% 4.04/4.29 inference(modus_ponens,[status(thm)],[16158, 16157])).
% 4.04/4.29 tff(16160,plain,
% 4.04/4.29 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))),
% 4.04/4.29 inference(unit_resolution,[status(thm)],[16159, 178, 104, 166, 251, 16107])).
% 4.04/4.29 tff(16161,plain,
% 4.04/4.29 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.04/4.29 inference(unit_resolution,[status(thm)],[16160, 16153, 16136])).
% 4.04/4.29 tff(16162,plain,
% 4.04/4.29 (~b(elem!1, s(elem!1))),
% 4.04/4.29 inference(modus_ponens,[status(thm)],[16161, 11733])).
% 4.04/4.29 tff(16163,plain,
% 4.04/4.29 (~(elem!1 = s(elem!1))),
% 4.04/4.29 inference(unit_resolution,[status(thm)],[748, 11736])).
% 4.04/4.29 tff(16164,plain,
% 4.04/4.29 (~r(elem!1, s(elem!1))),
% 4.04/4.29 inference(unit_resolution,[status(thm)],[12189, 16150, 437])).
% 4.04/4.29 tff(16165,plain,
% 4.04/4.29 (b(elem!1, s(elem!1))),
% 4.04/4.29 inference(unit_resolution,[status(thm)],[756, 16164, 16163])).
% 4.04/4.29 tff(16166,plain,
% 4.04/4.29 ($false),
% 4.04/4.29 inference(unit_resolution,[status(thm)],[16165, 16162])).
% 4.04/4.29 tff(16167,plain,(b(s(s(s(s(z)))), s(s(z))) | (~(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(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (~b(z, s(s(z)))) | (~r(z, elem!1)) | b(z, s(s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | b(elem!1, z) | (s(s(z)) = elem!1) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 4.04/4.29 tff(16168,plain,
% 4.04/4.29 ($false),
% 4.04/4.29 inference(unit_resolution,[status(thm)],[16167, 10801, 5723, 104, 166, 251, 679, 273, 521, 1, 147, 86, 12, 5618])).
% 4.04/4.29 tff(16169,plain,(b(elem!1, z) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(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))))))))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~r(z, elem!1)) | b(z, s(s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(z))) | (s(s(z)) = elem!1) | r(s(s(z)), z) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 4.04/4.29 tff(16170,plain,
% 4.04/4.29 (b(elem!1, z)),
% 4.04/4.29 inference(unit_resolution,[status(thm)],[16169, 86, 166, 251, 679, 273, 521, 1, 147, 104, 12, 5618, 290])).
% 4.04/4.29 tff(16171,plain,
% 4.04/4.29 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.04/4.29 inference(modus_ponens,[status(thm)],[16170, 4356])).
% 4.04/4.29 tff(16172,plain,
% 4.04/4.29 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.04/4.29 inference(unit_resolution,[status(thm)],[4057, 16171, 5619, 166, 273])).
% 4.04/4.29 tff(16173,plain,
% 4.04/4.29 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.04/4.29 inference(unit_resolution,[status(thm)],[3578, 16172])).
% 4.04/4.29 tff(16174,plain,
% 4.04/4.29 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z))))))))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 4.04/4.29 inference(monotonicity,[status(thm)],[11730])).
% 4.04/4.29 tff(16175,plain,
% 4.04/4.29 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.04/4.29 inference(symmetry,[status(thm)],[16174])).
% 4.04/4.29 tff(16176,plain,
% 4.04/4.29 (s(s(s(s(z)))) = s(s(s(s(s(s(s(s(z))))))))),
% 4.04/4.29 inference(transitivity,[status(thm)],[2491, 2823])).
% 4.04/4.29 tff(16177,plain,
% 4.04/4.29 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(s(s(z)))))))))),
% 4.04/4.29 inference(monotonicity,[status(thm)],[16176])).
% 4.04/4.29 tff(16178,plain,
% 4.04/4.29 (inj_0(s(s(s(s(s(s(s(s(z))))))))) = inj_0(s(s(s(s(z)))))),
% 4.04/4.29 inference(symmetry,[status(thm)],[16177])).
% 4.04/4.29 tff(16179,plain,
% 4.04/4.29 (s(s(s(s(s(s(s(z))))))) = s(s(s(z)))),
% 4.04/4.29 inference(transitivity,[status(thm)],[2829, 16178, 11])).
% 4.04/4.29 tff(16180,plain,
% 4.04/4.29 ($false),
% 4.04/4.29 inference(unit_resolution,[status(thm)],[1104, 16179])).
% 4.04/4.29 tff(16181,plain,((~(s(elem!1) = s(s(s(s(z)))))) | (~(elem!1 = s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.04/4.29 tff(16182,plain,
% 4.04/4.29 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.04/4.29 inference(unit_resolution,[status(thm)],[16181, 679])).
% 4.04/4.29 tff(16183,plain,
% 4.04/4.29 (~(s(s(s(s(z)))) = s(elem!1))),
% 4.04/4.29 inference(unit_resolution,[status(thm)],[2168, 16182])).
% 4.04/4.29 tff(16184,plain,
% 4.04/4.29 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.04/4.29 inference(monotonicity,[status(thm)],[679])).
% 4.04/4.29 tff(16185,plain,
% 4.04/4.29 ((s(elem!1) = elem!1) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 4.04/4.29 inference(transitivity,[status(thm)],[16184, 655])).
% 4.04/4.29 tff(16186,plain,
% 4.04/4.29 ((~(s(elem!1) = elem!1)) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 4.04/4.29 inference(monotonicity,[status(thm)],[16185])).
% 4.04/4.29 tff(16187,plain,
% 4.04/4.29 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 4.04/4.29 inference(modus_ponens,[status(thm)],[11736, 16186])).
% 4.04/4.29 tff(16188,plain,
% 4.04/4.29 (b(s(elem!1), s(s(s(s(z)))))),
% 4.04/4.29 inference(unit_resolution,[status(thm)],[1084, 12433, 16182])).
% 4.04/4.29 tff(16189,plain,
% 4.04/4.29 (~b(s(s(s(s(z)))), s(elem!1))),
% 4.04/4.29 inference(unit_resolution,[status(thm)],[15104, 16188, 104, 107, 193, 16187, 363])).
% 4.04/4.29 tff(16190,plain,
% 4.04/4.29 (r(s(s(s(s(z)))), s(elem!1))),
% 4.04/4.29 inference(unit_resolution,[status(thm)],[2173, 16189, 16183])).
% 4.04/4.29 tff(16191,plain,
% 4.04/4.29 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.04/4.29 inference(modus_ponens,[status(thm)],[16190, 16175])).
% 4.04/4.29 tff(16192,plain,
% 4.04/4.29 (r(s(elem!1), s(s(z))) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 4.04/4.29 inference(monotonicity,[status(thm)],[2823])).
% 4.04/4.29 tff(16193,plain,
% 4.04/4.29 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 4.04/4.29 inference(modus_ponens,[status(thm)],[363, 16192])).
% 4.04/4.29 tff(16194,plain,
% 4.04/4.29 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))))),
% 4.04/4.29 inference(rewrite,[status(thm)],[])).
% 4.04/4.29 tff(16195,plain,
% 4.04/4.29 (((~r(s(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(z)))), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))))),
% 4.04/4.29 inference(rewrite,[status(thm)],[])).
% 4.04/4.29 tff(16196,plain,
% 4.04/4.29 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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(z)))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z))))))))))))),
% 4.04/4.29 inference(monotonicity,[status(thm)],[16195])).
% 4.04/4.29 tff(16197,plain,
% 4.04/4.29 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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(z)))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))))),
% 4.04/4.29 inference(transitivity,[status(thm)],[16196, 16194])).
% 4.04/4.29 tff(16198,plain,
% 4.04/4.29 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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(z)))), s(s(s(s(s(s(s(s(z)))))))))))),
% 4.04/4.29 inference(quant_inst,[status(thm)],[])).
% 4.04/4.29 tff(16199,plain,
% 4.04/4.29 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z))))))))))),
% 4.04/4.29 inference(modus_ponens,[status(thm)],[16198, 16197])).
% 4.04/4.29 tff(16200,plain,
% 4.04/4.29 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.04/4.29 inference(unit_resolution,[status(thm)],[16199, 118, 193, 16193])).
% 4.04/4.29 tff(16201,plain,
% 4.04/4.29 ($false),
% 4.04/4.29 inference(unit_resolution,[status(thm)],[16200, 16191])).
% 4.04/4.29 tff(16202,plain,((~r(s(elem!1), s(s(z)))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), 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(z))))), inference(lemma,lemma(discharge,[]))).
% 4.04/4.29 tff(16203,plain,
% 4.04/4.29 (~r(s(elem!1), s(s(z)))),
% 4.04/4.29 inference(unit_resolution,[status(thm)],[16202, 103, 679, 104, 16173])).
% 4.04/4.29 tff(16204,plain,
% 4.04/4.29 (b(s(elem!1), s(s(z)))),
% 4.04/4.29 inference(unit_resolution,[status(thm)],[421, 16203, 10483])).
% 4.04/4.29 tff(16205,plain,
% 4.04/4.29 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 4.04/4.29 inference(modus_ponens,[status(thm)],[16204, 11737])).
% 4.04/4.29 tff(16206,plain,
% 4.04/4.29 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.29 inference(modus_ponens,[status(thm)],[727, 11735])).
% 4.04/4.29 tff(16207,plain,
% 4.04/4.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 4.04/4.29 inference(rewrite,[status(thm)],[])).
% 4.04/4.29 tff(16208,plain,
% 4.04/4.29 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 4.04/4.29 inference(rewrite,[status(thm)],[])).
% 4.04/4.29 tff(16209,plain,
% 4.04/4.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))))),
% 4.04/4.30 inference(monotonicity,[status(thm)],[16208])).
% 4.04/4.30 tff(16210,plain,
% 4.04/4.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 4.04/4.30 inference(transitivity,[status(thm)],[16209, 16207])).
% 4.04/4.30 tff(16211,plain,
% 4.04/4.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))))),
% 4.04/4.30 inference(quant_inst,[status(thm)],[])).
% 4.04/4.30 tff(16212,plain,
% 4.04/4.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))),
% 4.04/4.30 inference(modus_ponens,[status(thm)],[16211, 16210])).
% 4.04/4.30 tff(16213,plain,
% 4.04/4.30 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.30 inference(unit_resolution,[status(thm)],[16212, 178, 3461, 166, 146, 16124])).
% 4.04/4.30 tff(16214,plain,
% 4.04/4.30 ($false),
% 4.04/4.30 inference(unit_resolution,[status(thm)],[16213, 16206])).
% 4.04/4.30 tff(16215,plain,((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.04/4.30 tff(16216,plain,
% 4.04/4.30 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.04/4.30 inference(unit_resolution,[status(thm)],[16215, 16205, 5619, 166, 16171, 679])).
% 4.04/4.30 tff(16217,plain,
% 4.04/4.30 (~r(s(elem!1), elem!1)),
% 4.04/4.30 inference(unit_resolution,[status(thm)],[16132, 16205, 273, 5619, 679, 521])).
% 4.04/4.30 tff(16218,plain,
% 4.04/4.30 (b(s(elem!1), elem!1)),
% 4.04/4.30 inference(unit_resolution,[status(thm)],[677, 16217, 11736])).
% 4.04/4.30 tff(16219,plain,
% 4.04/4.30 ($false),
% 4.04/4.30 inference(unit_resolution,[status(thm)],[686, 16218, 16216, 679])).
% 4.04/4.30 tff(16220,plain,(b(s(s(s(s(z)))), s(s(z))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~r(z, 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))))))))) | b(z, s(s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (s(s(z)) = elem!1) | r(s(s(z)), z) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 4.14/4.30 tff(16221,plain,
% 4.14/4.30 (b(s(s(s(s(z)))), s(s(z)))),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[16220, 11726, 166, 273, 521, 104, 251, 1, 147, 12, 5618, 290])).
% 4.14/4.30 tff(16222,plain,
% 4.14/4.30 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 4.14/4.30 inference(monotonicity,[status(thm)],[11726])).
% 4.14/4.30 tff(16223,plain,
% 4.14/4.30 (s(s(s(s(s(s(s(s(z)))))))) = s(elem!1)),
% 4.14/4.30 inference(symmetry,[status(thm)],[16222])).
% 4.14/4.30 tff(16224,plain,
% 4.14/4.30 (b(s(s(s(s(s(s(s(s(z)))))))), z) <=> b(s(elem!1), z)),
% 4.14/4.30 inference(monotonicity,[status(thm)],[16223])).
% 4.14/4.30 tff(16225,plain,
% 4.14/4.30 (b(s(elem!1), z) <=> b(s(s(s(s(s(s(s(s(z)))))))), z)),
% 4.14/4.30 inference(symmetry,[status(thm)],[16224])).
% 4.14/4.30 tff(16226,plain,
% 4.14/4.30 (~(s(elem!1) = s(s(z)))),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[2832, 11726])).
% 4.14/4.30 tff(16227,plain,
% 4.14/4.30 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[2840, 16226])).
% 4.14/4.30 tff(16228,plain,
% 4.14/4.30 (~(elem!1 = s(s(s(elem!1))))),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[2859, 16227, 11726])).
% 4.14/4.30 tff(16229,plain,
% 4.14/4.30 (~(s(s(s(elem!1))) = elem!1)),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[2489, 16228])).
% 4.14/4.30 tff(16230,plain,
% 4.14/4.30 (~(s(elem!1) = elem!1)),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[2150, 16229])).
% 4.14/4.30 tff(16231,plain,
% 4.14/4.30 (b(s(s(z)), s(s(s(s(s(s(s(s(z))))))))) <=> b(s(s(z)), s(elem!1))),
% 4.14/4.30 inference(monotonicity,[status(thm)],[11730])).
% 4.14/4.30 tff(16232,plain,
% 4.14/4.30 (b(s(s(z)), s(elem!1)) <=> b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 4.14/4.30 inference(symmetry,[status(thm)],[16231])).
% 4.14/4.30 tff(16233,plain,
% 4.14/4.30 (~(s(s(z)) = s(elem!1))),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[1058, 10483])).
% 4.14/4.30 tff(16234,plain,
% 4.14/4.30 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) <=> (~b(s(s(s(s(z)))), s(elem!1)))),
% 4.14/4.30 inference(monotonicity,[status(thm)],[15448])).
% 4.14/4.30 tff(16235,plain,
% 4.14/4.30 (b(s(elem!1), s(s(s(s(z)))))),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[1084, 13109, 16182])).
% 4.14/4.30 tff(16236,plain,
% 4.14/4.30 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 4.14/4.30 inference(modus_ponens,[status(thm)],[16235, 16138])).
% 4.14/4.30 tff(16237,assumption,(b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 4.14/4.30 tff(16238,plain,
% 4.14/4.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(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(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(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(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 4.14/4.30 inference(rewrite,[status(thm)],[])).
% 4.14/4.30 tff(16239,plain,
% 4.14/4.30 (((~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(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(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))))))))) | (~b(s(s(s(s(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(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(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 4.14/4.30 inference(rewrite,[status(thm)],[])).
% 4.14/4.30 tff(16240,plain,
% 4.14/4.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(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))))))))) | (~b(s(s(s(s(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(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(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(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))))),
% 4.14/4.30 inference(monotonicity,[status(thm)],[16239])).
% 4.14/4.30 tff(16241,plain,
% 4.14/4.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(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))))))))) | (~b(s(s(s(s(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(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(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(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 4.14/4.30 inference(transitivity,[status(thm)],[16240, 16238])).
% 4.14/4.30 tff(16242,plain,
% 4.14/4.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(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))))))))) | (~b(s(s(s(s(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(s(z)))))))))))),
% 4.14/4.30 inference(quant_inst,[status(thm)],[])).
% 4.14/4.30 tff(16243,plain,
% 4.14/4.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(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(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))),
% 4.14/4.30 inference(modus_ponens,[status(thm)],[16242, 16241])).
% 4.14/4.30 tff(16244,plain,
% 4.14/4.30 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[16243, 178, 104, 251, 16237, 16236])).
% 4.14/4.30 tff(16245,plain,
% 4.14/4.30 (~b(s(s(s(s(z)))), s(elem!1))),
% 4.14/4.30 inference(modus_ponens,[status(thm)],[16244, 16234])).
% 4.14/4.30 tff(16246,plain,
% 4.14/4.30 (r(s(s(s(s(z)))), s(elem!1))),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[2173, 16245, 16183])).
% 4.14/4.30 tff(16247,plain,
% 4.14/4.30 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.14/4.30 inference(modus_ponens,[status(thm)],[16246, 16175])).
% 4.14/4.30 tff(16248,plain,
% 4.14/4.30 (r(s(s(z)), s(s(s(s(s(s(s(s(z))))))))) <=> r(s(s(z)), s(elem!1))),
% 4.14/4.30 inference(monotonicity,[status(thm)],[11730])).
% 4.14/4.30 tff(16249,plain,
% 4.14/4.30 (r(s(s(z)), s(elem!1)) <=> r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 4.14/4.30 inference(symmetry,[status(thm)],[16248])).
% 4.14/4.30 tff(16250,plain,
% 4.14/4.30 (r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 4.14/4.30 inference(modus_ponens,[status(thm)],[1329, 16249])).
% 4.14/4.30 tff(16251,plain,
% 4.14/4.30 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))))),
% 4.14/4.30 inference(rewrite,[status(thm)],[])).
% 4.14/4.30 tff(16252,plain,
% 4.14/4.30 (((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(z)), s(s(s(s(s(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(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))))),
% 4.14/4.30 inference(rewrite,[status(thm)],[])).
% 4.14/4.30 tff(16253,plain,
% 4.14/4.30 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z))))))))))))),
% 4.14/4.30 inference(monotonicity,[status(thm)],[16252])).
% 4.14/4.30 tff(16254,plain,
% 4.14/4.30 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))))),
% 4.14/4.30 inference(transitivity,[status(thm)],[16253, 16251])).
% 4.14/4.30 tff(16255,plain,
% 4.14/4.30 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 4.14/4.30 inference(quant_inst,[status(thm)],[])).
% 4.14/4.30 tff(16256,plain,
% 4.14/4.30 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z))))))))))),
% 4.14/4.30 inference(modus_ponens,[status(thm)],[16255, 16254])).
% 4.14/4.30 tff(16257,plain,
% 4.14/4.30 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[16256, 118, 147, 16250])).
% 4.14/4.30 tff(16258,plain,
% 4.14/4.30 ($false),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[16257, 16247])).
% 4.14/4.30 tff(16259,plain,((~r(s(s(z)), s(elem!1))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.30 tff(16260,plain,
% 4.14/4.30 (~r(s(s(z)), s(elem!1))),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[16259, 16206, 147, 104, 251, 679])).
% 4.14/4.30 tff(16261,plain,
% 4.14/4.30 (b(s(s(z)), s(elem!1))),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[1067, 16260, 16233])).
% 4.14/4.30 tff(16262,plain,
% 4.14/4.30 (b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 4.14/4.30 inference(modus_ponens,[status(thm)],[16261, 16232])).
% 4.14/4.30 tff(16263,plain,
% 4.14/4.30 (~b(s(elem!1), s(s(s(s(z)))))),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[2529, 16261, 104, 166, 727])).
% 4.14/4.30 tff(16264,plain,
% 4.14/4.30 (r(s(elem!1), s(s(s(s(z)))))),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[1084, 16263, 16182])).
% 4.14/4.30 tff(16265,plain,
% 4.14/4.30 (~r(z, s(elem!1))),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[2766, 16264, 145])).
% 4.14/4.30 tff(16266,plain,
% 4.14/4.30 (b(z, s(elem!1))),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[2351, 16265])).
% 4.14/4.30 tff(16267,plain,
% 4.14/4.30 (b(z, s(s(s(s(s(s(s(s(z)))))))))),
% 4.14/4.30 inference(modus_ponens,[status(thm)],[16266, 16109])).
% 4.14/4.30 tff(16268,plain,
% 4.14/4.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 4.14/4.30 inference(rewrite,[status(thm)],[])).
% 4.14/4.30 tff(16269,plain,
% 4.14/4.30 (((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 4.14/4.30 inference(rewrite,[status(thm)],[])).
% 4.14/4.30 tff(16270,plain,
% 4.14/4.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))))),
% 4.14/4.30 inference(monotonicity,[status(thm)],[16269])).
% 4.14/4.30 tff(16271,plain,
% 4.14/4.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 4.14/4.30 inference(transitivity,[status(thm)],[16270, 16268])).
% 4.14/4.30 tff(16272,plain,
% 4.14/4.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(z)))))),
% 4.14/4.30 inference(quant_inst,[status(thm)],[])).
% 4.14/4.30 tff(16273,plain,
% 4.14/4.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))),
% 4.14/4.30 inference(modus_ponens,[status(thm)],[16272, 16271])).
% 4.14/4.30 tff(16274,plain,
% 4.14/4.30 (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[16273, 178, 273, 166, 16206, 16267])).
% 4.14/4.30 tff(16275,plain,
% 4.14/4.30 ($false),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[16274, 16262])).
% 4.14/4.30 tff(16276,plain,((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.30 tff(16277,plain,
% 4.14/4.30 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[16276, 11726, 273, 166, 47, 104, 147, 251])).
% 4.14/4.30 tff(16278,plain,
% 4.14/4.30 (~b(s(elem!1), elem!1)),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[686, 16277, 11726])).
% 4.14/4.30 tff(16279,plain,
% 4.14/4.30 (r(s(elem!1), elem!1)),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[677, 16278, 16230])).
% 4.14/4.30 tff(16280,plain,
% 4.14/4.30 (~r(s(elem!1), z)),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[1284, 16279, 521])).
% 4.14/4.30 tff(16281,plain,
% 4.14/4.30 (b(s(elem!1), z)),
% 4.14/4.30 inference(unit_resolution,[status(thm)],[774, 16280])).
% 4.14/4.30 tff(16282,plain,
% 4.14/4.30 (b(s(s(s(s(s(s(s(s(z)))))))), z)),
% 4.14/4.30 inference(modus_ponens,[status(thm)],[16281, 16225])).
% 4.14/4.30 tff(16283,plain,
% 4.14/4.30 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 4.14/4.30 inference(monotonicity,[status(thm)],[16223])).
% 4.14/4.30 tff(16284,plain,
% 4.14/4.30 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 4.14/4.30 inference(symmetry,[status(thm)],[16283])).
% 4.14/4.30 tff(16285,plain,
% 4.14/4.31 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[16181, 11726])).
% 4.14/4.31 tff(16286,plain,
% 4.14/4.31 (~r(s(elem!1), s(s(s(s(z)))))),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[6776, 16281, 273, 147, 16226, 5619])).
% 4.14/4.31 tff(16287,plain,
% 4.14/4.31 (b(s(elem!1), s(s(s(s(z)))))),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[1084, 16286, 16285])).
% 4.14/4.31 tff(16288,plain,
% 4.14/4.31 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 4.14/4.31 inference(modus_ponens,[status(thm)],[16287, 16284])).
% 4.14/4.31 tff(16289,plain,
% 4.14/4.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 4.14/4.31 inference(rewrite,[status(thm)],[])).
% 4.14/4.31 tff(16290,plain,
% 4.14/4.31 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 4.14/4.31 inference(rewrite,[status(thm)],[])).
% 4.14/4.31 tff(16291,plain,
% 4.14/4.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))))),
% 4.14/4.31 inference(monotonicity,[status(thm)],[16290])).
% 4.14/4.31 tff(16292,plain,
% 4.14/4.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 4.14/4.31 inference(transitivity,[status(thm)],[16291, 16289])).
% 4.14/4.31 tff(16293,plain,
% 4.14/4.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 4.14/4.31 inference(quant_inst,[status(thm)],[])).
% 4.14/4.31 tff(16294,plain,
% 4.14/4.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))),
% 4.14/4.31 inference(modus_ponens,[status(thm)],[16293, 16292])).
% 4.14/4.31 tff(16295,plain,
% 4.14/4.31 (~b(s(s(s(s(z)))), z)),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[16294, 178, 273, 16221, 16288, 16282])).
% 4.14/4.31 tff(16296,plain,
% 4.14/4.31 (r(s(s(s(s(z)))), z)),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[191, 16295])).
% 4.14/4.31 tff(16297,plain,
% 4.14/4.31 (r(elem!1, s(s(z))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.14/4.31 inference(monotonicity,[status(thm)],[11726])).
% 4.14/4.31 tff(16298,plain,
% 4.14/4.31 (r(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> r(elem!1, s(s(z)))),
% 4.14/4.31 inference(symmetry,[status(thm)],[16297])).
% 4.14/4.31 tff(16299,plain,
% 4.14/4.31 ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) <=> (~r(elem!1, s(s(z))))),
% 4.14/4.31 inference(monotonicity,[status(thm)],[16298])).
% 4.14/4.31 tff(16300,plain,
% 4.14/4.31 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 4.14/4.31 inference(monotonicity,[status(thm)],[16223])).
% 4.14/4.31 tff(16301,plain,
% 4.14/4.31 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.14/4.31 inference(transitivity,[status(thm)],[16300, 377])).
% 4.14/4.31 tff(16302,plain,
% 4.14/4.31 ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z)))))))))),
% 4.14/4.31 inference(symmetry,[status(thm)],[16301])).
% 4.14/4.31 tff(16303,plain,
% 4.14/4.31 ((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z))))))))))),
% 4.14/4.31 inference(monotonicity,[status(thm)],[16302])).
% 4.14/4.31 tff(16304,plain,
% 4.14/4.31 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.14/4.31 inference(monotonicity,[status(thm)],[11726])).
% 4.14/4.31 tff(16305,plain,
% 4.14/4.31 ((~(s(elem!1) = elem!1)) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 4.14/4.31 inference(monotonicity,[status(thm)],[16304])).
% 4.14/4.31 tff(16306,plain,
% 4.14/4.31 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.14/4.31 inference(modus_ponens,[status(thm)],[16230, 16305])).
% 4.14/4.31 tff(16307,plain,
% 4.14/4.31 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z)))))))))),
% 4.14/4.31 inference(modus_ponens,[status(thm)],[16306, 16303])).
% 4.14/4.31 tff(16308,plain,
% 4.14/4.31 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z))))))))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 4.14/4.31 inference(monotonicity,[status(thm)],[16223])).
% 4.14/4.31 tff(16309,plain,
% 4.14/4.31 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.14/4.31 inference(symmetry,[status(thm)],[16308])).
% 4.14/4.31 tff(16310,plain,
% 4.14/4.31 (~(s(s(s(s(z)))) = s(elem!1))),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[2168, 16285])).
% 4.14/4.31 tff(16311,plain,
% 4.14/4.31 (r(s(s(z)), s(s(s(s(s(s(s(s(z))))))))) <=> r(s(s(z)), s(elem!1))),
% 4.14/4.31 inference(monotonicity,[status(thm)],[16223])).
% 4.14/4.31 tff(16312,plain,
% 4.14/4.31 (r(s(s(z)), s(elem!1)) <=> r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 4.14/4.31 inference(symmetry,[status(thm)],[16311])).
% 4.14/4.31 tff(16313,plain,
% 4.14/4.31 (~(s(s(z)) = s(elem!1))),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[1058, 16226])).
% 4.14/4.31 tff(16314,plain,
% 4.14/4.31 (b(s(s(z)), s(s(s(s(s(s(s(s(z))))))))) <=> b(s(s(z)), s(elem!1))),
% 4.14/4.31 inference(monotonicity,[status(thm)],[16223])).
% 4.14/4.31 tff(16315,plain,
% 4.14/4.31 ((~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) <=> (~b(s(s(z)), s(elem!1)))),
% 4.14/4.31 inference(monotonicity,[status(thm)],[16314])).
% 4.14/4.31 tff(16316,plain,
% 4.14/4.31 (b(z, s(s(s(s(s(s(s(s(z))))))))) <=> b(z, s(elem!1))),
% 4.14/4.31 inference(monotonicity,[status(thm)],[16223])).
% 4.14/4.31 tff(16317,plain,
% 4.14/4.31 (b(z, s(elem!1)) <=> b(z, s(s(s(s(s(s(s(s(z)))))))))),
% 4.14/4.31 inference(symmetry,[status(thm)],[16316])).
% 4.14/4.31 tff(16318,plain,
% 4.14/4.31 (~r(z, s(elem!1))),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[7070, 16279, 521])).
% 4.14/4.31 tff(16319,plain,
% 4.14/4.31 (b(z, s(elem!1))),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[2351, 16318])).
% 4.14/4.31 tff(16320,plain,
% 4.14/4.31 (b(z, s(s(s(s(s(s(s(s(z)))))))))),
% 4.14/4.31 inference(modus_ponens,[status(thm)],[16319, 16317])).
% 4.14/4.31 tff(16321,plain,
% 4.14/4.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))))),
% 4.14/4.31 inference(rewrite,[status(thm)],[])).
% 4.14/4.31 tff(16322,plain,
% 4.14/4.31 (((~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))))),
% 4.14/4.31 inference(rewrite,[status(thm)],[])).
% 4.14/4.31 tff(16323,plain,
% 4.14/4.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z))))))))))))),
% 4.14/4.31 inference(monotonicity,[status(thm)],[16322])).
% 4.14/4.31 tff(16324,plain,
% 4.14/4.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))))),
% 4.14/4.31 inference(transitivity,[status(thm)],[16323, 16321])).
% 4.14/4.31 tff(16325,plain,
% 4.14/4.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(z)))))),
% 4.14/4.31 inference(quant_inst,[status(thm)],[])).
% 4.14/4.31 tff(16326,plain,
% 4.14/4.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z))))))))))),
% 4.14/4.31 inference(modus_ponens,[status(thm)],[16325, 16324])).
% 4.14/4.31 tff(16327,plain,
% 4.14/4.31 (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[16326, 178, 5619, 273, 16320, 16282])).
% 4.14/4.31 tff(16328,plain,
% 4.14/4.31 (~b(s(s(z)), s(elem!1))),
% 4.14/4.31 inference(modus_ponens,[status(thm)],[16327, 16315])).
% 4.14/4.31 tff(16329,plain,
% 4.14/4.31 (r(s(s(z)), s(elem!1))),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[1067, 16328, 16313])).
% 4.14/4.31 tff(16330,plain,
% 4.14/4.31 (r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 4.14/4.31 inference(modus_ponens,[status(thm)],[16329, 16312])).
% 4.14/4.31 tff(16331,plain,
% 4.14/4.31 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.14/4.31 inference(modus_ponens,[status(thm)],[6400, 16175])).
% 4.14/4.31 tff(16332,assumption,(r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))), introduced(assumption)).
% 4.14/4.31 tff(16333,plain,
% 4.14/4.31 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[16256, 118, 147, 16332])).
% 4.14/4.31 tff(16334,plain,
% 4.14/4.31 ($false),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[16333, 16331])).
% 4.14/4.31 tff(16335,plain,((~r(s(s(s(s(z)))), s(elem!1))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z))))))))))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.31 tff(16336,plain,
% 4.14/4.31 (~r(s(s(s(s(z)))), s(elem!1))),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[16335, 11726, 147, 16330])).
% 4.14/4.31 tff(16337,plain,
% 4.14/4.31 (b(s(s(s(s(z)))), s(elem!1))),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[2173, 16336, 16310])).
% 4.14/4.31 tff(16338,plain,
% 4.14/4.31 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.14/4.31 inference(modus_ponens,[status(thm)],[16337, 16309])).
% 4.14/4.31 tff(16339,plain,
% 4.14/4.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(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(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(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(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 4.14/4.31 inference(rewrite,[status(thm)],[])).
% 4.14/4.31 tff(16340,plain,
% 4.14/4.31 (((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(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(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(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(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(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 4.14/4.31 inference(rewrite,[status(thm)],[])).
% 4.14/4.31 tff(16341,plain,
% 4.14/4.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(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(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(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(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))))),
% 4.14/4.31 inference(monotonicity,[status(thm)],[16340])).
% 4.14/4.31 tff(16342,plain,
% 4.14/4.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(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(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(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(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 4.14/4.31 inference(transitivity,[status(thm)],[16341, 16339])).
% 4.14/4.31 tff(16343,plain,
% 4.14/4.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(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(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.14/4.31 inference(quant_inst,[status(thm)],[])).
% 4.14/4.31 tff(16344,plain,
% 4.14/4.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(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(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))),
% 4.14/4.31 inference(modus_ponens,[status(thm)],[16343, 16342])).
% 4.14/4.31 tff(16345,plain,
% 4.14/4.31 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[16344, 178, 104, 251, 16288])).
% 4.14/4.31 tff(16346,plain,
% 4.14/4.31 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[16345, 16338])).
% 4.14/4.31 tff(16347,plain,
% 4.14/4.31 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))),
% 4.14/4.31 inference(rewrite,[status(thm)],[])).
% 4.14/4.31 tff(16348,plain,
% 4.14/4.31 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))),
% 4.14/4.31 inference(quant_inst,[status(thm)],[])).
% 4.14/4.31 tff(16349,plain,
% 4.14/4.31 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.14/4.31 inference(modus_ponens,[status(thm)],[16348, 16347])).
% 4.14/4.31 tff(16350,plain,
% 4.14/4.31 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[16349, 41, 16346])).
% 4.14/4.31 tff(16351,plain,
% 4.14/4.31 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[16350, 16307])).
% 4.14/4.31 tff(16352,plain,
% 4.14/4.31 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))),
% 4.14/4.31 inference(rewrite,[status(thm)],[])).
% 4.14/4.31 tff(16353,plain,
% 4.14/4.31 (((~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(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(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))),
% 4.14/4.31 inference(rewrite,[status(thm)],[])).
% 4.14/4.31 tff(16354,plain,
% 4.14/4.31 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z))))))))))))),
% 4.14/4.31 inference(monotonicity,[status(thm)],[16353])).
% 4.14/4.31 tff(16355,plain,
% 4.14/4.31 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))),
% 4.14/4.31 inference(transitivity,[status(thm)],[16354, 16352])).
% 4.14/4.31 tff(16356,plain,
% 4.14/4.31 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 4.14/4.31 inference(quant_inst,[status(thm)],[])).
% 4.14/4.31 tff(16357,plain,
% 4.14/4.31 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z))))))))))),
% 4.14/4.31 inference(modus_ponens,[status(thm)],[16356, 16355])).
% 4.14/4.31 tff(16358,plain,
% 4.14/4.31 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[16357, 118, 16330, 16351])).
% 4.14/4.31 tff(16359,plain,
% 4.14/4.31 (~r(elem!1, s(s(z)))),
% 4.14/4.31 inference(modus_ponens,[status(thm)],[16358, 16299])).
% 4.14/4.31 tff(16360,plain,
% 4.14/4.31 (b(elem!1, s(s(z)))),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[467, 16359, 312])).
% 4.14/4.31 tff(16361,plain,
% 4.14/4.31 (~r(elem!1, z)),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[13518, 16360, 817, 16296, 16221, 469])).
% 4.14/4.31 tff(16362,plain,
% 4.14/4.31 (b(elem!1, z)),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[498, 16361, 290])).
% 4.14/4.31 tff(16363,plain,
% 4.14/4.31 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.14/4.31 inference(modus_ponens,[status(thm)],[16362, 11727])).
% 4.14/4.31 tff(16364,plain,
% 4.14/4.31 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[3578, 16358])).
% 4.14/4.31 tff(16365,plain,
% 4.14/4.31 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[4057, 16364, 5619, 166, 273])).
% 4.14/4.31 tff(16366,plain,
% 4.14/4.31 ($false),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[16365, 16363])).
% 4.14/4.31 tff(16367,plain,((~b(s(s(z)), elem!1)) | (elem!1 = z) | (elem!1 = s(s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, 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))))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, elem!1)) | b(z, s(s(s(s(z))))) | (s(s(z)) = elem!1) | r(s(s(z)), z) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.31 tff(16368,plain,
% 4.14/4.31 (~b(s(s(z)), elem!1)),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[16367, 12, 469, 166, 273, 104, 251, 147, 521, 1, 290, 5618, 644])).
% 4.14/4.31 tff(16369,plain,
% 4.14/4.31 (r(s(s(z)), elem!1)),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[448, 16368, 12])).
% 4.14/4.31 tff(16370,plain,
% 4.14/4.31 (r(s(s(s(s(z)))), elem!1)),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[8548, 11095, 104, 251, 469, 5721])).
% 4.14/4.31 tff(16371,plain,
% 4.14/4.31 (~r(s(s(s(s(z)))), s(s(z)))),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[3329, 16370, 438])).
% 4.14/4.31 tff(16372,plain,
% 4.14/4.31 (b(s(s(s(s(z)))), s(s(z)))),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[102, 16371])).
% 4.14/4.31 tff(16373,plain,
% 4.14/4.31 (b(elem!1, s(s(s(s(z)))))),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[483, 5721, 469])).
% 4.14/4.31 tff(16374,plain,
% 4.14/4.31 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[11098, 701, 251, 16373, 104, 644])).
% 4.14/4.31 tff(16375,plain,
% 4.14/4.31 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[11027, 16374, 521])).
% 4.14/4.31 tff(16376,plain,
% 4.14/4.31 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[133, 16375])).
% 4.14/4.31 tff(16377,plain,
% 4.14/4.31 (~r(s(s(s(s(z)))), z)),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[3137, 16370, 521])).
% 4.14/4.31 tff(16378,plain,
% 4.14/4.31 (b(s(s(s(s(z)))), z)),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[191, 16377])).
% 4.14/4.31 tff(16379,plain,
% 4.14/4.31 ($false),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[298, 16378, 16376, 104, 273, 16372])).
% 4.14/4.31 tff(16380,plain,((elem!1 = s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(s(s(s(z))))) | r(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.31 tff(16381,plain,
% 4.14/4.31 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[16380, 16369, 273, 521, 104, 251, 469, 11716, 644])).
% 4.14/4.31 tff(16382,plain,
% 4.14/4.31 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.14/4.31 inference(monotonicity,[status(thm)],[16381])).
% 4.14/4.31 tff(16383,plain,
% 4.14/4.31 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(z)), elem!1)),
% 4.14/4.31 inference(symmetry,[status(thm)],[16382])).
% 4.14/4.31 tff(16384,plain,
% 4.14/4.31 (b(s(s(z)), elem!1)),
% 4.14/4.31 inference(modus_ponens,[status(thm)],[166, 16383])).
% 4.14/4.31 tff(16385,plain,
% 4.14/4.31 ($false),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[16368, 16384])).
% 4.14/4.31 tff(16386,plain,((s(s(z)) = elem!1) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~r(z, 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))))))))) | (elem!1 = s(s(s(s(z))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | b(z, s(s(s(s(z))))) | (elem!1 = z) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 4.14/4.31 tff(16387,plain,
% 4.14/4.31 (s(s(z)) = elem!1),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[16386, 11715, 144, 166, 104, 11349, 469, 644, 147, 1, 290, 10792])).
% 4.14/4.31 tff(16388,plain,
% 4.14/4.31 (r(z, s(s(z))) <=> r(z, elem!1)),
% 4.14/4.31 inference(monotonicity,[status(thm)],[16387])).
% 4.14/4.31 tff(16389,plain,
% 4.14/4.31 (r(z, elem!1) <=> r(z, s(s(z)))),
% 4.14/4.31 inference(symmetry,[status(thm)],[16388])).
% 4.14/4.31 tff(16390,plain,
% 4.14/4.31 (r(z, s(s(z)))),
% 4.14/4.31 inference(modus_ponens,[status(thm)],[11715, 16389])).
% 4.14/4.31 tff(16391,plain,
% 4.14/4.31 ($false),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[48, 16390])).
% 4.14/4.31 tff(16392,plain,(r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(z, s(s(z))) | (~b(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)))))) | (elem!1 = s(s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | b(z, s(s(s(s(z))))) | (elem!1 = z) | b(z, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.31 tff(16393,plain,
% 4.14/4.31 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[16392, 469, 166, 104, 48, 147, 1, 290, 4235])).
% 4.14/4.31 tff(16394,plain,
% 4.14/4.31 (~r(elem!1, z)),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[10809, 16393, 4236])).
% 4.14/4.31 tff(16395,plain,
% 4.14/4.31 (b(elem!1, z)),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[498, 16394, 290])).
% 4.14/4.31 tff(16396,plain,
% 4.14/4.31 (~r(z, elem!1)),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[3818, 16393, 4236])).
% 4.14/4.31 tff(16397,plain,
% 4.14/4.31 (b(z, elem!1)),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[585, 16396, 318])).
% 4.14/4.31 tff(16398,plain,
% 4.14/4.31 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[703, 11614])).
% 4.14/4.31 tff(16399,plain,
% 4.14/4.31 (~b(s(s(z)), elem!1)),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[11004, 506, 3461, 273, 818])).
% 4.14/4.31 tff(16400,plain,
% 4.14/4.31 (r(s(s(z)), elem!1)),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[448, 12, 16399])).
% 4.14/4.31 tff(16401,plain,
% 4.14/4.31 (~r(elem!1, s(s(s(s(z)))))),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[8763, 16400, 147])).
% 4.14/4.31 tff(16402,plain,
% 4.14/4.31 (b(elem!1, s(s(s(s(z)))))),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[483, 16401, 469])).
% 4.14/4.31 tff(16403,plain,
% 4.14/4.31 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[10799, 147, 47])).
% 4.14/4.31 tff(16404,plain,
% 4.14/4.31 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[5101, 147, 47, 3461])).
% 4.14/4.31 tff(16405,plain,
% 4.14/4.31 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.14/4.31 inference(unit_resolution,[status(thm)],[10755, 16404])).
% 4.14/4.31 tff(16406,plain,
% 4.14/4.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))),
% 4.14/4.31 inference(rewrite,[status(thm)],[])).
% 4.14/4.31 tff(16407,plain,
% 4.14/4.31 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))),
% 4.14/4.32 inference(rewrite,[status(thm)],[])).
% 4.14/4.32 tff(16408,plain,
% 4.14/4.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z))))),
% 4.14/4.32 inference(monotonicity,[status(thm)],[16407])).
% 4.14/4.32 tff(16409,plain,
% 4.14/4.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))),
% 4.14/4.32 inference(transitivity,[status(thm)],[16408, 16406])).
% 4.14/4.32 tff(16410,plain,
% 4.14/4.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)))),
% 4.14/4.32 inference(quant_inst,[status(thm)],[])).
% 4.14/4.32 tff(16411,plain,
% 4.14/4.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z))),
% 4.14/4.32 inference(modus_ponens,[status(thm)],[16410, 16409])).
% 4.14/4.32 tff(16412,plain,
% 4.14/4.32 (~b(elem!1, s(s(z)))),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[16411, 178, 818, 506, 3461, 273])).
% 4.14/4.32 tff(16413,plain,
% 4.14/4.32 (r(elem!1, s(s(z)))),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[467, 312, 16412])).
% 4.14/4.32 tff(16414,plain,
% 4.14/4.32 (~r(s(s(s(s(z)))), elem!1)),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[10883, 193, 16413])).
% 4.14/4.32 tff(16415,plain,
% 4.14/4.32 (b(s(s(s(s(z)))), elem!1)),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[3142, 16414, 551])).
% 4.14/4.32 tff(16416,plain,
% 4.14/4.32 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[3928, 178, 104, 16415, 1301, 11349])).
% 4.14/4.32 tff(16417,plain,
% 4.14/4.32 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[3444, 16416, 16398])).
% 4.14/4.32 tff(16418,plain,
% 4.14/4.32 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[2956, 118, 16400, 16417])).
% 4.14/4.32 tff(16419,plain,
% 4.14/4.32 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[3578, 16418])).
% 4.14/4.32 tff(16420,plain,
% 4.14/4.32 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[4057, 16419, 3461, 166, 273])).
% 4.14/4.32 tff(16421,plain,
% 4.14/4.32 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[133, 16420])).
% 4.14/4.32 tff(16422,plain,
% 4.14/4.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 4.14/4.32 inference(rewrite,[status(thm)],[])).
% 4.14/4.32 tff(16423,plain,
% 4.14/4.32 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 4.14/4.32 inference(rewrite,[status(thm)],[])).
% 4.14/4.32 tff(16424,plain,
% 4.14/4.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))))),
% 4.14/4.32 inference(monotonicity,[status(thm)],[16423])).
% 4.14/4.32 tff(16425,plain,
% 4.14/4.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 4.14/4.32 inference(transitivity,[status(thm)],[16424, 16422])).
% 4.14/4.32 tff(16426,plain,
% 4.14/4.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 4.14/4.32 inference(quant_inst,[status(thm)],[])).
% 4.14/4.32 tff(16427,plain,
% 4.14/4.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))),
% 4.14/4.32 inference(modus_ponens,[status(thm)],[16426, 16425])).
% 4.14/4.32 tff(16428,plain,
% 4.14/4.32 ($false),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[16427, 178, 818, 506, 3771, 168, 1301])).
% 4.14/4.32 tff(16429,plain,((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.32 tff(16430,plain,
% 4.14/4.32 (~b(s(s(s(s(z)))), z)),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[16429, 16415, 506, 818, 1301])).
% 4.14/4.32 tff(16431,plain,
% 4.14/4.32 (b(elem!1, s(s(s(elem!1))))),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[10659, 16430, 1, 16399, 16412])).
% 4.14/4.32 tff(16432,plain,
% 4.14/4.32 (~r(s(s(s(elem!1))), elem!1)),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[4283, 16415, 104, 4235, 12, 469, 16412, 16399, 818, 47, 193])).
% 4.14/4.32 tff(16433,plain,
% 4.14/4.32 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, elem!1)),
% 4.14/4.32 inference(monotonicity,[status(thm)],[1519])).
% 4.14/4.32 tff(16434,plain,
% 4.14/4.32 (b(elem!1, elem!1) <=> b(elem!1, s(s(s(elem!1))))),
% 4.14/4.32 inference(symmetry,[status(thm)],[16433])).
% 4.14/4.32 tff(16435,plain,
% 4.14/4.32 ((~b(elem!1, elem!1)) <=> (~b(elem!1, s(s(s(elem!1)))))),
% 4.14/4.32 inference(monotonicity,[status(thm)],[16434])).
% 4.14/4.32 tff(16436,plain,
% 4.14/4.32 (~b(elem!1, s(s(s(elem!1))))),
% 4.14/4.32 inference(modus_ponens,[status(thm)],[3220, 16435])).
% 4.14/4.32 tff(16437,plain,
% 4.14/4.32 ($false),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[2042, 16436])).
% 4.14/4.32 tff(16438,plain,((~(s(s(s(elem!1))) = elem!1)) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.32 tff(16439,plain,
% 4.14/4.32 (~(s(s(s(elem!1))) = elem!1)),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[16438, 16431])).
% 4.14/4.32 tff(16440,plain,
% 4.14/4.32 (b(s(s(s(elem!1))), elem!1)),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[570, 16439, 16432])).
% 4.14/4.32 tff(16441,plain,
% 4.14/4.32 (~b(z, s(s(s(elem!1))))),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[12925, 16440, 818, 506, 16431])).
% 4.14/4.32 tff(16442,plain,
% 4.14/4.32 (r(z, s(s(s(elem!1))))),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[2095, 16441])).
% 4.14/4.32 tff(16443,plain,
% 4.14/4.32 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[5130, 16442, 16421])).
% 4.14/4.32 tff(16444,plain,
% 4.14/4.32 (b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[5118, 16443, 4254])).
% 4.14/4.32 tff(16445,plain,
% 4.14/4.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), 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(s(s(s(s(z))))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), 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(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 4.14/4.32 inference(rewrite,[status(thm)],[])).
% 4.14/4.32 tff(16446,plain,
% 4.14/4.32 (((~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(s(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(elem!1))), 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))), 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(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 4.14/4.32 inference(rewrite,[status(thm)],[])).
% 4.14/4.32 tff(16447,plain,
% 4.14/4.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(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(elem!1))), s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), 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(s(s(s(s(z))))))), s(s(s(elem!1)))))))),
% 4.14/4.32 inference(monotonicity,[status(thm)],[16446])).
% 4.14/4.32 tff(16448,plain,
% 4.14/4.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(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(elem!1))), s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), 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(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 4.14/4.32 inference(transitivity,[status(thm)],[16447, 16445])).
% 4.14/4.32 tff(16449,plain,
% 4.14/4.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(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(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 4.14/4.32 inference(quant_inst,[status(thm)],[])).
% 4.14/4.32 tff(16450,plain,
% 4.14/4.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), 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(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 4.14/4.32 inference(modus_ponens,[status(thm)],[16449, 16448])).
% 4.14/4.32 tff(16451,plain,
% 4.14/4.32 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[16450, 178, 16440, 104, 16415, 16444])).
% 4.14/4.32 tff(16452,plain,
% 4.14/4.32 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[4173, 16451, 4171])).
% 4.14/4.32 tff(16453,plain,
% 4.14/4.32 (s(elem!1) = s(s(z))),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[2840, 16452])).
% 4.14/4.32 tff(16454,plain,
% 4.14/4.32 (~(elem!1 = s(s(s(s(elem!1)))))),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[1422, 16453])).
% 4.14/4.32 tff(16455,plain,
% 4.14/4.32 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[1509, 16454])).
% 4.14/4.32 tff(16456,plain,
% 4.14/4.32 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[1649, 16455])).
% 4.14/4.32 tff(16457,plain,
% 4.14/4.32 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[3404, 16456])).
% 4.14/4.32 tff(16458,plain,
% 4.14/4.32 (s(s(elem!1)) = s(s(s(z)))),
% 4.14/4.32 inference(monotonicity,[status(thm)],[16453])).
% 4.14/4.32 tff(16459,plain,
% 4.14/4.32 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 4.14/4.32 inference(monotonicity,[status(thm)],[16458])).
% 4.14/4.32 tff(16460,plain,
% 4.14/4.32 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 4.14/4.32 inference(monotonicity,[status(thm)],[16459])).
% 4.14/4.32 tff(16461,plain,
% 4.14/4.32 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 4.14/4.32 inference(symmetry,[status(thm)],[16460])).
% 4.14/4.32 tff(16462,plain,
% 4.14/4.32 (r(s(s(s(elem!1))), s(s(z)))),
% 4.14/4.32 inference(modus_ponens,[status(thm)],[193, 16461])).
% 4.14/4.32 tff(16463,plain,
% 4.14/4.32 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[6503, 16462, 16442, 3461, 2484, 273])).
% 4.14/4.32 tff(16464,plain,
% 4.14/4.32 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 4.14/4.32 inference(monotonicity,[status(thm)],[16458])).
% 4.14/4.32 tff(16465,plain,
% 4.14/4.32 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.14/4.32 inference(symmetry,[status(thm)],[16464])).
% 4.14/4.32 tff(16466,plain,
% 4.14/4.32 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 4.14/4.32 inference(symmetry,[status(thm)],[16459])).
% 4.14/4.32 tff(16467,plain,
% 4.14/4.32 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 4.14/4.32 inference(monotonicity,[status(thm)],[16466])).
% 4.14/4.32 tff(16468,plain,
% 4.14/4.32 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.14/4.32 inference(transitivity,[status(thm)],[16467, 16465])).
% 4.14/4.32 tff(16469,plain,
% 4.14/4.32 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.14/4.32 inference(modus_ponens,[status(thm)],[1126, 16468])).
% 4.14/4.32 tff(16470,plain,
% 4.14/4.32 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[15187, 16469, 104, 16415, 11349, 16431, 16453])).
% 4.14/4.32 tff(16471,plain,
% 4.14/4.32 ($false),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[3409, 16470, 16463, 16457])).
% 4.14/4.32 tff(16472,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (s(s(elem!1)) = s(s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | r(s(s(s(elem!1))), s(s(s(s(z))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))) | b(z, s(s(s(s(z))))) | b(z, s(s(s(s(s(s(s(z)))))))) | (s(s(z)) = elem!1) | (elem!1 = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.32 tff(16473,plain,
% 4.14/4.32 (~r(s(s(s(s(z)))), s(s(z)))),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[16472, 16402, 3461, 2484, 273, 16405, 16403, 818, 506, 166, 104, 1, 4235, 12, 469])).
% 4.14/4.32 tff(16474,plain,
% 4.14/4.32 (b(s(s(s(s(z)))), s(s(z)))),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[102, 16473])).
% 4.14/4.32 tff(16475,plain,
% 4.14/4.32 (~r(s(s(s(s(z)))), elem!1)),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[9471, 16474, 104, 1265, 16400, 11349])).
% 4.14/4.32 tff(16476,plain,
% 4.14/4.32 (b(s(s(s(s(z)))), elem!1)),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[3142, 16475, 551])).
% 4.14/4.32 tff(16477,plain,
% 4.14/4.32 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[3928, 178, 104, 16476, 16402, 11349])).
% 4.14/4.32 tff(16478,plain,
% 4.14/4.32 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[3444, 16477, 16398])).
% 4.14/4.32 tff(16479,plain,
% 4.14/4.32 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[2956, 118, 16400, 16478])).
% 4.14/4.32 tff(16480,plain,
% 4.14/4.32 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[3578, 16479])).
% 4.14/4.32 tff(16481,plain,
% 4.14/4.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), 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(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), 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(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 4.14/4.32 inference(rewrite,[status(thm)],[])).
% 4.14/4.32 tff(16482,plain,
% 4.14/4.32 (((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(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))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), 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(s(z)))))) | (~b(s(s(z)), 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(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 4.14/4.32 inference(rewrite,[status(thm)],[])).
% 4.14/4.32 tff(16483,plain,
% 4.14/4.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(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))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), 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(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 4.14/4.32 inference(monotonicity,[status(thm)],[16482])).
% 4.14/4.32 tff(16484,plain,
% 4.14/4.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(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))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), 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(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 4.14/4.32 inference(transitivity,[status(thm)],[16483, 16481])).
% 4.14/4.32 tff(16485,plain,
% 4.14/4.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(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))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 4.14/4.32 inference(quant_inst,[status(thm)],[])).
% 4.14/4.32 tff(16486,plain,
% 4.14/4.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 4.14/4.32 inference(modus_ponens,[status(thm)],[16485, 16484])).
% 4.14/4.32 tff(16487,plain,
% 4.14/4.32 ($false),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[16486, 178, 104, 166, 11349, 16474, 16480])).
% 4.14/4.32 tff(16488,plain,((s(s(z)) = elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (s(s(elem!1)) = s(s(z))) | (~b(z, s(s(z)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | b(z, s(s(s(s(z))))) | b(z, s(s(s(s(s(s(s(z)))))))) | (elem!1 = s(s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.32 tff(16489,plain,
% 4.14/4.32 (s(s(z)) = elem!1),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[16488, 16393, 166, 104, 10793, 3340, 144, 16397, 16395, 1, 4235, 469, 147])).
% 4.14/4.32 tff(16490,plain,
% 4.14/4.32 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.14/4.32 inference(monotonicity,[status(thm)],[16489])).
% 4.14/4.32 tff(16491,plain,
% 4.14/4.32 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.14/4.32 inference(symmetry,[status(thm)],[16490])).
% 4.14/4.32 tff(16492,plain,
% 4.14/4.32 ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) <=> (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 4.14/4.32 inference(monotonicity,[status(thm)],[16491])).
% 4.14/4.32 tff(16493,plain,
% 4.14/4.32 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[11707, 16489, 104, 11613, 4254, 47, 4236, 144, 16397, 147, 10792])).
% 4.14/4.32 tff(16494,plain,
% 4.14/4.32 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.14/4.32 inference(modus_ponens,[status(thm)],[16493, 16492])).
% 4.14/4.32 tff(16495,plain,
% 4.14/4.32 ($false),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[166, 16494])).
% 4.14/4.32 tff(16496,plain,((elem!1 = s(s(s(s(z))))) | (~b(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)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | b(z, s(s(s(s(z))))) | b(z, s(s(s(s(s(s(s(z)))))))) | (elem!1 = z) | r(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.32 tff(16497,plain,
% 4.14/4.32 (elem!1 = s(s(s(s(z))))),
% 4.14/4.32 inference(unit_resolution,[status(thm)],[16496, 11612, 104, 10794, 1, 4235, 290, 48])).
% 4.14/4.32 tff(16498,plain,
% 4.14/4.32 (s(elem!1) = s(s(s(s(s(z)))))),
% 4.14/4.32 inference(monotonicity,[status(thm)],[16497])).
% 4.14/4.32 tff(16499,plain,
% 4.14/4.32 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 4.14/4.32 inference(monotonicity,[status(thm)],[16498])).
% 4.14/4.32 tff(16500,plain,
% 4.14/4.32 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 4.14/4.32 inference(symmetry,[status(thm)],[16499])).
% 4.14/4.32 tff(16501,plain,
% 4.14/4.32 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 4.14/4.32 inference(monotonicity,[status(thm)],[16499])).
% 4.14/4.32 tff(16502,plain,
% 4.14/4.32 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 4.14/4.32 inference(symmetry,[status(thm)],[16501])).
% 4.14/4.32 tff(16503,plain,
% 4.14/4.32 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 4.14/4.32 inference(monotonicity,[status(thm)],[16502, 16500])).
% 4.14/4.32 tff(16504,plain,
% 4.14/4.32 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 4.14/4.32 inference(symmetry,[status(thm)],[16503])).
% 4.14/4.32 tff(16505,plain,
% 4.14/4.32 (s(s(s(s(z)))) = elem!1),
% 4.14/4.32 inference(symmetry,[status(thm)],[16497])).
% 4.14/4.32 tff(16506,plain,
% 4.14/4.32 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(elem!1)) = elem!1)),
% 4.14/4.32 inference(monotonicity,[status(thm)],[16505])).
% 4.14/4.32 tff(16507,plain,
% 4.14/4.32 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 4.14/4.32 inference(commutativity,[status(thm)],[])).
% 4.14/4.32 tff(16508,plain,
% 4.14/4.32 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 4.14/4.32 inference(monotonicity,[status(thm)],[16500])).
% 4.14/4.32 tff(16509,plain,
% 4.14/4.32 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 4.14/4.32 inference(transitivity,[status(thm)],[16508, 16507])).
% 4.14/4.32 tff(16510,plain,
% 4.14/4.32 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(s(elem!1)) = elem!1)),
% 4.14/4.32 inference(transitivity,[status(thm)],[16509, 16506])).
% 4.14/4.32 tff(16511,plain,
% 4.14/4.32 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(elem!1)) = elem!1))),
% 4.14/4.32 inference(monotonicity,[status(thm)],[16510])).
% 4.14/4.33 tff(16512,plain,
% 4.14/4.33 (~(s(s(elem!1)) = elem!1)),
% 4.14/4.33 inference(modus_ponens,[status(thm)],[3698, 16511])).
% 4.14/4.33 tff(16513,plain,
% 4.14/4.33 (~(s(elem!1) = s(s(elem!1)))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[979, 16512])).
% 4.14/4.33 tff(16514,plain,
% 4.14/4.33 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[3356, 16513])).
% 4.14/4.33 tff(16515,plain,
% 4.14/4.33 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[3404, 16514])).
% 4.14/4.33 tff(16516,plain,
% 4.14/4.33 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 4.14/4.33 inference(monotonicity,[status(thm)],[16499, 16497])).
% 4.14/4.33 tff(16517,plain,
% 4.14/4.33 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> r(s(s(elem!1)), elem!1)),
% 4.14/4.33 inference(symmetry,[status(thm)],[16516])).
% 4.14/4.33 tff(16518,plain,
% 4.14/4.33 ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) <=> (~r(s(s(elem!1)), elem!1))),
% 4.14/4.33 inference(monotonicity,[status(thm)],[16517])).
% 4.14/4.33 tff(16519,plain,
% 4.14/4.33 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[11534, 16497, 47, 10794, 10793, 144])).
% 4.14/4.33 tff(16520,plain,
% 4.14/4.33 (~r(s(s(elem!1)), elem!1)),
% 4.14/4.33 inference(modus_ponens,[status(thm)],[16519, 16518])).
% 4.14/4.33 tff(16521,plain,
% 4.14/4.33 (b(s(s(elem!1)), elem!1)),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[3362, 16520, 16512])).
% 4.14/4.33 tff(16522,plain,
% 4.14/4.33 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.14/4.33 inference(monotonicity,[status(thm)],[16497])).
% 4.14/4.33 tff(16523,plain,
% 4.14/4.33 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), elem!1)),
% 4.14/4.33 inference(symmetry,[status(thm)],[16522])).
% 4.14/4.33 tff(16524,plain,
% 4.14/4.33 (~(s(elem!1) = s(s(z)))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[11438, 16497])).
% 4.14/4.33 tff(16525,plain,
% 4.14/4.33 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[2840, 16524])).
% 4.14/4.33 tff(16526,plain,
% 4.14/4.33 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[4173, 16525, 10800])).
% 4.14/4.33 tff(16527,plain,
% 4.14/4.33 (b(s(s(s(elem!1))), elem!1)),
% 4.14/4.33 inference(modus_ponens,[status(thm)],[16526, 16523])).
% 4.14/4.33 tff(16528,plain,
% 4.14/4.33 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.14/4.33 inference(monotonicity,[status(thm)],[16497])).
% 4.14/4.33 tff(16529,plain,
% 4.14/4.33 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 4.14/4.33 inference(symmetry,[status(thm)],[16528])).
% 4.14/4.33 tff(16530,plain,
% 4.14/4.33 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.14/4.33 inference(monotonicity,[status(thm)],[16501])).
% 4.14/4.33 tff(16531,plain,
% 4.14/4.33 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.14/4.33 inference(symmetry,[status(thm)],[16530])).
% 4.14/4.33 tff(16532,plain,
% 4.14/4.33 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(elem!1))))),
% 4.14/4.33 inference(transitivity,[status(thm)],[16531, 16529])).
% 4.14/4.33 tff(16533,plain,
% 4.14/4.33 (b(elem!1, s(s(s(elem!1))))),
% 4.14/4.33 inference(modus_ponens,[status(thm)],[11349, 16532])).
% 4.14/4.33 tff(16534,plain,
% 4.14/4.33 (~b(z, s(s(s(elem!1))))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[11477, 16497, 4235])).
% 4.14/4.33 tff(16535,plain,
% 4.14/4.33 (r(z, s(s(s(elem!1))))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[2095, 16534])).
% 4.14/4.33 tff(16536,plain,
% 4.14/4.33 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.14/4.33 inference(monotonicity,[status(thm)],[16497])).
% 4.14/4.33 tff(16537,plain,
% 4.14/4.33 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.14/4.33 inference(symmetry,[status(thm)],[16536])).
% 4.14/4.33 tff(16538,plain,
% 4.14/4.33 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.14/4.33 inference(modus_ponens,[status(thm)],[11349, 16537])).
% 4.14/4.33 tff(16539,plain,
% 4.14/4.33 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[348, 16512])).
% 4.14/4.33 tff(16540,plain,
% 4.14/4.33 (~b(z, elem!1)),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[1846, 16497, 1])).
% 4.14/4.33 tff(16541,plain,
% 4.14/4.33 (r(z, elem!1)),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[585, 16540, 318])).
% 4.14/4.33 tff(16542,plain,
% 4.14/4.33 (~r(s(elem!1), elem!1)),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[11444, 16541, 144, 10794, 10793, 16497])).
% 4.14/4.33 tff(16543,plain,
% 4.14/4.33 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.14/4.33 inference(monotonicity,[status(thm)],[16497])).
% 4.14/4.33 tff(16544,plain,
% 4.14/4.33 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = elem!1)),
% 4.14/4.33 inference(symmetry,[status(thm)],[16543])).
% 4.14/4.33 tff(16545,plain,
% 4.14/4.33 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 4.14/4.33 inference(monotonicity,[status(thm)],[16544])).
% 4.14/4.33 tff(16546,plain,
% 4.14/4.33 (~(s(s(s(elem!1))) = elem!1)),
% 4.14/4.33 inference(modus_ponens,[status(thm)],[16525, 16545])).
% 4.14/4.33 tff(16547,plain,
% 4.14/4.33 (~(s(elem!1) = elem!1)),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[2150, 16546])).
% 4.14/4.33 tff(16548,plain,
% 4.14/4.33 (b(s(elem!1), elem!1)),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[677, 16547, 16542])).
% 4.14/4.33 tff(16549,plain,
% 4.14/4.33 (~b(elem!1, s(elem!1))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[11607, 16548, 16527, 16539, 16533, 16521, 16513, 16535])).
% 4.14/4.33 tff(16550,plain,
% 4.14/4.33 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[871, 16549, 16538])).
% 4.14/4.33 tff(16551,plain,
% 4.14/4.33 (~(s(s(z)) = s(elem!1))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[1058, 16524])).
% 4.14/4.33 tff(16552,plain,
% 4.14/4.33 (~(elem!1 = s(elem!1))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[748, 16547])).
% 4.14/4.33 tff(16553,plain,
% 4.14/4.33 (r(elem!1, s(elem!1))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[756, 16549, 16552])).
% 4.14/4.33 tff(16554,plain,
% 4.14/4.33 (~r(s(s(z)), s(elem!1))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[12646, 16553, 10794, 16497])).
% 4.14/4.33 tff(16555,plain,
% 4.14/4.33 (b(s(s(z)), s(elem!1))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[1067, 16554, 16551])).
% 4.14/4.33 tff(16556,plain,
% 4.14/4.33 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(s(z)))))),
% 4.14/4.33 inference(monotonicity,[status(thm)],[16497])).
% 4.14/4.33 tff(16557,plain,
% 4.14/4.33 (b(s(elem!1), s(s(s(s(z)))))),
% 4.14/4.33 inference(modus_ponens,[status(thm)],[16548, 16556])).
% 4.14/4.33 tff(16558,plain,
% 4.14/4.33 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[2529, 16557, 104, 11612, 16555])).
% 4.14/4.33 tff(16559,plain,
% 4.14/4.33 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[395, 16558, 16550])).
% 4.14/4.33 tff(16560,plain,
% 4.14/4.33 (r(s(elem!1), s(s(s(elem!1))))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[14608, 16559, 16497])).
% 4.14/4.33 tff(16561,plain,
% 4.14/4.33 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[11597, 16560, 16535, 16513])).
% 4.14/4.33 tff(16562,plain,
% 4.14/4.33 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[3375, 16561, 16514])).
% 4.14/4.33 tff(16563,plain,
% 4.14/4.33 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[5500, 16562, 16533, 16527, 16521])).
% 4.14/4.33 tff(16564,plain,
% 4.14/4.33 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[3409, 16563, 16515])).
% 4.14/4.33 tff(16565,plain,
% 4.14/4.33 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 4.14/4.33 inference(modus_ponens,[status(thm)],[16564, 16504])).
% 4.14/4.33 tff(16566,plain,
% 4.14/4.33 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 4.14/4.33 inference(monotonicity,[status(thm)],[16498])).
% 4.14/4.33 tff(16567,plain,
% 4.14/4.33 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 4.14/4.33 inference(modus_ponens,[status(thm)],[16559, 16566])).
% 4.14/4.33 tff(16568,plain,
% 4.14/4.33 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 4.14/4.33 inference(monotonicity,[status(thm)],[16498, 16499])).
% 4.14/4.33 tff(16569,plain,
% 4.14/4.33 (~b(s(elem!1), s(s(elem!1)))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[5490, 16562, 16533, 16521, 16548])).
% 4.14/4.33 tff(16570,plain,
% 4.14/4.33 (r(s(elem!1), s(s(elem!1)))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[1028, 16569, 16513])).
% 4.14/4.33 tff(16571,plain,
% 4.14/4.33 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 4.14/4.33 inference(modus_ponens,[status(thm)],[16570, 16568])).
% 4.14/4.33 tff(16572,plain,
% 4.14/4.33 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 4.14/4.33 inference(rewrite,[status(thm)],[])).
% 4.14/4.33 tff(16573,plain,
% 4.14/4.33 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 4.14/4.33 inference(rewrite,[status(thm)],[])).
% 4.14/4.33 tff(16574,plain,
% 4.14/4.33 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))))),
% 4.14/4.33 inference(monotonicity,[status(thm)],[16573])).
% 4.14/4.33 tff(16575,plain,
% 4.14/4.33 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 4.14/4.33 inference(transitivity,[status(thm)],[16574, 16572])).
% 4.14/4.33 tff(16576,plain,
% 4.14/4.33 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 4.14/4.33 inference(quant_inst,[status(thm)],[])).
% 4.14/4.33 tff(16577,plain,
% 4.14/4.33 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 4.14/4.33 inference(modus_ponens,[status(thm)],[16576, 16575])).
% 4.14/4.33 tff(16578,plain,
% 4.14/4.33 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[16577, 118, 16571, 16567])).
% 4.14/4.33 tff(16579,plain,
% 4.14/4.33 ($false),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[16578, 16565])).
% 4.14/4.33 tff(16580,plain,(b(s(s(z)), s(s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | b(z, s(s(s(s(s(s(s(z)))))))) | b(z, s(s(s(s(z))))) | (elem!1 = z) | r(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.33 tff(16581,plain,
% 4.14/4.33 (b(s(s(z)), s(s(s(s(z)))))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[16580, 4235, 104, 1, 290, 48])).
% 4.14/4.33 tff(16582,plain,
% 4.14/4.33 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[7917, 10484])).
% 4.14/4.33 tff(16583,plain,
% 4.14/4.33 (~b(z, elem!1)),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[4243, 679, 4235])).
% 4.14/4.33 tff(16584,plain,
% 4.14/4.33 (r(z, elem!1)),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[585, 16583, 318])).
% 4.14/4.33 tff(16585,plain,
% 4.14/4.33 (~b(s(s(z)), elem!1)),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[10835, 679, 286])).
% 4.14/4.33 tff(16586,plain,
% 4.14/4.33 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[3818, 16584, 4236])).
% 4.14/4.33 tff(16587,plain,
% 4.14/4.33 (~(s(s(z)) = elem!1)),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[11305, 16586, 287])).
% 4.14/4.33 tff(16588,plain,
% 4.14/4.33 (r(s(s(z)), elem!1)),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[448, 16587, 16585])).
% 4.14/4.33 tff(16589,plain,
% 4.14/4.33 (~r(s(s(s(elem!1))), elem!1)),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[6388, 16588, 16584, 5619, 273])).
% 4.14/4.33 tff(16590,plain,
% 4.14/4.33 (b(s(s(s(elem!1))), elem!1)),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[570, 16589, 10489])).
% 4.14/4.33 tff(16591,plain,
% 4.14/4.33 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[10584, 16590, 679])).
% 4.14/4.33 tff(16592,plain,
% 4.14/4.33 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.14/4.33 inference(monotonicity,[status(thm)],[679])).
% 4.14/4.33 tff(16593,plain,
% 4.14/4.33 ((elem!1 = s(s(s(z)))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(z))))),
% 4.14/4.33 inference(monotonicity,[status(thm)],[679])).
% 4.14/4.33 tff(16594,plain,
% 4.14/4.33 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 4.14/4.33 inference(symmetry,[status(thm)],[16593])).
% 4.14/4.33 tff(16595,plain,
% 4.14/4.33 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 4.14/4.33 inference(transitivity,[status(thm)],[16594, 10421])).
% 4.14/4.33 tff(16596,plain,
% 4.14/4.33 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(s(s(s(z))) = elem!1))),
% 4.14/4.33 inference(monotonicity,[status(thm)],[16595])).
% 4.14/4.33 tff(16597,plain,
% 4.14/4.33 (~(s(s(s(z))) = elem!1)),
% 4.14/4.33 inference(modus_ponens,[status(thm)],[1104, 16596])).
% 4.14/4.33 tff(16598,plain,
% 4.14/4.33 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.14/4.33 inference(monotonicity,[status(thm)],[679])).
% 4.14/4.33 tff(16599,plain,
% 4.14/4.33 (r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(z))), elem!1)),
% 4.14/4.33 inference(symmetry,[status(thm)],[16598])).
% 4.14/4.33 tff(16600,plain,
% 4.14/4.33 ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) <=> (~r(s(s(s(z))), elem!1))),
% 4.14/4.33 inference(monotonicity,[status(thm)],[16599])).
% 4.14/4.33 tff(16601,plain,
% 4.14/4.33 (~r(s(s(s(z))), elem!1)),
% 4.14/4.33 inference(modus_ponens,[status(thm)],[11415, 16600])).
% 4.14/4.33 tff(16602,plain,
% 4.14/4.33 (b(s(s(s(z))), elem!1)),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[4981, 16601, 16597])).
% 4.14/4.33 tff(16603,plain,
% 4.14/4.33 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.14/4.33 inference(modus_ponens,[status(thm)],[16602, 16592])).
% 4.14/4.33 tff(16604,plain,
% 4.14/4.33 ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[8227, 178, 104, 251, 3002])).
% 4.14/4.33 tff(16605,plain,
% 4.14/4.33 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[16604, 1126])).
% 4.14/4.33 tff(16606,plain,
% 4.14/4.33 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 16605])).
% 4.14/4.33 tff(16607,plain,
% 4.14/4.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))))),
% 4.14/4.33 inference(rewrite,[status(thm)],[])).
% 4.14/4.33 tff(16608,plain,
% 4.14/4.33 (((~b(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))))))))) | (~b(s(s(s(z))), s(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(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(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(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))))),
% 4.14/4.33 inference(rewrite,[status(thm)],[])).
% 4.14/4.33 tff(16609,plain,
% 4.14/4.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(s(z))), s(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(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 4.14/4.33 inference(monotonicity,[status(thm)],[16608])).
% 4.14/4.33 tff(16610,plain,
% 4.14/4.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(s(z))), s(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(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))))),
% 4.14/4.33 inference(transitivity,[status(thm)],[16609, 16607])).
% 4.14/4.33 tff(16611,plain,
% 4.14/4.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(s(z))), s(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(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 4.14/4.33 inference(quant_inst,[status(thm)],[])).
% 4.14/4.33 tff(16612,plain,
% 4.14/4.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z)))))),
% 4.14/4.33 inference(modus_ponens,[status(thm)],[16611, 16610])).
% 4.14/4.33 tff(16613,plain,
% 4.14/4.33 ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[16612, 178, 167, 251, 3002])).
% 4.14/4.33 tff(16614,plain,
% 4.14/4.33 (~b(s(s(z)), s(s(s(z))))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[16613, 1126])).
% 4.14/4.33 tff(16615,plain,
% 4.14/4.33 (r(s(s(z)), s(s(s(z))))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[5088, 16614])).
% 4.14/4.33 tff(16616,plain,
% 4.14/4.33 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 4.14/4.33 inference(rewrite,[status(thm)],[])).
% 4.14/4.33 tff(16617,plain,
% 4.14/4.33 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 4.14/4.33 inference(rewrite,[status(thm)],[])).
% 4.14/4.33 tff(16618,plain,
% 4.14/4.33 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))))),
% 4.14/4.33 inference(monotonicity,[status(thm)],[16617])).
% 4.14/4.33 tff(16619,plain,
% 4.14/4.33 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 4.14/4.33 inference(transitivity,[status(thm)],[16618, 16616])).
% 4.14/4.33 tff(16620,plain,
% 4.14/4.33 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 4.14/4.33 inference(quant_inst,[status(thm)],[])).
% 4.14/4.33 tff(16621,plain,
% 4.14/4.33 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 4.14/4.33 inference(modus_ponens,[status(thm)],[16620, 16619])).
% 4.14/4.33 tff(16622,plain,
% 4.14/4.33 ($false),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[16621, 118, 224, 16615, 16606])).
% 4.14/4.33 tff(16623,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(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(s(z))))))))) | (~b(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))))))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.33 tff(16624,plain,
% 4.14/4.33 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[16623, 16603, 167, 11349, 287, 104])).
% 4.14/4.33 tff(16625,plain,
% 4.14/4.33 (r(s(s(s(z))), s(s(s(s(z)))))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[10755, 16624])).
% 4.14/4.33 tff(16626,plain,
% 4.14/4.33 (~b(z, s(s(s(elem!1))))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[8252, 3251, 145, 8246, 4891])).
% 4.14/4.33 tff(16627,plain,
% 4.14/4.33 ($false),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[2095, 16626, 8021])).
% 4.14/4.33 tff(16628,plain,((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.33 tff(16629,plain,
% 4.14/4.33 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[16628, 16625, 11613, 47])).
% 4.14/4.33 tff(16630,plain,
% 4.14/4.33 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[4173, 16629, 10484])).
% 4.14/4.33 tff(16631,plain,
% 4.14/4.33 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[4103, 16630, 104, 11349, 16591])).
% 4.14/4.33 tff(16632,plain,
% 4.14/4.33 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[10664, 16631, 16582])).
% 4.14/4.33 tff(16633,plain,
% 4.14/4.33 (~r(elem!1, s(s(s(s(z)))))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[529, 16584, 47])).
% 4.14/4.33 tff(16634,plain,
% 4.14/4.33 ((s(s(s(s(z)))) = elem!1) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))),
% 4.14/4.33 inference(monotonicity,[status(thm)],[679])).
% 4.14/4.33 tff(16635,plain,
% 4.14/4.33 ((s(s(s(s(z)))) = elem!1) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(z)))))),
% 4.14/4.33 inference(transitivity,[status(thm)],[16634, 214])).
% 4.14/4.33 tff(16636,plain,
% 4.14/4.33 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 4.14/4.33 inference(symmetry,[status(thm)],[16635])).
% 4.14/4.33 tff(16637,plain,
% 4.14/4.33 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(z)))))),
% 4.14/4.33 inference(transitivity,[status(thm)],[16636, 501])).
% 4.14/4.33 tff(16638,plain,
% 4.14/4.33 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(s(s(z))))))),
% 4.14/4.33 inference(monotonicity,[status(thm)],[16637])).
% 4.14/4.33 tff(16639,plain,
% 4.14/4.33 (~(elem!1 = s(s(s(s(z)))))),
% 4.14/4.33 inference(modus_ponens,[status(thm)],[79, 16638])).
% 4.14/4.33 tff(16640,plain,
% 4.14/4.33 (~r(s(s(s(s(z)))), s(s(z)))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[11089, 16629, 287, 104, 47, 290, 5619, 273, 16588, 16639, 4235, 16633])).
% 4.14/4.33 tff(16641,plain,
% 4.14/4.33 (b(s(s(s(s(z)))), s(s(z)))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[102, 16640])).
% 4.14/4.33 tff(16642,plain,
% 4.14/4.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 4.14/4.33 inference(rewrite,[status(thm)],[])).
% 4.14/4.33 tff(16643,plain,
% 4.14/4.33 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 4.14/4.33 inference(rewrite,[status(thm)],[])).
% 4.14/4.33 tff(16644,plain,
% 4.14/4.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 4.14/4.33 inference(monotonicity,[status(thm)],[16643])).
% 4.14/4.33 tff(16645,plain,
% 4.14/4.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 4.14/4.33 inference(transitivity,[status(thm)],[16644, 16642])).
% 4.14/4.33 tff(16646,plain,
% 4.14/4.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 4.14/4.33 inference(quant_inst,[status(thm)],[])).
% 4.14/4.33 tff(16647,plain,
% 4.14/4.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)) | (~b(s(s(s(s(z)))), s(s(z))))),
% 4.14/4.33 inference(modus_ponens,[status(thm)],[16646, 16645])).
% 4.14/4.33 tff(16648,plain,
% 4.14/4.33 (~b(s(s(s(s(z)))), z)),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[16647, 178, 5619, 273, 167, 16641])).
% 4.14/4.33 tff(16649,plain,
% 4.14/4.33 (r(s(s(s(s(z)))), z)),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[191, 16648])).
% 4.14/4.33 tff(16650,plain,
% 4.14/4.33 (~r(z, s(s(s(elem!1))))),
% 4.14/4.33 inference(unit_resolution,[status(thm)],[3287, 16649, 16632])).
% 4.14/4.34 tff(16651,plain,
% 4.14/4.34 (b(z, s(s(s(elem!1))))),
% 4.14/4.34 inference(unit_resolution,[status(thm)],[2095, 16650])).
% 4.14/4.34 tff(16652,plain,
% 4.14/4.34 (b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 4.14/4.34 inference(modus_ponens,[status(thm)],[16651, 10540])).
% 4.14/4.34 tff(16653,plain,
% 4.14/4.34 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z))))))))))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.14/4.34 inference(monotonicity,[status(thm)],[4345])).
% 4.14/4.34 tff(16654,plain,
% 4.14/4.34 (b(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(s(s(s(s(s(s(s(z)))))))))))),
% 4.14/4.34 inference(symmetry,[status(thm)],[16653])).
% 4.14/4.34 tff(16655,plain,
% 4.14/4.34 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.14/4.34 inference(monotonicity,[status(thm)],[679])).
% 4.14/4.34 tff(16656,plain,
% 4.14/4.34 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 4.14/4.34 inference(transitivity,[status(thm)],[16655, 16654])).
% 4.14/4.34 tff(16657,plain,
% 4.14/4.34 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.14/4.34 inference(monotonicity,[status(thm)],[679])).
% 4.14/4.34 tff(16658,plain,
% 4.14/4.34 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(z)))), elem!1)),
% 4.14/4.34 inference(symmetry,[status(thm)],[16657])).
% 4.14/4.34 tff(16659,plain,
% 4.14/4.34 (b(s(s(s(s(z)))), elem!1)),
% 4.14/4.34 inference(modus_ponens,[status(thm)],[11349, 16658])).
% 4.14/4.34 tff(16660,plain,
% 4.14/4.34 (b(elem!1, s(s(s(s(z)))))),
% 4.14/4.34 inference(modus_ponens,[status(thm)],[104, 3430])).
% 4.14/4.34 tff(16661,plain,
% 4.14/4.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, 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(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, 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(s(s(z)))), s(s(z)))))),
% 4.14/4.34 inference(rewrite,[status(thm)],[])).
% 4.14/4.34 tff(16662,plain,
% 4.14/4.34 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, 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(s(s(z)))), s(s(z)))))),
% 4.14/4.34 inference(rewrite,[status(thm)],[])).
% 4.14/4.34 tff(16663,plain,
% 4.14/4.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, 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(s(s(z)))), s(s(z))))))),
% 4.14/4.34 inference(monotonicity,[status(thm)],[16662])).
% 4.14/4.34 tff(16664,plain,
% 4.14/4.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, 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(s(s(z)))), s(s(z)))))),
% 4.14/4.34 inference(transitivity,[status(thm)],[16663, 16661])).
% 4.14/4.34 tff(16665,plain,
% 4.14/4.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 4.14/4.34 inference(quant_inst,[status(thm)],[])).
% 4.14/4.34 tff(16666,plain,
% 4.14/4.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, 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(s(s(z)))), s(s(z))))),
% 4.14/4.34 inference(modus_ponens,[status(thm)],[16665, 16664])).
% 4.14/4.34 tff(16667,plain,
% 4.14/4.34 ((~b(elem!1, 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(s(s(z)))), s(s(z))))),
% 4.14/4.34 inference(unit_resolution,[status(thm)],[16666, 178])).
% 4.14/4.34 tff(16668,plain,
% 4.14/4.34 (~b(elem!1, s(s(z)))),
% 4.14/4.34 inference(unit_resolution,[status(thm)],[16667, 16641, 167, 16660, 16659])).
% 4.14/4.34 tff(16669,plain,
% 4.14/4.34 (b(elem!1, s(s(s(elem!1))))),
% 4.14/4.34 inference(unit_resolution,[status(thm)],[10659, 16648, 1, 16585, 16668])).
% 4.14/4.34 tff(16670,plain,
% 4.14/4.34 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 4.14/4.34 inference(modus_ponens,[status(thm)],[16669, 16656])).
% 4.14/4.34 tff(16671,plain,
% 4.14/4.34 (~r(s(s(s(z))), z)),
% 4.14/4.34 inference(unit_resolution,[status(thm)],[4899, 118, 47, 16625])).
% 4.14/4.34 tff(16672,plain,
% 4.14/4.34 (b(s(s(s(z))), z)),
% 4.14/4.34 inference(unit_resolution,[status(thm)],[4903, 41, 77, 16671])).
% 4.14/4.34 tff(16673,plain,
% 4.14/4.34 (b(elem!1, z)),
% 4.14/4.34 inference(unit_resolution,[status(thm)],[10874, 16649, 273, 286, 4235, 16639, 16629, 104, 47, 290, 5618])).
% 4.14/4.34 tff(16674,plain,
% 4.14/4.34 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.14/4.34 inference(modus_ponens,[status(thm)],[16673, 4356])).
% 4.14/4.34 tff(16675,plain,
% 4.14/4.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 4.14/4.34 inference(rewrite,[status(thm)],[])).
% 4.14/4.34 tff(16676,plain,
% 4.14/4.34 (((~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 4.14/4.34 inference(rewrite,[status(thm)],[])).
% 4.14/4.34 tff(16677,plain,
% 4.14/4.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z))))))))))))))),
% 4.14/4.34 inference(monotonicity,[status(thm)],[16676])).
% 4.14/4.34 tff(16678,plain,
% 4.14/4.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 4.14/4.34 inference(transitivity,[status(thm)],[16677, 16675])).
% 4.14/4.34 tff(16679,plain,
% 4.14/4.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.14/4.34 inference(quant_inst,[status(thm)],[])).
% 4.14/4.34 tff(16680,plain,
% 4.14/4.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z))))))))))))),
% 4.14/4.34 inference(modus_ponens,[status(thm)],[16679, 16678])).
% 4.14/4.34 tff(16681,plain,
% 4.14/4.34 ($false),
% 4.14/4.34 inference(unit_resolution,[status(thm)],[16680, 178, 16674, 16672, 16603, 16670, 16652])).
% 4.14/4.34 tff(16682,plain,((~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | b(z, s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (elem!1 = z) | r(s(s(z)), z) | b(z, s(s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.34 tff(16683,plain,
% 4.14/4.34 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 4.14/4.34 inference(unit_resolution,[status(thm)],[16682, 286, 273, 4235, 104, 290, 5618, 1, 167])).
% 4.14/4.34 tff(16684,assumption,(~r(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 4.14/4.34 tff(16685,plain,
% 4.14/4.34 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.14/4.34 inference(unit_resolution,[status(thm)],[212, 203, 47])).
% 4.14/4.34 tff(16686,plain,
% 4.14/4.34 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.14/4.34 inference(unit_resolution,[status(thm)],[222, 16685])).
% 4.14/4.34 tff(16687,plain,
% 4.14/4.34 (~(s(s(s(s(z)))) = elem!1)),
% 4.14/4.34 inference(unit_resolution,[status(thm)],[504, 3179])).
% 4.14/4.34 tff(16688,plain,
% 4.14/4.34 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.14/4.34 inference(unit_resolution,[status(thm)],[691, 644, 701])).
% 4.14/4.34 tff(16689,plain,
% 4.14/4.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.14/4.34 inference(rewrite,[status(thm)],[])).
% 4.14/4.34 tff(16690,plain,
% 4.14/4.34 (((~b(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))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~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(z)), elem!1))) <=> ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.14/4.34 inference(rewrite,[status(thm)],[])).
% 4.14/4.34 tff(16691,plain,
% 4.14/4.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~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(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 4.14/4.34 inference(monotonicity,[status(thm)],[16690])).
% 4.14/4.34 tff(16692,plain,
% 4.14/4.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~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(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.14/4.34 inference(transitivity,[status(thm)],[16691, 16689])).
% 4.14/4.34 tff(16693,plain,
% 4.14/4.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~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(z)), elem!1)))),
% 4.14/4.34 inference(quant_inst,[status(thm)],[])).
% 4.14/4.34 tff(16694,plain,
% 4.14/4.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 4.14/4.34 inference(modus_ponens,[status(thm)],[16693, 16692])).
% 4.14/4.34 tff(16695,plain,
% 4.14/4.34 ($false),
% 4.14/4.34 inference(unit_resolution,[status(thm)],[16694, 178, 817, 869, 1301, 167, 251])).
% 4.14/4.34 tff(16696,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.34 tff(16697,plain,
% 4.14/4.34 (~b(s(s(z)), elem!1)),
% 4.14/4.34 inference(unit_resolution,[status(thm)],[16696, 1301, 251, 167, 16688])).
% 4.14/4.34 tff(16698,plain,
% 4.14/4.34 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.14/4.34 inference(unit_resolution,[status(thm)],[11098, 1301, 251, 644, 104, 701])).
% 4.14/4.34 tff(16699,plain,
% 4.14/4.34 (~r(s(s(z)), elem!1)),
% 4.14/4.34 inference(unit_resolution,[status(thm)],[11351, 16698, 224])).
% 4.14/4.34 tff(16700,plain,
% 4.14/4.34 ($false),
% 4.14/4.34 inference(unit_resolution,[status(thm)],[448, 16699, 16697, 12])).
% 4.14/4.34 tff(16701,plain,((~b(elem!1, s(s(s(s(z)))))) | (s(s(z)) = elem!1) | (~r(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))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (elem!1 = s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.34 tff(16702,plain,
% 4.14/4.34 (~b(elem!1, s(s(s(s(z)))))),
% 4.14/4.34 inference(unit_resolution,[status(thm)],[16701, 644, 224, 251, 167, 12, 104, 701])).
% 4.14/4.34 tff(16703,plain,
% 4.14/4.34 (r(elem!1, s(s(s(s(z)))))),
% 4.14/4.34 inference(unit_resolution,[status(thm)],[483, 16702, 3179])).
% 4.14/4.34 tff(16704,plain,
% 4.14/4.34 (~r(elem!1, z)),
% 4.14/4.34 inference(unit_resolution,[status(thm)],[478, 16703, 47])).
% 4.14/4.34 tff(16705,plain,
% 4.14/4.34 (b(elem!1, z)),
% 4.14/4.34 inference(unit_resolution,[status(thm)],[498, 16704, 290])).
% 4.14/4.34 tff(16706,plain,
% 4.14/4.34 (~b(s(s(z)), elem!1)),
% 4.14/4.34 inference(unit_resolution,[status(thm)],[11004, 16705, 3461, 273, 818])).
% 4.14/4.34 tff(16707,plain,
% 4.14/4.34 (r(s(s(z)), elem!1)),
% 4.14/4.34 inference(unit_resolution,[status(thm)],[448, 16706, 12])).
% 4.14/4.34 tff(16708,plain,
% 4.14/4.34 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.14/4.34 inference(unit_resolution,[status(thm)],[11351, 16707, 224])).
% 4.14/4.34 tff(16709,plain,
% 4.14/4.34 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.14/4.34 inference(unit_resolution,[status(thm)],[3444, 16708, 4245])).
% 4.14/4.34 tff(16710,plain,
% 4.14/4.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.14/4.34 inference(rewrite,[status(thm)],[])).
% 4.14/4.34 tff(16711,plain,
% 4.14/4.34 (((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(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)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))) <=> ((~b(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(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.14/4.34 inference(rewrite,[status(thm)],[])).
% 4.14/4.34 tff(16712,plain,
% 4.14/4.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(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)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 4.14/4.34 inference(monotonicity,[status(thm)],[16711])).
% 4.14/4.34 tff(16713,plain,
% 4.14/4.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(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)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.14/4.34 inference(transitivity,[status(thm)],[16712, 16710])).
% 4.14/4.34 tff(16714,plain,
% 4.14/4.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(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)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 4.14/4.34 inference(quant_inst,[status(thm)],[])).
% 4.14/4.34 tff(16715,plain,
% 4.14/4.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 4.14/4.34 inference(modus_ponens,[status(thm)],[16714, 16713])).
% 4.14/4.34 tff(16716,plain,
% 4.14/4.34 (~b(s(s(s(s(z)))), elem!1)),
% 4.14/4.34 inference(unit_resolution,[status(thm)],[16715, 178, 104, 16688, 251, 16709])).
% 4.14/4.34 tff(16717,plain,
% 4.14/4.34 (r(s(s(s(s(z)))), elem!1)),
% 4.14/4.34 inference(unit_resolution,[status(thm)],[3142, 16716, 16687])).
% 4.14/4.34 tff(16718,plain,
% 4.14/4.34 (~b(elem!1, s(s(z)))),
% 4.14/4.34 inference(unit_resolution,[status(thm)],[16411, 178, 818, 16705, 3461, 273])).
% 4.14/4.34 tff(16719,plain,
% 4.14/4.34 (r(elem!1, s(s(z)))),
% 4.14/4.34 inference(unit_resolution,[status(thm)],[467, 16718, 312])).
% 4.14/4.34 tff(16720,plain,
% 4.14/4.34 (~r(s(s(s(s(z)))), s(s(z)))),
% 4.14/4.34 inference(unit_resolution,[status(thm)],[3785, 16719, 16703])).
% 4.14/4.34 tff(16721,plain,
% 4.14/4.34 (b(s(s(s(s(z)))), s(s(z)))),
% 4.14/4.34 inference(unit_resolution,[status(thm)],[102, 16720])).
% 4.14/4.34 tff(16722,plain,
% 4.14/4.34 (~b(s(s(s(s(z)))), z)),
% 4.14/4.34 inference(unit_resolution,[status(thm)],[16647, 178, 3461, 273, 167, 16721])).
% 4.14/4.34 tff(16723,plain,
% 4.14/4.34 (b(elem!1, s(s(s(elem!1))))),
% 4.14/4.34 inference(unit_resolution,[status(thm)],[10659, 16722, 1, 16706, 16718])).
% 4.14/4.34 tff(16724,plain,
% 4.14/4.34 (~(s(s(s(elem!1))) = elem!1)),
% 4.14/4.34 inference(unit_resolution,[status(thm)],[16438, 16723])).
% 4.14/4.34 tff(16725,plain,
% 4.14/4.34 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.14/4.34 inference(unit_resolution,[status(thm)],[8038, 16724, 47, 818, 16705, 16717])).
% 4.14/4.34 tff(16726,plain,
% 4.14/4.34 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 4.14/4.34 inference(unit_resolution,[status(thm)],[3502, 16687])).
% 4.14/4.34 tff(16727,plain,
% 4.14/4.34 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.14/4.34 inference(unit_resolution,[status(thm)],[2574, 178, 818, 16705, 16688, 16709])).
% 4.14/4.34 tff(16728,plain,
% 4.14/4.34 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.14/4.34 inference(unit_resolution,[status(thm)],[133, 16727])).
% 4.14/4.35 tff(16729,plain,
% 4.14/4.35 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[8089, 178, 104, 167, 251, 16721])).
% 4.14/4.35 tff(16730,plain,
% 4.14/4.35 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[3578, 16729])).
% 4.14/4.35 tff(16731,plain,
% 4.14/4.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 4.14/4.35 inference(rewrite,[status(thm)],[])).
% 4.14/4.35 tff(16732,plain,
% 4.14/4.35 (((~b(s(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(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(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(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 4.14/4.35 inference(rewrite,[status(thm)],[])).
% 4.14/4.35 tff(16733,plain,
% 4.14/4.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(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(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))))),
% 4.14/4.35 inference(monotonicity,[status(thm)],[16732])).
% 4.14/4.35 tff(16734,plain,
% 4.14/4.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(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(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 4.14/4.35 inference(transitivity,[status(thm)],[16733, 16731])).
% 4.14/4.35 tff(16735,plain,
% 4.14/4.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(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(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.14/4.35 inference(quant_inst,[status(thm)],[])).
% 4.14/4.35 tff(16736,plain,
% 4.14/4.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 4.14/4.35 inference(modus_ponens,[status(thm)],[16735, 16734])).
% 4.14/4.35 tff(16737,plain,
% 4.14/4.35 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[16736, 178, 2042, 104, 869, 3831])).
% 4.14/4.35 tff(16738,plain,
% 4.14/4.35 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[5118, 16737, 3521])).
% 4.14/4.35 tff(16739,plain,
% 4.14/4.35 (~r(z, s(s(s(elem!1))))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[5130, 16738, 108])).
% 4.14/4.35 tff(16740,plain,
% 4.14/4.35 (b(z, s(s(s(elem!1))))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[2095, 16739])).
% 4.14/4.35 tff(16741,plain,
% 4.14/4.35 ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[9019, 178, 273, 167, 3831])).
% 4.14/4.35 tff(16742,plain,
% 4.14/4.35 (~b(s(s(s(elem!1))), s(s(z)))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[16741, 16740])).
% 4.14/4.35 tff(16743,plain,
% 4.14/4.35 (~r(s(s(s(elem!1))), s(s(z)))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[10401, 16738, 107])).
% 4.14/4.35 tff(16744,plain,
% 4.14/4.35 ($false),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[4209, 41, 16743, 16742, 4181])).
% 4.14/4.35 tff(16745,plain,((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(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(s(s(s(z))))))), z)) | (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.35 tff(16746,plain,
% 4.14/4.35 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[16745, 16730, 167, 273, 16728, 16726, 16723, 104, 16688])).
% 4.14/4.35 tff(16747,plain,
% 4.14/4.35 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[4173, 16746, 16725])).
% 4.14/4.35 tff(16748,plain,
% 4.14/4.35 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(s(z)))))),
% 4.14/4.35 inference(monotonicity,[status(thm)],[16747])).
% 4.14/4.35 tff(16749,plain,
% 4.14/4.35 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(s(elem!1))))),
% 4.14/4.35 inference(symmetry,[status(thm)],[16748])).
% 4.14/4.35 tff(16750,plain,
% 4.14/4.35 ((~b(elem!1, s(s(s(s(z)))))) <=> (~b(elem!1, s(s(s(elem!1)))))),
% 4.14/4.35 inference(monotonicity,[status(thm)],[16749])).
% 4.14/4.35 tff(16751,plain,
% 4.14/4.35 (~b(elem!1, s(s(s(elem!1))))),
% 4.14/4.35 inference(modus_ponens,[status(thm)],[16702, 16750])).
% 4.14/4.35 tff(16752,plain,
% 4.14/4.35 ($false),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[16723, 16751])).
% 4.14/4.35 tff(16753,plain,(r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, elem!1)) | b(z, s(s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (s(s(z)) = elem!1) | (elem!1 = z) | (elem!1 = s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.35 tff(16754,plain,
% 4.14/4.35 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[16753, 12, 273, 104, 818, 1, 3461, 16686, 224, 167, 290, 701])).
% 4.14/4.35 tff(16755,plain,
% 4.14/4.35 (~r(elem!1, z)),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[10809, 16754, 203])).
% 4.14/4.35 tff(16756,plain,
% 4.14/4.35 (b(elem!1, z)),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[498, 16755, 290])).
% 4.14/4.35 tff(16757,plain,
% 4.14/4.35 (~r(s(s(z)), elem!1)),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[2803, 16754, 224])).
% 4.14/4.35 tff(16758,plain,
% 4.14/4.35 (b(s(s(z)), elem!1)),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[448, 16757, 12])).
% 4.14/4.35 tff(16759,plain,
% 4.14/4.35 ($false),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[11004, 16758, 16756, 3461, 273, 818])).
% 4.14/4.35 tff(16760,plain,((s(s(z)) = elem!1) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(z, elem!1)) | (elem!1 = z) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | b(z, s(s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (elem!1 = s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.35 tff(16761,plain,
% 4.14/4.35 (s(s(z)) = elem!1),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[16760, 818, 273, 5619, 290, 287, 203, 104, 1, 167, 701])).
% 4.14/4.35 tff(16762,plain,
% 4.14/4.35 (s(s(s(z))) = s(elem!1)),
% 4.14/4.35 inference(monotonicity,[status(thm)],[16761])).
% 4.14/4.35 tff(16763,plain,
% 4.14/4.35 (s(s(s(s(z)))) = s(s(elem!1))),
% 4.14/4.35 inference(monotonicity,[status(thm)],[16762])).
% 4.14/4.35 tff(16764,plain,
% 4.14/4.35 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 4.14/4.35 inference(monotonicity,[status(thm)],[16763])).
% 4.14/4.35 tff(16765,plain,
% 4.14/4.35 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), elem!1)),
% 4.14/4.35 inference(monotonicity,[status(thm)],[16761])).
% 4.14/4.35 tff(16766,plain,
% 4.14/4.35 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(elem!1)), elem!1)),
% 4.14/4.35 inference(transitivity,[status(thm)],[16765, 16764])).
% 4.14/4.35 tff(16767,plain,
% 4.14/4.35 (b(s(s(z)), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 4.14/4.35 inference(monotonicity,[status(thm)],[16761])).
% 4.14/4.35 tff(16768,plain,
% 4.14/4.35 (b(elem!1, s(s(s(s(z)))))),
% 4.14/4.35 inference(modus_ponens,[status(thm)],[167, 16767])).
% 4.14/4.35 tff(16769,plain,
% 4.14/4.35 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[1353, 10916, 551])).
% 4.14/4.35 tff(16770,plain,
% 4.14/4.35 (~(s(s(s(s(z)))) = s(elem!1))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[2168, 16769])).
% 4.14/4.35 tff(16771,plain,
% 4.14/4.35 (~b(s(s(s(s(z)))), elem!1)),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[16429, 168, 11684, 818, 1301])).
% 4.14/4.35 tff(16772,plain,
% 4.14/4.35 (~b(s(s(s(s(z)))), s(s(z)))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[8526, 16771, 1324])).
% 4.14/4.35 tff(16773,plain,
% 4.14/4.35 (r(s(s(s(s(z)))), s(s(z)))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[102, 16772])).
% 4.14/4.35 tff(16774,plain,
% 4.14/4.35 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 4.14/4.35 inference(monotonicity,[status(thm)],[3505])).
% 4.14/4.35 tff(16775,plain,
% 4.14/4.35 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[11305, 1324, 287])).
% 4.14/4.35 tff(16776,plain,
% 4.14/4.35 (~r(s(s(z)), elem!1)),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[2803, 16775, 287])).
% 4.14/4.35 tff(16777,plain,
% 4.14/4.35 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[11013, 16772, 104, 203, 273, 286, 145, 469, 168, 16776, 290, 5618])).
% 4.14/4.35 tff(16778,plain,
% 4.14/4.35 (r(s(s(s(z))), s(s(s(s(z)))))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[10755, 16777])).
% 4.14/4.35 tff(16779,plain,
% 4.14/4.35 (r(s(elem!1), s(s(s(s(z)))))),
% 4.14/4.35 inference(modus_ponens,[status(thm)],[16778, 16774])).
% 4.14/4.35 tff(16780,plain,
% 4.14/4.35 (~r(s(elem!1), s(s(z)))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[3949, 16779, 16773])).
% 4.14/4.35 tff(16781,plain,
% 4.14/4.35 (b(s(elem!1), s(s(z)))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[421, 16780, 10976])).
% 4.14/4.35 tff(16782,plain,
% 4.14/4.35 (r(s(elem!1), s(s(elem!1))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 4.14/4.35 inference(monotonicity,[status(thm)],[3507])).
% 4.14/4.35 tff(16783,plain,
% 4.14/4.35 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(elem!1), s(s(elem!1)))),
% 4.14/4.35 inference(symmetry,[status(thm)],[16782])).
% 4.14/4.35 tff(16784,plain,
% 4.14/4.35 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(elem!1), s(s(elem!1)))),
% 4.14/4.35 inference(transitivity,[status(thm)],[16774, 16783])).
% 4.14/4.35 tff(16785,plain,
% 4.14/4.35 (r(s(elem!1), s(s(elem!1)))),
% 4.14/4.35 inference(modus_ponens,[status(thm)],[16778, 16784])).
% 4.14/4.35 tff(16786,plain,
% 4.14/4.35 (~r(z, s(elem!1))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[5550, 118, 16785, 8134])).
% 4.14/4.35 tff(16787,plain,
% 4.14/4.35 (b(z, s(elem!1))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[2351, 16786])).
% 4.14/4.35 tff(16788,plain,
% 4.14/4.35 (~b(s(s(s(s(z)))), s(elem!1))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[10985, 16787, 273, 168, 16781])).
% 4.14/4.35 tff(16789,plain,
% 4.14/4.35 (r(s(s(s(s(z)))), elem!1)),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[3142, 16771, 551])).
% 4.14/4.35 tff(16790,plain,
% 4.14/4.35 (~r(s(elem!1), elem!1)),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[7010, 908, 3132])).
% 4.14/4.35 tff(16791,plain,
% 4.14/4.35 (b(s(elem!1), elem!1)),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[677, 16790, 725])).
% 4.14/4.35 tff(16792,plain,
% 4.14/4.35 ($false),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[1396, 16791, 7466, 506, 854, 818])).
% 4.14/4.35 tff(16793,plain,((~r(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (s(elem!1) = elem!1) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.35 tff(16794,plain,
% 4.14/4.35 (~b(elem!1, s(elem!1))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[16793, 16779, 818, 11684, 16789, 10915, 145])).
% 4.14/4.35 tff(16795,plain,
% 4.14/4.35 (r(elem!1, s(elem!1))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[756, 16794, 10913])).
% 4.14/4.35 tff(16796,plain,
% 4.14/4.35 (~r(s(s(s(s(z)))), s(elem!1))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[10992, 16795, 16789])).
% 4.14/4.35 tff(16797,plain,
% 4.14/4.35 ($false),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[2173, 16796, 16788, 16770])).
% 4.14/4.35 tff(16798,plain,((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(z, elem!1)) | (~r(z, s(s(s(s(z)))))) | (~(s(s(z)) = elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | (elem!1 = s(s(s(s(z))))) | (elem!1 = z) | r(s(s(z)), z) | (~b(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.35 tff(16799,plain,
% 4.14/4.35 (~b(s(s(s(s(z)))), z)),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[16798, 818, 273, 47, 16761, 104, 203, 286, 3179, 290, 5618, 16768])).
% 4.14/4.35 tff(16800,plain,
% 4.14/4.35 (r(s(s(s(s(z)))), z)),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[191, 16799])).
% 4.14/4.35 tff(16801,plain,
% 4.14/4.35 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[11227, 86, 286, 203, 145, 104, 16776, 469, 273, 194, 290, 5618])).
% 4.14/4.35 tff(16802,plain,
% 4.14/4.35 (r(s(s(s(z))), s(s(s(s(z)))))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[10755, 16801])).
% 4.14/4.35 tff(16803,plain,
% 4.14/4.35 (r(s(elem!1), s(s(elem!1)))),
% 4.14/4.35 inference(modus_ponens,[status(thm)],[16802, 16784])).
% 4.14/4.35 tff(16804,plain,
% 4.14/4.35 (~r(s(elem!1), z)),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[5542, 118, 16803, 8134])).
% 4.14/4.35 tff(16805,plain,
% 4.14/4.35 (b(s(elem!1), z)),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[774, 16804])).
% 4.14/4.35 tff(16806,plain,
% 4.14/4.35 (~b(s(s(s(s(z)))), elem!1)),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[3774, 86, 1324])).
% 4.14/4.35 tff(16807,plain,
% 4.14/4.35 (r(s(s(s(s(z)))), elem!1)),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[3142, 16806, 551])).
% 4.14/4.35 tff(16808,plain,
% 4.14/4.35 (r(s(elem!1), s(s(s(s(z)))))),
% 4.14/4.35 inference(modus_ponens,[status(thm)],[16802, 16774])).
% 4.14/4.35 tff(16809,plain,
% 4.14/4.35 (~r(s(elem!1), elem!1)),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[7010, 16808, 16807])).
% 4.14/4.35 tff(16810,plain,
% 4.14/4.35 (b(s(elem!1), elem!1)),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[677, 16809, 10915])).
% 4.14/4.35 tff(16811,plain,
% 4.14/4.35 (~r(z, s(elem!1))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[5550, 118, 16803, 8134])).
% 4.14/4.35 tff(16812,plain,
% 4.14/4.35 (b(z, s(elem!1))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[2351, 16811])).
% 4.14/4.35 tff(16813,plain,
% 4.14/4.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)))),
% 4.14/4.35 inference(rewrite,[status(thm)],[])).
% 4.14/4.35 tff(16814,plain,
% 4.14/4.35 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1)))) <=> ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)))),
% 4.14/4.35 inference(rewrite,[status(thm)],[])).
% 4.14/4.35 tff(16815,plain,
% 4.14/4.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z))))),
% 4.14/4.35 inference(monotonicity,[status(thm)],[16814])).
% 4.14/4.35 tff(16816,plain,
% 4.14/4.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)))),
% 4.14/4.35 inference(transitivity,[status(thm)],[16815, 16813])).
% 4.14/4.35 tff(16817,plain,
% 4.14/4.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))))),
% 4.14/4.35 inference(quant_inst,[status(thm)],[])).
% 4.14/4.35 tff(16818,plain,
% 4.14/4.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z))),
% 4.14/4.35 inference(modus_ponens,[status(thm)],[16817, 16816])).
% 4.14/4.35 tff(16819,plain,
% 4.14/4.35 ($false),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[16818, 178, 818, 11684, 16812, 16810, 16805])).
% 4.14/4.35 tff(16820,plain,(b(s(s(s(s(z)))), s(s(z))) | (~b(z, elem!1)) | (~(s(s(z)) = elem!1)) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (elem!1 = s(s(s(s(z))))) | (~b(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (elem!1 = z) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 4.14/4.35 tff(16821,plain,
% 4.14/4.35 (b(s(s(s(s(z)))), s(s(z)))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[16820, 818, 16761, 286, 203, 47, 104, 3179, 273, 16800, 290, 5618])).
% 4.14/4.35 tff(16822,plain,
% 4.14/4.35 (b(s(s(elem!1)), elem!1)),
% 4.14/4.35 inference(modus_ponens,[status(thm)],[16821, 16766])).
% 4.14/4.35 tff(16823,plain,
% 4.14/4.35 ((s(s(elem!1)) = s(s(z))) <=> (s(s(elem!1)) = elem!1)),
% 4.14/4.35 inference(monotonicity,[status(thm)],[16761])).
% 4.14/4.35 tff(16824,plain,
% 4.14/4.35 ((s(s(elem!1)) = s(s(z))) <=> (elem!1 = s(s(elem!1)))),
% 4.14/4.35 inference(transitivity,[status(thm)],[16823, 1542])).
% 4.14/4.35 tff(16825,plain,
% 4.14/4.35 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(elem!1 = s(s(elem!1))))),
% 4.14/4.35 inference(monotonicity,[status(thm)],[16824])).
% 4.14/4.35 tff(16826,plain,
% 4.14/4.35 (~(elem!1 = s(s(elem!1)))),
% 4.14/4.35 inference(modus_ponens,[status(thm)],[3340, 16825])).
% 4.14/4.35 tff(16827,plain,
% 4.14/4.35 (~b(elem!1, s(s(z)))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[3223, 16761])).
% 4.14/4.35 tff(16828,plain,
% 4.14/4.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(z)))))),
% 4.14/4.35 inference(rewrite,[status(thm)],[])).
% 4.14/4.35 tff(16829,plain,
% 4.14/4.35 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(z)))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(z)))))),
% 4.14/4.35 inference(rewrite,[status(thm)],[])).
% 4.14/4.35 tff(16830,plain,
% 4.14/4.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(z)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(z))))))),
% 4.14/4.35 inference(monotonicity,[status(thm)],[16829])).
% 4.14/4.35 tff(16831,plain,
% 4.14/4.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(z)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(z)))))),
% 4.14/4.35 inference(transitivity,[status(thm)],[16830, 16828])).
% 4.14/4.35 tff(16832,plain,
% 4.14/4.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(z)))) | (~b(z, s(s(z)))))),
% 4.14/4.35 inference(quant_inst,[status(thm)],[])).
% 4.14/4.35 tff(16833,plain,
% 4.14/4.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(z))))),
% 4.14/4.35 inference(modus_ponens,[status(thm)],[16832, 16831])).
% 4.14/4.35 tff(16834,plain,
% 4.14/4.35 (~b(s(s(z)), s(s(z)))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[16833, 178, 5619, 273])).
% 4.14/4.35 tff(16835,plain,
% 4.14/4.35 (elem!1 = s(s(z))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[3230, 16761])).
% 4.14/4.35 tff(16836,plain,
% 4.14/4.35 (~b(s(s(z)), elem!1)),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[3238, 16835, 16834])).
% 4.14/4.35 tff(16837,plain,
% 4.14/4.35 (b(elem!1, s(s(s(elem!1))))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[10659, 16799, 1, 16836, 16827])).
% 4.14/4.35 tff(16838,plain,
% 4.14/4.35 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(s(elem!1)))),
% 4.14/4.35 inference(monotonicity,[status(thm)],[16763])).
% 4.14/4.35 tff(16839,plain,
% 4.14/4.35 ((~r(elem!1, s(s(s(s(z)))))) <=> (~r(elem!1, s(s(elem!1))))),
% 4.14/4.35 inference(monotonicity,[status(thm)],[16838])).
% 4.14/4.35 tff(16840,plain,
% 4.14/4.35 (r(s(s(z)), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 4.14/4.35 inference(monotonicity,[status(thm)],[16761])).
% 4.14/4.35 tff(16841,plain,
% 4.14/4.35 ((~r(s(s(z)), s(s(s(s(z)))))) <=> (~r(elem!1, s(s(s(s(z))))))),
% 4.14/4.35 inference(monotonicity,[status(thm)],[16840])).
% 4.14/4.35 tff(16842,plain,
% 4.14/4.35 (~r(elem!1, s(s(s(s(z)))))),
% 4.14/4.35 inference(modus_ponens,[status(thm)],[16684, 16841])).
% 4.14/4.35 tff(16843,plain,
% 4.14/4.35 (~r(elem!1, s(s(elem!1)))),
% 4.14/4.35 inference(modus_ponens,[status(thm)],[16842, 16839])).
% 4.14/4.35 tff(16844,plain,
% 4.14/4.35 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 4.14/4.35 inference(monotonicity,[status(thm)],[16762])).
% 4.14/4.35 tff(16845,plain,
% 4.14/4.35 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 4.14/4.35 inference(transitivity,[status(thm)],[16844, 3881])).
% 4.14/4.35 tff(16846,plain,
% 4.14/4.35 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 4.14/4.35 inference(monotonicity,[status(thm)],[16845])).
% 4.14/4.35 tff(16847,plain,
% 4.14/4.35 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.14/4.35 inference(modus_ponens,[status(thm)],[11613, 16846])).
% 4.14/4.35 tff(16848,plain,
% 4.14/4.35 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[1649, 16847])).
% 4.14/4.35 tff(16849,plain,
% 4.14/4.35 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[3404, 16848])).
% 4.14/4.35 tff(16850,plain,
% 4.14/4.35 (r(s(s(s(s(z)))), z) <=> r(s(s(elem!1)), z)),
% 4.14/4.35 inference(monotonicity,[status(thm)],[16763])).
% 4.14/4.35 tff(16851,plain,
% 4.14/4.35 (r(s(s(elem!1)), z)),
% 4.14/4.35 inference(modus_ponens,[status(thm)],[16800, 16850])).
% 4.14/4.35 tff(16852,plain,
% 4.14/4.35 (b(s(s(z)), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 4.14/4.35 inference(monotonicity,[status(thm)],[16761])).
% 4.14/4.35 tff(16853,plain,
% 4.14/4.35 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 4.14/4.35 inference(symmetry,[status(thm)],[16852])).
% 4.14/4.35 tff(16854,plain,
% 4.14/4.35 (b(s(s(z)), s(s(s(elem!1))))),
% 4.14/4.35 inference(modus_ponens,[status(thm)],[16837, 16853])).
% 4.14/4.35 tff(16855,plain,
% 4.14/4.35 ((s(elem!1) = s(s(z))) <=> (s(elem!1) = elem!1)),
% 4.14/4.35 inference(monotonicity,[status(thm)],[16761])).
% 4.14/4.35 tff(16856,plain,
% 4.14/4.35 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(z)))),
% 4.14/4.35 inference(symmetry,[status(thm)],[16855])).
% 4.14/4.35 tff(16857,plain,
% 4.14/4.35 ((elem!1 = s(s(s(z)))) <=> (elem!1 = s(elem!1))),
% 4.14/4.35 inference(monotonicity,[status(thm)],[16762])).
% 4.14/4.35 tff(16858,plain,
% 4.14/4.35 ((elem!1 = s(s(s(z)))) <=> (s(elem!1) = elem!1)),
% 4.14/4.35 inference(transitivity,[status(thm)],[16857, 3190])).
% 4.14/4.35 tff(16859,plain,
% 4.14/4.35 ((elem!1 = s(s(s(z)))) <=> (s(elem!1) = s(s(z)))),
% 4.14/4.35 inference(transitivity,[status(thm)],[16858, 16856])).
% 4.14/4.35 tff(16860,plain,
% 4.14/4.35 ((~(elem!1 = s(s(s(z))))) <=> (~(s(elem!1) = s(s(z))))),
% 4.14/4.35 inference(monotonicity,[status(thm)],[16859])).
% 4.14/4.35 tff(16861,plain,
% 4.14/4.35 ((s(s(z)) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 4.14/4.35 inference(monotonicity,[status(thm)],[16761])).
% 4.14/4.35 tff(16862,plain,
% 4.14/4.35 ((~(s(s(z)) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 4.14/4.35 inference(monotonicity,[status(thm)],[16861])).
% 4.14/4.35 tff(16863,plain,
% 4.14/4.35 (~(elem!1 = s(s(s(z))))),
% 4.14/4.35 inference(modus_ponens,[status(thm)],[3205, 16862])).
% 4.14/4.35 tff(16864,plain,
% 4.14/4.35 (~(s(elem!1) = s(s(z)))),
% 4.14/4.35 inference(modus_ponens,[status(thm)],[16863, 16860])).
% 4.14/4.35 tff(16865,plain,
% 4.14/4.35 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[2840, 16864])).
% 4.14/4.35 tff(16866,plain,
% 4.14/4.35 (~r(z, s(s(s(elem!1))))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[10669, 16821, 167, 16854, 16865, 16800, 47])).
% 4.14/4.35 tff(16867,plain,
% 4.14/4.35 (b(z, s(s(s(elem!1))))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[2095, 16866])).
% 4.14/4.35 tff(16868,plain,
% 4.14/4.35 (~b(s(s(s(elem!1))), z)),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[7978, 16867, 273, 5619, 16854])).
% 4.14/4.35 tff(16869,plain,
% 4.14/4.35 (r(s(s(s(elem!1))), z)),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[1565, 16868])).
% 4.14/4.35 tff(16870,plain,
% 4.14/4.35 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 4.14/4.35 inference(rewrite,[status(thm)],[])).
% 4.14/4.35 tff(16871,plain,
% 4.14/4.35 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 4.14/4.35 inference(quant_inst,[status(thm)],[])).
% 4.14/4.35 tff(16872,plain,
% 4.14/4.35 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 4.14/4.35 inference(modus_ponens,[status(thm)],[16871, 16870])).
% 4.14/4.35 tff(16873,plain,
% 4.14/4.35 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[16872, 118, 16869, 16851])).
% 4.14/4.35 tff(16874,plain,
% 4.14/4.35 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[3409, 16873, 16849])).
% 4.14/4.35 tff(16875,plain,
% 4.14/4.35 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))),
% 4.14/4.35 inference(rewrite,[status(thm)],[])).
% 4.14/4.35 tff(16876,plain,
% 4.14/4.35 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))),
% 4.14/4.35 inference(rewrite,[status(thm)],[])).
% 4.14/4.35 tff(16877,plain,
% 4.14/4.35 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z))))),
% 4.14/4.35 inference(monotonicity,[status(thm)],[16876])).
% 4.14/4.35 tff(16878,plain,
% 4.14/4.35 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))),
% 4.14/4.35 inference(transitivity,[status(thm)],[16877, 16875])).
% 4.14/4.35 tff(16879,plain,
% 4.14/4.35 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 4.14/4.35 inference(quant_inst,[status(thm)],[])).
% 4.14/4.35 tff(16880,plain,
% 4.14/4.35 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z))),
% 4.14/4.35 inference(modus_ponens,[status(thm)],[16879, 16878])).
% 4.14/4.35 tff(16881,plain,
% 4.14/4.35 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[16880, 118, 16869, 16851])).
% 4.14/4.35 tff(16882,plain,
% 4.14/4.35 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[3375, 16881, 16848])).
% 4.14/4.35 tff(16883,plain,
% 4.14/4.35 ($false),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[5479, 16882, 16874, 16843, 16837, 16826, 16822])).
% 4.14/4.35 tff(16884,plain,((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (elem!1 = z) | r(s(s(z)), z) | b(z, s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))) | (elem!1 = s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.35 tff(16885,plain,
% 4.14/4.35 (~b(z, elem!1)),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[16884, 701, 167, 286, 4236, 104, 290, 5618, 1, 16684, 273])).
% 4.14/4.35 tff(16886,plain,
% 4.14/4.35 (r(z, elem!1)),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[585, 16885, 318])).
% 4.14/4.35 tff(16887,plain,
% 4.14/4.35 (~r(elem!1, s(s(s(s(z)))))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[529, 16886, 47])).
% 4.14/4.35 tff(16888,plain,
% 4.14/4.35 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[3818, 16886, 4236])).
% 4.14/4.35 tff(16889,plain,
% 4.14/4.35 (~(s(s(z)) = elem!1)),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[11305, 16888, 287])).
% 4.14/4.35 tff(16890,plain,
% 4.14/4.35 (~b(elem!1, s(s(s(s(z)))))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[16701, 16888, 287, 11349, 167, 16889, 104, 701])).
% 4.14/4.35 tff(16891,plain,
% 4.14/4.35 (elem!1 = s(s(s(s(z))))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[483, 16890, 16887])).
% 4.14/4.35 tff(16892,plain,
% 4.14/4.35 (s(elem!1) = s(s(s(s(s(z)))))),
% 4.14/4.35 inference(monotonicity,[status(thm)],[16891])).
% 4.14/4.35 tff(16893,plain,
% 4.14/4.35 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 4.14/4.35 inference(monotonicity,[status(thm)],[16892])).
% 4.14/4.35 tff(16894,plain,
% 4.14/4.35 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 4.14/4.35 inference(monotonicity,[status(thm)],[16893])).
% 4.14/4.35 tff(16895,plain,
% 4.14/4.35 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.14/4.35 inference(monotonicity,[status(thm)],[16894])).
% 4.14/4.35 tff(16896,plain,
% 4.14/4.35 (r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 4.14/4.35 inference(symmetry,[status(thm)],[16895])).
% 4.14/4.35 tff(16897,plain,
% 4.14/4.35 ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) <=> (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 4.14/4.35 inference(monotonicity,[status(thm)],[16896])).
% 4.14/4.35 tff(16898,plain,
% 4.14/4.35 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 4.14/4.35 inference(modus_ponens,[status(thm)],[11415, 16897])).
% 4.14/4.35 tff(16899,plain,
% 4.14/4.35 (b(s(s(s(z))), s(s(s(elem!1))))),
% 4.14/4.35 inference(unit_resolution,[status(thm)],[9126, 16898, 11613])).
% 4.14/4.35 tff(16900,plain,
% 4.14/4.35 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.14/4.35 inference(monotonicity,[status(thm)],[16894])).
% 4.14/4.35 tff(16901,plain,
% 4.14/4.35 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.14/4.35 inference(symmetry,[status(thm)],[16900])).
% 4.14/4.35 tff(16902,plain,
% 4.14/4.35 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.14/4.35 inference(modus_ponens,[status(thm)],[11349, 16901])).
% 4.14/4.35 tff(16903,plain,
% 4.14/4.35 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.14/4.35 inference(monotonicity,[status(thm)],[16894])).
% 4.14/4.35 tff(16904,plain,
% 4.14/4.35 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 4.14/4.35 inference(symmetry,[status(thm)],[16903])).
% 4.14/4.35 tff(16905,plain,
% 4.14/4.35 ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(s(z)), s(s(s(elem!1)))))),
% 4.14/4.35 inference(monotonicity,[status(thm)],[16904])).
% 4.14/4.35 tff(16906,plain,
% 4.14/4.35 (~b(s(s(z)), s(s(s(elem!1))))),
% 4.14/4.35 inference(modus_ponens,[status(thm)],[286, 16905])).
% 4.14/4.36 tff(16907,plain,
% 4.14/4.36 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(s(s(z)))))),
% 4.14/4.36 inference(monotonicity,[status(thm)],[16891])).
% 4.14/4.36 tff(16908,plain,
% 4.14/4.36 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(z)), elem!1)),
% 4.14/4.36 inference(symmetry,[status(thm)],[16907])).
% 4.14/4.36 tff(16909,plain,
% 4.14/4.36 ((~r(s(s(z)), s(s(s(s(z)))))) <=> (~r(s(s(z)), elem!1))),
% 4.14/4.36 inference(monotonicity,[status(thm)],[16908])).
% 4.14/4.36 tff(16910,plain,
% 4.14/4.36 (~r(s(s(z)), elem!1)),
% 4.14/4.36 inference(modus_ponens,[status(thm)],[16684, 16909])).
% 4.14/4.36 tff(16911,plain,
% 4.14/4.36 (s(s(s(s(z)))) = elem!1),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[325, 16891])).
% 4.14/4.36 tff(16912,plain,
% 4.14/4.36 (~(s(s(elem!1)) = elem!1)),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[338, 16911, 16889])).
% 4.14/4.36 tff(16913,plain,
% 4.14/4.36 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[348, 16912])).
% 4.14/4.36 tff(16914,plain,
% 4.14/4.36 (~b(z, s(s(s(elem!1))))),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[11477, 16891, 4235])).
% 4.14/4.36 tff(16915,plain,
% 4.14/4.36 (r(z, s(s(s(elem!1))))),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[2095, 16914])).
% 4.14/4.36 tff(16916,plain,
% 4.14/4.36 (~(s(elem!1) = elem!1)),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[672, 16912])).
% 4.14/4.36 tff(16917,plain,
% 4.14/4.36 (b(z, s(s(s(s(s(z)))))) <=> b(z, s(elem!1))),
% 4.14/4.36 inference(symmetry,[status(thm)],[2310])).
% 4.14/4.36 tff(16918,plain,
% 4.14/4.36 ((~b(z, s(s(s(s(s(z))))))) <=> (~b(z, s(elem!1)))),
% 4.14/4.36 inference(monotonicity,[status(thm)],[16917])).
% 4.14/4.36 tff(16919,plain,
% 4.14/4.36 (r(elem!1, s(s(z))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 4.14/4.36 inference(monotonicity,[status(thm)],[319])).
% 4.14/4.36 tff(16920,plain,
% 4.14/4.36 (r(s(s(s(s(z)))), s(s(z))) <=> r(elem!1, s(s(z)))),
% 4.14/4.36 inference(symmetry,[status(thm)],[16919])).
% 4.14/4.36 tff(16921,plain,
% 4.14/4.36 ((~r(s(s(s(s(z)))), s(s(z)))) <=> (~r(elem!1, s(s(z))))),
% 4.14/4.36 inference(monotonicity,[status(thm)],[16920])).
% 4.14/4.36 tff(16922,plain,
% 4.14/4.36 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(s(s(z)))))),
% 4.14/4.36 inference(monotonicity,[status(thm)],[319])).
% 4.14/4.36 tff(16923,plain,
% 4.14/4.36 ((s(elem!1) = elem!1) <=> (s(s(s(s(z)))) = s(elem!1))),
% 4.14/4.36 inference(transitivity,[status(thm)],[16922, 2163])).
% 4.14/4.36 tff(16924,plain,
% 4.14/4.36 ((~(s(elem!1) = elem!1)) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 4.14/4.36 inference(monotonicity,[status(thm)],[16923])).
% 4.14/4.36 tff(16925,plain,
% 4.14/4.36 (~(s(s(s(s(z)))) = s(elem!1))),
% 4.14/4.36 inference(modus_ponens,[status(thm)],[725, 16924])).
% 4.14/4.36 tff(16926,plain,
% 4.14/4.36 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(s(s(z)))))),
% 4.14/4.36 inference(transitivity,[status(thm)],[16923, 2164])).
% 4.14/4.36 tff(16927,plain,
% 4.14/4.36 ((~(s(elem!1) = elem!1)) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 4.14/4.36 inference(monotonicity,[status(thm)],[16926])).
% 4.14/4.36 tff(16928,plain,
% 4.14/4.36 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.14/4.36 inference(modus_ponens,[status(thm)],[725, 16927])).
% 4.14/4.36 tff(16929,plain,
% 4.14/4.36 (~b(s(s(s(s(z)))), z)),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[12557, 5723, 319])).
% 4.14/4.36 tff(16930,plain,
% 4.14/4.36 (r(s(s(s(s(z)))), z)),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[191, 16929])).
% 4.14/4.36 tff(16931,plain,
% 4.14/4.36 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.14/4.36 inference(monotonicity,[status(thm)],[319])).
% 4.14/4.36 tff(16932,plain,
% 4.14/4.36 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), elem!1)),
% 4.14/4.36 inference(symmetry,[status(thm)],[16931])).
% 4.14/4.36 tff(16933,plain,
% 4.14/4.36 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[2840, 11439])).
% 4.14/4.36 tff(16934,plain,
% 4.14/4.36 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[4173, 3822, 16933])).
% 4.14/4.36 tff(16935,plain,
% 4.14/4.36 (b(s(s(s(elem!1))), elem!1)),
% 4.14/4.36 inference(modus_ponens,[status(thm)],[16934, 16932])).
% 4.14/4.36 tff(16936,plain,
% 4.14/4.36 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.14/4.36 inference(monotonicity,[status(thm)],[350])).
% 4.14/4.36 tff(16937,plain,
% 4.14/4.36 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))),
% 4.14/4.36 inference(monotonicity,[status(thm)],[352, 320])).
% 4.14/4.36 tff(16938,plain,
% 4.14/4.36 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 4.14/4.36 inference(transitivity,[status(thm)],[16937, 4625])).
% 4.14/4.36 tff(16939,plain,
% 4.14/4.36 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.14/4.36 inference(transitivity,[status(thm)],[16938, 16936])).
% 4.14/4.36 tff(16940,plain,
% 4.14/4.36 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 4.14/4.36 inference(monotonicity,[status(thm)],[16939])).
% 4.14/4.36 tff(16941,plain,
% 4.14/4.36 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.14/4.36 inference(modus_ponens,[status(thm)],[356, 16940])).
% 4.14/4.36 tff(16942,plain,
% 4.14/4.36 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(elem!1), s(s(z)))),
% 4.14/4.36 inference(symmetry,[status(thm)],[2747])).
% 4.14/4.36 tff(16943,plain,
% 4.14/4.36 ((~b(s(s(s(s(s(z))))), s(s(z)))) <=> (~b(s(elem!1), s(s(z))))),
% 4.14/4.36 inference(monotonicity,[status(thm)],[16942])).
% 4.14/4.36 tff(16944,plain,
% 4.14/4.36 (b(s(elem!1), elem!1)),
% 4.14/4.36 inference(modus_ponens,[status(thm)],[1069, 13355])).
% 4.14/4.36 tff(16945,plain,
% 4.14/4.36 (~r(elem!1, s(elem!1))),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[12189, 2333, 437])).
% 4.14/4.36 tff(16946,plain,
% 4.14/4.36 (~b(elem!1, s(elem!1))),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[7389, 2333, 557, 1597, 356, 683])).
% 4.14/4.36 tff(16947,plain,
% 4.14/4.36 ($false),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[756, 16946, 16945, 750])).
% 4.14/4.36 tff(16948,plain,((~r(z, s(elem!1))) | (elem!1 = s(elem!1)) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(elem!1), elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.36 tff(16949,plain,
% 4.14/4.36 (~r(z, s(elem!1))),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[16948, 16944, 557, 1597, 356, 750, 437])).
% 4.14/4.36 tff(16950,plain,
% 4.14/4.36 (b(z, s(elem!1))),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[2351, 16949])).
% 4.14/4.36 tff(16951,plain,
% 4.14/4.36 (b(z, s(s(s(s(s(z))))))),
% 4.14/4.36 inference(modus_ponens,[status(thm)],[16950, 2310])).
% 4.14/4.36 tff(16952,plain,
% 4.14/4.36 ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[2754, 178, 273, 167, 2746])).
% 4.14/4.36 tff(16953,plain,
% 4.14/4.36 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[16952, 16951])).
% 4.14/4.36 tff(16954,plain,
% 4.14/4.36 (~b(s(elem!1), s(s(z)))),
% 4.14/4.36 inference(modus_ponens,[status(thm)],[16953, 16943])).
% 4.14/4.36 tff(16955,plain,
% 4.14/4.36 (r(s(elem!1), s(s(z)))),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[421, 16954, 11439])).
% 4.14/4.36 tff(16956,plain,
% 4.14/4.36 (~b(s(s(s(s(z)))), s(elem!1))),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[14913, 16955, 104, 224, 16941, 193, 1069])).
% 4.14/4.36 tff(16957,plain,
% 4.14/4.36 (r(s(s(s(s(z)))), s(elem!1))),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[2173, 16956, 2508])).
% 4.14/4.36 tff(16958,plain,
% 4.14/4.36 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 4.14/4.36 inference(modus_ponens,[status(thm)],[16957, 12637])).
% 4.14/4.36 tff(16959,plain,
% 4.14/4.36 (r(s(s(s(s(s(z))))), s(s(z)))),
% 4.14/4.36 inference(modus_ponens,[status(thm)],[16955, 362])).
% 4.14/4.36 tff(16960,plain,
% 4.14/4.36 ($false),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[15635, 118, 193, 16959, 16958])).
% 4.14/4.36 tff(16961,plain,((~b(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~(elem!1 = s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (elem!1 = s(elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.36 tff(16962,plain,
% 4.14/4.36 (~b(s(elem!1), s(s(s(s(z)))))),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[16961, 193, 319, 2508, 104, 224, 273, 167, 557, 16935, 356, 750, 437])).
% 4.14/4.36 tff(16963,plain,
% 4.14/4.36 (r(s(elem!1), s(s(s(s(z)))))),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[1084, 16962, 1369])).
% 4.14/4.36 tff(16964,plain,
% 4.14/4.36 (~r(z, s(elem!1))),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[2766, 16963, 145])).
% 4.14/4.36 tff(16965,plain,
% 4.14/4.36 (b(z, s(elem!1))),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[2351, 16964])).
% 4.14/4.36 tff(16966,plain,
% 4.14/4.36 (b(z, s(s(s(s(s(z))))))),
% 4.14/4.36 inference(modus_ponens,[status(thm)],[16965, 2310])).
% 4.14/4.36 tff(16967,plain,
% 4.14/4.36 (~r(s(elem!1), z)),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[916, 16963, 194])).
% 4.14/4.36 tff(16968,plain,
% 4.14/4.36 (~r(s(s(s(s(s(z))))), z)),
% 4.14/4.36 inference(modus_ponens,[status(thm)],[16967, 2313])).
% 4.14/4.36 tff(16969,plain,
% 4.14/4.36 (b(s(s(s(s(s(z))))), z)),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[410, 41, 242, 16968])).
% 4.14/4.36 tff(16970,plain,
% 4.14/4.36 (~r(s(elem!1), s(s(z)))),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[3949, 16963, 193])).
% 4.14/4.36 tff(16971,plain,
% 4.14/4.36 (b(s(elem!1), s(s(z)))),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[421, 16970, 11439])).
% 4.14/4.36 tff(16972,plain,
% 4.14/4.36 (b(s(s(s(s(s(z))))), s(s(z)))),
% 4.14/4.36 inference(modus_ponens,[status(thm)],[16971, 2747])).
% 4.14/4.36 tff(16973,plain,
% 4.14/4.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 4.14/4.36 inference(rewrite,[status(thm)],[])).
% 4.14/4.36 tff(16974,plain,
% 4.14/4.36 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 4.14/4.36 inference(rewrite,[status(thm)],[])).
% 4.14/4.36 tff(16975,plain,
% 4.14/4.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 4.14/4.36 inference(monotonicity,[status(thm)],[16974])).
% 4.14/4.36 tff(16976,plain,
% 4.14/4.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 4.14/4.36 inference(transitivity,[status(thm)],[16975, 16973])).
% 4.14/4.36 tff(16977,plain,
% 4.14/4.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))))),
% 4.14/4.36 inference(quant_inst,[status(thm)],[])).
% 4.14/4.36 tff(16978,plain,
% 4.14/4.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 4.14/4.36 inference(modus_ponens,[status(thm)],[16977, 16976])).
% 4.14/4.36 tff(16979,plain,
% 4.14/4.36 ($false),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[16978, 178, 3461, 273, 16972, 16969, 16966])).
% 4.14/4.36 tff(16980,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~(elem!1 = s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (s(elem!1) = s(s(s(s(z))))) | (s(s(s(s(z)))) = s(elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1)) | (elem!1 = s(elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.36 tff(16981,plain,
% 4.14/4.36 (~r(s(s(s(s(z)))), s(s(z)))),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[16980, 16930, 273, 319, 5619, 145, 16928, 16925, 104, 224, 167, 557, 356, 749, 10801])).
% 4.14/4.36 tff(16982,plain,
% 4.14/4.36 (~r(elem!1, s(s(z)))),
% 4.14/4.36 inference(modus_ponens,[status(thm)],[16981, 16921])).
% 4.14/4.36 tff(16983,assumption,(b(s(s(s(z))), s(s(s(elem!1))))), introduced(assumption)).
% 4.14/4.36 tff(16984,plain,
% 4.14/4.36 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.14/4.36 inference(monotonicity,[status(thm)],[352])).
% 4.14/4.36 tff(16985,plain,
% 4.14/4.36 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.14/4.36 inference(symmetry,[status(thm)],[16984])).
% 4.14/4.36 tff(16986,plain,
% 4.14/4.36 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.14/4.36 inference(modus_ponens,[status(thm)],[251, 16985])).
% 4.14/4.36 tff(16987,plain,
% 4.14/4.36 (b(s(s(s(s(z)))), s(s(z)))),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[102, 16981])).
% 4.14/4.36 tff(16988,plain,
% 4.14/4.36 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[8089, 178, 104, 167, 251, 16987])).
% 4.14/4.36 tff(16989,plain,
% 4.14/4.36 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[3578, 16988])).
% 4.14/4.36 tff(16990,plain,
% 4.14/4.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~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(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~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(z))), s(s(s(elem!1))))))),
% 4.14/4.36 inference(rewrite,[status(thm)],[])).
% 4.14/4.36 tff(16991,plain,
% 4.14/4.36 (((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~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(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)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~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(z))), s(s(s(elem!1))))))),
% 4.14/4.36 inference(rewrite,[status(thm)],[])).
% 4.14/4.36 tff(16992,plain,
% 4.14/4.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(z))), s(s(s(elem!1))))) | (~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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~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(z))), s(s(s(elem!1)))))))),
% 4.14/4.36 inference(monotonicity,[status(thm)],[16991])).
% 4.14/4.36 tff(16993,plain,
% 4.14/4.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(z))), s(s(s(elem!1))))) | (~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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~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(z))), s(s(s(elem!1))))))),
% 4.14/4.36 inference(transitivity,[status(thm)],[16992, 16990])).
% 4.14/4.36 tff(16994,plain,
% 4.14/4.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(z))), s(s(s(elem!1))))) | (~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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 4.14/4.36 inference(quant_inst,[status(thm)],[])).
% 4.14/4.36 tff(16995,plain,
% 4.14/4.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~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(z))), s(s(s(elem!1)))))),
% 4.14/4.36 inference(modus_ponens,[status(thm)],[16994, 16993])).
% 4.14/4.36 tff(16996,plain,
% 4.14/4.36 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[16995, 178, 104, 1126, 3828, 16983])).
% 4.14/4.36 tff(16997,plain,
% 4.14/4.36 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 16996])).
% 4.14/4.36 tff(16998,plain,
% 4.14/4.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 4.14/4.36 inference(rewrite,[status(thm)],[])).
% 4.14/4.36 tff(16999,plain,
% 4.14/4.36 (((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 4.14/4.36 inference(rewrite,[status(thm)],[])).
% 4.14/4.36 tff(17000,plain,
% 4.14/4.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 4.14/4.36 inference(monotonicity,[status(thm)],[16999])).
% 4.14/4.36 tff(17001,plain,
% 4.14/4.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 4.14/4.36 inference(transitivity,[status(thm)],[17000, 16998])).
% 4.14/4.36 tff(17002,plain,
% 4.14/4.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 4.14/4.36 inference(quant_inst,[status(thm)],[])).
% 4.14/4.36 tff(17003,plain,
% 4.14/4.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 4.14/4.36 inference(modus_ponens,[status(thm)],[17002, 17001])).
% 4.14/4.36 tff(17004,plain,
% 4.14/4.36 (~b(s(s(z)), s(s(s(z))))),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[17003, 178, 167, 1126, 3828, 16983])).
% 4.14/4.36 tff(17005,plain,
% 4.14/4.36 (r(s(s(z)), s(s(s(z))))),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[5088, 17004])).
% 4.14/4.36 tff(17006,plain,
% 4.14/4.36 ($false),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[16016, 118, 17005, 107, 16997])).
% 4.14/4.36 tff(17007,plain,((~b(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(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(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.36 tff(17008,plain,
% 4.14/4.36 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[17007, 16989, 104, 167, 16986, 16983])).
% 4.14/4.36 tff(17009,plain,
% 4.14/4.36 (r(s(s(s(z))), s(s(s(s(z)))))),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[10755, 17008])).
% 4.14/4.36 tff(17010,plain,
% 4.14/4.36 (~r(s(s(s(z))), z)),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[4899, 118, 145, 17009])).
% 4.14/4.36 tff(17011,plain,
% 4.14/4.36 (b(s(s(s(z))), z)),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[4903, 41, 77, 17010])).
% 4.14/4.36 tff(17012,plain,
% 4.14/4.36 (~r(z, s(s(s(z))))),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[4910, 118, 145, 17009])).
% 4.14/4.36 tff(17013,plain,
% 4.14/4.36 (b(z, s(s(s(z))))),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[4920, 17012])).
% 4.14/4.36 tff(17014,plain,
% 4.14/4.36 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.14/4.36 inference(monotonicity,[status(thm)],[350])).
% 4.14/4.36 tff(17015,plain,
% 4.14/4.36 (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(s(z))))))),
% 4.14/4.36 inference(symmetry,[status(thm)],[17014])).
% 4.14/4.36 tff(17016,plain,
% 4.14/4.36 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.14/4.36 inference(monotonicity,[status(thm)],[352])).
% 4.14/4.36 tff(17017,plain,
% 4.14/4.36 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(elem!1))))),
% 4.14/4.36 inference(transitivity,[status(thm)],[13345, 2486])).
% 4.14/4.36 tff(17018,plain,
% 4.14/4.36 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 4.14/4.36 inference(monotonicity,[status(thm)],[17017])).
% 4.14/4.36 tff(17019,plain,
% 4.14/4.36 (~(elem!1 = s(s(s(elem!1))))),
% 4.14/4.36 inference(modus_ponens,[status(thm)],[16933, 17018])).
% 4.14/4.36 tff(17020,plain,
% 4.14/4.36 (~(s(s(z)) = s(elem!1))),
% 4.14/4.36 inference(unit_resolution,[status(thm)],[1058, 11439])).
% 4.14/4.36 tff(17021,plain,
% 4.14/4.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 4.14/4.36 inference(rewrite,[status(thm)],[])).
% 4.14/4.36 tff(17022,plain,
% 4.14/4.36 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 4.14/4.37 inference(rewrite,[status(thm)],[])).
% 4.14/4.37 tff(17023,plain,
% 4.14/4.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 4.14/4.37 inference(monotonicity,[status(thm)],[17022])).
% 4.14/4.37 tff(17024,plain,
% 4.14/4.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 4.14/4.37 inference(transitivity,[status(thm)],[17023, 17021])).
% 4.14/4.37 tff(17025,plain,
% 4.14/4.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(z)))))),
% 4.14/4.37 inference(quant_inst,[status(thm)],[])).
% 4.14/4.37 tff(17026,plain,
% 4.14/4.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 4.14/4.37 inference(modus_ponens,[status(thm)],[17025, 17024])).
% 4.14/4.37 tff(17027,plain,
% 4.14/4.37 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[17026, 178, 273, 167, 2746, 13560])).
% 4.14/4.37 tff(17028,plain,
% 4.14/4.37 (~b(s(s(z)), s(elem!1))),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[2330, 17027, 319])).
% 4.14/4.37 tff(17029,plain,
% 4.14/4.37 (r(s(s(z)), s(elem!1))),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[1067, 17028, 17020])).
% 4.14/4.37 tff(17030,plain,
% 4.14/4.37 (b(s(elem!1), s(s(s(elem!1))))),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[6127, 17029, 4218, 5396])).
% 4.14/4.37 tff(17031,plain,
% 4.14/4.37 (~r(elem!1, s(s(s(elem!1))))),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[3421, 437, 557])).
% 4.14/4.37 tff(17032,plain,
% 4.14/4.37 (b(elem!1, s(s(s(elem!1))))),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[2054, 17031, 1586])).
% 4.14/4.37 tff(17033,plain,
% 4.14/4.37 (~(s(s(z)) = elem!1)),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[6206, 437, 5618])).
% 4.14/4.37 tff(17034,plain,
% 4.14/4.37 (~(elem!1 = s(s(z)))),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[311, 17033])).
% 4.14/4.37 tff(17035,plain,
% 4.14/4.37 (b(elem!1, s(s(z)))),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[467, 17034, 460])).
% 4.14/4.37 tff(17036,plain,
% 4.14/4.37 (b(s(s(z)), elem!1)),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[448, 17033, 10828])).
% 4.14/4.37 tff(17037,plain,
% 4.14/4.37 (~b(s(s(z)), s(s(s(elem!1))))),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[15603, 178, 1597, 17036, 17035, 17032])).
% 4.14/4.37 tff(17038,plain,
% 4.14/4.37 (r(s(s(z)), s(s(s(elem!1))))),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[4223, 17037])).
% 4.14/4.37 tff(17039,plain,
% 4.14/4.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)))),
% 4.14/4.37 inference(rewrite,[status(thm)],[])).
% 4.14/4.37 tff(17040,plain,
% 4.14/4.37 (((~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(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)))),
% 4.14/4.37 inference(rewrite,[status(thm)],[])).
% 4.14/4.37 tff(17041,plain,
% 4.14/4.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1))))),
% 4.14/4.37 inference(monotonicity,[status(thm)],[17040])).
% 4.14/4.37 tff(17042,plain,
% 4.14/4.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)))),
% 4.14/4.37 inference(transitivity,[status(thm)],[17041, 17039])).
% 4.14/4.37 tff(17043,plain,
% 4.14/4.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))))),
% 4.14/4.37 inference(quant_inst,[status(thm)],[])).
% 4.14/4.37 tff(17044,plain,
% 4.14/4.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1))),
% 4.14/4.37 inference(modus_ponens,[status(thm)],[17043, 17042])).
% 4.14/4.37 tff(17045,plain,
% 4.14/4.37 (~b(s(s(z)), s(elem!1))),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[17044, 178, 683, 17036, 17032, 5888])).
% 4.14/4.37 tff(17046,plain,
% 4.14/4.37 (r(s(s(z)), s(elem!1))),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[1067, 17045, 1060])).
% 4.14/4.37 tff(17047,plain,
% 4.14/4.37 ($false),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[6276, 118, 1551, 17046, 17038])).
% 4.14/4.37 tff(17048,plain,((~r(elem!1, z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (s(s(z)) = 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))))) | r(elem!1, s(s(z))) | (elem!1 = s(s(s(elem!1)))) | r(s(s(z)), elem!1) | (~r(z, s(s(s(elem!1))))) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 4.14/4.37 tff(17049,plain,
% 4.14/4.37 (~r(s(s(s(elem!1))), s(elem!1))),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[17048, 17030, 1597, 17020, 437, 460, 16944, 17019, 10828, 557, 5618])).
% 4.14/4.37 tff(17050,plain,
% 4.14/4.37 (b(s(s(s(elem!1))), s(elem!1))),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[373, 17049, 356])).
% 4.14/4.37 tff(17051,plain,
% 4.14/4.37 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.14/4.37 inference(modus_ponens,[status(thm)],[17050, 17016])).
% 4.14/4.37 tff(17052,plain,
% 4.14/4.37 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 4.14/4.37 inference(modus_ponens,[status(thm)],[17051, 17015])).
% 4.14/4.37 tff(17053,plain,
% 4.14/4.37 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[2754, 178, 273, 167, 2746, 13560])).
% 4.14/4.37 tff(17054,plain,
% 4.14/4.37 (~b(s(elem!1), s(s(z)))),
% 4.14/4.37 inference(modus_ponens,[status(thm)],[17053, 16943])).
% 4.14/4.37 tff(17055,plain,
% 4.14/4.37 (r(s(elem!1), s(s(z)))),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[421, 17054, 11439])).
% 4.14/4.37 tff(17056,plain,
% 4.14/4.37 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[390, 17055, 224])).
% 4.14/4.37 tff(17057,plain,
% 4.14/4.37 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[395, 17056, 16941])).
% 4.14/4.37 tff(17058,plain,
% 4.14/4.37 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 4.14/4.37 inference(modus_ponens,[status(thm)],[17057, 376])).
% 4.14/4.37 tff(17059,plain,
% 4.14/4.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 4.14/4.37 inference(rewrite,[status(thm)],[])).
% 4.14/4.37 tff(17060,plain,
% 4.14/4.37 (((~b(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))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 4.14/4.37 inference(rewrite,[status(thm)],[])).
% 4.14/4.37 tff(17061,plain,
% 4.14/4.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 4.14/4.37 inference(monotonicity,[status(thm)],[17060])).
% 4.14/4.37 tff(17062,plain,
% 4.14/4.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 4.14/4.37 inference(transitivity,[status(thm)],[17061, 17059])).
% 4.14/4.37 tff(17063,plain,
% 4.14/4.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 4.14/4.37 inference(quant_inst,[status(thm)],[])).
% 4.14/4.37 tff(17064,plain,
% 4.14/4.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 4.14/4.37 inference(modus_ponens,[status(thm)],[17063, 17062])).
% 4.14/4.37 tff(17065,plain,
% 4.14/4.37 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[17064, 178, 104, 251, 2746, 17058])).
% 4.14/4.37 tff(17066,plain,
% 4.14/4.37 ($false),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[17065, 17052])).
% 4.14/4.37 tff(17067,plain,((~b(s(elem!1), s(s(s(s(z)))))) | (~(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))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | r(elem!1, s(s(z))) | r(s(s(z)), elem!1) | (~r(z, s(s(s(elem!1))))) | r(s(s(z)), z) | b(s(s(z)), s(s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.37 tff(17068,plain,
% 4.14/4.37 (~b(s(elem!1), s(s(s(s(z)))))),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[17067, 13560, 104, 251, 224, 356, 1597, 437, 460, 10828, 557, 5618, 4218, 273, 167, 319])).
% 4.14/4.37 tff(17069,plain,
% 4.14/4.37 (r(s(elem!1), s(s(s(s(z)))))),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[1084, 17068, 1369])).
% 4.14/4.37 tff(17070,plain,
% 4.14/4.37 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 4.14/4.37 inference(modus_ponens,[status(thm)],[17069, 13567])).
% 4.14/4.37 tff(17071,plain,
% 4.14/4.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 4.14/4.37 inference(rewrite,[status(thm)],[])).
% 4.14/4.37 tff(17072,plain,
% 4.14/4.37 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 4.14/4.37 inference(quant_inst,[status(thm)],[])).
% 4.14/4.37 tff(17073,plain,
% 4.14/4.37 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 4.14/4.37 inference(modus_ponens,[status(thm)],[17072, 17071])).
% 4.14/4.37 tff(17074,plain,
% 4.14/4.37 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[17073, 118, 17070, 4891])).
% 4.14/4.37 tff(17075,plain,
% 4.14/4.37 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[9830, 41, 11413, 17074])).
% 4.14/4.37 tff(17076,plain,
% 4.14/4.37 (~r(s(elem!1), z)),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[916, 17069, 194])).
% 4.14/4.37 tff(17077,plain,
% 4.14/4.37 (~r(s(s(s(s(s(z))))), z)),
% 4.14/4.37 inference(modus_ponens,[status(thm)],[17076, 2313])).
% 4.14/4.37 tff(17078,plain,
% 4.14/4.37 (b(s(s(s(s(s(z))))), z)),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[410, 41, 242, 17077])).
% 4.14/4.37 tff(17079,plain,
% 4.14/4.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 4.14/4.37 inference(rewrite,[status(thm)],[])).
% 4.14/4.37 tff(17080,plain,
% 4.14/4.37 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 4.14/4.37 inference(rewrite,[status(thm)],[])).
% 4.14/4.37 tff(17081,plain,
% 4.14/4.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 4.14/4.37 inference(monotonicity,[status(thm)],[17080])).
% 4.14/4.37 tff(17082,plain,
% 4.14/4.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 4.14/4.37 inference(transitivity,[status(thm)],[17081, 17079])).
% 4.14/4.37 tff(17083,plain,
% 4.14/4.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))))),
% 4.14/4.37 inference(quant_inst,[status(thm)],[])).
% 4.14/4.37 tff(17084,plain,
% 4.14/4.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 4.14/4.37 inference(modus_ponens,[status(thm)],[17083, 17082])).
% 4.14/4.37 tff(17085,plain,
% 4.14/4.37 ($false),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[17084, 178, 17078, 13560, 3008, 1127, 17075])).
% 4.14/4.37 tff(17086,plain,((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~(elem!1 = s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (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))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | r(elem!1, s(s(z))) | r(s(s(z)), elem!1) | (~r(z, s(s(s(elem!1))))) | r(s(s(z)), z) | b(s(s(z)), s(s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.37 tff(17087,plain,
% 4.14/4.37 (~b(z, s(s(s(s(s(z))))))),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[17086, 17013, 17011, 17009, 319, 16930, 16928, 104, 251, 224, 356, 16935, 10801, 16982, 10828, 557, 5618, 4218, 273, 167])).
% 4.14/4.37 tff(17088,plain,
% 4.14/4.37 (~b(z, s(elem!1))),
% 4.14/4.37 inference(modus_ponens,[status(thm)],[17087, 16918])).
% 4.14/4.37 tff(17089,plain,
% 4.14/4.37 (r(z, s(elem!1))),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[2351, 17088])).
% 4.14/4.37 tff(17090,plain,
% 4.14/4.37 (~r(s(elem!1), elem!1)),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[7070, 17089, 521])).
% 4.14/4.37 tff(17091,plain,
% 4.14/4.37 (~b(s(elem!1), elem!1)),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[16948, 17089, 557, 16935, 356, 749, 10801])).
% 4.14/4.37 tff(17092,plain,
% 4.14/4.37 ($false),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[677, 17091, 17090, 725])).
% 4.14/4.37 tff(17093,plain,(b(elem!1, z) | (s(elem!1) = elem!1) | (~r(z, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(z, elem!1)) | (~(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))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | r(s(s(z)), elem!1) | r(s(s(z)), z) | b(s(s(z)), s(s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 4.14/4.37 tff(17094,plain,
% 4.14/4.37 (b(elem!1, z)),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[17093, 16916, 16915, 16913, 16886, 16891, 104, 11349, 287, 16910, 5618, 16906, 273, 167, 47, 16899, 290])).
% 4.14/4.37 tff(17095,plain,
% 4.14/4.37 (b(s(s(s(s(z)))), z)),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[3172, 17094, 16891])).
% 4.14/4.37 tff(17096,plain,
% 4.14/4.37 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[14852, 17095, 104, 5619, 167])).
% 4.14/4.37 tff(17097,plain,
% 4.14/4.37 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[3578, 17096])).
% 4.14/4.37 tff(17098,plain,
% 4.14/4.37 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[17007, 17097, 104, 167, 16902, 16899])).
% 4.14/4.37 tff(17099,plain,
% 4.14/4.37 (r(s(s(s(z))), s(s(s(s(z)))))),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[10755, 17098])).
% 4.14/4.37 tff(17100,plain,
% 4.14/4.37 (~r(s(s(s(z))), z)),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[4899, 118, 47, 17099])).
% 4.14/4.37 tff(17101,plain,
% 4.14/4.37 (b(s(s(s(z))), z)),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[4903, 41, 77, 17100])).
% 4.14/4.37 tff(17102,plain,
% 4.14/4.37 (~r(z, s(s(s(z))))),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[4910, 118, 47, 17099])).
% 4.14/4.37 tff(17103,plain,
% 4.14/4.37 (b(z, s(s(s(z))))),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[4920, 17102])).
% 4.14/4.37 tff(17104,plain,
% 4.14/4.37 (~b(s(s(z)), s(s(s(z))))),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[7639, 178, 5619, 273, 17103, 17101])).
% 4.14/4.37 tff(17105,plain,
% 4.14/4.37 (r(s(s(z)), s(s(s(z))))),
% 4.14/4.37 inference(unit_resolution,[status(thm)],[5088, 17104])).
% 4.14/4.37 tff(17106,plain,
% 4.14/4.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 4.14/4.37 inference(rewrite,[status(thm)],[])).
% 4.14/4.37 tff(17107,plain,
% 4.14/4.37 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 4.14/4.37 inference(rewrite,[status(thm)],[])).
% 4.14/4.37 tff(17108,plain,
% 4.14/4.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))))),
% 4.14/4.38 inference(monotonicity,[status(thm)],[17107])).
% 4.14/4.38 tff(17109,plain,
% 4.14/4.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 4.14/4.38 inference(transitivity,[status(thm)],[17108, 17106])).
% 4.14/4.38 tff(17110,plain,
% 4.14/4.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 4.14/4.38 inference(quant_inst,[status(thm)],[])).
% 4.14/4.38 tff(17111,plain,
% 4.14/4.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))),
% 4.14/4.38 inference(modus_ponens,[status(thm)],[17110, 17109])).
% 4.14/4.38 tff(17112,plain,
% 4.14/4.38 (~b(s(s(s(z))), s(s(z)))),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[17111, 178, 5619, 273, 17103, 17101])).
% 4.14/4.38 tff(17113,plain,
% 4.14/4.38 (r(s(s(s(z))), s(s(z)))),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[4966, 17112])).
% 4.14/4.38 tff(17114,plain,
% 4.14/4.38 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[1175, 118, 17113, 17097])).
% 4.14/4.38 tff(17115,plain,
% 4.14/4.38 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 17114])).
% 4.14/4.38 tff(17116,plain,
% 4.14/4.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 4.14/4.38 inference(rewrite,[status(thm)],[])).
% 4.14/4.38 tff(17117,plain,
% 4.14/4.38 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 4.14/4.38 inference(rewrite,[status(thm)],[])).
% 4.14/4.38 tff(17118,plain,
% 4.14/4.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 4.14/4.38 inference(monotonicity,[status(thm)],[17117])).
% 4.14/4.38 tff(17119,plain,
% 4.14/4.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 4.14/4.38 inference(transitivity,[status(thm)],[17118, 17116])).
% 4.14/4.38 tff(17120,plain,
% 4.14/4.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 4.14/4.38 inference(quant_inst,[status(thm)],[])).
% 4.14/4.38 tff(17121,plain,
% 4.14/4.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 4.14/4.38 inference(modus_ponens,[status(thm)],[17120, 17119])).
% 4.14/4.38 tff(17122,plain,
% 4.14/4.38 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[17121, 178, 104, 17095, 17101, 17115])).
% 4.14/4.38 tff(17123,plain,
% 4.14/4.38 (r(s(s(s(s(z)))), s(s(s(z))))),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[11185, 17122])).
% 4.14/4.38 tff(17124,plain,
% 4.14/4.38 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 4.14/4.38 inference(rewrite,[status(thm)],[])).
% 4.14/4.38 tff(17125,plain,
% 4.14/4.38 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 4.14/4.38 inference(rewrite,[status(thm)],[])).
% 4.14/4.38 tff(17126,plain,
% 4.14/4.38 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 4.14/4.38 inference(monotonicity,[status(thm)],[17125])).
% 4.14/4.38 tff(17127,plain,
% 4.14/4.38 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 4.14/4.38 inference(transitivity,[status(thm)],[17126, 17124])).
% 4.14/4.38 tff(17128,plain,
% 4.14/4.38 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 4.14/4.38 inference(quant_inst,[status(thm)],[])).
% 4.14/4.38 tff(17129,plain,
% 4.14/4.38 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 4.14/4.38 inference(modus_ponens,[status(thm)],[17128, 17127])).
% 4.14/4.38 tff(17130,plain,
% 4.14/4.38 (~r(s(s(s(s(z)))), s(s(z)))),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[17129, 118, 17123, 17105])).
% 4.14/4.38 tff(17131,plain,
% 4.14/4.38 (b(s(s(s(s(z)))), s(s(z)))),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[102, 17130])).
% 4.14/4.38 tff(17132,plain,
% 4.14/4.38 ($false),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[16647, 178, 5619, 273, 17095, 167, 17131])).
% 4.14/4.38 tff(17133,plain,((elem!1 = s(s(s(s(s(s(s(z)))))))) | (~b(z, s(s(z)))) | (~b(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(z)), z) | (elem!1 = z) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | r(s(s(z)), s(s(s(s(z))))) | b(z, s(s(s(s(s(s(s(z)))))))) | b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.38 tff(17134,plain,
% 4.14/4.38 (r(s(s(z)), s(s(s(s(z)))))),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[17133, 16683, 167, 104, 5618, 290, 286, 273, 4235, 1])).
% 4.14/4.38 tff(17135,plain,
% 4.14/4.38 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[5101, 17134, 47, 5619])).
% 4.14/4.38 tff(17136,plain,
% 4.14/4.38 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[10755, 17135])).
% 4.14/4.38 tff(17137,plain,
% 4.14/4.38 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[16623, 17136, 167, 11349, 287, 104])).
% 4.14/4.38 tff(17138,plain,
% 4.14/4.38 ($false),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[5031, 41, 17137, 11415, 10712])).
% 4.14/4.38 tff(17139,plain,(b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | (~b(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(z)), z) | (elem!1 = z) | (~b(z, s(s(z)))) | b(z, s(s(s(s(s(s(s(z)))))))) | b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.38 tff(17140,plain,
% 4.14/4.38 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[17139, 16581, 104, 10792, 290, 144, 4235, 1])).
% 4.14/4.38 tff(17141,plain,
% 4.14/4.38 (~b(s(s(s(s(z)))), s(s(z)))),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[259, 17140, 104, 11349, 16581])).
% 4.14/4.38 tff(17142,plain,
% 4.14/4.38 (r(s(s(s(s(z)))), s(s(z)))),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[102, 17141])).
% 4.14/4.38 tff(17143,plain,
% 4.14/4.38 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[9047, 178, 104, 17140, 16581, 11349])).
% 4.14/4.38 tff(17144,plain,
% 4.14/4.38 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[3578, 17143])).
% 4.14/4.38 tff(17145,plain,
% 4.14/4.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.14/4.38 inference(rewrite,[status(thm)],[])).
% 4.14/4.38 tff(17146,plain,
% 4.14/4.38 (((~b(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))))))))) | (~b(s(s(z)), s(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(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(z)), 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.14/4.38 inference(rewrite,[status(thm)],[])).
% 4.14/4.38 tff(17147,plain,
% 4.14/4.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(z)), s(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(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z))))))),
% 4.14/4.38 inference(monotonicity,[status(thm)],[17146])).
% 4.14/4.38 tff(17148,plain,
% 4.14/4.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(z)), s(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(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.14/4.38 inference(transitivity,[status(thm)],[17147, 17145])).
% 4.14/4.38 tff(17149,plain,
% 4.14/4.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(z)), s(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(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.14/4.38 inference(quant_inst,[status(thm)],[])).
% 4.14/4.38 tff(17150,plain,
% 4.14/4.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z))))),
% 4.14/4.38 inference(modus_ponens,[status(thm)],[17149, 17148])).
% 4.14/4.38 tff(17151,plain,
% 4.14/4.38 (~b(s(s(s(z))), s(s(z)))),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[17150, 178, 166, 167, 3922, 1126])).
% 4.14/4.38 tff(17152,plain,
% 4.14/4.38 (r(s(s(s(z))), s(s(z)))),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[4966, 17151])).
% 4.14/4.38 tff(17153,plain,
% 4.14/4.38 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[8218, 17152, 107])).
% 4.14/4.38 tff(17154,plain,
% 4.14/4.38 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[8696, 118, 193, 17152])).
% 4.14/4.38 tff(17155,plain,
% 4.14/4.38 (b(s(s(s(s(z)))), s(s(s(z))))),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[11185, 17154])).
% 4.14/4.38 tff(17156,plain,
% 4.14/4.38 ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[11182, 178, 104, 3922, 1126])).
% 4.14/4.38 tff(17157,plain,
% 4.14/4.38 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[17156, 17155])).
% 4.14/4.38 tff(17158,plain,
% 4.14/4.38 ($false),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[5031, 41, 17157, 17153, 10712])).
% 4.14/4.38 tff(17159,plain,((~b(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(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.38 tff(17160,plain,
% 4.14/4.38 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[17159, 17144, 104, 16581, 17140, 17142])).
% 4.14/4.38 tff(17161,plain,
% 4.14/4.38 (r(s(s(s(z))), s(s(s(s(z)))))),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[10755, 17160])).
% 4.14/4.38 tff(17162,plain,
% 4.14/4.38 (~r(s(s(s(z))), z)),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[4899, 118, 47, 17161])).
% 4.14/4.38 tff(17163,plain,
% 4.14/4.38 (b(s(s(s(z))), z)),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[4903, 41, 77, 17162])).
% 4.14/4.38 tff(17164,plain,
% 4.14/4.38 (~r(z, s(s(s(z))))),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[4910, 118, 47, 17161])).
% 4.14/4.38 tff(17165,plain,
% 4.14/4.38 (b(z, s(s(s(z))))),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[4920, 17164])).
% 4.14/4.38 tff(17166,plain,
% 4.14/4.38 (~b(s(s(s(z))), s(s(z)))),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[17111, 178, 10793, 144, 17165, 17163])).
% 4.14/4.38 tff(17167,plain,
% 4.14/4.38 (r(s(s(s(z))), s(s(z)))),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[4966, 17166])).
% 4.14/4.38 tff(17168,plain,
% 4.14/4.38 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 4.14/4.38 inference(rewrite,[status(thm)],[])).
% 4.14/4.38 tff(17169,plain,
% 4.14/4.38 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 4.14/4.38 inference(quant_inst,[status(thm)],[])).
% 4.14/4.38 tff(17170,plain,
% 4.14/4.38 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 4.14/4.38 inference(modus_ponens,[status(thm)],[17169, 17168])).
% 4.14/4.38 tff(17171,plain,
% 4.14/4.38 ($false),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[17170, 118, 17142, 17167, 17161])).
% 4.14/4.38 tff(17172,plain,(b(z, s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (elem!1 = z) | b(z, s(s(s(s(z))))) | r(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.38 tff(17173,plain,
% 4.14/4.38 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[17172, 290, 104, 1, 48])).
% 4.14/4.38 tff(17174,assumption,(~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 4.14/4.38 tff(17175,plain,
% 4.14/4.38 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[222, 17174])).
% 4.14/4.38 tff(17176,plain,
% 4.14/4.38 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[5624, 10794, 17175])).
% 4.14/4.38 tff(17177,plain,
% 4.14/4.38 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[249, 17176])).
% 4.14/4.38 tff(17178,plain,
% 4.14/4.38 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[3569, 193, 145, 204, 3461, 273])).
% 4.14/4.38 tff(17179,plain,
% 4.14/4.38 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[3578, 17178])).
% 4.14/4.38 tff(17180,plain,
% 4.14/4.38 ($false),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[3920, 118, 204, 193, 17179])).
% 4.14/4.38 tff(17181,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.38 tff(17182,plain,
% 4.14/4.38 (~r(s(s(s(s(z)))), s(s(z)))),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[17181, 17175, 47, 5619, 273])).
% 4.14/4.38 tff(17183,plain,
% 4.14/4.38 (b(s(s(s(s(z)))), s(s(z)))),
% 4.14/4.38 inference(unit_resolution,[status(thm)],[102, 17182])).
% 4.14/4.38 tff(17184,plain,
% 4.14/4.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 4.14/4.38 inference(rewrite,[status(thm)],[])).
% 4.14/4.38 tff(17185,plain,
% 4.14/4.38 (((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 4.14/4.38 inference(rewrite,[status(thm)],[])).
% 4.14/4.38 tff(17186,plain,
% 4.14/4.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 4.14/4.39 inference(monotonicity,[status(thm)],[17185])).
% 4.14/4.39 tff(17187,plain,
% 4.14/4.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 4.14/4.39 inference(transitivity,[status(thm)],[17186, 17184])).
% 4.14/4.39 tff(17188,plain,
% 4.14/4.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 4.14/4.39 inference(quant_inst,[status(thm)],[])).
% 4.14/4.39 tff(17189,plain,
% 4.14/4.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))),
% 4.14/4.39 inference(modus_ponens,[status(thm)],[17188, 17187])).
% 4.14/4.39 tff(17190,plain,
% 4.14/4.39 (~b(s(s(s(s(z)))), z)),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[17189, 178, 273, 17177, 17183, 595])).
% 4.14/4.39 tff(17191,plain,
% 4.14/4.39 (r(s(s(s(s(z)))), z)),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[191, 17190])).
% 4.14/4.39 tff(17192,plain,
% 4.14/4.39 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(z)))), elem!1)),
% 4.14/4.39 inference(monotonicity,[status(thm)],[699])).
% 4.14/4.39 tff(17193,plain,
% 4.14/4.39 (r(s(s(s(s(z)))), elem!1)),
% 4.14/4.39 inference(modus_ponens,[status(thm)],[204, 17192])).
% 4.14/4.39 tff(17194,plain,
% 4.14/4.39 (~r(elem!1, z)),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[6033, 17193, 194])).
% 4.14/4.39 tff(17195,plain,
% 4.14/4.39 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(z)), elem!1)),
% 4.14/4.39 inference(monotonicity,[status(thm)],[699])).
% 4.14/4.39 tff(17196,plain,
% 4.14/4.39 (b(s(s(z)), elem!1)),
% 4.14/4.39 inference(modus_ponens,[status(thm)],[166, 17195])).
% 4.14/4.39 tff(17197,plain,
% 4.14/4.39 (b(z, s(s(s(s(s(s(s(z)))))))) <=> b(z, elem!1)),
% 4.14/4.39 inference(monotonicity,[status(thm)],[699])).
% 4.14/4.39 tff(17198,plain,
% 4.14/4.39 (b(z, elem!1)),
% 4.14/4.39 inference(modus_ponens,[status(thm)],[595, 17197])).
% 4.14/4.39 tff(17199,plain,
% 4.14/4.39 (~b(elem!1, z)),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[11004, 17198, 3461, 273, 17196])).
% 4.14/4.39 tff(17200,plain,
% 4.14/4.39 ($false),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[498, 17199, 17194, 290])).
% 4.14/4.39 tff(17201,plain,((~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (elem!1 = z) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.39 tff(17202,plain,
% 4.14/4.39 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[17201, 17191, 5619, 273, 290, 595, 17175, 17177])).
% 4.14/4.39 tff(17203,plain,
% 4.14/4.39 ($false),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[3567, 178, 3461, 273, 166, 595, 1146])).
% 4.14/4.39 tff(17204,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.39 tff(17205,plain,
% 4.14/4.39 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[17204, 17177, 273, 5619, 595])).
% 4.14/4.39 tff(17206,plain,
% 4.14/4.39 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[3578, 17205])).
% 4.14/4.39 tff(17207,plain,
% 4.14/4.39 (~b(s(s(s(s(z)))), z)),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[17189, 178, 273, 166, 202, 595])).
% 4.14/4.39 tff(17208,plain,
% 4.14/4.39 (r(s(s(s(s(z)))), z)),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[191, 17207])).
% 4.14/4.39 tff(17209,plain,
% 4.14/4.39 (~b(elem!1, s(s(z)))),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[11938, 10801, 551, 817, 17208, 202, 469])).
% 4.14/4.39 tff(17210,plain,
% 4.14/4.39 ((s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 4.14/4.39 inference(symmetry,[status(thm)],[8707])).
% 4.14/4.39 tff(17211,plain,
% 4.14/4.39 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(s(s(s(s(s(z)))))))))),
% 4.14/4.39 inference(monotonicity,[status(thm)],[17210])).
% 4.14/4.39 tff(17212,plain,
% 4.14/4.39 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 4.14/4.39 inference(modus_ponens,[status(thm)],[4511, 17211])).
% 4.14/4.39 tff(17213,plain,
% 4.14/4.39 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), elem!1)),
% 4.14/4.39 inference(symmetry,[status(thm)],[8290])).
% 4.14/4.39 tff(17214,plain,
% 4.14/4.39 ((~b(s(s(z)), s(s(s(elem!1))))) <=> (~b(s(s(z)), elem!1))),
% 4.14/4.39 inference(monotonicity,[status(thm)],[17213])).
% 4.14/4.39 tff(17215,plain,
% 4.14/4.39 (~b(s(s(z)), elem!1)),
% 4.14/4.39 inference(modus_ponens,[status(thm)],[4218, 17214])).
% 4.14/4.39 tff(17216,plain,
% 4.14/4.39 ($false),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[817, 17215])).
% 4.14/4.39 tff(17217,plain,((~(elem!1 = s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | b(s(s(z)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.39 tff(17218,plain,
% 4.14/4.39 (b(s(s(z)), s(s(s(elem!1))))),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[17217, 1527, 817])).
% 4.14/4.39 tff(17219,plain,
% 4.14/4.39 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.14/4.39 inference(modus_ponens,[status(thm)],[869, 3810])).
% 4.14/4.39 tff(17220,plain,
% 4.14/4.39 (b(elem!1, z) <=> b(s(s(s(elem!1))), z)),
% 4.14/4.39 inference(monotonicity,[status(thm)],[1527])).
% 4.14/4.39 tff(17221,plain,
% 4.14/4.39 (~b(elem!1, s(s(s(s(z)))))),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[1309, 869, 104, 818, 595])).
% 4.14/4.39 tff(17222,plain,
% 4.14/4.39 (r(elem!1, s(s(s(s(z)))))),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[483, 17221, 469])).
% 4.14/4.39 tff(17223,plain,
% 4.14/4.39 (~r(elem!1, z)),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[478, 17222, 145])).
% 4.14/4.39 tff(17224,plain,
% 4.14/4.39 (b(elem!1, z)),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[498, 17223, 290])).
% 4.14/4.39 tff(17225,plain,
% 4.14/4.39 (b(s(s(s(elem!1))), z)),
% 4.14/4.39 inference(modus_ponens,[status(thm)],[17224, 17220])).
% 4.14/4.39 tff(17226,plain,
% 4.14/4.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 4.14/4.39 inference(rewrite,[status(thm)],[])).
% 4.14/4.39 tff(17227,plain,
% 4.14/4.39 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(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(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 4.14/4.39 inference(rewrite,[status(thm)],[])).
% 4.14/4.39 tff(17228,plain,
% 4.14/4.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))))),
% 4.14/4.39 inference(monotonicity,[status(thm)],[17227])).
% 4.14/4.39 tff(17229,plain,
% 4.14/4.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 4.14/4.39 inference(transitivity,[status(thm)],[17228, 17226])).
% 4.14/4.39 tff(17230,plain,
% 4.14/4.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 4.14/4.39 inference(quant_inst,[status(thm)],[])).
% 4.14/4.39 tff(17231,plain,
% 4.14/4.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 4.14/4.39 inference(modus_ponens,[status(thm)],[17230, 17229])).
% 4.14/4.39 tff(17232,plain,
% 4.14/4.39 ($false),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[17231, 178, 17225, 3461, 4291, 595, 17219])).
% 4.14/4.39 tff(17233,plain,((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(s(s(elem!1))))) | (elem!1 = z) | (~r(z, s(s(s(s(z)))))) | (elem!1 = s(s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.39 tff(17234,plain,
% 4.14/4.39 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[17233, 5619, 17218, 595, 1527, 290, 145, 4520, 104, 7961])).
% 4.14/4.39 tff(17235,plain,
% 4.14/4.39 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[691, 17234, 17212])).
% 4.14/4.39 tff(17236,plain,
% 4.14/4.39 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 4.14/4.39 inference(monotonicity,[status(thm)],[2855])).
% 4.14/4.39 tff(17237,plain,
% 4.14/4.39 (r(elem!1, s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 4.14/4.39 inference(symmetry,[status(thm)],[17236])).
% 4.14/4.39 tff(17238,plain,
% 4.14/4.39 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(z))) = elem!1)),
% 4.14/4.39 inference(monotonicity,[status(thm)],[2855])).
% 4.14/4.39 tff(17239,plain,
% 4.14/4.39 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(z))))),
% 4.14/4.39 inference(transitivity,[status(thm)],[17238, 10420])).
% 4.14/4.39 tff(17240,plain,
% 4.14/4.39 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(s(z)))))),
% 4.14/4.39 inference(monotonicity,[status(thm)],[17239])).
% 4.14/4.39 tff(17241,plain,
% 4.14/4.39 (~(elem!1 = s(s(s(z))))),
% 4.14/4.39 inference(modus_ponens,[status(thm)],[8246, 17240])).
% 4.14/4.39 tff(17242,plain,
% 4.14/4.39 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 4.14/4.39 inference(monotonicity,[status(thm)],[2855])).
% 4.14/4.39 tff(17243,plain,
% 4.14/4.39 ((~b(s(s(s(elem!1))), s(s(s(z))))) <=> (~b(elem!1, s(s(s(z)))))),
% 4.14/4.39 inference(monotonicity,[status(thm)],[17242])).
% 4.14/4.39 tff(17244,plain,
% 4.14/4.39 ((s(s(s(s(z)))) = elem!1) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 4.14/4.39 inference(monotonicity,[status(thm)],[1527])).
% 4.14/4.39 tff(17245,plain,
% 4.14/4.39 ((s(s(s(s(z)))) = elem!1) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.14/4.39 inference(transitivity,[status(thm)],[17244, 3289])).
% 4.14/4.39 tff(17246,plain,
% 4.14/4.39 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(s(s(s(elem!1))) = s(s(s(s(z))))))),
% 4.14/4.39 inference(monotonicity,[status(thm)],[17245])).
% 4.14/4.39 tff(17247,plain,
% 4.14/4.39 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.14/4.39 inference(modus_ponens,[status(thm)],[4510, 17246])).
% 4.14/4.39 tff(17248,plain,
% 4.14/4.39 (~r(z, s(s(z)))),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[11793, 5723, 290, 5618, 461])).
% 4.14/4.39 tff(17249,plain,
% 4.14/4.39 (b(z, s(s(z)))),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[143, 17248])).
% 4.14/4.39 tff(17250,plain,
% 4.14/4.39 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[8280, 17249, 194, 202, 595, 145, 2043, 461])).
% 4.14/4.39 tff(17251,plain,
% 4.14/4.39 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[4173, 17250, 17247])).
% 4.14/4.39 tff(17252,plain,
% 4.14/4.39 (b(s(s(s(s(z)))), elem!1)),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[3142, 10826, 4510])).
% 4.14/4.39 tff(17253,plain,
% 4.14/4.39 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.14/4.39 inference(modus_ponens,[status(thm)],[17252, 3290])).
% 4.14/4.39 tff(17254,plain,
% 4.14/4.39 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[8949, 178, 2043, 104, 595, 17251])).
% 4.14/4.39 tff(17255,plain,
% 4.14/4.39 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[5118, 17254, 4511])).
% 4.14/4.39 tff(17256,plain,
% 4.14/4.39 (~b(s(s(z)), s(s(s(s(z)))))),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[10667, 17253, 202, 17251, 4291])).
% 4.14/4.39 tff(17257,plain,
% 4.14/4.39 (r(s(s(z)), s(s(s(s(z)))))),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[164, 17256])).
% 4.14/4.39 tff(17258,plain,
% 4.14/4.39 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[5101, 17257, 5619, 145])).
% 4.14/4.39 tff(17259,plain,
% 4.14/4.39 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[4928, 17258, 4890])).
% 4.14/4.39 tff(17260,plain,
% 4.14/4.39 (~b(z, s(s(s(z))))),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[9431, 17259, 104, 17255, 17251, 8246, 2043, 595])).
% 4.14/4.39 tff(17261,plain,
% 4.14/4.39 (r(z, s(s(s(z))))),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[4920, 17260])).
% 4.14/4.39 tff(17262,plain,
% 4.14/4.39 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[4961, 17261, 194])).
% 4.14/4.39 tff(17263,plain,
% 4.14/4.39 (b(s(s(s(s(z)))), s(s(s(z))))),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[4950, 17262, 4938])).
% 4.14/4.39 tff(17264,plain,
% 4.14/4.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 4.14/4.39 inference(rewrite,[status(thm)],[])).
% 4.14/4.39 tff(17265,plain,
% 4.14/4.39 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(s(z)))), 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(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 4.14/4.39 inference(rewrite,[status(thm)],[])).
% 4.14/4.39 tff(17266,plain,
% 4.14/4.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 4.14/4.39 inference(monotonicity,[status(thm)],[17265])).
% 4.14/4.39 tff(17267,plain,
% 4.14/4.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 4.14/4.39 inference(transitivity,[status(thm)],[17266, 17264])).
% 4.14/4.39 tff(17268,plain,
% 4.14/4.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 4.14/4.39 inference(quant_inst,[status(thm)],[])).
% 4.14/4.39 tff(17269,plain,
% 4.14/4.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 4.14/4.39 inference(modus_ponens,[status(thm)],[17268, 17267])).
% 4.14/4.39 tff(17270,plain,
% 4.14/4.39 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[17269, 178, 17259, 17263, 17253, 17251])).
% 4.14/4.39 tff(17271,plain,
% 4.14/4.39 (~b(elem!1, s(s(s(z))))),
% 4.14/4.39 inference(modus_ponens,[status(thm)],[17270, 17243])).
% 4.14/4.39 tff(17272,plain,
% 4.14/4.39 (((~![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)))))),
% 4.14/4.39 inference(rewrite,[status(thm)],[])).
% 4.14/4.39 tff(17273,plain,
% 4.14/4.39 ((~![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)))))),
% 4.14/4.39 inference(quant_inst,[status(thm)],[])).
% 4.14/4.39 tff(17274,plain,
% 4.14/4.39 ((~![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))))),
% 4.14/4.39 inference(modus_ponens,[status(thm)],[17273, 17272])).
% 4.14/4.39 tff(17275,plain,
% 4.14/4.39 ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z))))),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[17274, 41])).
% 4.14/4.39 tff(17276,plain,
% 4.14/4.39 (r(elem!1, s(s(s(z))))),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[17275, 17271, 17241])).
% 4.14/4.39 tff(17277,plain,
% 4.14/4.39 (r(s(s(s(elem!1))), s(s(s(z))))),
% 4.14/4.39 inference(modus_ponens,[status(thm)],[17276, 17237])).
% 4.14/4.39 tff(17278,plain,
% 4.14/4.39 (~b(s(s(s(elem!1))), z)),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[7978, 17249, 2043, 4291, 5619])).
% 4.14/4.39 tff(17279,plain,
% 4.14/4.39 (r(s(s(s(elem!1))), z)),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[1565, 17278])).
% 4.14/4.39 tff(17280,plain,
% 4.14/4.39 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 4.14/4.39 inference(rewrite,[status(thm)],[])).
% 4.14/4.39 tff(17281,plain,
% 4.14/4.39 (((~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 4.14/4.39 inference(rewrite,[status(thm)],[])).
% 4.14/4.39 tff(17282,plain,
% 4.14/4.39 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 4.14/4.39 inference(monotonicity,[status(thm)],[17281])).
% 4.14/4.39 tff(17283,plain,
% 4.14/4.39 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 4.14/4.39 inference(transitivity,[status(thm)],[17282, 17280])).
% 4.14/4.39 tff(17284,plain,
% 4.14/4.39 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), z)))),
% 4.14/4.39 inference(quant_inst,[status(thm)],[])).
% 4.14/4.39 tff(17285,plain,
% 4.14/4.39 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 4.14/4.39 inference(modus_ponens,[status(thm)],[17284, 17283])).
% 4.14/4.39 tff(17286,plain,
% 4.14/4.39 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[17285, 118, 17279, 17261])).
% 4.14/4.39 tff(17287,plain,
% 4.14/4.39 ($false),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[17286, 17277])).
% 4.14/4.39 tff(17288,plain,(b(elem!1, z) | (~(elem!1 = s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | b(elem!1, s(s(z))) | (elem!1 = z) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 4.14/4.39 tff(17289,plain,
% 4.14/4.39 (b(elem!1, z)),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[17288, 5618, 194, 104, 8246, 2043, 595, 145, 202, 17218, 461, 290, 1527])).
% 4.14/4.39 tff(17290,plain,
% 4.14/4.39 (~b(z, s(s(z)))),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[11004, 17289, 7961, 817, 5619])).
% 4.14/4.39 tff(17291,plain,
% 4.14/4.39 (r(z, s(s(z)))),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[143, 17290])).
% 4.14/4.39 tff(17292,plain,
% 4.14/4.39 (~r(s(s(z)), s(s(s(s(z)))))),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[3478, 17291, 145])).
% 4.14/4.39 tff(17293,plain,
% 4.14/4.39 (b(s(s(z)), s(s(s(s(z)))))),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[164, 17292])).
% 4.14/4.39 tff(17294,plain,
% 4.14/4.39 (~r(elem!1, s(s(s(s(z)))))),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[9221, 118, 1265, 204])).
% 4.14/4.39 tff(17295,plain,
% 4.14/4.39 (b(elem!1, s(s(s(s(z)))))),
% 4.14/4.39 inference(unit_resolution,[status(thm)],[483, 17294, 3130])).
% 4.14/4.39 tff(17296,plain,
% 4.14/4.39 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 4.14/4.39 inference(rewrite,[status(thm)],[])).
% 4.14/4.39 tff(17297,plain,
% 4.14/4.39 (((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~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(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 4.14/4.39 inference(rewrite,[status(thm)],[])).
% 4.14/4.39 tff(17298,plain,
% 4.14/4.39 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), elem!1))))),
% 4.14/4.39 inference(monotonicity,[status(thm)],[17297])).
% 4.14/4.39 tff(17299,plain,
% 4.14/4.39 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 4.14/4.40 inference(transitivity,[status(thm)],[17298, 17296])).
% 4.14/4.40 tff(17300,plain,
% 4.14/4.40 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 4.14/4.40 inference(quant_inst,[status(thm)],[])).
% 4.14/4.40 tff(17301,plain,
% 4.14/4.40 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), elem!1))),
% 4.14/4.40 inference(modus_ponens,[status(thm)],[17300, 17299])).
% 4.14/4.40 tff(17302,plain,
% 4.14/4.40 (~r(s(s(s(s(z)))), elem!1)),
% 4.14/4.40 inference(unit_resolution,[status(thm)],[17301, 118, 1265, 204])).
% 4.14/4.40 tff(17303,plain,
% 4.14/4.40 (b(s(s(s(s(z)))), elem!1)),
% 4.14/4.40 inference(unit_resolution,[status(thm)],[3142, 17302, 323])).
% 4.14/4.40 tff(17304,plain,
% 4.14/4.40 ($false),
% 4.14/4.40 inference(unit_resolution,[status(thm)],[3149, 178, 817, 17303, 17295, 167, 202])).
% 4.14/4.40 tff(17305,plain,((~r(elem!1, s(s(s(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)))), s(s(z)))) | (s(s(s(s(z)))) = elem!1) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.14/4.40 tff(17306,plain,
% 4.14/4.40 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.14/4.40 inference(unit_resolution,[status(thm)],[17305, 17293, 17235, 202, 4510, 817])).
% 4.14/4.40 tff(17307,plain,
% 4.14/4.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 4.14/4.40 inference(rewrite,[status(thm)],[])).
% 4.14/4.40 tff(17308,plain,
% 4.14/4.40 (((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 4.14/4.40 inference(rewrite,[status(thm)],[])).
% 4.14/4.40 tff(17309,plain,
% 4.14/4.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 4.14/4.40 inference(monotonicity,[status(thm)],[17308])).
% 4.14/4.40 tff(17310,plain,
% 4.14/4.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 4.14/4.40 inference(transitivity,[status(thm)],[17309, 17307])).
% 4.14/4.40 tff(17311,plain,
% 4.14/4.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 4.24/4.40 inference(quant_inst,[status(thm)],[])).
% 4.24/4.40 tff(17312,plain,
% 4.24/4.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 4.24/4.40 inference(modus_ponens,[status(thm)],[17311, 17310])).
% 4.24/4.40 tff(17313,plain,
% 4.24/4.40 (~b(s(s(z)), s(s(z)))),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[17312, 178, 817, 202])).
% 4.24/4.40 tff(17314,plain,
% 4.24/4.40 (~(elem!1 = s(s(z)))),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[3238, 817, 17313])).
% 4.24/4.40 tff(17315,plain,
% 4.24/4.40 (r(elem!1, s(s(z)))),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[467, 17314, 461])).
% 4.24/4.40 tff(17316,plain,
% 4.24/4.40 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[3113, 17235, 17315])).
% 4.24/4.40 tff(17317,plain,
% 4.24/4.40 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[249, 17316])).
% 4.24/4.40 tff(17318,plain,
% 4.24/4.40 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[259, 17293, 104, 202, 17317])).
% 4.24/4.40 tff(17319,plain,
% 4.24/4.40 ($false),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[222, 17318, 17306])).
% 4.24/4.40 tff(17320,plain,(r(s(s(z)), z) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | b(elem!1, s(s(z))) | (elem!1 = z) | (~(elem!1 = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.40 tff(17321,plain,
% 4.24/4.40 (r(s(s(z)), z)),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[17320, 1527, 202, 817, 145, 194, 8246, 2043, 595, 461, 290, 104])).
% 4.24/4.40 tff(17322,plain,
% 4.24/4.40 (~r(elem!1, z)),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[493, 8295, 202, 4520, 106, 145, 165])).
% 4.24/4.40 tff(17323,plain,
% 4.24/4.40 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[261, 106, 202, 104, 145])).
% 4.24/4.40 tff(17324,plain,
% 4.24/4.40 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[271, 17323])).
% 4.24/4.40 tff(17325,plain,
% 4.24/4.40 (b(elem!1, s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 4.24/4.40 inference(monotonicity,[status(thm)],[1527])).
% 4.24/4.40 tff(17326,plain,
% 4.24/4.40 ((~b(elem!1, s(s(z)))) <=> (~b(s(s(s(elem!1))), s(s(z))))),
% 4.24/4.40 inference(monotonicity,[status(thm)],[17325])).
% 4.24/4.40 tff(17327,plain,
% 4.24/4.40 (~b(s(s(s(elem!1))), s(s(z)))),
% 4.24/4.40 inference(modus_ponens,[status(thm)],[461, 17326])).
% 4.24/4.40 tff(17328,plain,
% 4.24/4.40 (r(s(s(s(elem!1))), s(s(z)))),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[4209, 41, 17327, 4181])).
% 4.24/4.40 tff(17329,plain,
% 4.24/4.40 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[3102, 224, 106])).
% 4.24/4.40 tff(17330,plain,
% 4.24/4.40 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[133, 17329])).
% 4.24/4.40 tff(17331,plain,
% 4.24/4.40 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[2820, 17330, 595, 2811, 1342, 8287])).
% 4.24/4.40 tff(17332,plain,
% 4.24/4.40 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[691, 17331, 701])).
% 4.24/4.40 tff(17333,plain,
% 4.24/4.40 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.40 inference(modus_ponens,[status(thm)],[17332, 5004])).
% 4.24/4.40 tff(17334,plain,
% 4.24/4.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 4.24/4.40 inference(rewrite,[status(thm)],[])).
% 4.24/4.40 tff(17335,plain,
% 4.24/4.40 (((~r(s(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(s(s(elem!1))), s(s(z))))) <=> ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 4.24/4.40 inference(rewrite,[status(thm)],[])).
% 4.24/4.40 tff(17336,plain,
% 4.24/4.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))))),
% 4.24/4.40 inference(monotonicity,[status(thm)],[17335])).
% 4.24/4.40 tff(17337,plain,
% 4.24/4.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 4.24/4.40 inference(transitivity,[status(thm)],[17336, 17334])).
% 4.24/4.40 tff(17338,plain,
% 4.24/4.40 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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(s(s(elem!1))), s(s(z)))))),
% 4.24/4.40 inference(quant_inst,[status(thm)],[])).
% 4.24/4.40 tff(17339,plain,
% 4.24/4.40 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 4.24/4.40 inference(modus_ponens,[status(thm)],[17338, 17337])).
% 4.24/4.40 tff(17340,plain,
% 4.24/4.40 ($false),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[17339, 118, 3859, 224, 17333])).
% 4.24/4.40 tff(17341,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~(elem!1 = s(s(s(elem!1))))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | r(z, elem!1) | r(elem!1, z) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.40 tff(17342,plain,
% 4.24/4.40 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[17341, 17328, 1527, 17212, 17324, 2811, 17322, 106])).
% 4.24/4.40 tff(17343,plain,
% 4.24/4.40 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[249, 17342])).
% 4.24/4.40 tff(17344,plain,
% 4.24/4.40 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[259, 17343, 104, 202, 165])).
% 4.24/4.40 tff(17345,plain,
% 4.24/4.40 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[222, 17344])).
% 4.24/4.40 tff(17346,plain,
% 4.24/4.40 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[17305, 17345, 165, 202, 4510, 817])).
% 4.24/4.40 tff(17347,plain,
% 4.24/4.40 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[691, 17346, 17212])).
% 4.24/4.40 tff(17348,plain,
% 4.24/4.40 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.40 inference(modus_ponens,[status(thm)],[17347, 3810])).
% 4.24/4.40 tff(17349,plain,
% 4.24/4.40 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[2498, 8288, 1527])).
% 4.24/4.40 tff(17350,plain,
% 4.24/4.40 (~(s(s(s(s(z)))) = s(elem!1))),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[2168, 17349])).
% 4.24/4.40 tff(17351,plain,
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% 4.24/4.40 inference(unit_resolution,[status(thm)],[498, 17322, 9186])).
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% 4.24/4.40 ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[279, 178, 104, 165, 17324])).
% 4.24/4.40 tff(17353,plain,
% 4.24/4.40 (~b(z, s(s(z)))),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[17352, 17343])).
% 4.24/4.40 tff(17354,plain,
% 4.24/4.40 (r(z, s(s(z)))),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[143, 17353])).
% 4.24/4.40 tff(17355,plain,
% 4.24/4.40 (r(elem!1, z)),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[2820, 2811, 595, 146, 869, 507])).
% 4.24/4.40 tff(17356,plain,
% 4.24/4.40 (~r(s(s(z)), z)),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[458, 17355, 450])).
% 4.24/4.40 tff(17357,plain,
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% 4.24/4.40 inference(rewrite,[status(thm)],[])).
% 4.24/4.40 tff(17358,plain,
% 4.24/4.40 (((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), z))) <=> ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.24/4.40 inference(rewrite,[status(thm)],[])).
% 4.24/4.40 tff(17359,plain,
% 4.24/4.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 4.24/4.40 inference(monotonicity,[status(thm)],[17358])).
% 4.24/4.40 tff(17360,plain,
% 4.24/4.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.24/4.40 inference(transitivity,[status(thm)],[17359, 17357])).
% 4.24/4.40 tff(17361,plain,
% 4.24/4.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), z)))),
% 4.24/4.40 inference(quant_inst,[status(thm)],[])).
% 4.24/4.40 tff(17362,plain,
% 4.24/4.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 4.24/4.40 inference(modus_ponens,[status(thm)],[17361, 17360])).
% 4.24/4.40 tff(17363,plain,
% 4.24/4.40 ((~b(z, elem!1)) | (~b(s(s(z)), z))),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[17362, 178, 817, 869, 595])).
% 4.24/4.40 tff(17364,plain,
% 4.24/4.40 (~b(s(s(z)), z)),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[17363, 3123])).
% 4.24/4.40 tff(17365,plain,
% 4.24/4.40 ($false),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[3249, 17364, 17356])).
% 4.24/4.40 tff(17366,plain,(r(z, elem!1) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(z)))) | (z = elem!1) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.40 tff(17367,plain,
% 4.24/4.40 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[17366, 17347, 817, 17324, 2811, 7960, 8287])).
% 4.24/4.40 tff(17368,plain,
% 4.24/4.40 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[133, 17367])).
% 4.24/4.40 tff(17369,plain,
% 4.24/4.40 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[123, 17368, 106])).
% 4.24/4.40 tff(17370,plain,
% 4.24/4.40 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[3578, 17369])).
% 4.24/4.40 tff(17371,plain,
% 4.24/4.40 (r(s(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))))))))),
% 4.24/4.40 inference(monotonicity,[status(thm)],[4021])).
% 4.24/4.40 tff(17372,plain,
% 4.24/4.40 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.40 inference(symmetry,[status(thm)],[17371])).
% 4.24/4.40 tff(17373,plain,
% 4.24/4.40 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[4015, 17350, 1527])).
% 4.24/4.40 tff(17374,plain,
% 4.24/4.40 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[4019, 17373])).
% 4.24/4.40 tff(17375,plain,
% 4.24/4.40 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(z)) = s(elem!1))),
% 4.24/4.40 inference(transitivity,[status(thm)],[3303, 1359])).
% 4.24/4.40 tff(17376,plain,
% 4.24/4.40 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(s(s(z)) = s(elem!1)))),
% 4.24/4.40 inference(monotonicity,[status(thm)],[17375])).
% 4.24/4.40 tff(17377,plain,
% 4.24/4.40 (~(s(s(z)) = s(elem!1))),
% 4.24/4.40 inference(modus_ponens,[status(thm)],[2131, 17376])).
% 4.24/4.40 tff(17378,plain,
% 4.24/4.40 (b(s(elem!1), s(s(z)))),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[421, 927, 3305])).
% 4.24/4.40 tff(17379,plain,
% 4.24/4.40 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[14677, 17378, 3261, 1146, 17377, 595, 166])).
% 4.24/4.40 tff(17380,plain,
% 4.24/4.40 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[395, 17379, 17374])).
% 4.24/4.40 tff(17381,plain,
% 4.24/4.40 (r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.40 inference(modus_ponens,[status(thm)],[17380, 17372])).
% 4.24/4.40 tff(17382,plain,
% 4.24/4.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 4.24/4.40 inference(rewrite,[status(thm)],[])).
% 4.24/4.40 tff(17383,plain,
% 4.24/4.40 (((~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 4.24/4.40 inference(rewrite,[status(thm)],[])).
% 4.24/4.40 tff(17384,plain,
% 4.24/4.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))))),
% 4.24/4.40 inference(monotonicity,[status(thm)],[17383])).
% 4.24/4.40 tff(17385,plain,
% 4.24/4.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 4.24/4.40 inference(transitivity,[status(thm)],[17384, 17382])).
% 4.24/4.40 tff(17386,plain,
% 4.24/4.40 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 4.24/4.40 inference(quant_inst,[status(thm)],[])).
% 4.24/4.40 tff(17387,plain,
% 4.24/4.40 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))),
% 4.24/4.40 inference(modus_ponens,[status(thm)],[17386, 17385])).
% 4.24/4.40 tff(17388,plain,
% 4.24/4.40 ((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[17387, 118, 204])).
% 4.24/4.40 tff(17389,plain,
% 4.24/4.40 (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[17388, 17381])).
% 4.24/4.40 tff(17390,plain,
% 4.24/4.40 (~r(s(s(s(s(z)))), s(elem!1))),
% 4.24/4.40 inference(modus_ponens,[status(thm)],[17389, 8899])).
% 4.24/4.40 tff(17391,plain,
% 4.24/4.40 (b(s(s(s(s(z)))), s(elem!1))),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[2173, 17390, 17350])).
% 4.24/4.40 tff(17392,plain,
% 4.24/4.40 (b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 4.24/4.40 inference(modus_ponens,[status(thm)],[17391, 8897])).
% 4.24/4.40 tff(17393,plain,
% 4.24/4.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 4.24/4.40 inference(rewrite,[status(thm)],[])).
% 4.24/4.40 tff(17394,plain,
% 4.24/4.40 (((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 4.24/4.40 inference(rewrite,[status(thm)],[])).
% 4.24/4.40 tff(17395,plain,
% 4.24/4.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))))),
% 4.24/4.40 inference(monotonicity,[status(thm)],[17394])).
% 4.24/4.40 tff(17396,plain,
% 4.24/4.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 4.24/4.40 inference(transitivity,[status(thm)],[17395, 17393])).
% 4.24/4.40 tff(17397,plain,
% 4.24/4.40 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 4.24/4.40 inference(quant_inst,[status(thm)],[])).
% 4.24/4.40 tff(17398,plain,
% 4.24/4.40 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))),
% 4.24/4.40 inference(modus_ponens,[status(thm)],[17397, 17396])).
% 4.24/4.40 tff(17399,plain,
% 4.24/4.40 ((~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[17398, 118, 204])).
% 4.24/4.40 tff(17400,plain,
% 4.24/4.40 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[17399, 17381])).
% 4.24/4.40 tff(17401,plain,
% 4.24/4.40 (~r(s(elem!1), s(s(s(s(z)))))),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[6511, 17400, 1527])).
% 4.24/4.40 tff(17402,plain,
% 4.24/4.40 (b(s(elem!1), s(s(s(s(z)))))),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[1084, 17401, 17349])).
% 4.24/4.40 tff(17403,plain,
% 4.24/4.40 (b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 4.24/4.40 inference(modus_ponens,[status(thm)],[17402, 3872])).
% 4.24/4.40 tff(17404,plain,
% 4.24/4.40 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[3907, 927, 3894])).
% 4.24/4.40 tff(17405,plain,
% 4.24/4.40 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[1170, 17404])).
% 4.24/4.40 tff(17406,plain,
% 4.24/4.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 4.24/4.40 inference(rewrite,[status(thm)],[])).
% 4.24/4.40 tff(17407,plain,
% 4.24/4.40 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 4.24/4.40 inference(rewrite,[status(thm)],[])).
% 4.24/4.40 tff(17408,plain,
% 4.24/4.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))))),
% 4.24/4.40 inference(monotonicity,[status(thm)],[17407])).
% 4.24/4.40 tff(17409,plain,
% 4.24/4.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 4.24/4.40 inference(transitivity,[status(thm)],[17408, 17406])).
% 4.24/4.40 tff(17410,plain,
% 4.24/4.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 4.24/4.40 inference(quant_inst,[status(thm)],[])).
% 4.24/4.40 tff(17411,plain,
% 4.24/4.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 4.24/4.40 inference(modus_ponens,[status(thm)],[17410, 17409])).
% 4.24/4.40 tff(17412,plain,
% 4.24/4.40 (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[17411, 178, 17405, 167, 202, 17403])).
% 4.24/4.40 tff(17413,plain,
% 4.24/4.40 ($false),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[17412, 17392])).
% 4.24/4.40 tff(17414,plain,(r(s(elem!1), s(s(z))) | (~(elem!1 = s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.40 tff(17415,plain,
% 4.24/4.40 (r(s(elem!1), s(s(z)))),
% 4.24/4.40 inference(unit_resolution,[status(thm)],[17414, 17370, 202, 165, 1527, 17354, 17345, 17324, 17343])).
% 4.24/4.41 tff(17416,plain,
% 4.24/4.41 (~b(s(elem!1), z)),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[2550, 363, 506, 450, 725, 818])).
% 4.24/4.41 tff(17417,plain,
% 4.24/4.41 ($false),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[774, 17416, 2400])).
% 4.24/4.41 tff(17418,plain,((~r(s(elem!1), s(s(z)))) | (~b(elem!1, z)) | (~r(elem!1, s(s(z)))) | (s(elem!1) = elem!1) | (~b(z, elem!1)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.41 tff(17419,plain,
% 4.24/4.41 (s(elem!1) = elem!1),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[17418, 17415, 7960, 17351, 7961, 106])).
% 4.24/4.41 tff(17420,plain,
% 4.24/4.41 (b(s(elem!1), s(s(z))) <=> b(elem!1, s(s(z)))),
% 4.24/4.41 inference(monotonicity,[status(thm)],[668])).
% 4.24/4.41 tff(17421,plain,
% 4.24/4.41 (b(elem!1, s(s(z))) <=> b(s(elem!1), s(s(z)))),
% 4.24/4.41 inference(symmetry,[status(thm)],[17420])).
% 4.24/4.41 tff(17422,plain,
% 4.24/4.41 ((~b(elem!1, s(s(z)))) <=> (~b(s(elem!1), s(s(z))))),
% 4.24/4.41 inference(monotonicity,[status(thm)],[17421])).
% 4.24/4.41 tff(17423,plain,
% 4.24/4.41 (~b(s(elem!1), s(s(z)))),
% 4.24/4.41 inference(modus_ponens,[status(thm)],[461, 17422])).
% 4.24/4.41 tff(17424,plain,
% 4.24/4.41 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[703, 12575])).
% 4.24/4.41 tff(17425,plain,
% 4.24/4.41 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[3901, 12578, 461])).
% 4.24/4.41 tff(17426,plain,
% 4.24/4.41 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[1170, 17425])).
% 4.24/4.41 tff(17427,plain,
% 4.24/4.41 (r(s(elem!1), s(s(z)))),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[3907, 17426, 13449])).
% 4.24/4.41 tff(17428,plain,
% 4.24/4.41 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.24/4.41 inference(monotonicity,[status(thm)],[668])).
% 4.24/4.41 tff(17429,plain,
% 4.24/4.41 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.41 inference(symmetry,[status(thm)],[17428])).
% 4.24/4.41 tff(17430,plain,
% 4.24/4.41 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.41 inference(modus_ponens,[status(thm)],[1265, 17429])).
% 4.24/4.41 tff(17431,plain,
% 4.24/4.41 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[390, 17430, 363])).
% 4.24/4.41 tff(17432,plain,
% 4.24/4.41 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[249, 17431])).
% 4.24/4.41 tff(17433,plain,
% 4.24/4.41 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[259, 17432, 202, 167, 104])).
% 4.24/4.41 tff(17434,plain,
% 4.24/4.41 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[222, 17433])).
% 4.24/4.41 tff(17435,plain,
% 4.24/4.41 ($false),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[17301, 118, 3132, 1265, 17434])).
% 4.24/4.41 tff(17436,plain,((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(z)))) | (~(s(elem!1) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.41 tff(17437,plain,
% 4.24/4.41 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[17436, 17427, 202, 167, 104, 3132, 668])).
% 4.24/4.41 tff(17438,plain,
% 4.24/4.41 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[691, 17437, 12575])).
% 4.24/4.41 tff(17439,plain,
% 4.24/4.41 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[2574, 178, 818, 506, 869, 3664])).
% 4.24/4.41 tff(17440,plain,
% 4.24/4.41 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[133, 17439])).
% 4.24/4.41 tff(17441,plain,
% 4.24/4.41 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[123, 17440, 106])).
% 4.24/4.41 tff(17442,plain,
% 4.24/4.41 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[3578, 17441])).
% 4.24/4.41 tff(17443,plain,
% 4.24/4.41 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[3670, 178, 818, 506, 869, 3664])).
% 4.24/4.41 tff(17444,plain,
% 4.24/4.41 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[271, 17443])).
% 4.24/4.41 tff(17445,plain,
% 4.24/4.41 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[212, 17444, 145])).
% 4.24/4.41 tff(17446,plain,
% 4.24/4.41 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[222, 17445])).
% 4.24/4.41 tff(17447,plain,
% 4.24/4.41 ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[8089, 178, 104, 167, 202])).
% 4.24/4.41 tff(17448,plain,
% 4.24/4.41 ($false),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[17447, 17446, 17442])).
% 4.24/4.41 tff(17449,plain,((~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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.41 tff(17450,plain,
% 4.24/4.41 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[17449, 17438, 167, 202, 145, 106, 818, 506, 104])).
% 4.24/4.41 tff(17451,plain,
% 4.24/4.41 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[3444, 17450, 17424])).
% 4.24/4.41 tff(17452,plain,
% 4.24/4.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))),
% 4.24/4.41 inference(rewrite,[status(thm)],[])).
% 4.24/4.41 tff(17453,plain,
% 4.24/4.41 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(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)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))),
% 4.24/4.41 inference(rewrite,[status(thm)],[])).
% 4.24/4.41 tff(17454,plain,
% 4.24/4.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1))))),
% 4.24/4.41 inference(monotonicity,[status(thm)],[17453])).
% 4.24/4.41 tff(17455,plain,
% 4.24/4.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))),
% 4.24/4.41 inference(transitivity,[status(thm)],[17454, 17452])).
% 4.24/4.41 tff(17456,plain,
% 4.24/4.41 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.24/4.41 inference(quant_inst,[status(thm)],[])).
% 4.24/4.41 tff(17457,plain,
% 4.24/4.41 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1))),
% 4.24/4.41 inference(modus_ponens,[status(thm)],[17456, 17455])).
% 4.24/4.41 tff(17458,plain,
% 4.24/4.41 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[17457, 118, 3132, 17451])).
% 4.24/4.41 tff(17459,plain,
% 4.24/4.41 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[222, 17458])).
% 4.24/4.41 tff(17460,plain,
% 4.24/4.41 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[259, 17459, 202, 167, 104])).
% 4.24/4.41 tff(17461,plain,
% 4.24/4.41 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[249, 17460])).
% 4.24/4.41 tff(17462,plain,
% 4.24/4.41 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[17447, 17459])).
% 4.24/4.41 tff(17463,plain,
% 4.24/4.41 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[3578, 17462])).
% 4.24/4.41 tff(17464,plain,
% 4.24/4.41 ($false),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[809, 17463, 17461, 106, 1042, 506, 17423, 507, 202, 12, 145])).
% 4.24/4.41 tff(17465,plain,((~(s(elem!1) = elem!1)) | (~r(s(s(z)), z)) | (~b(elem!1, z)) | (z = elem!1) | (~b(s(s(s(s(z)))), s(s(z)))) | (s(s(z)) = elem!1) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | b(elem!1, s(s(z))) | (s(s(s(s(z)))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.41 tff(17466,plain,
% 4.24/4.41 (~r(s(s(s(s(z)))), elem!1)),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[17465, 17419, 145, 104, 202, 8287, 8295, 17351, 165, 106, 7961, 461, 17350])).
% 4.24/4.41 tff(17467,plain,
% 4.24/4.41 (b(s(s(s(s(z)))), elem!1)),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[3142, 17466, 4510])).
% 4.24/4.41 tff(17468,plain,
% 4.24/4.41 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.24/4.41 inference(modus_ponens,[status(thm)],[17467, 3290])).
% 4.24/4.41 tff(17469,plain,
% 4.24/4.41 ($false),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[5351, 178, 17218, 17343, 202, 17468, 17348])).
% 4.24/4.41 tff(17470,plain,((~(elem!1 = s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | b(elem!1, s(s(z))) | (~b(s(s(z)), elem!1)) | r(z, elem!1) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.41 tff(17471,plain,
% 4.24/4.41 (r(z, elem!1)),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[17470, 17321, 145, 104, 202, 461, 817, 1527, 2043])).
% 4.24/4.41 tff(17472,plain,
% 4.24/4.41 (~r(s(s(z)), s(s(s(s(z)))))),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[155, 17321, 145])).
% 4.24/4.41 tff(17473,plain,
% 4.24/4.41 (b(s(s(z)), s(s(s(s(z)))))),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[164, 17472])).
% 4.24/4.41 tff(17474,plain,
% 4.24/4.41 ($false),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[3151, 17473, 17471, 817, 202, 4510, 194, 145])).
% 4.24/4.41 tff(17475,plain,((~(elem!1 = s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | b(elem!1, s(s(z))) | (~b(z, s(s(s(elem!1))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 4.24/4.41 tff(17476,plain,
% 4.24/4.41 (~(elem!1 = s(s(s(elem!1))))),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[17475, 17209, 290, 202, 145, 104, 17208, 2043, 11613, 595, 817])).
% 4.24/4.41 tff(17477,plain,
% 4.24/4.41 (r(elem!1, z)),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[498, 5723, 3873])).
% 4.24/4.41 tff(17478,plain,
% 4.24/4.41 (~r(s(s(s(elem!1))), z)),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[6071, 17477, 3311])).
% 4.24/4.41 tff(17479,plain,
% 4.24/4.41 (b(s(s(s(elem!1))), z)),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[1565, 17478])).
% 4.24/4.41 tff(17480,plain,
% 4.24/4.41 (~b(s(s(s(elem!1))), s(s(z)))),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[8106, 178, 2043, 17479, 5619, 273])).
% 4.24/4.41 tff(17481,plain,
% 4.24/4.41 (r(s(s(s(elem!1))), s(s(z)))),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[4209, 41, 17480, 4181])).
% 4.24/4.41 tff(17482,plain,
% 4.24/4.41 ($false),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[9259, 118, 3311, 6643, 17481])).
% 4.24/4.41 tff(17483,plain,(b(elem!1, z) | (~r(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | b(elem!1, s(s(z))) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 4.24/4.41 tff(17484,plain,
% 4.24/4.41 (~r(elem!1, s(s(s(elem!1))))),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[17483, 17209, 273, 5618, 2043, 5723])).
% 4.24/4.41 tff(17485,plain,
% 4.24/4.41 (b(elem!1, s(s(s(elem!1))))),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[2054, 17484, 17476])).
% 4.24/4.41 tff(17486,plain,
% 4.24/4.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 4.24/4.41 inference(rewrite,[status(thm)],[])).
% 4.24/4.41 tff(17487,plain,
% 4.24/4.41 (((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(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(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 4.24/4.41 inference(rewrite,[status(thm)],[])).
% 4.24/4.41 tff(17488,plain,
% 4.24/4.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z))))))))),
% 4.24/4.41 inference(monotonicity,[status(thm)],[17487])).
% 4.24/4.41 tff(17489,plain,
% 4.24/4.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 4.24/4.41 inference(transitivity,[status(thm)],[17488, 17486])).
% 4.24/4.41 tff(17490,plain,
% 4.24/4.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 4.24/4.41 inference(quant_inst,[status(thm)],[])).
% 4.24/4.41 tff(17491,plain,
% 4.24/4.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z))))))),
% 4.24/4.41 inference(modus_ponens,[status(thm)],[17490, 17489])).
% 4.24/4.41 tff(17492,plain,
% 4.24/4.41 ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[17491, 178, 817, 104, 1301])).
% 4.24/4.41 tff(17493,plain,
% 4.24/4.41 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[17492, 166])).
% 4.24/4.41 tff(17494,plain,
% 4.24/4.41 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[3444, 17493, 3914])).
% 4.24/4.41 tff(17495,plain,
% 4.24/4.41 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[11027, 17494, 521])).
% 4.24/4.41 tff(17496,plain,
% 4.24/4.41 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[133, 17495])).
% 4.24/4.41 tff(17497,plain,
% 4.24/4.41 ($false),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[3486, 178, 3461, 273, 166, 595, 17496])).
% 4.24/4.41 tff(17498,plain,((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~b(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))))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.41 tff(17499,plain,
% 4.24/4.41 (~r(z, elem!1)),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[17498, 10812, 595, 166, 273, 5619, 817, 104, 3914])).
% 4.24/4.41 tff(17500,plain,
% 4.24/4.41 (b(z, elem!1)),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[585, 17499, 318])).
% 4.24/4.41 tff(17501,plain,
% 4.24/4.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 4.24/4.41 inference(rewrite,[status(thm)],[])).
% 4.24/4.41 tff(17502,plain,
% 4.24/4.41 (((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), z))) <=> ((~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 4.24/4.41 inference(rewrite,[status(thm)],[])).
% 4.24/4.41 tff(17503,plain,
% 4.24/4.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))))),
% 4.24/4.41 inference(monotonicity,[status(thm)],[17502])).
% 4.24/4.41 tff(17504,plain,
% 4.24/4.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 4.24/4.41 inference(transitivity,[status(thm)],[17503, 17501])).
% 4.24/4.41 tff(17505,plain,
% 4.24/4.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), z)))),
% 4.24/4.41 inference(quant_inst,[status(thm)],[])).
% 4.24/4.41 tff(17506,plain,
% 4.24/4.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))),
% 4.24/4.41 inference(modus_ponens,[status(thm)],[17505, 17504])).
% 4.24/4.41 tff(17507,plain,
% 4.24/4.41 ($false),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[17506, 178, 17500, 2043, 817, 5619, 17485])).
% 4.24/4.41 tff(17508,plain,(b(elem!1, z) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | r(s(s(z)), z) | (elem!1 = z) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (elem!1 = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.41 tff(17509,plain,
% 4.24/4.41 (b(elem!1, z)),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[17508, 817, 2043, 595, 166, 273, 104, 3914, 5618, 290, 202, 145, 469])).
% 4.24/4.41 tff(17510,plain,
% 4.24/4.41 (~b(z, elem!1)),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[11004, 17509, 5619, 273, 817])).
% 4.24/4.41 tff(17511,plain,
% 4.24/4.41 (r(z, elem!1)),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[585, 17510, 318])).
% 4.24/4.41 tff(17512,plain,
% 4.24/4.41 (~r(elem!1, s(s(s(s(z)))))),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[529, 17511, 145])).
% 4.24/4.41 tff(17513,plain,
% 4.24/4.41 (~b(elem!1, s(s(s(s(z)))))),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[17498, 17511, 595, 166, 273, 5619, 817, 104, 3914])).
% 4.24/4.41 tff(17514,plain,
% 4.24/4.41 ($false),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[483, 17513, 17512, 469])).
% 4.24/4.41 tff(17515,plain,((~b(s(s(z)), elem!1)) | (elem!1 = s(s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~r(z, s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | r(s(s(z)), z) | (elem!1 = z) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.41 tff(17516,plain,
% 4.24/4.41 (~b(s(s(z)), elem!1)),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[17515, 3914, 595, 166, 273, 104, 469, 47, 2043, 5618, 290, 202])).
% 4.24/4.41 tff(17517,plain,
% 4.24/4.41 (s(s(z)) = elem!1),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[448, 17516, 10828])).
% 4.24/4.41 tff(17518,plain,
% 4.24/4.41 (elem!1 = s(s(z))),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[3230, 17517])).
% 4.24/4.41 tff(17519,plain,
% 4.24/4.41 (b(elem!1, z)),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[6641, 17518, 5618])).
% 4.24/4.41 tff(17520,plain,
% 4.24/4.41 (b(z, s(s(z))) <=> b(z, elem!1)),
% 4.24/4.41 inference(monotonicity,[status(thm)],[17517])).
% 4.24/4.41 tff(17521,plain,
% 4.24/4.41 (b(z, elem!1)),
% 4.24/4.41 inference(modus_ponens,[status(thm)],[273, 17520])).
% 4.24/4.41 tff(17522,plain,
% 4.24/4.41 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.24/4.41 inference(monotonicity,[status(thm)],[17517])).
% 4.24/4.41 tff(17523,plain,
% 4.24/4.41 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.24/4.41 inference(modus_ponens,[status(thm)],[166, 17522])).
% 4.24/4.41 tff(17524,plain,
% 4.24/4.41 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[3672, 17523, 595, 17521, 17519])).
% 4.24/4.41 tff(17525,plain,
% 4.24/4.41 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[3444, 17524, 3914])).
% 4.24/4.41 tff(17526,plain,
% 4.24/4.41 (~b(elem!1, s(s(z)))),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[3223, 17517])).
% 4.24/4.41 tff(17527,plain,
% 4.24/4.41 (b(elem!1, s(s(s(elem!1))))),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[10659, 17526, 1, 17207, 17516])).
% 4.24/4.41 tff(17528,plain,
% 4.24/4.41 (~(s(s(s(elem!1))) = elem!1)),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[16438, 17527])).
% 4.24/4.41 tff(17529,plain,
% 4.24/4.41 (~b(s(s(s(elem!1))), elem!1)),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[12925, 17521, 2043, 17519, 17527])).
% 4.24/4.41 tff(17530,plain,
% 4.24/4.41 (r(s(s(s(elem!1))), elem!1)),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[570, 17529, 17528])).
% 4.24/4.41 tff(17531,plain,
% 4.24/4.41 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[4252, 118, 17530, 17525])).
% 4.24/4.41 tff(17532,plain,
% 4.24/4.41 (s(s(s(z))) = s(elem!1)),
% 4.24/4.41 inference(monotonicity,[status(thm)],[17517])).
% 4.24/4.41 tff(17533,plain,
% 4.24/4.41 (s(s(s(s(z)))) = s(s(elem!1))),
% 4.24/4.41 inference(monotonicity,[status(thm)],[17532])).
% 4.24/4.41 tff(17534,plain,
% 4.24/4.41 (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)))),
% 4.24/4.41 inference(monotonicity,[status(thm)],[17533])).
% 4.24/4.41 tff(17535,plain,
% 4.24/4.41 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.24/4.41 inference(modus_ponens,[status(thm)],[104, 17534])).
% 4.24/4.41 tff(17536,plain,
% 4.24/4.41 ((s(elem!1) = s(s(z))) <=> (s(elem!1) = elem!1)),
% 4.24/4.41 inference(monotonicity,[status(thm)],[17517])).
% 4.24/4.41 tff(17537,plain,
% 4.24/4.41 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(z)))),
% 4.24/4.41 inference(symmetry,[status(thm)],[17536])).
% 4.24/4.41 tff(17538,plain,
% 4.24/4.41 ((~(s(elem!1) = elem!1)) <=> (~(s(elem!1) = s(s(z))))),
% 4.24/4.41 inference(monotonicity,[status(thm)],[17537])).
% 4.24/4.41 tff(17539,plain,
% 4.24/4.41 (~(s(elem!1) = elem!1)),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[2150, 17528])).
% 4.24/4.41 tff(17540,plain,
% 4.24/4.41 (~(s(elem!1) = s(s(z)))),
% 4.24/4.41 inference(modus_ponens,[status(thm)],[17539, 17538])).
% 4.24/4.41 tff(17541,plain,
% 4.24/4.41 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.24/4.41 inference(unit_resolution,[status(thm)],[2840, 17540])).
% 4.24/4.41 tff(17542,plain,
% 4.24/4.41 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[4173, 17541, 4171])).
% 4.24/4.42 tff(17543,plain,
% 4.24/4.42 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[10679, 17542, 17517])).
% 4.24/4.42 tff(17544,plain,
% 4.24/4.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(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(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(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(elem!1))))))),
% 4.24/4.42 inference(rewrite,[status(thm)],[])).
% 4.24/4.42 tff(17545,plain,
% 4.24/4.42 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(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))))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(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(elem!1))))))),
% 4.24/4.42 inference(rewrite,[status(thm)],[])).
% 4.24/4.42 tff(17546,plain,
% 4.24/4.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(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(elem!1)))))))),
% 4.24/4.42 inference(monotonicity,[status(thm)],[17545])).
% 4.24/4.42 tff(17547,plain,
% 4.24/4.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(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(elem!1))))))),
% 4.24/4.42 inference(transitivity,[status(thm)],[17546, 17544])).
% 4.24/4.42 tff(17548,plain,
% 4.24/4.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 4.24/4.42 inference(quant_inst,[status(thm)],[])).
% 4.24/4.42 tff(17549,plain,
% 4.24/4.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 4.24/4.42 inference(modus_ponens,[status(thm)],[17548, 17547])).
% 4.24/4.42 tff(17550,plain,
% 4.24/4.42 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[17549, 178, 2043, 17543, 595, 17535])).
% 4.24/4.42 tff(17551,plain,
% 4.24/4.42 ($false),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[5118, 17550, 17531, 4254])).
% 4.24/4.42 tff(17552,plain,((s(s(s(s(s(s(s(z))))))) = elem!1) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | r(s(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(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | b(z, s(s(s(s(z))))) | r(s(s(z)), z) | r(s(s(z)), elem!1) | (elem!1 = s(s(s(s(z))))) | (elem!1 = z) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.42 tff(17553,plain,
% 4.24/4.42 (elem!1 = s(s(s(s(z))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[17552, 10828, 595, 10800, 104, 166, 273, 1, 5618, 3914, 2043, 290, 202])).
% 4.24/4.42 tff(17554,plain,
% 4.24/4.42 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(s(z)))))),
% 4.24/4.42 inference(monotonicity,[status(thm)],[17553])).
% 4.24/4.42 tff(17555,plain,
% 4.24/4.42 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), elem!1)),
% 4.24/4.42 inference(symmetry,[status(thm)],[17554])).
% 4.24/4.42 tff(17556,plain,
% 4.24/4.42 ((~b(s(s(z)), s(s(s(s(z)))))) <=> (~b(s(s(z)), elem!1))),
% 4.24/4.42 inference(monotonicity,[status(thm)],[17555])).
% 4.24/4.42 tff(17557,plain,
% 4.24/4.42 (~b(s(s(z)), elem!1)),
% 4.24/4.42 inference(modus_ponens,[status(thm)],[105, 17556])).
% 4.24/4.42 tff(17558,plain,
% 4.24/4.42 (s(s(s(s(z)))) = elem!1),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[325, 17553])).
% 4.24/4.42 tff(17559,plain,
% 4.24/4.42 (b(elem!1, s(s(z)))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[4509, 17558, 202])).
% 4.24/4.42 tff(17560,plain,
% 4.24/4.42 (~(s(s(z)) = elem!1)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[3223, 17559])).
% 4.24/4.42 tff(17561,plain,
% 4.24/4.42 (b(s(s(z)), elem!1)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[448, 17560, 10828])).
% 4.24/4.42 tff(17562,plain,
% 4.24/4.42 ($false),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[17561, 17557])).
% 4.24/4.42 tff(17563,plain,(r(s(s(z)), elem!1) | b(s(s(z)), s(s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | b(z, s(s(s(s(z))))) | r(s(s(z)), z) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~b(z, s(s(s(elem!1))))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 4.24/4.42 tff(17564,plain,
% 4.24/4.42 (r(s(s(z)), elem!1)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[17563, 2043, 17183, 595, 104, 17177, 273, 1, 5618, 17202, 105, 290])).
% 4.24/4.42 tff(17565,plain,
% 4.24/4.42 ($false),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[2956, 118, 438, 2953, 107])).
% 4.24/4.42 tff(17566,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.42 tff(17567,plain,
% 4.24/4.42 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[17566, 17564, 17206])).
% 4.24/4.42 tff(17568,plain,
% 4.24/4.42 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[3444, 17567, 17202])).
% 4.24/4.42 tff(17569,plain,
% 4.24/4.42 (~r(elem!1, s(s(s(s(z)))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[8763, 17564, 10794])).
% 4.24/4.42 tff(17570,plain,
% 4.24/4.42 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 4.24/4.42 inference(monotonicity,[status(thm)],[16985])).
% 4.24/4.42 tff(17571,plain,
% 4.24/4.42 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.24/4.42 inference(modus_ponens,[status(thm)],[17174, 17570])).
% 4.24/4.42 tff(17572,plain,
% 4.24/4.42 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.24/4.42 inference(monotonicity,[status(thm)],[319])).
% 4.24/4.42 tff(17573,plain,
% 4.24/4.42 (~b(z, elem!1)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[1846, 319, 1])).
% 4.24/4.42 tff(17574,plain,
% 4.24/4.42 (b(z, s(s(s(elem!1)))) <=> b(z, elem!1)),
% 4.24/4.42 inference(monotonicity,[status(thm)],[1519])).
% 4.24/4.42 tff(17575,plain,
% 4.24/4.42 (b(z, elem!1) <=> b(z, s(s(s(elem!1))))),
% 4.24/4.42 inference(symmetry,[status(thm)],[17574])).
% 4.24/4.42 tff(17576,plain,
% 4.24/4.42 ((~b(z, elem!1)) <=> (~b(z, s(s(s(elem!1)))))),
% 4.24/4.42 inference(monotonicity,[status(thm)],[17575])).
% 4.24/4.42 tff(17577,plain,
% 4.24/4.42 (~b(z, s(s(s(elem!1))))),
% 4.24/4.42 inference(modus_ponens,[status(thm)],[5786, 17576])).
% 4.24/4.42 tff(17578,plain,
% 4.24/4.42 ($false),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[2043, 17577])).
% 4.24/4.42 tff(17579,plain,((~(s(s(s(elem!1))) = elem!1)) | (~b(z, s(s(s(elem!1))))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.24/4.42 tff(17580,plain,
% 4.24/4.42 (~(s(s(s(elem!1))) = elem!1)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[17579, 17573, 2043])).
% 4.24/4.42 tff(17581,plain,
% 4.24/4.42 (~(elem!1 = s(s(s(elem!1))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[1530, 17580])).
% 4.24/4.42 tff(17582,plain,
% 4.24/4.42 (r(z, elem!1)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[585, 17573, 318])).
% 4.24/4.42 tff(17583,plain,
% 4.24/4.42 (~b(elem!1, z)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[3172, 319, 3170])).
% 4.24/4.42 tff(17584,plain,
% 4.24/4.42 (r(elem!1, z)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[498, 17583, 290])).
% 4.24/4.42 tff(17585,plain,
% 4.24/4.42 (~r(elem!1, s(s(s(elem!1))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[15029, 17584, 3461, 273, 166, 319, 17582])).
% 4.24/4.42 tff(17586,plain,
% 4.24/4.42 (b(elem!1, s(s(s(elem!1))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[2054, 17585, 17581])).
% 4.24/4.42 tff(17587,plain,
% 4.24/4.42 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.24/4.42 inference(modus_ponens,[status(thm)],[17586, 17572])).
% 4.24/4.42 tff(17588,plain,
% 4.24/4.42 ($false),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[17587, 17571])).
% 4.24/4.42 tff(17589,plain,((~(elem!1 = s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (elem!1 = z) | (~b(z, s(s(s(elem!1))))) | b(s(s(s(s(z)))), z) | b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.42 tff(17590,plain,
% 4.24/4.42 (~(elem!1 = s(s(s(s(z)))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[17589, 2043, 5619, 273, 17177, 290, 17174, 17190, 1])).
% 4.24/4.42 tff(17591,plain,
% 4.24/4.42 (b(elem!1, s(s(s(s(z)))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[483, 17590, 17569])).
% 4.24/4.42 tff(17592,plain,
% 4.24/4.42 ((~(s(s(s(s(s(s(s(z))))))) = elem!1)) <=> (~(elem!1 = s(s(s(s(s(s(s(z)))))))))),
% 4.24/4.42 inference(monotonicity,[status(thm)],[836])).
% 4.24/4.42 tff(17593,plain,
% 4.24/4.42 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 4.24/4.42 inference(modus_ponens,[status(thm)],[17202, 17592])).
% 4.24/4.42 tff(17594,plain,
% 4.24/4.42 (~(s(s(s(s(z)))) = elem!1)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[504, 17590])).
% 4.24/4.42 tff(17595,plain,
% 4.24/4.42 ((~b(z, s(s(s(s(z)))))) <=> (~b(z, s(s(s(elem!1)))))),
% 4.24/4.42 inference(monotonicity,[status(thm)],[1636])).
% 4.24/4.42 tff(17596,plain,
% 4.24/4.42 (~b(z, s(s(s(elem!1))))),
% 4.24/4.42 inference(modus_ponens,[status(thm)],[1, 17595])).
% 4.24/4.42 tff(17597,plain,
% 4.24/4.42 ($false),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[2043, 17596])).
% 4.24/4.42 tff(17598,plain,((~(s(elem!1) = s(s(z)))) | (~b(z, s(s(s(elem!1))))) | b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.42 tff(17599,plain,
% 4.24/4.42 (~(s(elem!1) = s(s(z)))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[17598, 2043, 1])).
% 4.24/4.42 tff(17600,plain,
% 4.24/4.42 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[2840, 17599])).
% 4.24/4.42 tff(17601,plain,
% 4.24/4.42 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[4173, 17600, 10800])).
% 4.24/4.42 tff(17602,plain,
% 4.24/4.42 (~b(s(s(z)), elem!1)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[17515, 17590, 595, 17177, 273, 104, 17202, 47, 2043, 5618, 290, 17183])).
% 4.24/4.42 tff(17603,plain,
% 4.24/4.42 (b(z, elem!1)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[17579, 3894, 2043])).
% 4.24/4.42 tff(17604,plain,
% 4.24/4.42 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[1309, 17603, 104, 595, 1301])).
% 4.24/4.42 tff(17605,plain,
% 4.24/4.42 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[691, 17604, 701])).
% 4.24/4.42 tff(17606,plain,
% 4.24/4.42 (~r(s(s(z)), s(s(s(elem!1))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[9492, 17605, 145, 3831, 8246, 202, 1126, 194, 104, 2043, 323, 438, 1527])).
% 4.24/4.42 tff(17607,plain,
% 4.24/4.42 (b(s(s(z)), s(s(s(elem!1))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[4223, 17606])).
% 4.24/4.42 tff(17608,plain,
% 4.24/4.42 (b(s(s(z)), elem!1)),
% 4.24/4.42 inference(modus_ponens,[status(thm)],[17607, 17213])).
% 4.24/4.42 tff(17609,plain,
% 4.24/4.42 ($false),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[3241, 17608])).
% 4.24/4.42 tff(17610,plain,((~(elem!1 = s(s(s(elem!1))))) | b(s(s(z)), elem!1) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (s(s(s(s(z)))) = elem!1) | (~r(s(s(z)), elem!1)) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.42 tff(17611,plain,
% 4.24/4.42 (~(elem!1 = s(s(s(elem!1))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[17610, 17602, 47, 17601, 11613, 17183, 10796, 17191, 104, 2043, 17594, 17564, 17593, 595, 17591])).
% 4.24/4.42 tff(17612,plain,
% 4.24/4.42 (b(s(s(s(elem!1))), elem!1)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[570, 11112, 6403])).
% 4.24/4.42 tff(17613,plain,
% 4.24/4.42 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[4173, 2857, 11628])).
% 4.24/4.42 tff(17614,plain,
% 4.24/4.42 (b(elem!1, s(s(s(elem!1))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[9401, 17613, 202, 147, 104, 701, 145, 194, 290, 2043, 3241, 323, 1586, 2857])).
% 4.24/4.42 tff(17615,plain,
% 4.24/4.42 ($false),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[6411, 17614, 17613])).
% 4.24/4.42 tff(17616,plain,((s(s(s(elem!1))) = s(s(s(s(z))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (elem!1 = z) | (~b(z, s(s(s(elem!1))))) | b(s(s(z)), elem!1) | (s(s(s(s(z)))) = elem!1) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.42 tff(17617,plain,
% 4.24/4.42 ($false),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[17616, 17612, 3143, 2857, 1301, 202, 147, 104, 701, 145, 194, 290, 2043, 3241, 323, 1586])).
% 4.24/4.42 tff(17618,plain,((~r(z, elem!1)) | (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(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (elem!1 = z) | (~b(z, s(s(s(elem!1))))) | b(s(s(z)), elem!1) | (s(s(s(s(z)))) = elem!1) | (elem!1 = s(s(s(elem!1)))) | (~r(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.42 tff(17619,plain,
% 4.24/4.42 (~r(z, elem!1)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[17618, 17591, 17600, 17183, 10794, 104, 17593, 47, 17191, 290, 2043, 17602, 17594, 17611, 17564, 5619, 273])).
% 4.24/4.42 tff(17620,plain,
% 4.24/4.42 (b(z, elem!1)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[585, 17619, 318])).
% 4.24/4.42 tff(17621,plain,
% 4.24/4.42 ($false),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[8447, 178, 17620, 104, 17591, 595, 17568])).
% 4.24/4.42 tff(17622,plain,((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (elem!1 = z) | (~b(z, s(s(z)))) | r(s(s(z)), z) | b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) | b(z, s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.42 tff(17623,plain,
% 4.24/4.42 (~b(z, s(s(s(elem!1))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[17622, 105, 595, 290, 273, 5618, 17174, 1, 104])).
% 4.24/4.42 tff(17624,plain,
% 4.24/4.42 (r(z, s(s(s(elem!1))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[2095, 17623])).
% 4.24/4.42 tff(17625,plain,
% 4.24/4.42 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[17204, 166, 273, 5619, 595])).
% 4.24/4.42 tff(17626,plain,
% 4.24/4.42 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[3578, 17625])).
% 4.24/4.42 tff(17627,plain,
% 4.24/4.42 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 4.24/4.42 inference(modus_ponens,[status(thm)],[3914, 17592])).
% 4.24/4.42 tff(17628,assumption,(~r(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 4.24/4.42 tff(17629,plain,
% 4.24/4.42 (b(s(s(s(s(z)))), s(s(z)))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[102, 17628])).
% 4.24/4.42 tff(17630,plain,
% 4.24/4.42 (~b(s(s(s(s(z)))), z)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[17189, 178, 273, 166, 17629, 595])).
% 4.24/4.42 tff(17631,plain,
% 4.24/4.42 (s(s(z)) = elem!1),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[448, 3241, 10828])).
% 4.24/4.42 tff(17632,plain,
% 4.24/4.42 ((s(elem!1) = s(s(z))) <=> (s(elem!1) = elem!1)),
% 4.24/4.42 inference(monotonicity,[status(thm)],[17631])).
% 4.24/4.42 tff(17633,plain,
% 4.24/4.42 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(z)))),
% 4.24/4.42 inference(symmetry,[status(thm)],[17632])).
% 4.24/4.42 tff(17634,plain,
% 4.24/4.42 ((~(s(elem!1) = elem!1)) <=> (~(s(elem!1) = s(s(z))))),
% 4.24/4.42 inference(monotonicity,[status(thm)],[17633])).
% 4.24/4.42 tff(17635,plain,
% 4.24/4.42 (~b(elem!1, s(s(z)))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[3223, 17631])).
% 4.24/4.42 tff(17636,plain,
% 4.24/4.42 (b(elem!1, s(s(s(elem!1))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[10659, 17635, 1, 3170, 3241])).
% 4.24/4.42 tff(17637,plain,
% 4.24/4.42 (~(s(s(s(elem!1))) = elem!1)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[16438, 17636])).
% 4.24/4.42 tff(17638,plain,
% 4.24/4.42 (~(s(elem!1) = elem!1)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[2150, 17637])).
% 4.24/4.42 tff(17639,plain,
% 4.24/4.42 (~(s(elem!1) = s(s(z)))),
% 4.24/4.42 inference(modus_ponens,[status(thm)],[17638, 17634])).
% 4.24/4.42 tff(17640,plain,
% 4.24/4.42 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[2840, 17639])).
% 4.24/4.42 tff(17641,plain,
% 4.24/4.42 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[4173, 17640, 4171])).
% 4.24/4.42 tff(17642,plain,
% 4.24/4.42 (s(s(s(z))) = s(elem!1)),
% 4.24/4.42 inference(monotonicity,[status(thm)],[17631])).
% 4.24/4.42 tff(17643,plain,
% 4.24/4.42 (s(s(s(s(z)))) = s(s(elem!1))),
% 4.24/4.42 inference(monotonicity,[status(thm)],[17642])).
% 4.24/4.42 tff(17644,plain,
% 4.24/4.42 (s(s(elem!1)) = s(s(s(s(z))))),
% 4.24/4.42 inference(symmetry,[status(thm)],[17643])).
% 4.24/4.42 tff(17645,plain,
% 4.24/4.42 (r(s(elem!1), s(s(elem!1))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 4.24/4.42 inference(monotonicity,[status(thm)],[17644])).
% 4.24/4.42 tff(17646,plain,
% 4.24/4.42 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(elem!1), s(s(elem!1)))),
% 4.24/4.42 inference(symmetry,[status(thm)],[17645])).
% 4.24/4.42 tff(17647,plain,
% 4.24/4.42 ((~r(s(elem!1), s(s(s(s(z)))))) <=> (~r(s(elem!1), s(s(elem!1))))),
% 4.24/4.42 inference(monotonicity,[status(thm)],[17646])).
% 4.24/4.42 tff(17648,plain,
% 4.24/4.42 (elem!1 = s(s(z))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[3230, 17631])).
% 4.24/4.42 tff(17649,plain,
% 4.24/4.42 (b(elem!1, z)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[6641, 17648, 5618])).
% 4.24/4.42 tff(17650,plain,
% 4.24/4.42 (~(elem!1 = s(s(s(s(z)))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[3172, 17649, 3170])).
% 4.24/4.42 tff(17651,plain,
% 4.24/4.42 (r(elem!1, s(s(s(s(z)))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[483, 17650, 13328])).
% 4.24/4.42 tff(17652,plain,
% 4.24/4.42 (~r(elem!1, s(elem!1))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[14364, 908, 470])).
% 4.24/4.42 tff(17653,plain,
% 4.24/4.42 ($false),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[7485, 17652, 908, 145, 461, 506, 725, 3461, 273, 194])).
% 4.24/4.42 tff(17654,plain,((~r(s(elem!1), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | b(elem!1, s(s(z))) | (~b(elem!1, z)) | (s(elem!1) = elem!1) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.42 tff(17655,plain,
% 4.24/4.42 (~r(s(elem!1), s(s(s(s(z)))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[17654, 17651, 47, 3244, 17649, 5619, 273, 17635, 17638])).
% 4.24/4.42 tff(17656,plain,
% 4.24/4.42 (~r(s(elem!1), s(s(elem!1)))),
% 4.24/4.42 inference(modus_ponens,[status(thm)],[17655, 17647])).
% 4.24/4.42 tff(17657,plain,
% 4.24/4.42 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 4.24/4.42 inference(monotonicity,[status(thm)],[17643])).
% 4.24/4.42 tff(17658,plain,
% 4.24/4.42 ((~r(s(s(s(s(z)))), elem!1)) <=> (~r(s(s(elem!1)), elem!1))),
% 4.24/4.42 inference(monotonicity,[status(thm)],[17657])).
% 4.24/4.42 tff(17659,plain,
% 4.24/4.42 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(z)))), elem!1)),
% 4.24/4.42 inference(monotonicity,[status(thm)],[17631])).
% 4.24/4.42 tff(17660,plain,
% 4.24/4.42 ((~r(s(s(s(s(z)))), s(s(z)))) <=> (~r(s(s(s(s(z)))), elem!1))),
% 4.24/4.42 inference(monotonicity,[status(thm)],[17659])).
% 4.24/4.42 tff(17661,plain,
% 4.24/4.42 (~r(s(s(s(s(z)))), elem!1)),
% 4.24/4.42 inference(modus_ponens,[status(thm)],[17628, 17660])).
% 4.24/4.42 tff(17662,plain,
% 4.24/4.42 (~r(s(s(elem!1)), elem!1)),
% 4.24/4.42 inference(modus_ponens,[status(thm)],[17661, 17658])).
% 4.24/4.42 tff(17663,plain,
% 4.24/4.42 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 4.24/4.42 inference(monotonicity,[status(thm)],[17642])).
% 4.24/4.42 tff(17664,plain,
% 4.24/4.42 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 4.24/4.42 inference(transitivity,[status(thm)],[17663, 3881])).
% 4.24/4.42 tff(17665,plain,
% 4.24/4.42 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 4.24/4.42 inference(monotonicity,[status(thm)],[17664])).
% 4.24/4.42 tff(17666,plain,
% 4.24/4.42 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.24/4.42 inference(modus_ponens,[status(thm)],[11613, 17665])).
% 4.24/4.42 tff(17667,plain,
% 4.24/4.42 (~(elem!1 = s(s(s(elem!1))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[1530, 17637])).
% 4.24/4.42 tff(17668,plain,
% 4.24/4.42 (~r(z, elem!1)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[529, 17651, 47])).
% 4.24/4.42 tff(17669,plain,
% 4.24/4.42 (b(z, elem!1)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[585, 17668, 318])).
% 4.24/4.42 tff(17670,plain,
% 4.24/4.42 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[1649, 17666])).
% 4.24/4.42 tff(17671,plain,
% 4.24/4.42 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.24/4.42 inference(monotonicity,[status(thm)],[17643])).
% 4.24/4.42 tff(17672,plain,
% 4.24/4.42 ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) <=> (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 4.24/4.42 inference(monotonicity,[status(thm)],[17671])).
% 4.24/4.42 tff(17673,plain,
% 4.24/4.42 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.24/4.42 inference(modus_ponens,[status(thm)],[5162, 17672])).
% 4.24/4.42 tff(17674,plain,
% 4.24/4.42 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[3375, 17673, 17670])).
% 4.24/4.42 tff(17675,plain,
% 4.24/4.42 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[5531, 17674, 557, 17669, 17667, 17666, 290, 17662, 17656])).
% 4.24/4.42 tff(17676,plain,
% 4.24/4.42 ($false),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[10679, 17675, 17641, 17631])).
% 4.24/4.42 tff(17677,plain,(b(s(s(z)), elem!1) | (~r(z, s(s(s(elem!1))))) | (elem!1 = z) | r(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(s(z)))), s(s(z))) | (~b(z, s(s(z)))) | b(elem!1, s(s(s(s(z))))) | b(s(s(s(s(z)))), z) | b(z, s(s(s(s(z))))) | r(s(s(z)), z) | r(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.24/4.42 tff(17678,plain,
% 4.24/4.42 (b(s(s(z)), elem!1)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[17677, 13328, 290, 10800, 17628, 273, 557, 3170, 1, 5618, 10828])).
% 4.24/4.42 tff(17679,plain,
% 4.24/4.42 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(s(z)))))),
% 4.24/4.42 inference(monotonicity,[status(thm)],[319])).
% 4.24/4.42 tff(17680,plain,
% 4.24/4.42 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), elem!1)),
% 4.24/4.42 inference(symmetry,[status(thm)],[17679])).
% 4.24/4.42 tff(17681,plain,
% 4.24/4.42 ((~b(s(s(z)), s(s(s(s(z)))))) <=> (~b(s(s(z)), elem!1))),
% 4.24/4.42 inference(monotonicity,[status(thm)],[17680])).
% 4.24/4.42 tff(17682,plain,
% 4.24/4.42 (~b(s(s(z)), elem!1)),
% 4.24/4.42 inference(modus_ponens,[status(thm)],[105, 17681])).
% 4.24/4.42 tff(17683,plain,
% 4.24/4.42 ($false),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[817, 17682])).
% 4.24/4.42 tff(17684,plain,((~(elem!1 = s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | b(s(s(z)), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.42 tff(17685,plain,
% 4.24/4.42 (~(elem!1 = s(s(s(s(z)))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[17684, 17678, 105])).
% 4.24/4.42 tff(17686,plain,
% 4.24/4.42 (r(elem!1, s(s(s(s(z)))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[483, 17685, 13328])).
% 4.24/4.42 tff(17687,plain,
% 4.24/4.42 (~r(z, elem!1)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[529, 17686, 47])).
% 4.24/4.42 tff(17688,plain,
% 4.24/4.42 (b(z, elem!1)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[585, 17687, 318])).
% 4.24/4.42 tff(17689,plain,
% 4.24/4.42 (~(elem!1 = s(s(z)))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[3238, 17678, 16834])).
% 4.24/4.42 tff(17690,plain,
% 4.24/4.42 (~r(elem!1, s(s(z)))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[5670, 17686, 10794])).
% 4.24/4.42 tff(17691,plain,
% 4.24/4.42 (b(elem!1, s(s(z)))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[467, 17690, 17689])).
% 4.24/4.42 tff(17692,plain,
% 4.24/4.42 ($false),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[10893, 17691, 17688, 273, 5619, 17678])).
% 4.24/4.42 tff(17693,plain,(b(elem!1, s(s(s(s(z))))) | (~b(z, s(s(z)))) | b(s(s(z)), s(s(s(s(z))))) | (elem!1 = z) | r(s(s(s(s(z)))), s(s(z))) | (~r(z, s(s(s(elem!1))))) | b(s(s(s(s(z)))), z) | b(z, s(s(s(s(z))))) | r(s(s(z)), z) | r(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.24/4.42 tff(17694,plain,
% 4.24/4.42 (b(elem!1, s(s(s(s(z)))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[17693, 10828, 105, 290, 17628, 557, 17630, 1, 5618, 273])).
% 4.24/4.42 tff(17695,plain,
% 4.24/4.42 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 4.24/4.42 inference(symmetry,[status(thm)],[9142])).
% 4.24/4.42 tff(17696,plain,
% 4.24/4.42 (b(s(s(z)), s(s(s(s(z)))))),
% 4.24/4.42 inference(modus_ponens,[status(thm)],[1301, 17695])).
% 4.24/4.42 tff(17697,plain,
% 4.24/4.42 ($false),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[105, 17696])).
% 4.24/4.42 tff(17698,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,[]))).
% 4.24/4.42 tff(17699,plain,
% 4.24/4.42 (~(s(s(z)) = elem!1)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[17698, 17694, 105])).
% 4.24/4.42 tff(17700,plain,
% 4.24/4.42 (b(s(s(z)), elem!1)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[448, 17699, 10828])).
% 4.24/4.42 tff(17701,plain,
% 4.24/4.42 ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[11723, 178, 104, 166, 17694])).
% 4.24/4.42 tff(17702,plain,
% 4.24/4.42 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[17701, 17700])).
% 4.24/4.42 tff(17703,plain,
% 4.24/4.42 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[691, 17702, 17627])).
% 4.24/4.42 tff(17704,plain,
% 4.24/4.42 (~(elem!1 = s(s(z)))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[311, 17699])).
% 4.24/4.42 tff(17705,plain,
% 4.24/4.42 (~r(z, elem!1)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[17498, 17700, 595, 166, 273, 5619, 17694, 104, 3914])).
% 4.24/4.42 tff(17706,plain,
% 4.24/4.42 (b(z, elem!1)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[585, 17705, 318])).
% 4.24/4.42 tff(17707,plain,
% 4.24/4.42 (~b(elem!1, s(s(z)))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[10893, 17706, 273, 5619, 17700])).
% 4.24/4.42 tff(17708,plain,
% 4.24/4.42 (r(elem!1, s(s(z)))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[467, 17707, 17704])).
% 4.24/4.42 tff(17709,plain,
% 4.24/4.42 ($false),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[639, 118, 17708, 17703, 17626])).
% 4.24/4.42 tff(17710,plain,(r(s(s(z)), elem!1) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | b(s(s(z)), s(s(s(s(z))))) | (elem!1 = z) | r(s(s(s(s(z)))), s(s(z))) | (~r(z, s(s(s(elem!1))))) | b(z, s(s(s(s(z))))) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 4.24/4.42 tff(17711,plain,
% 4.24/4.42 (r(s(s(z)), elem!1)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[17710, 17177, 104, 273, 595, 17202, 105, 290, 17182, 17624, 1, 5618])).
% 4.24/4.42 tff(17712,plain,
% 4.24/4.42 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[17566, 17711, 17206])).
% 4.24/4.42 tff(17713,plain,
% 4.24/4.42 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[3444, 17712, 17202])).
% 4.24/4.42 tff(17714,plain,
% 4.24/4.42 (~r(elem!1, s(s(s(s(z)))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[8763, 17711, 10794])).
% 4.24/4.42 tff(17715,plain,
% 4.24/4.42 (b(z, s(s(s(elem!1))))),
% 4.24/4.42 inference(modus_ponens,[status(thm)],[595, 11473])).
% 4.24/4.42 tff(17716,plain,
% 4.24/4.42 ($false),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[3242, 17715])).
% 4.24/4.42 tff(17717,plain,((~(elem!1 = s(s(s(s(z)))))) | b(z, s(s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.42 tff(17718,plain,
% 4.24/4.42 (~(elem!1 = s(s(s(s(z)))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[17717, 17623, 595])).
% 4.24/4.42 tff(17719,plain,
% 4.24/4.42 (b(elem!1, s(s(s(s(z)))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[483, 17718, 17714])).
% 4.24/4.42 tff(17720,plain,
% 4.24/4.42 (~(s(s(s(s(z)))) = elem!1)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[504, 17718])).
% 4.24/4.42 tff(17721,plain,
% 4.24/4.42 (~(s(s(z)) = elem!1)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[17698, 17719, 105])).
% 4.24/4.42 tff(17722,plain,
% 4.24/4.42 (~r(s(s(s(s(z)))), s(s(z)))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[17181, 204, 145, 3461, 273])).
% 4.24/4.42 tff(17723,plain,
% 4.24/4.42 (b(s(s(s(s(z)))), s(s(z)))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[102, 17722])).
% 4.24/4.42 tff(17724,plain,
% 4.24/4.42 (~b(s(s(s(s(z)))), z)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[17189, 178, 273, 166, 17723, 595])).
% 4.24/4.42 tff(17725,plain,
% 4.24/4.42 (r(s(s(s(s(z)))), z)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[191, 17724])).
% 4.24/4.42 tff(17726,plain,
% 4.24/4.42 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[3287, 557, 17725])).
% 4.24/4.42 tff(17727,plain,
% 4.24/4.42 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[17201, 17725, 3461, 273, 290, 595, 204, 166])).
% 4.24/4.42 tff(17728,plain,
% 4.24/4.42 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 4.24/4.42 inference(modus_ponens,[status(thm)],[17727, 17592])).
% 4.24/4.42 tff(17729,plain,
% 4.24/4.42 (~r(s(s(s(s(z)))), elem!1)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[3137, 521, 17725])).
% 4.24/4.42 tff(17730,plain,
% 4.24/4.42 (b(s(s(s(s(z)))), elem!1)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[3142, 17729, 323])).
% 4.24/4.42 tff(17731,plain,
% 4.24/4.42 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[4173, 2857, 4171])).
% 4.24/4.42 tff(17732,plain,
% 4.24/4.42 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[10664, 9301, 3293])).
% 4.24/4.42 tff(17733,plain,
% 4.24/4.42 (elem!1 = s(s(s(elem!1)))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[2489, 1519])).
% 4.24/4.42 tff(17734,plain,
% 4.24/4.42 (~(s(s(s(z))) = elem!1)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[4830, 17733, 2484])).
% 4.24/4.42 tff(17735,plain,
% 4.24/4.42 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[5113, 17733, 145, 3461, 3828, 701, 3831, 17734, 438, 104])).
% 4.24/4.42 tff(17736,plain,
% 4.24/4.42 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[5118, 17735, 3521])).
% 4.24/4.42 tff(17737,plain,
% 4.24/4.42 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[5130, 17736, 557])).
% 4.24/4.42 tff(17738,plain,
% 4.24/4.42 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[133, 17737])).
% 4.24/4.42 tff(17739,plain,
% 4.24/4.42 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[4057, 17738, 3461, 166, 273])).
% 4.24/4.42 tff(17740,plain,
% 4.24/4.42 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[3578, 17739])).
% 4.24/4.42 tff(17741,plain,
% 4.24/4.42 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.24/4.42 inference(monotonicity,[status(thm)],[1519])).
% 4.24/4.42 tff(17742,plain,
% 4.24/4.42 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.24/4.42 inference(modus_ponens,[status(thm)],[17736, 17741])).
% 4.24/4.42 tff(17743,plain,
% 4.24/4.42 ($false),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[2956, 118, 438, 17742, 17740])).
% 4.24/4.42 tff(17744,plain,((~(s(s(s(elem!1))) = elem!1)) | (~r(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.42 tff(17745,plain,
% 4.24/4.42 (~(s(s(s(elem!1))) = elem!1)),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[17744, 17732, 3461, 166, 273, 557, 3521, 145, 438, 701, 17731, 104, 2484])).
% 4.24/4.42 tff(17746,plain,
% 4.24/4.42 (~(elem!1 = s(s(s(elem!1))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[1530, 17745])).
% 4.24/4.42 tff(17747,plain,
% 4.24/4.42 (b(elem!1, s(s(s(elem!1))))),
% 4.24/4.42 inference(unit_resolution,[status(thm)],[2054, 17746, 4512])).
% 4.24/4.42 tff(17748,plain,
% 4.24/4.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 4.24/4.42 inference(rewrite,[status(thm)],[])).
% 4.24/4.42 tff(17749,plain,
% 4.24/4.42 (((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, 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(s(z)))), elem!1))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 4.24/4.43 inference(rewrite,[status(thm)],[])).
% 4.24/4.43 tff(17750,plain,
% 4.24/4.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, 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(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 4.24/4.43 inference(monotonicity,[status(thm)],[17749])).
% 4.24/4.43 tff(17751,plain,
% 4.24/4.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, 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(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 4.24/4.43 inference(transitivity,[status(thm)],[17750, 17748])).
% 4.24/4.43 tff(17752,plain,
% 4.24/4.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, 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(s(z)))), elem!1)))),
% 4.24/4.43 inference(quant_inst,[status(thm)],[])).
% 4.24/4.43 tff(17753,plain,
% 4.24/4.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 4.24/4.43 inference(modus_ponens,[status(thm)],[17752, 17751])).
% 4.24/4.43 tff(17754,plain,
% 4.24/4.43 ($false),
% 4.24/4.43 inference(unit_resolution,[status(thm)],[17753, 178, 17747, 3771, 1301, 17732, 17731])).
% 4.24/4.43 tff(17755,plain,((s(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(elem!1, s(s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(z))) | r(s(s(s(s(z)))), s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.43 tff(17756,plain,
% 4.24/4.43 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 4.24/4.43 inference(unit_resolution,[status(thm)],[17755, 17730, 557, 438, 3461, 166, 273, 1301, 9310, 145, 3792, 17728, 104, 3340, 17726, 4171])).
% 4.24/4.43 tff(17757,plain,
% 4.24/4.43 (s(elem!1) = s(s(z))),
% 4.24/4.43 inference(unit_resolution,[status(thm)],[2840, 17756])).
% 4.24/4.43 tff(17758,plain,
% 4.24/4.43 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 4.24/4.43 inference(monotonicity,[status(thm)],[17757])).
% 4.24/4.43 tff(17759,plain,
% 4.24/4.43 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 4.24/4.43 inference(symmetry,[status(thm)],[17758])).
% 4.24/4.43 tff(17760,plain,
% 4.24/4.43 (s(z) = elem!1),
% 4.24/4.43 inference(transitivity,[status(thm)],[71, 17759, 304])).
% 4.24/4.43 tff(17761,plain,
% 4.24/4.43 (r(s(z), s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.24/4.43 inference(monotonicity,[status(thm)],[17760])).
% 4.24/4.43 tff(17762,plain,
% 4.24/4.43 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(s(z), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.43 inference(symmetry,[status(thm)],[17761])).
% 4.24/4.43 tff(17763,plain,
% 4.24/4.43 (~(s(z) = s(s(z)))),
% 4.24/4.43 inference(unit_resolution,[status(thm)],[2610, 17757, 12])).
% 4.24/4.43 tff(17764,plain,
% 4.24/4.43 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.24/4.43 inference(unit_resolution,[status(thm)],[17204, 166, 273, 3461, 595])).
% 4.24/4.43 tff(17765,plain,
% 4.24/4.43 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.24/4.43 inference(unit_resolution,[status(thm)],[3578, 17764])).
% 4.24/4.43 tff(17766,plain,
% 4.24/4.43 (elem!1 = s(z)),
% 4.24/4.43 inference(transitivity,[status(thm)],[517, 17758, 70])).
% 4.24/4.43 tff(17767,plain,
% 4.24/4.43 (b(elem!1, s(s(s(s(z))))) <=> b(s(z), s(s(s(s(z)))))),
% 4.24/4.43 inference(monotonicity,[status(thm)],[17766])).
% 4.24/4.43 tff(17768,plain,
% 4.24/4.43 (b(s(z), s(s(s(s(z)))))),
% 4.24/4.43 inference(modus_ponens,[status(thm)],[1301, 17767])).
% 4.24/4.43 tff(17769,plain,
% 4.24/4.43 (b(elem!1, s(s(z))) <=> b(s(z), s(s(z)))),
% 4.24/4.43 inference(symmetry,[status(thm)],[1872])).
% 4.24/4.43 tff(17770,plain,
% 4.24/4.43 ((~b(elem!1, s(s(z)))) <=> (~b(s(z), s(s(z))))),
% 4.24/4.43 inference(monotonicity,[status(thm)],[17769])).
% 4.24/4.43 tff(17771,plain,
% 4.24/4.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 4.24/4.43 inference(rewrite,[status(thm)],[])).
% 4.24/4.43 tff(17772,plain,
% 4.24/4.43 (((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 4.24/4.43 inference(rewrite,[status(thm)],[])).
% 4.24/4.43 tff(17773,plain,
% 4.24/4.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 4.24/4.43 inference(monotonicity,[status(thm)],[17772])).
% 4.24/4.43 tff(17774,plain,
% 4.24/4.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 4.24/4.43 inference(transitivity,[status(thm)],[17773, 17771])).
% 4.24/4.43 tff(17775,plain,
% 4.24/4.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 4.24/4.43 inference(quant_inst,[status(thm)],[])).
% 4.24/4.43 tff(17776,plain,
% 4.24/4.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 4.24/4.43 inference(modus_ponens,[status(thm)],[17775, 17774])).
% 4.24/4.43 tff(17777,plain,
% 4.24/4.43 ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 4.24/4.43 inference(unit_resolution,[status(thm)],[17776, 178])).
% 4.24/4.43 tff(17778,plain,
% 4.24/4.43 (~b(elem!1, s(s(z)))),
% 4.24/4.43 inference(unit_resolution,[status(thm)],[17777, 869, 166, 3771, 202])).
% 4.24/4.43 tff(17779,plain,
% 4.24/4.43 (~b(s(z), s(s(z)))),
% 4.24/4.43 inference(modus_ponens,[status(thm)],[17778, 17770])).
% 4.24/4.43 tff(17780,plain,
% 4.24/4.43 (r(s(z), s(s(z)))),
% 4.24/4.43 inference(unit_resolution,[status(thm)],[1619, 41, 17779, 2653])).
% 4.24/4.43 tff(17781,plain,
% 4.24/4.43 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.24/4.43 inference(unit_resolution,[status(thm)],[2640, 118, 17780, 107])).
% 4.24/4.43 tff(17782,plain,
% 4.24/4.43 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.24/4.43 inference(unit_resolution,[status(thm)],[615, 41, 612, 17781])).
% 4.24/4.43 tff(17783,plain,
% 4.24/4.43 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(s(z), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.43 inference(monotonicity,[status(thm)],[518])).
% 4.24/4.43 tff(17784,plain,
% 4.24/4.43 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.43 inference(modus_ponens,[status(thm)],[869, 17783])).
% 4.24/4.43 tff(17785,plain,
% 4.24/4.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(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(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(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(z), s(s(s(s(s(s(s(z))))))))))),
% 4.24/4.43 inference(rewrite,[status(thm)],[])).
% 4.24/4.43 tff(17786,plain,
% 4.24/4.43 (((~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(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(s(z))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 4.24/4.43 inference(rewrite,[status(thm)],[])).
% 4.24/4.43 tff(17787,plain,
% 4.24/4.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(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(z), s(s(s(s(s(s(s(z)))))))))))),
% 4.24/4.43 inference(monotonicity,[status(thm)],[17786])).
% 4.24/4.43 tff(17788,plain,
% 4.24/4.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(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(z), s(s(s(s(s(s(s(z))))))))))),
% 4.24/4.43 inference(transitivity,[status(thm)],[17787, 17785])).
% 4.24/4.43 tff(17789,plain,
% 4.24/4.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 4.24/4.43 inference(quant_inst,[status(thm)],[])).
% 4.24/4.43 tff(17790,plain,
% 4.24/4.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 4.24/4.43 inference(modus_ponens,[status(thm)],[17789, 17788])).
% 4.24/4.43 tff(17791,plain,
% 4.24/4.43 ($false),
% 4.24/4.43 inference(unit_resolution,[status(thm)],[17790, 178, 104, 15173, 14891, 17784, 17782])).
% 4.24/4.43 tff(17792,plain,((~b(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(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (s(z) = s(s(z))) | (~(s(elem!1) = s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.43 tff(17793,plain,
% 4.24/4.43 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.24/4.43 inference(unit_resolution,[status(thm)],[17792, 17768, 104, 17765, 17763, 17757, 166, 17730, 17723])).
% 4.24/4.43 tff(17794,plain,
% 4.24/4.43 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.24/4.43 inference(unit_resolution,[status(thm)],[691, 17793, 17728])).
% 4.24/4.43 tff(17795,plain,
% 4.24/4.43 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.43 inference(modus_ponens,[status(thm)],[17794, 17762])).
% 4.24/4.43 tff(17796,plain,
% 4.24/4.43 (~r(elem!1, s(s(s(elem!1))))),
% 4.24/4.43 inference(unit_resolution,[status(thm)],[10847, 438, 3461, 273, 437, 521])).
% 4.24/4.43 tff(17797,plain,
% 4.24/4.43 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 4.24/4.43 inference(unit_resolution,[status(thm)],[17755, 557, 1301, 17796, 3461, 166, 273, 3771, 3521, 145, 438, 17627, 104, 2484, 17726, 4171])).
% 4.24/4.43 tff(17798,plain,
% 4.24/4.43 (s(elem!1) = s(s(z))),
% 4.24/4.43 inference(unit_resolution,[status(thm)],[2840, 17797])).
% 4.24/4.43 tff(17799,plain,
% 4.24/4.43 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 4.24/4.43 inference(monotonicity,[status(thm)],[17798])).
% 4.24/4.43 tff(17800,plain,
% 4.24/4.43 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 4.24/4.43 inference(symmetry,[status(thm)],[17799])).
% 4.24/4.43 tff(17801,plain,
% 4.24/4.43 (s(z) = elem!1),
% 4.24/4.43 inference(transitivity,[status(thm)],[71, 17800, 304])).
% 4.24/4.43 tff(17802,plain,
% 4.24/4.43 (r(s(s(z)), s(z)) <=> r(s(s(z)), elem!1)),
% 4.24/4.43 inference(monotonicity,[status(thm)],[17801])).
% 4.24/4.43 tff(17803,plain,
% 4.24/4.43 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(z))),
% 4.24/4.43 inference(symmetry,[status(thm)],[17802])).
% 4.24/4.43 tff(17804,plain,
% 4.24/4.43 (r(s(s(z)), s(z))),
% 4.24/4.43 inference(modus_ponens,[status(thm)],[438, 17803])).
% 4.24/4.43 tff(17805,plain,
% 4.24/4.43 (elem!1 = s(z)),
% 4.24/4.43 inference(transitivity,[status(thm)],[517, 17799, 70])).
% 4.24/4.43 tff(17806,plain,
% 4.24/4.43 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(z))),
% 4.24/4.43 inference(monotonicity,[status(thm)],[17805])).
% 4.24/4.43 tff(17807,plain,
% 4.24/4.43 (s(s(elem!1)) = s(s(s(z)))),
% 4.24/4.43 inference(monotonicity,[status(thm)],[17798])).
% 4.24/4.43 tff(17808,plain,
% 4.24/4.43 ((s(s(elem!1)) = elem!1) <=> (s(s(s(z))) = elem!1)),
% 4.24/4.43 inference(monotonicity,[status(thm)],[17807])).
% 4.24/4.43 tff(17809,plain,
% 4.24/4.43 ((s(s(elem!1)) = elem!1) <=> (elem!1 = s(s(s(z))))),
% 4.24/4.43 inference(transitivity,[status(thm)],[17808, 10420])).
% 4.24/4.43 tff(17810,plain,
% 4.24/4.43 ((s(s(elem!1)) = elem!1) <=> (s(s(s(z))) = elem!1)),
% 4.24/4.43 inference(transitivity,[status(thm)],[17809, 10421])).
% 4.24/4.43 tff(17811,plain,
% 4.24/4.43 ((~(s(s(elem!1)) = elem!1)) <=> (~(s(s(s(z))) = elem!1))),
% 4.24/4.43 inference(monotonicity,[status(thm)],[17810])).
% 4.24/4.43 tff(17812,plain,
% 4.24/4.43 (~(elem!1 = s(s(s(s(elem!1)))))),
% 4.24/4.43 inference(unit_resolution,[status(thm)],[1422, 17798])).
% 4.24/4.43 tff(17813,plain,
% 4.24/4.43 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.24/4.43 inference(unit_resolution,[status(thm)],[1509, 17812])).
% 4.24/4.43 tff(17814,plain,
% 4.24/4.43 (~(elem!1 = s(s(elem!1)))),
% 4.24/4.43 inference(unit_resolution,[status(thm)],[1539, 17813])).
% 4.24/4.43 tff(17815,plain,
% 4.24/4.43 (~(s(s(elem!1)) = elem!1)),
% 4.24/4.43 inference(unit_resolution,[status(thm)],[1546, 17814])).
% 4.24/4.43 tff(17816,plain,
% 4.24/4.43 (~(s(s(s(z))) = elem!1)),
% 4.24/4.43 inference(modus_ponens,[status(thm)],[17815, 17811])).
% 4.24/4.43 tff(17817,plain,
% 4.24/4.43 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 4.24/4.43 inference(unit_resolution,[status(thm)],[4168, 17797])).
% 4.24/4.43 tff(17818,plain,
% 4.24/4.43 (b(elem!1, s(s(s(elem!1))))),
% 4.24/4.43 inference(unit_resolution,[status(thm)],[4162, 17817, 1301])).
% 4.24/4.43 tff(17819,plain,
% 4.24/4.43 (~(s(s(s(elem!1))) = elem!1)),
% 4.24/4.43 inference(unit_resolution,[status(thm)],[16438, 17818])).
% 4.24/4.43 tff(17820,plain,
% 4.24/4.43 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(z))),
% 4.24/4.43 inference(monotonicity,[status(thm)],[518])).
% 4.24/4.43 tff(17821,plain,
% 4.24/4.43 ((s(s(elem!1)) = elem!1) <=> (s(s(s(z))) = elem!1)),
% 4.24/4.43 inference(monotonicity,[status(thm)],[545])).
% 4.24/4.43 tff(17822,plain,
% 4.24/4.43 ((s(s(elem!1)) = elem!1) <=> (elem!1 = s(s(s(z))))),
% 4.24/4.43 inference(transitivity,[status(thm)],[17821, 10420])).
% 4.24/4.43 tff(17823,plain,
% 4.24/4.43 ((s(s(elem!1)) = elem!1) <=> (s(s(s(z))) = elem!1)),
% 4.24/4.43 inference(transitivity,[status(thm)],[17822, 10421])).
% 4.24/4.43 tff(17824,plain,
% 4.24/4.43 ((~(s(s(elem!1)) = elem!1)) <=> (~(s(s(s(z))) = elem!1))),
% 4.24/4.43 inference(monotonicity,[status(thm)],[17823])).
% 4.24/4.43 tff(17825,plain,
% 4.24/4.43 (~(s(s(s(z))) = elem!1)),
% 4.24/4.43 inference(modus_ponens,[status(thm)],[15139, 17824])).
% 4.24/4.43 tff(17826,plain,
% 4.24/4.43 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.24/4.43 inference(symmetry,[status(thm)],[15169])).
% 4.24/4.43 tff(17827,plain,
% 4.24/4.43 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.24/4.43 inference(unit_resolution,[status(thm)],[11027, 108, 521])).
% 4.24/4.43 tff(17828,plain,
% 4.24/4.43 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.24/4.43 inference(unit_resolution,[status(thm)],[3444, 17827, 3914])).
% 4.24/4.43 tff(17829,plain,
% 4.24/4.43 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.24/4.43 inference(modus_ponens,[status(thm)],[17828, 17826])).
% 4.24/4.43 tff(17830,plain,
% 4.24/4.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.24/4.43 inference(rewrite,[status(thm)],[])).
% 4.24/4.43 tff(17831,plain,
% 4.24/4.43 (((~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(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(s(s(s(z))))))), 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(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.24/4.43 inference(rewrite,[status(thm)],[])).
% 4.24/4.43 tff(17832,plain,
% 4.24/4.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 4.24/4.43 inference(monotonicity,[status(thm)],[17831])).
% 4.24/4.43 tff(17833,plain,
% 4.24/4.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.24/4.43 inference(transitivity,[status(thm)],[17832, 17830])).
% 4.24/4.43 tff(17834,plain,
% 4.24/4.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.24/4.43 inference(quant_inst,[status(thm)],[])).
% 4.24/4.43 tff(17835,plain,
% 4.24/4.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 4.24/4.43 inference(modus_ponens,[status(thm)],[17834, 17833])).
% 4.24/4.43 tff(17836,plain,
% 4.24/4.43 ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 4.24/4.43 inference(unit_resolution,[status(thm)],[17835, 178, 104, 15173, 1126])).
% 4.24/4.43 tff(17837,plain,
% 4.24/4.43 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.43 inference(unit_resolution,[status(thm)],[17836, 17829])).
% 4.24/4.43 tff(17838,plain,
% 4.24/4.43 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.43 inference(unit_resolution,[status(thm)],[5031, 41, 17837, 10712])).
% 4.24/4.43 tff(17839,plain,
% 4.24/4.43 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 4.24/4.43 inference(unit_resolution,[status(thm)],[5042, 118, 204, 17838])).
% 4.24/4.43 tff(17840,plain,
% 4.24/4.43 (b(s(s(s(s(z)))), s(s(s(z))))),
% 4.24/4.43 inference(unit_resolution,[status(thm)],[11185, 17839])).
% 4.24/4.43 tff(17841,plain,
% 4.24/4.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))),
% 4.24/4.43 inference(rewrite,[status(thm)],[])).
% 4.24/4.43 tff(17842,plain,
% 4.24/4.43 (((~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(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))),
% 4.24/4.43 inference(rewrite,[status(thm)],[])).
% 4.24/4.43 tff(17843,plain,
% 4.24/4.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1))))),
% 4.24/4.44 inference(monotonicity,[status(thm)],[17842])).
% 4.24/4.44 tff(17844,plain,
% 4.24/4.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))),
% 4.24/4.44 inference(transitivity,[status(thm)],[17843, 17841])).
% 4.24/4.44 tff(17845,plain,
% 4.24/4.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 4.24/4.44 inference(quant_inst,[status(thm)],[])).
% 4.24/4.44 tff(17846,plain,
% 4.24/4.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1))),
% 4.24/4.44 inference(modus_ponens,[status(thm)],[17845, 17844])).
% 4.24/4.44 tff(17847,plain,
% 4.24/4.44 ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[17846, 178, 3771, 1301, 1126])).
% 4.24/4.44 tff(17848,plain,
% 4.24/4.44 (~b(s(s(s(z))), elem!1)),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[17847, 17840])).
% 4.24/4.44 tff(17849,plain,
% 4.24/4.44 (r(s(s(s(z))), elem!1)),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[4981, 17848, 17825])).
% 4.24/4.44 tff(17850,plain,
% 4.24/4.44 (r(s(s(s(z))), s(z))),
% 4.24/4.44 inference(modus_ponens,[status(thm)],[17849, 17820])).
% 4.24/4.44 tff(17851,plain,
% 4.24/4.44 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(s(z), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.44 inference(symmetry,[status(thm)],[2622])).
% 4.24/4.44 tff(17852,plain,
% 4.24/4.44 (~r(elem!1, s(s(s(elem!1))))),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[3319, 557, 521])).
% 4.24/4.44 tff(17853,plain,
% 4.24/4.44 (b(elem!1, s(s(s(elem!1))))),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[2054, 17852, 1586])).
% 4.24/4.44 tff(17854,plain,
% 4.24/4.44 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[5130, 557, 108])).
% 4.24/4.44 tff(17855,plain,
% 4.24/4.44 (b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[5118, 17854, 3521])).
% 4.24/4.44 tff(17856,plain,
% 4.24/4.44 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[3444, 11094, 3914])).
% 4.24/4.44 tff(17857,plain,
% 4.24/4.44 (~r(s(s(s(elem!1))), elem!1)),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[565, 521, 557])).
% 4.24/4.44 tff(17858,plain,
% 4.24/4.44 (b(s(s(s(elem!1))), elem!1)),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[570, 17857, 949])).
% 4.24/4.44 tff(17859,plain,
% 4.24/4.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 4.24/4.44 inference(rewrite,[status(thm)],[])).
% 4.24/4.44 tff(17860,plain,
% 4.24/4.44 (((~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(s(s(s(s(s(s(s(z))))))), s(s(s(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(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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 4.24/4.44 inference(rewrite,[status(thm)],[])).
% 4.24/4.44 tff(17861,plain,
% 4.24/4.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(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(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))))),
% 4.24/4.44 inference(monotonicity,[status(thm)],[17860])).
% 4.24/4.44 tff(17862,plain,
% 4.24/4.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(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(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 4.24/4.44 inference(transitivity,[status(thm)],[17861, 17859])).
% 4.24/4.44 tff(17863,plain,
% 4.24/4.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(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(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.24/4.44 inference(quant_inst,[status(thm)],[])).
% 4.24/4.44 tff(17864,plain,
% 4.24/4.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 4.24/4.44 inference(modus_ponens,[status(thm)],[17863, 17862])).
% 4.24/4.44 tff(17865,plain,
% 4.24/4.44 ($false),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[17864, 178, 17858, 2042, 869, 17856, 3829])).
% 4.24/4.44 tff(17866,plain,((~r(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (s(s(s(elem!1))) = elem!1) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.44 tff(17867,plain,
% 4.24/4.44 ($false),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[17866, 17855, 17853, 108, 869, 3914, 949, 521, 557])).
% 4.24/4.44 tff(17868,plain,((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (s(s(s(elem!1))) = elem!1) | (~r(z, elem!1)) | (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.44 tff(17869,plain,
% 4.24/4.44 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[17868, 108, 3914, 3521, 521, 557, 949, 1585])).
% 4.24/4.44 tff(17870,plain,
% 4.24/4.44 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[691, 17869, 17627])).
% 4.24/4.44 tff(17871,plain,
% 4.24/4.44 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.44 inference(modus_ponens,[status(thm)],[17870, 17851])).
% 4.24/4.44 tff(17872,plain,
% 4.24/4.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))))),
% 4.24/4.44 inference(rewrite,[status(thm)],[])).
% 4.24/4.44 tff(17873,plain,
% 4.24/4.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))))),
% 4.24/4.44 inference(quant_inst,[status(thm)],[])).
% 4.24/4.44 tff(17874,plain,
% 4.24/4.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z)))),
% 4.24/4.44 inference(modus_ponens,[status(thm)],[17873, 17872])).
% 4.24/4.44 tff(17875,plain,
% 4.24/4.44 ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z)))),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[17874, 118, 17838])).
% 4.24/4.44 tff(17876,plain,
% 4.24/4.44 ($false),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[17875, 17871, 17850])).
% 4.24/4.44 tff(17877,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~(s(elem!1) = 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)))))) | (~r(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)))))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~r(z, elem!1)) | (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.24/4.44 tff(17878,plain,
% 4.24/4.44 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[17877, 17798, 3771, 1301, 1126, 204, 104, 3914, 521, 3521, 557, 17819])).
% 4.24/4.44 tff(17879,plain,
% 4.24/4.44 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[133, 17878])).
% 4.24/4.44 tff(17880,plain,
% 4.24/4.44 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[4057, 17879, 3461, 166, 273])).
% 4.24/4.44 tff(17881,plain,
% 4.24/4.44 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[3578, 17880])).
% 4.24/4.44 tff(17882,plain,
% 4.24/4.44 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 4.24/4.44 inference(monotonicity,[status(thm)],[17807])).
% 4.24/4.44 tff(17883,plain,
% 4.24/4.44 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.24/4.44 inference(symmetry,[status(thm)],[17882])).
% 4.24/4.44 tff(17884,plain,
% 4.24/4.44 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 4.24/4.44 inference(monotonicity,[status(thm)],[17807])).
% 4.24/4.44 tff(17885,plain,
% 4.24/4.44 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 4.24/4.44 inference(symmetry,[status(thm)],[17884])).
% 4.24/4.44 tff(17886,plain,
% 4.24/4.44 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 4.24/4.44 inference(monotonicity,[status(thm)],[17885])).
% 4.24/4.44 tff(17887,plain,
% 4.24/4.44 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.24/4.44 inference(transitivity,[status(thm)],[17886, 17883])).
% 4.24/4.44 tff(17888,plain,
% 4.24/4.44 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.24/4.44 inference(modus_ponens,[status(thm)],[1126, 17887])).
% 4.24/4.44 tff(17889,plain,
% 4.24/4.44 (r(elem!1, z) <=> r(s(z), z)),
% 4.24/4.44 inference(monotonicity,[status(thm)],[17805])).
% 4.24/4.44 tff(17890,plain,
% 4.24/4.44 (r(s(z), z)),
% 4.24/4.44 inference(modus_ponens,[status(thm)],[437, 17889])).
% 4.24/4.44 tff(17891,assumption,(r(s(z), z)), introduced(assumption)).
% 4.24/4.44 tff(17892,plain,
% 4.24/4.44 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 4.24/4.44 inference(symmetry,[status(thm)],[15161])).
% 4.24/4.44 tff(17893,plain,
% 4.24/4.44 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[5042, 118, 204, 8216])).
% 4.24/4.44 tff(17894,plain,
% 4.24/4.44 (b(s(s(s(s(z)))), s(s(s(z))))),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[11185, 17893])).
% 4.24/4.44 tff(17895,plain,
% 4.24/4.44 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 4.24/4.44 inference(modus_ponens,[status(thm)],[17894, 17892])).
% 4.24/4.44 tff(17896,plain,
% 4.24/4.44 (~r(s(s(s(z))), s(s(z)))),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[8218, 8216, 107])).
% 4.24/4.44 tff(17897,plain,
% 4.24/4.44 (b(s(s(s(z))), s(s(z)))),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[4966, 17896])).
% 4.24/4.44 tff(17898,plain,
% 4.24/4.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 4.24/4.44 inference(rewrite,[status(thm)],[])).
% 4.24/4.44 tff(17899,plain,
% 4.24/4.44 (((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 4.24/4.44 inference(rewrite,[status(thm)],[])).
% 4.24/4.44 tff(17900,plain,
% 4.24/4.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))))),
% 4.24/4.44 inference(monotonicity,[status(thm)],[17899])).
% 4.24/4.44 tff(17901,plain,
% 4.24/4.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 4.24/4.44 inference(transitivity,[status(thm)],[17900, 17898])).
% 4.24/4.44 tff(17902,plain,
% 4.24/4.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)))),
% 4.24/4.44 inference(quant_inst,[status(thm)],[])).
% 4.24/4.44 tff(17903,plain,
% 4.24/4.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))),
% 4.24/4.44 inference(modus_ponens,[status(thm)],[17902, 17901])).
% 4.24/4.44 tff(17904,plain,
% 4.24/4.44 (~b(s(s(s(z))), z)),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[17903, 178, 273, 166, 595, 17897])).
% 4.24/4.44 tff(17905,plain,
% 4.24/4.44 (r(s(s(s(z))), z)),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[4903, 41, 77, 17904])).
% 4.24/4.44 tff(17906,plain,
% 4.24/4.44 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(s(z))))),
% 4.24/4.44 inference(monotonicity,[status(thm)],[518, 545])).
% 4.24/4.44 tff(17907,plain,
% 4.24/4.44 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 4.24/4.44 inference(symmetry,[status(thm)],[17906])).
% 4.24/4.44 tff(17908,plain,
% 4.24/4.44 ((~r(s(z), s(s(s(z))))) <=> (~r(elem!1, s(s(elem!1))))),
% 4.24/4.44 inference(monotonicity,[status(thm)],[17907])).
% 4.24/4.44 tff(17909,plain,
% 4.24/4.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 4.24/4.44 inference(rewrite,[status(thm)],[])).
% 4.24/4.44 tff(17910,plain,
% 4.24/4.44 (((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 4.24/4.44 inference(rewrite,[status(thm)],[])).
% 4.24/4.44 tff(17911,plain,
% 4.24/4.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))))),
% 4.24/4.44 inference(monotonicity,[status(thm)],[17910])).
% 4.24/4.44 tff(17912,plain,
% 4.24/4.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 4.24/4.44 inference(transitivity,[status(thm)],[17911, 17909])).
% 4.24/4.44 tff(17913,plain,
% 4.24/4.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))),
% 4.24/4.44 inference(quant_inst,[status(thm)],[])).
% 4.24/4.44 tff(17914,plain,
% 4.24/4.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))),
% 4.24/4.44 inference(modus_ponens,[status(thm)],[17913, 17912])).
% 4.24/4.44 tff(17915,plain,
% 4.24/4.44 (~r(s(z), s(s(s(z))))),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[17914, 118, 17891, 16062])).
% 4.24/4.44 tff(17916,plain,
% 4.24/4.44 (~r(elem!1, s(s(elem!1)))),
% 4.24/4.44 inference(modus_ponens,[status(thm)],[17915, 17908])).
% 4.24/4.44 tff(17917,plain,
% 4.24/4.44 (r(s(s(s(z))), s(z)) <=> r(s(s(elem!1)), elem!1)),
% 4.24/4.44 inference(symmetry,[status(thm)],[15178])).
% 4.24/4.44 tff(17918,plain,
% 4.24/4.44 ((~r(s(s(s(z))), s(z))) <=> (~r(s(s(elem!1)), elem!1))),
% 4.24/4.44 inference(monotonicity,[status(thm)],[17917])).
% 4.24/4.44 tff(17919,plain,
% 4.24/4.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 4.24/4.44 inference(rewrite,[status(thm)],[])).
% 4.24/4.44 tff(17920,plain,
% 4.24/4.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 4.24/4.44 inference(quant_inst,[status(thm)],[])).
% 4.24/4.44 tff(17921,plain,
% 4.24/4.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 4.24/4.44 inference(modus_ponens,[status(thm)],[17920, 17919])).
% 4.24/4.44 tff(17922,plain,
% 4.24/4.44 (~r(s(s(s(z))), s(z))),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[17921, 118, 17891, 16062])).
% 4.24/4.44 tff(17923,plain,
% 4.24/4.44 (~r(s(s(elem!1)), elem!1)),
% 4.24/4.44 inference(modus_ponens,[status(thm)],[17922, 17918])).
% 4.24/4.44 tff(17924,plain,
% 4.24/4.44 (b(s(s(elem!1)), elem!1)),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[3362, 17923, 15139])).
% 4.24/4.44 tff(17925,plain,
% 4.24/4.44 ($false),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[5479, 17924, 17916, 2042, 3511, 15138, 3512])).
% 4.24/4.44 tff(17926,plain,((~r(s(s(s(z))), z)) | (~b(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)))) | (~(s(elem!1) = s(s(z)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.44 tff(17927,plain,
% 4.24/4.44 ($false),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[17926, 17905, 17895, 515, 17891, 3511, 2042])).
% 4.24/4.44 tff(17928,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~(s(elem!1) = s(s(z)))) | (~r(s(z), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.44 tff(17929,plain,
% 4.24/4.44 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[17928, 17798, 17890, 17888, 17818, 273, 166, 595, 204, 17881])).
% 4.24/4.44 tff(17930,plain,
% 4.24/4.44 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[5031, 41, 17929, 10712])).
% 4.24/4.44 tff(17931,plain,
% 4.24/4.44 (~b(z, s(s(s(z))))),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[8518, 17930])).
% 4.24/4.44 tff(17932,plain,
% 4.24/4.44 (r(z, s(s(s(z))))),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[4920, 17931])).
% 4.24/4.44 tff(17933,plain,
% 4.24/4.44 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[4961, 17932, 17725])).
% 4.24/4.44 tff(17934,plain,
% 4.24/4.44 (b(s(s(s(s(z)))), s(s(s(z))))),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[11185, 17933])).
% 4.24/4.44 tff(17935,plain,
% 4.24/4.44 (~b(s(s(s(z))), elem!1)),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[17847, 17934])).
% 4.24/4.44 tff(17936,plain,
% 4.24/4.44 (r(s(s(s(z))), elem!1)),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[4981, 17935, 17816])).
% 4.24/4.44 tff(17937,plain,
% 4.24/4.44 (r(s(s(s(z))), s(z))),
% 4.24/4.44 inference(modus_ponens,[status(thm)],[17936, 17806])).
% 4.24/4.44 tff(17938,plain,
% 4.24/4.44 (~b(s(s(z)), s(s(s(z))))),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[1228, 17930])).
% 4.24/4.44 tff(17939,plain,
% 4.24/4.44 (r(s(s(z)), s(s(s(z))))),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[5088, 17938])).
% 4.24/4.44 tff(17940,plain,
% 4.24/4.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 4.24/4.44 inference(rewrite,[status(thm)],[])).
% 4.24/4.44 tff(17941,plain,
% 4.24/4.44 (((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 4.24/4.44 inference(rewrite,[status(thm)],[])).
% 4.24/4.44 tff(17942,plain,
% 4.24/4.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 4.24/4.44 inference(monotonicity,[status(thm)],[17941])).
% 4.24/4.44 tff(17943,plain,
% 4.24/4.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 4.24/4.44 inference(transitivity,[status(thm)],[17942, 17940])).
% 4.24/4.44 tff(17944,plain,
% 4.24/4.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 4.24/4.44 inference(quant_inst,[status(thm)],[])).
% 4.24/4.44 tff(17945,plain,
% 4.24/4.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 4.24/4.44 inference(modus_ponens,[status(thm)],[17944, 17943])).
% 4.24/4.44 tff(17946,plain,
% 4.24/4.44 ($false),
% 4.24/4.44 inference(unit_resolution,[status(thm)],[17945, 118, 17939, 17937, 17804])).
% 4.24/4.44 tff(17947,plain,((~r(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~r(z, elem!1)) | (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(z))) | r(s(s(s(elem!1))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.45 tff(17948,plain,
% 4.24/4.45 (~r(elem!1, z)),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[17947, 17730, 557, 1126, 104, 595, 166, 273, 204, 3461, 17727, 438, 1301, 9310, 521, 145, 3340, 4171])).
% 4.24/4.45 tff(17949,plain,
% 4.24/4.45 (b(elem!1, z)),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[498, 17948, 290])).
% 4.24/4.45 tff(17950,plain,
% 4.24/4.45 (b(s(z), z)),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[593, 17757, 17949])).
% 4.24/4.45 tff(17951,plain,
% 4.24/4.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)))),
% 4.24/4.45 inference(rewrite,[status(thm)],[])).
% 4.24/4.45 tff(17952,plain,
% 4.24/4.45 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)))),
% 4.24/4.45 inference(rewrite,[status(thm)],[])).
% 4.24/4.45 tff(17953,plain,
% 4.24/4.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z))))),
% 4.24/4.45 inference(monotonicity,[status(thm)],[17952])).
% 4.24/4.45 tff(17954,plain,
% 4.24/4.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)))),
% 4.24/4.45 inference(transitivity,[status(thm)],[17953, 17951])).
% 4.24/4.45 tff(17955,plain,
% 4.24/4.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 4.24/4.45 inference(quant_inst,[status(thm)],[])).
% 4.24/4.45 tff(17956,plain,
% 4.24/4.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z))),
% 4.24/4.45 inference(modus_ponens,[status(thm)],[17955, 17954])).
% 4.24/4.45 tff(17957,plain,
% 4.24/4.45 (~b(s(z), s(s(z)))),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[17956, 178, 3461, 166, 595, 17950])).
% 4.24/4.45 tff(17958,plain,
% 4.24/4.45 (r(s(z), s(s(z)))),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[2657, 17957, 17763])).
% 4.24/4.45 tff(17959,plain,
% 4.24/4.45 ($false),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[2630, 118, 17958, 17765, 17795])).
% 4.24/4.45 tff(17960,plain,((~r(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))) | (s(s(z)) = elem!1) | (elem!1 = z) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), elem!1)) | (~b(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | r(s(s(s(elem!1))), s(s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.24/4.45 tff(17961,plain,
% 4.24/4.45 (~r(z, elem!1)),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[17960, 17177, 104, 5619, 595, 17719, 17721, 290, 17624, 17711, 273, 47, 10800, 10796, 17175, 17720])).
% 4.24/4.45 tff(17962,plain,
% 4.24/4.45 (b(z, elem!1)),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[585, 17961, 318])).
% 4.24/4.45 tff(17963,plain,
% 4.24/4.45 ($false),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[8447, 178, 17962, 104, 17719, 595, 17713])).
% 4.24/4.45 tff(17964,plain,(b(s(s(z)), s(s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (elem!1 = z) | (~b(z, s(s(z)))) | b(z, s(s(s(s(z))))) | r(s(s(z)), z) | b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.45 tff(17965,plain,
% 4.24/4.45 (b(s(s(z)), s(s(s(s(z)))))),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[17964, 17174, 17173, 290, 144, 1, 10792, 104])).
% 4.24/4.45 tff(17966,plain,
% 4.24/4.45 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[7840, 178, 144, 104, 17965, 17173])).
% 4.24/4.45 tff(17967,plain,
% 4.24/4.45 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[3578, 17966])).
% 4.24/4.45 tff(17968,plain,
% 4.24/4.45 (~r(s(s(s(s(z)))), s(s(z)))),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[17181, 17175, 47, 10793, 144])).
% 4.24/4.45 tff(17969,plain,
% 4.24/4.45 (b(s(s(s(s(z)))), s(s(z)))),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[102, 17968])).
% 4.24/4.45 tff(17970,plain,
% 4.24/4.45 ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[16647, 178, 10793, 144, 17969])).
% 4.24/4.45 tff(17971,plain,
% 4.24/4.45 (~b(s(s(s(s(z)))), z)),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[17970, 17965])).
% 4.24/4.45 tff(17972,plain,
% 4.24/4.45 (r(s(s(s(s(z)))), z)),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[191, 17971])).
% 4.24/4.45 tff(17973,plain,
% 4.24/4.45 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[279, 178, 144, 104, 17965, 17173])).
% 4.24/4.45 tff(17974,plain,
% 4.24/4.45 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[249, 17973])).
% 4.24/4.45 tff(17975,plain,
% 4.24/4.45 (~r(s(s(s(s(z)))), s(s(z)))),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[17181, 204, 47, 10793, 144])).
% 4.24/4.45 tff(17976,plain,
% 4.24/4.45 (b(s(s(s(s(z)))), s(s(z)))),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[102, 17975])).
% 4.24/4.45 tff(17977,plain,
% 4.24/4.45 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 4.24/4.45 inference(commutativity,[status(thm)],[])).
% 4.24/4.45 tff(17978,plain,
% 4.24/4.45 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 4.24/4.45 inference(symmetry,[status(thm)],[17977])).
% 4.24/4.45 tff(17979,plain,
% 4.24/4.45 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(s(z)))))),
% 4.24/4.45 inference(monotonicity,[status(thm)],[17978])).
% 4.24/4.45 tff(17980,plain,
% 4.24/4.45 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 4.24/4.45 inference(modus_ponens,[status(thm)],[11613, 17979])).
% 4.24/4.45 tff(17981,plain,
% 4.24/4.45 (~r(s(s(s(s(z)))), s(s(z)))),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[17181, 204, 47, 3461, 273])).
% 4.24/4.45 tff(17982,plain,
% 4.24/4.45 (b(s(s(s(s(z)))), s(s(z)))),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[102, 17981])).
% 4.24/4.45 tff(17983,plain,
% 4.24/4.45 ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[16647, 178, 3461, 273, 17982])).
% 4.24/4.45 tff(17984,plain,
% 4.24/4.45 (~b(s(s(s(s(z)))), z)),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[17983, 167])).
% 4.24/4.45 tff(17985,plain,
% 4.24/4.45 (r(s(s(s(s(z)))), z)),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[191, 17984])).
% 4.24/4.45 tff(17986,plain,
% 4.24/4.45 ((~b(elem!1, s(s(s(s(z)))))) <=> (~b(s(s(z)), s(s(s(s(z))))))),
% 4.24/4.45 inference(monotonicity,[status(thm)],[17695])).
% 4.24/4.45 tff(17987,plain,
% 4.24/4.45 (~b(s(s(z)), s(s(s(s(z)))))),
% 4.24/4.45 inference(modus_ponens,[status(thm)],[13328, 17986])).
% 4.24/4.45 tff(17988,plain,
% 4.24/4.45 ($false),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[167, 17987])).
% 4.24/4.45 tff(17989,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,[]))).
% 4.24/4.45 tff(17990,plain,
% 4.24/4.45 (~(s(s(z)) = elem!1)),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[17989, 13328, 167])).
% 4.24/4.45 tff(17991,plain,
% 4.24/4.45 (b(s(s(z)), elem!1)),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[448, 17990, 10828])).
% 4.24/4.45 tff(17992,plain,
% 4.24/4.45 (r(elem!1, s(s(s(s(z)))))),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[483, 3179, 13328])).
% 4.24/4.45 tff(17993,plain,
% 4.24/4.45 (~b(elem!1, z)),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[11004, 818, 3461, 273, 817])).
% 4.24/4.45 tff(17994,plain,
% 4.24/4.45 (r(elem!1, z)),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[498, 17993, 290])).
% 4.24/4.45 tff(17995,plain,
% 4.24/4.45 ($false),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[478, 17994, 17992, 47])).
% 4.24/4.45 tff(17996,plain,((~b(z, elem!1)) | (elem!1 = z) | b(elem!1, s(s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.45 tff(17997,plain,
% 4.24/4.45 (~b(z, elem!1)),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[17996, 13328, 290, 3461, 273, 17991, 1])).
% 4.24/4.45 tff(17998,plain,
% 4.24/4.45 (r(z, elem!1)),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[585, 17997, 318])).
% 4.24/4.45 tff(17999,plain,
% 4.24/4.45 (s(s(s(s(z)))) = elem!1),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[3151, 17998, 17982, 167, 17985, 17991, 47])).
% 4.24/4.45 tff(18000,plain,
% 4.24/4.45 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(z))), elem!1)),
% 4.24/4.45 inference(monotonicity,[status(thm)],[17999])).
% 4.24/4.45 tff(18001,plain,
% 4.24/4.45 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 4.24/4.45 inference(symmetry,[status(thm)],[18000])).
% 4.24/4.45 tff(18002,plain,
% 4.24/4.45 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 4.24/4.45 inference(monotonicity,[status(thm)],[17999])).
% 4.24/4.45 tff(18003,plain,
% 4.24/4.45 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 4.24/4.45 inference(transitivity,[status(thm)],[18002, 10421])).
% 4.24/4.45 tff(18004,plain,
% 4.24/4.45 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(z))) = elem!1))),
% 4.24/4.45 inference(monotonicity,[status(thm)],[18003])).
% 4.24/4.45 tff(18005,plain,
% 4.24/4.45 (~(s(s(s(z))) = elem!1)),
% 4.24/4.45 inference(modus_ponens,[status(thm)],[4938, 18004])).
% 4.24/4.45 tff(18006,plain,
% 4.24/4.45 (~r(elem!1, s(s(s(s(z)))))),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[529, 17998, 47])).
% 4.24/4.45 tff(18007,plain,
% 4.24/4.45 (elem!1 = s(s(s(s(z))))),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[483, 18006, 13328])).
% 4.24/4.45 tff(18008,plain,
% 4.24/4.45 (~b(elem!1, z)),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[3172, 18007, 17984])).
% 4.24/4.45 tff(18009,plain,
% 4.24/4.45 (r(elem!1, z)),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[498, 18008, 290])).
% 4.24/4.45 tff(18010,plain,
% 4.24/4.45 (s(s(s(s(s(z))))) = s(elem!1)),
% 4.24/4.45 inference(monotonicity,[status(thm)],[17999])).
% 4.24/4.45 tff(18011,plain,
% 4.24/4.45 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 4.24/4.45 inference(monotonicity,[status(thm)],[18010])).
% 4.24/4.45 tff(18012,plain,
% 4.24/4.45 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 4.24/4.45 inference(monotonicity,[status(thm)],[18011])).
% 4.24/4.45 tff(18013,plain,
% 4.24/4.45 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(elem!1))))),
% 4.24/4.45 inference(monotonicity,[status(thm)],[18012])).
% 4.24/4.45 tff(18014,plain,
% 4.24/4.45 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.24/4.45 inference(monotonicity,[status(thm)],[17999])).
% 4.24/4.45 tff(18015,plain,
% 4.24/4.45 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.24/4.45 inference(modus_ponens,[status(thm)],[204, 18014])).
% 4.24/4.45 tff(18016,plain,
% 4.24/4.45 (r(elem!1, s(s(s(elem!1))))),
% 4.24/4.45 inference(modus_ponens,[status(thm)],[18015, 18013])).
% 4.24/4.45 tff(18017,plain,
% 4.24/4.45 (~r(s(s(s(elem!1))), z)),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[6071, 18016, 18009])).
% 4.24/4.45 tff(18018,plain,
% 4.24/4.45 (b(s(s(s(elem!1))), z)),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[1565, 18017])).
% 4.24/4.45 tff(18019,plain,
% 4.24/4.45 (b(z, s(s(s(elem!1))))),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[17717, 18007, 595])).
% 4.24/4.45 tff(18020,plain,
% 4.24/4.45 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[7840, 178, 273, 104, 167, 595])).
% 4.24/4.45 tff(18021,plain,
% 4.24/4.45 (r(s(s(s(elem!1))), s(s(z)))),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[14415, 18007, 18020])).
% 4.24/4.45 tff(18022,assumption,(r(s(s(s(z))), elem!1)), introduced(assumption)).
% 4.24/4.45 tff(18023,plain,
% 4.24/4.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 4.24/4.45 inference(rewrite,[status(thm)],[])).
% 4.24/4.45 tff(18024,plain,
% 4.24/4.45 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 4.24/4.45 inference(quant_inst,[status(thm)],[])).
% 4.24/4.45 tff(18025,plain,
% 4.24/4.45 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z))),
% 4.24/4.45 inference(modus_ponens,[status(thm)],[18024, 18023])).
% 4.24/4.45 tff(18026,plain,
% 4.24/4.45 (~r(s(s(s(z))), z)),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[18025, 118, 521, 18022])).
% 4.24/4.45 tff(18027,plain,
% 4.24/4.45 (b(s(s(s(z))), z)),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[4903, 41, 77, 18026])).
% 4.24/4.45 tff(18028,plain,
% 4.24/4.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 4.24/4.45 inference(rewrite,[status(thm)],[])).
% 4.24/4.45 tff(18029,plain,
% 4.24/4.45 (((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(z)))))) <=> ((~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 4.24/4.45 inference(rewrite,[status(thm)],[])).
% 4.24/4.45 tff(18030,plain,
% 4.24/4.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), elem!1))))),
% 4.24/4.45 inference(monotonicity,[status(thm)],[18029])).
% 4.24/4.45 tff(18031,plain,
% 4.24/4.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 4.24/4.45 inference(transitivity,[status(thm)],[18030, 18028])).
% 4.24/4.45 tff(18032,plain,
% 4.24/4.45 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))))),
% 4.24/4.45 inference(quant_inst,[status(thm)],[])).
% 4.24/4.45 tff(18033,plain,
% 4.24/4.45 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), elem!1))),
% 4.24/4.45 inference(modus_ponens,[status(thm)],[18032, 18031])).
% 4.24/4.45 tff(18034,plain,
% 4.24/4.45 (~r(z, s(s(s(z))))),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[18033, 118, 521, 18022])).
% 4.24/4.45 tff(18035,plain,
% 4.24/4.45 (b(z, s(s(s(z))))),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[4920, 18034])).
% 4.24/4.45 tff(18036,plain,
% 4.24/4.45 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[8207, 178, 2043, 7976, 18035, 18027])).
% 4.24/4.45 tff(18037,plain,
% 4.24/4.45 (r(s(s(s(z))), s(s(s(elem!1))))),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[9126, 18036, 8246])).
% 4.24/4.45 tff(18038,plain,
% 4.24/4.45 (~b(s(s(s(z))), s(s(z)))),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[17111, 178, 3461, 273, 18035, 18027])).
% 4.24/4.45 tff(18039,plain,
% 4.24/4.45 (r(s(s(s(z))), s(s(z)))),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[4966, 18038])).
% 4.24/4.45 tff(18040,plain,
% 4.24/4.45 ($false),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[4975, 118, 3859, 18039, 18037])).
% 4.24/4.45 tff(18041,plain,((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.45 tff(18042,plain,
% 4.24/4.45 (~r(s(s(s(z))), elem!1)),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[18041, 18021, 11613, 3461, 273, 18019, 18018, 17998])).
% 4.24/4.45 tff(18043,plain,
% 4.24/4.45 (b(s(s(s(z))), elem!1)),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[4981, 18042, 18005])).
% 4.24/4.45 tff(18044,plain,
% 4.24/4.45 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.24/4.45 inference(modus_ponens,[status(thm)],[18043, 18001])).
% 4.24/4.45 tff(18045,plain,
% 4.24/4.45 (~b(s(s(s(z))), s(s(z)))),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[4963, 18044, 273, 17982, 167, 17985])).
% 4.24/4.45 tff(18046,plain,
% 4.24/4.45 (r(s(s(s(z))), s(s(z)))),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[4966, 18045])).
% 4.24/4.45 tff(18047,plain,
% 4.24/4.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 4.24/4.45 inference(rewrite,[status(thm)],[])).
% 4.24/4.45 tff(18048,plain,
% 4.24/4.45 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 4.24/4.45 inference(rewrite,[status(thm)],[])).
% 4.24/4.45 tff(18049,plain,
% 4.24/4.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 4.24/4.45 inference(monotonicity,[status(thm)],[18048])).
% 4.24/4.45 tff(18050,plain,
% 4.24/4.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 4.24/4.45 inference(transitivity,[status(thm)],[18049, 18047])).
% 4.24/4.45 tff(18051,plain,
% 4.24/4.45 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 4.24/4.45 inference(quant_inst,[status(thm)],[])).
% 4.24/4.45 tff(18052,plain,
% 4.24/4.45 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 4.24/4.45 inference(modus_ponens,[status(thm)],[18051, 18050])).
% 4.24/4.45 tff(18053,plain,
% 4.24/4.45 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[18052, 118, 18021, 18046])).
% 4.24/4.45 tff(18054,plain,
% 4.24/4.45 (((~![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)))))),
% 4.24/4.45 inference(rewrite,[status(thm)],[])).
% 4.24/4.45 tff(18055,plain,
% 4.24/4.45 ((~![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)))))),
% 4.24/4.45 inference(quant_inst,[status(thm)],[])).
% 4.24/4.45 tff(18056,plain,
% 4.24/4.45 ((~![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))))),
% 4.24/4.45 inference(modus_ponens,[status(thm)],[18055, 18054])).
% 4.24/4.45 tff(18057,plain,
% 4.24/4.45 ((s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z))))),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[18056, 41, 18053])).
% 4.24/4.45 tff(18058,plain,
% 4.24/4.45 (b(s(s(s(elem!1))), s(s(s(z))))),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[18057, 17980])).
% 4.24/4.45 tff(18059,plain,
% 4.24/4.45 (r(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 4.24/4.45 inference(monotonicity,[status(thm)],[18012])).
% 4.24/4.45 tff(18060,plain,
% 4.24/4.45 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[279, 178, 273, 104, 167, 595])).
% 4.24/4.45 tff(18061,plain,
% 4.24/4.45 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[249, 18060])).
% 4.24/4.45 tff(18062,plain,
% 4.24/4.45 (r(s(s(z)), s(s(s(elem!1))))),
% 4.24/4.45 inference(modus_ponens,[status(thm)],[18061, 18059])).
% 4.24/4.45 tff(18063,plain,
% 4.24/4.45 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[8364, 18044, 17982, 167, 18062])).
% 4.24/4.45 tff(18064,plain,
% 4.24/4.45 (b(s(s(s(z))), s(s(s(elem!1))))),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[9126, 18063, 11613])).
% 4.24/4.45 tff(18065,plain,
% 4.24/4.45 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 4.24/4.45 inference(monotonicity,[status(thm)],[17999])).
% 4.24/4.45 tff(18066,plain,
% 4.24/4.45 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 4.24/4.45 inference(monotonicity,[status(thm)],[18012])).
% 4.24/4.45 tff(18067,plain,
% 4.24/4.45 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.24/4.45 inference(monotonicity,[status(thm)],[17999])).
% 4.24/4.45 tff(18068,plain,
% 4.24/4.45 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.24/4.45 inference(modus_ponens,[status(thm)],[104, 18067])).
% 4.24/4.45 tff(18069,plain,
% 4.24/4.45 (b(s(s(s(elem!1))), elem!1)),
% 4.24/4.45 inference(modus_ponens,[status(thm)],[18068, 18066])).
% 4.24/4.45 tff(18070,plain,
% 4.24/4.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 4.24/4.45 inference(rewrite,[status(thm)],[])).
% 4.24/4.45 tff(18071,plain,
% 4.24/4.45 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 4.24/4.45 inference(rewrite,[status(thm)],[])).
% 4.24/4.45 tff(18072,plain,
% 4.24/4.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 4.24/4.45 inference(monotonicity,[status(thm)],[18071])).
% 4.24/4.45 tff(18073,plain,
% 4.24/4.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 4.24/4.45 inference(transitivity,[status(thm)],[18072, 18070])).
% 4.24/4.45 tff(18074,plain,
% 4.24/4.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))))),
% 4.24/4.45 inference(quant_inst,[status(thm)],[])).
% 4.24/4.45 tff(18075,plain,
% 4.24/4.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 4.24/4.45 inference(modus_ponens,[status(thm)],[18074, 18073])).
% 4.24/4.45 tff(18076,plain,
% 4.24/4.45 ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[18075, 178, 18019, 18069, 18043])).
% 4.24/4.45 tff(18077,plain,
% 4.24/4.45 (~b(z, s(s(s(z))))),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[18076, 18064])).
% 4.24/4.45 tff(18078,plain,
% 4.24/4.45 (r(z, s(s(s(z))))),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[4920, 18077])).
% 4.24/4.45 tff(18079,plain,
% 4.24/4.45 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[4961, 18078, 17985])).
% 4.24/4.45 tff(18080,plain,
% 4.24/4.45 (b(s(s(s(s(z)))), s(s(s(z))))),
% 4.24/4.45 inference(unit_resolution,[status(thm)],[11185, 18079])).
% 4.24/4.45 tff(18081,plain,
% 4.24/4.45 (b(elem!1, s(s(s(z))))),
% 4.24/4.46 inference(modus_ponens,[status(thm)],[18080, 18065])).
% 4.24/4.46 tff(18082,plain,
% 4.24/4.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(z))))))),
% 4.24/4.46 inference(rewrite,[status(thm)],[])).
% 4.24/4.46 tff(18083,plain,
% 4.24/4.46 (((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(z))))))),
% 4.24/4.46 inference(rewrite,[status(thm)],[])).
% 4.24/4.46 tff(18084,plain,
% 4.24/4.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(z)))))))),
% 4.24/4.46 inference(monotonicity,[status(thm)],[18083])).
% 4.24/4.46 tff(18085,plain,
% 4.24/4.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(z))))))),
% 4.24/4.46 inference(transitivity,[status(thm)],[18084, 18082])).
% 4.24/4.46 tff(18086,plain,
% 4.24/4.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 4.24/4.46 inference(quant_inst,[status(thm)],[])).
% 4.24/4.46 tff(18087,plain,
% 4.24/4.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(z)))))),
% 4.24/4.46 inference(modus_ponens,[status(thm)],[18086, 18085])).
% 4.24/4.46 tff(18088,plain,
% 4.24/4.46 ($false),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[18087, 178, 18069, 18081, 18043, 18064, 18058])).
% 4.24/4.46 tff(18089,plain,(b(elem!1, s(s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(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)))))) | (elem!1 = z) | (~b(z, s(s(s(s(s(s(s(z))))))))) | b(z, s(s(s(s(z))))) | r(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.24/4.46 tff(18090,plain,
% 4.24/4.46 (b(elem!1, s(s(s(s(z)))))),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[18089, 10828, 144, 10793, 204, 104, 290, 17173, 1, 167])).
% 4.24/4.46 tff(18091,plain,
% 4.24/4.46 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[279, 178, 144, 104, 167, 17173])).
% 4.24/4.46 tff(18092,plain,
% 4.24/4.46 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[249, 18091])).
% 4.24/4.46 tff(18093,plain,
% 4.24/4.46 (~r(s(s(z)), s(s(s(s(z)))))),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[5624, 18092, 204])).
% 4.24/4.46 tff(18094,plain,
% 4.24/4.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 4.24/4.46 inference(rewrite,[status(thm)],[])).
% 4.24/4.46 tff(18095,plain,
% 4.24/4.46 (((~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(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z))))) <=> ((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 4.24/4.46 inference(rewrite,[status(thm)],[])).
% 4.24/4.46 tff(18096,plain,
% 4.24/4.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z))))))))),
% 4.24/4.46 inference(monotonicity,[status(thm)],[18095])).
% 4.24/4.46 tff(18097,plain,
% 4.24/4.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 4.24/4.46 inference(transitivity,[status(thm)],[18096, 18094])).
% 4.24/4.46 tff(18098,plain,
% 4.24/4.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))))),
% 4.24/4.46 inference(quant_inst,[status(thm)],[])).
% 4.24/4.46 tff(18099,plain,
% 4.24/4.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z))))))),
% 4.24/4.46 inference(modus_ponens,[status(thm)],[18098, 18097])).
% 4.24/4.46 tff(18100,plain,
% 4.24/4.46 (~b(s(s(z)), elem!1)),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[18099, 178, 818, 273, 1301, 167])).
% 4.24/4.46 tff(18101,plain,
% 4.24/4.46 (s(s(z)) = elem!1),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[448, 18100, 10828])).
% 4.24/4.46 tff(18102,plain,
% 4.24/4.46 (s(s(s(z))) = s(elem!1)),
% 4.24/4.46 inference(monotonicity,[status(thm)],[18101])).
% 4.24/4.46 tff(18103,plain,
% 4.24/4.46 (s(s(s(s(z)))) = s(s(elem!1))),
% 4.24/4.46 inference(monotonicity,[status(thm)],[18102])).
% 4.24/4.46 tff(18104,plain,
% 4.24/4.46 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 4.24/4.46 inference(monotonicity,[status(thm)],[18103])).
% 4.24/4.46 tff(18105,plain,
% 4.24/4.46 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.24/4.46 inference(monotonicity,[status(thm)],[18103, 18104])).
% 4.24/4.46 tff(18106,plain,
% 4.24/4.46 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 4.24/4.46 inference(symmetry,[status(thm)],[18105])).
% 4.24/4.46 tff(18107,plain,
% 4.24/4.46 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 4.24/4.46 inference(monotonicity,[status(thm)],[18102])).
% 4.24/4.46 tff(18108,plain,
% 4.24/4.46 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 4.24/4.46 inference(transitivity,[status(thm)],[18107, 3881])).
% 4.24/4.46 tff(18109,plain,
% 4.24/4.46 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 4.24/4.46 inference(monotonicity,[status(thm)],[18108])).
% 4.24/4.46 tff(18110,plain,
% 4.24/4.46 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.24/4.46 inference(modus_ponens,[status(thm)],[8686, 18109])).
% 4.24/4.46 tff(18111,plain,
% 4.24/4.46 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[1649, 18110])).
% 4.24/4.46 tff(18112,plain,
% 4.24/4.46 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(s(elem!1)))),
% 4.24/4.46 inference(monotonicity,[status(thm)],[18103])).
% 4.24/4.46 tff(18113,plain,
% 4.24/4.46 ((~r(elem!1, s(s(s(s(z)))))) <=> (~r(elem!1, s(s(elem!1))))),
% 4.24/4.46 inference(monotonicity,[status(thm)],[18112])).
% 4.24/4.46 tff(18114,plain,
% 4.24/4.46 (r(s(s(z)), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 4.24/4.46 inference(monotonicity,[status(thm)],[18101])).
% 4.24/4.46 tff(18115,plain,
% 4.24/4.46 ((~r(s(s(z)), s(s(s(s(z)))))) <=> (~r(elem!1, s(s(s(s(z))))))),
% 4.24/4.46 inference(monotonicity,[status(thm)],[18114])).
% 4.24/4.46 tff(18116,plain,
% 4.24/4.46 (~r(elem!1, s(s(s(s(z)))))),
% 4.24/4.46 inference(modus_ponens,[status(thm)],[16684, 18115])).
% 4.24/4.46 tff(18117,plain,
% 4.24/4.46 (~r(elem!1, s(s(elem!1)))),
% 4.24/4.46 inference(modus_ponens,[status(thm)],[18116, 18113])).
% 4.24/4.46 tff(18118,plain,
% 4.24/4.46 ((s(s(elem!1)) = s(s(z))) <=> (s(s(elem!1)) = elem!1)),
% 4.24/4.46 inference(monotonicity,[status(thm)],[18101])).
% 4.24/4.46 tff(18119,plain,
% 4.24/4.46 ((s(s(elem!1)) = s(s(z))) <=> (elem!1 = s(s(elem!1)))),
% 4.24/4.46 inference(transitivity,[status(thm)],[18118, 1542])).
% 4.24/4.46 tff(18120,plain,
% 4.24/4.46 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(elem!1 = s(s(elem!1))))),
% 4.24/4.46 inference(monotonicity,[status(thm)],[18119])).
% 4.24/4.46 tff(18121,plain,
% 4.24/4.46 (~(elem!1 = s(s(elem!1)))),
% 4.24/4.46 inference(modus_ponens,[status(thm)],[2484, 18120])).
% 4.24/4.46 tff(18122,plain,
% 4.24/4.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 4.24/4.46 inference(rewrite,[status(thm)],[])).
% 4.24/4.46 tff(18123,plain,
% 4.24/4.46 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 4.24/4.46 inference(rewrite,[status(thm)],[])).
% 4.24/4.46 tff(18124,plain,
% 4.24/4.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z))))))))),
% 4.24/4.46 inference(monotonicity,[status(thm)],[18123])).
% 4.24/4.46 tff(18125,plain,
% 4.24/4.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 4.24/4.46 inference(transitivity,[status(thm)],[18124, 18122])).
% 4.24/4.46 tff(18126,plain,
% 4.24/4.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)))),
% 4.24/4.46 inference(quant_inst,[status(thm)],[])).
% 4.24/4.46 tff(18127,plain,
% 4.24/4.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z))))))),
% 4.24/4.46 inference(modus_ponens,[status(thm)],[18126, 18125])).
% 4.24/4.46 tff(18128,plain,
% 4.24/4.46 ((~b(z, elem!1)) | (~b(elem!1, s(s(z))))),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[18127, 178, 273, 1301, 167])).
% 4.24/4.46 tff(18129,plain,
% 4.24/4.46 (~b(elem!1, s(s(z)))),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[18128, 818])).
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% 4.24/4.46 ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[16647, 178, 3461, 273, 202])).
% 4.24/4.46 tff(18131,plain,
% 4.24/4.46 (~b(s(s(s(s(z)))), z)),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[18130, 167])).
% 4.24/4.46 tff(18132,plain,
% 4.24/4.46 (b(elem!1, s(s(s(elem!1))))),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[10659, 18100, 1, 18131, 18129])).
% 4.24/4.46 tff(18133,plain,
% 4.24/4.46 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 4.24/4.46 inference(monotonicity,[status(thm)],[18103])).
% 4.24/4.46 tff(18134,plain,
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% 4.24/4.46 inference(unit_resolution,[status(thm)],[8526, 18101, 202])).
% 4.24/4.46 tff(18135,plain,
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% 4.24/4.46 inference(modus_ponens,[status(thm)],[18134, 18133])).
% 4.24/4.46 tff(18136,plain,
% 4.24/4.46 ((s(elem!1) = s(s(z))) <=> (s(elem!1) = elem!1)),
% 4.24/4.46 inference(monotonicity,[status(thm)],[18101])).
% 4.24/4.46 tff(18137,plain,
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% 4.24/4.46 inference(symmetry,[status(thm)],[18136])).
% 4.24/4.46 tff(18138,plain,
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% 4.24/4.46 inference(monotonicity,[status(thm)],[18137])).
% 4.24/4.46 tff(18139,plain,
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% 4.24/4.46 inference(unit_resolution,[status(thm)],[16438, 18132])).
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% 4.24/4.46 inference(unit_resolution,[status(thm)],[2150, 18139])).
% 4.24/4.46 tff(18141,plain,
% 4.24/4.46 (~(s(elem!1) = s(s(z)))),
% 4.24/4.46 inference(modus_ponens,[status(thm)],[18140, 18138])).
% 4.24/4.46 tff(18142,plain,
% 4.24/4.46 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[2840, 18141])).
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% 4.24/4.46 inference(unit_resolution,[status(thm)],[191, 18131])).
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% 4.24/4.46 (b(s(s(z)), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 4.24/4.46 inference(monotonicity,[status(thm)],[18101])).
% 4.24/4.46 tff(18145,plain,
% 4.24/4.46 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 4.24/4.46 inference(symmetry,[status(thm)],[18144])).
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% 4.24/4.46 (b(s(s(z)), s(s(s(elem!1))))),
% 4.24/4.46 inference(modus_ponens,[status(thm)],[18132, 18145])).
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% 4.24/4.46 inference(unit_resolution,[status(thm)],[10669, 18146, 167, 202, 18142, 18143, 47])).
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% 4.24/4.46 inference(unit_resolution,[status(thm)],[2095, 18147])).
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% 4.24/4.46 inference(unit_resolution,[status(thm)],[8280, 18148, 273, 595, 202, 47, 18143, 18129])).
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% 4.24/4.46 inference(unit_resolution,[status(thm)],[4173, 18149, 18142])).
% 4.24/4.46 tff(18151,plain,
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% 4.24/4.46 inference(unit_resolution,[status(thm)],[10679, 18150, 18101])).
% 4.24/4.46 tff(18152,plain,
% 4.24/4.46 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[5479, 18151, 18135, 18132, 18121, 18117])).
% 4.24/4.46 tff(18153,plain,
% 4.24/4.46 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[3375, 18152, 18111])).
% 4.24/4.46 tff(18154,plain,
% 4.24/4.46 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 4.24/4.46 inference(modus_ponens,[status(thm)],[18153, 18106])).
% 4.24/4.46 tff(18155,plain,
% 4.24/4.46 (elem!1 = s(s(z))),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[3230, 18101])).
% 4.24/4.46 tff(18156,plain,
% 4.24/4.46 (~b(s(s(s(elem!1))), z)),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[7978, 18148, 273, 3461, 18146])).
% 4.24/4.46 tff(18157,plain,
% 4.24/4.46 (r(s(s(s(elem!1))), z)),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[1565, 18156])).
% 4.24/4.46 tff(18158,plain,
% 4.24/4.46 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[7142, 18157, 18155, 18143])).
% 4.24/4.46 tff(18159,plain,
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% 4.24/4.46 inference(unit_resolution,[status(thm)],[18158, 18154])).
% 4.24/4.46 tff(18160,plain,((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(z))))) | (s(s(elem!1)) = s(s(z))) | b(z, s(s(s(s(z))))) | r(s(s(z)), elem!1) | (~b(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.46 tff(18161,plain,
% 4.24/4.46 (~b(z, elem!1)),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[18160, 10828, 10793, 17173, 17976, 167, 18093, 3340, 1, 144, 18090])).
% 4.24/4.46 tff(18162,plain,
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% 4.24/4.46 inference(unit_resolution,[status(thm)],[585, 18161, 318])).
% 4.24/4.46 tff(18163,plain,
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% 4.24/4.46 inference(modus_ponens,[status(thm)],[521, 7049])).
% 4.24/4.46 tff(18164,plain,
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% 4.24/4.46 inference(unit_resolution,[status(thm)],[48, 18163])).
% 4.24/4.46 tff(18165,plain,((~(s(s(z)) = elem!1)) | r(z, s(s(z))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.46 tff(18166,plain,
% 4.24/4.46 (~(s(s(z)) = elem!1)),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[18165, 18162, 48])).
% 4.24/4.46 tff(18167,plain,
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% 4.24/4.46 inference(unit_resolution,[status(thm)],[448, 18166, 10828])).
% 4.24/4.46 tff(18168,plain,
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% 4.24/4.46 inference(unit_resolution,[status(thm)],[16647, 178, 10793, 144, 17976])).
% 4.24/4.46 tff(18170,plain,
% 4.24/4.46 (~b(s(s(s(s(z)))), z)),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[18169, 167])).
% 4.24/4.46 tff(18171,plain,
% 4.24/4.46 (r(s(s(s(s(z)))), z)),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[191, 18170])).
% 4.24/4.46 tff(18172,plain,
% 4.24/4.46 (s(s(s(s(z)))) = elem!1),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[3151, 18167, 17976, 167, 18171, 18162, 47])).
% 4.24/4.46 tff(18173,plain,
% 4.24/4.46 ($false),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[4509, 18172, 18168, 17976])).
% 4.24/4.46 tff(18174,plain,(r(s(s(z)), elem!1) | (~b(s(s(z)), s(s(s(s(z)))))) | r(z, s(s(z))) | b(z, s(s(s(s(z))))) | (~r(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)))))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 4.24/4.46 tff(18175,plain,
% 4.24/4.46 (r(s(s(z)), elem!1)),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[18174, 17965, 48, 1, 17175, 104, 290])).
% 4.24/4.46 tff(18176,plain,
% 4.24/4.46 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[2803, 18175, 17974])).
% 4.24/4.46 tff(18177,plain,
% 4.24/4.46 (~r(s(s(z)), s(s(s(s(z)))))),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[5624, 17974, 17175])).
% 4.24/4.46 tff(18178,plain,
% 4.24/4.46 ((~r(s(s(z)), s(s(s(s(z)))))) <=> (~r(s(s(z)), elem!1))),
% 4.24/4.46 inference(monotonicity,[status(thm)],[13352])).
% 4.24/4.46 tff(18179,plain,
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% 4.24/4.46 inference(modus_ponens,[status(thm)],[16684, 18178])).
% 4.24/4.46 tff(18180,plain,
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% 4.24/4.46 inference(unit_resolution,[status(thm)],[438, 18179])).
% 4.24/4.46 tff(18181,plain,((~(elem!1 = s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | r(s(s(z)), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.46 tff(18182,plain,
% 4.24/4.46 (~(elem!1 = s(s(s(s(z)))))),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[18181, 18175, 18177])).
% 4.24/4.46 tff(18183,plain,
% 4.24/4.46 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[17566, 18175, 17967])).
% 4.24/4.46 tff(18184,plain,
% 4.24/4.46 ($false),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[13328, 16660])).
% 4.24/4.46 tff(18185,plain,((~(elem!1 = s(s(s(s(s(s(s(z))))))))) | b(elem!1, s(s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.46 tff(18186,plain,
% 4.24/4.46 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[18185, 13328, 104])).
% 4.24/4.46 tff(18187,plain,
% 4.24/4.46 (r(elem!1, s(s(s(s(z)))))),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[483, 13328, 469])).
% 4.24/4.46 tff(18188,plain,
% 4.24/4.46 (~r(z, elem!1)),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[529, 18187, 145])).
% 4.24/4.46 tff(18189,plain,
% 4.24/4.46 (b(z, elem!1)),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[585, 18188, 318])).
% 4.24/4.46 tff(18190,plain,
% 4.24/4.46 (~r(elem!1, z)),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[478, 18187, 145])).
% 4.24/4.46 tff(18191,plain,
% 4.24/4.46 (b(elem!1, z)),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[498, 18190, 290])).
% 4.24/4.46 tff(18192,plain,
% 4.24/4.46 ($false),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[3672, 11096, 11095, 595, 818, 506])).
% 4.24/4.46 tff(18193,plain,((elem!1 = s(s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.46 tff(18194,plain,
% 4.24/4.46 ($false),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[18193, 18191, 18189, 595, 18186, 605, 644])).
% 4.24/4.46 tff(18195,plain,(b(elem!1, s(s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (elem!1 = z) | (~r(z, s(s(s(s(z)))))) | (elem!1 = s(s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.46 tff(18196,plain,
% 4.24/4.46 (b(elem!1, s(s(s(s(z)))))),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[18195, 18183, 17173, 18176, 290, 47, 18182, 104])).
% 4.24/4.46 tff(18197,plain,
% 4.24/4.46 (~(s(s(s(s(z)))) = elem!1)),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[504, 18182])).
% 4.24/4.46 tff(18198,plain,
% 4.24/4.46 (~r(s(s(s(s(z)))), elem!1)),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[3137, 521, 18143])).
% 4.24/4.46 tff(18199,plain,
% 4.24/4.46 (b(s(s(s(s(z)))), elem!1)),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[3142, 18198, 323])).
% 4.24/4.46 tff(18200,plain,
% 4.24/4.46 (~b(s(s(z)), elem!1)),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[3151, 521, 202, 167, 18143, 323, 47])).
% 4.24/4.46 tff(18201,plain,
% 4.24/4.46 (~b(elem!1, s(s(z)))),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[16667, 18199, 202, 167, 1301])).
% 4.24/4.46 tff(18202,plain,
% 4.24/4.46 (b(elem!1, s(s(s(elem!1))))),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[10659, 18201, 1, 18131, 18200])).
% 4.24/4.46 tff(18203,plain,
% 4.24/4.46 (~(s(s(s(elem!1))) = elem!1)),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[16438, 18202])).
% 4.24/4.46 tff(18204,plain,
% 4.24/4.46 (b(s(s(s(elem!1))), elem!1)),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[570, 18203, 11112])).
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% 4.24/4.46 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
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% 4.24/4.46 tff(18206,plain,
% 4.24/4.46 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
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% 4.24/4.46 tff(18207,plain,
% 4.24/4.46 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[3578, 18020])).
% 4.24/4.46 tff(18208,plain,
% 4.24/4.46 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[17566, 438, 18207])).
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% 4.24/4.46 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
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% 4.24/4.46 tff(18210,plain,
% 4.24/4.46 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.24/4.46 inference(modus_ponens,[status(thm)],[18209, 17826])).
% 4.24/4.46 tff(18211,plain,
% 4.24/4.46 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
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% 4.24/4.46 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.46 inference(modus_ponens,[status(thm)],[18211, 17783])).
% 4.24/4.46 tff(18213,plain,
% 4.24/4.46 (b(s(z), s(s(s(s(z)))))),
% 4.24/4.46 inference(modus_ponens,[status(thm)],[1301, 1875])).
% 4.24/4.46 tff(18214,plain,
% 4.24/4.46 (b(s(s(s(s(z)))), s(z))),
% 4.24/4.46 inference(modus_ponens,[status(thm)],[3771, 1569])).
% 4.24/4.46 tff(18215,plain,
% 4.24/4.46 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[17790, 178, 104, 18214, 18213, 18212])).
% 4.24/4.46 tff(18216,plain,
% 4.24/4.46 ($false),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[18215, 18210])).
% 4.24/4.46 tff(18217,plain,((~(s(elem!1) = s(s(z)))) | (~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)) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.46 tff(18218,plain,
% 4.24/4.46 (~(s(elem!1) = s(s(z)))),
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% 4.24/4.46 inference(unit_resolution,[status(thm)],[4173, 18219, 18205])).
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% 4.24/4.46 inference(unit_resolution,[status(thm)],[11287, 4904, 3461, 273, 224])).
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% 4.24/4.46 inference(unit_resolution,[status(thm)],[10755, 18240])).
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% 4.24/4.46 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 18244])).
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% 4.24/4.46 inference(unit_resolution,[status(thm)],[8218, 18243, 17967])).
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% 4.24/4.46 inference(unit_resolution,[status(thm)],[5031, 41, 18246, 10712])).
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% 4.24/4.46 inference(unit_resolution,[status(thm)],[8267, 178, 104, 17173, 18241])).
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% 4.24/4.46 inference(unit_resolution,[status(thm)],[18248, 18247])).
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% 4.24/4.46 inference(unit_resolution,[status(thm)],[4920, 18249])).
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% 4.24/4.46 inference(unit_resolution,[status(thm)],[4961, 18250, 17972])).
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% 4.24/4.46 (b(s(s(s(s(z)))), s(s(s(z))))),
% 4.24/4.46 inference(unit_resolution,[status(thm)],[11185, 18251])).
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% 4.24/4.46 inference(monotonicity,[status(thm)],[18259])).
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% 4.24/4.46 inference(monotonicity,[status(thm)],[18260])).
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% 4.24/4.46 inference(monotonicity,[status(thm)],[18263])).
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% 4.24/4.47 ((s(s(z)) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
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% 4.24/4.47 ((~(s(s(z)) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
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% 4.24/4.47 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
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% 4.24/4.47 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(elem!1) = s(s(elem!1)))),
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% 4.24/4.47 ((~(s(s(s(s(z)))) = s(elem!1))) <=> (~(s(s(elem!1)) = s(elem!1)))),
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% 4.24/4.47 tff(18312,plain,
% 4.24/4.47 (r(s(s(elem!1)), s(elem!1))),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[1006, 18311, 1000])).
% 4.24/4.47 tff(18313,plain,
% 4.24/4.47 (~b(z, s(elem!1))),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[8509, 727])).
% 4.24/4.47 tff(18314,plain,
% 4.24/4.47 (r(z, s(elem!1))),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[2351, 18313])).
% 4.24/4.47 tff(18315,plain,
% 4.24/4.47 ($false),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[10967, 18314, 18312, 5226])).
% 4.24/4.47 tff(18316,plain,((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(elem!1)))) | (s(s(elem!1)) = s(elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(s(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(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.47 tff(18317,plain,
% 4.24/4.47 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[18316, 18308, 18306, 18272, 17173, 18295, 18293])).
% 4.24/4.47 tff(18318,plain,
% 4.24/4.47 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[395, 18317, 18290])).
% 4.24/4.47 tff(18319,plain,
% 4.24/4.47 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 4.24/4.47 inference(monotonicity,[status(thm)],[11624])).
% 4.24/4.47 tff(18320,plain,
% 4.24/4.47 (~(s(s(s(elem!1))) = elem!1)),
% 4.24/4.47 inference(modus_ponens,[status(thm)],[1683, 18319])).
% 4.24/4.47 tff(18321,plain,
% 4.24/4.47 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[18195, 644, 595, 13328, 290, 145, 469, 104])).
% 4.24/4.47 tff(18322,plain,
% 4.24/4.47 (~b(s(s(z)), s(s(s(s(z)))))),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[17989, 1324, 13328])).
% 4.24/4.47 tff(18323,plain,
% 4.24/4.47 (r(s(s(z)), s(s(s(s(z)))))),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[164, 18322])).
% 4.24/4.47 tff(18324,plain,
% 4.24/4.47 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[10799, 18323, 145])).
% 4.24/4.47 tff(18325,plain,
% 4.24/4.47 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[4173, 11629, 18324])).
% 4.24/4.47 tff(18326,plain,
% 4.24/4.47 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[10679, 18325, 1324])).
% 4.24/4.47 tff(18327,plain,
% 4.24/4.47 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.24/4.47 inference(modus_ponens,[status(thm)],[11613, 11668])).
% 4.24/4.47 tff(18328,plain,
% 4.24/4.47 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[1649, 18327])).
% 4.24/4.47 tff(18329,plain,
% 4.24/4.47 (~(s(s(elem!1)) = elem!1)),
% 4.24/4.47 inference(modus_ponens,[status(thm)],[3340, 8801])).
% 4.24/4.47 tff(18330,plain,
% 4.24/4.47 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[691, 644, 18186])).
% 4.24/4.47 tff(18331,plain,
% 4.24/4.47 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[5101, 18323, 145, 3461])).
% 4.24/4.47 tff(18332,plain,
% 4.24/4.47 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[10755, 18331])).
% 4.24/4.47 tff(18333,plain,
% 4.24/4.47 (b(s(elem!1), s(s(s(s(z)))))),
% 4.24/4.47 inference(modus_ponens,[status(thm)],[18332, 8119])).
% 4.24/4.47 tff(18334,plain,
% 4.24/4.47 (b(s(elem!1), s(s(elem!1)))),
% 4.24/4.47 inference(modus_ponens,[status(thm)],[18333, 8488])).
% 4.24/4.47 tff(18335,plain,
% 4.24/4.47 (r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.47 inference(monotonicity,[status(thm)],[3505])).
% 4.24/4.47 tff(18336,plain,
% 4.24/4.47 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.47 inference(symmetry,[status(thm)],[18335])).
% 4.24/4.47 tff(18337,plain,
% 4.24/4.47 (~(s(s(elem!1)) = s(elem!1))),
% 4.24/4.47 inference(modus_ponens,[status(thm)],[16770, 10924])).
% 4.24/4.47 tff(18338,plain,
% 4.24/4.47 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[18316, 8134, 18337, 18334, 595, 8176, 18309])).
% 4.24/4.47 tff(18339,plain,
% 4.24/4.47 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[395, 18338, 8112])).
% 4.24/4.47 tff(18340,plain,
% 4.24/4.47 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.47 inference(modus_ponens,[status(thm)],[18339, 18336])).
% 4.24/4.47 tff(18341,plain,
% 4.24/4.47 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[11305, 644, 1324])).
% 4.24/4.47 tff(18342,plain,
% 4.24/4.47 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[249, 18341])).
% 4.24/4.47 tff(18343,plain,
% 4.24/4.47 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[17204, 18342, 273, 3461, 595])).
% 4.24/4.47 tff(18344,plain,
% 4.24/4.47 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[3578, 18343])).
% 4.24/4.47 tff(18345,plain,
% 4.24/4.47 (~r(s(s(s(z))), s(s(z)))),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[8218, 18344, 18340])).
% 4.24/4.47 tff(18346,plain,
% 4.24/4.47 (b(s(s(s(z))), s(s(z)))),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[4966, 18345])).
% 4.24/4.47 tff(18347,plain,
% 4.24/4.47 (b(s(elem!1), elem!1)),
% 4.24/4.47 inference(modus_ponens,[status(thm)],[18346, 8531])).
% 4.24/4.47 tff(18348,plain,
% 4.24/4.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 4.24/4.47 inference(rewrite,[status(thm)],[])).
% 4.24/4.47 tff(18349,plain,
% 4.24/4.47 (((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(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)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 4.24/4.47 inference(rewrite,[status(thm)],[])).
% 4.24/4.47 tff(18350,plain,
% 4.24/4.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(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)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 4.24/4.47 inference(monotonicity,[status(thm)],[18349])).
% 4.24/4.47 tff(18351,plain,
% 4.24/4.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(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)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 4.24/4.47 inference(transitivity,[status(thm)],[18350, 18348])).
% 4.24/4.47 tff(18352,plain,
% 4.24/4.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(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)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 4.24/4.47 inference(quant_inst,[status(thm)],[])).
% 4.24/4.47 tff(18353,plain,
% 4.24/4.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 4.24/4.47 inference(modus_ponens,[status(thm)],[18352, 18351])).
% 4.24/4.47 tff(18354,plain,
% 4.24/4.47 (~b(s(s(elem!1)), elem!1)),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[18353, 178, 18347, 18334, 18330, 18309])).
% 4.24/4.47 tff(18355,plain,
% 4.24/4.47 (r(s(s(elem!1)), elem!1)),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[3362, 18354, 18329])).
% 4.24/4.47 tff(18356,plain,
% 4.24/4.47 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))),
% 4.24/4.47 inference(rewrite,[status(thm)],[])).
% 4.24/4.47 tff(18357,plain,
% 4.24/4.47 (((~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)))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))),
% 4.24/4.47 inference(rewrite,[status(thm)],[])).
% 4.24/4.47 tff(18358,plain,
% 4.24/4.47 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1))))),
% 4.24/4.47 inference(monotonicity,[status(thm)],[18357])).
% 4.24/4.47 tff(18359,plain,
% 4.24/4.47 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))),
% 4.24/4.47 inference(transitivity,[status(thm)],[18358, 18356])).
% 4.24/4.47 tff(18360,plain,
% 4.24/4.47 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 4.24/4.47 inference(quant_inst,[status(thm)],[])).
% 4.24/4.47 tff(18361,plain,
% 4.24/4.47 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1))),
% 4.24/4.47 inference(modus_ponens,[status(thm)],[18360, 18359])).
% 4.24/4.47 tff(18362,plain,
% 4.24/4.47 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[18361, 118, 556, 3365])).
% 4.24/4.47 tff(18363,plain,
% 4.24/4.47 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[3375, 18362, 1655])).
% 4.24/4.47 tff(18364,plain,
% 4.24/4.47 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[4252, 118, 556, 2953])).
% 4.24/4.47 tff(18365,plain,
% 4.24/4.47 (b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[5118, 18364, 3521])).
% 4.24/4.47 tff(18366,plain,
% 4.24/4.47 ($false),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[3518, 178, 3512, 3511, 3829, 3504, 18309])).
% 4.24/4.47 tff(18367,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(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(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.47 tff(18368,plain,
% 4.24/4.47 ($false),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[18367, 18365, 18363, 3512, 3504, 18309])).
% 4.24/4.47 tff(18369,plain,((~r(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(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(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.47 tff(18370,plain,
% 4.24/4.47 (~r(s(s(s(elem!1))), elem!1)),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[18369, 18355, 8176, 18309, 4254, 18328, 18326, 18321])).
% 4.24/4.47 tff(18371,plain,
% 4.24/4.47 (b(s(s(s(elem!1))), elem!1)),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[570, 18370, 18320])).
% 4.24/4.47 tff(18372,plain,
% 4.24/4.47 (~r(elem!1, z)),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[478, 13329, 145])).
% 4.24/4.47 tff(18373,plain,
% 4.24/4.47 (b(elem!1, z)),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[498, 18372, 290])).
% 4.24/4.47 tff(18374,plain,
% 4.24/4.47 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[18367, 3829, 3512, 3504, 18309])).
% 4.24/4.47 tff(18375,plain,
% 4.24/4.47 (~r(elem!1, s(s(s(elem!1))))),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[3377, 18374, 3358, 346])).
% 4.24/4.47 tff(18376,plain,
% 4.24/4.47 (b(elem!1, s(s(s(elem!1))))),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[2054, 18375, 1586])).
% 4.24/4.47 tff(18377,plain,
% 4.24/4.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(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(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(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(elem!1))))))),
% 4.24/4.47 inference(rewrite,[status(thm)],[])).
% 4.24/4.47 tff(18378,plain,
% 4.24/4.47 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(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))))))), s(s(s(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(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(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(elem!1))))))),
% 4.24/4.47 inference(rewrite,[status(thm)],[])).
% 4.24/4.47 tff(18379,plain,
% 4.24/4.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(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(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(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(elem!1)))))))),
% 4.24/4.47 inference(monotonicity,[status(thm)],[18378])).
% 4.24/4.47 tff(18380,plain,
% 4.24/4.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(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(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(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(elem!1))))))),
% 4.24/4.47 inference(transitivity,[status(thm)],[18379, 18377])).
% 4.24/4.47 tff(18381,plain,
% 4.24/4.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(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(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.24/4.47 inference(quant_inst,[status(thm)],[])).
% 4.24/4.47 tff(18382,plain,
% 4.24/4.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 4.24/4.47 inference(modus_ponens,[status(thm)],[18381, 18380])).
% 4.24/4.47 tff(18383,plain,
% 4.24/4.47 ($false),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[18382, 178, 18376, 3512, 869, 3829, 3504])).
% 4.24/4.47 tff(18384,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (elem!1 = s(s(s(elem!1)))) | b(s(s(elem!1)), elem!1) | (s(s(elem!1)) = elem!1) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.47 tff(18385,plain,
% 4.24/4.47 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[18384, 18354, 18326, 8176, 11627, 18330, 18329, 18309])).
% 4.24/4.47 tff(18386,plain,
% 4.24/4.47 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[5118, 18385, 4254])).
% 4.24/4.47 tff(18387,plain,
% 4.24/4.47 (~r(elem!1, s(s(s(elem!1))))),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[8969, 18386, 18321])).
% 4.24/4.47 tff(18388,plain,
% 4.24/4.47 (b(elem!1, s(s(s(elem!1))))),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[2054, 18387, 11627])).
% 4.24/4.47 tff(18389,plain,
% 4.24/4.47 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[2820, 18330, 318, 595, 2811, 18372])).
% 4.24/4.47 tff(18390,plain,
% 4.24/4.47 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[133, 18389])).
% 4.24/4.47 tff(18391,plain,
% 4.24/4.47 (~r(z, s(s(s(elem!1))))),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[5130, 18386, 18390])).
% 4.24/4.47 tff(18392,plain,
% 4.24/4.47 (b(z, s(s(s(elem!1))))),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[2095, 18391])).
% 4.24/4.47 tff(18393,plain,
% 4.24/4.47 ($false),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[12925, 18392, 18388, 18373, 18256, 18371])).
% 4.24/4.47 tff(18394,plain,(r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~(s(s(z)) = elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | r(z, elem!1) | b(elem!1, s(s(s(s(z))))) | (elem!1 = z) | (~r(z, s(s(s(s(z)))))) | (elem!1 = s(s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.47 tff(18395,plain,
% 4.24/4.47 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[18394, 18293, 18258, 144, 10793, 17173, 2811, 13328, 290, 47, 18301, 104])).
% 4.24/4.47 tff(18396,plain,
% 4.24/4.47 (~r(elem!1, s(elem!1))),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[2935, 18395, 18318])).
% 4.24/4.47 tff(18397,plain,
% 4.24/4.47 (b(elem!1, s(elem!1))),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[756, 18396, 18289])).
% 4.24/4.47 tff(18398,plain,
% 4.24/4.47 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 4.24/4.47 inference(monotonicity,[status(thm)],[18259])).
% 4.24/4.47 tff(18399,plain,
% 4.24/4.47 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 4.24/4.47 inference(transitivity,[status(thm)],[18398, 3881])).
% 4.24/4.47 tff(18400,plain,
% 4.24/4.47 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 4.24/4.47 inference(monotonicity,[status(thm)],[18399])).
% 4.24/4.47 tff(18401,plain,
% 4.24/4.47 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.24/4.47 inference(modus_ponens,[status(thm)],[11613, 18400])).
% 4.24/4.47 tff(18402,plain,
% 4.24/4.47 (r(elem!1, s(s(s(s(z)))))),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[483, 18301, 13328])).
% 4.24/4.47 tff(18403,plain,
% 4.24/4.47 (~r(elem!1, z)),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[478, 18402, 47])).
% 4.24/4.47 tff(18404,plain,
% 4.24/4.47 (b(elem!1, z)),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[498, 18403, 290])).
% 4.24/4.47 tff(18405,plain,
% 4.24/4.47 ((~(elem!1 = s(s(s(z))))) <=> (~(s(elem!1) = elem!1))),
% 4.24/4.47 inference(monotonicity,[status(thm)],[18277])).
% 4.24/4.47 tff(18406,plain,
% 4.24/4.47 (~(s(elem!1) = elem!1)),
% 4.24/4.47 inference(modus_ponens,[status(thm)],[18282, 18405])).
% 4.24/4.47 tff(18407,plain,
% 4.24/4.47 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.24/4.47 inference(rewrite,[status(thm)],[])).
% 4.24/4.47 tff(18408,plain,
% 4.24/4.47 (((~r(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), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.24/4.47 inference(rewrite,[status(thm)],[])).
% 4.24/4.47 tff(18409,plain,
% 4.24/4.47 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 4.24/4.47 inference(monotonicity,[status(thm)],[18408])).
% 4.24/4.47 tff(18410,plain,
% 4.24/4.47 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.24/4.47 inference(transitivity,[status(thm)],[18409, 18407])).
% 4.24/4.47 tff(18411,plain,
% 4.24/4.47 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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), elem!1)))),
% 4.24/4.47 inference(quant_inst,[status(thm)],[])).
% 4.24/4.47 tff(18412,plain,
% 4.24/4.47 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 4.24/4.47 inference(modus_ponens,[status(thm)],[18411, 18410])).
% 4.24/4.47 tff(18413,plain,
% 4.24/4.47 (~r(s(elem!1), elem!1)),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[18412, 118, 18395, 18318])).
% 4.24/4.47 tff(18414,plain,
% 4.24/4.47 (b(s(elem!1), elem!1)),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[677, 18413, 18406])).
% 4.24/4.47 tff(18415,plain,
% 4.24/4.47 (~b(z, s(elem!1))),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[1396, 18414, 18256, 18404, 18397])).
% 4.24/4.47 tff(18416,plain,
% 4.24/4.47 (r(z, s(elem!1))),
% 4.24/4.47 inference(unit_resolution,[status(thm)],[2351, 18415])).
% 4.24/4.47 tff(18417,plain,
% 4.24/4.47 (r(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.24/4.47 inference(monotonicity,[status(thm)],[18258])).
% 4.24/4.48 tff(18418,plain,
% 4.24/4.48 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.48 inference(symmetry,[status(thm)],[18417])).
% 4.24/4.48 tff(18419,plain,
% 4.24/4.48 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.48 inference(modus_ponens,[status(thm)],[18395, 18418])).
% 4.24/4.48 tff(18420,plain,
% 4.24/4.48 (~r(s(elem!1), s(s(z)))),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[390, 18419, 18318])).
% 4.24/4.48 tff(18421,plain,
% 4.24/4.48 (~b(s(elem!1), z)),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[9589, 18420, 48, 18303, 18397, 18396, 10792])).
% 4.24/4.48 tff(18422,plain,
% 4.24/4.48 (r(s(elem!1), z)),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[774, 18421])).
% 4.24/4.48 tff(18423,plain,
% 4.24/4.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 4.24/4.48 inference(rewrite,[status(thm)],[])).
% 4.24/4.48 tff(18424,plain,
% 4.24/4.48 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 4.24/4.48 inference(rewrite,[status(thm)],[])).
% 4.24/4.48 tff(18425,plain,
% 4.24/4.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 4.24/4.48 inference(monotonicity,[status(thm)],[18424])).
% 4.24/4.48 tff(18426,plain,
% 4.24/4.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 4.24/4.48 inference(transitivity,[status(thm)],[18425, 18423])).
% 4.24/4.48 tff(18427,plain,
% 4.24/4.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 4.24/4.48 inference(quant_inst,[status(thm)],[])).
% 4.24/4.48 tff(18428,plain,
% 4.24/4.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 4.24/4.48 inference(modus_ponens,[status(thm)],[18427, 18426])).
% 4.24/4.48 tff(18429,plain,
% 4.24/4.48 ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[18428, 178, 854, 3512, 5391])).
% 4.24/4.48 tff(18430,plain,
% 4.24/4.48 (~b(s(s(s(elem!1))), s(elem!1))),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[18429, 2042])).
% 4.24/4.48 tff(18431,plain,
% 4.24/4.48 (r(s(s(s(elem!1))), s(elem!1))),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[373, 18430, 356])).
% 4.24/4.48 tff(18432,plain,
% 4.24/4.48 (~r(z, s(s(s(elem!1))))),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[5447, 18431, 2333])).
% 4.24/4.48 tff(18433,plain,
% 4.24/4.48 (b(z, s(s(s(elem!1))))),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[2095, 18432])).
% 4.24/4.48 tff(18434,plain,
% 4.24/4.48 (~r(s(s(s(elem!1))), z)),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[1557, 18431, 844])).
% 4.24/4.48 tff(18435,plain,
% 4.24/4.48 (b(s(s(s(elem!1))), z)),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[1565, 18434])).
% 4.24/4.48 tff(18436,plain,
% 4.24/4.48 (~b(s(s(z)), s(s(s(elem!1))))),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[7978, 18435, 273, 3461, 18433])).
% 4.24/4.48 tff(18437,plain,
% 4.24/4.48 ($false),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[18436, 11635])).
% 4.24/4.48 tff(18438,plain,((~b(elem!1, s(s(s(elem!1))))) | (~(s(s(z)) = elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.48 tff(18439,plain,
% 4.24/4.48 (~b(elem!1, s(s(s(elem!1))))),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[18438, 18258, 144, 10793, 18422, 18416, 18401, 18397, 18286, 18272])).
% 4.24/4.48 tff(18440,plain,
% 4.24/4.48 (b(s(s(s(s(z)))), z)),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[10412, 18439, 1, 18186, 18257, 18262])).
% 4.24/4.48 tff(18441,plain,
% 4.24/4.48 (b(s(s(elem!1)), z)),
% 4.24/4.48 inference(modus_ponens,[status(thm)],[18440, 18261])).
% 4.24/4.48 tff(18442,plain,
% 4.24/4.48 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[703, 18186])).
% 4.24/4.48 tff(18443,plain,
% 4.24/4.48 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 4.24/4.48 inference(monotonicity,[status(thm)],[18258])).
% 4.24/4.48 tff(18444,plain,
% 4.24/4.48 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 4.24/4.48 inference(transitivity,[status(thm)],[18443, 1526])).
% 4.24/4.48 tff(18445,plain,
% 4.24/4.48 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 4.24/4.48 inference(transitivity,[status(thm)],[18444, 2486])).
% 4.24/4.48 tff(18446,plain,
% 4.24/4.48 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 4.24/4.48 inference(monotonicity,[status(thm)],[18445])).
% 4.24/4.48 tff(18447,plain,
% 4.24/4.48 (~(elem!1 = s(s(s(elem!1))))),
% 4.24/4.48 inference(modus_ponens,[status(thm)],[1683, 18446])).
% 4.24/4.48 tff(18448,plain,
% 4.24/4.48 (r(elem!1, s(s(s(elem!1))))),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[2054, 18439, 18447])).
% 4.24/4.48 tff(18449,plain,
% 4.24/4.48 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[3502, 18302])).
% 4.24/4.48 tff(18450,plain,
% 4.24/4.48 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[1649, 18401])).
% 4.24/4.48 tff(18451,plain,
% 4.24/4.48 (r(elem!1, s(s(elem!1)))),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[9352, 18268, 18258])).
% 4.24/4.48 tff(18452,plain,
% 4.24/4.48 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[5845, 18448, 18451])).
% 4.24/4.48 tff(18453,plain,
% 4.24/4.48 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[3375, 18452, 18450])).
% 4.24/4.48 tff(18454,plain,
% 4.24/4.48 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[18367, 18453, 18286, 18295, 18293])).
% 4.24/4.48 tff(18455,plain,
% 4.24/4.48 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[5118, 18454, 18449])).
% 4.24/4.48 tff(18456,plain,
% 4.24/4.48 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[8969, 18455, 18448])).
% 4.24/4.48 tff(18457,plain,
% 4.24/4.48 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[3444, 18456, 18442])).
% 4.24/4.48 tff(18458,plain,
% 4.24/4.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~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))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 4.24/4.48 inference(rewrite,[status(thm)],[])).
% 4.24/4.48 tff(18459,plain,
% 4.24/4.48 (((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~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(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), z))) <=> ((~b(z, elem!1)) | (~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))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 4.24/4.48 inference(rewrite,[status(thm)],[])).
% 4.24/4.48 tff(18460,plain,
% 4.24/4.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~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(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 4.24/4.48 inference(monotonicity,[status(thm)],[18459])).
% 4.24/4.48 tff(18461,plain,
% 4.24/4.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~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(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~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))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 4.24/4.48 inference(transitivity,[status(thm)],[18460, 18458])).
% 4.24/4.48 tff(18462,plain,
% 4.24/4.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~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(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), z)))),
% 4.24/4.48 inference(quant_inst,[status(thm)],[])).
% 4.24/4.48 tff(18463,plain,
% 4.24/4.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 4.24/4.48 inference(modus_ponens,[status(thm)],[18462, 18461])).
% 4.24/4.48 tff(18464,plain,
% 4.24/4.48 ($false),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[18463, 178, 818, 6604, 595, 3664, 18309])).
% 4.24/4.48 tff(18465,plain,((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.48 tff(18466,plain,
% 4.24/4.48 (~b(s(s(elem!1)), z)),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[18465, 18457, 18256, 17173, 18293])).
% 4.24/4.48 tff(18467,plain,
% 4.24/4.48 ($false),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[18466, 18441])).
% 4.24/4.48 tff(18468,plain,(r(z, elem!1) | b(z, s(s(s(s(z))))) | r(z, s(s(z))) | b(elem!1, s(s(s(s(z))))) | (elem!1 = z) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | r(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.24/4.48 tff(18469,plain,
% 4.24/4.48 (r(z, elem!1)),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[18468, 10828, 48, 13328, 290, 104, 1])).
% 4.24/4.48 tff(18470,plain,
% 4.24/4.48 (~r(elem!1, s(s(s(s(z)))))),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[529, 18469, 47])).
% 4.24/4.48 tff(18471,plain,
% 4.24/4.48 (elem!1 = s(s(s(s(z))))),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[483, 18470, 13328])).
% 4.24/4.48 tff(18472,plain,
% 4.24/4.48 (s(elem!1) = s(s(s(s(s(z)))))),
% 4.24/4.48 inference(monotonicity,[status(thm)],[18471])).
% 4.24/4.48 tff(18473,plain,
% 4.24/4.48 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 4.24/4.48 inference(monotonicity,[status(thm)],[18472])).
% 4.24/4.48 tff(18474,plain,
% 4.24/4.48 (b(z, s(s(elem!1))) <=> b(z, s(s(s(s(s(s(z)))))))),
% 4.24/4.48 inference(monotonicity,[status(thm)],[18473])).
% 4.24/4.48 tff(18475,plain,
% 4.24/4.48 (b(z, s(s(s(s(s(s(z))))))) <=> b(z, s(s(elem!1)))),
% 4.24/4.48 inference(symmetry,[status(thm)],[18474])).
% 4.24/4.48 tff(18476,plain,
% 4.24/4.48 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 4.24/4.48 inference(monotonicity,[status(thm)],[18473, 18471])).
% 4.24/4.48 tff(18477,plain,
% 4.24/4.48 (~(s(s(z)) = elem!1)),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[18165, 18469, 48])).
% 4.24/4.48 tff(18478,plain,
% 4.24/4.48 (s(s(s(s(z)))) = elem!1),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[325, 18471])).
% 4.24/4.48 tff(18479,plain,
% 4.24/4.48 (~(s(s(elem!1)) = elem!1)),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[338, 18478, 18477])).
% 4.24/4.48 tff(18480,plain,
% 4.24/4.48 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.24/4.48 inference(monotonicity,[status(thm)],[18471])).
% 4.24/4.48 tff(18481,plain,
% 4.24/4.48 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), elem!1)),
% 4.24/4.48 inference(symmetry,[status(thm)],[18480])).
% 4.24/4.48 tff(18482,plain,
% 4.24/4.48 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 4.24/4.48 inference(monotonicity,[status(thm)],[18473])).
% 4.24/4.48 tff(18483,plain,
% 4.24/4.48 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 4.24/4.48 inference(monotonicity,[status(thm)],[18482])).
% 4.24/4.48 tff(18484,plain,
% 4.24/4.48 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.24/4.48 inference(symmetry,[status(thm)],[18483])).
% 4.24/4.48 tff(18485,plain,
% 4.24/4.48 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), elem!1)),
% 4.24/4.48 inference(transitivity,[status(thm)],[18484, 18481])).
% 4.24/4.48 tff(18486,plain,
% 4.24/4.48 (b(s(s(s(elem!1))), elem!1)),
% 4.24/4.48 inference(modus_ponens,[status(thm)],[104, 18485])).
% 4.24/4.48 tff(18487,plain,
% 4.24/4.48 (~(s(elem!1) = s(s(elem!1)))),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[979, 18479])).
% 4.24/4.48 tff(18488,plain,
% 4.24/4.48 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[3356, 18487])).
% 4.24/4.48 tff(18489,plain,
% 4.24/4.48 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.48 inference(monotonicity,[status(thm)],[18482])).
% 4.24/4.48 tff(18490,plain,
% 4.24/4.48 (r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.24/4.48 inference(symmetry,[status(thm)],[18489])).
% 4.24/4.48 tff(18491,plain,
% 4.24/4.48 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 4.24/4.48 inference(symmetry,[status(thm)],[18473])).
% 4.24/4.48 tff(18492,plain,
% 4.24/4.48 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.48 inference(monotonicity,[status(thm)],[18491])).
% 4.24/4.48 tff(18493,plain,
% 4.24/4.48 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.24/4.48 inference(transitivity,[status(thm)],[18492, 18490])).
% 4.24/4.48 tff(18494,plain,
% 4.24/4.48 ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) <=> (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 4.24/4.48 inference(monotonicity,[status(thm)],[18493])).
% 4.24/4.48 tff(18495,plain,
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% 4.24/4.48 inference(unit_resolution,[status(thm)],[448, 18477, 10828])).
% 4.24/4.48 tff(18496,plain,
% 4.24/4.48 (b(s(s(z)), s(s(s(s(z)))))),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[17684, 18471, 18495])).
% 4.24/4.48 tff(18497,plain,
% 4.24/4.48 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[279, 178, 144, 104, 18496, 17173])).
% 4.24/4.48 tff(18498,plain,
% 4.24/4.48 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[249, 18497])).
% 4.24/4.48 tff(18499,plain,
% 4.24/4.48 ((s(s(s(s(s(s(z)))))) = s(s(z))) <=> (s(s(elem!1)) = s(s(z)))),
% 4.24/4.48 inference(monotonicity,[status(thm)],[18491])).
% 4.24/4.48 tff(18500,plain,
% 4.24/4.48 ((s(s(elem!1)) = s(s(z))) <=> (s(s(s(s(s(s(z)))))) = s(s(z)))),
% 4.24/4.48 inference(symmetry,[status(thm)],[18499])).
% 4.24/4.48 tff(18501,plain,
% 4.24/4.48 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(s(s(s(s(z)))))) = s(s(z))))),
% 4.24/4.48 inference(monotonicity,[status(thm)],[18500])).
% 4.24/4.48 tff(18502,plain,
% 4.24/4.48 (~(s(s(s(s(s(s(z)))))) = s(s(z)))),
% 4.24/4.48 inference(modus_ponens,[status(thm)],[3340, 18501])).
% 4.24/4.48 tff(18503,plain,
% 4.24/4.48 ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[14128, 178, 10793, 18255, 17173])).
% 4.24/4.48 tff(18504,plain,
% 4.24/4.48 (~b(s(s(s(s(z)))), z)),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[18503, 18496])).
% 4.24/4.48 tff(18505,plain,
% 4.24/4.48 (r(s(s(s(s(z)))), z)),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[191, 18504])).
% 4.24/4.48 tff(18506,assumption,(r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 4.24/4.48 tff(18507,plain,
% 4.24/4.48 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[881, 18506])).
% 4.24/4.48 tff(18508,plain,
% 4.24/4.48 ((s(s(z)) = s(s(s(s(s(s(z))))))) | b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[9714, 41, 18507])).
% 4.24/4.48 tff(18509,plain,
% 4.24/4.48 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[18508, 9710])).
% 4.24/4.48 tff(18510,plain,
% 4.24/4.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 4.24/4.48 inference(rewrite,[status(thm)],[])).
% 4.24/4.48 tff(18511,plain,
% 4.24/4.48 (((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 4.24/4.48 inference(rewrite,[status(thm)],[])).
% 4.24/4.48 tff(18512,plain,
% 4.24/4.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))))),
% 4.24/4.48 inference(monotonicity,[status(thm)],[18511])).
% 4.24/4.48 tff(18513,plain,
% 4.24/4.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 4.24/4.48 inference(transitivity,[status(thm)],[18512, 18510])).
% 4.24/4.48 tff(18514,plain,
% 4.24/4.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 4.24/4.48 inference(quant_inst,[status(thm)],[])).
% 4.24/4.48 tff(18515,plain,
% 4.24/4.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))),
% 4.24/4.48 inference(modus_ponens,[status(thm)],[18514, 18513])).
% 4.24/4.48 tff(18516,plain,
% 4.24/4.48 ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[18515, 118, 224])).
% 4.24/4.48 tff(18517,plain,
% 4.24/4.48 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[18516, 18506])).
% 4.24/4.48 tff(18518,plain,
% 4.24/4.48 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[6139, 18517, 6134])).
% 4.24/4.48 tff(18519,plain,
% 4.24/4.48 ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[6107, 178, 3461, 273, 18518])).
% 4.24/4.48 tff(18520,plain,
% 4.24/4.48 (~b(s(s(s(s(s(s(z)))))), z)),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[18519, 18509])).
% 4.24/4.48 tff(18521,plain,
% 4.24/4.48 (((~![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))),
% 4.24/4.48 inference(rewrite,[status(thm)],[])).
% 4.24/4.48 tff(18522,plain,
% 4.24/4.48 ((~![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))),
% 4.24/4.48 inference(quant_inst,[status(thm)],[])).
% 4.24/4.48 tff(18523,plain,
% 4.24/4.48 ((~![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)),
% 4.24/4.48 inference(modus_ponens,[status(thm)],[18522, 18521])).
% 4.24/4.48 tff(18524,plain,
% 4.24/4.48 (r(s(s(s(s(s(s(z)))))), z)),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[18523, 41, 433, 18520])).
% 4.24/4.48 tff(18525,plain,
% 4.24/4.48 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[7294, 118, 194, 18524])).
% 4.24/4.48 tff(18526,plain,
% 4.24/4.48 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[7299, 41, 18525, 3698])).
% 4.24/4.48 tff(18527,plain,
% 4.24/4.48 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 4.24/4.48 inference(monotonicity,[status(thm)],[351, 319])).
% 4.24/4.48 tff(18528,plain,
% 4.24/4.48 (b(s(s(elem!1)), z) <=> b(s(s(s(s(s(s(z)))))), z)),
% 4.24/4.48 inference(monotonicity,[status(thm)],[351])).
% 4.24/4.48 tff(18529,plain,
% 4.24/4.48 (b(s(s(s(s(s(s(z)))))), z) <=> b(s(s(elem!1)), z)),
% 4.24/4.48 inference(symmetry,[status(thm)],[18528])).
% 4.24/4.48 tff(18530,plain,
% 4.24/4.48 ((~b(s(s(s(s(s(s(z)))))), z)) <=> (~b(s(s(elem!1)), z))),
% 4.24/4.48 inference(monotonicity,[status(thm)],[18529])).
% 4.24/4.48 tff(18531,plain,
% 4.24/4.48 (~b(s(s(elem!1)), z)),
% 4.24/4.48 inference(modus_ponens,[status(thm)],[18520, 18530])).
% 4.24/4.48 tff(18532,plain,
% 4.24/4.48 (r(s(s(elem!1)), z)),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[6600, 18531])).
% 4.24/4.48 tff(18533,plain,
% 4.24/4.48 (~r(s(s(elem!1)), elem!1)),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[6593, 18532, 521])).
% 4.24/4.48 tff(18534,plain,
% 4.24/4.48 (b(s(s(elem!1)), elem!1)),
% 4.24/4.48 inference(unit_resolution,[status(thm)],[3362, 18533, 346])).
% 4.24/4.48 tff(18535,plain,
% 4.24/4.48 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 4.24/4.48 inference(modus_ponens,[status(thm)],[18534, 18527])).
% 4.24/4.48 tff(18536,plain,
% 4.24/4.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(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(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(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(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 4.24/4.48 inference(rewrite,[status(thm)],[])).
% 4.24/4.48 tff(18537,plain,
% 4.24/4.48 (((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~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(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(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(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 4.24/4.48 inference(rewrite,[status(thm)],[])).
% 4.24/4.48 tff(18538,plain,
% 4.24/4.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~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(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(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(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(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 4.24/4.49 inference(monotonicity,[status(thm)],[18537])).
% 4.24/4.49 tff(18539,plain,
% 4.24/4.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~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(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(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(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(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 4.24/4.49 inference(transitivity,[status(thm)],[18538, 18536])).
% 4.24/4.49 tff(18540,plain,
% 4.24/4.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~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(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(z)))))),
% 4.24/4.49 inference(quant_inst,[status(thm)],[])).
% 4.24/4.49 tff(18541,plain,
% 4.24/4.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))),
% 4.24/4.49 inference(modus_ponens,[status(thm)],[18540, 18539])).
% 4.24/4.49 tff(18542,plain,
% 4.24/4.49 ($false),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[18541, 178, 167, 18535, 18518, 18509, 18526])).
% 4.24/4.49 tff(18543,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~(elem!1 = s(s(s(s(z)))))) | (s(s(elem!1)) = elem!1) | (~r(z, elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (s(s(s(s(s(s(z)))))) = s(s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.49 tff(18544,plain,
% 4.24/4.49 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[18543, 18496, 18505, 18471, 18479, 18469, 10793, 144, 18502, 18498])).
% 4.24/4.49 tff(18545,plain,
% 4.24/4.49 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.24/4.49 inference(modus_ponens,[status(thm)],[18544, 18494])).
% 4.24/4.49 tff(18546,plain,
% 4.24/4.49 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[3375, 18545, 18488])).
% 4.24/4.49 tff(18547,plain,
% 4.24/4.49 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.24/4.49 inference(monotonicity,[status(thm)],[18471])).
% 4.24/4.49 tff(18548,plain,
% 4.24/4.49 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 4.24/4.49 inference(symmetry,[status(thm)],[18547])).
% 4.24/4.49 tff(18549,plain,
% 4.24/4.49 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.49 inference(monotonicity,[status(thm)],[18482])).
% 4.24/4.49 tff(18550,plain,
% 4.24/4.49 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.24/4.49 inference(symmetry,[status(thm)],[18549])).
% 4.24/4.49 tff(18551,plain,
% 4.24/4.49 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(elem!1))))),
% 4.24/4.49 inference(transitivity,[status(thm)],[18550, 18548])).
% 4.24/4.49 tff(18552,plain,
% 4.24/4.49 (b(elem!1, s(s(s(elem!1))))),
% 4.24/4.49 inference(modus_ponens,[status(thm)],[18255, 18551])).
% 4.24/4.49 tff(18553,plain,
% 4.24/4.49 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[3404, 18488])).
% 4.24/4.49 tff(18554,plain,
% 4.24/4.49 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[7840, 178, 144, 104, 18496, 17173])).
% 4.24/4.49 tff(18555,plain,
% 4.24/4.49 (r(s(s(s(elem!1))), s(s(z)))),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[14415, 18554, 18471])).
% 4.24/4.49 tff(18556,plain,
% 4.24/4.49 (~(s(s(z)) = s(s(s(s(s(s(z)))))))),
% 4.24/4.49 inference(modus_ponens,[status(thm)],[18502, 9709])).
% 4.24/4.49 tff(18557,plain,
% 4.24/4.49 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.49 inference(monotonicity,[status(thm)],[18491])).
% 4.24/4.49 tff(18558,plain,
% 4.24/4.49 (b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.49 inference(symmetry,[status(thm)],[18557])).
% 4.24/4.49 tff(18559,plain,
% 4.24/4.49 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.49 inference(monotonicity,[status(thm)],[18482])).
% 4.24/4.49 tff(18560,plain,
% 4.24/4.49 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.49 inference(modus_ponens,[status(thm)],[18546, 18559])).
% 4.24/4.49 tff(18561,plain,
% 4.24/4.49 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.49 inference(modus_ponens,[status(thm)],[18560, 18558])).
% 4.24/4.49 tff(18562,plain,
% 4.24/4.49 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> b(s(s(elem!1)), elem!1)),
% 4.24/4.49 inference(symmetry,[status(thm)],[18527])).
% 4.24/4.49 tff(18563,plain,
% 4.24/4.49 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) <=> (~b(s(s(elem!1)), elem!1))),
% 4.24/4.49 inference(monotonicity,[status(thm)],[18562])).
% 4.24/4.49 tff(18564,assumption,(b(s(s(z)), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 4.24/4.49 tff(18565,assumption,(b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 4.24/4.49 tff(18566,plain,
% 4.24/4.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(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(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(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(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 4.24/4.49 inference(rewrite,[status(thm)],[])).
% 4.24/4.49 tff(18567,plain,
% 4.24/4.49 (((~b(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))))))))) | (~b(s(s(s(s(s(s(z)))))), s(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(s(s(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(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 4.24/4.49 inference(rewrite,[status(thm)],[])).
% 4.24/4.49 tff(18568,plain,
% 4.24/4.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(s(s(s(s(z)))))), s(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(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(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(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 4.24/4.49 inference(monotonicity,[status(thm)],[18567])).
% 4.24/4.49 tff(18569,plain,
% 4.24/4.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(s(s(s(s(z)))))), s(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(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(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(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 4.24/4.49 inference(transitivity,[status(thm)],[18568, 18566])).
% 4.24/4.49 tff(18570,plain,
% 4.24/4.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(s(s(s(s(z)))))), s(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(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 4.24/4.49 inference(quant_inst,[status(thm)],[])).
% 4.24/4.49 tff(18571,plain,
% 4.24/4.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(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(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 4.24/4.49 inference(modus_ponens,[status(thm)],[18570, 18569])).
% 4.24/4.49 tff(18572,plain,
% 4.24/4.49 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[18571, 178, 167, 251, 18565])).
% 4.24/4.49 tff(18573,plain,
% 4.24/4.49 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[18572, 18564])).
% 4.24/4.49 tff(18574,plain,
% 4.24/4.49 (~b(s(s(elem!1)), elem!1)),
% 4.24/4.49 inference(modus_ponens,[status(thm)],[18573, 18563])).
% 4.24/4.49 tff(18575,plain,
% 4.24/4.49 (r(s(s(elem!1)), elem!1)),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[3362, 18574, 346])).
% 4.24/4.49 tff(18576,plain,
% 4.24/4.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 4.24/4.49 inference(rewrite,[status(thm)],[])).
% 4.24/4.49 tff(18577,plain,
% 4.24/4.49 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 4.24/4.49 inference(rewrite,[status(thm)],[])).
% 4.24/4.49 tff(18578,plain,
% 4.24/4.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 4.24/4.49 inference(monotonicity,[status(thm)],[18577])).
% 4.24/4.49 tff(18579,plain,
% 4.24/4.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 4.24/4.49 inference(transitivity,[status(thm)],[18578, 18576])).
% 4.24/4.49 tff(18580,plain,
% 4.24/4.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 4.24/4.49 inference(quant_inst,[status(thm)],[])).
% 4.24/4.49 tff(18581,plain,
% 4.24/4.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 4.24/4.49 inference(modus_ponens,[status(thm)],[18580, 18579])).
% 4.24/4.49 tff(18582,plain,
% 4.24/4.49 ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[18581, 178, 3461, 595, 18565])).
% 4.24/4.49 tff(18583,plain,
% 4.24/4.49 (~b(s(s(s(s(s(s(z)))))), z)),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[18582, 18564])).
% 4.24/4.49 tff(18584,plain,
% 4.24/4.49 (~b(s(s(elem!1)), z)),
% 4.24/4.49 inference(modus_ponens,[status(thm)],[18583, 18530])).
% 4.24/4.49 tff(18585,plain,
% 4.24/4.49 (r(s(s(elem!1)), z)),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[6600, 18584])).
% 4.24/4.49 tff(18586,plain,
% 4.24/4.49 ($false),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[6593, 18585, 18575, 521])).
% 4.24/4.49 tff(18587,plain,((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(z, elem!1)) | (s(s(elem!1)) = elem!1) | (~(elem!1 = s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(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(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.49 tff(18588,plain,
% 4.24/4.49 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[18587, 18469, 18479, 18471, 10793, 17173, 18561, 18496, 18255])).
% 4.24/4.49 tff(18589,plain,
% 4.24/4.49 ((s(s(z)) = s(s(s(s(s(s(z))))))) | r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[9714, 41, 18588])).
% 4.24/4.49 tff(18590,plain,
% 4.24/4.49 (r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[18589, 18556])).
% 4.24/4.49 tff(18591,plain,
% 4.24/4.49 (r(s(s(z)), s(s(elem!1)))),
% 4.24/4.49 inference(modus_ponens,[status(thm)],[6939, 11507])).
% 4.24/4.49 tff(18592,plain,
% 4.24/4.49 ($false),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[6471, 18591])).
% 4.24/4.49 tff(18593,plain,((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | r(s(s(z)), s(s(elem!1))) | (~(elem!1 = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.49 tff(18594,plain,
% 4.24/4.49 (r(s(s(z)), s(s(elem!1)))),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[18593, 18590, 18471])).
% 4.24/4.49 tff(18595,plain,
% 4.24/4.49 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[6454, 18594, 18555])).
% 4.24/4.49 tff(18596,plain,
% 4.24/4.49 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[3409, 18595, 18553])).
% 4.24/4.49 tff(18597,plain,
% 4.24/4.49 (~b(s(s(elem!1)), elem!1)),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[5500, 18596, 18552, 18546, 18486])).
% 4.24/4.49 tff(18598,plain,
% 4.24/4.49 (r(s(s(elem!1)), elem!1)),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[3362, 18597, 18479])).
% 4.24/4.49 tff(18599,plain,
% 4.24/4.49 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 4.24/4.49 inference(modus_ponens,[status(thm)],[18598, 18476])).
% 4.24/4.49 tff(18600,plain,
% 4.24/4.49 (~r(z, s(s(s(s(s(s(z)))))))),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[11497, 118, 47, 18599])).
% 4.24/4.49 tff(18601,plain,
% 4.24/4.49 ((z = s(s(s(s(s(s(z))))))) | b(z, s(s(s(s(s(s(z)))))))),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[11502, 41, 18600])).
% 4.24/4.49 tff(18602,plain,
% 4.24/4.49 (b(z, s(s(s(s(s(s(z)))))))),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[18601, 11490])).
% 4.24/4.49 tff(18603,plain,
% 4.24/4.49 (b(z, s(s(elem!1)))),
% 4.24/4.49 inference(modus_ponens,[status(thm)],[18602, 18475])).
% 4.24/4.49 tff(18604,plain,
% 4.24/4.49 (b(z, s(s(s(elem!1))))),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[17717, 18471, 17173])).
% 4.24/4.49 tff(18605,plain,
% 4.24/4.49 (~r(s(s(elem!1)), z)),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[6593, 18598, 18469])).
% 4.24/4.49 tff(18606,plain,
% 4.24/4.49 (b(s(s(elem!1)), z)),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[6600, 18605])).
% 4.24/4.49 tff(18607,plain,
% 4.24/4.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(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(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(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(s(s(elem!1)), s(s(s(elem!1))))))),
% 4.24/4.49 inference(rewrite,[status(thm)],[])).
% 4.24/4.49 tff(18608,plain,
% 4.24/4.49 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z))) <=> ((~b(z, s(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(s(s(elem!1)), s(s(s(elem!1))))))),
% 4.24/4.49 inference(rewrite,[status(thm)],[])).
% 4.24/4.49 tff(18609,plain,
% 4.24/4.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(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(s(s(elem!1)), s(s(s(elem!1)))))))),
% 4.24/4.49 inference(monotonicity,[status(thm)],[18608])).
% 4.24/4.49 tff(18610,plain,
% 4.24/4.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(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(s(s(elem!1)), s(s(s(elem!1))))))),
% 4.24/4.49 inference(transitivity,[status(thm)],[18609, 18607])).
% 4.24/4.49 tff(18611,plain,
% 4.24/4.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 4.24/4.49 inference(quant_inst,[status(thm)],[])).
% 4.24/4.49 tff(18612,plain,
% 4.24/4.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 4.24/4.49 inference(modus_ponens,[status(thm)],[18611, 18610])).
% 4.24/4.49 tff(18613,plain,
% 4.24/4.49 ($false),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[18612, 178, 2043, 6604, 6477, 3512, 3511])).
% 4.24/4.49 tff(18614,plain,((~b(s(s(s(elem!1))), 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(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.49 tff(18615,plain,
% 4.24/4.49 (~b(z, s(s(elem!1)))),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[18614, 18606, 18604, 18546, 18596])).
% 4.24/4.49 tff(18616,plain,
% 4.24/4.49 ($false),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[18615, 18603])).
% 4.24/4.49 tff(18617,plain,(r(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))))) | r(z, s(s(z))) | (elem!1 = z) | b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.49 tff(18618,plain,
% 4.24/4.49 (r(s(s(z)), elem!1)),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[18617, 13328, 104, 48, 290, 1])).
% 4.24/4.49 tff(18619,plain,
% 4.24/4.49 (~r(s(s(z)), s(s(s(s(z)))))),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[8763, 470, 438])).
% 4.24/4.49 tff(18620,plain,
% 4.24/4.49 (b(s(s(z)), s(s(s(s(z)))))),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[164, 18619])).
% 4.24/4.49 tff(18621,plain,
% 4.24/4.49 (~(s(s(z)) = elem!1)),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[17989, 18620, 13328])).
% 4.24/4.49 tff(18622,plain,
% 4.24/4.49 (~r(z, elem!1)),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[529, 470, 47])).
% 4.24/4.49 tff(18623,plain,
% 4.24/4.49 (b(z, elem!1)),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[585, 18622, 318])).
% 4.24/4.49 tff(18624,plain,
% 4.24/4.49 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[279, 178, 273, 104, 18620, 595])).
% 4.24/4.49 tff(18625,plain,
% 4.24/4.49 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[249, 18624])).
% 4.24/4.49 tff(18626,plain,
% 4.24/4.49 (~(elem!1 = s(s(z)))),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[311, 18621])).
% 4.24/4.49 tff(18627,plain,
% 4.24/4.49 (~r(elem!1, z)),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[478, 470, 47])).
% 4.24/4.49 tff(18628,plain,
% 4.24/4.49 (b(elem!1, z)),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[498, 18627, 290])).
% 4.24/4.49 tff(18629,plain,
% 4.24/4.49 (~b(elem!1, s(s(z)))),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[16411, 178, 18623, 18628, 3461, 273])).
% 4.24/4.49 tff(18630,plain,
% 4.24/4.49 (r(elem!1, s(s(z)))),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[467, 18629, 18626])).
% 4.24/4.49 tff(18631,plain,
% 4.24/4.49 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[3113, 18630, 18625])).
% 4.24/4.49 tff(18632,plain,
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% 4.24/4.49 inference(unit_resolution,[status(thm)],[16753, 18631, 18625, 273, 104, 251, 1, 3461, 18623, 18621, 18620, 290, 18186])).
% 4.24/4.49 tff(18633,plain,((~r(elem!1, s(s(s(s(z)))))) | (~b(z, 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(z, s(s(s(s(z))))) | (~b(s(s(z)), z)) | (elem!1 = z) | (~b(z, s(s(s(s(s(s(s(z))))))))) | b(elem!1, s(s(s(s(z))))) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.24/4.49 tff(18634,plain,
% 4.24/4.49 (~r(elem!1, s(s(s(s(z)))))),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[18633, 13328, 104, 18255, 1, 10793, 290, 17173, 144, 18618])).
% 4.24/4.49 tff(18635,plain,
% 4.24/4.49 (elem!1 = s(s(s(s(z))))),
% 4.24/4.49 inference(unit_resolution,[status(thm)],[483, 18634, 13328])).
% 4.24/4.49 tff(18636,plain,
% 4.24/4.49 (s(elem!1) = s(s(s(s(s(z)))))),
% 4.24/4.49 inference(monotonicity,[status(thm)],[18635])).
% 4.24/4.49 tff(18637,plain,
% 4.24/4.49 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 4.24/4.49 inference(monotonicity,[status(thm)],[18636])).
% 4.24/4.49 tff(18638,plain,
% 4.24/4.49 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 4.24/4.49 inference(symmetry,[status(thm)],[18637])).
% 4.24/4.49 tff(18639,plain,
% 4.24/4.49 ((s(s(s(s(s(s(z)))))) = s(s(z))) <=> (s(s(elem!1)) = s(s(z)))),
% 4.24/4.49 inference(monotonicity,[status(thm)],[18638])).
% 4.24/4.49 tff(18640,plain,
% 4.24/4.49 ((s(s(elem!1)) = s(s(z))) <=> (s(s(s(s(s(s(z)))))) = s(s(z)))),
% 4.24/4.49 inference(symmetry,[status(thm)],[18639])).
% 4.24/4.50 tff(18641,plain,
% 4.24/4.50 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(s(s(s(s(z)))))) = s(s(z))))),
% 4.24/4.50 inference(monotonicity,[status(thm)],[18640])).
% 4.24/4.50 tff(18642,plain,
% 4.24/4.50 (~(s(s(s(s(s(s(z)))))) = s(s(z)))),
% 4.24/4.50 inference(modus_ponens,[status(thm)],[3340, 18641])).
% 4.24/4.50 tff(18643,plain,
% 4.24/4.50 (~(s(s(z)) = s(s(s(s(s(s(z)))))))),
% 4.24/4.50 inference(modus_ponens,[status(thm)],[18642, 9709])).
% 4.24/4.50 tff(18644,plain,
% 4.24/4.50 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 4.24/4.50 inference(monotonicity,[status(thm)],[18637])).
% 4.24/4.50 tff(18645,plain,
% 4.24/4.50 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.50 inference(monotonicity,[status(thm)],[18637, 18644])).
% 4.24/4.50 tff(18646,plain,
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% 4.24/4.50 inference(unit_resolution,[status(thm)],[325, 18635])).
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% 4.24/4.50 inference(unit_resolution,[status(thm)],[1846, 18635, 1])).
% 4.24/4.50 tff(18648,plain,
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% 4.24/4.50 inference(unit_resolution,[status(thm)],[585, 18647, 318])).
% 4.24/4.50 tff(18649,plain,
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% 4.24/4.50 inference(unit_resolution,[status(thm)],[18165, 18648, 48])).
% 4.24/4.50 tff(18650,plain,
% 4.24/4.50 (~(s(s(elem!1)) = elem!1)),
% 4.24/4.50 inference(unit_resolution,[status(thm)],[338, 18649, 18646])).
% 4.24/4.50 tff(18651,plain,
% 4.24/4.50 (~(s(elem!1) = s(s(elem!1)))),
% 4.24/4.50 inference(unit_resolution,[status(thm)],[979, 18650])).
% 4.24/4.50 tff(18652,plain,
% 4.24/4.50 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 4.24/4.50 inference(unit_resolution,[status(thm)],[3356, 18651])).
% 4.24/4.50 tff(18653,plain,
% 4.24/4.50 (b(z, s(s(s(elem!1))))),
% 4.24/4.50 inference(unit_resolution,[status(thm)],[17717, 18635, 17173])).
% 4.24/4.50 tff(18654,plain,
% 4.24/4.50 (~(s(s(s(elem!1))) = elem!1)),
% 4.24/4.50 inference(unit_resolution,[status(thm)],[17579, 18653, 18647])).
% 4.24/4.50 tff(18655,plain,
% 4.24/4.50 (~r(s(s(s(elem!1))), elem!1)),
% 4.24/4.50 inference(unit_resolution,[status(thm)],[6388, 18648, 18618, 10793, 144])).
% 4.24/4.50 tff(18656,plain,
% 4.24/4.50 (b(s(s(s(elem!1))), elem!1)),
% 4.24/4.50 inference(unit_resolution,[status(thm)],[570, 18655, 18654])).
% 4.24/4.50 tff(18657,plain,
% 4.24/4.50 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 4.24/4.50 inference(monotonicity,[status(thm)],[18637, 18635])).
% 4.24/4.50 tff(18658,plain,
% 4.24/4.50 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> r(s(s(elem!1)), elem!1)),
% 4.24/4.50 inference(symmetry,[status(thm)],[18657])).
% 4.24/4.50 tff(18659,plain,
% 4.24/4.50 ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) <=> (~r(s(s(elem!1)), elem!1))),
% 4.24/4.50 inference(monotonicity,[status(thm)],[18658])).
% 4.24/4.50 tff(18660,plain,
% 4.24/4.50 (r(s(s(z)), s(s(s(s(z)))))),
% 4.24/4.50 inference(unit_resolution,[status(thm)],[18181, 18635, 18618])).
% 4.24/4.50 tff(18661,plain,
% 4.24/4.50 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 4.24/4.50 inference(unit_resolution,[status(thm)],[11534, 18660, 47, 18635, 10793, 144])).
% 4.24/4.50 tff(18662,plain,
% 4.24/4.50 (~r(s(s(elem!1)), elem!1)),
% 4.24/4.50 inference(modus_ponens,[status(thm)],[18661, 18659])).
% 4.24/4.50 tff(18663,plain,
% 4.24/4.50 (b(s(s(elem!1)), elem!1)),
% 4.24/4.50 inference(unit_resolution,[status(thm)],[3362, 18662, 18650])).
% 4.24/4.50 tff(18664,plain,
% 4.24/4.50 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.24/4.50 inference(monotonicity,[status(thm)],[18635])).
% 4.24/4.50 tff(18665,plain,
% 4.24/4.50 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 4.24/4.50 inference(symmetry,[status(thm)],[18664])).
% 4.24/4.50 tff(18666,plain,
% 4.24/4.50 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.24/4.50 inference(monotonicity,[status(thm)],[18644])).
% 4.24/4.50 tff(18667,plain,
% 4.24/4.50 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.24/4.50 inference(symmetry,[status(thm)],[18666])).
% 4.24/4.50 tff(18668,plain,
% 4.24/4.50 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(elem!1))))),
% 4.24/4.50 inference(transitivity,[status(thm)],[18667, 18665])).
% 4.24/4.50 tff(18669,plain,
% 4.24/4.50 (b(elem!1, s(s(s(elem!1))))),
% 4.24/4.50 inference(modus_ponens,[status(thm)],[18255, 18668])).
% 4.24/4.50 tff(18670,plain,
% 4.24/4.50 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 4.24/4.50 inference(unit_resolution,[status(thm)],[3404, 18652])).
% 4.24/4.50 tff(18671,plain,
% 4.24/4.50 (~(s(elem!1) = elem!1)),
% 4.24/4.50 inference(unit_resolution,[status(thm)],[2150, 18654])).
% 4.24/4.50 tff(18672,plain,
% 4.24/4.50 (~r(s(elem!1), elem!1)),
% 4.24/4.50 inference(unit_resolution,[status(thm)],[11444, 18660, 144, 18635, 10793, 18648])).
% 4.24/4.50 tff(18673,plain,
% 4.34/4.50 (b(s(elem!1), elem!1)),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[677, 18672, 18671])).
% 4.34/4.50 tff(18674,plain,
% 4.34/4.50 (~(elem!1 = s(elem!1))),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[748, 18671])).
% 4.34/4.50 tff(18675,plain,
% 4.34/4.50 (s(s(s(s(s(z))))) = s(elem!1)),
% 4.34/4.50 inference(symmetry,[status(thm)],[18636])).
% 4.34/4.50 tff(18676,plain,
% 4.34/4.50 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.34/4.50 inference(monotonicity,[status(thm)],[18675])).
% 4.34/4.50 tff(18677,plain,
% 4.34/4.50 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))),
% 4.34/4.50 inference(monotonicity,[status(thm)],[18644, 18636])).
% 4.34/4.50 tff(18678,plain,
% 4.34/4.50 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 4.34/4.50 inference(transitivity,[status(thm)],[18677, 4625])).
% 4.34/4.50 tff(18679,plain,
% 4.34/4.50 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.34/4.50 inference(transitivity,[status(thm)],[18678, 18676])).
% 4.34/4.50 tff(18680,plain,
% 4.34/4.50 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.50 inference(monotonicity,[status(thm)],[18679])).
% 4.34/4.50 tff(18681,plain,
% 4.34/4.50 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[348, 18650])).
% 4.34/4.50 tff(18682,plain,
% 4.34/4.50 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.34/4.50 inference(modus_ponens,[status(thm)],[18681, 18680])).
% 4.34/4.50 tff(18683,plain,
% 4.34/4.50 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.50 inference(monotonicity,[status(thm)],[320])).
% 4.34/4.50 tff(18684,plain,
% 4.34/4.50 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.50 inference(monotonicity,[status(thm)],[320, 352])).
% 4.34/4.50 tff(18685,plain,
% 4.34/4.50 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 4.34/4.50 inference(symmetry,[status(thm)],[18684])).
% 4.34/4.50 tff(18686,plain,
% 4.34/4.50 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 4.34/4.50 inference(transitivity,[status(thm)],[376, 18685])).
% 4.34/4.50 tff(18687,plain,
% 4.34/4.50 (b(s(elem!1), s(s(s(elem!1))))),
% 4.34/4.50 inference(modus_ponens,[status(thm)],[727, 18686])).
% 4.34/4.50 tff(18688,plain,
% 4.34/4.50 (b(s(elem!1), s(s(s(s(z)))))),
% 4.34/4.50 inference(modus_ponens,[status(thm)],[683, 13354])).
% 4.34/4.50 tff(18689,plain,
% 4.34/4.50 (~b(s(s(z)), s(elem!1))),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[2529, 727, 104, 166, 18688])).
% 4.34/4.50 tff(18690,plain,
% 4.34/4.50 (r(s(s(z)), s(elem!1))),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[1067, 18689, 17020])).
% 4.34/4.50 tff(18691,plain,
% 4.34/4.50 (~r(elem!1, s(elem!1))),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[12646, 18690, 319, 147])).
% 4.34/4.50 tff(18692,plain,
% 4.34/4.50 (b(elem!1, s(elem!1))),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[756, 18691, 750])).
% 4.34/4.50 tff(18693,plain,
% 4.34/4.50 (~b(s(elem!1), s(s(s(elem!1))))),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[6834, 18692, 1597, 683, 2042])).
% 4.34/4.50 tff(18694,plain,
% 4.34/4.50 ($false),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[18693, 18687])).
% 4.34/4.50 tff(18695,plain,((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (elem!1 = s(elem!1)) | (~r(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(z)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.50 tff(18696,plain,
% 4.34/4.50 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[18695, 166, 1597, 683, 2042, 750, 147, 104, 319])).
% 4.34/4.50 tff(18697,plain,
% 4.34/4.50 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[395, 18696, 2286])).
% 4.34/4.50 tff(18698,plain,
% 4.34/4.50 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.50 inference(modus_ponens,[status(thm)],[18697, 18683])).
% 4.34/4.50 tff(18699,plain,
% 4.34/4.50 (b(s(elem!1), s(s(z)))),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[2307, 18696, 319, 166, 17765, 2286])).
% 4.34/4.50 tff(18700,plain,
% 4.34/4.50 (b(s(s(s(s(s(z))))), s(s(z)))),
% 4.34/4.50 inference(modus_ponens,[status(thm)],[18699, 2747])).
% 4.34/4.50 tff(18701,plain,
% 4.34/4.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 4.34/4.50 inference(rewrite,[status(thm)],[])).
% 4.34/4.50 tff(18702,plain,
% 4.34/4.50 (((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 4.34/4.50 inference(rewrite,[status(thm)],[])).
% 4.34/4.50 tff(18703,plain,
% 4.34/4.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 4.34/4.50 inference(monotonicity,[status(thm)],[18702])).
% 4.34/4.50 tff(18704,plain,
% 4.34/4.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 4.34/4.50 inference(transitivity,[status(thm)],[18703, 18701])).
% 4.34/4.50 tff(18705,plain,
% 4.34/4.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))),
% 4.34/4.50 inference(quant_inst,[status(thm)],[])).
% 4.34/4.50 tff(18706,plain,
% 4.34/4.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 4.34/4.50 inference(modus_ponens,[status(thm)],[18705, 18704])).
% 4.34/4.50 tff(18707,plain,
% 4.34/4.50 (~b(s(s(s(s(s(z))))), z)),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[18706, 178, 273, 166, 595, 18700])).
% 4.34/4.50 tff(18708,plain,
% 4.34/4.50 (r(s(s(s(s(s(z))))), z)),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[410, 41, 242, 18707])).
% 4.34/4.50 tff(18709,plain,
% 4.34/4.50 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(s(s(s(z))))))), z)),
% 4.34/4.50 inference(monotonicity,[status(thm)],[352])).
% 4.34/4.50 tff(18710,plain,
% 4.34/4.50 (b(z, s(s(s(elem!1))))),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[17717, 319, 595])).
% 4.34/4.50 tff(18711,plain,
% 4.34/4.50 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.50 inference(monotonicity,[status(thm)],[352])).
% 4.34/4.50 tff(18712,plain,
% 4.34/4.50 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 4.34/4.50 inference(symmetry,[status(thm)],[18711])).
% 4.34/4.50 tff(18713,plain,
% 4.34/4.50 (b(s(s(z)), s(s(s(elem!1))))),
% 4.34/4.50 inference(modus_ponens,[status(thm)],[166, 18712])).
% 4.34/4.50 tff(18714,plain,
% 4.34/4.50 (~b(s(s(s(elem!1))), z)),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[7978, 18713, 273, 3461, 18710])).
% 4.34/4.50 tff(18715,plain,
% 4.34/4.50 (r(s(s(s(elem!1))), z)),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[1565, 18714])).
% 4.34/4.50 tff(18716,plain,
% 4.34/4.50 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.34/4.50 inference(modus_ponens,[status(thm)],[18715, 18709])).
% 4.34/4.50 tff(18717,plain,
% 4.34/4.50 ($false),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[13204, 118, 18716, 18708, 18698])).
% 4.34/4.50 tff(18718,plain,((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(s(s(s(z)))))) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (elem!1 = s(elem!1)) | (~r(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(z)), z))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.50 tff(18719,plain,
% 4.34/4.50 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[18718, 18635, 17173, 144, 18682, 18656, 18673, 18669, 18674, 18660, 104, 10793])).
% 4.34/4.50 tff(18720,plain,
% 4.34/4.50 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[249, 18719])).
% 4.34/4.50 tff(18721,plain,
% 4.34/4.50 (~(s(elem!1) = s(s(z)))),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[11438, 18635])).
% 4.34/4.50 tff(18722,plain,
% 4.34/4.50 (~(s(s(z)) = s(elem!1))),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[1058, 18721])).
% 4.34/4.50 tff(18723,plain,
% 4.34/4.50 (~(s(elem!1) = s(s(s(elem!1))))),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[5395, 18681])).
% 4.34/4.50 tff(18724,plain,
% 4.34/4.50 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.50 inference(monotonicity,[status(thm)],[18644])).
% 4.34/4.50 tff(18725,plain,
% 4.34/4.50 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 4.34/4.50 inference(symmetry,[status(thm)],[18724])).
% 4.34/4.50 tff(18726,plain,
% 4.34/4.50 ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(s(z)), s(s(s(elem!1)))))),
% 4.34/4.50 inference(monotonicity,[status(thm)],[18725])).
% 4.34/4.50 tff(18727,plain,
% 4.34/4.50 (~b(s(s(z)), s(s(s(elem!1))))),
% 4.34/4.50 inference(modus_ponens,[status(thm)],[18719, 18726])).
% 4.34/4.50 tff(18728,plain,
% 4.34/4.50 (b(s(elem!1), s(s(s(elem!1))))),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[6127, 1329, 4218, 5425])).
% 4.34/4.50 tff(18729,plain,
% 4.34/4.50 (~r(elem!1, s(elem!1))),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[12646, 1329, 319, 147])).
% 4.34/4.50 tff(18730,plain,
% 4.34/4.50 (b(elem!1, s(elem!1))),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[756, 18729, 750])).
% 4.34/4.50 tff(18731,plain,
% 4.34/4.50 ($false),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[6834, 18730, 18728, 1597, 683, 2042])).
% 4.34/4.50 tff(18732,plain,((~r(s(s(z)), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (elem!1 = s(elem!1)) | b(s(s(z)), s(s(s(elem!1)))) | (s(elem!1) = s(s(s(elem!1)))) | (~(elem!1 = s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.50 tff(18733,plain,
% 4.34/4.50 (~r(s(s(z)), s(elem!1))),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[18732, 18656, 18673, 18669, 18674, 18727, 18723, 18635, 18660])).
% 4.34/4.50 tff(18734,plain,
% 4.34/4.50 (b(s(s(z)), s(elem!1))),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[1067, 18733, 18722])).
% 4.34/4.50 tff(18735,plain,
% 4.34/4.50 (b(s(s(z)), s(s(s(s(s(z))))))),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[2330, 18734, 18635])).
% 4.34/4.50 tff(18736,plain,
% 4.34/4.50 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 4.34/4.50 inference(modus_ponens,[status(thm)],[5434, 18527])).
% 4.34/4.50 tff(18737,plain,
% 4.34/4.50 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 4.34/4.50 inference(modus_ponens,[status(thm)],[18688, 2693])).
% 4.34/4.50 tff(18738,plain,
% 4.34/4.50 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.50 inference(monotonicity,[status(thm)],[351, 352])).
% 4.34/4.50 tff(18739,plain,
% 4.34/4.50 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 4.34/4.50 inference(symmetry,[status(thm)],[17572])).
% 4.34/4.50 tff(18740,plain,
% 4.34/4.50 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(elem!1))))),
% 4.34/4.50 inference(transitivity,[status(thm)],[16985, 18739])).
% 4.34/4.50 tff(18741,plain,
% 4.34/4.50 (b(elem!1, s(s(s(elem!1))))),
% 4.34/4.50 inference(modus_ponens,[status(thm)],[251, 18740])).
% 4.34/4.50 tff(18742,plain,
% 4.34/4.50 (~r(s(s(s(elem!1))), s(elem!1))),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[5980, 5972, 5227])).
% 4.34/4.50 tff(18743,plain,
% 4.34/4.50 (b(s(s(s(elem!1))), s(elem!1))),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[373, 18742, 356])).
% 4.34/4.50 tff(18744,plain,
% 4.34/4.50 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.34/4.50 inference(modus_ponens,[status(thm)],[18743, 17016])).
% 4.34/4.50 tff(18745,plain,
% 4.34/4.50 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 4.34/4.50 inference(modus_ponens,[status(thm)],[18744, 17015])).
% 4.34/4.50 tff(18746,plain,
% 4.34/4.50 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.50 inference(monotonicity,[status(thm)],[16938])).
% 4.34/4.50 tff(18747,plain,
% 4.34/4.50 (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 4.34/4.50 inference(modus_ponens,[status(thm)],[356, 18746])).
% 4.34/4.50 tff(18748,plain,
% 4.34/4.50 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 4.34/4.50 inference(symmetry,[status(thm)],[351])).
% 4.34/4.50 tff(18749,plain,
% 4.34/4.50 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 4.34/4.50 inference(monotonicity,[status(thm)],[353, 18748])).
% 4.34/4.50 tff(18750,plain,
% 4.34/4.50 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 4.34/4.50 inference(symmetry,[status(thm)],[18749])).
% 4.34/4.50 tff(18751,plain,
% 4.34/4.50 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 4.34/4.50 inference(modus_ponens,[status(thm)],[5227, 18750])).
% 4.34/4.50 tff(18752,plain,
% 4.34/4.50 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 4.34/4.50 inference(monotonicity,[status(thm)],[320, 351])).
% 4.34/4.50 tff(18753,plain,
% 4.34/4.50 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 4.34/4.50 inference(modus_ponens,[status(thm)],[5972, 18752])).
% 4.34/4.50 tff(18754,plain,
% 4.34/4.50 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[16577, 118, 18753, 18751])).
% 4.34/4.50 tff(18755,assumption,(~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 4.34/4.50 tff(18756,assumption,(~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 4.34/4.50 tff(18757,assumption,(~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 4.34/4.50 tff(18758,plain,
% 4.34/4.50 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) | r(s(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(s(z))))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.50 inference(rewrite,[status(thm)],[])).
% 4.34/4.50 tff(18759,plain,
% 4.34/4.50 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.50 inference(quant_inst,[status(thm)],[])).
% 4.34/4.50 tff(18760,plain,
% 4.34/4.50 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.50 inference(modus_ponens,[status(thm)],[18759, 18758])).
% 4.34/4.50 tff(18761,plain,
% 4.34/4.50 ($false),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[18760, 41, 18757, 18756, 18755])).
% 4.34/4.50 tff(18762,plain,(b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) | (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.50 tff(18763,plain,
% 4.34/4.50 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[18762, 18754, 18747])).
% 4.34/4.50 tff(18764,plain,
% 4.34/4.50 ($false),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[17064, 178, 104, 251, 1664, 18763, 18745])).
% 4.34/4.50 tff(18765,plain,((~r(s(elem!1), 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))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~(elem!1 = s(s(s(s(z)))))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.50 tff(18766,plain,
% 4.34/4.50 (~r(s(elem!1), s(s(elem!1)))),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[18765, 5227, 251, 18737, 319, 356, 104])).
% 4.34/4.50 tff(18767,plain,
% 4.34/4.50 (b(s(elem!1), s(s(elem!1)))),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[1028, 18766, 984])).
% 4.34/4.50 tff(18768,plain,
% 4.34/4.50 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[5490, 18767, 683, 18741, 5434])).
% 4.34/4.50 tff(18769,plain,
% 4.34/4.50 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[3375, 18768, 5889])).
% 4.34/4.50 tff(18770,plain,
% 4.34/4.50 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.50 inference(modus_ponens,[status(thm)],[18769, 18738])).
% 4.34/4.50 tff(18771,plain,
% 4.34/4.50 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[880, 118, 224, 18770])).
% 4.34/4.50 tff(18772,plain,
% 4.34/4.50 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[18515, 118, 224, 18770])).
% 4.34/4.50 tff(18773,plain,
% 4.34/4.50 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[6139, 18772, 6134])).
% 4.34/4.50 tff(18774,plain,
% 4.34/4.50 (r(z, s(s(elem!1))) <=> r(z, s(s(s(s(s(s(z)))))))),
% 4.34/4.50 inference(monotonicity,[status(thm)],[351])).
% 4.34/4.50 tff(18775,plain,
% 4.34/4.50 (r(z, s(s(s(s(s(s(z))))))) <=> r(z, s(s(elem!1)))),
% 4.34/4.50 inference(symmetry,[status(thm)],[18774])).
% 4.34/4.50 tff(18776,assumption,(~r(s(s(z)), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 4.34/4.50 tff(18777,plain,
% 4.34/4.50 ((s(s(z)) = s(s(s(s(s(s(z))))))) | b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[9714, 41, 18776])).
% 4.34/4.50 tff(18778,plain,
% 4.34/4.50 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[18777, 9710])).
% 4.34/4.50 tff(18779,plain,
% 4.34/4.50 (~b(z, s(s(s(s(s(s(z)))))))),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[7684, 178, 3461, 273, 6067, 18778])).
% 4.34/4.50 tff(18780,plain,
% 4.34/4.50 ((z = s(s(s(s(s(s(z))))))) | r(z, s(s(s(s(s(s(z)))))))),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[11502, 41, 18779])).
% 4.34/4.50 tff(18781,plain,
% 4.34/4.50 (r(z, s(s(s(s(s(s(z)))))))),
% 4.34/4.50 inference(unit_resolution,[status(thm)],[18780, 11490])).
% 4.34/4.50 tff(18782,plain,
% 4.34/4.50 (r(z, s(s(elem!1)))),
% 4.34/4.50 inference(modus_ponens,[status(thm)],[18781, 18775])).
% 4.34/4.50 tff(18783,plain,
% 4.34/4.50 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 4.34/4.50 inference(monotonicity,[status(thm)],[320, 351])).
% 4.34/4.50 tff(18784,plain,
% 4.34/4.50 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) <=> b(s(elem!1), s(s(elem!1)))),
% 4.34/4.50 inference(symmetry,[status(thm)],[18783])).
% 4.34/4.50 tff(18785,plain,
% 4.34/4.50 ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) <=> (~b(s(elem!1), s(s(elem!1))))),
% 4.34/4.50 inference(monotonicity,[status(thm)],[18784])).
% 4.34/4.50 tff(18786,plain,
% 4.34/4.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), 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)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), 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)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 4.34/4.50 inference(rewrite,[status(thm)],[])).
% 4.34/4.50 tff(18787,plain,
% 4.34/4.50 (((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), 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)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 4.34/4.50 inference(rewrite,[status(thm)],[])).
% 4.34/4.50 tff(18788,plain,
% 4.34/4.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), 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)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))))),
% 4.34/4.51 inference(monotonicity,[status(thm)],[18787])).
% 4.34/4.51 tff(18789,plain,
% 4.34/4.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), 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)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 4.34/4.51 inference(transitivity,[status(thm)],[18788, 18786])).
% 4.34/4.51 tff(18790,plain,
% 4.34/4.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 4.34/4.51 inference(quant_inst,[status(thm)],[])).
% 4.34/4.51 tff(18791,plain,
% 4.34/4.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 4.34/4.51 inference(modus_ponens,[status(thm)],[18790, 18789])).
% 4.34/4.51 tff(18792,plain,
% 4.34/4.51 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[18791, 178, 1665, 1664, 6154, 18778])).
% 4.34/4.51 tff(18793,plain,
% 4.34/4.51 (~b(s(elem!1), s(s(elem!1)))),
% 4.34/4.51 inference(modus_ponens,[status(thm)],[18792, 18785])).
% 4.34/4.51 tff(18794,plain,
% 4.34/4.51 (r(s(elem!1), s(s(elem!1)))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[1028, 18793, 984])).
% 4.34/4.51 tff(18795,plain,
% 4.34/4.51 (~r(z, s(s(elem!1)))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[8156, 18794, 5227, 356, 2043])).
% 4.34/4.51 tff(18796,plain,
% 4.34/4.51 ($false),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[18795, 18782])).
% 4.34/4.51 tff(18797,plain,((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~(elem!1 = s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(z, s(s(s(elem!1))))) | (s(elem!1) = s(s(elem!1))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(s(z))))))) | (s(s(s(s(s(s(z)))))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.51 tff(18798,plain,
% 4.34/4.51 ($false),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[18797, 18773, 18771, 5227, 356, 2043, 984, 3461, 273, 1665, 18737, 18736, 319, 6134])).
% 4.34/4.51 tff(18799,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(z, s(s(s(elem!1))))) | (s(elem!1) = s(s(elem!1))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~(elem!1 = s(s(s(s(z)))))) | (s(s(s(s(s(s(z)))))) = s(s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), 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))))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.51 tff(18800,plain,
% 4.34/4.51 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[18799, 18681, 18653, 18651, 10793, 144, 18735, 18635, 18642, 18720, 18673, 18663, 18255, 104])).
% 4.34/4.51 tff(18801,plain,
% 4.34/4.51 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[3409, 18800, 18670])).
% 4.34/4.51 tff(18802,plain,
% 4.34/4.51 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[5500, 18801, 18669, 18663, 18656])).
% 4.34/4.51 tff(18803,plain,
% 4.34/4.51 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[3375, 18802, 18652])).
% 4.34/4.51 tff(18804,plain,
% 4.34/4.51 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.51 inference(modus_ponens,[status(thm)],[18803, 18645])).
% 4.34/4.51 tff(18805,plain,
% 4.34/4.51 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[880, 118, 18720, 18804])).
% 4.34/4.51 tff(18806,plain,
% 4.34/4.51 ((s(s(z)) = s(s(s(s(s(s(z))))))) | b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[9714, 41, 18805])).
% 4.34/4.51 tff(18807,plain,
% 4.34/4.51 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[18806, 18643])).
% 4.34/4.51 tff(18808,plain,
% 4.34/4.51 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[18515, 118, 18720, 18804])).
% 4.34/4.51 tff(18809,plain,
% 4.34/4.51 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[6139, 18808, 18642])).
% 4.34/4.51 tff(18810,plain,
% 4.34/4.51 (~b(z, s(s(s(s(s(s(z)))))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[7684, 178, 10793, 144, 18809, 18807])).
% 4.34/4.51 tff(18811,plain,
% 4.34/4.51 ((z = s(s(s(s(s(s(z))))))) | r(z, s(s(s(s(s(s(z)))))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[11502, 41, 18810])).
% 4.34/4.51 tff(18812,plain,
% 4.34/4.51 (r(z, s(s(s(s(s(s(z)))))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[18811, 11490])).
% 4.34/4.51 tff(18813,plain,
% 4.34/4.51 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 4.34/4.51 inference(monotonicity,[status(thm)],[18636, 18637])).
% 4.34/4.51 tff(18814,plain,
% 4.34/4.51 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 4.34/4.51 inference(monotonicity,[status(thm)],[18636, 18637])).
% 4.34/4.51 tff(18815,plain,
% 4.34/4.51 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) <=> b(s(elem!1), s(s(elem!1)))),
% 4.34/4.51 inference(symmetry,[status(thm)],[18814])).
% 4.34/4.51 tff(18816,plain,
% 4.34/4.51 ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) <=> (~b(s(elem!1), s(s(elem!1))))),
% 4.34/4.51 inference(monotonicity,[status(thm)],[18815])).
% 4.34/4.51 tff(18817,plain,
% 4.34/4.51 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 4.34/4.51 inference(monotonicity,[status(thm)],[18637, 18635])).
% 4.34/4.51 tff(18818,plain,
% 4.34/4.51 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 4.34/4.51 inference(modus_ponens,[status(thm)],[18663, 18817])).
% 4.34/4.51 tff(18819,plain,
% 4.34/4.51 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 4.34/4.51 inference(monotonicity,[status(thm)],[18675])).
% 4.34/4.51 tff(18820,plain,
% 4.34/4.51 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 4.34/4.51 inference(symmetry,[status(thm)],[18819])).
% 4.34/4.51 tff(18821,plain,
% 4.34/4.51 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(s(z)))))),
% 4.34/4.51 inference(monotonicity,[status(thm)],[18635])).
% 4.34/4.51 tff(18822,plain,
% 4.34/4.51 (b(s(elem!1), s(s(s(s(z)))))),
% 4.34/4.51 inference(modus_ponens,[status(thm)],[18673, 18821])).
% 4.34/4.51 tff(18823,plain,
% 4.34/4.51 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 4.34/4.51 inference(modus_ponens,[status(thm)],[18822, 18820])).
% 4.34/4.51 tff(18824,plain,
% 4.34/4.51 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[18791, 178, 18735, 18823, 18818, 18807])).
% 4.34/4.51 tff(18825,plain,
% 4.34/4.51 (~b(s(elem!1), s(s(elem!1)))),
% 4.34/4.51 inference(modus_ponens,[status(thm)],[18824, 18816])).
% 4.34/4.51 tff(18826,plain,
% 4.34/4.51 (r(s(elem!1), s(s(elem!1)))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[1028, 18825, 18651])).
% 4.34/4.51 tff(18827,plain,
% 4.34/4.51 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 4.34/4.51 inference(modus_ponens,[status(thm)],[18826, 18813])).
% 4.34/4.51 tff(18828,plain,
% 4.34/4.51 (~r(s(s(s(s(s(z))))), z)),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[9797, 118, 18827, 18812])).
% 4.34/4.51 tff(18829,plain,
% 4.34/4.51 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.51 inference(monotonicity,[status(thm)],[18636])).
% 4.34/4.51 tff(18830,plain,
% 4.34/4.51 (~r(s(elem!1), s(s(s(elem!1))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[5994, 18826, 18803])).
% 4.34/4.51 tff(18831,plain,
% 4.34/4.51 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[14608, 18830, 18635])).
% 4.34/4.51 tff(18832,plain,
% 4.34/4.51 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[395, 18831, 18682])).
% 4.34/4.51 tff(18833,plain,
% 4.34/4.51 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.51 inference(modus_ponens,[status(thm)],[18832, 18829])).
% 4.34/4.51 tff(18834,plain,
% 4.34/4.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, 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(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, 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(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 4.34/4.51 inference(rewrite,[status(thm)],[])).
% 4.34/4.51 tff(18835,plain,
% 4.34/4.51 (((~b(z, 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(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, 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(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 4.34/4.51 inference(rewrite,[status(thm)],[])).
% 4.34/4.51 tff(18836,plain,
% 4.34/4.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, 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(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 4.34/4.51 inference(monotonicity,[status(thm)],[18835])).
% 4.34/4.51 tff(18837,plain,
% 4.34/4.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, 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(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 4.34/4.51 inference(transitivity,[status(thm)],[18836, 18834])).
% 4.34/4.51 tff(18838,plain,
% 4.34/4.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 4.34/4.51 inference(quant_inst,[status(thm)],[])).
% 4.34/4.51 tff(18839,plain,
% 4.34/4.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 4.34/4.51 inference(modus_ponens,[status(thm)],[18838, 18837])).
% 4.34/4.51 tff(18840,plain,
% 4.34/4.51 (~b(s(s(s(s(s(z))))), z)),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[18839, 178, 10793, 18255, 17173, 18735, 18823, 18833])).
% 4.34/4.51 tff(18841,plain,
% 4.34/4.51 ($false),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[410, 41, 242, 18840, 18828])).
% 4.34/4.51 tff(18842,plain,(b(elem!1, s(s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | r(z, s(s(z))) | b(z, s(s(s(s(z))))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 4.34/4.51 tff(18843,plain,
% 4.34/4.51 (b(elem!1, s(s(s(s(z)))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[18842, 290, 48, 1, 104])).
% 4.34/4.51 tff(18844,plain,
% 4.34/4.51 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[4162, 3240, 18843])).
% 4.34/4.51 tff(18845,plain,
% 4.34/4.51 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[4168, 18844])).
% 4.34/4.51 tff(18846,plain,
% 4.34/4.51 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[4162, 3240, 1301])).
% 4.34/4.51 tff(18847,plain,
% 4.34/4.51 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[4168, 18846])).
% 4.34/4.51 tff(18848,plain,
% 4.34/4.51 ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[14128, 178, 3461, 251, 595])).
% 4.34/4.51 tff(18849,plain,
% 4.34/4.51 (~b(s(s(s(s(z)))), z)),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[18848, 167])).
% 4.34/4.51 tff(18850,plain,
% 4.34/4.51 (~b(elem!1, s(s(z)))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[18127, 178, 818, 273, 1301, 167])).
% 4.34/4.51 tff(18851,plain,
% 4.34/4.51 ($false),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[10659, 18850, 18100, 1, 3240, 18849])).
% 4.34/4.51 tff(18852,plain,((~b(s(s(z)), s(s(s(s(z)))))) | b(z, s(s(s(s(z))))) | b(elem!1, s(s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.51 tff(18853,plain,
% 4.34/4.51 (~b(s(s(z)), s(s(s(s(z)))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[18852, 818, 3240, 1, 273, 1301, 5619, 251, 595])).
% 4.34/4.51 tff(18854,plain,
% 4.34/4.51 (r(s(s(z)), s(s(s(s(z)))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[164, 18853])).
% 4.34/4.51 tff(18855,plain,
% 4.34/4.51 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[10799, 18854, 47])).
% 4.34/4.51 tff(18856,plain,
% 4.34/4.51 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[4173, 18855, 18847])).
% 4.34/4.51 tff(18857,plain,
% 4.34/4.51 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[8447, 178, 818, 104, 1301, 595])).
% 4.34/4.51 tff(18858,plain,
% 4.34/4.51 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[1309, 818, 104, 595, 1301])).
% 4.34/4.51 tff(18859,plain,
% 4.34/4.51 (~(s(s(z)) = elem!1)),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[17698, 18853, 1301])).
% 4.34/4.51 tff(18860,plain,
% 4.34/4.51 (~(elem!1 = s(s(s(elem!1))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[4187, 3242, 818])).
% 4.34/4.51 tff(18861,plain,
% 4.34/4.51 (r(elem!1, s(s(s(elem!1))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[2054, 18860, 3240])).
% 4.34/4.51 tff(18862,plain,
% 4.34/4.51 (~r(elem!1, z)),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[3421, 18861, 3243])).
% 4.34/4.51 tff(18863,plain,
% 4.34/4.51 (b(elem!1, z)),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[498, 18862, 290])).
% 4.34/4.51 tff(18864,plain,
% 4.34/4.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.34/4.51 inference(rewrite,[status(thm)],[])).
% 4.34/4.51 tff(18865,plain,
% 4.34/4.51 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, 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)))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.34/4.51 inference(rewrite,[status(thm)],[])).
% 4.34/4.51 tff(18866,plain,
% 4.34/4.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 4.34/4.51 inference(monotonicity,[status(thm)],[18865])).
% 4.34/4.51 tff(18867,plain,
% 4.34/4.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.34/4.51 inference(transitivity,[status(thm)],[18866, 18864])).
% 4.34/4.51 tff(18868,plain,
% 4.34/4.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 4.34/4.51 inference(quant_inst,[status(thm)],[])).
% 4.34/4.51 tff(18869,plain,
% 4.34/4.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.51 inference(modus_ponens,[status(thm)],[18868, 18867])).
% 4.34/4.51 tff(18870,plain,
% 4.34/4.51 (~b(s(s(s(s(z)))), z)),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[18869, 178, 18863, 1301, 251, 595])).
% 4.34/4.51 tff(18871,plain,
% 4.34/4.51 (~b(elem!1, s(s(z)))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[16411, 178, 818, 18863, 3461, 273])).
% 4.34/4.51 tff(18872,plain,
% 4.34/4.51 (b(s(s(z)), elem!1)),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[10659, 3170, 461, 3240, 1])).
% 4.34/4.51 tff(18873,plain,
% 4.34/4.51 (~b(s(s(z)), z)),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[8677, 193, 1130, 145])).
% 4.34/4.51 tff(18874,plain,
% 4.34/4.51 ($false),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[3249, 18873, 3424])).
% 4.34/4.51 tff(18875,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~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(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.51 tff(18876,plain,
% 4.34/4.51 (~r(s(s(s(s(z)))), s(s(z)))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[18875, 3437, 47, 3244])).
% 4.34/4.51 tff(18877,plain,
% 4.34/4.51 (b(s(s(s(s(z)))), s(s(z)))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[102, 18876])).
% 4.34/4.51 tff(18878,plain,
% 4.34/4.51 (~(s(s(s(s(z)))) = elem!1)),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[4509, 18877, 461])).
% 4.34/4.51 tff(18879,plain,
% 4.34/4.51 (~r(z, elem!1)),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[3151, 9104, 18872, 18877, 18878, 3244, 47])).
% 4.34/4.51 tff(18880,plain,
% 4.34/4.51 (~r(s(s(s(s(z)))), s(s(z)))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[18875, 1130, 47, 3244])).
% 4.34/4.51 tff(18881,plain,
% 4.34/4.51 (b(s(s(s(s(z)))), s(s(z)))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[102, 18880])).
% 4.34/4.51 tff(18882,plain,
% 4.34/4.51 (~(s(s(s(s(z)))) = elem!1)),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[4509, 18881, 461])).
% 4.34/4.51 tff(18883,plain,
% 4.34/4.51 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[3502, 18882])).
% 4.34/4.51 tff(18884,plain,
% 4.34/4.51 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[4173, 3381, 4170])).
% 4.34/4.51 tff(18885,plain,
% 4.34/4.51 (s(elem!1) = s(s(z))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[2840, 18884])).
% 4.34/4.51 tff(18886,plain,
% 4.34/4.51 (s(s(elem!1)) = s(s(s(z)))),
% 4.34/4.51 inference(monotonicity,[status(thm)],[18885])).
% 4.34/4.51 tff(18887,plain,
% 4.34/4.51 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 4.34/4.51 inference(monotonicity,[status(thm)],[18886])).
% 4.34/4.51 tff(18888,plain,
% 4.34/4.51 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 4.34/4.51 inference(monotonicity,[status(thm)],[18885])).
% 4.34/4.51 tff(18889,plain,
% 4.34/4.51 (elem!1 = s(z)),
% 4.34/4.51 inference(transitivity,[status(thm)],[517, 18888, 70])).
% 4.34/4.51 tff(18890,plain,
% 4.34/4.51 (r(elem!1, s(s(s(elem!1)))) <=> r(s(z), s(s(s(s(z)))))),
% 4.34/4.51 inference(monotonicity,[status(thm)],[18889, 18887])).
% 4.34/4.51 tff(18891,plain,
% 4.34/4.51 (r(s(z), s(s(s(s(z))))) <=> r(elem!1, s(s(s(elem!1))))),
% 4.34/4.51 inference(symmetry,[status(thm)],[18890])).
% 4.34/4.51 tff(18892,plain,
% 4.34/4.51 (r(elem!1, s(s(s(s(z))))) <=> r(s(z), s(s(s(s(z)))))),
% 4.34/4.51 inference(monotonicity,[status(thm)],[18889])).
% 4.34/4.51 tff(18893,plain,
% 4.34/4.51 (~(elem!1 = s(s(s(s(z)))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[11438, 18885])).
% 4.34/4.51 tff(18894,plain,
% 4.34/4.51 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[4168, 18884])).
% 4.34/4.51 tff(18895,plain,
% 4.34/4.51 (~b(elem!1, s(s(s(s(z)))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[4162, 18894, 3240])).
% 4.34/4.51 tff(18896,plain,
% 4.34/4.51 (r(elem!1, s(s(s(s(z)))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[483, 18895, 18893])).
% 4.34/4.51 tff(18897,plain,
% 4.34/4.51 (r(s(z), s(s(s(s(z)))))),
% 4.34/4.51 inference(modus_ponens,[status(thm)],[18896, 18892])).
% 4.34/4.51 tff(18898,plain,
% 4.34/4.51 (r(elem!1, s(s(s(elem!1))))),
% 4.34/4.51 inference(modus_ponens,[status(thm)],[18897, 18891])).
% 4.34/4.51 tff(18899,plain,
% 4.34/4.51 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[4843, 1130, 47])).
% 4.34/4.51 tff(18900,plain,
% 4.34/4.51 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[271, 18899])).
% 4.34/4.51 tff(18901,plain,
% 4.34/4.51 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[2832, 18885])).
% 4.34/4.51 tff(18902,plain,
% 4.34/4.51 (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(s(z)))))),
% 4.34/4.51 inference(monotonicity,[status(thm)],[18887])).
% 4.34/4.51 tff(18903,plain,
% 4.34/4.51 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.34/4.51 inference(symmetry,[status(thm)],[18902])).
% 4.34/4.51 tff(18904,plain,
% 4.34/4.51 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.34/4.51 inference(modus_ponens,[status(thm)],[1130, 18903])).
% 4.34/4.51 tff(18905,plain,
% 4.34/4.51 (~b(s(s(s(s(z)))), s(s(z)))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[5612, 18904, 557, 18901, 1, 3170, 18900, 461, 18898])).
% 4.34/4.51 tff(18906,plain,
% 4.34/4.51 ((s(elem!1) = elem!1) <=> (s(s(z)) = elem!1)),
% 4.34/4.51 inference(monotonicity,[status(thm)],[18885])).
% 4.34/4.51 tff(18907,plain,
% 4.34/4.51 ((s(elem!1) = elem!1) <=> (elem!1 = s(s(z)))),
% 4.34/4.51 inference(transitivity,[status(thm)],[18906, 1666])).
% 4.34/4.51 tff(18908,plain,
% 4.34/4.51 ((~(s(elem!1) = elem!1)) <=> (~(elem!1 = s(s(z))))),
% 4.34/4.51 inference(monotonicity,[status(thm)],[18907])).
% 4.34/4.51 tff(18909,plain,
% 4.34/4.51 (~(elem!1 = s(s(s(s(elem!1)))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[1422, 18885])).
% 4.34/4.51 tff(18910,plain,
% 4.34/4.51 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[1509, 18909])).
% 4.34/4.51 tff(18911,plain,
% 4.34/4.51 (~(elem!1 = s(s(elem!1)))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[1539, 18910])).
% 4.34/4.51 tff(18912,plain,
% 4.34/4.51 (~(s(s(elem!1)) = elem!1)),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[1546, 18911])).
% 4.34/4.51 tff(18913,plain,
% 4.34/4.51 (~(s(elem!1) = elem!1)),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[672, 18912])).
% 4.34/4.51 tff(18914,plain,
% 4.34/4.51 (~(elem!1 = s(s(z)))),
% 4.34/4.51 inference(modus_ponens,[status(thm)],[18913, 18908])).
% 4.34/4.51 tff(18915,plain,
% 4.34/4.51 (r(elem!1, s(s(z)))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[467, 18914, 461])).
% 4.34/4.51 tff(18916,plain,
% 4.34/4.51 (~r(s(s(s(s(z)))), s(s(z)))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[3785, 18915, 18896])).
% 4.34/4.51 tff(18917,plain,
% 4.34/4.51 ($false),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[102, 18916, 18905])).
% 4.34/4.51 tff(18918,plain,((~r(z, s(s(s(elem!1))))) | b(z, s(s(s(s(z))))) | b(s(s(s(s(z)))), z) | b(elem!1, s(s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | b(elem!1, s(s(s(elem!1)))) | b(s(s(s(elem!1))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.51 tff(18919,plain,
% 4.34/4.51 (~r(z, s(s(s(elem!1))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[18918, 4170, 3170, 461, 1130, 3240, 1])).
% 4.34/4.51 tff(18920,plain,
% 4.34/4.51 (b(z, s(s(s(elem!1))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[2095, 18919])).
% 4.34/4.51 tff(18921,plain,
% 4.34/4.51 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[8061, 18920, 1130, 18883, 47])).
% 4.34/4.51 tff(18922,plain,
% 4.34/4.51 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[4173, 18921, 4170])).
% 4.34/4.51 tff(18923,plain,
% 4.34/4.51 (s(elem!1) = s(s(z))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[2840, 18922])).
% 4.34/4.51 tff(18924,plain,
% 4.34/4.51 (s(s(elem!1)) = s(s(s(z)))),
% 4.34/4.51 inference(monotonicity,[status(thm)],[18923])).
% 4.34/4.51 tff(18925,plain,
% 4.34/4.51 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 4.34/4.51 inference(monotonicity,[status(thm)],[18924])).
% 4.34/4.51 tff(18926,plain,
% 4.34/4.51 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(s(z)))))),
% 4.34/4.51 inference(monotonicity,[status(thm)],[18925])).
% 4.34/4.51 tff(18927,plain,
% 4.34/4.51 (b(z, s(s(s(s(z))))) <=> b(z, s(s(s(elem!1))))),
% 4.34/4.51 inference(symmetry,[status(thm)],[18926])).
% 4.34/4.51 tff(18928,plain,
% 4.34/4.51 ((~b(z, s(s(s(s(z)))))) <=> (~b(z, s(s(s(elem!1)))))),
% 4.34/4.51 inference(monotonicity,[status(thm)],[18927])).
% 4.34/4.51 tff(18929,plain,
% 4.34/4.51 (~b(z, s(s(s(elem!1))))),
% 4.34/4.51 inference(modus_ponens,[status(thm)],[1, 18928])).
% 4.34/4.51 tff(18930,plain,
% 4.34/4.51 ($false),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[18920, 18929])).
% 4.34/4.51 tff(18931,plain,(b(s(s(s(elem!1))), s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | b(s(s(s(s(z)))), z) | b(elem!1, s(s(z))) | b(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.51 tff(18932,plain,
% 4.34/4.51 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[18931, 3437, 1, 3170, 461, 3240])).
% 4.34/4.51 tff(18933,plain,
% 4.34/4.51 (b(s(s(s(s(z)))), elem!1)),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[3308, 1527, 3293])).
% 4.34/4.51 tff(18934,plain,
% 4.34/4.51 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.34/4.51 inference(modus_ponens,[status(thm)],[18933, 3290])).
% 4.34/4.51 tff(18935,plain,
% 4.34/4.51 (b(s(s(z)), s(s(s(elem!1))))),
% 4.34/4.51 inference(modus_ponens,[status(thm)],[817, 8290])).
% 4.34/4.51 tff(18936,plain,
% 4.34/4.51 ($false),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[4816, 178, 18935, 167, 202, 18934, 3831])).
% 4.34/4.51 tff(18937,plain,((~(elem!1 = s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | r(s(s(s(s(z)))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.51 tff(18938,plain,
% 4.34/4.51 (~(elem!1 = s(s(s(elem!1))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[18937, 5162, 18877, 18932, 18872, 9104])).
% 4.34/4.51 tff(18939,plain,
% 4.34/4.51 (r(elem!1, s(s(s(elem!1))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[2054, 18938, 3240])).
% 4.34/4.51 tff(18940,plain,
% 4.34/4.51 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[3502, 18878])).
% 4.34/4.51 tff(18941,plain,
% 4.34/4.51 (~r(elem!1, z)),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[3421, 18939, 557])).
% 4.34/4.51 tff(18942,plain,
% 4.34/4.51 (~r(z, elem!1)),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[3319, 18939, 557])).
% 4.34/4.51 tff(18943,plain,
% 4.34/4.51 (~r(s(s(z)), z)),
% 4.34/4.51 inference(unit_resolution,[status(thm)],[1831, 1823, 557])).
% 4.34/4.51 tff(18944,plain,
% 4.34/4.51 (b(s(s(z)), z)),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[3249, 18943])).
% 4.34/4.52 tff(18945,plain,
% 4.34/4.52 (~(elem!1 = z)),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[3276, 6603, 461])).
% 4.34/4.52 tff(18946,plain,
% 4.34/4.52 (b(elem!1, z)),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[498, 18945, 1342])).
% 4.34/4.52 tff(18947,plain,
% 4.34/4.52 (~(z = elem!1)),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[317, 18945])).
% 4.34/4.52 tff(18948,plain,
% 4.34/4.52 (b(z, elem!1)),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[585, 18947, 2811])).
% 4.34/4.52 tff(18949,plain,
% 4.34/4.52 ($false),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[11002, 178, 18948, 18946, 817, 18944, 6603])).
% 4.34/4.52 tff(18950,plain,((~r(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | r(z, elem!1) | r(elem!1, z) | b(elem!1, s(s(z))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.52 tff(18951,plain,
% 4.34/4.52 (~r(s(s(z)), s(s(s(elem!1))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[18950, 18942, 18872, 18941, 461, 557])).
% 4.34/4.52 tff(18952,plain,
% 4.34/4.52 (b(s(s(z)), s(s(s(elem!1))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[4223, 18951])).
% 4.34/4.52 tff(18953,plain,
% 4.34/4.52 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[10667, 18952, 9104, 18877, 18932])).
% 4.34/4.52 tff(18954,plain,
% 4.34/4.52 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[10664, 18953, 5162])).
% 4.34/4.52 tff(18955,plain,
% 4.34/4.52 (b(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(s(z)))))),
% 4.34/4.52 inference(symmetry,[status(thm)],[4605])).
% 4.34/4.52 tff(18956,plain,
% 4.34/4.52 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 4.34/4.52 inference(modus_ponens,[status(thm)],[3829, 18955])).
% 4.34/4.52 tff(18957,plain,
% 4.34/4.52 ($false),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[3428, 18956])).
% 4.34/4.52 tff(18958,plain,((~(s(s(s(s(z)))) = s(s(s(elem!1))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.52 tff(18959,plain,
% 4.34/4.52 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[18958, 18954, 3428])).
% 4.34/4.52 tff(18960,plain,
% 4.34/4.52 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[5118, 18959, 18940])).
% 4.34/4.52 tff(18961,plain,
% 4.34/4.52 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[7917, 18954])).
% 4.34/4.52 tff(18962,plain,
% 4.34/4.52 (s(elem!1) = s(s(z))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[2840, 18961])).
% 4.34/4.52 tff(18963,plain,
% 4.34/4.52 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[2832, 18962])).
% 4.34/4.52 tff(18964,plain,
% 4.34/4.52 ($false),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[5612, 18963, 18960, 18877, 557, 1, 3170, 9172, 461, 18939])).
% 4.34/4.52 tff(18965,plain,((~r(z, s(s(s(elem!1))))) | b(z, s(s(s(s(z))))) | b(s(s(s(s(z)))), z) | b(elem!1, s(s(z))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | b(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.52 tff(18966,plain,
% 4.34/4.52 (~r(z, s(s(s(elem!1))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[18965, 3428, 3170, 461, 1, 3240])).
% 4.34/4.52 tff(18967,plain,
% 4.34/4.52 (b(z, s(s(s(elem!1))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[2095, 18966])).
% 4.34/4.52 tff(18968,plain,
% 4.34/4.52 (~(s(s(z)) = elem!1)),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[9162, 9106, 9104, 9099, 18877, 18967, 3244, 9097, 18932, 18878])).
% 4.34/4.52 tff(18969,plain,
% 4.34/4.52 (~(elem!1 = s(s(z)))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[311, 18968])).
% 4.34/4.52 tff(18970,plain,
% 4.34/4.52 (r(elem!1, s(s(z)))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[467, 18969, 461])).
% 4.34/4.52 tff(18971,plain,
% 4.34/4.52 (~r(z, s(s(z)))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[5266, 13, 1858, 202, 3311, 461, 1, 3170])).
% 4.34/4.52 tff(18972,plain,
% 4.34/4.52 (~b(z, s(s(z)))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[3276, 5198, 461])).
% 4.34/4.52 tff(18973,plain,
% 4.34/4.52 ($false),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[143, 18972, 18971])).
% 4.34/4.52 tff(18974,plain,((~(z = elem!1)) | b(elem!1, s(s(z))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(s(elem!1))))) | b(z, s(s(s(s(z))))) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 4.34/4.52 tff(18975,plain,
% 4.34/4.52 (~(z = elem!1)),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[18974, 9198, 461, 18877, 9097, 1, 3170])).
% 4.34/4.52 tff(18976,plain,
% 4.34/4.52 (~r(s(s(z)), s(s(s(s(z)))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[9102, 3437, 145])).
% 4.34/4.52 tff(18977,plain,
% 4.34/4.52 (b(s(s(z)), s(s(s(s(z)))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[164, 18976])).
% 4.34/4.52 tff(18978,plain,
% 4.34/4.52 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[4843, 3437, 145])).
% 4.34/4.52 tff(18979,plain,
% 4.34/4.52 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[271, 18978])).
% 4.34/4.52 tff(18980,plain,
% 4.34/4.52 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[17366, 507, 817, 18979, 2811, 450, 3447])).
% 4.34/4.52 tff(18981,plain,
% 4.34/4.52 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[691, 18980, 701])).
% 4.34/4.52 tff(18982,plain,
% 4.34/4.52 ($false),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[11999, 118, 1130, 1265, 470])).
% 4.34/4.52 tff(18983,plain,((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.52 tff(18984,plain,
% 4.34/4.52 (~r(elem!1, s(s(s(s(z)))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[18983, 18981, 3437])).
% 4.34/4.52 tff(18985,plain,
% 4.34/4.52 (b(elem!1, s(s(s(s(z)))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[483, 18984, 3130])).
% 4.34/4.52 tff(18986,plain,
% 4.34/4.52 (~b(z, s(s(z)))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[18099, 178, 2812, 817, 18985, 18977])).
% 4.34/4.52 tff(18987,plain,
% 4.34/4.52 (r(z, s(s(z)))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[143, 18986])).
% 4.34/4.52 tff(18988,plain,
% 4.34/4.52 (~r(elem!1, z)),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[8416, 18987, 450])).
% 4.34/4.52 tff(18989,plain,
% 4.34/4.52 (b(elem!1, z)),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[498, 18988, 2809])).
% 4.34/4.52 tff(18990,plain,
% 4.34/4.52 (~r(s(s(s(s(z)))), elem!1)),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[3457, 18989, 3428, 145, 2812, 18985])).
% 4.34/4.52 tff(18991,plain,
% 4.34/4.52 (b(s(s(s(s(z)))), elem!1)),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[3142, 18990, 323])).
% 4.34/4.52 tff(18992,plain,
% 4.34/4.52 ($false),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[3149, 178, 817, 18991, 18985, 18977, 202])).
% 4.34/4.52 tff(18993,plain,((z = elem!1) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (s(s(s(s(z)))) = elem!1) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.34/4.52 tff(18994,plain,
% 4.34/4.52 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[18993, 18975, 18877, 18878, 3428, 47, 18970, 18872, 18879])).
% 4.34/4.52 tff(18995,plain,
% 4.34/4.52 (r(elem!1, s(s(z))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.34/4.52 inference(monotonicity,[status(thm)],[18994])).
% 4.34/4.52 tff(18996,plain,
% 4.34/4.52 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.34/4.52 inference(modus_ponens,[status(thm)],[18970, 18995])).
% 4.34/4.52 tff(18997,plain,
% 4.34/4.52 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.34/4.52 inference(monotonicity,[status(thm)],[18994])).
% 4.34/4.52 tff(18998,plain,
% 4.34/4.52 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.34/4.52 inference(modus_ponens,[status(thm)],[9097, 18997])).
% 4.34/4.52 tff(18999,plain,
% 4.34/4.52 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 4.34/4.52 inference(monotonicity,[status(thm)],[18994])).
% 4.34/4.52 tff(19000,plain,
% 4.34/4.52 (s(s(elem!1)) = s(s(s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.52 inference(monotonicity,[status(thm)],[18999])).
% 4.34/4.52 tff(19001,plain,
% 4.34/4.52 (s(s(s(elem!1))) = s(s(s(s(s(s(s(s(s(s(z))))))))))),
% 4.34/4.52 inference(monotonicity,[status(thm)],[19000])).
% 4.34/4.52 tff(19002,plain,
% 4.34/4.52 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))),
% 4.34/4.52 inference(monotonicity,[status(thm)],[19001])).
% 4.34/4.52 tff(19003,plain,
% 4.34/4.52 (r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 4.34/4.52 inference(symmetry,[status(thm)],[19002])).
% 4.34/4.52 tff(19004,plain,
% 4.34/4.52 (r(s(s(z)), s(s(s(elem!1))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[4223, 4218])).
% 4.34/4.52 tff(19005,plain,
% 4.34/4.52 (~(elem!1 = s(s(s(elem!1))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[17217, 4218, 817])).
% 4.34/4.52 tff(19006,plain,
% 4.34/4.52 (r(elem!1, s(s(s(elem!1))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[2054, 19005, 3240])).
% 4.34/4.52 tff(19007,plain,
% 4.34/4.52 (~(s(s(s(elem!1))) = elem!1)),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[2489, 19005])).
% 4.34/4.52 tff(19008,plain,
% 4.34/4.52 (~(s(elem!1) = elem!1)),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[2150, 19007])).
% 4.34/4.52 tff(19009,plain,
% 4.34/4.52 (~(elem!1 = s(elem!1))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[748, 19008])).
% 4.34/4.52 tff(19010,plain,
% 4.34/4.52 (~(s(s(z)) = elem!1)),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[9162, 19009, 167, 1126, 202, 2043, 194, 19006, 3831, 4510])).
% 4.34/4.52 tff(19011,plain,
% 4.34/4.52 (~(elem!1 = s(s(z)))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[311, 19010])).
% 4.34/4.52 tff(19012,plain,
% 4.34/4.52 (r(elem!1, s(s(z)))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[467, 19011, 461])).
% 4.34/4.52 tff(19013,plain,
% 4.34/4.52 ($false),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[5715, 118, 19006, 19012, 19004])).
% 4.34/4.52 tff(19014,plain,(b(s(s(z)), s(s(s(elem!1)))) | b(elem!1, 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(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | b(elem!1, s(s(s(elem!1)))) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.52 tff(19015,plain,
% 4.34/4.52 (b(s(s(z)), s(s(s(elem!1))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[19014, 9104, 461, 9099, 18877, 18967, 3244, 18932, 3240, 18872])).
% 4.34/4.52 tff(19016,plain,
% 4.34/4.52 (r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[10512, 18994, 18877, 18932, 19015, 9104])).
% 4.34/4.52 tff(19017,plain,
% 4.34/4.52 (r(s(s(s(elem!1))), s(s(z)))),
% 4.34/4.52 inference(modus_ponens,[status(thm)],[19016, 19003])).
% 4.34/4.52 tff(19018,plain,
% 4.34/4.52 ($false),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[10401, 19017, 18998, 18996])).
% 4.34/4.52 tff(19019,plain,((elem!1 = s(s(s(elem!1)))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | b(elem!1, s(s(z))) | b(z, s(s(s(s(z))))) | b(s(s(s(s(z)))), z) | b(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.52 tff(19020,plain,
% 4.34/4.52 (elem!1 = s(s(s(elem!1)))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[19019, 3428, 461, 1, 3170, 3240])).
% 4.34/4.52 tff(19021,plain,
% 4.34/4.52 ((z = elem!1) <=> (z = s(s(s(elem!1))))),
% 4.34/4.52 inference(monotonicity,[status(thm)],[19020])).
% 4.34/4.52 tff(19022,plain,
% 4.34/4.52 ((z = elem!1) <=> (s(s(s(elem!1))) = z)),
% 4.34/4.52 inference(transitivity,[status(thm)],[19021, 2087])).
% 4.34/4.52 tff(19023,plain,
% 4.34/4.52 ((s(s(s(elem!1))) = z) <=> (z = elem!1)),
% 4.34/4.52 inference(symmetry,[status(thm)],[19022])).
% 4.34/4.52 tff(19024,plain,
% 4.34/4.52 ((~(s(s(s(elem!1))) = z)) <=> (~(z = elem!1))),
% 4.34/4.52 inference(monotonicity,[status(thm)],[19023])).
% 4.34/4.52 tff(19025,plain,
% 4.34/4.52 (~(z = elem!1)),
% 4.34/4.52 inference(modus_ponens,[status(thm)],[940, 19024])).
% 4.34/4.52 tff(19026,plain,
% 4.34/4.52 ((elem!1 = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 4.34/4.52 inference(monotonicity,[status(thm)],[19020])).
% 4.34/4.52 tff(19027,plain,
% 4.34/4.52 ((elem!1 = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 4.34/4.52 inference(transitivity,[status(thm)],[19026, 3539])).
% 4.34/4.52 tff(19028,plain,
% 4.34/4.52 ((s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 4.34/4.52 inference(symmetry,[status(thm)],[19027])).
% 4.34/4.52 tff(19029,plain,
% 4.34/4.52 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.52 inference(monotonicity,[status(thm)],[19028])).
% 4.34/4.52 tff(19030,plain,
% 4.34/4.52 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 4.34/4.52 inference(modus_ponens,[status(thm)],[18940, 19029])).
% 4.34/4.52 tff(19031,plain,
% 4.34/4.52 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(elem!1))))),
% 4.34/4.52 inference(monotonicity,[status(thm)],[19020])).
% 4.34/4.52 tff(19032,plain,
% 4.34/4.52 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 4.34/4.52 inference(symmetry,[status(thm)],[19031])).
% 4.34/4.52 tff(19033,plain,
% 4.34/4.52 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(z)))),
% 4.34/4.52 inference(transitivity,[status(thm)],[19032, 1666])).
% 4.34/4.52 tff(19034,plain,
% 4.34/4.52 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(z))))),
% 4.34/4.52 inference(monotonicity,[status(thm)],[19033])).
% 4.34/4.52 tff(19035,plain,
% 4.34/4.52 (~(elem!1 = s(s(z)))),
% 4.34/4.52 inference(modus_ponens,[status(thm)],[1683, 19034])).
% 4.34/4.52 tff(19036,plain,
% 4.34/4.52 (r(elem!1, s(s(z)))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[467, 19035, 461])).
% 4.34/4.52 tff(19037,plain,
% 4.34/4.52 ($false),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[18993, 19036, 19030, 18877, 18878, 3428, 47, 19025, 18872, 18879])).
% 4.34/4.52 tff(19038,plain,(b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | b(elem!1, s(s(z))) | b(z, s(s(s(s(z))))) | b(s(s(s(s(z)))), z) | b(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.52 tff(19039,plain,
% 4.34/4.52 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[19038, 3170, 1, 461, 3240])).
% 4.34/4.52 tff(19040,plain,
% 4.34/4.52 (~b(elem!1, z)),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[11004, 818, 3271, 817, 3250])).
% 4.34/4.52 tff(19041,plain,
% 4.34/4.52 (r(elem!1, z)),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[498, 19040, 290])).
% 4.34/4.52 tff(19042,plain,
% 4.34/4.52 (~(s(s(z)) = elem!1)),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[6206, 19041, 3245])).
% 4.34/4.52 tff(19043,plain,
% 4.34/4.52 (b(s(elem!1), s(s(z)))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[16105, 19042, 1, 86, 147, 19040, 3245])).
% 4.34/4.52 tff(19044,plain,
% 4.34/4.52 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[12552, 19043, 86])).
% 4.34/4.52 tff(19045,plain,
% 4.34/4.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 4.34/4.52 inference(rewrite,[status(thm)],[])).
% 4.34/4.52 tff(19046,plain,
% 4.34/4.52 (((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z))) <=> ((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 4.34/4.52 inference(rewrite,[status(thm)],[])).
% 4.34/4.52 tff(19047,plain,
% 4.34/4.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1))))),
% 4.34/4.52 inference(monotonicity,[status(thm)],[19046])).
% 4.34/4.52 tff(19048,plain,
% 4.34/4.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 4.34/4.52 inference(transitivity,[status(thm)],[19047, 19045])).
% 4.34/4.52 tff(19049,plain,
% 4.34/4.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)))),
% 4.34/4.52 inference(quant_inst,[status(thm)],[])).
% 4.34/4.52 tff(19050,plain,
% 4.34/4.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1))),
% 4.34/4.52 inference(modus_ponens,[status(thm)],[19049, 19048])).
% 4.34/4.52 tff(19051,plain,
% 4.34/4.52 (~b(s(elem!1), z)),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[19050, 178, 818, 817, 3271, 19043])).
% 4.34/4.52 tff(19052,plain,
% 4.34/4.52 (r(s(elem!1), z)),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[774, 19051])).
% 4.34/4.52 tff(19053,plain,
% 4.34/4.52 (~r(s(elem!1), s(s(s(s(z)))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[916, 19052, 194])).
% 4.34/4.52 tff(19054,plain,
% 4.34/4.52 (b(s(elem!1), s(s(s(s(z)))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[1084, 19053, 19044])).
% 4.34/4.52 tff(19055,plain,
% 4.34/4.52 (~r(elem!1, s(s(s(s(z)))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[478, 19041, 47])).
% 4.34/4.52 tff(19056,plain,
% 4.34/4.52 (b(elem!1, s(s(s(s(z)))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[483, 19055, 3179])).
% 4.34/4.52 tff(19057,plain,
% 4.34/4.52 (~r(s(s(s(s(z)))), elem!1)),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[6033, 19041, 194])).
% 4.34/4.52 tff(19058,plain,
% 4.34/4.52 (b(s(s(s(s(z)))), elem!1)),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[3142, 19057, 16687])).
% 4.34/4.52 tff(19059,plain,
% 4.34/4.52 (~r(elem!1, s(elem!1))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[2711, 19052, 19041])).
% 4.34/4.52 tff(19060,plain,
% 4.34/4.52 (b(elem!1, s(elem!1))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[756, 19059, 749])).
% 4.34/4.52 tff(19061,plain,
% 4.34/4.52 (~r(s(elem!1), elem!1)),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[13694, 19052, 19041])).
% 4.34/4.52 tff(19062,plain,
% 4.34/4.52 (b(s(elem!1), elem!1)),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[677, 19061, 725])).
% 4.34/4.52 tff(19063,plain,
% 4.34/4.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 4.34/4.52 inference(rewrite,[status(thm)],[])).
% 4.34/4.52 tff(19064,plain,
% 4.34/4.52 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 4.34/4.52 inference(rewrite,[status(thm)],[])).
% 4.34/4.52 tff(19065,plain,
% 4.34/4.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 4.34/4.52 inference(monotonicity,[status(thm)],[19064])).
% 4.34/4.52 tff(19066,plain,
% 4.34/4.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 4.34/4.52 inference(transitivity,[status(thm)],[19065, 19063])).
% 4.34/4.52 tff(19067,plain,
% 4.34/4.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(elem!1))))),
% 4.34/4.52 inference(quant_inst,[status(thm)],[])).
% 4.34/4.52 tff(19068,plain,
% 4.34/4.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))),
% 4.34/4.52 inference(modus_ponens,[status(thm)],[19067, 19066])).
% 4.34/4.52 tff(19069,plain,
% 4.34/4.52 ($false),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[19068, 178, 19062, 817, 19060, 19043, 19058, 19056, 19054])).
% 4.34/4.52 tff(19070,plain,((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (s(elem!1) = elem!1) | (~r(s(s(s(s(z)))), z)) | b(s(s(s(s(z)))), s(s(z))) | b(z, s(s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 4.34/4.52 tff(19071,plain,
% 4.34/4.52 (~b(z, elem!1)),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[19070, 9105, 18872, 3244, 86, 1, 147, 3277])).
% 4.34/4.52 tff(19072,plain,
% 4.34/4.52 (r(z, elem!1)),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[585, 19071, 3787])).
% 4.34/4.52 tff(19073,plain,
% 4.34/4.52 (~r(elem!1, s(s(s(s(z)))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[529, 19072, 47])).
% 4.34/4.52 tff(19074,plain,
% 4.34/4.52 (~(elem!1 = z)),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[3276, 9002, 461])).
% 4.34/4.52 tff(19075,plain,
% 4.34/4.52 (~(z = elem!1)),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[317, 19074])).
% 4.34/4.52 tff(19076,plain,
% 4.34/4.52 (~b(elem!1, z)),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[11004, 818, 9002, 817, 5619])).
% 4.34/4.52 tff(19077,plain,
% 4.34/4.52 (r(elem!1, z)),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[498, 19076, 290])).
% 4.34/4.52 tff(19078,plain,
% 4.34/4.52 (~(s(s(z)) = elem!1)),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[6206, 19077, 5618])).
% 4.34/4.52 tff(19079,plain,
% 4.34/4.52 (~(s(elem!1) = s(s(z)))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[15260, 19078, 47, 193, 9002, 19076, 3179, 5619, 147])).
% 4.34/4.52 tff(19080,plain,
% 4.34/4.52 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[2840, 19079])).
% 4.34/4.52 tff(19081,plain,
% 4.34/4.52 (~r(z, s(s(s(elem!1))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[3421, 19077, 3311])).
% 4.34/4.52 tff(19082,plain,
% 4.34/4.52 (b(z, s(s(s(elem!1))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[2095, 19081])).
% 4.34/4.52 tff(19083,plain,
% 4.34/4.52 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[8234, 19082, 147, 47])).
% 4.34/4.52 tff(19084,plain,
% 4.34/4.52 ($false),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[4173, 19083, 19080, 4170])).
% 4.34/4.52 tff(19085,plain,((~b(z, elem!1)) | b(s(s(s(elem!1))), s(s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(s(elem!1))))) | r(s(s(z)), z) | (elem!1 = z) | (~b(s(s(z)), elem!1)) | b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.52 tff(19086,plain,
% 4.34/4.52 (~b(z, elem!1)),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[19085, 3311, 147, 193, 4170, 5618, 290, 817, 1])).
% 4.34/4.52 tff(19087,plain,
% 4.34/4.52 (r(z, elem!1)),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[585, 19086, 318])).
% 4.34/4.52 tff(19088,plain,
% 4.34/4.52 (~r(elem!1, s(s(s(s(z)))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[529, 19087, 47])).
% 4.34/4.52 tff(19089,plain,
% 4.34/4.52 (~r(z, s(s(s(elem!1))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[3319, 19087, 3311])).
% 4.34/4.52 tff(19090,plain,
% 4.34/4.52 (b(z, s(s(s(elem!1))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[2095, 19089])).
% 4.34/4.52 tff(19091,plain,
% 4.34/4.52 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[8234, 19090, 147, 47])).
% 4.34/4.52 tff(19092,plain,
% 4.34/4.52 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[4173, 19091, 4170])).
% 4.34/4.52 tff(19093,plain,
% 4.34/4.52 (s(elem!1) = s(s(z))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[2840, 19092])).
% 4.34/4.52 tff(19094,plain,
% 4.34/4.52 (~(elem!1 = s(s(s(s(z)))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[11438, 19093])).
% 4.34/4.52 tff(19095,plain,
% 4.34/4.52 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[4168, 19092])).
% 4.34/4.52 tff(19096,plain,
% 4.34/4.52 (~b(elem!1, s(s(s(s(z)))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[4162, 19095, 3240])).
% 4.34/4.52 tff(19097,plain,
% 4.34/4.52 ($false),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[483, 19096, 19094, 19088])).
% 4.34/4.52 tff(19098,plain,((~r(elem!1, s(s(s(elem!1))))) | b(elem!1, s(s(s(elem!1)))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | r(s(s(z)), z) | (elem!1 = z) | (~b(s(s(z)), elem!1)) | b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.52 tff(19099,plain,
% 4.34/4.52 (~r(elem!1, s(s(s(elem!1))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[19098, 4170, 3240, 147, 193, 5618, 19074, 817, 1])).
% 4.34/4.52 tff(19100,plain,
% 4.34/4.52 (elem!1 = s(s(s(elem!1)))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[2054, 19099, 3240])).
% 4.34/4.52 tff(19101,plain,
% 4.34/4.52 (~b(z, s(s(s(elem!1))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[7967, 19100, 461, 1, 193, 4170])).
% 4.34/4.52 tff(19102,plain,
% 4.34/4.52 (~b(z, elem!1)),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[4187, 19101, 19100])).
% 4.34/4.52 tff(19103,plain,
% 4.34/4.52 (r(z, elem!1)),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[585, 19102, 19075])).
% 4.34/4.52 tff(19104,plain,
% 4.34/4.52 (~r(elem!1, s(s(s(s(z)))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[529, 19103, 47])).
% 4.34/4.52 tff(19105,plain,
% 4.34/4.52 (r(z, s(s(s(elem!1))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[2095, 19101])).
% 4.34/4.52 tff(19106,plain,
% 4.34/4.52 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[3259, 19105, 47])).
% 4.34/4.52 tff(19107,plain,
% 4.34/4.52 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[4173, 19106, 4170])).
% 4.34/4.52 tff(19108,plain,
% 4.34/4.52 (s(elem!1) = s(s(z))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[2840, 19107])).
% 4.34/4.52 tff(19109,plain,
% 4.34/4.52 (~(elem!1 = s(s(s(s(z)))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[11438, 19108])).
% 4.34/4.52 tff(19110,plain,
% 4.34/4.52 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[4168, 19107])).
% 4.34/4.52 tff(19111,plain,
% 4.34/4.52 (~b(elem!1, s(s(s(s(z)))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[4162, 19110, 3240])).
% 4.34/4.52 tff(19112,plain,
% 4.34/4.52 ($false),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[483, 19111, 19109, 19104])).
% 4.34/4.52 tff(19113,plain,(b(s(s(s(elem!1))), s(s(s(s(z))))) | b(elem!1, s(s(s(elem!1)))) | b(elem!1, s(s(z))) | b(z, s(s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | r(s(s(z)), z) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.52 tff(19114,plain,
% 4.34/4.52 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[19113, 147, 461, 1, 103, 3240, 8005, 18872])).
% 4.34/4.52 tff(19115,plain,
% 4.34/4.52 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(elem!1), elem!1)),
% 4.34/4.52 inference(symmetry,[status(thm)],[4024])).
% 4.34/4.52 tff(19116,plain,
% 4.34/4.52 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(elem!1), elem!1)),
% 4.34/4.52 inference(transitivity,[status(thm)],[4022, 19115])).
% 4.34/4.52 tff(19117,plain,
% 4.34/4.52 (b(s(s(s(s(z)))), elem!1)),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[3308, 1527, 5149])).
% 4.34/4.52 tff(19118,plain,
% 4.34/4.52 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.34/4.52 inference(modus_ponens,[status(thm)],[19117, 3290])).
% 4.34/4.52 tff(19119,plain,
% 4.34/4.52 (~(s(s(z)) = elem!1)),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[3774, 19117, 86])).
% 4.34/4.52 tff(19120,plain,
% 4.34/4.52 (~(s(s(s(z))) = elem!1)),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[4830, 1527, 4320])).
% 4.34/4.52 tff(19121,plain,
% 4.34/4.52 (r(z, elem!1)),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[585, 4853, 3787])).
% 4.34/4.52 tff(19122,plain,
% 4.34/4.52 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[3845, 19118, 3243, 19121, 1527, 47])).
% 4.34/4.52 tff(19123,plain,
% 4.34/4.52 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[271, 19122])).
% 4.34/4.52 tff(19124,plain,
% 4.34/4.52 (~(elem!1 = s(s(z)))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[311, 19119])).
% 4.34/4.52 tff(19125,plain,
% 4.34/4.52 (r(elem!1, s(s(z)))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[467, 19124, 461])).
% 4.34/4.52 tff(19126,plain,
% 4.34/4.52 (r(s(s(s(elem!1))), s(s(z)))),
% 4.34/4.52 inference(modus_ponens,[status(thm)],[19125, 6447])).
% 4.34/4.52 tff(19127,plain,
% 4.34/4.52 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[5063, 3615, 1126, 1527, 3831, 3828, 104, 4970])).
% 4.34/4.52 tff(19128,plain,
% 4.34/4.52 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[5118, 19127, 3521])).
% 4.34/4.52 tff(19129,plain,
% 4.34/4.52 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[5130, 19128, 557])).
% 4.34/4.52 tff(19130,plain,
% 4.34/4.52 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[133, 19129])).
% 4.34/4.52 tff(19131,plain,
% 4.34/4.52 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[10401, 19128, 3859])).
% 4.34/4.52 tff(19132,plain,
% 4.34/4.52 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[3578, 19131])).
% 4.34/4.52 tff(19133,plain,
% 4.34/4.52 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[1154, 19132, 595, 19130, 273])).
% 4.34/4.52 tff(19134,plain,
% 4.34/4.52 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[249, 19133])).
% 4.34/4.52 tff(19135,plain,
% 4.34/4.52 ($false),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[17339, 118, 3859, 19134, 3615])).
% 4.34/4.52 tff(19136,plain,((~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~(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(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.34/4.52 tff(19137,plain,
% 4.34/4.52 (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[19136, 3521, 595, 3549, 557, 3859, 5635, 1527, 3831, 3828, 104, 4970])).
% 4.34/4.52 tff(19138,plain,
% 4.34/4.52 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[3612, 41, 19137, 11632])).
% 4.34/4.52 tff(19139,plain,
% 4.34/4.52 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[4103, 19138, 3828, 3831, 104])).
% 4.34/4.52 tff(19140,plain,
% 4.34/4.52 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[222, 19139])).
% 4.34/4.52 tff(19141,plain,
% 4.34/4.52 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[5624, 19140, 147])).
% 4.34/4.52 tff(19142,plain,
% 4.34/4.52 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.52 inference(unit_resolution,[status(thm)],[249, 19141])).
% 4.34/4.52 tff(19143,plain,
% 4.34/4.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 4.34/4.52 inference(rewrite,[status(thm)],[])).
% 4.34/4.52 tff(19144,plain,
% 4.34/4.52 (((~b(s(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(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 4.34/4.52 inference(rewrite,[status(thm)],[])).
% 4.34/4.52 tff(19145,plain,
% 4.34/4.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))))),
% 4.34/4.53 inference(monotonicity,[status(thm)],[19144])).
% 4.34/4.53 tff(19146,plain,
% 4.34/4.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 4.34/4.53 inference(transitivity,[status(thm)],[19145, 19143])).
% 4.34/4.53 tff(19147,plain,
% 4.34/4.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 4.34/4.53 inference(quant_inst,[status(thm)],[])).
% 4.34/4.53 tff(19148,plain,
% 4.34/4.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 4.34/4.53 inference(modus_ponens,[status(thm)],[19147, 19146])).
% 4.34/4.53 tff(19149,plain,
% 4.34/4.53 ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[19148, 178, 4291, 104, 3831])).
% 4.34/4.53 tff(19150,plain,
% 4.34/4.53 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[19149, 19142])).
% 4.34/4.53 tff(19151,plain,
% 4.34/4.53 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[3569, 19140, 145, 193, 3461, 3549])).
% 4.34/4.53 tff(19152,plain,
% 4.34/4.53 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[3578, 19151])).
% 4.34/4.53 tff(19153,plain,
% 4.34/4.53 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[10401, 19152, 3859])).
% 4.34/4.53 tff(19154,plain,
% 4.34/4.53 ($false),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[5118, 19153, 19150, 3521])).
% 4.34/4.53 tff(19155,plain,((s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(elem!1))))) | (~(elem!1 = s(s(s(elem!1))))) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.34/4.53 tff(19156,plain,
% 4.34/4.53 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[19155, 19126, 17218, 104, 3831, 47, 103, 8674, 147, 19118, 19123, 3243, 1527, 19120])).
% 4.34/4.53 tff(19157,plain,
% 4.34/4.53 (s(s(s(s(z)))) = elem!1),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[3502, 19156])).
% 4.34/4.53 tff(19158,plain,
% 4.34/4.53 (~(s(s(elem!1)) = elem!1)),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[338, 19157, 19119])).
% 4.34/4.53 tff(19159,plain,
% 4.34/4.53 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[348, 19158])).
% 4.34/4.53 tff(19160,plain,
% 4.34/4.53 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 4.34/4.53 inference(monotonicity,[status(thm)],[3300])).
% 4.34/4.53 tff(19161,plain,
% 4.34/4.53 (r(elem!1, s(elem!1)) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 4.34/4.53 inference(transitivity,[status(thm)],[10049, 19160])).
% 4.34/4.53 tff(19162,plain,
% 4.34/4.53 ((~r(elem!1, s(elem!1))) <=> (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 4.34/4.53 inference(monotonicity,[status(thm)],[19161])).
% 4.34/4.53 tff(19163,plain,
% 4.34/4.53 (elem!1 = s(s(s(s(z))))),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[504, 19157])).
% 4.34/4.53 tff(19164,plain,
% 4.34/4.53 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(z)))),
% 4.34/4.53 inference(monotonicity,[status(thm)],[3300])).
% 4.34/4.53 tff(19165,plain,
% 4.34/4.53 (~b(elem!1, z)),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[3172, 19163, 3170])).
% 4.34/4.53 tff(19166,plain,
% 4.34/4.53 (b(s(elem!1), s(s(z)))),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[16105, 19165, 1, 86, 147, 19119, 8005])).
% 4.34/4.53 tff(19167,plain,
% 4.34/4.53 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 4.34/4.53 inference(modus_ponens,[status(thm)],[19166, 19164])).
% 4.34/4.53 tff(19168,plain,
% 4.34/4.53 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[2498, 1527, 4320])).
% 4.34/4.53 tff(19169,plain,
% 4.34/4.53 (r(elem!1, z)),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[498, 19165, 3277])).
% 4.34/4.53 tff(19170,plain,
% 4.34/4.53 (b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 4.34/4.53 inference(modus_ponens,[status(thm)],[2695, 3872])).
% 4.34/4.53 tff(19171,plain,
% 4.34/4.53 (~r(s(elem!1), elem!1)),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[13694, 844, 437])).
% 4.34/4.53 tff(19172,plain,
% 4.34/4.53 (b(s(elem!1), elem!1)),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[677, 19171, 1548])).
% 4.34/4.53 tff(19173,plain,
% 4.34/4.53 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 4.34/4.53 inference(modus_ponens,[status(thm)],[19172, 3998])).
% 4.34/4.53 tff(19174,plain,
% 4.34/4.53 (r(s(s(s(elem!1))), z)),
% 4.34/4.53 inference(modus_ponens,[status(thm)],[437, 8300])).
% 4.34/4.53 tff(19175,plain,
% 4.34/4.53 (~r(s(s(s(elem!1))), s(elem!1))),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[1557, 844, 19174])).
% 4.34/4.53 tff(19176,plain,
% 4.34/4.53 (b(s(s(s(elem!1))), s(elem!1))),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[373, 19175, 356])).
% 4.34/4.53 tff(19177,plain,
% 4.34/4.53 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 4.34/4.53 inference(modus_ponens,[status(thm)],[19176, 3868])).
% 4.34/4.53 tff(19178,plain,
% 4.34/4.53 ($false),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[3971, 178, 19177, 19173, 3828, 3831, 19170])).
% 4.34/4.53 tff(19179,plain,((~r(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~(elem!1 = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1)) | (s(elem!1) = s(s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.53 tff(19180,plain,
% 4.34/4.53 (~r(s(elem!1), z)),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[19179, 19169, 3831, 1527, 19159, 19168, 19118, 3244])).
% 4.34/4.53 tff(19181,plain,
% 4.34/4.53 (~r(s(s(s(s(elem!1)))), z)),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[3991, 19180, 1527])).
% 4.34/4.53 tff(19182,plain,
% 4.34/4.53 (b(s(s(s(s(elem!1)))), z)),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[1716, 19181])).
% 4.34/4.53 tff(19183,plain,
% 4.34/4.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 4.34/4.53 inference(rewrite,[status(thm)],[])).
% 4.34/4.53 tff(19184,plain,
% 4.34/4.53 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 4.34/4.53 inference(rewrite,[status(thm)],[])).
% 4.34/4.53 tff(19185,plain,
% 4.34/4.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1))))))))),
% 4.34/4.53 inference(monotonicity,[status(thm)],[19184])).
% 4.34/4.53 tff(19186,plain,
% 4.34/4.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 4.34/4.53 inference(transitivity,[status(thm)],[19185, 19183])).
% 4.34/4.53 tff(19187,plain,
% 4.34/4.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 4.34/4.53 inference(quant_inst,[status(thm)],[])).
% 4.34/4.53 tff(19188,plain,
% 4.34/4.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1))))))),
% 4.34/4.53 inference(modus_ponens,[status(thm)],[19187, 19186])).
% 4.34/4.53 tff(19189,plain,
% 4.34/4.53 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[19188, 178, 8674, 19182, 3271, 19167])).
% 4.34/4.53 tff(19190,plain,
% 4.34/4.53 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[2136, 19189])).
% 4.34/4.53 tff(19191,plain,
% 4.34/4.53 (r(s(s(z)), s(elem!1))),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[2155, 19190, 3894])).
% 4.34/4.53 tff(19192,plain,
% 4.34/4.53 (~r(elem!1, s(elem!1))),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[12646, 19191, 147, 19163])).
% 4.34/4.53 tff(19193,plain,
% 4.34/4.53 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 4.34/4.53 inference(modus_ponens,[status(thm)],[19192, 19162])).
% 4.34/4.53 tff(19194,plain,
% 4.34/4.53 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 4.34/4.53 inference(symmetry,[status(thm)],[19160])).
% 4.34/4.53 tff(19195,plain,
% 4.34/4.53 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(elem!1, s(elem!1))),
% 4.34/4.53 inference(transitivity,[status(thm)],[19194, 10050])).
% 4.34/4.53 tff(19196,plain,
% 4.34/4.53 ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) <=> (~r(elem!1, s(elem!1)))),
% 4.34/4.53 inference(monotonicity,[status(thm)],[19195])).
% 4.34/4.53 tff(19197,plain,
% 4.34/4.53 (~r(elem!1, s(elem!1))),
% 4.34/4.53 inference(modus_ponens,[status(thm)],[3963, 19196])).
% 4.34/4.53 tff(19198,plain,
% 4.34/4.53 (b(s(elem!1), s(s(s(s(z)))))),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[10314, 356, 461, 3170, 19197, 5618])).
% 4.34/4.53 tff(19199,plain,
% 4.34/4.53 (b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 4.34/4.53 inference(modus_ponens,[status(thm)],[19198, 3872])).
% 4.34/4.53 tff(19200,plain,
% 4.34/4.53 (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[3973, 1658, 3831, 3963, 3961, 3828])).
% 4.34/4.53 tff(19201,plain,
% 4.34/4.53 ($false),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[19200, 19199])).
% 4.34/4.53 tff(19202,plain,((s(s(s(elem!1))) = s(elem!1)) | (~(elem!1 = s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | b(elem!1, s(s(z))) | b(s(s(s(s(z)))), z) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 4.34/4.53 tff(19203,plain,
% 4.34/4.53 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[19202, 19193, 3831, 1527, 19159, 19118, 461, 3170, 8005])).
% 4.34/4.53 tff(19204,plain,
% 4.34/4.53 (r(s(elem!1), elem!1)),
% 4.34/4.53 inference(modus_ponens,[status(thm)],[19203, 19116])).
% 4.34/4.53 tff(19205,plain,
% 4.34/4.53 (b(z, s(elem!1)) <=> b(z, s(s(s(s(elem!1)))))),
% 4.34/4.53 inference(monotonicity,[status(thm)],[3300])).
% 4.34/4.53 tff(19206,plain,
% 4.34/4.53 (b(z, s(s(s(s(elem!1))))) <=> b(z, s(elem!1))),
% 4.34/4.53 inference(symmetry,[status(thm)],[19205])).
% 4.34/4.53 tff(19207,plain,
% 4.34/4.53 ((~b(z, s(s(s(s(elem!1)))))) <=> (~b(z, s(elem!1)))),
% 4.34/4.53 inference(monotonicity,[status(thm)],[19206])).
% 4.34/4.53 tff(19208,plain,
% 4.34/4.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 4.34/4.53 inference(rewrite,[status(thm)],[])).
% 4.34/4.53 tff(19209,plain,
% 4.34/4.53 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 4.34/4.53 inference(rewrite,[status(thm)],[])).
% 4.34/4.53 tff(19210,plain,
% 4.34/4.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z))))))),
% 4.34/4.53 inference(monotonicity,[status(thm)],[19209])).
% 4.34/4.53 tff(19211,plain,
% 4.34/4.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 4.34/4.53 inference(transitivity,[status(thm)],[19210, 19208])).
% 4.34/4.53 tff(19212,plain,
% 4.34/4.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))))),
% 4.34/4.53 inference(quant_inst,[status(thm)],[])).
% 4.34/4.53 tff(19213,plain,
% 4.34/4.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 4.34/4.53 inference(modus_ponens,[status(thm)],[19212, 19211])).
% 4.34/4.53 tff(19214,plain,
% 4.34/4.53 (~b(z, s(s(s(s(elem!1)))))),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[19213, 178, 8674, 19182, 3271, 19167])).
% 4.34/4.53 tff(19215,plain,
% 4.34/4.53 (~b(z, s(elem!1))),
% 4.34/4.53 inference(modus_ponens,[status(thm)],[19214, 19207])).
% 4.34/4.53 tff(19216,plain,
% 4.34/4.53 (r(z, s(elem!1))),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[2351, 19215])).
% 4.34/4.53 tff(19217,plain,
% 4.34/4.53 (~r(s(elem!1), elem!1)),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[7070, 19216, 19121])).
% 4.34/4.53 tff(19218,plain,
% 4.34/4.53 ($false),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[19217, 19204])).
% 4.34/4.53 tff(19219,plain,((~(elem!1 = s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | b(elem!1, s(s(z))) | b(s(s(s(s(z)))), z) | (~r(s(s(z)), s(s(s(s(z)))))) | b(z, s(s(s(s(z))))) | b(s(s(s(s(z)))), s(s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | b(z, s(s(s(elem!1)))) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.53 tff(19220,plain,
% 4.34/4.53 (~(elem!1 = s(s(s(elem!1))))),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[19219, 3242, 461, 3170, 147, 1, 86, 19039, 19114, 18872])).
% 4.34/4.53 tff(19221,plain,
% 4.34/4.53 (r(elem!1, s(s(s(elem!1))))),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[2054, 19220, 3240])).
% 4.34/4.53 tff(19222,plain,
% 4.34/4.53 (~r(z, elem!1)),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[3319, 19221, 3243])).
% 4.34/4.53 tff(19223,plain,
% 4.34/4.53 (b(z, elem!1)),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[585, 19222, 3787])).
% 4.34/4.53 tff(19224,plain,
% 4.34/4.53 (~r(elem!1, z)),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[3421, 19221, 3243])).
% 4.34/4.53 tff(19225,plain,
% 4.34/4.53 (b(elem!1, z)),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[498, 19224, 3277])).
% 4.34/4.53 tff(19226,plain,
% 4.34/4.53 ($false),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[11004, 19225, 19223, 3271, 18872, 8674])).
% 4.34/4.53 tff(19227,plain,(b(z, s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | b(elem!1, s(s(z))) | b(s(s(s(s(z)))), z) | (~r(s(s(z)), s(s(s(s(z)))))) | b(z, s(s(s(s(z))))) | b(s(s(s(s(z)))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.53 tff(19228,plain,
% 4.34/4.53 (b(z, s(s(s(elem!1))))),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[19227, 147, 461, 3170, 3240, 1, 86])).
% 4.34/4.53 tff(19229,plain,
% 4.34/4.53 (b(elem!1, z)),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[17483, 9097, 19228, 3271, 461, 8005])).
% 4.34/4.53 tff(19230,plain,
% 4.34/4.53 (~(elem!1 = s(s(s(s(z)))))),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[3172, 19229, 3170])).
% 4.34/4.53 tff(19231,plain,
% 4.34/4.53 (b(elem!1, s(s(s(s(z)))))),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[483, 19230, 19073])).
% 4.34/4.53 tff(19232,plain,
% 4.34/4.53 (b(elem!1, z)),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[17483, 3311, 2043, 8681, 461, 8005])).
% 4.34/4.53 tff(19233,plain,
% 4.34/4.53 (~r(s(s(s(s(z)))), elem!1)),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[3137, 521, 3244])).
% 4.34/4.53 tff(19234,plain,
% 4.34/4.53 (~(elem!1 = s(s(s(s(z)))))),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[3172, 506, 3170])).
% 4.34/4.53 tff(19235,plain,
% 4.34/4.53 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[8548, 19234, 104, 19233, 251, 5721])).
% 4.34/4.53 tff(19236,plain,
% 4.34/4.53 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[691, 19235, 644])).
% 4.34/4.53 tff(19237,plain,
% 4.34/4.53 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 4.34/4.53 inference(monotonicity,[status(thm)],[19236])).
% 4.34/4.53 tff(19238,plain,
% 4.34/4.53 (s(s(s(s(s(s(s(s(z)))))))) = s(elem!1)),
% 4.34/4.53 inference(symmetry,[status(thm)],[19237])).
% 4.34/4.53 tff(19239,plain,
% 4.34/4.53 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(z))) <=> b(s(elem!1), s(s(z)))),
% 4.34/4.53 inference(monotonicity,[status(thm)],[19238])).
% 4.34/4.53 tff(19240,plain,
% 4.34/4.53 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 4.34/4.53 inference(symmetry,[status(thm)],[19239])).
% 4.34/4.53 tff(19241,plain,
% 4.34/4.53 (~(s(elem!1) = s(s(z)))),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[2832, 19236])).
% 4.34/4.53 tff(19242,plain,
% 4.34/4.53 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 4.34/4.53 inference(monotonicity,[status(thm)],[19238])).
% 4.34/4.53 tff(19243,plain,
% 4.34/4.53 ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) <=> (~r(s(elem!1), s(s(z))))),
% 4.34/4.53 inference(monotonicity,[status(thm)],[19242])).
% 4.34/4.53 tff(19244,plain,
% 4.34/4.53 (r(elem!1, s(elem!1)) <=> r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.34/4.53 inference(monotonicity,[status(thm)],[19236])).
% 4.34/4.53 tff(19245,plain,
% 4.34/4.53 (b(elem!1, z) <=> b(s(s(s(s(s(s(s(z))))))), z)),
% 4.34/4.53 inference(monotonicity,[status(thm)],[19236])).
% 4.34/4.53 tff(19246,plain,
% 4.34/4.53 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.34/4.53 inference(modus_ponens,[status(thm)],[506, 19245])).
% 4.34/4.53 tff(19247,plain,
% 4.34/4.53 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.53 inference(monotonicity,[status(thm)],[19236])).
% 4.34/4.53 tff(19248,plain,
% 4.34/4.53 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.53 inference(modus_ponens,[status(thm)],[817, 19247])).
% 4.34/4.53 tff(19249,plain,
% 4.34/4.53 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.34/4.53 inference(monotonicity,[status(thm)],[19236])).
% 4.34/4.53 tff(19250,plain,
% 4.34/4.53 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.34/4.53 inference(modus_ponens,[status(thm)],[3311, 19249])).
% 4.34/4.53 tff(19251,plain,
% 4.34/4.53 (r(elem!1, s(s(z))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.34/4.53 inference(monotonicity,[status(thm)],[19236])).
% 4.34/4.53 tff(19252,plain,
% 4.34/4.53 (~(s(s(s(s(z)))) = elem!1)),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[504, 19234])).
% 4.34/4.53 tff(19253,plain,
% 4.34/4.53 (b(s(s(s(s(z)))), elem!1)),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[3142, 19252, 19233])).
% 4.34/4.53 tff(19254,plain,
% 4.34/4.53 (~(s(s(z)) = elem!1)),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[3774, 19253, 86])).
% 4.34/4.53 tff(19255,plain,
% 4.34/4.53 (~(elem!1 = s(s(z)))),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[311, 19254])).
% 4.34/4.53 tff(19256,plain,
% 4.34/4.53 (r(elem!1, s(s(z)))),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[467, 19255, 461])).
% 4.34/4.53 tff(19257,plain,
% 4.34/4.53 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.34/4.53 inference(modus_ponens,[status(thm)],[19256, 19251])).
% 4.34/4.53 tff(19258,plain,
% 4.34/4.53 (~r(s(s(s(elem!1))), s(s(z)))),
% 4.34/4.53 inference(unit_resolution,[status(thm)],[10401, 19257, 19250])).
% 4.34/4.53 tff(19259,plain,
% 4.34/4.53 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(z))) <=> b(s(elem!1), s(s(z)))),
% 4.34/4.53 inference(monotonicity,[status(thm)],[11730])).
% 4.34/4.53 tff(19260,plain,
% 4.34/4.53 ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) <=> (~b(s(elem!1), s(s(z))))),
% 4.34/4.53 inference(monotonicity,[status(thm)],[19259])).
% 4.34/4.53 tff(19261,plain,
% 4.34/4.53 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))) <=> r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.34/4.53 inference(monotonicity,[status(thm)],[11730])).
% 4.34/4.53 tff(19262,plain,
% 4.34/4.53 (r(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.53 inference(symmetry,[status(thm)],[19261])).
% 4.34/4.53 tff(19263,plain,
% 4.34/4.53 ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) <=> (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))),
% 4.34/4.53 inference(monotonicity,[status(thm)],[19262])).
% 4.34/4.53 tff(19264,plain,
% 4.34/4.53 (r(elem!1, s(elem!1)) <=> r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.34/4.53 inference(monotonicity,[status(thm)],[679])).
% 4.34/4.53 tff(19265,plain,
% 4.34/4.53 ((~r(elem!1, s(elem!1))) <=> (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 4.34/4.53 inference(monotonicity,[status(thm)],[19264])).
% 4.34/4.53 tff(19266,plain,
% 4.34/4.53 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.34/4.53 inference(modus_ponens,[status(thm)],[744, 19265])).
% 4.34/4.53 tff(19267,plain,
% 4.34/4.53 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.53 inference(modus_ponens,[status(thm)],[19266, 19263])).
% 4.34/4.53 tff(19268,plain,
% 4.34/4.53 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 4.34/4.53 inference(monotonicity,[status(thm)],[11730])).
% 4.34/4.53 tff(19269,plain,
% 4.34/4.53 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.34/4.53 inference(transitivity,[status(thm)],[19268, 377])).
% 4.34/4.53 tff(19270,plain,
% 4.34/4.53 ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.53 inference(symmetry,[status(thm)],[19269])).
% 4.34/4.53 tff(19271,plain,
% 4.34/4.53 ((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z))))))))))),
% 4.34/4.53 inference(monotonicity,[status(thm)],[19270])).
% 4.34/4.53 tff(19272,plain,
% 4.34/4.53 ((~(s(elem!1) = elem!1)) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.53 inference(monotonicity,[status(thm)],[16184])).
% 4.34/4.53 tff(19273,plain,
% 4.34/4.53 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.34/4.53 inference(modus_ponens,[status(thm)],[725, 19272])).
% 4.34/4.53 tff(19274,plain,
% 4.34/4.53 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.54 inference(modus_ponens,[status(thm)],[19273, 19271])).
% 4.34/4.54 tff(19275,plain,
% 4.34/4.54 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[16349, 41])).
% 4.34/4.54 tff(19276,plain,
% 4.34/4.54 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[19275, 19274, 19267])).
% 4.34/4.54 tff(19277,plain,
% 4.34/4.54 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.34/4.54 inference(modus_ponens,[status(thm)],[19276, 11731])).
% 4.34/4.54 tff(19278,assumption,(b(s(s(s(s(s(s(s(z))))))), s(elem!1))), introduced(assumption)).
% 4.34/4.54 tff(19279,plain,
% 4.34/4.54 ($false),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[14258, 178, 855, 3461, 166, 146, 19278])).
% 4.34/4.54 tff(19280,plain,((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.54 tff(19281,plain,
% 4.34/4.54 (~b(z, s(elem!1))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[19280, 19277, 5619, 166, 146])).
% 4.34/4.54 tff(19282,plain,
% 4.34/4.54 (r(z, s(elem!1))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[2351, 19281])).
% 4.34/4.54 tff(19283,plain,
% 4.34/4.54 (~r(s(elem!1), elem!1)),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[7070, 19282, 521])).
% 4.34/4.54 tff(19284,plain,
% 4.34/4.54 (b(s(elem!1), elem!1)),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[677, 19283, 725])).
% 4.34/4.54 tff(19285,plain,
% 4.34/4.54 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[686, 19284, 679])).
% 4.34/4.54 tff(19286,plain,
% 4.34/4.54 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.54 inference(modus_ponens,[status(thm)],[19285, 11735])).
% 4.34/4.54 tff(19287,plain,
% 4.34/4.54 ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[16212, 178, 5619, 166, 146])).
% 4.34/4.54 tff(19288,plain,
% 4.34/4.54 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[19287, 19286])).
% 4.34/4.54 tff(19289,plain,
% 4.34/4.54 (~b(s(elem!1), s(s(z)))),
% 4.34/4.54 inference(modus_ponens,[status(thm)],[19288, 19260])).
% 4.34/4.54 tff(19290,plain,
% 4.34/4.54 (r(s(elem!1), s(s(z)))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[421, 19289, 10483])).
% 4.34/4.54 tff(19291,plain,
% 4.34/4.54 ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) <=> (~b(s(elem!1), s(s(s(s(z))))))),
% 4.34/4.54 inference(monotonicity,[status(thm)],[16137])).
% 4.34/4.54 tff(19292,plain,
% 4.34/4.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(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(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(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(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 4.34/4.54 inference(rewrite,[status(thm)],[])).
% 4.34/4.54 tff(19293,plain,
% 4.34/4.54 (((~b(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))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(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(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(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(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 4.34/4.54 inference(rewrite,[status(thm)],[])).
% 4.34/4.54 tff(19294,plain,
% 4.34/4.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(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(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(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(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(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))))),
% 4.34/4.54 inference(monotonicity,[status(thm)],[19293])).
% 4.34/4.54 tff(19295,plain,
% 4.34/4.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(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(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(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(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(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 4.34/4.54 inference(transitivity,[status(thm)],[19294, 19292])).
% 4.34/4.54 tff(19296,plain,
% 4.34/4.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(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(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(s(s(s(s(z)))))))))))),
% 4.34/4.54 inference(quant_inst,[status(thm)],[])).
% 4.34/4.54 tff(19297,plain,
% 4.34/4.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))),
% 4.34/4.54 inference(modus_ponens,[status(thm)],[19296, 19295])).
% 4.34/4.54 tff(19298,plain,
% 4.34/4.54 ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[19297, 178, 104, 251, 19276])).
% 4.34/4.54 tff(19299,plain,
% 4.34/4.54 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[19298, 19286])).
% 4.34/4.54 tff(19300,plain,
% 4.34/4.54 (~b(s(elem!1), s(s(s(s(z)))))),
% 4.34/4.54 inference(modus_ponens,[status(thm)],[19299, 19291])).
% 4.34/4.54 tff(19301,plain,
% 4.34/4.54 (s(s(s(elem!1))) = s(elem!1)),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[10314, 19300, 461, 3170, 744, 5618])).
% 4.34/4.54 tff(19302,plain,
% 4.34/4.54 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 4.34/4.54 inference(monotonicity,[status(thm)],[340])).
% 4.34/4.54 tff(19303,plain,
% 4.34/4.54 (r(s(elem!1), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 4.34/4.54 inference(symmetry,[status(thm)],[19302])).
% 4.34/4.54 tff(19304,plain,
% 4.34/4.54 (r(s(s(s(elem!1))), s(s(z)))),
% 4.34/4.54 inference(modus_ponens,[status(thm)],[363, 19303])).
% 4.34/4.54 tff(19305,plain,
% 4.34/4.54 ($false),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[5810, 19304])).
% 4.34/4.54 tff(19306,plain,((~r(s(elem!1), s(s(z)))) | r(s(s(s(elem!1))), s(s(z))) | (~(s(s(s(elem!1))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.54 tff(19307,plain,
% 4.34/4.54 ($false),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[19306, 19301, 19290, 5810])).
% 4.34/4.54 tff(19308,plain,(r(elem!1, s(elem!1)) | r(s(s(s(elem!1))), s(s(z))) | b(elem!1, s(s(z))) | b(s(s(s(s(z)))), z) | r(s(s(z)), z) | (~(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))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (s(elem!1) = elem!1) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.54 tff(19309,plain,
% 4.34/4.54 (r(elem!1, s(elem!1))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[19308, 19258, 461, 3170, 8005, 19236, 104, 251, 19248, 19246, 725, 521])).
% 4.34/4.54 tff(19310,plain,
% 4.34/4.54 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.34/4.54 inference(modus_ponens,[status(thm)],[19309, 19244])).
% 4.34/4.54 tff(19311,assumption,(r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))), introduced(assumption)).
% 4.34/4.54 tff(19312,plain,
% 4.34/4.54 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.54 inference(modus_ponens,[status(thm)],[15198, 19262])).
% 4.34/4.54 tff(19313,plain,
% 4.34/4.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))))),
% 4.34/4.54 inference(rewrite,[status(thm)],[])).
% 4.34/4.54 tff(19314,plain,
% 4.34/4.54 (((~r(s(s(s(s(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(s(s(s(z))))))), s(s(s(s(s(s(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(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))))),
% 4.34/4.54 inference(rewrite,[status(thm)],[])).
% 4.34/4.54 tff(19315,plain,
% 4.34/4.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(z))))))),
% 4.34/4.54 inference(monotonicity,[status(thm)],[19314])).
% 4.34/4.54 tff(19316,plain,
% 4.34/4.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))))),
% 4.34/4.54 inference(transitivity,[status(thm)],[19315, 19313])).
% 4.34/4.54 tff(19317,plain,
% 4.34/4.54 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 4.34/4.54 inference(quant_inst,[status(thm)],[])).
% 4.34/4.54 tff(19318,plain,
% 4.34/4.54 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(z))))),
% 4.34/4.54 inference(modus_ponens,[status(thm)],[19317, 19316])).
% 4.34/4.54 tff(19319,plain,
% 4.34/4.54 ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(z))))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[19318, 118, 107])).
% 4.34/4.54 tff(19320,plain,
% 4.34/4.54 ($false),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[19319, 19312, 19311])).
% 4.34/4.54 tff(19321,plain,((~r(s(s(s(s(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(s(s(s(z))))))), s(elem!1))) | (~(elem!1 = s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.54 tff(19322,plain,
% 4.34/4.54 (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[19321, 19257, 19310, 19236])).
% 4.34/4.54 tff(19323,plain,
% 4.34/4.54 (~r(s(elem!1), s(s(z)))),
% 4.34/4.54 inference(modus_ponens,[status(thm)],[19322, 19243])).
% 4.34/4.54 tff(19324,plain,
% 4.34/4.54 (b(s(elem!1), s(s(z)))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[421, 19323, 19241])).
% 4.34/4.54 tff(19325,plain,
% 4.34/4.54 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 4.34/4.54 inference(modus_ponens,[status(thm)],[19324, 19240])).
% 4.34/4.54 tff(19326,plain,
% 4.34/4.54 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[16215, 19236, 8674, 19248, 19246, 19325])).
% 4.34/4.54 tff(19327,plain,
% 4.34/4.54 (~b(s(elem!1), elem!1)),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[686, 19326, 19236])).
% 4.34/4.54 tff(19328,plain,
% 4.34/4.54 (r(s(elem!1), elem!1)),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[677, 19327, 725])).
% 4.34/4.54 tff(19329,plain,
% 4.34/4.54 (~r(z, s(elem!1))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[7070, 19328, 521])).
% 4.34/4.54 tff(19330,plain,
% 4.34/4.54 (~r(s(elem!1), s(s(s(elem!1))))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[10317, 19309, 3311])).
% 4.34/4.54 tff(19331,plain,
% 4.34/4.54 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[12552, 19324, 86])).
% 4.34/4.54 tff(19332,plain,
% 4.34/4.54 (~(s(s(s(s(z)))) = s(elem!1))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[2168, 19331])).
% 4.34/4.54 tff(19333,plain,
% 4.34/4.54 (~(s(s(elem!1)) = elem!1)),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[2510, 19332, 19236])).
% 4.34/4.54 tff(19334,plain,
% 4.34/4.54 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[348, 19333])).
% 4.34/4.54 tff(19335,plain,
% 4.34/4.54 (~(s(elem!1) = s(s(s(elem!1))))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[5395, 19334])).
% 4.34/4.54 tff(19336,plain,
% 4.34/4.54 (b(s(elem!1), s(s(s(elem!1))))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[5432, 19335, 19330])).
% 4.34/4.54 tff(19337,plain,
% 4.34/4.54 (~r(s(s(s(elem!1))), s(elem!1))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[1591, 19309, 3311])).
% 4.34/4.54 tff(19338,plain,
% 4.34/4.54 (b(s(s(s(elem!1))), s(elem!1))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[373, 19334, 19337])).
% 4.34/4.54 tff(19339,plain,
% 4.34/4.54 (~(s(elem!1) = elem!1)),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[790, 766, 506])).
% 4.34/4.54 tff(19340,plain,
% 4.34/4.54 (~r(s(elem!1), elem!1)),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[1284, 12569, 521])).
% 4.34/4.54 tff(19341,plain,
% 4.34/4.54 ($false),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[677, 19340, 19339, 2141])).
% 4.34/4.54 tff(19342,plain,(b(s(elem!1), z) | b(s(elem!1), elem!1) | (~r(z, elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.54 tff(19343,plain,
% 4.34/4.54 (b(s(elem!1), z)),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[19342, 19327, 506, 521])).
% 4.34/4.54 tff(19344,plain,
% 4.34/4.54 (~b(z, s(elem!1))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[6736, 19343, 2043, 19338, 19336])).
% 4.34/4.54 tff(19345,plain,
% 4.34/4.54 ($false),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[2351, 19344, 19329])).
% 4.34/4.54 tff(19346,plain,((~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (s(elem!1) = elem!1) | b(s(s(s(s(z)))), s(s(z))) | (~r(elem!1, s(s(s(elem!1))))) | b(elem!1, s(s(z))) | b(s(s(s(s(z)))), z) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), elem!1)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(elem!1, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.54 tff(19347,plain,
% 4.34/4.54 ($false),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[19346, 223, 3819, 521, 725, 86, 3311, 461, 3170, 104, 2043, 817, 19232, 530])).
% 4.34/4.54 tff(19348,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (s(elem!1) = elem!1) | b(s(s(s(s(z)))), s(s(z))) | (~r(elem!1, s(s(s(elem!1))))) | b(elem!1, s(s(z))) | b(s(s(s(s(z)))), z) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.54 tff(19349,plain,
% 4.34/4.54 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[19348, 19072, 9105, 86, 9097, 461, 3170, 19039, 19228, 18872, 47])).
% 4.34/4.54 tff(19350,plain,
% 4.34/4.54 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[271, 19349])).
% 4.34/4.54 tff(19351,plain,
% 4.34/4.54 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[3559, 224, 103])).
% 4.34/4.54 tff(19352,plain,
% 4.34/4.54 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[222, 19351])).
% 4.34/4.54 tff(19353,plain,
% 4.34/4.54 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[19346, 19352, 521, 725, 86, 3311, 461, 3170, 104, 2043, 817, 506, 5721])).
% 4.34/4.54 tff(19354,plain,
% 4.34/4.54 ($false),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[3111, 118, 19256, 224, 19353])).
% 4.34/4.54 tff(19355,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (s(elem!1) = elem!1) | b(s(s(s(s(z)))), s(s(z))) | (~r(elem!1, s(s(s(elem!1))))) | b(elem!1, s(s(z))) | b(s(s(s(s(z)))), z) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | r(elem!1, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.54 tff(19356,plain,
% 4.34/4.54 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[19355, 19072, 9105, 86, 9097, 461, 3170, 19039, 19228, 18872, 19229, 19073])).
% 4.34/4.54 tff(19357,plain,
% 4.34/4.54 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[249, 19356])).
% 4.34/4.54 tff(19358,plain,
% 4.34/4.54 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[17498, 19357, 3271, 19350, 19072, 8674, 18872, 19039, 19231])).
% 4.34/4.54 tff(19359,plain,
% 4.34/4.54 (b(z, s(s(s(s(s(s(s(z)))))))) <=> b(z, elem!1)),
% 4.34/4.54 inference(monotonicity,[status(thm)],[19358])).
% 4.34/4.54 tff(19360,plain,
% 4.34/4.54 (b(z, elem!1) <=> b(z, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.54 inference(symmetry,[status(thm)],[19359])).
% 4.34/4.54 tff(19361,plain,
% 4.34/4.54 ((~b(z, elem!1)) <=> (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.54 inference(monotonicity,[status(thm)],[19360])).
% 4.34/4.54 tff(19362,plain,
% 4.34/4.54 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.54 inference(modus_ponens,[status(thm)],[19071, 19361])).
% 4.34/4.54 tff(19363,plain,
% 4.34/4.54 ($false),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[19350, 19362])).
% 4.34/4.54 tff(19364,plain,((elem!1 = s(s(s(elem!1)))) | b(s(s(s(s(z)))), s(s(z))) | b(elem!1, s(s(z))) | b(s(s(s(s(z)))), z) | b(z, s(s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | b(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.54 tff(19365,plain,
% 4.34/4.54 (elem!1 = s(s(s(elem!1)))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[19364, 147, 461, 3170, 1, 86, 3240])).
% 4.34/4.54 tff(19366,plain,
% 4.34/4.54 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[2498, 19365, 4320])).
% 4.34/4.54 tff(19367,plain,
% 4.34/4.54 (b(elem!1, z) <=> b(s(s(s(elem!1))), z)),
% 4.34/4.54 inference(monotonicity,[status(thm)],[19365])).
% 4.34/4.54 tff(19368,plain,
% 4.34/4.54 (b(s(s(s(elem!1))), z) <=> b(elem!1, z)),
% 4.34/4.54 inference(symmetry,[status(thm)],[19367])).
% 4.34/4.54 tff(19369,plain,
% 4.34/4.54 ((~b(s(s(s(elem!1))), z)) <=> (~b(elem!1, z))),
% 4.34/4.54 inference(monotonicity,[status(thm)],[19368])).
% 4.34/4.54 tff(19370,plain,
% 4.34/4.54 (b(s(s(z)), s(s(s(elem!1))))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[17217, 19365, 18872])).
% 4.34/4.54 tff(19371,plain,
% 4.34/4.54 (~b(s(s(s(elem!1))), z)),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[7978, 19370, 8674, 3271, 19228])).
% 4.34/4.54 tff(19372,plain,
% 4.34/4.54 (~b(elem!1, z)),
% 4.34/4.54 inference(modus_ponens,[status(thm)],[19371, 19369])).
% 4.34/4.54 tff(19373,plain,
% 4.34/4.54 (b(z, elem!1) <=> b(z, s(s(s(elem!1))))),
% 4.34/4.54 inference(monotonicity,[status(thm)],[19365])).
% 4.34/4.54 tff(19374,plain,
% 4.34/4.54 (b(z, s(s(s(elem!1)))) <=> b(z, elem!1)),
% 4.34/4.54 inference(symmetry,[status(thm)],[19373])).
% 4.34/4.54 tff(19375,plain,
% 4.34/4.54 (b(z, elem!1)),
% 4.34/4.54 inference(modus_ponens,[status(thm)],[19228, 19374])).
% 4.34/4.54 tff(19376,plain,
% 4.34/4.54 (s(elem!1) = elem!1),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[19070, 19375, 18872, 3244, 86, 1, 147, 3277])).
% 4.34/4.54 tff(19377,plain,
% 4.34/4.54 (s(s(elem!1)) = elem!1),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[672, 19376])).
% 4.34/4.54 tff(19378,plain,
% 4.34/4.54 (elem!1 = s(s(elem!1))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[1546, 19377])).
% 4.34/4.54 tff(19379,plain,
% 4.34/4.54 (s(s(s(elem!1))) = s(elem!1)),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[1539, 19378])).
% 4.34/4.54 tff(19380,plain,
% 4.34/4.54 ($false),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[750, 3886])).
% 4.34/4.54 tff(19381,plain,((~(s(s(s(elem!1))) = s(elem!1))) | (elem!1 = s(elem!1)) | (~(elem!1 = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.54 tff(19382,plain,
% 4.34/4.54 (elem!1 = s(elem!1)),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[19381, 19379, 19365])).
% 4.34/4.54 tff(19383,plain,
% 4.34/4.54 (~b(s(elem!1), z)),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[12026, 19382, 19372])).
% 4.34/4.54 tff(19384,plain,
% 4.34/4.54 (r(s(elem!1), z)),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[774, 19383])).
% 4.34/4.54 tff(19385,plain,
% 4.34/4.54 (~r(s(elem!1), s(s(s(s(z)))))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[916, 19384, 3244])).
% 4.34/4.54 tff(19386,plain,
% 4.34/4.54 (~(s(s(s(s(z)))) = s(elem!1))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[2168, 19366])).
% 4.34/4.54 tff(19387,plain,
% 4.34/4.54 (r(elem!1, z) <=> r(s(s(s(elem!1))), z)),
% 4.34/4.54 inference(monotonicity,[status(thm)],[19365])).
% 4.34/4.54 tff(19388,plain,
% 4.34/4.54 (r(s(s(s(elem!1))), z) <=> r(elem!1, z)),
% 4.34/4.54 inference(symmetry,[status(thm)],[19387])).
% 4.34/4.54 tff(19389,plain,
% 4.34/4.54 (r(s(s(s(elem!1))), z)),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[1565, 19371])).
% 4.34/4.54 tff(19390,plain,
% 4.34/4.54 (r(elem!1, z)),
% 4.34/4.54 inference(modus_ponens,[status(thm)],[19389, 19388])).
% 4.34/4.54 tff(19391,plain,
% 4.34/4.54 (~(elem!1 = s(s(s(s(z)))))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[1846, 19375, 1])).
% 4.34/4.54 tff(19392,plain,
% 4.34/4.54 (s(s(s(elem!1))) = elem!1),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[1530, 19365])).
% 4.34/4.54 tff(19393,plain,
% 4.34/4.54 (elem!1 = s(s(s(s(elem!1))))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[1509, 19379])).
% 4.34/4.54 tff(19394,plain,
% 4.34/4.54 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[3901, 19393, 461])).
% 4.34/4.54 tff(19395,plain,
% 4.34/4.54 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[1170, 19394])).
% 4.34/4.54 tff(19396,plain,
% 4.34/4.54 (r(s(elem!1), s(s(z)))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[3907, 19395, 19392])).
% 4.34/4.54 tff(19397,plain,
% 4.34/4.54 (~b(s(elem!1), s(s(s(s(z)))))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[14977, 19396, 3244, 103, 3271, 8674, 19391, 19390, 19386, 19039, 19384, 47])).
% 4.34/4.54 tff(19398,plain,
% 4.34/4.54 ($false),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[1084, 19397, 19385, 19366])).
% 4.34/4.54 tff(19399,plain,((~r(s(s(z)), s(s(s(s(z)))))) | b(elem!1, s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | b(z, s(s(s(s(z))))) | b(s(s(s(s(z)))), z) | b(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.54 tff(19400,plain,
% 4.34/4.54 (~r(s(s(z)), s(s(s(s(z)))))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[19399, 86, 461, 1, 3170, 3240])).
% 4.34/4.54 tff(19401,plain,
% 4.34/4.54 (b(s(s(z)), s(s(s(s(z)))))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[164, 19400])).
% 4.34/4.54 tff(19402,plain,
% 4.34/4.54 (~b(elem!1, z)),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[11004, 818, 273, 817, 3461])).
% 4.34/4.54 tff(19403,plain,
% 4.34/4.54 (r(elem!1, z)),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[498, 19402, 290])).
% 4.34/4.54 tff(19404,plain,
% 4.34/4.54 (~(elem!1 = s(s(s(elem!1))))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[4187, 818, 3242])).
% 4.34/4.54 tff(19405,plain,
% 4.34/4.54 (r(elem!1, s(s(s(elem!1))))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[2054, 19404, 3240])).
% 4.34/4.54 tff(19406,plain,
% 4.34/4.54 ($false),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[3421, 19405, 19403, 3243])).
% 4.34/4.54 tff(19407,plain,((~b(z, elem!1)) | b(elem!1, s(s(s(elem!1)))) | (elem!1 = z) | b(z, s(s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.54 tff(19408,plain,
% 4.34/4.54 (~b(z, elem!1)),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[19407, 3242, 8780, 3240, 8681, 817, 3250])).
% 4.34/4.54 tff(19409,plain,
% 4.34/4.54 (r(z, elem!1)),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[585, 19408, 8792])).
% 4.34/4.54 tff(19410,plain,
% 4.34/4.54 (~r(elem!1, s(s(s(elem!1))))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[3319, 19409, 3243])).
% 4.34/4.54 tff(19411,plain,
% 4.34/4.54 (elem!1 = s(s(s(elem!1)))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[2054, 19410, 3240])).
% 4.34/4.54 tff(19412,plain,
% 4.34/4.54 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.54 inference(monotonicity,[status(thm)],[19411])).
% 4.34/4.54 tff(19413,plain,
% 4.34/4.54 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.54 inference(symmetry,[status(thm)],[19412])).
% 4.34/4.54 tff(19414,plain,
% 4.34/4.54 ((~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) <=> (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.54 inference(monotonicity,[status(thm)],[19413])).
% 4.34/4.54 tff(19415,plain,
% 4.34/4.54 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.34/4.54 inference(monotonicity,[status(thm)],[19411])).
% 4.34/4.54 tff(19416,plain,
% 4.34/4.54 (b(s(s(s(s(z)))), elem!1)),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[3308, 19411, 4175])).
% 4.34/4.54 tff(19417,plain,
% 4.34/4.54 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.34/4.54 inference(modus_ponens,[status(thm)],[19416, 19415])).
% 4.34/4.54 tff(19418,plain,
% 4.34/4.54 (b(s(s(z)), s(s(s(elem!1))))),
% 4.34/4.54 inference(unit_resolution,[status(thm)],[17217, 19411, 817])).
% 4.34/4.54 tff(19419,plain,
% 4.34/4.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(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(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(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(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 4.34/4.54 inference(rewrite,[status(thm)],[])).
% 4.34/4.54 tff(19420,plain,
% 4.34/4.54 (((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(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(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 4.34/4.54 inference(rewrite,[status(thm)],[])).
% 4.34/4.54 tff(19421,plain,
% 4.34/4.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(z)), s(s(s(elem!1))))) | (~b(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(z)), s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(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(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 4.34/4.54 inference(monotonicity,[status(thm)],[19420])).
% 4.34/4.54 tff(19422,plain,
% 4.34/4.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(z)), s(s(s(elem!1))))) | (~b(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(z)), s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(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(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 4.34/4.54 inference(transitivity,[status(thm)],[19421, 19419])).
% 4.34/4.54 tff(19423,plain,
% 4.34/4.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(z)), s(s(s(elem!1))))) | (~b(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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 4.34/4.54 inference(quant_inst,[status(thm)],[])).
% 4.34/4.54 tff(19424,plain,
% 4.34/4.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(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(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 4.34/4.55 inference(modus_ponens,[status(thm)],[19423, 19422])).
% 4.34/4.55 tff(19425,plain,
% 4.34/4.55 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[19424, 178, 19418, 104, 167, 19417])).
% 4.34/4.55 tff(19426,plain,
% 4.34/4.55 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[3578, 19425])).
% 4.34/4.55 tff(19427,plain,
% 4.34/4.55 (r(elem!1, s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 4.34/4.55 inference(monotonicity,[status(thm)],[19411])).
% 4.34/4.55 tff(19428,plain,
% 4.34/4.55 (~(s(s(z)) = elem!1)),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[3774, 19416, 86])).
% 4.34/4.55 tff(19429,plain,
% 4.34/4.55 (~(elem!1 = s(s(z)))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[311, 19428])).
% 4.34/4.55 tff(19430,plain,
% 4.34/4.55 (r(elem!1, s(s(z)))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[467, 19429, 461])).
% 4.34/4.55 tff(19431,plain,
% 4.34/4.55 (r(s(s(s(elem!1))), s(s(z)))),
% 4.34/4.55 inference(modus_ponens,[status(thm)],[19430, 19427])).
% 4.34/4.55 tff(19432,plain,
% 4.34/4.55 (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[7850, 118, 19431, 19426])).
% 4.34/4.55 tff(19433,plain,
% 4.34/4.55 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(modus_ponens,[status(thm)],[19432, 19414])).
% 4.34/4.55 tff(19434,plain,
% 4.34/4.55 (s(elem!1) = s(s(s(s(elem!1))))),
% 4.34/4.55 inference(monotonicity,[status(thm)],[19411])).
% 4.34/4.55 tff(19435,plain,
% 4.34/4.55 ((s(elem!1) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(z)))),
% 4.34/4.55 inference(monotonicity,[status(thm)],[19434])).
% 4.34/4.55 tff(19436,plain,
% 4.34/4.55 ((s(elem!1) = s(s(z))) <=> (s(s(z)) = s(s(s(s(elem!1)))))),
% 4.34/4.55 inference(transitivity,[status(thm)],[19435, 2129])).
% 4.34/4.55 tff(19437,plain,
% 4.34/4.55 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(elem!1) = s(s(z)))),
% 4.34/4.55 inference(symmetry,[status(thm)],[19436])).
% 4.34/4.55 tff(19438,plain,
% 4.34/4.55 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(s(elem!1) = s(s(z))))),
% 4.34/4.55 inference(monotonicity,[status(thm)],[19437])).
% 4.34/4.55 tff(19439,plain,
% 4.34/4.55 (~(s(elem!1) = s(s(z)))),
% 4.34/4.55 inference(modus_ponens,[status(thm)],[2131, 19438])).
% 4.34/4.55 tff(19440,plain,
% 4.34/4.55 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[2840, 19439])).
% 4.34/4.55 tff(19441,plain,
% 4.34/4.55 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[2859, 19440, 19411])).
% 4.34/4.55 tff(19442,plain,
% 4.34/4.55 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[3845, 19417, 3243, 19409, 19411, 145])).
% 4.34/4.55 tff(19443,plain,
% 4.34/4.55 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[271, 19442])).
% 4.34/4.55 tff(19444,plain,
% 4.34/4.55 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[279, 178, 8681, 104, 167, 19443])).
% 4.34/4.55 tff(19445,plain,
% 4.34/4.55 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[249, 19444])).
% 4.34/4.55 tff(19446,plain,
% 4.34/4.55 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[3559, 19445, 103])).
% 4.34/4.55 tff(19447,plain,
% 4.34/4.55 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[222, 19446])).
% 4.34/4.55 tff(19448,plain,
% 4.34/4.55 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.34/4.55 inference(monotonicity,[status(thm)],[19411])).
% 4.34/4.55 tff(19449,plain,
% 4.34/4.55 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 4.34/4.55 inference(symmetry,[status(thm)],[19448])).
% 4.34/4.55 tff(19450,plain,
% 4.34/4.55 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[4173, 19440, 4519])).
% 4.34/4.55 tff(19451,plain,
% 4.34/4.55 (b(elem!1, s(s(s(s(z)))))),
% 4.34/4.55 inference(modus_ponens,[status(thm)],[19450, 19449])).
% 4.34/4.55 tff(19452,plain,
% 4.34/4.55 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[16696, 19451, 817, 167, 19447])).
% 4.34/4.55 tff(19453,plain,
% 4.34/4.55 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[691, 19452, 19441])).
% 4.34/4.55 tff(19454,plain,
% 4.34/4.55 ($false),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[19453, 19433])).
% 4.34/4.55 tff(19455,plain,(b(z, s(s(s(elem!1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | b(elem!1, s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | b(elem!1, s(s(s(elem!1)))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.55 tff(19456,plain,
% 4.34/4.55 (b(z, s(s(s(elem!1))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[19455, 19401, 18872, 19039, 47, 461, 86, 3240, 3244])).
% 4.34/4.55 tff(19457,plain,
% 4.34/4.55 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[7967, 1527, 461, 1, 193, 2043])).
% 4.34/4.55 tff(19458,plain,
% 4.34/4.55 ($false),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[9008, 178, 2043, 9002, 17218, 167, 19457])).
% 4.34/4.55 tff(19459,plain,((~(elem!1 = s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | b(elem!1, s(s(z))) | b(z, s(s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.55 tff(19460,plain,
% 4.34/4.55 (~(elem!1 = s(s(s(elem!1))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[19459, 19456, 19401, 461, 1, 103, 18872])).
% 4.34/4.55 tff(19461,plain,
% 4.34/4.55 (r(elem!1, s(s(s(elem!1))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[2054, 19460, 3240])).
% 4.34/4.55 tff(19462,plain,
% 4.34/4.55 (b(elem!1, z)),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[17483, 19461, 19456, 3271, 461, 8005])).
% 4.34/4.55 tff(19463,plain,
% 4.34/4.55 (~b(z, elem!1)),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[11004, 19462, 3271, 18872, 8674])).
% 4.34/4.55 tff(19464,plain,
% 4.34/4.55 (r(z, elem!1)),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[585, 19463, 3787])).
% 4.34/4.55 tff(19465,plain,
% 4.34/4.55 (~r(elem!1, s(s(s(s(z)))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[529, 19464, 47])).
% 4.34/4.55 tff(19466,plain,
% 4.34/4.55 (~(s(s(s(elem!1))) = elem!1)),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[2489, 19460])).
% 4.34/4.55 tff(19467,plain,
% 4.34/4.55 (~(s(elem!1) = elem!1)),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[2150, 19466])).
% 4.34/4.55 tff(19468,plain,
% 4.34/4.55 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[19355, 19464, 19461, 86, 19467, 461, 3170, 19039, 19456, 18872, 19462, 19465])).
% 4.34/4.55 tff(19469,plain,
% 4.34/4.55 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[249, 19468])).
% 4.34/4.55 tff(19470,plain,
% 4.34/4.55 (~(elem!1 = s(s(s(s(z)))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[3172, 19462, 3170])).
% 4.34/4.55 tff(19471,plain,
% 4.34/4.55 (b(elem!1, s(s(s(s(z)))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[483, 19465, 19470])).
% 4.34/4.55 tff(19472,plain,
% 4.34/4.55 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[19348, 19464, 19467, 86, 19461, 461, 3170, 19039, 19456, 18872, 47])).
% 4.34/4.55 tff(19473,plain,
% 4.34/4.55 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[271, 19472])).
% 4.34/4.55 tff(19474,plain,
% 4.34/4.55 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[17498, 19473, 3271, 19471, 19464, 8674, 18872, 19039, 19469])).
% 4.34/4.55 tff(19475,plain,
% 4.34/4.55 (b(z, s(s(s(s(s(s(s(z)))))))) <=> b(z, elem!1)),
% 4.34/4.55 inference(monotonicity,[status(thm)],[19474])).
% 4.34/4.55 tff(19476,plain,
% 4.34/4.55 (b(z, elem!1) <=> b(z, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(symmetry,[status(thm)],[19475])).
% 4.34/4.55 tff(19477,plain,
% 4.34/4.55 ((~b(z, elem!1)) <=> (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.55 inference(monotonicity,[status(thm)],[19476])).
% 4.34/4.55 tff(19478,plain,
% 4.34/4.55 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(modus_ponens,[status(thm)],[19463, 19477])).
% 4.34/4.55 tff(19479,plain,
% 4.34/4.55 ($false),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[19473, 19478])).
% 4.34/4.55 tff(19480,plain,(b(s(s(s(s(z)))), s(s(z))) | b(elem!1, s(s(z))) | b(s(s(s(s(z)))), z) | b(elem!1, s(s(s(elem!1)))) | b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.55 tff(19481,plain,
% 4.34/4.55 (b(s(s(s(s(z)))), s(s(z)))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[19480, 3170, 461, 3240, 1])).
% 4.34/4.55 tff(19482,plain,
% 4.34/4.55 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[4173, 2857, 3822])).
% 4.34/4.55 tff(19483,plain,
% 4.34/4.55 ($false),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[4818, 17732, 19482, 3261, 202, 557, 145])).
% 4.34/4.55 tff(19484,plain,((s(s(s(elem!1))) = s(s(s(s(z))))) | (~r(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.55 tff(19485,plain,
% 4.34/4.55 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[19484, 3261, 19481, 3243, 47, 5149])).
% 4.34/4.55 tff(19486,plain,
% 4.34/4.55 (s(elem!1) = s(s(z))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[2840, 19485])).
% 4.34/4.55 tff(19487,plain,
% 4.34/4.55 ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(z)) = s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(monotonicity,[status(thm)],[19486])).
% 4.34/4.55 tff(19488,plain,
% 4.34/4.55 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(symmetry,[status(thm)],[19487])).
% 4.34/4.55 tff(19489,plain,
% 4.34/4.55 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.55 inference(monotonicity,[status(thm)],[19488])).
% 4.34/4.55 tff(19490,plain,
% 4.34/4.55 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(modus_ponens,[status(thm)],[244, 19489])).
% 4.34/4.55 tff(19491,plain,
% 4.34/4.55 (~(s(s(s(s(z)))) = elem!1)),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[4509, 19481, 461])).
% 4.34/4.55 tff(19492,plain,
% 4.34/4.55 (~r(z, elem!1)),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[3151, 9175, 18872, 19481, 19491, 3244, 47])).
% 4.34/4.55 tff(19493,plain,
% 4.34/4.55 (~(s(s(z)) = elem!1)),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[7053, 19492, 3261])).
% 4.34/4.55 tff(19494,plain,
% 4.34/4.55 (~(elem!1 = s(s(z)))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[311, 19493])).
% 4.34/4.55 tff(19495,plain,
% 4.34/4.55 (r(elem!1, s(s(z)))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[467, 19494, 461])).
% 4.34/4.55 tff(19496,plain,
% 4.34/4.55 (r(elem!1, s(elem!1))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[1047, 19486, 19495])).
% 4.34/4.55 tff(19497,plain,
% 4.34/4.55 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[2832, 19486])).
% 4.34/4.55 tff(19498,plain,
% 4.34/4.55 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 4.34/4.55 inference(monotonicity,[status(thm)],[19486])).
% 4.34/4.55 tff(19499,plain,
% 4.34/4.55 (elem!1 = s(z)),
% 4.34/4.55 inference(transitivity,[status(thm)],[517, 19498, 70])).
% 4.34/4.55 tff(19500,plain,
% 4.34/4.55 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(s(z), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(monotonicity,[status(thm)],[19499])).
% 4.34/4.55 tff(19501,plain,
% 4.34/4.55 (b(s(z), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(symmetry,[status(thm)],[19500])).
% 4.34/4.55 tff(19502,plain,
% 4.34/4.55 ((~b(s(z), s(s(s(s(s(s(s(z))))))))) <=> (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.55 inference(monotonicity,[status(thm)],[19501])).
% 4.34/4.55 tff(19503,plain,
% 4.34/4.55 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 4.34/4.55 inference(symmetry,[status(thm)],[19498])).
% 4.34/4.55 tff(19504,plain,
% 4.34/4.55 (s(z) = elem!1),
% 4.34/4.55 inference(transitivity,[status(thm)],[71, 19503, 304])).
% 4.34/4.55 tff(19505,plain,
% 4.34/4.55 (b(s(s(z)), s(z)) <=> b(s(s(z)), elem!1)),
% 4.34/4.55 inference(monotonicity,[status(thm)],[19504])).
% 4.34/4.55 tff(19506,plain,
% 4.34/4.55 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(z))),
% 4.34/4.55 inference(symmetry,[status(thm)],[19505])).
% 4.34/4.55 tff(19507,plain,
% 4.34/4.55 (b(s(s(z)), s(z))),
% 4.34/4.55 inference(modus_ponens,[status(thm)],[18872, 19506])).
% 4.34/4.55 tff(19508,plain,
% 4.34/4.55 (~r(elem!1, z)),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[8416, 19495, 3261])).
% 4.34/4.55 tff(19509,plain,
% 4.34/4.55 (~(elem!1 = s(s(s(s(z)))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[325, 19491])).
% 4.34/4.55 tff(19510,plain,
% 4.34/4.55 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[4168, 19485])).
% 4.34/4.55 tff(19511,plain,
% 4.34/4.55 (~b(elem!1, s(s(s(s(z)))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[4162, 19510, 3240])).
% 4.34/4.55 tff(19512,plain,
% 4.34/4.55 (r(elem!1, s(s(s(s(z)))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[483, 19511, 19509])).
% 4.34/4.55 tff(19513,plain,
% 4.34/4.55 (~(elem!1 = s(s(s(s(elem!1)))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[1422, 19486])).
% 4.34/4.55 tff(19514,plain,
% 4.34/4.55 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[1509, 19513])).
% 4.34/4.55 tff(19515,plain,
% 4.34/4.55 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[1649, 19514])).
% 4.34/4.55 tff(19516,plain,
% 4.34/4.55 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[1657, 19515])).
% 4.34/4.55 tff(19517,plain,
% 4.34/4.55 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[1695, 19516])).
% 4.34/4.55 tff(19518,plain,
% 4.34/4.55 (z = elem!1),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[4868, 4513, 461, 3242, 3261])).
% 4.34/4.55 tff(19519,plain,
% 4.34/4.55 ($false),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[317, 19518, 4851])).
% 4.34/4.55 tff(19520,plain,(r(elem!1, s(s(s(elem!1)))) | b(elem!1, s(s(z))) | b(z, s(s(s(elem!1)))) | (~r(z, s(s(z)))) | b(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.55 tff(19521,plain,
% 4.34/4.55 (r(elem!1, s(s(s(elem!1))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[19520, 3261, 3242, 461, 3240])).
% 4.34/4.55 tff(19522,plain,
% 4.34/4.55 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[3404, 19515])).
% 4.34/4.55 tff(19523,plain,
% 4.34/4.55 (~(elem!1 = z)),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[5261, 19522, 3261, 19481, 19521, 19517, 19512])).
% 4.34/4.55 tff(19524,plain,
% 4.34/4.55 (b(elem!1, z)),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[498, 19523, 19508])).
% 4.34/4.55 tff(19525,plain,
% 4.34/4.55 (b(s(z), z)),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[593, 19524, 19486])).
% 4.34/4.55 tff(19526,plain,
% 4.34/4.55 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[8067, 3261, 19481, 19039, 47])).
% 4.34/4.55 tff(19527,plain,
% 4.34/4.55 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[271, 19526])).
% 4.34/4.55 tff(19528,plain,
% 4.34/4.55 (~(z = elem!1)),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[18974, 19517, 461, 19481, 19521, 1, 3170])).
% 4.34/4.55 tff(19529,plain,
% 4.34/4.55 (~(elem!1 = s(s(s(elem!1))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[4868, 19528, 461, 3242, 3261])).
% 4.34/4.55 tff(19530,plain,
% 4.34/4.55 (~(s(s(s(elem!1))) = elem!1)),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[2489, 19529])).
% 4.34/4.55 tff(19531,plain,
% 4.34/4.55 (~r(z, elem!1)),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[3151, 9175, 817, 202, 4510, 3244, 47])).
% 4.34/4.55 tff(19532,plain,
% 4.34/4.55 (~(s(s(z)) = elem!1)),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[7053, 19531, 3261])).
% 4.34/4.55 tff(19533,plain,
% 4.34/4.55 (~(elem!1 = s(s(z)))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[311, 19532])).
% 4.34/4.55 tff(19534,plain,
% 4.34/4.55 (r(elem!1, s(s(z)))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[467, 19533, 461])).
% 4.34/4.55 tff(19535,plain,
% 4.34/4.55 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[8067, 3261, 202, 104, 47])).
% 4.34/4.55 tff(19536,plain,
% 4.34/4.55 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[271, 19535])).
% 4.34/4.55 tff(19537,plain,
% 4.34/4.55 (r(elem!1, s(elem!1))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[1047, 515, 450])).
% 4.34/4.55 tff(19538,plain,
% 4.34/4.55 ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(z)) = s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(monotonicity,[status(thm)],[515])).
% 4.34/4.55 tff(19539,plain,
% 4.34/4.55 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(symmetry,[status(thm)],[19538])).
% 4.34/4.55 tff(19540,plain,
% 4.34/4.55 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.55 inference(monotonicity,[status(thm)],[19539])).
% 4.34/4.55 tff(19541,plain,
% 4.34/4.55 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(modus_ponens,[status(thm)],[244, 19540])).
% 4.34/4.55 tff(19542,plain,
% 4.34/4.55 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[2239, 286, 515])).
% 4.34/4.55 tff(19543,plain,
% 4.34/4.55 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[395, 19542, 19541])).
% 4.34/4.55 tff(19544,plain,
% 4.34/4.55 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[2935, 19543, 19537])).
% 4.34/4.55 tff(19545,plain,
% 4.34/4.55 (~(z = elem!1)),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[5266, 3261, 1858, 202, 3311, 461, 1, 3170])).
% 4.34/4.55 tff(19546,plain,
% 4.34/4.55 ($false),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[2820, 19545, 5787, 595, 146, 869, 9173])).
% 4.34/4.55 tff(19547,plain,((~r(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(s(elem!1))))) | b(elem!1, s(s(z))) | b(z, s(s(s(s(z))))) | b(s(s(s(s(z)))), z) | (~r(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.55 tff(19548,plain,
% 4.34/4.55 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[19547, 3104, 3261, 595, 1858, 202, 3311, 461, 1, 3170, 450])).
% 4.34/4.55 tff(19549,plain,
% 4.34/4.55 ($false),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[691, 19548, 19544, 12393])).
% 4.34/4.55 tff(19550,plain,(b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | (~r(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(s(elem!1))))) | b(elem!1, s(s(z))) | b(z, s(s(s(s(z))))) | b(s(s(s(s(z)))), z) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), z)) | (~(s(elem!1) = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.55 tff(19551,plain,
% 4.34/4.55 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[19550, 515, 19536, 8397, 202, 3311, 461, 1, 3170, 19534, 106, 3261])).
% 4.34/4.55 tff(19552,plain,
% 4.34/4.55 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[259, 19551, 104, 202, 9175])).
% 4.34/4.55 tff(19553,plain,
% 4.34/4.55 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[222, 19552])).
% 4.34/4.55 tff(19554,plain,
% 4.34/4.55 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[17305, 19553, 9175, 202, 4510, 817])).
% 4.34/4.55 tff(19555,plain,
% 4.34/4.55 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[691, 19554, 12393])).
% 4.34/4.55 tff(19556,plain,
% 4.34/4.55 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(modus_ponens,[status(thm)],[19555, 17783])).
% 4.34/4.55 tff(19557,plain,
% 4.34/4.55 (b(s(s(z)), s(z))),
% 4.34/4.55 inference(modus_ponens,[status(thm)],[817, 536])).
% 4.34/4.55 tff(19558,plain,
% 4.34/4.55 (~(z = elem!1)),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[18974, 8397, 461, 202, 3311, 1, 3170])).
% 4.34/4.55 tff(19559,plain,
% 4.34/4.55 (b(z, elem!1)),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[585, 19558, 19531])).
% 4.34/4.55 tff(19560,plain,
% 4.34/4.55 (~r(elem!1, z)),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[8416, 19534, 3261])).
% 4.34/4.55 tff(19561,plain,
% 4.34/4.55 (~(elem!1 = z)),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[2808, 19558])).
% 4.34/4.55 tff(19562,plain,
% 4.34/4.55 (b(elem!1, z)),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[498, 19561, 19560])).
% 4.34/4.55 tff(19563,plain,
% 4.34/4.55 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[3672, 19555, 19562, 19536, 19559])).
% 4.34/4.55 tff(19564,plain,
% 4.34/4.55 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[3444, 19563, 15168])).
% 4.34/4.55 tff(19565,plain,
% 4.34/4.55 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(monotonicity,[status(thm)],[546])).
% 4.34/4.55 tff(19566,plain,
% 4.34/4.55 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(symmetry,[status(thm)],[19565])).
% 4.34/4.55 tff(19567,plain,
% 4.34/4.55 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(modus_ponens,[status(thm)],[19553, 19566])).
% 4.34/4.55 tff(19568,plain,
% 4.34/4.55 (~r(s(s(s(elem!1))), elem!1)),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[3682, 19567, 19564])).
% 4.34/4.55 tff(19569,plain,
% 4.34/4.55 (b(s(s(s(elem!1))), elem!1)),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[570, 19568, 949])).
% 4.34/4.55 tff(19570,plain,
% 4.34/4.55 (b(s(s(s(s(z)))), s(z))),
% 4.34/4.55 inference(modus_ponens,[status(thm)],[19569, 547])).
% 4.34/4.55 tff(19571,plain,
% 4.34/4.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 4.34/4.55 inference(rewrite,[status(thm)],[])).
% 4.34/4.55 tff(19572,plain,
% 4.34/4.55 (((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(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(s(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(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 4.34/4.55 inference(rewrite,[status(thm)],[])).
% 4.34/4.55 tff(19573,plain,
% 4.34/4.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(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(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 4.34/4.55 inference(monotonicity,[status(thm)],[19572])).
% 4.34/4.55 tff(19574,plain,
% 4.34/4.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(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(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 4.34/4.55 inference(transitivity,[status(thm)],[19573, 19571])).
% 4.34/4.55 tff(19575,plain,
% 4.34/4.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(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(s(s(z)))), s(s(z)))))),
% 4.34/4.55 inference(quant_inst,[status(thm)],[])).
% 4.34/4.55 tff(19576,plain,
% 4.34/4.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.55 inference(modus_ponens,[status(thm)],[19575, 19574])).
% 4.34/4.55 tff(19577,plain,
% 4.34/4.55 ($false),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[19576, 178, 19551, 202, 19570, 19557, 19556])).
% 4.34/4.55 tff(19578,plain,((~(s(elem!1) = s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (s(s(s(elem!1))) = elem!1) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(elem!1))))) | b(elem!1, s(s(z))) | b(z, s(s(s(s(z))))) | b(s(s(s(s(z)))), z) | (~r(s(s(z)), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.55 tff(19579,plain,
% 4.34/4.55 (~r(s(s(z)), z)),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[19578, 19530, 19486, 18872, 19039, 19521, 461, 1, 3170, 19481, 3261])).
% 4.34/4.55 tff(19580,plain,
% 4.34/4.55 (b(s(s(z)), z)),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[3249, 19579])).
% 4.34/4.55 tff(19581,plain,
% 4.34/4.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 4.34/4.55 inference(rewrite,[status(thm)],[])).
% 4.34/4.55 tff(19582,plain,
% 4.34/4.55 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 4.34/4.55 inference(rewrite,[status(thm)],[])).
% 4.34/4.55 tff(19583,plain,
% 4.34/4.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 4.34/4.55 inference(monotonicity,[status(thm)],[19582])).
% 4.34/4.55 tff(19584,plain,
% 4.34/4.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 4.34/4.55 inference(transitivity,[status(thm)],[19583, 19581])).
% 4.34/4.55 tff(19585,plain,
% 4.34/4.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))),
% 4.34/4.55 inference(quant_inst,[status(thm)],[])).
% 4.34/4.55 tff(19586,plain,
% 4.34/4.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.55 inference(modus_ponens,[status(thm)],[19585, 19584])).
% 4.34/4.55 tff(19587,plain,
% 4.34/4.55 ($false),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[19586, 178, 3461, 595, 1791, 12750, 4669])).
% 4.34/4.55 tff(19588,plain,((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.55 tff(19589,plain,
% 4.34/4.55 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[19588, 19580, 19527, 19525, 19507])).
% 4.34/4.55 tff(19590,plain,
% 4.34/4.55 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(modus_ponens,[status(thm)],[19589, 19502])).
% 4.34/4.55 tff(19591,plain,
% 4.34/4.55 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[691, 19590, 19497])).
% 4.34/4.55 tff(19592,plain,
% 4.34/4.55 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[2935, 19591, 19496])).
% 4.34/4.55 tff(19593,plain,
% 4.34/4.55 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[395, 19592, 19490])).
% 4.34/4.55 tff(19594,plain,
% 4.34/4.55 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[17305, 19591, 9175, 19481, 19491, 18872])).
% 4.34/4.55 tff(19595,plain,
% 4.34/4.55 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[222, 19594])).
% 4.34/4.55 tff(19596,plain,
% 4.34/4.55 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[259, 19595, 19039, 19481, 9175])).
% 4.34/4.55 tff(19597,plain,
% 4.34/4.55 ($false),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[2239, 19596, 19593, 19486])).
% 4.34/4.55 tff(19598,plain,((~r(z, s(s(z)))) | b(elem!1, s(s(z))) | b(z, s(s(s(s(z))))) | b(s(s(s(s(z)))), z) | b(z, s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.55 tff(19599,plain,
% 4.34/4.55 (~r(z, s(s(z)))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[19598, 3242, 1, 3170, 461, 3240])).
% 4.34/4.55 tff(19600,plain,
% 4.34/4.55 (b(z, s(s(z)))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[143, 19599])).
% 4.34/4.55 tff(19601,plain,
% 4.34/4.55 (r(z, elem!1)),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[585, 4853, 3874])).
% 4.34/4.55 tff(19602,plain,
% 4.34/4.55 (~r(elem!1, s(s(s(s(z)))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[529, 19601, 145])).
% 4.34/4.55 tff(19603,plain,
% 4.34/4.55 (b(elem!1, s(s(s(s(z)))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[483, 19602, 4520])).
% 4.34/4.55 tff(19604,plain,
% 4.34/4.55 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[4162, 19603, 3240])).
% 4.34/4.55 tff(19605,plain,
% 4.34/4.55 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[4168, 19604])).
% 4.34/4.55 tff(19606,plain,
% 4.34/4.55 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[2859, 19605, 1527])).
% 4.34/4.55 tff(19607,plain,
% 4.34/4.55 (~r(s(s(s(s(z)))), elem!1)),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[3137, 19601, 194])).
% 4.34/4.55 tff(19608,plain,
% 4.34/4.55 (~b(s(s(z)), s(s(s(s(z)))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[3151, 19601, 817, 202, 4510, 194, 145])).
% 4.34/4.55 tff(19609,plain,
% 4.34/4.55 (r(s(s(z)), s(s(s(s(z)))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[164, 19608])).
% 4.34/4.55 tff(19610,plain,
% 4.34/4.55 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[703, 19606])).
% 4.34/4.55 tff(19611,plain,
% 4.34/4.55 (~r(s(s(z)), z)),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[155, 19609, 145])).
% 4.34/4.55 tff(19612,plain,
% 4.34/4.55 (b(s(s(z)), z)),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[3249, 19611])).
% 4.34/4.55 tff(19613,plain,
% 4.34/4.55 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[10664, 19604, 4175])).
% 4.34/4.55 tff(19614,plain,
% 4.34/4.55 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[3845, 19613, 3243, 19601, 1527, 145])).
% 4.34/4.55 tff(19615,plain,
% 4.34/4.55 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[271, 19614])).
% 4.34/4.55 tff(19616,plain,
% 4.34/4.55 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[17498, 19615, 273, 19603, 19601, 19612, 817, 104, 19610])).
% 4.34/4.55 tff(19617,plain,
% 4.34/4.55 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[249, 19616])).
% 4.34/4.55 tff(19618,plain,
% 4.34/4.55 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[5624, 19617, 19609])).
% 4.34/4.55 tff(19619,plain,
% 4.34/4.55 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[222, 19618])).
% 4.34/4.55 tff(19620,plain,
% 4.34/4.55 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[8548, 19619, 104, 4520, 19607, 19602])).
% 4.34/4.55 tff(19621,plain,
% 4.34/4.55 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[691, 19620, 19606])).
% 4.34/4.55 tff(19622,plain,
% 4.34/4.55 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.55 inference(modus_ponens,[status(thm)],[19621, 5004])).
% 4.34/4.55 tff(19623,plain,
% 4.34/4.55 ($false),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[17339, 118, 17328, 19617, 19622])).
% 4.34/4.55 tff(19624,plain,((~(elem!1 = s(s(s(elem!1))))) | b(elem!1, s(s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~r(z, s(s(s(s(z)))))) | b(elem!1, s(s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.55 tff(19625,plain,
% 4.34/4.55 (~(elem!1 = s(s(s(elem!1))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[19624, 19600, 19039, 461, 18872, 47, 3240, 19481, 3244, 3242])).
% 4.34/4.55 tff(19626,plain,
% 4.34/4.55 (r(elem!1, s(s(s(elem!1))))),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[2054, 19625, 3240])).
% 4.34/4.55 tff(19627,plain,
% 4.34/4.55 (~r(elem!1, z)),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[3421, 19626, 3243])).
% 4.34/4.55 tff(19628,plain,
% 4.34/4.55 (~(elem!1 = z)),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[3276, 19600, 461])).
% 4.34/4.55 tff(19629,plain,
% 4.34/4.55 (~(z = elem!1)),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[317, 19628])).
% 4.34/4.55 tff(19630,plain,
% 4.34/4.55 (~r(z, elem!1)),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[3319, 19626, 3243])).
% 4.34/4.55 tff(19631,plain,
% 4.34/4.55 (b(z, elem!1)),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[585, 19630, 19629])).
% 4.34/4.55 tff(19632,plain,
% 4.34/4.55 (~b(s(s(z)), z)),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[19407, 19631, 3242, 3240, 19628, 18872, 19600])).
% 4.34/4.55 tff(19633,plain,
% 4.34/4.55 (r(s(s(z)), z)),
% 4.34/4.55 inference(unit_resolution,[status(thm)],[3249, 19632])).
% 4.34/4.56 tff(19634,plain,
% 4.34/4.56 (~(s(s(z)) = elem!1)),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[1345, 19633, 19627])).
% 4.34/4.56 tff(19635,plain,
% 4.34/4.56 (~r(s(s(z)), s(s(s(s(z)))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[155, 19633, 47])).
% 4.34/4.56 tff(19636,plain,
% 4.34/4.56 (b(s(s(z)), s(s(s(s(z)))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[164, 19635])).
% 4.34/4.56 tff(19637,plain,
% 4.34/4.56 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[261, 19633, 19481, 19039, 47])).
% 4.34/4.56 tff(19638,plain,
% 4.34/4.56 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[271, 19637])).
% 4.34/4.56 tff(19639,plain,
% 4.34/4.56 ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[7840, 178, 19600, 19039, 19636])).
% 4.34/4.56 tff(19640,plain,
% 4.34/4.56 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[19639, 19638])).
% 4.34/4.56 tff(19641,plain,
% 4.34/4.56 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[3578, 19640])).
% 4.34/4.56 tff(19642,plain,
% 4.34/4.56 (b(elem!1, z)),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[498, 19627, 19628])).
% 4.34/4.56 tff(19643,plain,
% 4.34/4.56 (~(s(s(s(elem!1))) = elem!1)),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[2489, 19625])).
% 4.34/4.56 tff(19644,plain,
% 4.34/4.56 (~(s(elem!1) = elem!1)),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[2150, 19643])).
% 4.34/4.56 tff(19645,plain,
% 4.34/4.56 (~b(s(elem!1), s(s(z)))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[3089, 19641, 47, 19509, 3244, 19600, 19644, 19633, 19634, 19642, 19629, 19636])).
% 4.34/4.56 tff(19646,plain,
% 4.34/4.56 ($false),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[2660, 19645, 19641, 19600, 19633, 3244, 47, 19636, 19628, 19634])).
% 4.34/4.56 tff(19647,plain,(b(z, s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | b(elem!1, s(s(z))) | b(z, s(s(s(s(z))))) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 4.34/4.56 tff(19648,plain,
% 4.34/4.56 ($false),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[19647, 18871, 18870, 1, 3240, 3242])).
% 4.34/4.56 tff(19649,plain,(b(z, s(s(s(elem!1)))) | b(z, s(s(s(s(z))))) | b(elem!1, s(s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 4.34/4.56 tff(19650,plain,
% 4.34/4.56 (b(z, s(s(s(elem!1))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[19649, 818, 3240, 1, 5619, 273, 1301, 251, 595, 290])).
% 4.34/4.56 tff(19651,plain,
% 4.34/4.56 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[691, 11145, 4289])).
% 4.34/4.56 tff(19652,plain,
% 4.34/4.56 (~b(elem!1, s(s(z)))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[10893, 817, 273, 3461, 818])).
% 4.34/4.56 tff(19653,plain,
% 4.34/4.56 (r(elem!1, s(s(z)))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[467, 19652, 462])).
% 4.34/4.56 tff(19654,plain,
% 4.34/4.56 ($false),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[3113, 19653, 19651, 287])).
% 4.34/4.56 tff(19655,plain,((~b(s(s(z)), elem!1)) | (elem!1 = s(s(z))) | b(elem!1, s(s(s(s(s(s(s(z)))))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, elem!1)) | b(s(s(z)), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.56 tff(19656,plain,
% 4.34/4.56 (~b(s(s(z)), elem!1)),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[19655, 286, 4289, 273, 3461, 818, 312])).
% 4.34/4.56 tff(19657,assumption,(~b(s(s(s(s(s(s(s(z))))))), elem!1)), introduced(assumption)).
% 4.34/4.56 tff(19658,plain,
% 4.34/4.56 (r(s(s(z)), elem!1)),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[448, 19656, 12])).
% 4.34/4.56 tff(19659,plain,
% 4.34/4.56 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[11351, 19658, 287])).
% 4.34/4.56 tff(19660,plain,
% 4.34/4.56 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[3444, 19659, 19657])).
% 4.34/4.56 tff(19661,plain,
% 4.34/4.56 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(z)))), elem!1)),
% 4.34/4.56 inference(monotonicity,[status(thm)],[19660])).
% 4.34/4.56 tff(19662,plain,
% 4.34/4.56 (b(s(s(s(s(z)))), elem!1)),
% 4.34/4.56 inference(modus_ponens,[status(thm)],[251, 19661])).
% 4.34/4.56 tff(19663,plain,
% 4.34/4.56 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[2803, 19658, 287])).
% 4.34/4.56 tff(19664,plain,
% 4.34/4.56 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[11098, 19663, 251, 1301, 104, 19659])).
% 4.34/4.56 tff(19665,plain,
% 4.34/4.56 (~(elem!1 = s(s(s(elem!1))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[2859, 19664, 18847])).
% 4.34/4.56 tff(19666,plain,
% 4.34/4.56 (r(elem!1, s(s(s(elem!1))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[2054, 19665, 3240])).
% 4.34/4.56 tff(19667,plain,
% 4.34/4.56 (~r(s(s(z)), s(s(s(elem!1))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[7973, 19666, 19658])).
% 4.34/4.56 tff(19668,plain,
% 4.34/4.56 (b(s(s(z)), s(s(s(elem!1))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[4223, 19667])).
% 4.34/4.56 tff(19669,plain,
% 4.34/4.56 (~b(s(s(s(elem!1))), z)),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[7978, 19668, 273, 3461, 2043])).
% 4.34/4.56 tff(19670,plain,
% 4.34/4.56 (r(s(s(s(elem!1))), z)),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[1565, 19669])).
% 4.34/4.56 tff(19671,plain,
% 4.34/4.56 (~r(elem!1, z)),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[6071, 19670, 19666])).
% 4.34/4.56 tff(19672,plain,
% 4.34/4.56 (b(elem!1, z)),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[498, 19671, 290])).
% 4.34/4.56 tff(19673,plain,
% 4.34/4.56 (~b(s(s(s(s(z)))), z)),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[16427, 178, 818, 19672, 19662, 1301])).
% 4.34/4.56 tff(19674,plain,
% 4.34/4.56 (~b(elem!1, s(s(z)))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[16411, 178, 818, 19672, 3461, 273])).
% 4.34/4.56 tff(19675,plain,
% 4.34/4.56 ($false),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[10659, 19674, 19673, 1, 3240, 19656])).
% 4.34/4.56 tff(19676,plain,(b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | b(z, s(s(s(s(z))))) | b(elem!1, s(s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (elem!1 = z) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | b(s(s(s(s(s(s(s(z))))))), elem!1) | (s(s(z)) = elem!1) | b(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.56 tff(19677,plain,
% 4.34/4.56 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[19676, 818, 3240, 1, 5619, 273, 1301, 251, 290, 19650, 104, 18857, 18859, 18858])).
% 4.34/4.56 tff(19678,plain,
% 4.34/4.56 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[17204, 19677, 273, 5619, 595])).
% 4.34/4.56 tff(19679,plain,
% 4.34/4.56 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[3578, 19678])).
% 4.34/4.56 tff(19680,plain,
% 4.34/4.56 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[2859, 1527, 2857])).
% 4.34/4.56 tff(19681,plain,
% 4.34/4.56 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[703, 19680])).
% 4.34/4.56 tff(19682,plain,
% 4.34/4.56 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[3444, 19681, 19657])).
% 4.34/4.56 tff(19683,plain,
% 4.34/4.56 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.34/4.56 inference(modus_ponens,[status(thm)],[19682, 10374])).
% 4.34/4.56 tff(19684,plain,
% 4.34/4.56 ($false),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[10401, 19683, 6448, 107])).
% 4.34/4.56 tff(19685,plain,((~(elem!1 = s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(z)))) | b(s(s(s(s(s(s(s(z))))))), elem!1) | (s(s(s(elem!1))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.56 tff(19686,plain,
% 4.34/4.56 (~(elem!1 = s(s(s(elem!1))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[19685, 14548, 107, 19657, 2857])).
% 4.34/4.56 tff(19687,plain,
% 4.34/4.56 (r(elem!1, s(s(s(elem!1))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[2054, 19686, 3240])).
% 4.34/4.56 tff(19688,plain,
% 4.34/4.56 (b(elem!1, z)),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[17483, 19687, 273, 5618, 461, 2043])).
% 4.34/4.56 tff(19689,plain,
% 4.34/4.56 (~b(s(s(z)), elem!1)),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[11004, 19688, 5619, 273, 818])).
% 4.34/4.56 tff(19690,plain,
% 4.34/4.56 (~b(s(s(z)), s(s(s(elem!1))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[4307, 19689, 104, 4289, 166, 3521, 19687, 3831])).
% 4.34/4.56 tff(19691,plain,
% 4.34/4.56 (r(s(s(z)), elem!1)),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[448, 19689, 12])).
% 4.34/4.56 tff(19692,plain,
% 4.34/4.56 (~r(s(s(z)), s(s(s(elem!1))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[7973, 19691, 19687])).
% 4.34/4.56 tff(19693,plain,
% 4.34/4.56 ($false),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[4223, 19692, 19690])).
% 4.34/4.56 tff(19694,plain,(b(elem!1, s(s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | b(elem!1, s(s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (s(s(z)) = elem!1) | (~b(z, s(s(z)))) | (~b(z, elem!1)) | r(s(s(z)), z) | (~b(z, s(s(s(elem!1))))) | b(elem!1, s(s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | b(s(s(s(s(s(s(s(z))))))), elem!1) | (s(s(s(elem!1))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.56 tff(19695,plain,
% 4.34/4.56 (b(elem!1, s(s(z)))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[19694, 18858, 104, 19677, 3521, 18856, 18859, 273, 818, 5618, 19650, 3240, 19679, 18857, 18847])).
% 4.34/4.56 tff(19696,plain,
% 4.34/4.56 (~b(s(s(z)), elem!1)),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[10893, 19695, 273, 5619, 818])).
% 4.34/4.56 tff(19697,plain,
% 4.34/4.56 (r(s(s(z)), elem!1)),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[448, 19696, 18859])).
% 4.34/4.56 tff(19698,plain,
% 4.34/4.56 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[17566, 19697, 19679])).
% 4.34/4.56 tff(19699,plain,
% 4.34/4.56 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[3444, 19698, 18857])).
% 4.34/4.56 tff(19700,plain,
% 4.34/4.56 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[703, 19699])).
% 4.34/4.56 tff(19701,plain,
% 4.34/4.56 (~(elem!1 = s(s(s(elem!1))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[2859, 19700, 18847])).
% 4.34/4.56 tff(19702,plain,
% 4.34/4.56 (r(elem!1, s(s(s(elem!1))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[2054, 19701, 3240])).
% 4.34/4.56 tff(19703,plain,
% 4.34/4.56 (~b(s(s(z)), s(s(s(elem!1))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[4307, 19702, 104, 18858, 19677, 3521, 19696, 18856])).
% 4.34/4.56 tff(19704,plain,
% 4.34/4.56 (~r(s(s(z)), s(s(s(elem!1))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[7973, 19702, 19697])).
% 4.34/4.56 tff(19705,plain,
% 4.34/4.56 ($false),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[4223, 19704, 19703])).
% 4.34/4.56 tff(19706,plain,((~b(z, elem!1)) | (~b(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)))) | b(elem!1, s(s(s(elem!1)))) | (~b(z, s(s(z)))) | r(s(s(z)), z) | (~b(z, s(s(s(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)))), s(s(s(s(s(s(s(z))))))))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 4.34/4.56 tff(19707,plain,
% 4.34/4.56 (~b(z, elem!1)),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[19706, 3240, 4254, 104, 144, 10792, 17173, 1, 18843, 18255, 290])).
% 4.34/4.56 tff(19708,plain,
% 4.34/4.56 (r(z, elem!1)),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[585, 19707, 318])).
% 4.34/4.56 tff(19709,plain,
% 4.34/4.56 (~(s(s(z)) = elem!1)),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[18165, 19708, 48])).
% 4.34/4.56 tff(19710,plain,
% 4.34/4.56 (~r(elem!1, s(s(s(elem!1))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[3319, 3243, 521])).
% 4.34/4.56 tff(19711,plain,
% 4.34/4.56 (elem!1 = s(s(s(elem!1)))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[2054, 19710, 3240])).
% 4.34/4.56 tff(19712,plain,
% 4.34/4.56 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[2859, 19711, 18847])).
% 4.34/4.56 tff(19713,plain,
% 4.34/4.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 4.34/4.56 inference(rewrite,[status(thm)],[])).
% 4.34/4.56 tff(19714,plain,
% 4.34/4.56 (((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 4.34/4.56 inference(rewrite,[status(thm)],[])).
% 4.34/4.56 tff(19715,plain,
% 4.34/4.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 4.34/4.56 inference(monotonicity,[status(thm)],[19714])).
% 4.34/4.56 tff(19716,plain,
% 4.34/4.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 4.34/4.56 inference(transitivity,[status(thm)],[19715, 19713])).
% 4.34/4.56 tff(19717,plain,
% 4.34/4.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))))),
% 4.34/4.56 inference(quant_inst,[status(thm)],[])).
% 4.34/4.56 tff(19718,plain,
% 4.34/4.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 4.34/4.56 inference(modus_ponens,[status(thm)],[19717, 19716])).
% 4.34/4.56 tff(19719,plain,
% 4.34/4.56 ($false),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[19718, 118, 557, 145, 3279])).
% 4.34/4.56 tff(19720,plain,((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.56 tff(19721,plain,
% 4.34/4.56 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[19720, 3243, 47])).
% 4.34/4.56 tff(19722,plain,
% 4.34/4.56 (b(s(s(s(s(z)))), elem!1)),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[3308, 19721, 19711])).
% 4.34/4.56 tff(19723,plain,
% 4.34/4.56 ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[4266, 178, 104, 1301, 251])).
% 4.34/4.56 tff(19724,plain,
% 4.34/4.56 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[19723, 19722])).
% 4.34/4.56 tff(19725,plain,
% 4.34/4.56 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[691, 19724, 19712])).
% 4.34/4.56 tff(19726,plain,
% 4.34/4.56 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[4173, 3260, 18847])).
% 4.34/4.56 tff(19727,plain,
% 4.34/4.56 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[10664, 19721, 18846])).
% 4.34/4.56 tff(19728,plain,
% 4.34/4.56 (s(s(s(elem!1))) = elem!1),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[1530, 19711])).
% 4.34/4.56 tff(19729,plain,
% 4.34/4.56 (~b(s(s(z)), elem!1)),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[17498, 166, 595, 1301, 273, 3461, 521, 104, 4245])).
% 4.34/4.56 tff(19730,plain,
% 4.34/4.56 (~r(s(s(z)), elem!1)),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[17744, 166, 3461, 557, 273, 1519, 3521, 145, 3828, 701, 3831, 104, 2484])).
% 4.34/4.56 tff(19731,plain,
% 4.34/4.56 ($false),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[448, 19730, 19729, 12])).
% 4.34/4.56 tff(19732,plain,((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (s(s(z)) = elem!1) | (~b(s(s(z)), z)) | (~r(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~(s(s(s(elem!1))) = elem!1)) | (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.56 tff(19733,plain,
% 4.34/4.56 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[19732, 3243, 3461, 12, 273, 19728, 4254, 47, 19727, 19712, 19726, 104, 2484, 595, 1301, 521])).
% 4.34/4.56 tff(19734,plain,
% 4.34/4.56 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[249, 19733])).
% 4.34/4.56 tff(19735,plain,
% 4.34/4.56 (~r(s(s(z)), elem!1)),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[2803, 19734, 19725])).
% 4.34/4.56 tff(19736,plain,
% 4.34/4.56 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[3113, 13066, 224])).
% 4.34/4.56 tff(19737,plain,
% 4.34/4.56 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[691, 19736, 19712])).
% 4.34/4.56 tff(19738,plain,
% 4.34/4.56 (r(s(s(s(s(z)))), elem!1)),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[8548, 19737, 104, 251, 469, 11716])).
% 4.34/4.56 tff(19739,plain,
% 4.34/4.56 (~r(s(s(s(s(z)))), s(s(z)))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[10883, 19738, 13066])).
% 4.34/4.56 tff(19740,plain,
% 4.34/4.56 (b(s(s(s(s(z)))), z)),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[19647, 461, 1, 3240, 3242])).
% 4.34/4.56 tff(19741,plain,
% 4.34/4.56 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[11098, 19736, 251, 1301, 104, 19712])).
% 4.34/4.56 tff(19742,plain,
% 4.34/4.56 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[11027, 19741, 521])).
% 4.34/4.56 tff(19743,plain,
% 4.34/4.56 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[133, 19742])).
% 4.34/4.56 tff(19744,plain,
% 4.34/4.56 (~b(s(s(s(s(z)))), s(s(z)))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[298, 19743, 104, 273, 19740])).
% 4.34/4.56 tff(19745,plain,
% 4.34/4.56 ($false),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[102, 19744, 19739])).
% 4.34/4.56 tff(19746,plain,(b(elem!1, s(s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(s(s(s(z))))) | (~r(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | b(z, s(s(s(s(z))))) | b(elem!1, s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | (elem!1 = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.56 tff(19747,plain,
% 4.34/4.56 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[19746, 461, 273, 251, 469, 521, 1301, 104, 1, 3240, 3242, 462])).
% 4.34/4.56 tff(19748,plain,
% 4.34/4.56 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[249, 19747])).
% 4.34/4.56 tff(19749,plain,
% 4.34/4.56 (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))))),
% 4.34/4.56 inference(monotonicity,[status(thm)],[19711])).
% 4.34/4.56 tff(19750,plain,
% 4.34/4.56 (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)),
% 4.34/4.56 inference(symmetry,[status(thm)],[19749])).
% 4.34/4.56 tff(19751,plain,
% 4.34/4.56 ((~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))),
% 4.34/4.56 inference(monotonicity,[status(thm)],[19750])).
% 4.34/4.56 tff(19752,plain,
% 4.34/4.56 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[4067, 178, 104, 251, 19727, 19726])).
% 4.34/4.56 tff(19753,plain,
% 4.34/4.56 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.34/4.56 inference(modus_ponens,[status(thm)],[19752, 19751])).
% 4.34/4.56 tff(19754,plain,
% 4.34/4.56 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[19685, 13066, 19711, 19753, 18847])).
% 4.34/4.56 tff(19755,plain,
% 4.34/4.56 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[3578, 19754])).
% 4.34/4.56 tff(19756,plain,
% 4.34/4.56 ($false),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[17204, 19755, 19748, 273, 3461, 595])).
% 4.34/4.56 tff(19757,plain,(b(elem!1, s(s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(s(s(s(z))))) | (~r(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | b(z, s(s(s(s(z))))) | b(elem!1, s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | (elem!1 = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.56 tff(19758,plain,
% 4.34/4.56 (b(elem!1, s(s(z)))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[19757, 3242, 3461, 595, 251, 469, 521, 1301, 104, 1, 3240, 273, 312])).
% 4.34/4.56 tff(19759,plain,
% 4.34/4.56 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.56 inference(monotonicity,[status(thm)],[19711])).
% 4.34/4.56 tff(19760,plain,
% 4.34/4.56 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.56 inference(modus_ponens,[status(thm)],[19725, 19759])).
% 4.34/4.56 tff(19761,plain,
% 4.34/4.56 (b(s(s(z)), s(s(s(elem!1))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[17217, 817, 1527])).
% 4.34/4.56 tff(19762,plain,
% 4.34/4.56 (~r(s(s(s(elem!1))), s(s(z)))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[17339, 118, 224, 3615])).
% 4.34/4.56 tff(19763,plain,
% 4.34/4.56 (b(s(s(s(elem!1))), s(s(z)))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[4209, 41, 19762, 4181])).
% 4.34/4.56 tff(19764,plain,
% 4.34/4.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 4.34/4.56 inference(rewrite,[status(thm)],[])).
% 4.34/4.56 tff(19765,plain,
% 4.34/4.56 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 4.34/4.56 inference(rewrite,[status(thm)],[])).
% 4.34/4.56 tff(19766,plain,
% 4.34/4.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 4.34/4.56 inference(monotonicity,[status(thm)],[19765])).
% 4.34/4.56 tff(19767,plain,
% 4.34/4.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 4.34/4.56 inference(transitivity,[status(thm)],[19766, 19764])).
% 4.34/4.56 tff(19768,plain,
% 4.34/4.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 4.34/4.56 inference(quant_inst,[status(thm)],[])).
% 4.34/4.56 tff(19769,plain,
% 4.34/4.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z))))),
% 4.34/4.56 inference(modus_ponens,[status(thm)],[19768, 19767])).
% 4.34/4.56 tff(19770,plain,
% 4.34/4.56 (~b(s(s(s(elem!1))), z)),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[19769, 178, 3461, 273, 19761, 19763])).
% 4.34/4.56 tff(19771,plain,
% 4.34/4.56 (r(s(s(s(elem!1))), z)),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[1565, 19770])).
% 4.34/4.56 tff(19772,plain,
% 4.34/4.56 (r(elem!1, z)),
% 4.34/4.56 inference(modus_ponens,[status(thm)],[19771, 8301])).
% 4.34/4.56 tff(19773,plain,
% 4.34/4.56 (r(s(s(s(s(z)))), z)),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[191, 18849])).
% 4.34/4.56 tff(19774,plain,
% 4.34/4.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, 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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, 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)))),
% 4.34/4.56 inference(rewrite,[status(thm)],[])).
% 4.34/4.56 tff(19775,plain,
% 4.34/4.56 (((~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(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z))))) <=> ((~b(s(s(z)), elem!1)) | (~b(elem!1, 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)))),
% 4.34/4.56 inference(rewrite,[status(thm)],[])).
% 4.34/4.56 tff(19776,plain,
% 4.34/4.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(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)), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, 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))))),
% 4.34/4.56 inference(monotonicity,[status(thm)],[19775])).
% 4.34/4.56 tff(19777,plain,
% 4.34/4.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(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)), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, 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)))),
% 4.34/4.56 inference(transitivity,[status(thm)],[19776, 19774])).
% 4.34/4.56 tff(19778,plain,
% 4.34/4.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(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)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))))),
% 4.34/4.56 inference(quant_inst,[status(thm)],[])).
% 4.34/4.56 tff(19779,plain,
% 4.34/4.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))),
% 4.34/4.56 inference(modus_ponens,[status(thm)],[19778, 19777])).
% 4.34/4.56 tff(19780,plain,
% 4.34/4.56 ($false),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[19779, 178, 817, 812, 3771, 1301, 167])).
% 4.34/4.56 tff(19781,plain,((~b(s(s(z)), elem!1)) | (~b(elem!1, 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))))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.56 tff(19782,plain,
% 4.34/4.56 (~b(s(s(s(s(z)))), elem!1)),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[19781, 167, 1301, 812, 817])).
% 4.34/4.56 tff(19783,plain,
% 4.34/4.56 (r(s(s(s(s(z)))), elem!1)),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[3142, 19782, 323])).
% 4.34/4.56 tff(19784,plain,
% 4.34/4.56 ($false),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[6033, 19783, 19773, 437])).
% 4.34/4.56 tff(19785,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, z)) | (s(s(s(s(z)))) = elem!1) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.56 tff(19786,plain,
% 4.34/4.56 (~b(s(s(z)), s(s(s(s(z)))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[19785, 19772, 323, 1301, 812, 817, 3461, 251, 595])).
% 4.34/4.56 tff(19787,plain,
% 4.34/4.56 (r(s(s(z)), s(s(s(s(z)))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[164, 19786])).
% 4.34/4.56 tff(19788,plain,
% 4.34/4.56 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[5101, 19787, 145, 3461])).
% 4.34/4.56 tff(19789,plain,
% 4.34/4.56 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[10755, 19788])).
% 4.34/4.56 tff(19790,plain,
% 4.34/4.56 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 4.34/4.56 inference(unit_resolution,[status(thm)],[5059, 118, 8216, 3615])).
% 4.34/4.57 tff(19791,plain,
% 4.34/4.57 (b(s(s(s(z))), s(s(s(elem!1))))),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[9126, 19790, 8246])).
% 4.34/4.57 tff(19792,plain,
% 4.34/4.57 (b(s(s(z)), s(s(s(z))))),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[5088, 11277])).
% 4.34/4.57 tff(19793,plain,
% 4.34/4.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 4.34/4.57 inference(rewrite,[status(thm)],[])).
% 4.34/4.57 tff(19794,plain,
% 4.34/4.57 (((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(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(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 4.34/4.57 inference(rewrite,[status(thm)],[])).
% 4.34/4.57 tff(19795,plain,
% 4.34/4.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(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(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 4.34/4.57 inference(monotonicity,[status(thm)],[19794])).
% 4.34/4.57 tff(19796,plain,
% 4.34/4.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(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(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 4.34/4.57 inference(transitivity,[status(thm)],[19795, 19793])).
% 4.34/4.57 tff(19797,plain,
% 4.34/4.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(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(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))))),
% 4.34/4.57 inference(quant_inst,[status(thm)],[])).
% 4.34/4.57 tff(19798,plain,
% 4.34/4.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 4.34/4.57 inference(modus_ponens,[status(thm)],[19797, 19796])).
% 4.34/4.57 tff(19799,plain,
% 4.34/4.57 ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[19798, 178, 4291, 1126, 3831])).
% 4.34/4.57 tff(19800,plain,
% 4.34/4.57 ($false),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[19799, 19792, 19791])).
% 4.34/4.57 tff(19801,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.57 tff(19802,plain,
% 4.34/4.57 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[19801, 19789, 19761, 3831, 8246, 224, 3615])).
% 4.34/4.57 tff(19803,plain,
% 4.34/4.57 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[5031, 41, 19802, 10712])).
% 4.34/4.57 tff(19804,plain,
% 4.34/4.57 ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[8267, 178, 104, 595, 19789])).
% 4.34/4.57 tff(19805,plain,
% 4.34/4.57 (~b(z, s(s(s(z))))),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[19804, 19803])).
% 4.34/4.57 tff(19806,plain,
% 4.34/4.57 (r(z, s(s(s(z))))),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[4920, 19805])).
% 4.34/4.57 tff(19807,plain,
% 4.34/4.57 ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[11182, 178, 104, 251, 19789])).
% 4.34/4.57 tff(19808,plain,
% 4.34/4.57 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[19807, 19803])).
% 4.34/4.57 tff(19809,plain,
% 4.34/4.57 (r(s(s(s(s(z)))), s(s(s(z))))),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[11185, 19808])).
% 4.34/4.57 tff(19810,plain,
% 4.34/4.57 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 4.34/4.57 inference(rewrite,[status(thm)],[])).
% 4.34/4.57 tff(19811,plain,
% 4.34/4.57 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 4.34/4.57 inference(rewrite,[status(thm)],[])).
% 4.34/4.57 tff(19812,plain,
% 4.34/4.57 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z)))))))),
% 4.34/4.57 inference(monotonicity,[status(thm)],[19811])).
% 4.34/4.57 tff(19813,plain,
% 4.34/4.57 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 4.34/4.57 inference(transitivity,[status(thm)],[19812, 19810])).
% 4.34/4.57 tff(19814,plain,
% 4.34/4.57 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 4.34/4.57 inference(quant_inst,[status(thm)],[])).
% 4.34/4.57 tff(19815,plain,
% 4.34/4.57 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z)))))),
% 4.34/4.57 inference(modus_ponens,[status(thm)],[19814, 19813])).
% 4.34/4.57 tff(19816,plain,
% 4.34/4.57 ($false),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[19815, 118, 145, 19809, 19806])).
% 4.34/4.57 tff(19817,plain,((~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, 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(elem!1))), s(s(s(s(z)))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (s(s(s(s(z)))) = elem!1) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~(elem!1 = s(s(s(elem!1))))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.57 tff(19818,plain,
% 4.34/4.57 (~b(s(s(z)), elem!1)),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[19817, 19734, 104, 595, 251, 19726, 8686, 19760, 3461, 551, 1301, 19758, 47, 19711, 273])).
% 4.34/4.57 tff(19819,plain,
% 4.34/4.57 ($false),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[448, 19818, 19735, 12])).
% 4.34/4.57 tff(19820,plain,(b(z, s(s(s(elem!1)))) | (s(s(z)) = elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, 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(z)), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (s(s(elem!1)) = s(s(z))) | (~r(z, elem!1)) | (elem!1 = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | b(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.57 tff(19821,plain,
% 4.34/4.57 (b(z, s(s(s(elem!1))))),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[19820, 19709, 104, 17173, 18255, 10793, 18843, 144, 3340, 19708, 469, 1, 3240])).
% 4.34/4.57 tff(19822,plain,
% 4.34/4.57 (~(s(s(s(elem!1))) = elem!1)),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[17579, 19821, 19707])).
% 4.34/4.57 tff(19823,plain,
% 4.34/4.57 (~r(elem!1, s(s(s(s(z)))))),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[529, 19708, 47])).
% 4.34/4.57 tff(19824,plain,
% 4.34/4.57 (~(elem!1 = s(s(s(elem!1))))),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[1530, 19822])).
% 4.34/4.57 tff(19825,plain,
% 4.34/4.57 (r(elem!1, s(s(s(elem!1))))),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[2054, 19824, 3240])).
% 4.34/4.57 tff(19826,plain,
% 4.34/4.57 (r(s(s(z)), elem!1)),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[448, 3241, 12])).
% 4.34/4.57 tff(19827,plain,
% 4.34/4.57 (~r(s(s(s(elem!1))), elem!1)),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[6388, 19826, 521, 3461, 273])).
% 4.34/4.57 tff(19828,plain,
% 4.34/4.57 (b(s(s(s(elem!1))), elem!1)),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[570, 19827, 949])).
% 4.34/4.57 tff(19829,plain,
% 4.34/4.57 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[4168, 4166])).
% 4.34/4.57 tff(19830,plain,
% 4.34/4.57 (~r(elem!1, z)),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[10847, 19826, 3461, 273, 521, 3311])).
% 4.34/4.57 tff(19831,plain,
% 4.34/4.57 (b(elem!1, z)),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[498, 19830, 290])).
% 4.34/4.57 tff(19832,plain,
% 4.34/4.57 (~b(s(s(s(s(z)))), z)),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[18869, 178, 19831, 1301, 251, 595])).
% 4.34/4.57 tff(19833,plain,
% 4.34/4.57 (r(s(s(s(s(z)))), z)),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[191, 19832])).
% 4.34/4.57 tff(19834,plain,
% 4.34/4.57 (~r(s(s(z)), s(s(s(elem!1))))),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[7973, 19826, 3311])).
% 4.34/4.57 tff(19835,plain,
% 4.34/4.57 (b(s(s(z)), s(s(s(elem!1))))),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[4223, 19834])).
% 4.34/4.57 tff(19836,plain,
% 4.34/4.57 (~b(s(s(s(elem!1))), z)),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[7978, 19835, 273, 3461, 2043])).
% 4.34/4.57 tff(19837,plain,
% 4.34/4.57 (r(s(s(s(elem!1))), z)),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[1565, 19836])).
% 4.34/4.57 tff(19838,plain,
% 4.34/4.57 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[7993, 118, 19837, 19833])).
% 4.34/4.57 tff(19839,plain,
% 4.34/4.57 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[4173, 19838, 19829])).
% 4.34/4.57 tff(19840,plain,
% 4.34/4.57 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[5340, 118, 19837, 19833])).
% 4.34/4.57 tff(19841,plain,
% 4.34/4.57 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[10664, 19840, 4166])).
% 4.34/4.57 tff(19842,plain,
% 4.34/4.57 (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[4103, 19841, 104, 251, 19839])).
% 4.34/4.57 tff(19843,plain,
% 4.34/4.57 (~r(s(s(s(s(z)))), elem!1)),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[3137, 19833, 521])).
% 4.34/4.57 tff(19844,plain,
% 4.34/4.57 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[8548, 19843, 104, 251, 469, 5721])).
% 4.34/4.57 tff(19845,plain,
% 4.34/4.57 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[9315, 19839, 104, 3311, 19826, 4254, 3241, 19844])).
% 4.34/4.57 tff(19846,plain,
% 4.34/4.57 ($false),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[10584, 19845, 19842, 19828])).
% 4.34/4.57 tff(19847,plain,(b(s(s(z)), elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (elem!1 = s(s(s(s(z))))) | r(elem!1, s(s(s(s(z))))) | (~r(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(elem!1))))) | (elem!1 = z) | (s(s(s(elem!1))) = elem!1) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.34/4.57 tff(19848,plain,
% 4.34/4.57 (b(s(s(z)), elem!1)),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[19847, 19825, 104, 18255, 18844, 469, 19823, 19708, 18843, 17173, 144, 10793, 19821, 290, 19822, 19709])).
% 4.34/4.57 tff(19849,plain,
% 4.34/4.57 (b(elem!1, z)),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[17483, 461, 273, 5618, 3311, 2043])).
% 4.34/4.57 tff(19850,plain,
% 4.34/4.57 (~b(s(s(s(s(z)))), z)),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[18869, 178, 19849, 1301, 251, 595])).
% 4.34/4.57 tff(19851,plain,
% 4.34/4.57 (b(s(s(s(s(z)))), s(s(z)))),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[19480, 19850, 1, 3240, 461])).
% 4.34/4.57 tff(19852,plain,
% 4.34/4.57 (r(s(s(s(s(z)))), z)),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[191, 19850])).
% 4.34/4.57 tff(19853,plain,
% 4.34/4.57 (~r(s(s(s(s(z)))), elem!1)),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[3137, 19852, 521])).
% 4.34/4.57 tff(19854,plain,
% 4.34/4.57 (b(s(s(s(s(z)))), elem!1)),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[3142, 19853, 323])).
% 4.34/4.57 tff(19855,plain,
% 4.34/4.57 (b(s(s(z)), elem!1)),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[10659, 19850, 1, 3240, 461])).
% 4.34/4.57 tff(19856,plain,
% 4.34/4.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 4.34/4.57 inference(rewrite,[status(thm)],[])).
% 4.34/4.57 tff(19857,plain,
% 4.34/4.57 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 4.34/4.57 inference(rewrite,[status(thm)],[])).
% 4.34/4.57 tff(19858,plain,
% 4.34/4.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 4.34/4.57 inference(monotonicity,[status(thm)],[19857])).
% 4.34/4.57 tff(19859,plain,
% 4.34/4.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 4.34/4.57 inference(transitivity,[status(thm)],[19858, 19856])).
% 4.34/4.57 tff(19860,plain,
% 4.34/4.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 4.34/4.57 inference(quant_inst,[status(thm)],[])).
% 4.34/4.57 tff(19861,plain,
% 4.34/4.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z))))),
% 4.34/4.57 inference(modus_ponens,[status(thm)],[19860, 19859])).
% 4.34/4.57 tff(19862,plain,
% 4.34/4.57 ($false),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[19861, 178, 19849, 19855, 5619, 19854, 19851])).
% 4.34/4.57 tff(19863,plain,(b(elem!1, s(s(z))) | (s(s(s(s(z)))) = elem!1) | (~r(z, elem!1)) | b(z, s(s(s(s(z))))) | b(elem!1, s(s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | r(s(s(z)), z) | (~r(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.57 tff(19864,plain,
% 4.34/4.57 (b(elem!1, s(s(z)))),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[19863, 19708, 551, 1, 3240, 18843, 18255, 17173, 144, 10792, 19825, 19821])).
% 4.34/4.57 tff(19865,plain,
% 4.34/4.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))),
% 4.34/4.57 inference(rewrite,[status(thm)],[])).
% 4.34/4.57 tff(19866,plain,
% 4.34/4.57 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1))) <=> ((~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))),
% 4.34/4.57 inference(rewrite,[status(thm)],[])).
% 4.34/4.57 tff(19867,plain,
% 4.34/4.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z))))),
% 4.34/4.57 inference(monotonicity,[status(thm)],[19866])).
% 4.34/4.57 tff(19868,plain,
% 4.34/4.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))),
% 4.34/4.57 inference(transitivity,[status(thm)],[19867, 19865])).
% 4.34/4.57 tff(19869,plain,
% 4.34/4.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)))),
% 4.34/4.57 inference(quant_inst,[status(thm)],[])).
% 4.34/4.57 tff(19870,plain,
% 4.34/4.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z))),
% 4.34/4.57 inference(modus_ponens,[status(thm)],[19869, 19868])).
% 4.34/4.57 tff(19871,plain,
% 4.34/4.57 ((~b(elem!1, z)) | (~b(s(s(z)), elem!1))),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[19870, 178, 10793, 144, 19864])).
% 4.34/4.57 tff(19872,plain,
% 4.34/4.57 (~b(elem!1, z)),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[19871, 19848])).
% 4.34/4.57 tff(19873,plain,
% 4.34/4.57 (r(elem!1, z)),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[498, 19872, 290])).
% 4.34/4.57 tff(19874,plain,
% 4.34/4.57 (~b(s(s(z)), s(s(s(s(z)))))),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[19785, 19873, 551, 18843, 19864, 19848, 10793, 18255, 17173])).
% 4.34/4.57 tff(19875,plain,
% 4.34/4.57 (r(s(s(z)), s(s(s(s(z)))))),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[164, 19874])).
% 4.34/4.57 tff(19876,plain,
% 4.34/4.57 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[10799, 19875, 47])).
% 4.34/4.57 tff(19877,plain,
% 4.34/4.57 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[4173, 19876, 18845])).
% 4.34/4.57 tff(19878,plain,
% 4.34/4.57 (~r(s(s(s(elem!1))), z)),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[6071, 19873, 19825])).
% 4.34/4.57 tff(19879,plain,
% 4.34/4.57 (b(s(s(s(elem!1))), z)),
% 4.34/4.57 inference(unit_resolution,[status(thm)],[1565, 19878])).
% 4.34/4.57 tff(19880,plain,
% 4.34/4.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 4.34/4.57 inference(rewrite,[status(thm)],[])).
% 4.34/4.57 tff(19881,plain,
% 4.34/4.57 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, 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)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(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(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 4.34/4.57 inference(rewrite,[status(thm)],[])).
% 4.34/4.57 tff(19882,plain,
% 4.34/4.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 4.34/4.57 inference(monotonicity,[status(thm)],[19881])).
% 4.34/4.57 tff(19883,plain,
% 4.34/4.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 4.34/4.57 inference(transitivity,[status(thm)],[19882, 19880])).
% 4.34/4.57 tff(19884,plain,
% 4.34/4.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 4.34/4.57 inference(quant_inst,[status(thm)],[])).
% 4.34/4.57 tff(19885,plain,
% 4.34/4.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 4.34/4.58 inference(modus_ponens,[status(thm)],[19884, 19883])).
% 4.34/4.58 tff(19886,plain,
% 4.34/4.58 (~b(s(s(s(s(z)))), z)),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[19885, 178, 19879, 18255, 17173, 19877])).
% 4.34/4.58 tff(19887,plain,
% 4.34/4.58 (r(s(s(s(s(z)))), z)),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[191, 19886])).
% 4.34/4.58 tff(19888,plain,
% 4.34/4.58 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[5101, 19875, 47, 10793])).
% 4.34/4.58 tff(19889,plain,
% 4.34/4.58 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[10755, 19888])).
% 4.34/4.58 tff(19890,plain,
% 4.34/4.58 (~b(s(s(s(s(z)))), s(s(z)))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[13518, 19887, 469, 19864, 19848, 19873])).
% 4.34/4.58 tff(19891,plain,
% 4.34/4.58 (r(s(s(s(s(z)))), s(s(z)))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[102, 19890])).
% 4.34/4.58 tff(19892,plain,
% 4.34/4.58 (~b(s(s(s(elem!1))), s(s(z)))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[8106, 178, 19821, 19879, 10793, 144])).
% 4.34/4.58 tff(19893,plain,
% 4.34/4.58 (r(s(s(s(elem!1))), s(s(z)))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[4209, 41, 19892, 4181])).
% 4.34/4.58 tff(19894,plain,
% 4.34/4.58 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[9024, 118, 19893, 19891])).
% 4.34/4.58 tff(19895,plain,
% 4.34/4.58 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[10664, 19894, 18844])).
% 4.34/4.58 tff(19896,plain,
% 4.34/4.58 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[10595, 19895, 104, 11613, 17173, 18255, 19821, 19877, 19889, 19887])).
% 4.34/4.58 tff(19897,plain,
% 4.34/4.58 (b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[5118, 19896, 4254])).
% 4.34/4.58 tff(19898,plain,
% 4.34/4.58 ($false),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[8949, 178, 19821, 104, 17173, 19877, 19897])).
% 4.34/4.58 tff(19899,plain,(b(elem!1, s(s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (elem!1 = s(s(s(s(z))))) | (elem!1 = z) | b(z, s(s(s(s(z))))) | r(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.58 tff(19900,plain,
% 4.34/4.58 (b(elem!1, s(s(s(elem!1))))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[19899, 469, 104, 290, 1, 48])).
% 4.34/4.58 tff(19901,plain,
% 4.34/4.58 (~(s(s(s(elem!1))) = elem!1)),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[16438, 2042])).
% 4.34/4.58 tff(19902,plain,
% 4.34/4.58 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[19720, 557, 145])).
% 4.34/4.58 tff(19903,plain,
% 4.34/4.58 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[2803, 224, 438])).
% 4.34/4.58 tff(19904,plain,
% 4.34/4.58 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[691, 19903, 18858])).
% 4.34/4.58 tff(19905,plain,
% 4.34/4.58 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 4.34/4.58 inference(monotonicity,[status(thm)],[19904])).
% 4.34/4.58 tff(19906,plain,
% 4.34/4.58 (s(s(s(s(s(s(s(s(z)))))))) = s(elem!1)),
% 4.34/4.58 inference(symmetry,[status(thm)],[19905])).
% 4.34/4.58 tff(19907,plain,
% 4.34/4.58 (b(z, s(s(s(s(s(s(s(s(z))))))))) <=> b(z, s(elem!1))),
% 4.34/4.58 inference(monotonicity,[status(thm)],[19906])).
% 4.34/4.58 tff(19908,plain,
% 4.34/4.58 (b(z, s(elem!1)) <=> b(z, s(s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.58 inference(symmetry,[status(thm)],[19907])).
% 4.34/4.58 tff(19909,plain,
% 4.34/4.58 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[16181, 19904])).
% 4.34/4.58 tff(19910,plain,
% 4.34/4.58 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 4.34/4.58 inference(monotonicity,[status(thm)],[19906])).
% 4.34/4.58 tff(19911,plain,
% 4.34/4.58 ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) <=> (~b(s(elem!1), s(s(s(s(z))))))),
% 4.34/4.58 inference(monotonicity,[status(thm)],[19910])).
% 4.34/4.58 tff(19912,plain,
% 4.34/4.58 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))) <=> r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.34/4.58 inference(monotonicity,[status(thm)],[19906])).
% 4.34/4.58 tff(19913,plain,
% 4.34/4.58 (r(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.58 inference(symmetry,[status(thm)],[19912])).
% 4.34/4.58 tff(19914,plain,
% 4.34/4.58 ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) <=> (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))),
% 4.34/4.58 inference(monotonicity,[status(thm)],[19913])).
% 4.34/4.58 tff(19915,plain,
% 4.34/4.58 (r(elem!1, s(elem!1)) <=> r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.34/4.58 inference(monotonicity,[status(thm)],[19904])).
% 4.34/4.58 tff(19916,plain,
% 4.34/4.58 ((~r(elem!1, s(elem!1))) <=> (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 4.34/4.58 inference(monotonicity,[status(thm)],[19915])).
% 4.34/4.58 tff(19917,plain,
% 4.34/4.58 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.58 inference(monotonicity,[status(thm)],[19904])).
% 4.34/4.58 tff(19918,plain,
% 4.34/4.58 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(z)))), elem!1)),
% 4.34/4.58 inference(symmetry,[status(thm)],[19917])).
% 4.34/4.58 tff(19919,plain,
% 4.34/4.58 (b(s(s(s(s(z)))), elem!1)),
% 4.34/4.58 inference(modus_ponens,[status(thm)],[251, 19918])).
% 4.34/4.58 tff(19920,plain,
% 4.34/4.58 (~(s(elem!1) = s(s(z)))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[2832, 19904])).
% 4.34/4.58 tff(19921,plain,
% 4.34/4.58 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[2840, 19920])).
% 4.34/4.58 tff(19922,plain,
% 4.34/4.58 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[4173, 19921, 4171])).
% 4.34/4.58 tff(19923,plain,
% 4.34/4.58 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[7917, 19921])).
% 4.34/4.58 tff(19924,plain,
% 4.34/4.58 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[10664, 19923, 3293])).
% 4.34/4.58 tff(19925,plain,
% 4.34/4.58 (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[4103, 19924, 104, 251, 19922])).
% 4.34/4.58 tff(19926,plain,
% 4.34/4.58 (~b(s(s(s(elem!1))), elem!1)),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[10584, 19925, 19904])).
% 4.34/4.58 tff(19927,plain,
% 4.34/4.58 (r(s(s(s(elem!1))), elem!1)),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[570, 19926, 949])).
% 4.34/4.58 tff(19928,plain,
% 4.34/4.58 (s(s(elem!1)) = s(s(s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.58 inference(monotonicity,[status(thm)],[19905])).
% 4.34/4.58 tff(19929,plain,
% 4.34/4.58 (s(s(s(elem!1))) = s(s(s(s(s(s(s(s(s(s(z))))))))))),
% 4.34/4.58 inference(monotonicity,[status(thm)],[19928])).
% 4.34/4.58 tff(19930,plain,
% 4.34/4.58 (s(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(s(elem!1)))),
% 4.34/4.58 inference(symmetry,[status(thm)],[19929])).
% 4.34/4.58 tff(19931,plain,
% 4.34/4.58 (r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.58 inference(monotonicity,[status(thm)],[19930])).
% 4.34/4.58 tff(19932,plain,
% 4.34/4.58 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.58 inference(symmetry,[status(thm)],[19931])).
% 4.34/4.58 tff(19933,plain,
% 4.34/4.58 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.58 inference(monotonicity,[status(thm)],[679])).
% 4.34/4.58 tff(19934,plain,
% 4.34/4.58 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.58 inference(modus_ponens,[status(thm)],[556, 19933])).
% 4.34/4.58 tff(19935,assumption,(~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 4.34/4.58 tff(19936,plain,
% 4.34/4.58 ($false),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[19935, 19934])).
% 4.34/4.58 tff(19937,plain,((~r(s(s(s(elem!1))), elem!1)) | r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))) | (~(elem!1 = s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.58 tff(19938,plain,
% 4.34/4.58 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[19937, 19927, 19904])).
% 4.34/4.58 tff(19939,plain,
% 4.34/4.58 (r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.58 inference(modus_ponens,[status(thm)],[19938, 19932])).
% 4.34/4.58 tff(19940,assumption,(r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 4.34/4.58 tff(19941,plain,
% 4.34/4.58 (r(s(s(z)), s(s(s(s(s(s(s(s(s(s(z))))))))))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 4.34/4.58 inference(monotonicity,[status(thm)],[4345])).
% 4.34/4.58 tff(19942,plain,
% 4.34/4.58 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 4.34/4.58 inference(symmetry,[status(thm)],[19941])).
% 4.34/4.58 tff(19943,plain,
% 4.34/4.58 (r(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 4.34/4.58 inference(modus_ponens,[status(thm)],[1823, 19942])).
% 4.34/4.58 tff(19944,plain,
% 4.34/4.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 4.34/4.58 inference(rewrite,[status(thm)],[])).
% 4.34/4.58 tff(19945,plain,
% 4.34/4.58 (((~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(s(s(z))))))))))))) <=> ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 4.34/4.58 inference(rewrite,[status(thm)],[])).
% 4.34/4.58 tff(19946,plain,
% 4.34/4.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(s(s(z))))))))))))))),
% 4.34/4.58 inference(monotonicity,[status(thm)],[19945])).
% 4.34/4.58 tff(19947,plain,
% 4.34/4.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 4.34/4.58 inference(transitivity,[status(thm)],[19946, 19944])).
% 4.34/4.58 tff(19948,plain,
% 4.34/4.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 4.34/4.58 inference(quant_inst,[status(thm)],[])).
% 4.34/4.58 tff(19949,plain,
% 4.34/4.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(s(s(z))))))))))))),
% 4.34/4.58 inference(modus_ponens,[status(thm)],[19948, 19947])).
% 4.34/4.58 tff(19950,plain,
% 4.34/4.58 ((~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(s(s(z))))))))))))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[19949, 118, 224])).
% 4.34/4.58 tff(19951,plain,
% 4.34/4.58 ($false),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[19950, 19943, 19940])).
% 4.34/4.58 tff(19952,plain,((~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~(elem!1 = s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.58 tff(19953,plain,
% 4.34/4.58 (~r(s(s(z)), s(s(s(elem!1))))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[19952, 19939, 224, 19904])).
% 4.34/4.58 tff(19954,plain,
% 4.34/4.58 (b(s(s(z)), s(s(s(elem!1))))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[4223, 19953])).
% 4.34/4.58 tff(19955,plain,
% 4.34/4.58 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[19801, 1126, 3615, 3831, 8246, 224, 4291])).
% 4.34/4.58 tff(19956,plain,
% 4.34/4.58 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[16623, 1126, 251, 167, 224, 104])).
% 4.34/4.58 tff(19957,plain,
% 4.34/4.58 ($false),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[5031, 41, 19956, 19955, 10712])).
% 4.34/4.58 tff(19958,plain,((~b(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(z)), s(s(s(s(z)))))) | (~r(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)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.58 tff(19959,plain,
% 4.34/4.58 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[19958, 167, 251, 224, 104, 3615, 3831, 8246, 4291])).
% 4.34/4.58 tff(19960,plain,
% 4.34/4.58 (r(s(s(s(z))), s(s(s(s(z)))))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[10755, 19959])).
% 4.34/4.58 tff(19961,plain,
% 4.34/4.58 (~r(s(s(s(z))), z)),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[4899, 118, 145, 19960])).
% 4.34/4.58 tff(19962,plain,
% 4.34/4.58 (b(s(s(s(z))), z)),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[4903, 41, 77, 19961])).
% 4.34/4.58 tff(19963,plain,
% 4.34/4.58 (~r(z, s(s(s(z))))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[4910, 118, 145, 19960])).
% 4.34/4.58 tff(19964,plain,
% 4.34/4.58 (b(z, s(s(s(z))))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[4920, 19963])).
% 4.34/4.58 tff(19965,plain,
% 4.34/4.58 (~b(s(s(s(z))), s(s(z)))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[17111, 178, 3461, 273, 19964, 19962])).
% 4.34/4.58 tff(19966,plain,
% 4.34/4.58 (r(s(s(s(z))), s(s(z)))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[4966, 19965])).
% 4.34/4.58 tff(19967,plain,
% 4.34/4.58 (~b(s(s(s(s(z)))), s(s(z)))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[10667, 167, 4291, 3831, 3828])).
% 4.34/4.58 tff(19968,plain,
% 4.34/4.58 (r(s(s(s(s(z)))), s(s(z)))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[102, 19967])).
% 4.34/4.58 tff(19969,plain,
% 4.34/4.58 ($false),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[17170, 118, 19968, 19966, 19960])).
% 4.34/4.58 tff(19970,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(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)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.58 tff(19971,plain,
% 4.34/4.58 (~b(s(s(z)), s(s(s(s(z)))))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[19970, 224, 273, 145, 251, 3461, 104, 19938, 19922, 11613, 19954, 19924])).
% 4.34/4.58 tff(19972,plain,
% 4.34/4.58 (r(s(s(z)), s(s(s(s(z)))))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[164, 19971])).
% 4.34/4.58 tff(19973,plain,
% 4.34/4.58 ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) <=> (~r(s(s(s(s(z)))), s(elem!1)))),
% 4.34/4.58 inference(monotonicity,[status(thm)],[16174])).
% 4.34/4.58 tff(19974,plain,
% 4.34/4.58 (~(s(s(elem!1)) = elem!1)),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[2510, 16183, 679])).
% 4.34/4.58 tff(19975,plain,
% 4.34/4.58 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[348, 19974])).
% 4.34/4.58 tff(19976,plain,
% 4.34/4.58 (~r(s(elem!1), elem!1)),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[12991, 147, 556, 438, 19975])).
% 4.34/4.58 tff(19977,plain,
% 4.34/4.58 (b(s(elem!1), elem!1)),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[677, 19976, 725])).
% 4.34/4.58 tff(19978,plain,
% 4.34/4.58 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[686, 19977, 679])).
% 4.34/4.58 tff(19979,plain,
% 4.34/4.58 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.58 inference(modus_ponens,[status(thm)],[19978, 11735])).
% 4.34/4.58 tff(19980,plain,
% 4.34/4.58 (~r(s(s(z)), s(elem!1))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[16259, 19979, 147, 104, 251, 679])).
% 4.34/4.58 tff(19981,plain,
% 4.34/4.58 (b(s(s(z)), s(elem!1))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[1067, 19980, 16233])).
% 4.34/4.58 tff(19982,plain,
% 4.34/4.58 (b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.58 inference(modus_ponens,[status(thm)],[19981, 16232])).
% 4.34/4.58 tff(19983,plain,
% 4.34/4.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 4.34/4.58 inference(rewrite,[status(thm)],[])).
% 4.34/4.58 tff(19984,plain,
% 4.34/4.58 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 4.34/4.58 inference(rewrite,[status(thm)],[])).
% 4.34/4.58 tff(19985,plain,
% 4.34/4.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))))),
% 4.34/4.58 inference(monotonicity,[status(thm)],[19984])).
% 4.34/4.58 tff(19986,plain,
% 4.34/4.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 4.34/4.58 inference(transitivity,[status(thm)],[19985, 19983])).
% 4.34/4.58 tff(19987,plain,
% 4.34/4.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))),
% 4.34/4.58 inference(quant_inst,[status(thm)],[])).
% 4.34/4.58 tff(19988,plain,
% 4.34/4.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.58 inference(modus_ponens,[status(thm)],[19987, 19986])).
% 4.34/4.58 tff(19989,plain,
% 4.34/4.58 ((~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z))))))))))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[19988, 178, 3461, 595, 19979])).
% 4.34/4.58 tff(19990,plain,
% 4.34/4.58 (~b(s(s(s(s(s(s(s(s(z)))))))), z)),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[19989, 19982])).
% 4.34/4.58 tff(19991,plain,
% 4.34/4.58 (r(s(s(s(s(s(s(s(s(z)))))))), z)),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[16121, 41, 16118, 19990])).
% 4.34/4.58 tff(19992,plain,
% 4.34/4.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))))),
% 4.34/4.58 inference(rewrite,[status(thm)],[])).
% 4.34/4.58 tff(19993,plain,
% 4.34/4.58 (((~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))))),
% 4.34/4.58 inference(rewrite,[status(thm)],[])).
% 4.34/4.58 tff(19994,plain,
% 4.34/4.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z))))))))))))),
% 4.34/4.58 inference(monotonicity,[status(thm)],[19993])).
% 4.34/4.58 tff(19995,plain,
% 4.34/4.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))))),
% 4.34/4.58 inference(transitivity,[status(thm)],[19994, 19992])).
% 4.34/4.58 tff(19996,plain,
% 4.34/4.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))))),
% 4.34/4.58 inference(quant_inst,[status(thm)],[])).
% 4.34/4.58 tff(19997,plain,
% 4.34/4.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z))))))))))),
% 4.34/4.58 inference(modus_ponens,[status(thm)],[19996, 19995])).
% 4.34/4.58 tff(19998,plain,
% 4.34/4.58 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[19997, 118, 194, 19991])).
% 4.34/4.58 tff(19999,plain,
% 4.34/4.58 (~r(s(s(s(s(z)))), s(elem!1))),
% 4.34/4.58 inference(modus_ponens,[status(thm)],[19998, 19973])).
% 4.34/4.58 tff(20000,plain,
% 4.34/4.58 ((~b(s(s(s(s(s(s(s(s(z)))))))), z)) <=> (~b(s(elem!1), z))),
% 4.34/4.58 inference(monotonicity,[status(thm)],[15438])).
% 4.34/4.58 tff(20001,plain,
% 4.34/4.58 (~b(s(elem!1), z)),
% 4.34/4.58 inference(modus_ponens,[status(thm)],[19990, 20000])).
% 4.34/4.58 tff(20002,plain,
% 4.34/4.58 (r(s(elem!1), z)),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[774, 20001])).
% 4.34/4.58 tff(20003,plain,
% 4.34/4.58 (~r(s(elem!1), s(s(s(s(z)))))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[916, 20002, 194])).
% 4.34/4.58 tff(20004,plain,
% 4.34/4.58 (b(s(elem!1), s(s(s(s(z)))))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[1084, 20003, 16182])).
% 4.34/4.58 tff(20005,plain,
% 4.34/4.58 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 4.34/4.58 inference(modus_ponens,[status(thm)],[20004, 16138])).
% 4.34/4.58 tff(20006,plain,
% 4.34/4.58 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[16243, 178, 104, 251, 19979, 20005])).
% 4.34/4.58 tff(20007,plain,
% 4.34/4.58 (~b(s(s(s(s(z)))), s(elem!1))),
% 4.34/4.58 inference(modus_ponens,[status(thm)],[20006, 16234])).
% 4.34/4.58 tff(20008,plain,
% 4.34/4.58 ($false),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[2173, 20007, 19999, 16183])).
% 4.34/4.58 tff(20009,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~(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))))))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = elem!1) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.58 tff(20010,plain,
% 4.34/4.58 (~r(s(s(s(s(z)))), z)),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[20009, 19972, 104, 251, 19904, 3461, 595, 5283, 19927, 438])).
% 4.34/4.58 tff(20011,plain,
% 4.34/4.58 (b(s(s(s(s(z)))), z)),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[191, 20010])).
% 4.34/4.58 tff(20012,plain,
% 4.34/4.58 (~b(elem!1, z)),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[16429, 20011, 1301, 818, 19919])).
% 4.34/4.58 tff(20013,plain,
% 4.34/4.58 (r(elem!1, z)),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[498, 20012, 290])).
% 4.34/4.58 tff(20014,plain,
% 4.34/4.58 (b(s(s(s(s(s(s(s(s(z)))))))), z) <=> b(s(elem!1), z)),
% 4.34/4.58 inference(monotonicity,[status(thm)],[19906])).
% 4.34/4.58 tff(20015,plain,
% 4.34/4.58 ((~b(s(s(s(s(s(s(s(s(z)))))))), z)) <=> (~b(s(elem!1), z))),
% 4.34/4.58 inference(monotonicity,[status(thm)],[20014])).
% 4.34/4.58 tff(20016,plain,
% 4.34/4.58 (b(s(s(z)), s(s(s(s(s(s(s(s(z))))))))) <=> b(s(s(z)), s(elem!1))),
% 4.34/4.58 inference(monotonicity,[status(thm)],[19906])).
% 4.34/4.58 tff(20017,plain,
% 4.34/4.58 (b(s(s(z)), s(elem!1)) <=> b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.58 inference(symmetry,[status(thm)],[20016])).
% 4.34/4.58 tff(20018,plain,
% 4.34/4.58 (~(s(s(z)) = s(elem!1))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[1058, 19920])).
% 4.34/4.58 tff(20019,plain,
% 4.34/4.58 (b(s(s(s(s(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))))))))),
% 4.34/4.58 inference(monotonicity,[status(thm)],[19906])).
% 4.34/4.58 tff(20020,plain,
% 4.34/4.58 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.58 inference(symmetry,[status(thm)],[20019])).
% 4.34/4.58 tff(20021,plain,
% 4.34/4.58 (~(s(s(s(s(z)))) = s(elem!1))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[2168, 19909])).
% 4.34/4.58 tff(20022,plain,
% 4.34/4.58 (~(s(s(elem!1)) = elem!1)),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[2510, 20021, 19904])).
% 4.34/4.58 tff(20023,plain,
% 4.34/4.58 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[348, 20022])).
% 4.34/4.58 tff(20024,plain,
% 4.34/4.58 (~r(s(elem!1), elem!1)),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[12991, 19972, 19927, 438, 20023])).
% 4.34/4.58 tff(20025,plain,
% 4.34/4.58 (b(s(elem!1), elem!1)),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[677, 20024, 5283])).
% 4.34/4.58 tff(20026,plain,
% 4.34/4.58 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[686, 20025, 19904])).
% 4.34/4.58 tff(20027,plain,
% 4.34/4.58 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.58 inference(modus_ponens,[status(thm)],[20026, 20020])).
% 4.34/4.58 tff(20028,plain,
% 4.34/4.58 (~r(s(s(z)), s(elem!1))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[16259, 20027, 19972, 104, 251, 19904])).
% 4.34/4.58 tff(20029,plain,
% 4.34/4.58 (b(s(s(z)), s(elem!1))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[1067, 20028, 20018])).
% 4.34/4.58 tff(20030,plain,
% 4.34/4.58 (b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.58 inference(modus_ponens,[status(thm)],[20029, 20017])).
% 4.34/4.58 tff(20031,plain,
% 4.34/4.58 ((~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z))))))))))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[19988, 178, 3461, 595, 20027])).
% 4.34/4.58 tff(20032,plain,
% 4.34/4.58 (~b(s(s(s(s(s(s(s(s(z)))))))), z)),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[20031, 20030])).
% 4.34/4.58 tff(20033,plain,
% 4.34/4.58 (~b(s(elem!1), z)),
% 4.34/4.58 inference(modus_ponens,[status(thm)],[20032, 20015])).
% 4.34/4.58 tff(20034,plain,
% 4.34/4.58 (r(s(elem!1), z)),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[774, 20033])).
% 4.34/4.58 tff(20035,plain,
% 4.34/4.58 (~r(elem!1, s(elem!1))),
% 4.34/4.58 inference(unit_resolution,[status(thm)],[2711, 20034, 20013])).
% 4.34/4.58 tff(20036,plain,
% 4.34/4.58 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.34/4.58 inference(modus_ponens,[status(thm)],[20035, 19916])).
% 4.34/4.58 tff(20037,plain,
% 4.34/4.58 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.58 inference(modus_ponens,[status(thm)],[20036, 19914])).
% 4.34/4.58 tff(20038,plain,
% 4.34/4.58 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 4.34/4.58 inference(monotonicity,[status(thm)],[19906])).
% 4.34/4.58 tff(20039,plain,
% 4.34/4.58 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.34/4.58 inference(transitivity,[status(thm)],[20038, 377])).
% 4.34/4.58 tff(20040,plain,
% 4.34/4.58 ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.58 inference(symmetry,[status(thm)],[20039])).
% 4.34/4.58 tff(20041,plain,
% 4.34/4.58 ((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z))))))))))),
% 4.34/4.58 inference(monotonicity,[status(thm)],[20040])).
% 4.34/4.58 tff(20042,plain,
% 4.34/4.58 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.34/4.58 inference(monotonicity,[status(thm)],[19904])).
% 4.34/4.58 tff(20043,plain,
% 4.34/4.58 ((~(s(elem!1) = elem!1)) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.58 inference(monotonicity,[status(thm)],[20042])).
% 4.34/4.58 tff(20044,plain,
% 4.34/4.58 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.34/4.58 inference(modus_ponens,[status(thm)],[5283, 20043])).
% 4.34/4.58 tff(20045,plain,
% 4.34/4.58 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.58 inference(modus_ponens,[status(thm)],[20044, 20041])).
% 4.34/4.58 tff(20046,plain,
% 4.34/4.58 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[19275, 20045, 20037])).
% 4.34/4.59 tff(20047,plain,
% 4.34/4.59 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[19297, 178, 104, 251, 20027])).
% 4.34/4.59 tff(20048,plain,
% 4.34/4.59 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[20047, 20046])).
% 4.34/4.59 tff(20049,plain,
% 4.34/4.59 (~b(s(elem!1), s(s(s(s(z)))))),
% 4.34/4.59 inference(modus_ponens,[status(thm)],[20048, 19911])).
% 4.34/4.59 tff(20050,plain,
% 4.34/4.59 (r(s(elem!1), s(s(s(s(z)))))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[1084, 20049, 19909])).
% 4.34/4.59 tff(20051,plain,
% 4.34/4.59 (~r(z, s(elem!1))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[2766, 20050, 145])).
% 4.34/4.59 tff(20052,plain,
% 4.34/4.59 (b(z, s(elem!1))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[2351, 20051])).
% 4.34/4.59 tff(20053,plain,
% 4.34/4.59 (b(z, s(s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.59 inference(modus_ponens,[status(thm)],[20052, 19908])).
% 4.34/4.59 tff(20054,plain,
% 4.34/4.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 4.34/4.59 inference(rewrite,[status(thm)],[])).
% 4.34/4.59 tff(20055,plain,
% 4.34/4.59 (((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(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(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 4.34/4.59 inference(rewrite,[status(thm)],[])).
% 4.34/4.59 tff(20056,plain,
% 4.34/4.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))))),
% 4.34/4.59 inference(monotonicity,[status(thm)],[20055])).
% 4.34/4.59 tff(20057,plain,
% 4.34/4.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 4.34/4.59 inference(transitivity,[status(thm)],[20056, 20054])).
% 4.34/4.59 tff(20058,plain,
% 4.34/4.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)))),
% 4.34/4.59 inference(quant_inst,[status(thm)],[])).
% 4.34/4.59 tff(20059,plain,
% 4.34/4.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))),
% 4.34/4.59 inference(modus_ponens,[status(thm)],[20058, 20057])).
% 4.34/4.59 tff(20060,plain,
% 4.34/4.59 ($false),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[20059, 178, 20011, 251, 595, 20046, 20053])).
% 4.34/4.59 tff(20061,plain,((~r(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))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (elem!1 = z) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~b(z, s(s(z)))) | (s(s(s(elem!1))) = elem!1) | r(s(s(s(s(z)))), s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.59 tff(20062,plain,
% 4.34/4.59 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[20061, 438, 595, 145, 104, 3461, 290, 1301, 818, 251, 273, 949, 3293, 4171])).
% 4.34/4.59 tff(20063,plain,
% 4.34/4.59 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[249, 20062])).
% 4.34/4.59 tff(20064,plain,
% 4.34/4.59 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[17204, 20063, 273, 3461, 595])).
% 4.34/4.59 tff(20065,plain,
% 4.34/4.59 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[3578, 20064])).
% 4.34/4.59 tff(20066,plain,
% 4.34/4.59 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[17566, 20065, 438])).
% 4.34/4.59 tff(20067,plain,
% 4.34/4.59 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[3444, 20066, 18857])).
% 4.34/4.59 tff(20068,plain,
% 4.34/4.59 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(z)), elem!1)),
% 4.34/4.59 inference(monotonicity,[status(thm)],[20067])).
% 4.34/4.59 tff(20069,plain,
% 4.34/4.59 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.59 inference(symmetry,[status(thm)],[20068])).
% 4.34/4.59 tff(20070,plain,
% 4.34/4.59 ((~b(s(s(z)), elem!1)) <=> (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.59 inference(monotonicity,[status(thm)],[20069])).
% 4.34/4.59 tff(20071,plain,
% 4.34/4.59 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.59 inference(modus_ponens,[status(thm)],[3241, 20070])).
% 4.34/4.59 tff(20072,plain,
% 4.34/4.59 ($false),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[20063, 20071])).
% 4.34/4.59 tff(20073,plain,((~r(s(s(z)), elem!1)) | b(s(s(z)), elem!1) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (elem!1 = z) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (s(s(s(elem!1))) = elem!1) | r(s(s(s(s(z)))), s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.59 tff(20074,plain,
% 4.34/4.59 (~r(s(s(z)), elem!1)),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[20073, 818, 273, 3461, 595, 145, 104, 290, 1301, 3241, 251, 19901, 19902, 3822])).
% 4.34/4.59 tff(20075,plain,
% 4.34/4.59 (s(s(z)) = elem!1),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[448, 20074, 3241])).
% 4.34/4.59 tff(20076,plain,
% 4.34/4.59 (s(s(s(z))) = s(elem!1)),
% 4.34/4.59 inference(monotonicity,[status(thm)],[20075])).
% 4.34/4.59 tff(20077,plain,
% 4.34/4.59 (s(s(s(s(z)))) = s(s(elem!1))),
% 4.34/4.59 inference(monotonicity,[status(thm)],[20076])).
% 4.34/4.59 tff(20078,plain,
% 4.34/4.59 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(elem!1)))),
% 4.34/4.59 inference(monotonicity,[status(thm)],[20077])).
% 4.34/4.59 tff(20079,plain,
% 4.34/4.59 (b(elem!1, s(s(elem!1)))),
% 4.34/4.59 inference(modus_ponens,[status(thm)],[1301, 20078])).
% 4.34/4.59 tff(20080,plain,
% 4.34/4.59 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 4.34/4.59 inference(monotonicity,[status(thm)],[20076])).
% 4.34/4.59 tff(20081,plain,
% 4.34/4.59 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 4.34/4.59 inference(transitivity,[status(thm)],[20080, 3881])).
% 4.34/4.59 tff(20082,plain,
% 4.34/4.59 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 4.34/4.59 inference(monotonicity,[status(thm)],[20081])).
% 4.34/4.59 tff(20083,plain,
% 4.34/4.59 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.34/4.59 inference(modus_ponens,[status(thm)],[11613, 20082])).
% 4.34/4.59 tff(20084,plain,
% 4.34/4.59 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[1649, 20083])).
% 4.34/4.59 tff(20085,plain,
% 4.34/4.59 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.34/4.59 inference(monotonicity,[status(thm)],[20077])).
% 4.34/4.59 tff(20086,plain,
% 4.34/4.59 ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) <=> (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 4.34/4.59 inference(monotonicity,[status(thm)],[20085])).
% 4.34/4.59 tff(20087,plain,
% 4.34/4.59 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.34/4.59 inference(modus_ponens,[status(thm)],[19902, 20086])).
% 4.34/4.59 tff(20088,plain,
% 4.34/4.59 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[3375, 20087, 20084])).
% 4.34/4.59 tff(20089,plain,
% 4.34/4.59 ((s(elem!1) = s(s(z))) <=> (s(elem!1) = elem!1)),
% 4.34/4.59 inference(monotonicity,[status(thm)],[20075])).
% 4.34/4.59 tff(20090,plain,
% 4.34/4.59 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(z)))),
% 4.34/4.59 inference(symmetry,[status(thm)],[20089])).
% 4.34/4.59 tff(20091,plain,
% 4.34/4.59 ((~(s(elem!1) = elem!1)) <=> (~(s(elem!1) = s(s(z))))),
% 4.34/4.59 inference(monotonicity,[status(thm)],[20090])).
% 4.34/4.59 tff(20092,plain,
% 4.34/4.59 (~(s(elem!1) = elem!1)),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[2150, 19901])).
% 4.34/4.59 tff(20093,plain,
% 4.34/4.59 (~(s(elem!1) = s(s(z)))),
% 4.34/4.59 inference(modus_ponens,[status(thm)],[20092, 20091])).
% 4.34/4.59 tff(20094,plain,
% 4.34/4.59 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[2840, 20093])).
% 4.34/4.59 tff(20095,plain,
% 4.34/4.59 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[4173, 20094, 3822])).
% 4.34/4.59 tff(20096,plain,
% 4.34/4.59 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[10679, 20095, 20075])).
% 4.34/4.59 tff(20097,plain,
% 4.34/4.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 4.34/4.59 inference(rewrite,[status(thm)],[])).
% 4.34/4.59 tff(20098,plain,
% 4.34/4.59 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 4.34/4.59 inference(rewrite,[status(thm)],[])).
% 4.34/4.59 tff(20099,plain,
% 4.34/4.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 4.34/4.59 inference(monotonicity,[status(thm)],[20098])).
% 4.34/4.59 tff(20100,plain,
% 4.34/4.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 4.34/4.59 inference(transitivity,[status(thm)],[20099, 20097])).
% 4.34/4.59 tff(20101,plain,
% 4.34/4.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))),
% 4.34/4.59 inference(quant_inst,[status(thm)],[])).
% 4.34/4.59 tff(20102,plain,
% 4.34/4.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 4.34/4.59 inference(modus_ponens,[status(thm)],[20101, 20100])).
% 4.34/4.59 tff(20103,plain,
% 4.34/4.59 (~b(s(s(s(elem!1))), elem!1)),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[20102, 178, 2042, 20096, 20088, 20079])).
% 4.34/4.59 tff(20104,plain,
% 4.34/4.59 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 4.34/4.59 inference(monotonicity,[status(thm)],[20075])).
% 4.34/4.59 tff(20105,plain,
% 4.34/4.59 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 4.34/4.59 inference(transitivity,[status(thm)],[20104, 3660])).
% 4.34/4.59 tff(20106,plain,
% 4.34/4.59 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = elem!1))),
% 4.34/4.59 inference(monotonicity,[status(thm)],[20105])).
% 4.34/4.59 tff(20107,plain,
% 4.34/4.59 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 4.34/4.59 inference(modus_ponens,[status(thm)],[244, 20106])).
% 4.34/4.59 tff(20108,plain,
% 4.34/4.59 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[3444, 20107, 18857])).
% 4.34/4.59 tff(20109,plain,
% 4.34/4.59 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.59 inference(monotonicity,[status(thm)],[20077])).
% 4.34/4.59 tff(20110,plain,
% 4.34/4.59 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.59 inference(modus_ponens,[status(thm)],[251, 20109])).
% 4.34/4.59 tff(20111,plain,
% 4.34/4.59 (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)))),
% 4.34/4.59 inference(monotonicity,[status(thm)],[20077])).
% 4.34/4.59 tff(20112,plain,
% 4.34/4.59 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.34/4.59 inference(modus_ponens,[status(thm)],[104, 20111])).
% 4.34/4.59 tff(20113,plain,
% 4.34/4.59 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 4.34/4.59 inference(monotonicity,[status(thm)],[20077])).
% 4.34/4.59 tff(20114,plain,
% 4.34/4.59 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(z)))), elem!1)),
% 4.34/4.59 inference(monotonicity,[status(thm)],[20075])).
% 4.34/4.59 tff(20115,plain,
% 4.34/4.59 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(elem!1)), elem!1)),
% 4.34/4.59 inference(transitivity,[status(thm)],[20114, 20113])).
% 4.34/4.59 tff(20116,plain,
% 4.34/4.59 (b(s(s(z)), s(s(s(s(z)))))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[17698, 20075, 1301])).
% 4.34/4.59 tff(20117,plain,
% 4.34/4.59 (~b(s(s(s(s(z)))), z)),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[18848, 20116])).
% 4.34/4.59 tff(20118,plain,
% 4.34/4.59 (r(s(s(s(s(z)))), z)),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[191, 20117])).
% 4.34/4.59 tff(20119,plain,
% 4.34/4.59 (b(s(s(z)), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 4.34/4.59 inference(monotonicity,[status(thm)],[20075])).
% 4.34/4.59 tff(20120,plain,
% 4.34/4.59 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 4.34/4.59 inference(symmetry,[status(thm)],[20119])).
% 4.34/4.59 tff(20121,plain,
% 4.34/4.59 (b(s(s(z)), s(s(s(elem!1))))),
% 4.34/4.59 inference(modus_ponens,[status(thm)],[2042, 20120])).
% 4.34/4.59 tff(20122,plain,
% 4.34/4.59 (~b(s(s(s(s(z)))), s(s(z)))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[10669, 20121, 557, 20116, 20094, 20118, 145])).
% 4.34/4.59 tff(20123,plain,
% 4.34/4.59 (r(s(s(s(s(z)))), s(s(z)))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[102, 20122])).
% 4.34/4.59 tff(20124,plain,
% 4.34/4.59 (r(s(s(elem!1)), elem!1)),
% 4.34/4.59 inference(modus_ponens,[status(thm)],[20123, 20115])).
% 4.34/4.59 tff(20125,plain,
% 4.34/4.59 (~r(s(s(s(elem!1))), elem!1)),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[18369, 20124, 20112, 20110, 3521, 20084, 20108, 20096])).
% 4.34/4.59 tff(20126,plain,
% 4.34/4.59 ($false),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[570, 20125, 20103, 19901])).
% 4.34/4.59 tff(20127,plain,((~b(z, elem!1)) | (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | b(s(s(z)), elem!1) | (~b(z, s(s(z)))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 4.34/4.59 tff(20128,plain,
% 4.34/4.59 (~b(z, elem!1)),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[20127, 3241, 2042, 557, 145, 251, 1301, 104, 3461, 595, 4254, 144, 290])).
% 4.34/4.59 tff(20129,plain,
% 4.34/4.59 (r(z, elem!1)),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[585, 20128, 318])).
% 4.34/4.59 tff(20130,plain,
% 4.34/4.59 (~r(s(s(s(elem!1))), elem!1)),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[565, 20129, 557])).
% 4.34/4.59 tff(20131,plain,
% 4.34/4.59 (b(s(s(s(elem!1))), elem!1)),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[570, 20130, 19901])).
% 4.34/4.59 tff(20132,plain,
% 4.34/4.59 (~(s(s(z)) = elem!1)),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[18165, 20129, 48])).
% 4.34/4.59 tff(20133,plain,
% 4.34/4.59 (r(s(s(z)), elem!1)),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[448, 20132, 3241])).
% 4.34/4.59 tff(20134,plain,
% 4.34/4.59 (~r(elem!1, s(s(s(s(z)))))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[529, 20129, 145])).
% 4.34/4.59 tff(20135,plain,
% 4.34/4.59 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[17566, 17765, 438])).
% 4.34/4.59 tff(20136,plain,
% 4.34/4.59 (b(s(s(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))))))))),
% 4.34/4.59 inference(monotonicity,[status(thm)],[546])).
% 4.34/4.59 tff(20137,plain,
% 4.34/4.59 (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))))))))),
% 4.34/4.59 inference(symmetry,[status(thm)],[20136])).
% 4.34/4.59 tff(20138,plain,
% 4.34/4.59 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.59 inference(modus_ponens,[status(thm)],[251, 20137])).
% 4.34/4.59 tff(20139,plain,
% 4.34/4.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), 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(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), 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(elem!1, s(s(s(s(z)))))))),
% 4.34/4.59 inference(rewrite,[status(thm)],[])).
% 4.34/4.59 tff(20140,plain,
% 4.34/4.59 (((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(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)))))))))) <=> ((~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))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 4.34/4.59 inference(rewrite,[status(thm)],[])).
% 4.34/4.59 tff(20141,plain,
% 4.34/4.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), 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(elem!1, s(s(s(s(z))))))))),
% 4.34/4.59 inference(monotonicity,[status(thm)],[20140])).
% 4.34/4.59 tff(20142,plain,
% 4.34/4.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), 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(elem!1, s(s(s(s(z)))))))),
% 4.34/4.59 inference(transitivity,[status(thm)],[20141, 20139])).
% 4.34/4.59 tff(20143,plain,
% 4.34/4.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(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))))))))))),
% 4.34/4.59 inference(quant_inst,[status(thm)],[])).
% 4.34/4.59 tff(20144,plain,
% 4.34/4.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z))))))),
% 4.34/4.59 inference(modus_ponens,[status(thm)],[20143, 20142])).
% 4.34/4.59 tff(20145,plain,
% 4.34/4.59 ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[20144, 178, 1597, 104, 1301])).
% 4.34/4.59 tff(20146,plain,
% 4.34/4.59 (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[20145, 18209])).
% 4.34/4.59 tff(20147,plain,
% 4.34/4.59 ($false),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[20146, 20138])).
% 4.34/4.59 tff(20148,plain,((~(s(elem!1) = s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.34/4.59 tff(20149,plain,
% 4.34/4.59 (~(s(elem!1) = s(s(z)))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[20148, 20135, 1597, 104, 1301, 251])).
% 4.34/4.59 tff(20150,plain,
% 4.34/4.59 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[2840, 20149])).
% 4.34/4.59 tff(20151,plain,
% 4.34/4.59 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[4173, 20150, 3822])).
% 4.34/4.59 tff(20152,plain,
% 4.34/4.59 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[7917, 20150])).
% 4.34/4.59 tff(20153,plain,
% 4.34/4.59 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[10664, 20152, 19902])).
% 4.34/4.59 tff(20154,plain,
% 4.34/4.59 (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[4103, 20153, 104, 251, 20151])).
% 4.34/4.59 tff(20155,plain,
% 4.34/4.59 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[10584, 20154, 1597])).
% 4.34/4.59 tff(20156,plain,
% 4.34/4.59 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[16380, 20155, 273, 251, 104, 469, 521, 530, 438])).
% 4.34/4.59 tff(20157,plain,
% 4.34/4.59 (~b(s(s(s(s(z)))), elem!1)),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[17755, 20155, 557, 438, 3461, 3792, 273, 1301, 4254, 145, 166, 20150, 104, 2484, 19902, 3822])).
% 4.34/4.59 tff(20158,plain,
% 4.34/4.59 (r(s(s(s(s(z)))), elem!1)),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[3142, 20157, 551])).
% 4.34/4.59 tff(20159,plain,
% 4.34/4.59 (~b(s(s(s(s(z)))), s(s(z)))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[9471, 20158, 104, 251, 438, 20156])).
% 4.34/4.59 tff(20160,plain,
% 4.34/4.59 (~r(s(s(s(s(z)))), s(s(z)))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[3329, 20158, 438])).
% 4.34/4.59 tff(20161,plain,
% 4.34/4.59 ($false),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[102, 20160, 20159])).
% 4.34/4.59 tff(20162,plain,((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(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)))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(z))) | (elem!1 = s(s(s(s(z))))) | (~r(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.59 tff(20163,plain,
% 4.34/4.59 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[20162, 20133, 104, 251, 557, 3461, 144, 1301, 145, 3340, 469, 20129, 20131, 595])).
% 4.34/4.59 tff(20164,plain,
% 4.34/4.59 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[249, 20163])).
% 4.34/4.59 tff(20165,plain,
% 4.34/4.59 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[2803, 20164, 20133])).
% 4.34/4.59 tff(20166,plain,
% 4.34/4.59 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[16380, 20165, 144, 251, 104, 469, 20129, 20134, 20133])).
% 4.34/4.59 tff(20167,plain,
% 4.34/4.59 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[10584, 20166, 20131])).
% 4.34/4.59 tff(20168,plain,
% 4.34/4.59 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[11351, 20164, 20133])).
% 4.34/4.59 tff(20169,plain,
% 4.34/4.59 (~(s(elem!1) = s(s(z)))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[20148, 20168, 20131, 104, 1301, 251])).
% 4.34/4.59 tff(20170,plain,
% 4.34/4.59 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[2840, 20169])).
% 4.34/4.59 tff(20171,plain,
% 4.34/4.59 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[4173, 20170, 3822])).
% 4.34/4.59 tff(20172,plain,
% 4.34/4.59 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[7917, 20170])).
% 4.34/4.59 tff(20173,plain,
% 4.34/4.59 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[10664, 20172, 19902])).
% 4.34/4.59 tff(20174,plain,
% 4.34/4.59 ($false),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[4103, 20173, 20171, 104, 251, 20167])).
% 4.34/4.59 tff(20175,plain,(b(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)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))) | (elem!1 = s(s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | r(z, s(s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 4.34/4.59 tff(20176,plain,
% 4.34/4.59 (b(s(s(z)), elem!1)),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[20175, 557, 18255, 18843, 469, 104, 10793, 47, 17173, 48, 19900, 290])).
% 4.34/4.59 tff(20177,plain,
% 4.34/4.59 (~b(s(s(z)), s(s(z)))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[16833, 178, 3461, 273])).
% 4.34/4.59 tff(20178,plain,
% 4.34/4.59 (~(elem!1 = s(s(z)))),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[3238, 817, 20177])).
% 4.34/4.59 tff(20179,plain,
% 4.34/4.59 ($false),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[19655, 18858, 818, 817, 273, 3461, 286, 20178])).
% 4.34/4.59 tff(20180,plain,((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | b(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(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.34/4.59 tff(20181,plain,
% 4.34/4.59 (~b(z, elem!1)),
% 4.34/4.59 inference(unit_resolution,[status(thm)],[20180, 286, 273, 3461, 817, 104, 595, 1301])).
% 4.34/4.60 tff(20182,plain,
% 4.34/4.60 (r(z, elem!1)),
% 4.34/4.60 inference(unit_resolution,[status(thm)],[585, 20181, 507])).
% 4.34/4.60 tff(20183,plain,
% 4.34/4.60 (~r(s(s(s(elem!1))), elem!1)),
% 4.34/4.60 inference(unit_resolution,[status(thm)],[565, 20182, 557])).
% 4.34/4.60 tff(20184,plain,
% 4.34/4.60 (b(s(s(s(elem!1))), elem!1)),
% 4.34/4.60 inference(unit_resolution,[status(thm)],[570, 20183, 19901])).
% 4.34/4.60 tff(20185,plain,
% 4.34/4.60 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.34/4.60 inference(unit_resolution,[status(thm)],[20148, 20184, 515, 104, 1301, 251])).
% 4.34/4.60 tff(20186,plain,
% 4.34/4.60 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.34/4.60 inference(modus_ponens,[status(thm)],[20185, 603])).
% 4.34/4.60 tff(20187,plain,
% 4.34/4.60 (b(s(elem!1), elem!1) <=> b(s(s(z)), elem!1)),
% 4.34/4.60 inference(monotonicity,[status(thm)],[515])).
% 4.34/4.60 tff(20188,plain,
% 4.34/4.60 (b(s(s(z)), elem!1) <=> b(s(elem!1), elem!1)),
% 4.34/4.60 inference(symmetry,[status(thm)],[20187])).
% 4.34/4.60 tff(20189,plain,
% 4.34/4.60 (b(s(elem!1), elem!1)),
% 4.34/4.60 inference(modus_ponens,[status(thm)],[817, 20188])).
% 4.34/4.60 tff(20190,plain,
% 4.34/4.60 (~(elem!1 = s(elem!1))),
% 4.34/4.60 inference(unit_resolution,[status(thm)],[748, 20092])).
% 4.34/4.60 tff(20191,plain,
% 4.34/4.60 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(z)))), elem!1)),
% 4.34/4.60 inference(symmetry,[status(thm)],[12391])).
% 4.34/4.60 tff(20192,plain,
% 4.34/4.60 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 4.34/4.60 inference(transitivity,[status(thm)],[547, 20191])).
% 4.34/4.60 tff(20193,plain,
% 4.34/4.60 (b(s(s(s(s(z)))), elem!1)),
% 4.34/4.60 inference(modus_ponens,[status(thm)],[20184, 20192])).
% 4.34/4.60 tff(20194,plain,
% 4.34/4.60 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.60 inference(unit_resolution,[status(thm)],[19723, 20193])).
% 4.34/4.60 tff(20195,plain,
% 4.34/4.60 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.34/4.60 inference(unit_resolution,[status(thm)],[691, 20194, 12393])).
% 4.34/4.60 tff(20196,plain,
% 4.34/4.60 (~r(elem!1, s(elem!1))),
% 4.34/4.60 inference(unit_resolution,[status(thm)],[2935, 20195, 19543])).
% 4.34/4.60 tff(20197,plain,
% 4.34/4.60 (b(elem!1, s(elem!1))),
% 4.34/4.60 inference(unit_resolution,[status(thm)],[756, 20196, 20190])).
% 4.34/4.60 tff(20198,plain,
% 4.34/4.60 (~b(s(s(elem!1)), elem!1)),
% 4.34/4.60 inference(unit_resolution,[status(thm)],[11607, 20197, 557, 1510, 20189, 20184, 15140, 2042])).
% 4.34/4.60 tff(20199,plain,
% 4.34/4.60 (r(s(s(elem!1)), elem!1)),
% 4.34/4.60 inference(unit_resolution,[status(thm)],[3362, 20198, 15139])).
% 4.34/4.60 tff(20200,plain,
% 4.34/4.60 (r(s(s(s(z))), s(z))),
% 4.34/4.60 inference(modus_ponens,[status(thm)],[20199, 15178])).
% 4.34/4.60 tff(20201,plain,
% 4.34/4.60 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))))),
% 4.34/4.60 inference(rewrite,[status(thm)],[])).
% 4.34/4.60 tff(20202,plain,
% 4.34/4.60 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))))),
% 4.34/4.60 inference(rewrite,[status(thm)],[])).
% 4.34/4.60 tff(20203,plain,
% 4.34/4.60 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z)))))),
% 4.34/4.60 inference(monotonicity,[status(thm)],[20202])).
% 4.34/4.60 tff(20204,plain,
% 4.34/4.60 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z))))),
% 4.34/4.60 inference(transitivity,[status(thm)],[20203, 20201])).
% 4.34/4.60 tff(20205,plain,
% 4.34/4.60 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.44/4.60 inference(quant_inst,[status(thm)],[])).
% 4.44/4.60 tff(20206,plain,
% 4.44/4.60 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(z)))),
% 4.44/4.60 inference(modus_ponens,[status(thm)],[20205, 20204])).
% 4.44/4.60 tff(20207,plain,
% 4.44/4.60 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.60 inference(unit_resolution,[status(thm)],[20206, 118, 20200, 20186])).
% 4.44/4.60 tff(20208,plain,
% 4.44/4.60 (r(z, s(z)) <=> r(z, elem!1)),
% 4.44/4.60 inference(monotonicity,[status(thm)],[534])).
% 4.44/4.60 tff(20209,plain,
% 4.44/4.60 (r(z, elem!1) <=> r(z, s(z))),
% 4.44/4.60 inference(symmetry,[status(thm)],[20208])).
% 4.44/4.60 tff(20210,plain,
% 4.44/4.60 (r(z, s(z))),
% 4.44/4.60 inference(modus_ponens,[status(thm)],[20182, 20209])).
% 4.44/4.60 tff(20211,plain,
% 4.44/4.60 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))))),
% 4.44/4.60 inference(rewrite,[status(thm)],[])).
% 4.44/4.60 tff(20212,plain,
% 4.44/4.60 (((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))))),
% 4.44/4.60 inference(rewrite,[status(thm)],[])).
% 4.44/4.60 tff(20213,plain,
% 4.44/4.60 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z)))))),
% 4.44/4.60 inference(monotonicity,[status(thm)],[20212])).
% 4.44/4.60 tff(20214,plain,
% 4.44/4.60 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))))),
% 4.44/4.60 inference(transitivity,[status(thm)],[20213, 20211])).
% 4.44/4.60 tff(20215,plain,
% 4.44/4.60 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))),
% 4.44/4.60 inference(quant_inst,[status(thm)],[])).
% 4.44/4.60 tff(20216,plain,
% 4.44/4.60 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z)))),
% 4.44/4.60 inference(modus_ponens,[status(thm)],[20215, 20214])).
% 4.44/4.60 tff(20217,plain,
% 4.44/4.60 (~r(z, s(s(s(z))))),
% 4.44/4.60 inference(unit_resolution,[status(thm)],[20216, 118, 20200, 20210])).
% 4.44/4.60 tff(20218,plain,
% 4.44/4.60 (b(z, s(s(s(z))))),
% 4.44/4.60 inference(unit_resolution,[status(thm)],[4920, 20217])).
% 4.44/4.60 tff(20219,plain,
% 4.44/4.60 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.44/4.60 inference(unit_resolution,[status(thm)],[11027, 20185, 20182])).
% 4.44/4.60 tff(20220,plain,
% 4.44/4.60 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.44/4.60 inference(unit_resolution,[status(thm)],[133, 20219])).
% 4.44/4.60 tff(20221,plain,
% 4.44/4.60 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.44/4.60 inference(unit_resolution,[status(thm)],[18239, 20220, 595, 3461, 273, 287, 145])).
% 4.44/4.60 tff(20222,plain,
% 4.44/4.60 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.44/4.60 inference(unit_resolution,[status(thm)],[10755, 20221])).
% 4.44/4.60 tff(20223,plain,
% 4.44/4.60 ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 4.44/4.60 inference(unit_resolution,[status(thm)],[8267, 178, 104, 595, 20222])).
% 4.44/4.60 tff(20224,plain,
% 4.44/4.60 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.60 inference(unit_resolution,[status(thm)],[20223, 20218])).
% 4.44/4.60 tff(20225,plain,
% 4.44/4.60 ($false),
% 4.44/4.60 inference(unit_resolution,[status(thm)],[5031, 41, 20224, 20207, 10712])).
% 4.44/4.60 tff(20226,plain,(b(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(z, s(s(s(s(s(s(s(z))))))))) | (~(s(elem!1) = s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (z = elem!1) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.60 tff(20227,plain,
% 4.44/4.60 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.60 inference(unit_resolution,[status(thm)],[20226, 515, 595, 104, 557, 2042, 1301, 251, 5619, 273, 47, 318, 817])).
% 4.44/4.60 tff(20228,plain,
% 4.44/4.60 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.44/4.60 inference(unit_resolution,[status(thm)],[17204, 20227, 273, 5619, 595])).
% 4.44/4.60 tff(20229,plain,
% 4.44/4.60 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.44/4.60 inference(unit_resolution,[status(thm)],[3578, 20228])).
% 4.44/4.60 tff(20230,plain,
% 4.44/4.60 (~(elem!1 = s(s(z)))),
% 4.44/4.60 inference(unit_resolution,[status(thm)],[3238, 817, 16834])).
% 4.44/4.60 tff(20231,plain,
% 4.44/4.60 (~r(z, elem!1)),
% 4.44/4.60 inference(unit_resolution,[status(thm)],[17498, 166, 595, 1301, 273, 5619, 817, 104, 15168])).
% 4.44/4.60 tff(20232,plain,
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% 4.44/4.60 inference(unit_resolution,[status(thm)],[585, 20231, 318])).
% 4.44/4.60 tff(20233,plain,
% 4.44/4.60 (~b(elem!1, s(s(z)))),
% 4.44/4.60 inference(unit_resolution,[status(thm)],[10893, 20232, 273, 5619, 817])).
% 4.44/4.60 tff(20234,plain,
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% 4.44/4.60 inference(unit_resolution,[status(thm)],[467, 20233, 20230])).
% 4.44/4.60 tff(20235,plain,
% 4.44/4.60 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.44/4.60 inference(unit_resolution,[status(thm)],[1309, 20232, 104, 595, 1301])).
% 4.44/4.60 tff(20236,plain,
% 4.44/4.60 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.44/4.60 inference(unit_resolution,[status(thm)],[691, 20235, 12393])).
% 4.44/4.60 tff(20237,plain,
% 4.44/4.60 (~b(elem!1, z)),
% 4.44/4.60 inference(unit_resolution,[status(thm)],[11004, 20232, 5619, 273, 817])).
% 4.44/4.60 tff(20238,plain,
% 4.44/4.60 (b(s(elem!1), s(s(z))) <=> b(s(s(z)), s(s(z)))),
% 4.44/4.60 inference(monotonicity,[status(thm)],[515])).
% 4.44/4.60 tff(20239,plain,
% 4.44/4.60 (b(s(s(z)), s(s(z))) <=> b(s(elem!1), s(s(z)))),
% 4.44/4.60 inference(symmetry,[status(thm)],[20238])).
% 4.44/4.60 tff(20240,plain,
% 4.44/4.60 ((~b(s(s(z)), s(s(z)))) <=> (~b(s(elem!1), s(s(z))))),
% 4.44/4.60 inference(monotonicity,[status(thm)],[20239])).
% 4.44/4.60 tff(20241,plain,
% 4.44/4.60 (~b(s(elem!1), s(s(z)))),
% 4.44/4.60 inference(modus_ponens,[status(thm)],[16834, 20240])).
% 4.44/4.60 tff(20242,plain,
% 4.44/4.60 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(z)))),
% 4.44/4.60 inference(monotonicity,[status(thm)],[515])).
% 4.44/4.60 tff(20243,plain,
% 4.44/4.60 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(z)) = s(s(s(s(z)))))),
% 4.44/4.60 inference(transitivity,[status(thm)],[20242, 157])).
% 4.44/4.60 tff(20244,plain,
% 4.44/4.60 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 4.44/4.60 inference(symmetry,[status(thm)],[20243])).
% 4.44/4.60 tff(20245,plain,
% 4.44/4.60 ((s(s(z)) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 4.44/4.60 inference(transitivity,[status(thm)],[20244, 2164])).
% 4.44/4.60 tff(20246,plain,
% 4.44/4.60 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 4.44/4.60 inference(monotonicity,[status(thm)],[20245])).
% 4.44/4.60 tff(20247,plain,
% 4.44/4.60 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.44/4.60 inference(modus_ponens,[status(thm)],[159, 20246])).
% 4.44/4.60 tff(20248,plain,
% 4.44/4.60 (~(s(s(z)) = elem!1)),
% 4.44/4.60 inference(unit_resolution,[status(thm)],[3230, 20230])).
% 4.44/4.60 tff(20249,plain,
% 4.44/4.60 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 4.44/4.60 inference(monotonicity,[status(thm)],[515])).
% 4.44/4.60 tff(20250,plain,
% 4.44/4.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 4.44/4.60 inference(rewrite,[status(thm)],[])).
% 4.44/4.60 tff(20251,plain,
% 4.44/4.60 (((~b(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(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1)))) <=> ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 4.44/4.60 inference(rewrite,[status(thm)],[])).
% 4.44/4.60 tff(20252,plain,
% 4.44/4.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 4.44/4.60 inference(monotonicity,[status(thm)],[20251])).
% 4.44/4.60 tff(20253,plain,
% 4.44/4.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 4.44/4.60 inference(transitivity,[status(thm)],[20252, 20250])).
% 4.44/4.60 tff(20254,plain,
% 4.44/4.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))))),
% 4.44/4.60 inference(quant_inst,[status(thm)],[])).
% 4.44/4.60 tff(20255,plain,
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% 4.44/4.60 inference(modus_ponens,[status(thm)],[20254, 20253])).
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% 4.44/4.60 tff(20258,plain,
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% 4.44/4.60 inference(unit_resolution,[status(thm)],[20257, 20232, 1301, 20189, 1388])).
% 4.44/4.60 tff(20259,plain,
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% 4.44/4.60 tff(20260,plain,
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% 4.44/4.60 inference(modus_ponens,[status(thm)],[20259, 20249])).
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% 4.44/4.60 tff(20262,plain,
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% 4.44/4.60 tff(20263,plain,
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% 4.44/4.60 tff(20264,plain,
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% 4.44/4.60 inference(unit_resolution,[status(thm)],[3113, 1265, 450])).
% 4.44/4.60 tff(20265,plain,
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% 4.44/4.60 inference(unit_resolution,[status(thm)],[249, 20264])).
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% 4.44/4.60 tff(20267,plain,
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% 4.44/4.60 inference(unit_resolution,[status(thm)],[259, 20267, 20265, 104, 202, 167])).
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% 4.44/4.60 tff(20270,plain,
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% 4.44/4.60 inference(unit_resolution,[status(thm)],[20269, 20263, 20261, 20236, 104, 20234, 817, 551])).
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% 4.44/4.60 tff(20272,plain,
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% 4.44/4.60 inference(unit_resolution,[status(thm)],[17492, 20227])).
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% 4.44/4.60 tff(20277,plain,
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% 4.44/4.60 inference(unit_resolution,[status(thm)],[20276, 20176, 144, 17173, 557, 290, 104, 1, 10792, 469, 18843, 19900, 18255])).
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% 4.44/4.60 inference(unit_resolution,[status(thm)],[2840, 20277])).
% 4.44/4.60 tff(20279,plain,
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% 4.44/4.60 tff(20280,plain,
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% 4.44/4.60 inference(unit_resolution,[status(thm)],[19720, 557, 47])).
% 4.44/4.60 tff(20281,plain,
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% 4.44/4.60 inference(unit_resolution,[status(thm)],[7917, 20278])).
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% 4.44/4.60 tff(20283,plain,
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% 4.44/4.60 tff(20285,plain,
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% 4.44/4.60 inference(modus_ponens,[status(thm)],[20290, 20289])).
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% 4.44/4.60 tff(20298,plain,
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% 4.44/4.60 tff(20299,plain,
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% 4.44/4.60 tff(20300,plain,
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% 4.44/4.60 tff(20301,plain,
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% 4.44/4.60 tff(20304,plain,
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% 4.44/4.60 tff(20307,plain,
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% 4.44/4.60 tff(20310,plain,
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% 4.44/4.60 tff(20311,plain,
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% 4.44/4.60 inference(unit_resolution,[status(thm)],[17204, 20310, 273, 3461, 595])).
% 4.44/4.60 tff(20312,plain,
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% 4.44/4.60 inference(unit_resolution,[status(thm)],[3578, 20311])).
% 4.44/4.60 tff(20313,plain,
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% 4.44/4.60 inference(unit_resolution,[status(thm)],[17492, 20310])).
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% 4.44/4.60 tff(20315,plain,
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% 4.44/4.60 tff(20316,plain,
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% 4.44/4.60 inference(unit_resolution,[status(thm)],[585, 20315, 507])).
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% 4.44/4.60 inference(unit_resolution,[status(thm)],[10893, 20316, 273, 3461, 817])).
% 4.44/4.60 tff(20318,plain,
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% 4.44/4.60 tff(20321,plain,
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% 4.44/4.60 tff(20322,plain,
% 4.44/4.60 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
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% 4.44/4.60 tff(20323,plain,
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% 4.44/4.60 inference(monotonicity,[status(thm)],[20322])).
% 4.44/4.60 tff(20324,plain,
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% 4.44/4.60 inference(monotonicity,[status(thm)],[20323])).
% 4.44/4.60 tff(20325,plain,
% 4.44/4.60 (s(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(s(elem!1)))),
% 4.44/4.60 inference(symmetry,[status(thm)],[20324])).
% 4.44/4.60 tff(20326,plain,
% 4.44/4.60 (b(s(s(s(s(s(s(s(s(s(s(z)))))))))), z) <=> b(s(s(s(elem!1))), z)),
% 4.44/4.60 inference(monotonicity,[status(thm)],[20325])).
% 4.44/4.60 tff(20327,plain,
% 4.44/4.60 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)),
% 4.44/4.60 inference(symmetry,[status(thm)],[20326])).
% 4.44/4.60 tff(20328,plain,
% 4.44/4.60 (r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.60 inference(monotonicity,[status(thm)],[20325])).
% 4.44/4.60 tff(20329,plain,
% 4.44/4.60 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.60 inference(symmetry,[status(thm)],[20328])).
% 4.44/4.60 tff(20330,plain,
% 4.44/4.60 (~(s(s(s(elem!1))) = elem!1)),
% 4.44/4.60 inference(unit_resolution,[status(thm)],[16438, 19900])).
% 4.44/4.60 tff(20331,plain,
% 4.44/4.60 (~b(s(s(s(elem!1))), elem!1)),
% 4.44/4.60 inference(unit_resolution,[status(thm)],[10584, 20321, 20283])).
% 4.44/4.60 tff(20332,plain,
% 4.44/4.60 (r(s(s(s(elem!1))), elem!1)),
% 4.44/4.60 inference(unit_resolution,[status(thm)],[570, 20331, 20330])).
% 4.44/4.60 tff(20333,plain,
% 4.44/4.60 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.60 inference(unit_resolution,[status(thm)],[19937, 20332, 20321])).
% 4.44/4.60 tff(20334,plain,
% 4.44/4.60 (r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.60 inference(modus_ponens,[status(thm)],[20333, 20329])).
% 4.44/4.60 tff(20335,plain,
% 4.44/4.60 (r(elem!1, z) <=> r(s(s(s(s(s(s(s(z))))))), z)),
% 4.44/4.60 inference(monotonicity,[status(thm)],[20321])).
% 4.44/4.60 tff(20336,plain,
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% 4.44/4.60 inference(unit_resolution,[status(thm)],[565, 20332, 557])).
% 4.44/4.61 tff(20337,plain,
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% 4.44/4.61 inference(unit_resolution,[status(thm)],[585, 20336, 318])).
% 4.44/4.61 tff(20338,plain,
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% 4.44/4.61 inference(unit_resolution,[status(thm)],[11004, 20337, 10793, 144, 20176])).
% 4.44/4.61 tff(20339,plain,
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% 4.44/4.61 inference(unit_resolution,[status(thm)],[498, 20338, 290])).
% 4.44/4.61 tff(20340,plain,
% 4.44/4.61 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.44/4.61 inference(modus_ponens,[status(thm)],[20339, 20335])).
% 4.44/4.61 tff(20341,plain,
% 4.44/4.61 (r(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)),
% 4.44/4.61 inference(modus_ponens,[status(thm)],[1552, 10553])).
% 4.44/4.61 tff(20342,plain,
% 4.44/4.61 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))))),
% 4.44/4.61 inference(rewrite,[status(thm)],[])).
% 4.44/4.61 tff(20343,plain,
% 4.44/4.61 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))))),
% 4.44/4.61 inference(quant_inst,[status(thm)],[])).
% 4.44/4.61 tff(20344,plain,
% 4.44/4.61 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z)))))))))),
% 4.44/4.61 inference(modus_ponens,[status(thm)],[20343, 20342])).
% 4.44/4.61 tff(20345,plain,
% 4.44/4.61 (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[20344, 118, 108, 19940])).
% 4.44/4.61 tff(20346,plain,
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% 4.44/4.61 inference(unit_resolution,[status(thm)],[20345, 20341])).
% 4.44/4.61 tff(20347,plain,((~r(s(s(s(elem!1))), z)) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.61 tff(20348,plain,
% 4.44/4.61 (~r(s(s(s(elem!1))), z)),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[20347, 20321, 20340, 20334])).
% 4.44/4.61 tff(20349,plain,
% 4.44/4.61 (b(s(s(s(elem!1))), z)),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[1565, 20348])).
% 4.44/4.61 tff(20350,plain,
% 4.44/4.61 (b(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)),
% 4.44/4.61 inference(modus_ponens,[status(thm)],[20349, 20327])).
% 4.44/4.61 tff(20351,plain,
% 4.44/4.61 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[10835, 20321, 20176])).
% 4.44/4.61 tff(20352,plain,
% 4.44/4.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))))),
% 4.44/4.61 inference(rewrite,[status(thm)],[])).
% 4.44/4.61 tff(20353,plain,
% 4.44/4.61 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))))),
% 4.44/4.61 inference(rewrite,[status(thm)],[])).
% 4.44/4.61 tff(20354,plain,
% 4.44/4.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z))))))),
% 4.44/4.61 inference(monotonicity,[status(thm)],[20353])).
% 4.44/4.61 tff(20355,plain,
% 4.44/4.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))))),
% 4.44/4.61 inference(transitivity,[status(thm)],[20354, 20352])).
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% 4.44/4.61 inference(quant_inst,[status(thm)],[])).
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% 4.44/4.61 inference(modus_ponens,[status(thm)],[20356, 20355])).
% 4.44/4.61 tff(20358,plain,
% 4.44/4.61 ((~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z))))),
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% 4.44/4.61 tff(20359,plain,
% 4.44/4.61 (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[20358, 20350])).
% 4.44/4.61 tff(20360,plain,
% 4.44/4.61 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))),
% 4.44/4.61 inference(monotonicity,[status(thm)],[20324])).
% 4.44/4.61 tff(20361,plain,
% 4.44/4.61 ((~r(s(s(s(elem!1))), s(s(z)))) <=> (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z))))),
% 4.44/4.61 inference(monotonicity,[status(thm)],[20360])).
% 4.44/4.61 tff(20362,plain,
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% 4.44/4.61 tff(20363,plain,
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% 4.44/4.61 tff(20364,plain,
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% 4.44/4.61 inference(unit_resolution,[status(thm)],[10893, 20337, 144, 10793, 20176])).
% 4.44/4.61 tff(20365,plain,
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% 4.44/4.61 tff(20366,plain,
% 4.44/4.61 (~r(s(s(s(elem!1))), s(s(z)))),
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% 4.44/4.61 tff(20367,plain,
% 4.44/4.61 (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))),
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% 4.44/4.61 tff(20368,plain,
% 4.44/4.61 (s(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(z))),
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% 4.44/4.61 tff(20369,plain,
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% 4.44/4.61 tff(20370,plain,
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% 4.44/4.61 tff(20371,plain,
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% 4.44/4.61 tff(20372,plain,((~r(z, s(s(s(elem!1))))) | (elem!1 = z) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (elem!1 = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.61 tff(20373,plain,
% 4.44/4.61 (~r(z, s(s(s(elem!1))))),
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% 4.44/4.61 tff(20374,plain,
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% 4.44/4.61 tff(20375,plain,
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% 4.44/4.61 inference(unit_resolution,[status(thm)],[17598, 20374, 1])).
% 4.44/4.61 tff(20376,plain,
% 4.44/4.61 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
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% 4.44/4.61 tff(20377,plain,
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% 4.44/4.61 inference(unit_resolution,[status(thm)],[18165, 521, 48])).
% 4.44/4.61 tff(20378,plain,
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% 4.44/4.61 tff(20379,plain,
% 4.44/4.61 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[2803, 20378, 224])).
% 4.44/4.61 tff(20380,plain,
% 4.44/4.61 ($false),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[16380, 20379, 20378, 144, 251, 104, 469, 701, 530, 521])).
% 4.44/4.61 tff(20381,plain,((~r(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)))))) | (elem!1 = s(s(s(s(z))))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | b(s(s(z)), elem!1) | r(z, s(s(z))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.61 tff(20382,plain,
% 4.44/4.61 (~r(z, elem!1)),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[20381, 224, 104, 469, 701, 251, 3241, 48, 145])).
% 4.44/4.61 tff(20383,plain,
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% 4.44/4.61 inference(unit_resolution,[status(thm)],[585, 20382, 507])).
% 4.44/4.61 tff(20384,plain,
% 4.44/4.61 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
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% 4.44/4.61 tff(20385,plain,
% 4.44/4.61 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[691, 20384, 701])).
% 4.44/4.61 tff(20386,plain,
% 4.44/4.61 (~r(s(s(z)), elem!1)),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[2803, 20385, 224])).
% 4.44/4.61 tff(20387,plain,
% 4.44/4.61 (s(s(z)) = elem!1),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[448, 20386, 3241])).
% 4.44/4.61 tff(20388,plain,
% 4.44/4.61 (s(s(s(z))) = s(elem!1)),
% 4.44/4.61 inference(monotonicity,[status(thm)],[20387])).
% 4.44/4.61 tff(20389,plain,
% 4.44/4.61 (s(s(s(s(z)))) = s(s(elem!1))),
% 4.44/4.61 inference(monotonicity,[status(thm)],[20388])).
% 4.44/4.61 tff(20390,plain,
% 4.44/4.61 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 4.44/4.61 inference(monotonicity,[status(thm)],[20389])).
% 4.44/4.61 tff(20391,plain,
% 4.44/4.61 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 4.44/4.61 inference(transitivity,[status(thm)],[20390, 3400])).
% 4.44/4.61 tff(20392,plain,
% 4.44/4.61 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 4.44/4.61 inference(monotonicity,[status(thm)],[20391])).
% 4.44/4.61 tff(20393,plain,
% 4.44/4.61 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 4.44/4.61 inference(modus_ponens,[status(thm)],[2857, 20392])).
% 4.44/4.61 tff(20394,plain,
% 4.44/4.61 (r(s(s(s(s(z)))), z) <=> r(s(s(elem!1)), z)),
% 4.44/4.61 inference(monotonicity,[status(thm)],[20389])).
% 4.44/4.61 tff(20395,plain,
% 4.44/4.61 (b(s(s(z)), s(s(s(s(z)))))),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[17698, 20387, 1301])).
% 4.44/4.61 tff(20396,plain,
% 4.44/4.61 ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[14128, 178, 5619, 251, 595])).
% 4.44/4.61 tff(20397,plain,
% 4.44/4.61 (~b(s(s(s(s(z)))), z)),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[20396, 20395])).
% 4.44/4.61 tff(20398,plain,
% 4.44/4.61 (r(s(s(s(s(z)))), z)),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[191, 20397])).
% 4.44/4.61 tff(20399,plain,
% 4.44/4.61 (r(s(s(elem!1)), z)),
% 4.44/4.61 inference(modus_ponens,[status(thm)],[20398, 20394])).
% 4.44/4.61 tff(20400,plain,
% 4.44/4.61 (b(s(s(z)), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 4.44/4.61 inference(monotonicity,[status(thm)],[20387])).
% 4.44/4.61 tff(20401,plain,
% 4.44/4.61 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 4.44/4.61 inference(symmetry,[status(thm)],[20400])).
% 4.44/4.61 tff(20402,plain,
% 4.44/4.61 (b(s(s(z)), s(s(s(elem!1))))),
% 4.44/4.61 inference(modus_ponens,[status(thm)],[2042, 20401])).
% 4.44/4.61 tff(20403,plain,
% 4.44/4.61 (~b(s(s(s(elem!1))), z)),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[7978, 20402, 144, 5619, 2043])).
% 4.44/4.61 tff(20404,plain,
% 4.44/4.61 (r(s(s(s(elem!1))), z)),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[1565, 20403])).
% 4.44/4.61 tff(20405,plain,
% 4.44/4.61 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[16880, 118, 20404, 20399])).
% 4.44/4.61 tff(20406,plain,
% 4.44/4.61 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[3375, 20405, 20393])).
% 4.44/4.61 tff(20407,plain,
% 4.44/4.61 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.61 inference(monotonicity,[status(thm)],[20389])).
% 4.44/4.61 tff(20408,plain,
% 4.44/4.61 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.61 inference(modus_ponens,[status(thm)],[251, 20407])).
% 4.44/4.61 tff(20409,plain,
% 4.44/4.61 (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)))),
% 4.44/4.61 inference(monotonicity,[status(thm)],[20389])).
% 4.44/4.61 tff(20410,plain,
% 4.44/4.61 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.44/4.61 inference(modus_ponens,[status(thm)],[104, 20409])).
% 4.44/4.61 tff(20411,plain,
% 4.44/4.61 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(elem!1)))),
% 4.44/4.61 inference(monotonicity,[status(thm)],[20389])).
% 4.44/4.61 tff(20412,plain,
% 4.44/4.61 (b(elem!1, s(s(elem!1)))),
% 4.44/4.61 inference(modus_ponens,[status(thm)],[1301, 20411])).
% 4.44/4.61 tff(20413,plain,
% 4.44/4.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 4.44/4.61 inference(rewrite,[status(thm)],[])).
% 4.44/4.61 tff(20414,plain,
% 4.44/4.61 (((~b(elem!1, 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(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 4.44/4.61 inference(rewrite,[status(thm)],[])).
% 4.44/4.61 tff(20415,plain,
% 4.44/4.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, 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(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 4.44/4.61 inference(monotonicity,[status(thm)],[20414])).
% 4.44/4.61 tff(20416,plain,
% 4.44/4.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, 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(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 4.44/4.61 inference(transitivity,[status(thm)],[20415, 20413])).
% 4.44/4.61 tff(20417,plain,
% 4.44/4.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, 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(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 4.44/4.61 inference(quant_inst,[status(thm)],[])).
% 4.44/4.61 tff(20418,plain,
% 4.44/4.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 4.44/4.61 inference(modus_ponens,[status(thm)],[20417, 20416])).
% 4.44/4.61 tff(20419,plain,
% 4.44/4.61 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[20418, 178, 20383, 595, 20412, 20410])).
% 4.44/4.61 tff(20420,plain,
% 4.44/4.61 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[3444, 20419, 4245])).
% 4.44/4.61 tff(20421,plain,
% 4.44/4.61 (elem!1 = s(s(z))),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[3230, 20387])).
% 4.44/4.61 tff(20422,plain,
% 4.44/4.61 (b(elem!1, z)),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[6641, 20421, 5618])).
% 4.44/4.61 tff(20423,plain,
% 4.44/4.61 (~b(s(s(s(elem!1))), elem!1)),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[12925, 20422, 2042, 2043, 20383])).
% 4.44/4.61 tff(20424,plain,
% 4.44/4.61 (r(s(s(s(elem!1))), elem!1)),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[570, 20423, 19901])).
% 4.44/4.61 tff(20425,plain,
% 4.44/4.61 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[4252, 118, 20424, 20420])).
% 4.44/4.61 tff(20426,plain,
% 4.44/4.61 (b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[5118, 20425, 4254])).
% 4.44/4.61 tff(20427,plain,
% 4.44/4.61 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 4.44/4.61 inference(transitivity,[status(thm)],[20391, 12033])).
% 4.44/4.61 tff(20428,plain,
% 4.44/4.61 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 4.44/4.61 inference(monotonicity,[status(thm)],[20427])).
% 4.44/4.61 tff(20429,plain,
% 4.44/4.61 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 4.44/4.61 inference(modus_ponens,[status(thm)],[2857, 20428])).
% 4.44/4.61 tff(20430,plain,
% 4.44/4.61 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[16872, 118, 20404, 20399])).
% 4.44/4.61 tff(20431,plain,
% 4.44/4.61 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[3409, 20430, 20429])).
% 4.44/4.61 tff(20432,plain,
% 4.44/4.61 ($false),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[18367, 20431, 20426, 20410, 20408, 20406])).
% 4.44/4.61 tff(20433,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(elem!1))))) | r(s(s(z)), z) | b(s(s(z)), elem!1) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (z = elem!1) | (elem!1 = s(s(s(s(z))))) | r(z, s(s(z))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.61 tff(20434,plain,
% 4.44/4.61 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[20433, 3241, 595, 2857, 251, 1301, 104, 2042, 5618, 2043, 701, 507, 469, 48, 145])).
% 4.44/4.61 tff(20435,plain,
% 4.44/4.61 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[249, 20434])).
% 4.44/4.61 tff(20436,plain,
% 4.44/4.61 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[17204, 20435, 144, 5619, 595])).
% 4.44/4.61 tff(20437,plain,
% 4.44/4.61 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[3578, 20436])).
% 4.44/4.61 tff(20438,plain,
% 4.44/4.61 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[3444, 18857, 3914])).
% 4.44/4.61 tff(20439,plain,
% 4.44/4.61 (~r(s(s(z)), elem!1)),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[17566, 20438, 107])).
% 4.44/4.61 tff(20440,plain,
% 4.44/4.61 (s(s(z)) = elem!1),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[448, 20439, 3241])).
% 4.44/4.61 tff(20441,plain,
% 4.44/4.61 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.44/4.61 inference(monotonicity,[status(thm)],[20440])).
% 4.44/4.61 tff(20442,plain,
% 4.44/4.61 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.61 inference(symmetry,[status(thm)],[20441])).
% 4.44/4.61 tff(20443,plain,
% 4.44/4.61 ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) <=> (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 4.44/4.61 inference(monotonicity,[status(thm)],[20442])).
% 4.44/4.61 tff(20444,plain,
% 4.44/4.61 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.61 inference(modus_ponens,[status(thm)],[18858, 20443])).
% 4.44/4.61 tff(20445,plain,
% 4.44/4.61 ($false),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[166, 20444])).
% 4.44/4.61 tff(20446,plain,((~b(z, elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | b(s(s(z)), elem!1) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.61 tff(20447,plain,
% 4.44/4.61 (~b(z, elem!1)),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[20446, 20435, 3241, 20437, 4245, 104, 1301, 595])).
% 4.44/4.61 tff(20448,plain,
% 4.44/4.61 (r(z, elem!1)),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[585, 20447, 507])).
% 4.44/4.61 tff(20449,plain,
% 4.44/4.61 (~(s(s(z)) = elem!1)),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[18165, 20448, 48])).
% 4.44/4.61 tff(20450,plain,
% 4.44/4.61 (r(s(s(z)), elem!1)),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[448, 20449, 3241])).
% 4.44/4.61 tff(20451,plain,
% 4.44/4.61 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[17566, 20450, 20437])).
% 4.44/4.61 tff(20452,plain,
% 4.44/4.61 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[3444, 20451, 4245])).
% 4.44/4.61 tff(20453,plain,
% 4.44/4.61 (~(elem!1 = s(s(z)))),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[311, 20449])).
% 4.44/4.61 tff(20454,plain,
% 4.44/4.61 (~r(elem!1, s(s(s(s(z)))))),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[529, 20448, 145])).
% 4.44/4.61 tff(20455,plain,
% 4.44/4.61 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[16380, 20450, 144, 251, 104, 469, 701, 20454, 20448])).
% 4.44/4.61 tff(20456,plain,
% 4.44/4.61 ($false),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[639, 118, 450, 1265, 107])).
% 4.44/4.61 tff(20457,plain,((~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.61 tff(20458,plain,
% 4.44/4.61 (~r(elem!1, s(s(z)))),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[20457, 20455, 20437])).
% 4.44/4.61 tff(20459,plain,
% 4.44/4.61 (b(elem!1, s(s(z)))),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[467, 20458, 20453])).
% 4.44/4.61 tff(20460,plain,
% 4.44/4.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(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(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(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(z)))), s(s(z)))))),
% 4.44/4.61 inference(rewrite,[status(thm)],[])).
% 4.44/4.61 tff(20461,plain,
% 4.44/4.61 (((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(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))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(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(z)))), s(s(z)))))),
% 4.44/4.61 inference(rewrite,[status(thm)],[])).
% 4.44/4.61 tff(20462,plain,
% 4.44/4.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(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))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(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(z)))), s(s(z))))))),
% 4.44/4.61 inference(monotonicity,[status(thm)],[20461])).
% 4.44/4.61 tff(20463,plain,
% 4.44/4.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(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))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(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(z)))), s(s(z)))))),
% 4.44/4.62 inference(transitivity,[status(thm)],[20462, 20460])).
% 4.44/4.62 tff(20464,plain,
% 4.44/4.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(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))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))),
% 4.44/4.62 inference(quant_inst,[status(thm)],[])).
% 4.44/4.62 tff(20465,plain,
% 4.44/4.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 4.44/4.62 inference(modus_ponens,[status(thm)],[20464, 20463])).
% 4.44/4.62 tff(20466,plain,
% 4.44/4.62 (~b(s(s(s(s(z)))), s(s(z)))),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[20465, 178, 20459, 20435, 1301, 251])).
% 4.44/4.62 tff(20467,plain,
% 4.44/4.62 (r(s(s(s(s(z)))), s(s(z)))),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[102, 20466])).
% 4.44/4.62 tff(20468,plain,
% 4.44/4.62 (~r(s(s(s(s(z)))), elem!1)),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[3329, 20467, 20450])).
% 4.44/4.62 tff(20469,plain,
% 4.44/4.62 (b(s(s(s(s(z)))), elem!1)),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[3142, 20468, 551])).
% 4.44/4.62 tff(20470,plain,
% 4.44/4.62 ($false),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[3928, 178, 104, 20469, 1301, 251, 20452])).
% 4.44/4.62 tff(20471,plain,(b(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)))), s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(s(s(s(z))))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | r(z, s(s(z))) | (~r(z, s(s(s(s(z)))))) | (z = elem!1) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~b(elem!1, s(s(s(elem!1))))) | r(s(s(z)), z) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.62 tff(20472,plain,
% 4.44/4.62 (b(s(s(z)), elem!1)),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[20471, 701, 1301, 251, 469, 104, 48, 145, 318, 595, 2857, 2042, 5618, 2043])).
% 4.44/4.62 tff(20473,plain,
% 4.44/4.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 4.44/4.62 inference(rewrite,[status(thm)],[])).
% 4.44/4.62 tff(20474,plain,
% 4.44/4.62 (((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 4.44/4.62 inference(rewrite,[status(thm)],[])).
% 4.44/4.62 tff(20475,plain,
% 4.44/4.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))))),
% 4.44/4.62 inference(monotonicity,[status(thm)],[20474])).
% 4.44/4.62 tff(20476,plain,
% 4.44/4.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 4.44/4.62 inference(transitivity,[status(thm)],[20475, 20473])).
% 4.44/4.62 tff(20477,plain,
% 4.44/4.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)))),
% 4.44/4.62 inference(quant_inst,[status(thm)],[])).
% 4.44/4.62 tff(20478,plain,
% 4.44/4.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))),
% 4.44/4.62 inference(modus_ponens,[status(thm)],[20477, 20476])).
% 4.44/4.62 tff(20479,plain,
% 4.44/4.62 ((~b(elem!1, z)) | (~b(s(s(z)), elem!1))),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[20478, 178, 2043, 5619, 2042])).
% 4.44/4.62 tff(20480,plain,
% 4.44/4.62 (~b(elem!1, z)),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[20479, 20472])).
% 4.44/4.62 tff(20481,plain,
% 4.44/4.62 (r(elem!1, z)),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[498, 20480, 290])).
% 4.44/4.62 tff(20482,plain,
% 4.44/4.62 (~b(s(s(z)), s(s(z)))),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[16833, 178, 5619, 144])).
% 4.44/4.62 tff(20483,plain,
% 4.44/4.62 (~(elem!1 = s(s(z)))),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[3238, 20472, 20482])).
% 4.44/4.62 tff(20484,plain,
% 4.44/4.62 (~b(z, elem!1)),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[17506, 178, 2043, 20472, 5619, 2042])).
% 4.44/4.62 tff(20485,plain,
% 4.44/4.62 (r(z, elem!1)),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[585, 20484, 318])).
% 4.44/4.62 tff(20486,plain,
% 4.44/4.62 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[17498, 20485, 595, 1301, 144, 5619, 4245, 104, 20472])).
% 4.44/4.62 tff(20487,plain,
% 4.44/4.62 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[249, 20486])).
% 4.44/4.62 tff(20488,plain,
% 4.44/4.62 (~r(elem!1, s(s(s(s(z)))))),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[478, 20481, 145])).
% 4.44/4.62 tff(20489,plain,
% 4.44/4.62 ($false),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[10901, 118, 521, 3132, 145])).
% 4.44/4.62 tff(20490,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.62 tff(20491,plain,
% 4.44/4.62 (~r(s(s(s(s(z)))), elem!1)),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[20490, 20485, 145])).
% 4.44/4.62 tff(20492,plain,
% 4.44/4.62 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[8548, 20491, 104, 251, 469, 20488])).
% 4.44/4.62 tff(20493,plain,
% 4.44/4.62 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[691, 20492, 701])).
% 4.44/4.62 tff(20494,plain,
% 4.44/4.62 (~r(elem!1, s(s(z)))),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[3113, 20493, 20487])).
% 4.44/4.62 tff(20495,plain,
% 4.44/4.62 (b(elem!1, s(s(z)))),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[467, 20494, 20483])).
% 4.44/4.62 tff(20496,plain,
% 4.44/4.62 (~b(s(s(z)), s(s(s(s(z)))))),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[19785, 20495, 551, 1301, 20481, 20472, 5619, 251, 595])).
% 4.44/4.62 tff(20497,plain,
% 4.44/4.62 (r(s(s(z)), s(s(s(s(z)))))),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[164, 20496])).
% 4.44/4.62 tff(20498,plain,
% 4.44/4.62 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[10799, 20497, 145])).
% 4.44/4.62 tff(20499,plain,
% 4.44/4.62 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[4173, 20498, 2857])).
% 4.44/4.62 tff(20500,plain,
% 4.44/4.62 (b(s(s(s(s(z)))), elem!1)),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[3142, 20491, 551])).
% 4.44/4.62 tff(20501,plain,
% 4.44/4.62 ($false),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[3928, 178, 104, 3771, 1301, 251, 3664])).
% 4.44/4.62 tff(20502,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.62 tff(20503,plain,
% 4.44/4.62 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[20502, 20500, 1301, 251, 104])).
% 4.44/4.62 tff(20504,plain,
% 4.44/4.62 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[3444, 20503, 4245])).
% 4.44/4.62 tff(20505,plain,
% 4.44/4.62 (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[3682, 556, 2953])).
% 4.44/4.62 tff(20506,plain,
% 4.44/4.62 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[3612, 41, 20505, 9361])).
% 4.44/4.62 tff(20507,plain,
% 4.44/4.62 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[11027, 2953, 521])).
% 4.44/4.62 tff(20508,plain,
% 4.44/4.62 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[133, 20507])).
% 4.44/4.62 tff(20509,plain,
% 4.44/4.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(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(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(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(s(s(s(s(s(z))))))), z)))),
% 4.44/4.62 inference(rewrite,[status(thm)],[])).
% 4.44/4.62 tff(20510,plain,
% 4.44/4.62 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(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(s(s(s(s(s(z))))))), z)))),
% 4.44/4.62 inference(rewrite,[status(thm)],[])).
% 4.44/4.62 tff(20511,plain,
% 4.44/4.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(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(s(s(s(s(s(z))))))), z))))),
% 4.44/4.62 inference(monotonicity,[status(thm)],[20510])).
% 4.44/4.62 tff(20512,plain,
% 4.44/4.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(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(s(s(s(s(s(z))))))), z)))),
% 4.44/4.62 inference(transitivity,[status(thm)],[20511, 20509])).
% 4.44/4.62 tff(20513,plain,
% 4.44/4.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(elem!1))))))),
% 4.44/4.62 inference(quant_inst,[status(thm)],[])).
% 4.44/4.62 tff(20514,plain,
% 4.44/4.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 4.44/4.62 inference(modus_ponens,[status(thm)],[20513, 20512])).
% 4.44/4.62 tff(20515,plain,
% 4.44/4.62 ($false),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[20514, 178, 2043, 6380, 595, 20508, 20506])).
% 4.44/4.62 tff(20516,plain,((~r(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.62 tff(20517,plain,
% 4.44/4.62 (~r(s(s(s(elem!1))), elem!1)),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[20516, 20485, 595, 20284, 2043, 20504])).
% 4.44/4.62 tff(20518,plain,
% 4.44/4.62 (b(s(s(s(elem!1))), elem!1)),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[570, 20517, 19901])).
% 4.44/4.62 tff(20519,plain,
% 4.44/4.62 ($false),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[6410, 178, 20518, 2042, 20500, 1301, 20499])).
% 4.44/4.62 tff(20520,plain,((elem!1 = s(s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~r(z, 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)))))) | (elem!1 = s(s(s(s(z))))) | (elem!1 = z) | r(z, s(s(z))) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 4.44/4.62 tff(20521,plain,
% 4.44/4.62 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[20520, 19900, 18843, 17173, 20374, 20376, 47, 18255, 104, 469, 290, 48, 10792])).
% 4.44/4.62 tff(20522,plain,
% 4.44/4.62 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 4.44/4.62 inference(monotonicity,[status(thm)],[20521])).
% 4.44/4.62 tff(20523,plain,
% 4.44/4.62 (s(s(elem!1)) = s(s(s(s(s(s(s(s(s(z)))))))))),
% 4.44/4.62 inference(monotonicity,[status(thm)],[20522])).
% 4.44/4.62 tff(20524,plain,
% 4.44/4.62 (s(s(s(elem!1))) = s(s(s(s(s(s(s(s(s(s(z))))))))))),
% 4.44/4.62 inference(monotonicity,[status(thm)],[20523])).
% 4.44/4.62 tff(20525,plain,
% 4.44/4.62 (s(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(s(elem!1)))),
% 4.44/4.62 inference(symmetry,[status(thm)],[20524])).
% 4.44/4.62 tff(20526,plain,
% 4.44/4.62 (b(z, s(s(s(s(s(s(s(s(s(s(z))))))))))) <=> b(z, s(s(s(elem!1))))),
% 4.44/4.62 inference(monotonicity,[status(thm)],[20525])).
% 4.44/4.62 tff(20527,plain,
% 4.44/4.62 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 4.44/4.62 inference(symmetry,[status(thm)],[20526])).
% 4.44/4.62 tff(20528,plain,
% 4.44/4.62 (b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 4.44/4.62 inference(modus_ponens,[status(thm)],[20374, 20527])).
% 4.44/4.62 tff(20529,plain,
% 4.44/4.62 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z))))))))))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.44/4.62 inference(monotonicity,[status(thm)],[20525])).
% 4.44/4.62 tff(20530,plain,
% 4.44/4.62 (b(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(s(s(s(s(s(s(s(z)))))))))))),
% 4.44/4.62 inference(symmetry,[status(thm)],[20529])).
% 4.44/4.62 tff(20531,plain,
% 4.44/4.62 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.44/4.62 inference(monotonicity,[status(thm)],[20521])).
% 4.44/4.62 tff(20532,plain,
% 4.44/4.62 (b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.44/4.62 inference(modus_ponens,[status(thm)],[19900, 20531])).
% 4.44/4.62 tff(20533,plain,
% 4.44/4.62 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 4.44/4.62 inference(modus_ponens,[status(thm)],[20532, 20530])).
% 4.44/4.62 tff(20534,plain,
% 4.44/4.62 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(s(s(s(s(z))))))))),
% 4.44/4.62 inference(monotonicity,[status(thm)],[20521])).
% 4.44/4.62 tff(20535,plain,
% 4.44/4.62 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(z)) = elem!1)),
% 4.44/4.62 inference(symmetry,[status(thm)],[20534])).
% 4.44/4.62 tff(20536,plain,
% 4.44/4.62 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(z)) = elem!1))),
% 4.44/4.62 inference(monotonicity,[status(thm)],[20535])).
% 4.44/4.62 tff(20537,plain,
% 4.44/4.62 (~(s(s(z)) = elem!1)),
% 4.44/4.62 inference(modus_ponens,[status(thm)],[244, 20536])).
% 4.44/4.62 tff(20538,plain,
% 4.44/4.62 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.62 inference(monotonicity,[status(thm)],[20521])).
% 4.44/4.62 tff(20539,plain,
% 4.44/4.62 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(elem!1))), elem!1)),
% 4.44/4.62 inference(symmetry,[status(thm)],[20538])).
% 4.44/4.62 tff(20540,plain,
% 4.44/4.62 (b(s(s(s(s(s(s(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))))))))),
% 4.44/4.62 inference(monotonicity,[status(thm)],[20525])).
% 4.44/4.62 tff(20541,plain,
% 4.44/4.62 (b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(elem!1))), elem!1)),
% 4.44/4.62 inference(transitivity,[status(thm)],[20540, 20539])).
% 4.44/4.62 tff(20542,plain,
% 4.44/4.62 ((~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(s(s(elem!1))), elem!1))),
% 4.44/4.62 inference(monotonicity,[status(thm)],[20541])).
% 4.44/4.62 tff(20543,plain,
% 4.44/4.62 ((~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) <=> (~b(s(s(s(elem!1))), z))),
% 4.44/4.62 inference(monotonicity,[status(thm)],[15441])).
% 4.44/4.62 tff(20544,assumption,(b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 4.44/4.62 tff(20545,assumption,(b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))), introduced(assumption)).
% 4.44/4.62 tff(20546,assumption,(b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))), introduced(assumption)).
% 4.44/4.62 tff(20547,plain,
% 4.44/4.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))))),
% 4.44/4.62 inference(rewrite,[status(thm)],[])).
% 4.44/4.62 tff(20548,plain,
% 4.44/4.62 (((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), z))) <=> ((~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))))),
% 4.44/4.62 inference(rewrite,[status(thm)],[])).
% 4.44/4.62 tff(20549,plain,
% 4.44/4.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z)))))))))))),
% 4.44/4.62 inference(monotonicity,[status(thm)],[20548])).
% 4.44/4.62 tff(20550,plain,
% 4.44/4.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))))),
% 4.44/4.62 inference(transitivity,[status(thm)],[20549, 20547])).
% 4.44/4.62 tff(20551,plain,
% 4.44/4.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)))),
% 4.44/4.62 inference(quant_inst,[status(thm)],[])).
% 4.44/4.62 tff(20552,plain,
% 4.44/4.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z)))))))))),
% 4.44/4.62 inference(modus_ponens,[status(thm)],[20551, 20550])).
% 4.44/4.62 tff(20553,plain,
% 4.44/4.62 ((~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z)))))))))),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[20552, 178, 595, 20546, 20545])).
% 4.44/4.62 tff(20554,plain,
% 4.44/4.62 (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[20553, 20544])).
% 4.44/4.62 tff(20555,plain,
% 4.44/4.62 (~b(s(s(s(elem!1))), z)),
% 4.44/4.62 inference(modus_ponens,[status(thm)],[20554, 20543])).
% 4.44/4.62 tff(20556,plain,
% 4.44/4.62 (r(s(s(s(elem!1))), z)),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[1565, 20555])).
% 4.44/4.62 tff(20557,plain,
% 4.44/4.62 (r(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)),
% 4.44/4.62 inference(modus_ponens,[status(thm)],[20556, 10553])).
% 4.44/4.62 tff(20558,plain,
% 4.44/4.62 (r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.44/4.62 inference(monotonicity,[status(thm)],[4345])).
% 4.44/4.62 tff(20559,plain,
% 4.44/4.62 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))),
% 4.44/4.62 inference(symmetry,[status(thm)],[20558])).
% 4.44/4.62 tff(20560,plain,
% 4.44/4.62 ((~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) <=> (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 4.44/4.62 inference(monotonicity,[status(thm)],[10495])).
% 4.44/4.62 tff(20561,plain,
% 4.44/4.62 ((~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z)))))))))),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[10871, 178, 104, 251, 20546])).
% 4.44/4.62 tff(20562,plain,
% 4.44/4.62 (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[20561, 20544])).
% 4.44/4.62 tff(20563,plain,
% 4.44/4.62 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.44/4.62 inference(modus_ponens,[status(thm)],[20562, 20560])).
% 4.44/4.62 tff(20564,plain,
% 4.44/4.62 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.44/4.62 inference(unit_resolution,[status(thm)],[4173, 20563, 2857])).
% 4.44/4.62 tff(20565,plain,
% 4.44/4.62 (r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))),
% 4.44/4.62 inference(modus_ponens,[status(thm)],[20564, 20559])).
% 4.44/4.62 tff(20566,plain,
% 4.44/4.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), 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(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), 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(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 4.44/4.63 inference(rewrite,[status(thm)],[])).
% 4.44/4.63 tff(20567,plain,
% 4.44/4.63 (((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(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(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 4.44/4.63 inference(rewrite,[status(thm)],[])).
% 4.44/4.63 tff(20568,plain,
% 4.44/4.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), 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(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z))))))))))))))),
% 4.44/4.63 inference(monotonicity,[status(thm)],[20567])).
% 4.44/4.63 tff(20569,plain,
% 4.44/4.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), 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(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 4.44/4.63 inference(transitivity,[status(thm)],[20568, 20566])).
% 4.44/4.63 tff(20570,plain,
% 4.44/4.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)))),
% 4.44/4.63 inference(quant_inst,[status(thm)],[])).
% 4.44/4.63 tff(20571,plain,
% 4.44/4.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), 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(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z))))))))))))),
% 4.44/4.63 inference(modus_ponens,[status(thm)],[20570, 20569])).
% 4.44/4.63 tff(20572,plain,
% 4.44/4.63 ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z))))))))))))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[20571, 178, 251, 595])).
% 4.44/4.63 tff(20573,plain,
% 4.44/4.63 (~b(s(s(s(s(z)))), z)),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[20572, 20546, 20545])).
% 4.44/4.63 tff(20574,plain,
% 4.44/4.63 (r(s(s(s(s(z)))), z)),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[191, 20573])).
% 4.44/4.63 tff(20575,plain,
% 4.44/4.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))))),
% 4.44/4.63 inference(rewrite,[status(thm)],[])).
% 4.44/4.63 tff(20576,plain,
% 4.44/4.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))))),
% 4.44/4.63 inference(quant_inst,[status(thm)],[])).
% 4.44/4.63 tff(20577,plain,
% 4.44/4.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z))))))),
% 4.44/4.63 inference(modus_ponens,[status(thm)],[20576, 20575])).
% 4.44/4.63 tff(20578,plain,
% 4.44/4.63 (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[20577, 118, 20574, 20565])).
% 4.44/4.63 tff(20579,plain,
% 4.44/4.63 ($false),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[20578, 20557])).
% 4.44/4.63 tff(20580,plain,((~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (s(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(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z))))))))))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.63 tff(20581,plain,
% 4.44/4.63 (~b(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[20580, 20521, 20376, 104, 18255, 20533, 17173, 20528])).
% 4.44/4.63 tff(20582,plain,
% 4.44/4.63 (~b(s(s(s(elem!1))), elem!1)),
% 4.44/4.63 inference(modus_ponens,[status(thm)],[20581, 20542])).
% 4.44/4.63 tff(20583,plain,
% 4.44/4.63 (r(s(s(s(elem!1))), elem!1)),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[570, 20582, 20330])).
% 4.44/4.63 tff(20584,plain,
% 4.44/4.63 (~(s(elem!1) = elem!1)),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[2150, 20330])).
% 4.44/4.63 tff(20585,plain,
% 4.44/4.63 ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z))))))))))))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[20571, 178, 18255, 17173])).
% 4.44/4.63 tff(20586,plain,
% 4.44/4.63 (~b(s(s(s(s(z)))), z)),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[20585, 20533, 20528])).
% 4.44/4.63 tff(20587,plain,
% 4.44/4.63 (r(s(s(s(s(z)))), z)),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[191, 20586])).
% 4.44/4.63 tff(20588,plain,
% 4.44/4.63 (r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.63 inference(monotonicity,[status(thm)],[4345])).
% 4.44/4.63 tff(20589,plain,
% 4.44/4.63 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.63 inference(symmetry,[status(thm)],[20588])).
% 4.44/4.63 tff(20590,plain,
% 4.44/4.63 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[19937, 556, 679])).
% 4.44/4.63 tff(20591,plain,
% 4.44/4.63 (r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.63 inference(modus_ponens,[status(thm)],[20590, 20589])).
% 4.44/4.63 tff(20592,plain,
% 4.44/4.63 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.63 inference(monotonicity,[status(thm)],[679])).
% 4.44/4.63 tff(20593,plain,
% 4.44/4.63 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.63 inference(modus_ponens,[status(thm)],[438, 20592])).
% 4.44/4.63 tff(20594,plain,
% 4.44/4.63 (~r(s(s(z)), s(s(s(elem!1))))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[19952, 20593, 679, 20591])).
% 4.44/4.63 tff(20595,plain,
% 4.44/4.63 (b(s(s(z)), s(s(s(elem!1))))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[4223, 20594])).
% 4.44/4.63 tff(20596,plain,
% 4.44/4.63 (~b(s(s(s(elem!1))), z)),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[7978, 20595, 273, 3461, 2043])).
% 4.44/4.63 tff(20597,plain,
% 4.44/4.63 (r(s(s(s(elem!1))), z)),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[1565, 20596])).
% 4.44/4.63 tff(20598,plain,
% 4.44/4.63 (r(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)),
% 4.44/4.63 inference(modus_ponens,[status(thm)],[20597, 10553])).
% 4.44/4.63 tff(20599,plain,
% 4.44/4.63 (~r(s(s(z)), s(s(s(s(z)))))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[20009, 438, 104, 251, 679, 3461, 595, 725, 556, 194])).
% 4.44/4.63 tff(20600,plain,
% 4.44/4.63 (b(s(s(z)), s(s(s(s(z)))))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[164, 20599])).
% 4.44/4.63 tff(20601,plain,
% 4.44/4.63 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[20347, 20597, 679, 20591])).
% 4.44/4.63 tff(20602,plain,
% 4.44/4.63 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[133, 20601])).
% 4.44/4.63 tff(20603,plain,
% 4.44/4.63 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[18239, 20602, 595, 3461, 273, 20593, 145])).
% 4.44/4.63 tff(20604,plain,
% 4.44/4.63 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[10755, 20603])).
% 4.44/4.63 tff(20605,plain,
% 4.44/4.63 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[19958, 20604, 251, 20590, 104, 20600, 20593, 8246, 20595])).
% 4.44/4.63 tff(20606,plain,
% 4.44/4.63 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[4173, 20605, 2857])).
% 4.44/4.63 tff(20607,plain,
% 4.44/4.63 (r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z)))))),
% 4.44/4.63 inference(modus_ponens,[status(thm)],[20606, 20559])).
% 4.44/4.63 tff(20608,plain,
% 4.44/4.63 ((~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), z)) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(z))))))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[20577, 118, 194])).
% 4.44/4.63 tff(20609,plain,
% 4.44/4.63 ($false),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[20608, 20607, 20598])).
% 4.44/4.63 tff(20610,plain,((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), z)) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (s(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)))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (s(elem!1) = elem!1) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.63 tff(20611,plain,
% 4.44/4.63 (~r(s(s(z)), elem!1)),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[20610, 20587, 20521, 20376, 18255, 104, 11613, 17173, 10793, 144, 47, 20374, 20584, 20583])).
% 4.44/4.63 tff(20612,plain,
% 4.44/4.63 (b(s(s(z)), elem!1)),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[448, 20611, 20537])).
% 4.44/4.63 tff(20613,plain,
% 4.44/4.63 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[10835, 20612, 20521])).
% 4.44/4.63 tff(20614,plain,
% 4.44/4.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 4.44/4.63 inference(rewrite,[status(thm)],[])).
% 4.44/4.63 tff(20615,plain,
% 4.44/4.63 (((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 4.44/4.63 inference(rewrite,[status(thm)],[])).
% 4.44/4.63 tff(20616,plain,
% 4.44/4.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z))))))))))))))),
% 4.44/4.63 inference(monotonicity,[status(thm)],[20615])).
% 4.44/4.63 tff(20617,plain,
% 4.44/4.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))))),
% 4.44/4.63 inference(transitivity,[status(thm)],[20616, 20614])).
% 4.44/4.63 tff(20618,plain,
% 4.44/4.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)))),
% 4.44/4.63 inference(quant_inst,[status(thm)],[])).
% 4.44/4.63 tff(20619,plain,
% 4.44/4.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))) | (~b(z, s(s(s(s(s(s(s(s(s(s(z))))))))))))),
% 4.44/4.63 inference(modus_ponens,[status(thm)],[20618, 20617])).
% 4.44/4.63 tff(20620,plain,
% 4.44/4.63 ($false),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[20619, 178, 10793, 20613, 17173, 20533, 20528])).
% 4.44/4.63 tff(20621,plain,((elem!1 = s(s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (elem!1 = z) | r(z, s(s(z))) | b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.63 tff(20622,plain,
% 4.44/4.63 (elem!1 = s(s(s(s(z))))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[20621, 290, 104, 48, 1])).
% 4.44/4.63 tff(20623,plain,
% 4.44/4.63 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(s(z)))), s(s(s(s(z)))))),
% 4.44/4.63 inference(monotonicity,[status(thm)],[20622])).
% 4.44/4.63 tff(20624,plain,
% 4.44/4.63 (b(s(s(s(s(z)))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 4.44/4.63 inference(symmetry,[status(thm)],[20623])).
% 4.44/4.63 tff(20625,plain,
% 4.44/4.63 ((~b(s(s(s(s(z)))), s(s(s(s(z)))))) <=> (~b(elem!1, s(s(s(s(z))))))),
% 4.44/4.63 inference(monotonicity,[status(thm)],[20624])).
% 4.44/4.63 tff(20626,plain,
% 4.44/4.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.44/4.63 inference(rewrite,[status(thm)],[])).
% 4.44/4.63 tff(20627,plain,
% 4.44/4.63 (((~b(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))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(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(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.44/4.63 inference(rewrite,[status(thm)],[])).
% 4.44/4.63 tff(20628,plain,
% 4.44/4.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 4.44/4.63 inference(monotonicity,[status(thm)],[20627])).
% 4.44/4.63 tff(20629,plain,
% 4.44/4.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.44/4.63 inference(transitivity,[status(thm)],[20628, 20626])).
% 4.44/4.63 tff(20630,plain,
% 4.44/4.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 4.44/4.63 inference(quant_inst,[status(thm)],[])).
% 4.44/4.63 tff(20631,plain,
% 4.44/4.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 4.44/4.63 inference(modus_ponens,[status(thm)],[20630, 20629])).
% 4.44/4.63 tff(20632,plain,
% 4.44/4.63 (~b(s(s(s(s(z)))), s(s(s(s(z)))))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[20631, 178, 104, 18255])).
% 4.44/4.63 tff(20633,plain,
% 4.44/4.63 (~b(elem!1, s(s(s(s(z)))))),
% 4.44/4.63 inference(modus_ponens,[status(thm)],[20632, 20625])).
% 4.44/4.63 tff(20634,plain,
% 4.44/4.63 ($false),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[18843, 20633])).
% 4.44/4.63 tff(20635,plain,((elem!1 = z) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | r(z, s(s(z))) | b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.63 tff(20636,plain,
% 4.44/4.63 (elem!1 = z),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[20635, 1, 48, 104])).
% 4.44/4.63 tff(20637,assumption,(~r(s(s(s(z))), z)), introduced(assumption)).
% 4.44/4.63 tff(20638,plain,
% 4.44/4.63 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 4.44/4.63 inference(transitivity,[status(thm)],[10729, 4164])).
% 4.44/4.63 tff(20639,plain,
% 4.44/4.63 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(s(z)))) = s(s(s(elem!1)))))),
% 4.44/4.63 inference(monotonicity,[status(thm)],[20638])).
% 4.44/4.63 tff(20640,plain,
% 4.44/4.63 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 4.44/4.63 inference(modus_ponens,[status(thm)],[4938, 20639])).
% 4.44/4.63 tff(20641,plain,
% 4.44/4.63 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[10664, 19902, 4166])).
% 4.44/4.63 tff(20642,plain,
% 4.44/4.63 ($false),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[5125, 20641, 10662, 145, 203, 3521, 557])).
% 4.44/4.63 tff(20643,plain,((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.63 tff(20644,plain,
% 4.44/4.63 (~r(z, s(s(s(elem!1))))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[20643, 203, 47, 10745, 20640, 10731])).
% 4.44/4.63 tff(20645,plain,
% 4.44/4.63 (b(z, s(s(s(elem!1))))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[2095, 20644])).
% 4.44/4.63 tff(20646,plain,
% 4.44/4.63 (~(s(elem!1) = s(s(z)))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[17598, 20645, 1])).
% 4.44/4.63 tff(20647,plain,
% 4.44/4.63 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(z), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.63 inference(monotonicity,[status(thm)],[929])).
% 4.44/4.63 tff(20648,plain,
% 4.44/4.63 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(z, s(s(s(s(s(s(s(z))))))))),
% 4.44/4.63 inference(monotonicity,[status(thm)],[928])).
% 4.44/4.63 tff(20649,plain,
% 4.44/4.63 (r(z, s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.44/4.63 inference(symmetry,[status(thm)],[20648])).
% 4.44/4.63 tff(20650,plain,
% 4.44/4.63 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.44/4.63 inference(modus_ponens,[status(thm)],[203, 20649])).
% 4.44/4.63 tff(20651,plain,
% 4.44/4.63 ((s(elem!1) = elem!1) <=> (s(elem!1) = z)),
% 4.44/4.63 inference(monotonicity,[status(thm)],[928])).
% 4.44/4.63 tff(20652,plain,
% 4.44/4.63 ((s(elem!1) = z) <=> (s(elem!1) = elem!1)),
% 4.44/4.63 inference(symmetry,[status(thm)],[20651])).
% 4.44/4.63 tff(20653,plain,
% 4.44/4.63 ((s(elem!1) = z) <=> (elem!1 = s(elem!1))),
% 4.44/4.63 inference(transitivity,[status(thm)],[20652, 3880])).
% 4.44/4.63 tff(20654,plain,
% 4.44/4.63 ((~(s(elem!1) = z)) <=> (~(elem!1 = s(elem!1)))),
% 4.44/4.63 inference(monotonicity,[status(thm)],[20653])).
% 4.44/4.63 tff(20655,plain,
% 4.44/4.63 (~(elem!1 = s(elem!1))),
% 4.44/4.63 inference(modus_ponens,[status(thm)],[769, 20654])).
% 4.44/4.63 tff(20656,plain,
% 4.44/4.63 (b(elem!1, s(s(s(elem!1)))) <=> b(z, s(s(s(elem!1))))),
% 4.44/4.63 inference(monotonicity,[status(thm)],[928])).
% 4.44/4.63 tff(20657,plain,
% 4.44/4.63 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 4.44/4.63 inference(symmetry,[status(thm)],[20656])).
% 4.44/4.63 tff(20658,plain,
% 4.44/4.63 (~r(z, s(s(s(elem!1))))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[20643, 203, 145, 10745, 20640, 10731])).
% 4.44/4.63 tff(20659,plain,
% 4.44/4.63 (b(z, s(s(s(elem!1))))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[2095, 20658])).
% 4.44/4.63 tff(20660,plain,
% 4.44/4.63 (b(elem!1, s(s(s(elem!1))))),
% 4.44/4.63 inference(modus_ponens,[status(thm)],[20659, 20657])).
% 4.44/4.63 tff(20661,plain,
% 4.44/4.63 ((~(s(elem!1) = z)) <=> (~(s(elem!1) = elem!1))),
% 4.44/4.63 inference(monotonicity,[status(thm)],[20652])).
% 4.44/4.63 tff(20662,plain,
% 4.44/4.63 (~(s(elem!1) = elem!1)),
% 4.44/4.63 inference(modus_ponens,[status(thm)],[769, 20661])).
% 4.44/4.63 tff(20663,plain,
% 4.44/4.63 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[11290, 224, 3461, 273, 203])).
% 4.44/4.63 tff(20664,assumption,(~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 4.44/4.63 tff(20665,assumption,(~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 4.44/4.63 tff(20666,plain,
% 4.44/4.63 ($false),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[5031, 41, 20665, 20664, 10712])).
% 4.44/4.63 tff(20667,plain,(b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.63 tff(20668,plain,
% 4.44/4.63 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[20667, 20663])).
% 4.44/4.63 tff(20669,plain,
% 4.44/4.63 (~r(s(s(z)), s(s(s(s(z)))))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[5624, 224, 204])).
% 4.44/4.63 tff(20670,plain,
% 4.44/4.63 (b(s(s(z)), s(s(s(s(z)))))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[164, 20669])).
% 4.44/4.63 tff(20671,plain,
% 4.44/4.63 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[7840, 178, 273, 104, 20670, 3551])).
% 4.44/4.63 tff(20672,plain,
% 4.44/4.63 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[3578, 20671])).
% 4.44/4.63 tff(20673,plain,
% 4.44/4.63 ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[16647, 178, 3461, 273, 17723])).
% 4.44/4.63 tff(20674,plain,
% 4.44/4.63 (~b(s(s(s(s(z)))), z)),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[20673, 20670])).
% 4.44/4.63 tff(20675,plain,
% 4.44/4.63 (r(s(s(s(s(z)))), z)),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[191, 20674])).
% 4.44/4.63 tff(20676,plain,
% 4.44/4.63 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(z))))),
% 4.44/4.63 inference(monotonicity,[status(thm)],[931])).
% 4.44/4.63 tff(20677,plain,
% 4.44/4.63 (b(elem!1, s(s(s(elem!1)))) <=> b(z, s(s(s(z))))),
% 4.44/4.63 inference(transitivity,[status(thm)],[20656, 20676])).
% 4.44/4.63 tff(20678,plain,
% 4.44/4.63 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 4.44/4.63 inference(monotonicity,[status(thm)],[931])).
% 4.44/4.63 tff(20679,plain,
% 4.44/4.63 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[3259, 5210, 145])).
% 4.44/4.63 tff(20680,plain,
% 4.44/4.63 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[4173, 20679, 10731])).
% 4.44/4.63 tff(20681,plain,
% 4.44/4.63 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.44/4.63 inference(modus_ponens,[status(thm)],[20680, 20678])).
% 4.44/4.63 tff(20682,plain,
% 4.44/4.63 (r(z, s(s(s(z))))),
% 4.44/4.63 inference(modus_ponens,[status(thm)],[3311, 15374])).
% 4.44/4.63 tff(20683,plain,
% 4.44/4.63 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[4961, 20682, 194])).
% 4.44/4.63 tff(20684,plain,
% 4.44/4.63 (b(s(s(s(s(z)))), s(s(s(z))))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[11185, 20683])).
% 4.44/4.63 tff(20685,plain,
% 4.44/4.63 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[1175, 118, 10748, 107])).
% 4.44/4.63 tff(20686,plain,
% 4.44/4.63 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 20685])).
% 4.44/4.63 tff(20687,plain,
% 4.44/4.63 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[8218, 10748, 107])).
% 4.44/4.63 tff(20688,plain,
% 4.44/4.63 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[5031, 41, 20687, 10712])).
% 4.44/4.63 tff(20689,plain,
% 4.44/4.63 ($false),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[8278, 178, 104, 1126, 6170, 20688, 20686])).
% 4.44/4.63 tff(20690,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.63 tff(20691,plain,
% 4.44/4.63 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[20690, 20684, 104, 107, 273, 202, 167, 194])).
% 4.44/4.63 tff(20692,plain,
% 4.44/4.63 ($false),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[20691, 20681])).
% 4.44/4.63 tff(20693,plain,((~r(elem!1, s(s(s(elem!1))))) | (~(elem!1 = 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(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.63 tff(20694,plain,
% 4.44/4.63 (~r(elem!1, s(s(s(elem!1))))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[20693, 20672, 104, 928, 273, 17723, 20670, 20675, 145])).
% 4.44/4.63 tff(20695,plain,
% 4.44/4.63 (b(elem!1, s(s(s(elem!1))))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[2054, 20694, 12085])).
% 4.44/4.63 tff(20696,plain,
% 4.44/4.63 (b(z, s(s(s(z))))),
% 4.44/4.63 inference(modus_ponens,[status(thm)],[20695, 20677])).
% 4.44/4.63 tff(20697,plain,
% 4.44/4.63 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[10753, 20696, 928, 104, 3551, 20672, 273, 17723, 20670, 20675])).
% 4.44/4.63 tff(20698,plain,
% 4.44/4.63 (r(s(s(s(z))), s(s(s(s(z)))))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[10755, 20697])).
% 4.44/4.63 tff(20699,plain,
% 4.44/4.63 (~r(s(s(s(z))), z)),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[4899, 118, 145, 20698])).
% 4.44/4.63 tff(20700,plain,
% 4.44/4.63 (b(s(s(s(z))), z)),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[4903, 41, 77, 20699])).
% 4.44/4.63 tff(20701,plain,
% 4.44/4.63 (~b(s(s(s(z))), s(s(z)))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[17111, 178, 3461, 273, 20696, 20700])).
% 4.44/4.63 tff(20702,plain,
% 4.44/4.63 (r(s(s(s(z))), s(s(z)))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[4966, 20701])).
% 4.44/4.63 tff(20703,plain,
% 4.44/4.63 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[1175, 118, 20702, 20672])).
% 4.44/4.63 tff(20704,plain,
% 4.44/4.63 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.44/4.63 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 20703])).
% 4.44/4.64 tff(20705,plain,
% 4.44/4.64 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[11287, 20700, 3461, 273, 224])).
% 4.44/4.64 tff(20706,plain,
% 4.44/4.64 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[5031, 41, 20705, 10712])).
% 4.44/4.64 tff(20707,plain,
% 4.44/4.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)))),
% 4.44/4.64 inference(rewrite,[status(thm)],[])).
% 4.44/4.64 tff(20708,plain,
% 4.44/4.64 (((~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(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)))),
% 4.44/4.64 inference(rewrite,[status(thm)],[])).
% 4.44/4.64 tff(20709,plain,
% 4.44/4.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z))))),
% 4.44/4.64 inference(monotonicity,[status(thm)],[20708])).
% 4.44/4.64 tff(20710,plain,
% 4.44/4.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)))),
% 4.44/4.64 inference(transitivity,[status(thm)],[20709, 20707])).
% 4.44/4.64 tff(20711,plain,
% 4.44/4.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)))),
% 4.44/4.64 inference(quant_inst,[status(thm)],[])).
% 4.44/4.64 tff(20712,plain,
% 4.44/4.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z))),
% 4.44/4.64 inference(modus_ponens,[status(thm)],[20711, 20710])).
% 4.44/4.64 tff(20713,plain,
% 4.44/4.64 ($false),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[20712, 178, 3551, 20696, 20700, 20706, 20704])).
% 4.44/4.64 tff(20714,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~(elem!1 = z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.64 tff(20715,plain,
% 4.44/4.64 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[20714, 204, 273, 145, 928, 104, 3461])).
% 4.44/4.64 tff(20716,plain,
% 4.44/4.64 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[249, 20715])).
% 4.44/4.64 tff(20717,plain,
% 4.44/4.64 ($false),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[3486, 178, 3461, 273, 166, 595, 146])).
% 4.44/4.64 tff(20718,plain,((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.64 tff(20719,plain,
% 4.44/4.64 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[20718, 20716, 273, 3461, 3551])).
% 4.44/4.64 tff(20720,plain,
% 4.44/4.64 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[133, 20719])).
% 4.44/4.64 tff(20721,plain,
% 4.44/4.64 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(z, s(s(s(s(s(s(s(z))))))))),
% 4.44/4.64 inference(monotonicity,[status(thm)],[928])).
% 4.44/4.64 tff(20722,plain,
% 4.44/4.64 (b(z, s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.44/4.64 inference(symmetry,[status(thm)],[20721])).
% 4.44/4.64 tff(20723,plain,
% 4.44/4.64 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.44/4.64 inference(modus_ponens,[status(thm)],[3551, 20722])).
% 4.44/4.64 tff(20724,plain,
% 4.44/4.64 (b(elem!1, s(s(z)))),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[3276, 928, 273])).
% 4.44/4.64 tff(20725,plain,
% 4.44/4.64 (~b(s(s(s(s(z)))), elem!1)),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[17777, 20716, 20724, 20723, 17723])).
% 4.44/4.64 tff(20726,plain,
% 4.44/4.64 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), z)),
% 4.44/4.64 inference(symmetry,[status(thm)],[5180])).
% 4.44/4.64 tff(20727,plain,
% 4.44/4.64 ((~b(s(s(s(s(z)))), elem!1)) <=> (~b(s(s(s(s(z)))), z))),
% 4.44/4.64 inference(monotonicity,[status(thm)],[20726])).
% 4.44/4.64 tff(20728,plain,
% 4.44/4.64 (~b(s(s(s(s(z)))), z)),
% 4.44/4.64 inference(modus_ponens,[status(thm)],[3278, 20727])).
% 4.44/4.64 tff(20729,plain,
% 4.44/4.64 ($false),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[168, 20728])).
% 4.44/4.64 tff(20730,plain,((~(z = elem!1)) | (~b(s(s(s(s(z)))), z)) | b(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.44/4.64 tff(20731,plain,
% 4.44/4.64 (~b(s(s(s(s(z)))), z)),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[20730, 20725, 12064])).
% 4.44/4.64 tff(20732,plain,
% 4.44/4.64 (r(s(s(s(s(z)))), z)),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[191, 20731])).
% 4.44/4.64 tff(20733,plain,
% 4.44/4.64 ($false),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[14923, 118, 20732, 204, 20720])).
% 4.44/4.64 tff(20734,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~(elem!1 = z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.64 tff(20735,plain,
% 4.44/4.64 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[20734, 3461, 273, 145, 928, 104])).
% 4.44/4.64 tff(20736,plain,
% 4.44/4.64 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[222, 20735])).
% 4.44/4.64 tff(20737,plain,
% 4.44/4.64 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[5101, 147, 145, 3461])).
% 4.44/4.64 tff(20738,plain,
% 4.44/4.64 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[10755, 20737])).
% 4.44/4.64 tff(20739,plain,
% 4.44/4.64 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[11182, 178, 104, 20736, 20738, 3002])).
% 4.44/4.64 tff(20740,plain,
% 4.44/4.64 (r(s(s(s(s(z)))), s(s(s(z))))),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[11185, 20739])).
% 4.44/4.64 tff(20741,plain,
% 4.44/4.64 ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[8227, 178, 104, 20736, 3002])).
% 4.44/4.64 tff(20742,plain,
% 4.44/4.64 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[20741, 20738])).
% 4.44/4.64 tff(20743,plain,
% 4.44/4.64 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 20742])).
% 4.44/4.64 tff(20744,plain,
% 4.44/4.64 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 4.44/4.64 inference(monotonicity,[status(thm)],[932, 931])).
% 4.44/4.64 tff(20745,plain,
% 4.44/4.64 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 4.44/4.64 inference(symmetry,[status(thm)],[20744])).
% 4.44/4.64 tff(20746,plain,
% 4.44/4.64 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 4.44/4.64 inference(modus_ponens,[status(thm)],[20740, 20745])).
% 4.44/4.64 tff(20747,plain,
% 4.44/4.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.44/4.64 inference(rewrite,[status(thm)],[])).
% 4.44/4.64 tff(20748,plain,
% 4.44/4.64 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.44/4.64 inference(rewrite,[status(thm)],[])).
% 4.44/4.64 tff(20749,plain,
% 4.44/4.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 4.44/4.64 inference(monotonicity,[status(thm)],[20748])).
% 4.44/4.64 tff(20750,plain,
% 4.44/4.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.44/4.64 inference(transitivity,[status(thm)],[20749, 20747])).
% 4.44/4.64 tff(20751,plain,
% 4.44/4.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.44/4.64 inference(quant_inst,[status(thm)],[])).
% 4.44/4.64 tff(20752,plain,
% 4.44/4.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 4.44/4.64 inference(modus_ponens,[status(thm)],[20751, 20750])).
% 4.44/4.64 tff(20753,plain,
% 4.44/4.64 ($false),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[20752, 178, 104, 168, 146, 1126, 3002])).
% 4.44/4.64 tff(20754,plain,((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.64 tff(20755,plain,
% 4.44/4.64 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[20754, 168, 104, 1126, 3002])).
% 4.44/4.64 tff(20756,plain,
% 4.44/4.64 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[133, 20755])).
% 4.44/4.64 tff(20757,plain,
% 4.44/4.64 ($false),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[16088, 118, 108, 16062, 16063])).
% 4.44/4.64 tff(20758,plain,((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.64 tff(20759,plain,
% 4.44/4.64 (~r(s(s(s(z))), z)),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[20758, 20756, 16063])).
% 4.44/4.64 tff(20760,plain,
% 4.44/4.64 (b(s(s(s(z))), z)),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[4903, 41, 77, 20759])).
% 4.44/4.64 tff(20761,plain,
% 4.44/4.64 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(z)))),
% 4.44/4.64 inference(monotonicity,[status(thm)],[12066])).
% 4.44/4.64 tff(20762,plain,
% 4.44/4.64 (b(s(s(s(s(elem!1)))), s(s(z))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 4.44/4.64 inference(symmetry,[status(thm)],[20761])).
% 4.44/4.64 tff(20763,plain,
% 4.44/4.64 (r(s(s(s(elem!1))), z) <=> r(s(s(s(z))), z)),
% 4.44/4.64 inference(monotonicity,[status(thm)],[931])).
% 4.44/4.64 tff(20764,plain,
% 4.44/4.64 (r(s(s(s(z))), z) <=> r(s(s(s(elem!1))), z)),
% 4.44/4.64 inference(symmetry,[status(thm)],[20763])).
% 4.44/4.64 tff(20765,plain,
% 4.44/4.64 ((~r(s(s(s(z))), z)) <=> (~r(s(s(s(elem!1))), z))),
% 4.44/4.64 inference(monotonicity,[status(thm)],[20764])).
% 4.44/4.64 tff(20766,plain,
% 4.44/4.64 (~r(s(s(s(elem!1))), z)),
% 4.44/4.64 inference(modus_ponens,[status(thm)],[20759, 20765])).
% 4.44/4.64 tff(20767,plain,
% 4.44/4.64 (b(s(s(s(elem!1))), z)),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[1565, 20766])).
% 4.44/4.64 tff(20768,plain,
% 4.44/4.64 (~b(s(s(z)), s(s(s(elem!1))))),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[7978, 20767, 273, 3461, 2043])).
% 4.44/4.64 tff(20769,plain,
% 4.44/4.64 (r(s(s(z)), s(s(s(elem!1))))),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[4223, 20768])).
% 4.44/4.64 tff(20770,plain,
% 4.44/4.64 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[3644, 20769, 3630])).
% 4.44/4.64 tff(20771,plain,
% 4.44/4.64 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[1170, 20770])).
% 4.44/4.64 tff(20772,plain,
% 4.44/4.64 (b(s(s(s(s(z)))), s(s(z)))),
% 4.44/4.64 inference(modus_ponens,[status(thm)],[20771, 20762])).
% 4.44/4.64 tff(20773,plain,
% 4.44/4.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 4.44/4.64 inference(rewrite,[status(thm)],[])).
% 4.44/4.64 tff(20774,plain,
% 4.44/4.64 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 4.44/4.64 inference(rewrite,[status(thm)],[])).
% 4.44/4.64 tff(20775,plain,
% 4.44/4.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z))))),
% 4.44/4.64 inference(monotonicity,[status(thm)],[20774])).
% 4.44/4.64 tff(20776,plain,
% 4.44/4.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 4.44/4.64 inference(transitivity,[status(thm)],[20775, 20773])).
% 4.44/4.64 tff(20777,plain,
% 4.44/4.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 4.44/4.64 inference(quant_inst,[status(thm)],[])).
% 4.44/4.64 tff(20778,plain,
% 4.44/4.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z))),
% 4.44/4.64 inference(modus_ponens,[status(thm)],[20777, 20776])).
% 4.44/4.64 tff(20779,plain,
% 4.44/4.64 ($false),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[20778, 178, 273, 168, 20772, 1126, 20760])).
% 4.44/4.64 tff(20780,plain,((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~(elem!1 = z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(elem!1))))) | (~r(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)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.64 tff(20781,plain,
% 4.44/4.64 (~b(s(s(s(s(z)))), z)),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[20780, 20738, 273, 928, 20746, 3461, 2043, 20743, 104, 3002])).
% 4.44/4.64 tff(20782,plain,
% 4.44/4.64 (r(s(s(s(s(z)))), z)),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[191, 20781])).
% 4.44/4.64 tff(20783,plain,
% 4.44/4.64 ($false),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[8379, 118, 194, 4953, 16062])).
% 4.44/4.64 tff(20784,plain,((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.64 tff(20785,plain,
% 4.44/4.64 (~r(s(s(s(z))), z)),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[20784, 20782, 20740])).
% 4.44/4.64 tff(20786,plain,
% 4.44/4.64 (b(s(s(s(z))), z)),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[4903, 41, 77, 20785])).
% 4.44/4.64 tff(20787,plain,
% 4.44/4.64 (b(z, s(s(s(z))))),
% 4.44/4.64 inference(modus_ponens,[status(thm)],[2043, 20676])).
% 4.44/4.64 tff(20788,plain,
% 4.44/4.64 (~b(s(s(z)), s(s(s(z))))),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[7639, 178, 3461, 273, 20787, 20786])).
% 4.44/4.64 tff(20789,plain,
% 4.44/4.64 (r(s(s(z)), s(s(s(z))))),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[5088, 20788])).
% 4.44/4.64 tff(20790,plain,
% 4.44/4.64 ($false),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[7239, 118, 147, 20740, 20789])).
% 4.44/4.64 tff(20791,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~(elem!1 = z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.64 tff(20792,plain,
% 4.44/4.64 (~r(s(s(z)), s(s(s(s(z)))))),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[20791, 20668, 273, 928, 20659, 104, 3461, 145])).
% 4.44/4.64 tff(20793,plain,
% 4.44/4.64 (b(s(s(z)), s(s(s(s(z)))))),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[164, 20792])).
% 4.44/4.64 tff(20794,plain,
% 4.44/4.64 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[16623, 20793, 20736, 20668, 224, 104])).
% 4.44/4.64 tff(20795,plain,
% 4.44/4.64 (r(s(s(s(z))), s(s(s(s(z)))))),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[10755, 20794])).
% 4.44/4.64 tff(20796,plain,
% 4.44/4.64 ($false),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[4899, 118, 145, 4891, 16062])).
% 4.44/4.64 tff(20797,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.64 tff(20798,plain,
% 4.44/4.64 (~r(s(s(s(z))), z)),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[20797, 20795, 145])).
% 4.44/4.64 tff(20799,plain,
% 4.44/4.64 (b(s(s(s(z))), z)),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[4903, 41, 77, 20798])).
% 4.44/4.64 tff(20800,plain,
% 4.44/4.64 (b(z, s(s(s(z))))),
% 4.44/4.64 inference(modus_ponens,[status(thm)],[20659, 20676])).
% 4.44/4.64 tff(20801,plain,
% 4.44/4.64 (~b(s(s(s(z))), s(s(z)))),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[17111, 178, 3461, 273, 20800, 20799])).
% 4.44/4.64 tff(20802,plain,
% 4.44/4.64 (r(s(s(s(z))), s(s(z)))),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[4966, 20801])).
% 4.44/4.64 tff(20803,plain,
% 4.44/4.64 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[1272, 20802, 20650, 224])).
% 4.44/4.64 tff(20804,plain,
% 4.44/4.64 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 4.44/4.64 inference(monotonicity,[status(thm)],[931])).
% 4.44/4.64 tff(20805,plain,
% 4.44/4.64 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.44/4.64 inference(symmetry,[status(thm)],[20804])).
% 4.44/4.64 tff(20806,plain,
% 4.44/4.64 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.44/4.64 inference(modus_ponens,[status(thm)],[20795, 20805])).
% 4.44/4.64 tff(20807,plain,
% 4.44/4.64 (~r(s(s(z)), s(s(s(s(z)))))),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[8234, 3251, 145, 2043])).
% 4.44/4.64 tff(20808,plain,
% 4.44/4.64 (b(s(s(z)), s(s(s(s(z)))))),
% 4.44/4.64 inference(unit_resolution,[status(thm)],[164, 20807])).
% 4.44/4.64 tff(20809,plain,
% 4.44/4.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))))),
% 4.44/4.64 inference(rewrite,[status(thm)],[])).
% 4.44/4.64 tff(20810,plain,
% 4.44/4.64 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))))),
% 4.44/4.64 inference(rewrite,[status(thm)],[])).
% 4.44/4.64 tff(20811,plain,
% 4.44/4.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z)))))))),
% 4.44/4.64 inference(monotonicity,[status(thm)],[20810])).
% 4.44/4.64 tff(20812,plain,
% 4.44/4.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))))),
% 4.44/4.64 inference(transitivity,[status(thm)],[20811, 20809])).
% 4.44/4.64 tff(20813,plain,
% 4.44/4.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 4.44/4.65 inference(quant_inst,[status(thm)],[])).
% 4.44/4.65 tff(20814,plain,
% 4.44/4.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z)))))),
% 4.44/4.65 inference(modus_ponens,[status(thm)],[20813, 20812])).
% 4.44/4.65 tff(20815,plain,
% 4.44/4.65 ($false),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[20814, 178, 3461, 168, 167, 3008, 6170])).
% 4.44/4.65 tff(20816,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.65 tff(20817,plain,
% 4.44/4.65 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[20816, 20808, 168, 3461, 20787])).
% 4.44/4.65 tff(20818,plain,
% 4.44/4.65 (r(s(s(s(s(z)))), s(s(s(z))))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[11185, 20817])).
% 4.44/4.65 tff(20819,plain,
% 4.44/4.65 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 4.44/4.65 inference(modus_ponens,[status(thm)],[20818, 20745])).
% 4.44/4.65 tff(20820,plain,
% 4.44/4.65 (r(s(s(s(z))), s(s(s(s(z)))))),
% 4.44/4.65 inference(modus_ponens,[status(thm)],[3251, 20804])).
% 4.44/4.65 tff(20821,assumption,(~r(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 4.44/4.65 tff(20822,plain,
% 4.44/4.65 ($false),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[20821, 20820])).
% 4.44/4.65 tff(20823,plain,(r(s(s(s(z))), s(s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.65 tff(20824,plain,
% 4.44/4.65 (r(s(s(s(z))), s(s(s(s(z)))))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[20823, 3251, 928])).
% 4.44/4.65 tff(20825,plain,
% 4.44/4.65 (~r(s(s(s(z))), z)),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[20797, 20824, 145])).
% 4.44/4.65 tff(20826,plain,
% 4.44/4.65 (~r(s(s(s(elem!1))), z)),
% 4.44/4.65 inference(modus_ponens,[status(thm)],[20825, 20765])).
% 4.44/4.65 tff(20827,plain,
% 4.44/4.65 (b(s(s(s(elem!1))), z)),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[1565, 20826])).
% 4.44/4.65 tff(20828,plain,
% 4.44/4.65 (~b(s(s(z)), s(s(s(elem!1))))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[7978, 20827, 273, 3461, 2043])).
% 4.44/4.65 tff(20829,plain,
% 4.44/4.65 (r(s(s(z)), s(s(s(elem!1))))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[4223, 20828])).
% 4.44/4.65 tff(20830,plain,
% 4.44/4.65 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[3644, 20829, 20819])).
% 4.44/4.65 tff(20831,plain,
% 4.44/4.65 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[1170, 20830])).
% 4.44/4.65 tff(20832,plain,
% 4.44/4.65 (b(s(s(s(s(z)))), s(s(z)))),
% 4.44/4.65 inference(modus_ponens,[status(thm)],[20831, 20762])).
% 4.44/4.65 tff(20833,plain,
% 4.44/4.65 ($false),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[16647, 178, 3461, 273, 168, 20808, 20832])).
% 4.44/4.65 tff(20834,plain,((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~(elem!1 = z)) | (~b(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.65 tff(20835,plain,
% 4.44/4.65 (~b(s(s(s(s(z)))), z)),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[20834, 20806, 273, 3461, 928, 20659, 145])).
% 4.44/4.65 tff(20836,plain,
% 4.44/4.65 (r(s(s(s(s(z)))), z)),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[191, 20835])).
% 4.44/4.65 tff(20837,plain,
% 4.44/4.65 ($false),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[17170, 118, 193, 1125, 4891])).
% 4.44/4.65 tff(20838,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.65 tff(20839,plain,
% 4.44/4.65 (~r(s(s(s(s(z)))), s(s(z)))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[20838, 20802, 20795])).
% 4.44/4.65 tff(20840,plain,
% 4.44/4.65 (b(s(s(s(s(z)))), s(s(z)))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[102, 20839])).
% 4.44/4.65 tff(20841,plain,
% 4.44/4.65 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[8089, 178, 104, 20793, 20736, 20840])).
% 4.44/4.65 tff(20842,plain,
% 4.44/4.65 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[3578, 20841])).
% 4.44/4.65 tff(20843,plain,
% 4.44/4.65 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[1175, 118, 20802, 20842])).
% 4.44/4.65 tff(20844,plain,
% 4.44/4.65 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 20843])).
% 4.44/4.65 tff(20845,plain,
% 4.44/4.65 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[1245, 178, 20800, 20799, 20668, 20844])).
% 4.44/4.65 tff(20846,plain,
% 4.44/4.65 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[133, 20845])).
% 4.44/4.65 tff(20847,plain,
% 4.44/4.65 (r(s(elem!1), elem!1) <=> r(s(z), z)),
% 4.44/4.65 inference(transitivity,[status(thm)],[12732, 14134])).
% 4.44/4.65 tff(20848,plain,
% 4.44/4.65 (r(s(z), z)),
% 4.44/4.65 inference(modus_ponens,[status(thm)],[1426, 20847])).
% 4.44/4.65 tff(20849,plain,
% 4.44/4.65 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[14138, 118, 108, 20848])).
% 4.44/4.65 tff(20850,plain,
% 4.44/4.65 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[615, 41, 612, 20849])).
% 4.44/4.65 tff(20851,plain,
% 4.44/4.65 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), z)),
% 4.44/4.65 inference(monotonicity,[status(thm)],[928])).
% 4.44/4.65 tff(20852,plain,
% 4.44/4.65 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(z)))), elem!1)),
% 4.44/4.65 inference(symmetry,[status(thm)],[20851])).
% 4.44/4.65 tff(20853,plain,
% 4.44/4.65 (r(s(s(s(s(z)))), elem!1)),
% 4.44/4.65 inference(modus_ponens,[status(thm)],[194, 20852])).
% 4.44/4.65 tff(20854,plain,
% 4.44/4.65 (~r(s(elem!1), s(s(s(s(z)))))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[7010, 1426, 20853])).
% 4.44/4.65 tff(20855,plain,
% 4.44/4.65 (b(s(elem!1), s(s(s(s(z)))))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[1084, 20854, 1369])).
% 4.44/4.65 tff(20856,plain,
% 4.44/4.65 (b(s(z), s(s(s(s(z)))))),
% 4.44/4.65 inference(modus_ponens,[status(thm)],[20855, 14888])).
% 4.44/4.65 tff(20857,plain,
% 4.44/4.65 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(z))),
% 4.44/4.65 inference(monotonicity,[status(thm)],[929])).
% 4.44/4.65 tff(20858,plain,
% 4.44/4.65 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(z)))), s(elem!1))),
% 4.44/4.65 inference(symmetry,[status(thm)],[20857])).
% 4.44/4.65 tff(20859,plain,
% 4.44/4.65 ((~r(s(s(s(s(z)))), s(z))) <=> (~r(s(s(s(s(z)))), s(elem!1)))),
% 4.44/4.65 inference(monotonicity,[status(thm)],[20858])).
% 4.44/4.65 tff(20860,plain,
% 4.44/4.65 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 4.44/4.65 inference(rewrite,[status(thm)],[])).
% 4.44/4.65 tff(20861,plain,
% 4.44/4.65 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 4.44/4.65 inference(quant_inst,[status(thm)],[])).
% 4.44/4.65 tff(20862,plain,
% 4.44/4.65 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))),
% 4.44/4.65 inference(modus_ponens,[status(thm)],[20861, 20860])).
% 4.44/4.65 tff(20863,plain,
% 4.44/4.65 (~r(s(s(s(s(z)))), s(z))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[20862, 118, 194, 20848])).
% 4.44/4.65 tff(20864,plain,
% 4.44/4.65 (~r(s(s(s(s(z)))), s(elem!1))),
% 4.44/4.65 inference(modus_ponens,[status(thm)],[20863, 20859])).
% 4.44/4.65 tff(20865,plain,
% 4.44/4.65 (b(s(s(s(s(z)))), s(elem!1))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[2173, 20864, 2169])).
% 4.44/4.65 tff(20866,plain,
% 4.44/4.65 (b(s(s(s(s(z)))), s(z))),
% 4.44/4.65 inference(modus_ponens,[status(thm)],[20865, 12849])).
% 4.44/4.65 tff(20867,plain,
% 4.44/4.65 ($false),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[14897, 178, 104, 251, 20866, 20856, 20850])).
% 4.44/4.65 tff(20868,plain,((~r(s(elem!1), 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))))))))) | (~(elem!1 = z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), z)) | (s(elem!1) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.65 tff(20869,plain,
% 4.44/4.65 (~r(s(elem!1), elem!1)),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[20868, 20846, 20736, 928, 104, 20836, 20803])).
% 4.44/4.65 tff(20870,plain,
% 4.44/4.65 (b(s(elem!1), elem!1)),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[677, 20869, 20662])).
% 4.44/4.65 tff(20871,plain,
% 4.44/4.65 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), z)),
% 4.44/4.65 inference(monotonicity,[status(thm)],[928])).
% 4.44/4.65 tff(20872,plain,
% 4.44/4.65 (r(s(s(s(elem!1))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 4.44/4.65 inference(symmetry,[status(thm)],[20871])).
% 4.44/4.65 tff(20873,plain,
% 4.44/4.65 (r(s(s(s(z))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 4.44/4.65 inference(transitivity,[status(thm)],[20764, 20872])).
% 4.44/4.65 tff(20874,plain,
% 4.44/4.65 ((~r(s(s(s(z))), z)) <=> (~r(s(s(s(elem!1))), elem!1))),
% 4.44/4.65 inference(monotonicity,[status(thm)],[20873])).
% 4.44/4.65 tff(20875,plain,
% 4.44/4.65 (~r(s(s(s(elem!1))), elem!1)),
% 4.44/4.65 inference(modus_ponens,[status(thm)],[20798, 20874])).
% 4.44/4.65 tff(20876,plain,
% 4.44/4.65 (b(s(s(s(elem!1))), elem!1)),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[570, 20875, 941])).
% 4.44/4.65 tff(20877,plain,
% 4.44/4.65 (b(s(elem!1), z)),
% 4.44/4.65 inference(modus_ponens,[status(thm)],[20870, 12061])).
% 4.44/4.65 tff(20878,plain,
% 4.44/4.65 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(z)), s(s(z)))),
% 4.44/4.65 inference(monotonicity,[status(thm)],[930])).
% 4.44/4.65 tff(20879,plain,
% 4.44/4.65 (b(s(s(z)), s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 4.44/4.65 inference(symmetry,[status(thm)],[20878])).
% 4.44/4.65 tff(20880,plain,
% 4.44/4.65 ((~b(s(s(z)), s(s(z)))) <=> (~b(s(s(elem!1)), s(s(z))))),
% 4.44/4.65 inference(monotonicity,[status(thm)],[20879])).
% 4.44/4.65 tff(20881,plain,
% 4.44/4.65 (~b(s(s(elem!1)), s(s(z)))),
% 4.44/4.65 inference(modus_ponens,[status(thm)],[20177, 20880])).
% 4.44/4.65 tff(20882,plain,
% 4.44/4.65 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 4.44/4.65 inference(monotonicity,[status(thm)],[5392])).
% 4.44/4.65 tff(20883,plain,
% 4.44/4.65 (inj_0(s(s(s(elem!1)))) = inj_0(s(elem!1))),
% 4.44/4.65 inference(symmetry,[status(thm)],[20882])).
% 4.44/4.65 tff(20884,plain,
% 4.44/4.65 (s(s(elem!1)) = elem!1),
% 4.44/4.65 inference(transitivity,[status(thm)],[344, 20883, 304])).
% 4.44/4.65 tff(20885,plain,
% 4.44/4.65 (b(s(s(elem!1)), s(s(z))) <=> b(elem!1, s(s(z)))),
% 4.44/4.65 inference(monotonicity,[status(thm)],[20884])).
% 4.44/4.65 tff(20886,plain,
% 4.44/4.65 (b(elem!1, s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 4.44/4.65 inference(symmetry,[status(thm)],[20885])).
% 4.44/4.65 tff(20887,plain,
% 4.44/4.65 (b(s(s(elem!1)), s(s(z)))),
% 4.44/4.65 inference(modus_ponens,[status(thm)],[812, 20886])).
% 4.44/4.65 tff(20888,plain,
% 4.44/4.65 ($false),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[6489, 20887])).
% 4.44/4.65 tff(20889,plain,(b(s(s(elem!1)), s(s(z))) | (~b(elem!1, s(s(z)))) | (~(s(elem!1) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.65 tff(20890,plain,
% 4.44/4.65 (~(s(elem!1) = s(s(s(elem!1))))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[20889, 20881, 20724])).
% 4.44/4.65 tff(20891,plain,
% 4.44/4.65 (~r(s(s(s(elem!1))), z)),
% 4.44/4.65 inference(modus_ponens,[status(thm)],[20798, 20765])).
% 4.44/4.65 tff(20892,plain,
% 4.44/4.65 (b(s(s(s(elem!1))), z)),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[1565, 20891])).
% 4.44/4.65 tff(20893,plain,
% 4.44/4.65 (~b(s(s(z)), s(s(s(elem!1))))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[7978, 20892, 273, 3461, 20659])).
% 4.44/4.65 tff(20894,plain,
% 4.44/4.65 (~b(s(s(z)), s(elem!1))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[14084, 854, 3461, 812, 853])).
% 4.44/4.65 tff(20895,plain,
% 4.44/4.65 (~r(s(s(z)), s(elem!1))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[6127, 11553, 4218, 5425])).
% 4.44/4.65 tff(20896,plain,
% 4.44/4.65 ($false),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[1067, 20895, 20894, 1060])).
% 4.44/4.65 tff(20897,plain,((~b(elem!1, s(elem!1))) | (s(s(z)) = s(elem!1)) | b(s(s(z)), s(s(s(elem!1)))) | (s(elem!1) = s(s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.65 tff(20898,plain,
% 4.44/4.65 (~b(elem!1, s(elem!1))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[20897, 20893, 2311, 20890, 3461, 20724, 20877, 20876, 20870, 20660])).
% 4.44/4.65 tff(20899,plain,
% 4.44/4.65 (r(elem!1, s(elem!1))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[756, 20898, 20655])).
% 4.44/4.65 tff(20900,plain,
% 4.44/4.65 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[2935, 20899, 20650])).
% 4.44/4.65 tff(20901,plain,
% 4.44/4.65 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[395, 20900, 14147])).
% 4.44/4.65 tff(20902,plain,
% 4.44/4.65 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.65 inference(modus_ponens,[status(thm)],[20901, 20647])).
% 4.44/4.65 tff(20903,plain,
% 4.44/4.65 (~(s(s(s(s(z)))) = s(elem!1))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[2168, 20803])).
% 4.44/4.65 tff(20904,plain,
% 4.44/4.65 (r(z, s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 4.44/4.65 inference(symmetry,[status(thm)],[5244])).
% 4.44/4.65 tff(20905,plain,
% 4.44/4.65 (r(elem!1, s(s(s(s(z)))))),
% 4.44/4.65 inference(modus_ponens,[status(thm)],[145, 20904])).
% 4.44/4.65 tff(20906,plain,
% 4.44/4.65 (~r(s(s(s(s(z)))), s(elem!1))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[11326, 20899, 20905])).
% 4.44/4.65 tff(20907,plain,
% 4.44/4.65 (b(s(s(s(s(z)))), s(elem!1))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[2173, 20906, 20903])).
% 4.44/4.65 tff(20908,plain,
% 4.44/4.65 (b(s(s(s(s(z)))), s(z))),
% 4.44/4.65 inference(modus_ponens,[status(thm)],[20907, 12849])).
% 4.44/4.65 tff(20909,plain,
% 4.44/4.65 (~b(s(s(z)), s(elem!1))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[6790, 908, 3461, 202, 273, 194, 1056])).
% 4.44/4.65 tff(20910,plain,
% 4.44/4.65 (r(s(s(z)), s(elem!1))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[1067, 20909, 2311])).
% 4.44/4.65 tff(20911,plain,
% 4.44/4.65 (b(elem!1, s(elem!1))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[756, 17652, 750])).
% 4.44/4.65 tff(20912,plain,
% 4.44/4.65 (~b(s(elem!1), s(s(s(elem!1))))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[6834, 20911, 1597, 683, 2042])).
% 4.44/4.65 tff(20913,plain,
% 4.44/4.65 ($false),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[6127, 20912, 20910, 4218, 5425])).
% 4.44/4.65 tff(20914,plain,((~r(s(elem!1), s(s(s(s(z)))))) | b(s(s(z)), s(s(s(elem!1)))) | (s(elem!1) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (elem!1 = s(elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (s(elem!1) = s(s(z))) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.65 tff(20915,plain,
% 4.44/4.65 (~r(s(elem!1), s(s(s(s(z)))))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[20914, 20893, 20890, 20876, 20870, 20660, 20655, 3461, 20840, 273, 20836, 1056, 20905])).
% 4.44/4.65 tff(20916,plain,
% 4.44/4.65 (b(s(elem!1), s(s(s(s(z)))))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[1084, 20915, 20803])).
% 4.44/4.65 tff(20917,plain,
% 4.44/4.65 (b(s(z), s(s(s(s(z)))))),
% 4.44/4.65 inference(modus_ponens,[status(thm)],[20916, 14888])).
% 4.44/4.65 tff(20918,plain,
% 4.44/4.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 4.44/4.65 inference(rewrite,[status(thm)],[])).
% 4.44/4.65 tff(20919,plain,
% 4.44/4.65 (((~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(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), 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(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 4.44/4.65 inference(rewrite,[status(thm)],[])).
% 4.44/4.65 tff(20920,plain,
% 4.44/4.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 4.44/4.65 inference(monotonicity,[status(thm)],[20919])).
% 4.44/4.65 tff(20921,plain,
% 4.44/4.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 4.44/4.65 inference(transitivity,[status(thm)],[20920, 20918])).
% 4.44/4.65 tff(20922,plain,
% 4.44/4.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 4.44/4.65 inference(quant_inst,[status(thm)],[])).
% 4.44/4.65 tff(20923,plain,
% 4.44/4.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 4.44/4.65 inference(modus_ponens,[status(thm)],[20922, 20921])).
% 4.44/4.65 tff(20924,plain,
% 4.44/4.65 ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[20923, 178, 104, 20736, 20917])).
% 4.44/4.65 tff(20925,plain,
% 4.44/4.65 ($false),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[20924, 20908, 20902])).
% 4.44/4.65 tff(20926,plain,((~r(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)))))) | (~(elem!1 = z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (s(elem!1) = s(s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.65 tff(20927,plain,
% 4.44/4.65 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[20926, 20646, 928, 5619, 273, 104, 47, 203])).
% 4.44/4.65 tff(20928,plain,
% 4.44/4.65 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[249, 20927])).
% 4.44/4.65 tff(20929,plain,
% 4.44/4.65 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[20834, 168, 273, 3461, 928, 20659, 145])).
% 4.44/4.65 tff(20930,plain,
% 4.44/4.65 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[4173, 20929, 10731])).
% 4.44/4.65 tff(20931,plain,
% 4.44/4.65 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.44/4.65 inference(modus_ponens,[status(thm)],[20930, 20678])).
% 4.44/4.65 tff(20932,plain,
% 4.44/4.65 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 4.44/4.65 inference(modus_ponens,[status(thm)],[4938, 15341])).
% 4.44/4.65 tff(20933,plain,
% 4.44/4.65 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 4.44/4.65 inference(monotonicity,[status(thm)],[931])).
% 4.44/4.65 tff(20934,plain,
% 4.44/4.65 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.44/4.65 inference(symmetry,[status(thm)],[20933])).
% 4.44/4.65 tff(20935,plain,
% 4.44/4.65 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.44/4.65 inference(transitivity,[status(thm)],[12078, 20934])).
% 4.44/4.65 tff(20936,plain,
% 4.44/4.65 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.44/4.65 inference(modus_ponens,[status(thm)],[3709, 20935])).
% 4.44/4.65 tff(20937,plain,
% 4.44/4.65 (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[4103, 20936, 104, 251, 3831])).
% 4.44/4.65 tff(20938,plain,
% 4.44/4.65 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.65 inference(monotonicity,[status(thm)],[931])).
% 4.44/4.65 tff(20939,plain,
% 4.44/4.65 (b(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))))))))),
% 4.44/4.65 inference(symmetry,[status(thm)],[20938])).
% 4.44/4.65 tff(20940,plain,
% 4.44/4.65 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.65 inference(modus_ponens,[status(thm)],[3002, 20939])).
% 4.44/4.65 tff(20941,plain,
% 4.44/4.65 ($false),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[8928, 20940])).
% 4.44/4.65 tff(20942,plain,((~b(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)))))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.65 tff(20943,plain,
% 4.44/4.65 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[20942, 20937, 928])).
% 4.44/4.65 tff(20944,plain,
% 4.44/4.65 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[20667, 20943])).
% 4.44/4.65 tff(20945,plain,
% 4.44/4.65 (~r(s(s(s(z))), z)),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[11272, 118, 203, 20944])).
% 4.44/4.65 tff(20946,plain,
% 4.44/4.65 (b(s(s(s(z))), z)),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[4903, 41, 77, 20945])).
% 4.44/4.65 tff(20947,plain,
% 4.44/4.65 (b(s(s(s(s(z)))), s(s(s(z))))),
% 4.44/4.65 inference(modus_ponens,[status(thm)],[3709, 12078])).
% 4.44/4.65 tff(20948,plain,
% 4.44/4.65 (~b(s(s(z)), s(s(s(s(z)))))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[20814, 178, 3461, 168, 20800, 20947])).
% 4.44/4.65 tff(20949,plain,
% 4.44/4.65 (r(s(s(z)), s(s(s(s(z)))))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[164, 20948])).
% 4.44/4.65 tff(20950,plain,
% 4.44/4.65 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[5101, 20949, 145, 3461])).
% 4.44/4.65 tff(20951,plain,
% 4.44/4.65 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[10755, 20950])).
% 4.44/4.65 tff(20952,plain,
% 4.44/4.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 4.44/4.65 inference(rewrite,[status(thm)],[])).
% 4.44/4.65 tff(20953,plain,
% 4.44/4.65 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 4.44/4.65 inference(rewrite,[status(thm)],[])).
% 4.44/4.65 tff(20954,plain,
% 4.44/4.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 4.44/4.65 inference(monotonicity,[status(thm)],[20953])).
% 4.44/4.65 tff(20955,plain,
% 4.44/4.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 4.44/4.65 inference(transitivity,[status(thm)],[20954, 20952])).
% 4.44/4.65 tff(20956,plain,
% 4.44/4.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 4.44/4.65 inference(quant_inst,[status(thm)],[])).
% 4.44/4.65 tff(20957,plain,
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% 4.44/4.65 inference(modus_ponens,[status(thm)],[20956, 20955])).
% 4.44/4.65 tff(20958,plain,
% 4.44/4.65 ($false),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[20957, 178, 168, 20951, 20800, 20947, 20946])).
% 4.44/4.65 tff(20959,plain,((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~(elem!1 = 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(s(elem!1))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.65 tff(20960,plain,
% 4.44/4.65 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[20959, 168, 203, 145, 3461, 928, 104, 20736, 20930])).
% 4.44/4.65 tff(20961,plain,
% 4.44/4.65 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[1988, 20960, 20932])).
% 4.44/4.65 tff(20962,plain,
% 4.44/4.65 (~r(s(s(s(elem!1))), z)),
% 4.44/4.65 inference(modus_ponens,[status(thm)],[20637, 20765])).
% 4.44/4.65 tff(20963,plain,
% 4.44/4.65 (b(s(s(s(z))), z)),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[4903, 41, 77, 20637])).
% 4.44/4.65 tff(20964,plain,
% 4.44/4.65 (b(s(s(s(elem!1))), z)),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[1565, 1560])).
% 4.44/4.65 tff(20965,plain,
% 4.44/4.65 (~b(s(s(z)), s(s(s(elem!1))))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[7978, 20964, 273, 3461, 2043])).
% 4.44/4.65 tff(20966,plain,
% 4.44/4.65 (r(s(s(z)), s(s(s(elem!1))))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[4223, 20965])).
% 4.44/4.65 tff(20967,plain,
% 4.44/4.65 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[3644, 20966, 3630])).
% 4.44/4.65 tff(20968,plain,
% 4.44/4.65 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[1170, 20967])).
% 4.44/4.65 tff(20969,plain,
% 4.44/4.65 (b(s(s(s(s(z)))), s(s(z)))),
% 4.44/4.65 inference(modus_ponens,[status(thm)],[20968, 20762])).
% 4.44/4.65 tff(20970,plain,
% 4.44/4.65 ($false),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[20778, 178, 273, 168, 20969, 1126, 20963])).
% 4.44/4.65 tff(20971,plain,(r(s(s(s(elem!1))), z) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~(elem!1 = z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(elem!1))))) | r(s(s(s(z))), z)), inference(lemma,lemma(discharge,[]))).
% 4.44/4.65 tff(20972,plain,
% 4.44/4.65 (r(s(s(s(elem!1))), z)),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[20971, 20637, 168, 1126, 928, 3630, 3461, 2043, 273])).
% 4.44/4.65 tff(20973,plain,
% 4.44/4.65 ($false),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[20972, 20962])).
% 4.44/4.65 tff(20974,plain,(r(s(s(s(z))), z) | (~(elem!1 = z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.65 tff(20975,plain,
% 4.44/4.65 (r(s(s(s(z))), z)),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[20974, 168, 928, 20931, 20961, 3461, 20659, 273])).
% 4.44/4.65 tff(20976,plain,
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% 4.44/4.65 inference(unit_resolution,[status(thm)],[11272, 118, 203, 16062, 8216])).
% 4.44/4.65 tff(20977,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.65 tff(20978,plain,
% 4.44/4.65 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[20977, 20975, 203])).
% 4.44/4.65 tff(20979,plain,
% 4.44/4.65 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.65 inference(unit_resolution,[status(thm)],[20667, 20978])).
% 4.44/4.65 tff(20980,plain,
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% 4.44/4.65 inference(unit_resolution,[status(thm)],[20791, 20979, 273, 928, 20659, 104, 3461, 145])).
% 4.44/4.65 tff(20981,plain,
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% 4.44/4.66 inference(unit_resolution,[status(thm)],[164, 20980])).
% 4.44/4.66 tff(20982,plain,
% 4.44/4.66 (~b(s(s(s(s(z)))), s(s(z)))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[259, 20981, 104, 20736, 166])).
% 4.44/4.66 tff(20983,plain,
% 4.44/4.66 (r(s(s(s(s(z)))), s(s(z)))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[102, 20982])).
% 4.44/4.66 tff(20984,plain,
% 4.44/4.66 ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[9047, 178, 104, 166, 20736])).
% 4.44/4.66 tff(20985,plain,
% 4.44/4.66 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[20984, 20981])).
% 4.44/4.66 tff(20986,plain,
% 4.44/4.66 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[3578, 20985])).
% 4.44/4.66 tff(20987,plain,
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% 4.44/4.66 inference(unit_resolution,[status(thm)],[17159, 20986, 20983, 104, 166, 20981, 20931])).
% 4.44/4.66 tff(20988,plain,((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~(elem!1 = z)) | (~b(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.66 tff(20989,plain,
% 4.44/4.66 (~b(s(s(s(s(z)))), z)),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[20988, 20928, 104, 273, 928, 5619, 47, 203])).
% 4.44/4.66 tff(20990,plain,
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% 4.44/4.66 tff(20991,plain,
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% 4.44/4.66 tff(20992,plain,((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | r(s(s(s(z))), z)), inference(lemma,lemma(discharge,[]))).
% 4.44/4.66 tff(20993,plain,
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% 4.44/4.66 inference(unit_resolution,[status(thm)],[20992, 20637, 273, 20787, 5619])).
% 4.44/4.66 tff(20994,plain,
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% 4.44/4.66 tff(20995,plain,
% 4.44/4.66 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
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% 4.44/4.66 tff(20996,plain,
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% 4.44/4.66 inference(unit_resolution,[status(thm)],[222, 20995])).
% 4.44/4.66 tff(20997,plain,
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% 4.44/4.66 inference(modus_ponens,[status(thm)],[2043, 20657])).
% 4.44/4.66 tff(20998,plain,
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% 4.44/4.66 inference(modus_ponens,[status(thm)],[20637, 20874])).
% 4.44/4.66 tff(20999,plain,
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% 4.44/4.66 tff(21000,plain,
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% 4.44/4.66 tff(21001,plain,
% 4.44/4.66 (~b(s(s(z)), s(s(s(elem!1))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[7978, 21000, 273, 5619, 2043])).
% 4.44/4.66 tff(21002,plain,
% 4.44/4.66 (~r(s(s(s(s(z)))), s(s(s(z))))),
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% 4.44/4.66 tff(21003,plain,
% 4.44/4.66 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[7220, 21002, 20853])).
% 4.44/4.66 tff(21004,plain,
% 4.44/4.66 (b(s(s(s(s(z)))), s(s(s(z))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[11185, 21002])).
% 4.44/4.66 tff(21005,plain,
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% 4.44/4.66 inference(unit_resolution,[status(thm)],[5101, 4891, 145, 3461])).
% 4.44/4.66 tff(21006,plain,
% 4.44/4.66 (b(s(s(z)), s(s(s(s(z)))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[164, 21005])).
% 4.44/4.66 tff(21007,plain,
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% 4.44/4.66 inference(unit_resolution,[status(thm)],[20838, 4891, 1125])).
% 4.44/4.66 tff(21008,plain,
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% 4.44/4.66 inference(unit_resolution,[status(thm)],[102, 21007])).
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% 4.44/4.66 tff(21010,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.66 tff(21011,plain,
% 4.44/4.66 (~r(s(s(s(z))), s(s(s(s(z)))))),
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% 4.44/4.66 inference(unit_resolution,[status(thm)],[11182, 178, 104, 20996, 21012])).
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% 4.44/4.66 tff(21015,plain,
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% 4.44/4.66 tff(21016,plain,
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% 4.44/4.66 tff(21029,plain,
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% 4.44/4.66 inference(unit_resolution,[status(thm)],[14170, 21029, 928, 166, 21019, 21017])).
% 4.44/4.66 tff(21031,plain,
% 4.44/4.66 (b(s(elem!1), z)),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[774, 21030])).
% 4.44/4.66 tff(21032,plain,
% 4.44/4.66 (~b(elem!1, s(elem!1))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[20897, 21031, 2311, 21023, 5619, 20724, 4218, 1597, 21021, 2042])).
% 4.44/4.66 tff(21033,plain,
% 4.44/4.66 (r(elem!1, s(elem!1))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[756, 21032, 20655])).
% 4.44/4.66 tff(21034,plain,
% 4.44/4.66 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[2935, 21033, 1265])).
% 4.44/4.66 tff(21035,plain,
% 4.44/4.66 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[395, 21034, 14147])).
% 4.44/4.66 tff(21036,plain,
% 4.44/4.66 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.66 inference(modus_ponens,[status(thm)],[21035, 20647])).
% 4.44/4.66 tff(21037,plain,
% 4.44/4.66 (~r(s(elem!1), s(s(s(s(z)))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[6776, 21031, 273, 1056, 21028, 5619])).
% 4.44/4.66 tff(21038,plain,
% 4.44/4.66 (b(s(elem!1), s(s(s(s(z)))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[1084, 21037, 21003])).
% 4.44/4.66 tff(21039,plain,
% 4.44/4.66 (b(s(z), s(s(s(s(z)))))),
% 4.44/4.66 inference(modus_ponens,[status(thm)],[21038, 14888])).
% 4.44/4.66 tff(21040,plain,
% 4.44/4.66 (~(s(s(s(s(z)))) = s(elem!1))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[2168, 21003])).
% 4.44/4.66 tff(21041,plain,
% 4.44/4.66 (r(elem!1, s(s(s(s(z)))))),
% 4.44/4.66 inference(modus_ponens,[status(thm)],[47, 20904])).
% 4.44/4.66 tff(21042,plain,
% 4.44/4.66 (~r(s(s(s(s(z)))), s(elem!1))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[11326, 21033, 21041])).
% 4.44/4.66 tff(21043,plain,
% 4.44/4.66 (b(s(s(s(s(z)))), s(elem!1))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[2173, 21042, 21040])).
% 4.44/4.66 tff(21044,plain,
% 4.44/4.66 (b(s(s(s(s(z)))), s(z))),
% 4.44/4.66 inference(modus_ponens,[status(thm)],[21043, 12849])).
% 4.44/4.66 tff(21045,plain,
% 4.44/4.66 ($false),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[20923, 178, 104, 20996, 21044, 21039, 21036])).
% 4.44/4.66 tff(21046,plain,(b(s(s(s(s(z)))), s(s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~(elem!1 = z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (s(elem!1) = s(s(z))) | b(s(s(z)), s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | b(z, s(s(s(s(z))))) | r(s(s(z)), z) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.66 tff(21047,plain,
% 4.44/4.66 (b(s(s(s(s(z)))), s(s(z)))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[21046, 21001, 928, 1265, 273, 17599, 104, 20999, 20997, 166, 1, 5618, 194, 20994])).
% 4.44/4.66 tff(21048,plain,
% 4.44/4.66 (~b(s(s(z)), s(s(s(s(z)))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[259, 21047, 104, 20996, 166])).
% 4.44/4.66 tff(21049,plain,
% 4.44/4.66 (r(s(s(z)), s(s(s(s(z)))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[164, 21048])).
% 4.44/4.66 tff(21050,plain,
% 4.44/4.66 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[20791, 21049, 273, 928, 2043, 104, 5619, 47])).
% 4.44/4.66 tff(21051,plain,
% 4.44/4.66 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[20667, 21050])).
% 4.44/4.66 tff(21052,plain,
% 4.44/4.66 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[8218, 21051, 20994])).
% 4.44/4.66 tff(21053,plain,
% 4.44/4.66 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[3578, 21052])).
% 4.44/4.66 tff(21054,plain,
% 4.44/4.66 ($false),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[16486, 178, 104, 166, 20996, 21047, 21053])).
% 4.44/4.66 tff(21055,plain,(r(s(s(s(z))), z) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~(elem!1 = z)) | (~b(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | b(z, s(s(s(s(z))))) | r(s(s(z)), z) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.66 tff(21056,plain,
% 4.44/4.66 (r(s(s(s(z))), z)),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[21055, 20928, 104, 273, 928, 20645, 20650, 1, 5618, 20990])).
% 4.44/4.66 tff(21057,plain,
% 4.44/4.66 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[20977, 21056, 203])).
% 4.44/4.66 tff(21058,plain,
% 4.44/4.66 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[20667, 21057])).
% 4.44/4.66 tff(21059,plain,
% 4.44/4.66 (~r(s(s(z)), s(s(s(s(z)))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[20791, 21058, 273, 928, 20645, 104, 5619, 47])).
% 4.44/4.66 tff(21060,plain,
% 4.44/4.66 (b(s(s(z)), s(s(s(s(z)))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[164, 21059])).
% 4.44/4.66 tff(21061,plain,
% 4.44/4.66 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[20797, 21056, 47])).
% 4.44/4.66 tff(21062,plain,
% 4.44/4.66 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[10755, 21061])).
% 4.44/4.66 tff(21063,plain,
% 4.44/4.66 (~b(s(s(s(s(z)))), s(s(z)))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[259, 21060, 104, 20996, 20928])).
% 4.44/4.66 tff(21064,plain,
% 4.44/4.66 (r(s(s(s(s(z)))), s(s(z)))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[102, 21063])).
% 4.44/4.66 tff(21065,plain,
% 4.44/4.66 ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[9047, 178, 104, 20928, 20996])).
% 4.44/4.66 tff(21066,plain,
% 4.44/4.66 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[21065, 21060])).
% 4.44/4.66 tff(21067,plain,
% 4.44/4.66 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[3578, 21066])).
% 4.44/4.66 tff(21068,plain,
% 4.44/4.66 ($false),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[17159, 21067, 21064, 104, 20928, 21062, 21060])).
% 4.44/4.66 tff(21069,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~(elem!1 = z)) | b(z, s(s(s(s(z))))) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 4.44/4.66 tff(21070,plain,
% 4.44/4.66 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[21069, 928, 273, 104, 1, 5618])).
% 4.44/4.66 tff(21071,plain,
% 4.44/4.66 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[271, 21070])).
% 4.44/4.66 tff(21072,plain,
% 4.44/4.66 ($false),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[4903, 41, 77, 7040, 20637])).
% 4.44/4.66 tff(21073,plain,(b(s(s(s(z))), z) | r(s(s(s(z))), z)), inference(lemma,lemma(discharge,[]))).
% 4.44/4.66 tff(21074,plain,
% 4.44/4.66 (b(s(s(s(z))), z)),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[21073, 20637])).
% 4.44/4.66 tff(21075,plain,
% 4.44/4.66 (b(s(elem!1), s(s(z)))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[16105, 147, 1, 21025, 86, 21024, 5618])).
% 4.44/4.66 tff(21076,plain,
% 4.44/4.66 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[12552, 21075, 86])).
% 4.44/4.66 tff(21077,plain,
% 4.44/4.66 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[5101, 147, 47, 5619])).
% 4.44/4.66 tff(21078,plain,
% 4.44/4.66 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[10755, 21077])).
% 4.44/4.66 tff(21079,plain,
% 4.44/4.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 4.44/4.66 inference(rewrite,[status(thm)],[])).
% 4.44/4.66 tff(21080,plain,
% 4.44/4.66 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, 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)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(z, s(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(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 4.44/4.66 inference(rewrite,[status(thm)],[])).
% 4.44/4.66 tff(21081,plain,
% 4.44/4.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z))))),
% 4.44/4.66 inference(monotonicity,[status(thm)],[21080])).
% 4.44/4.66 tff(21082,plain,
% 4.44/4.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 4.44/4.66 inference(transitivity,[status(thm)],[21081, 21079])).
% 4.44/4.66 tff(21083,plain,
% 4.44/4.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 4.44/4.66 inference(quant_inst,[status(thm)],[])).
% 4.44/4.66 tff(21084,plain,
% 4.44/4.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z))),
% 4.44/4.66 inference(modus_ponens,[status(thm)],[21083, 21082])).
% 4.44/4.66 tff(21085,plain,
% 4.44/4.66 ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[21084, 178, 20996, 21071, 1127])).
% 4.44/4.66 tff(21086,plain,
% 4.44/4.66 (~b(s(s(s(s(z)))), z)),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[21085, 21078])).
% 4.44/4.66 tff(21087,plain,
% 4.44/4.66 (r(s(s(s(s(z)))), z)),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[191, 21086])).
% 4.44/4.66 tff(21088,plain,
% 4.44/4.66 (b(s(z), s(s(z)))),
% 4.44/4.66 inference(modus_ponens,[status(thm)],[21075, 14161])).
% 4.44/4.66 tff(21089,plain,
% 4.44/4.66 (b(s(elem!1), elem!1) <=> b(s(z), z)),
% 4.44/4.66 inference(transitivity,[status(thm)],[12061, 12120])).
% 4.44/4.66 tff(21090,plain,
% 4.44/4.66 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[20718, 166, 273, 3461, 595])).
% 4.44/4.66 tff(21091,plain,
% 4.44/4.66 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[133, 21090])).
% 4.44/4.66 tff(21092,plain,
% 4.44/4.66 (~r(s(elem!1), elem!1)),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[20868, 21091, 251, 928, 104, 194, 1369])).
% 4.44/4.66 tff(21093,plain,
% 4.44/4.66 (b(s(elem!1), elem!1)),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[677, 21092, 20662])).
% 4.44/4.66 tff(21094,plain,
% 4.44/4.66 (b(s(z), z)),
% 4.44/4.66 inference(modus_ponens,[status(thm)],[21093, 21089])).
% 4.44/4.66 tff(21095,plain,
% 4.44/4.66 ($false),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[17956, 178, 3461, 10110, 166, 595, 21094])).
% 4.44/4.66 tff(21096,plain,((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = 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)))))) | (~r(s(s(s(s(z)))), z)) | (s(elem!1) = s(s(s(s(z))))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.66 tff(21097,plain,
% 4.44/4.66 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[21096, 21088, 5619, 21071, 928, 20996, 104, 21087, 21076, 273])).
% 4.44/4.66 tff(21098,plain,
% 4.44/4.66 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[249, 21097])).
% 4.44/4.66 tff(21099,plain,
% 4.44/4.66 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[11287, 21098, 5619, 273, 1127])).
% 4.44/4.66 tff(21100,plain,
% 4.44/4.66 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[20667, 21099])).
% 4.44/4.66 tff(21101,plain,
% 4.44/4.66 (~b(z, s(s(s(elem!1))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[20791, 21100, 273, 928, 147, 104, 5619, 47])).
% 4.44/4.66 tff(21102,plain,
% 4.44/4.66 (r(z, s(s(s(elem!1))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[2095, 21101])).
% 4.44/4.66 tff(21103,plain,
% 4.44/4.66 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[4173, 16403, 10731])).
% 4.44/4.66 tff(21104,plain,
% 4.44/4.66 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[20942, 21100, 928])).
% 4.44/4.66 tff(21105,plain,
% 4.44/4.66 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[4103, 21104, 104, 20996, 21103])).
% 4.44/4.66 tff(21106,plain,
% 4.44/4.66 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[10664, 21105, 20640])).
% 4.44/4.66 tff(21107,plain,
% 4.44/4.66 ($false),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[19720, 21106, 21102, 47])).
% 4.44/4.66 tff(21108,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~(elem!1 = z)) | (~b(s(s(s(z))), z)) | b(s(s(s(s(z)))), s(s(z))) | b(z, s(s(s(s(z))))) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 4.44/4.66 tff(21109,plain,
% 4.44/4.66 (~r(s(s(z)), s(s(s(s(z)))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[21108, 86, 273, 928, 21074, 104, 1, 5618])).
% 4.44/4.66 tff(21110,plain,
% 4.44/4.66 (b(s(s(z)), s(s(s(s(z)))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[164, 21109])).
% 4.44/4.66 tff(21111,plain,
% 4.44/4.66 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[279, 178, 273, 104, 21110, 21071])).
% 4.44/4.66 tff(21112,plain,
% 4.44/4.66 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[249, 21111])).
% 4.44/4.66 tff(21113,plain,
% 4.44/4.66 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[11287, 21112, 5619, 273, 21074])).
% 4.44/4.66 tff(21114,plain,
% 4.44/4.66 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[20667, 21113])).
% 4.44/4.66 tff(21115,plain,
% 4.44/4.66 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[16623, 21114, 20996, 21110, 21112, 104])).
% 4.44/4.66 tff(21116,plain,
% 4.44/4.66 (r(s(s(s(z))), s(s(s(s(z)))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[10755, 21115])).
% 4.44/4.66 tff(21117,plain,
% 4.44/4.66 (~r(s(s(s(z))), s(s(z)))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[20838, 21116, 103])).
% 4.44/4.66 tff(21118,plain,
% 4.44/4.66 (b(s(s(s(z))), s(s(z)))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[4966, 21117])).
% 4.44/4.66 tff(21119,plain,
% 4.44/4.66 (~b(z, s(s(s(z))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[20992, 21118, 273, 20637, 5619])).
% 4.44/4.66 tff(21120,plain,
% 4.44/4.66 (r(z, s(s(s(z))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[4920, 21119])).
% 4.44/4.66 tff(21121,plain,
% 4.44/4.66 ($false),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[4910, 118, 47, 21120, 21116])).
% 4.44/4.66 tff(21122,plain,(b(s(s(s(s(z)))), s(s(z))) | (~b(z, s(s(z)))) | r(s(s(s(z))), z) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~(elem!1 = z)) | b(z, s(s(s(s(z))))) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 4.44/4.66 tff(21123,plain,
% 4.44/4.66 (b(s(s(s(s(z)))), s(s(z)))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[21122, 20637, 273, 104, 928, 1, 5618])).
% 4.44/4.66 tff(21124,plain,
% 4.44/4.66 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[11287, 224, 3461, 273, 21074])).
% 4.44/4.66 tff(21125,plain,
% 4.44/4.66 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[20667, 21124])).
% 4.44/4.66 tff(21126,plain,
% 4.44/4.66 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[7840, 178, 273, 104, 21006, 595])).
% 4.44/4.66 tff(21127,plain,
% 4.44/4.66 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[3578, 21126])).
% 4.44/4.66 tff(21128,plain,
% 4.44/4.66 (~b(s(s(s(z))), s(s(z)))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[20992, 4921, 273, 20637, 3461])).
% 4.44/4.66 tff(21129,plain,
% 4.44/4.66 (r(s(s(s(z))), s(s(z)))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[4966, 21128])).
% 4.44/4.66 tff(21130,plain,
% 4.44/4.66 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[1175, 118, 21129, 21127])).
% 4.44/4.66 tff(21131,plain,
% 4.44/4.66 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 21130])).
% 4.44/4.66 tff(21132,plain,
% 4.44/4.66 ($false),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[20712, 178, 595, 4921, 21074, 3002, 21131])).
% 4.44/4.66 tff(21133,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | r(s(s(s(z))), z) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.66 tff(21134,plain,
% 4.44/4.66 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[21133, 21125, 595, 273, 20637, 3461, 104, 145])).
% 4.44/4.66 tff(21135,plain,
% 4.44/4.66 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[10755, 21134])).
% 4.44/4.66 tff(21136,plain,
% 4.44/4.66 ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[21084, 178, 20736, 595, 21074])).
% 4.44/4.66 tff(21137,plain,
% 4.44/4.66 (~b(s(s(s(s(z)))), z)),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[21136, 21135])).
% 4.44/4.66 tff(21138,plain,
% 4.44/4.66 (r(s(s(s(s(z)))), z)),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[191, 21137])).
% 4.44/4.66 tff(21139,plain,
% 4.44/4.66 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[20942, 21125, 928])).
% 4.44/4.66 tff(21140,plain,
% 4.44/4.66 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[20823, 21134, 928])).
% 4.44/4.66 tff(21141,plain,
% 4.44/4.66 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[4173, 21140, 10731])).
% 4.44/4.66 tff(21142,plain,
% 4.44/4.66 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[4103, 21141, 104, 20736, 21139])).
% 4.44/4.66 tff(21143,plain,
% 4.44/4.66 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[10664, 21142, 20640])).
% 4.44/4.66 tff(21144,plain,
% 4.44/4.66 (~b(s(s(z)), s(s(s(s(z)))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[16623, 21135, 20736, 21125, 224, 104])).
% 4.44/4.66 tff(21145,plain,
% 4.44/4.66 (r(s(s(z)), s(s(s(s(z)))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[164, 21144])).
% 4.44/4.66 tff(21146,plain,
% 4.44/4.66 (~b(z, s(s(s(elem!1))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[20791, 21145, 273, 928, 21125, 104, 3461, 145])).
% 4.44/4.66 tff(21147,plain,
% 4.44/4.66 (r(z, s(s(s(elem!1))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[2095, 21146])).
% 4.44/4.66 tff(21148,plain,
% 4.44/4.66 ($false),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[3287, 21147, 21143, 21138])).
% 4.44/4.66 tff(21149,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~(elem!1 = z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | r(s(s(s(z))), z)), inference(lemma,lemma(discharge,[]))).
% 4.44/4.66 tff(21150,plain,
% 4.44/4.66 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[21149, 20637, 928, 104, 5619, 47, 21071, 273])).
% 4.44/4.66 tff(21151,plain,
% 4.44/4.66 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[249, 21150])).
% 4.44/4.66 tff(21152,plain,
% 4.44/4.66 (~b(s(s(z)), s(s(s(s(z)))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[259, 21151, 104, 20996, 21123])).
% 4.44/4.66 tff(21153,plain,
% 4.44/4.66 (r(s(s(z)), s(s(s(s(z)))))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[164, 21152])).
% 4.44/4.66 tff(21154,plain,
% 4.44/4.66 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[17204, 21151, 273, 5619, 21071])).
% 4.44/4.66 tff(21155,plain,
% 4.44/4.66 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.44/4.66 inference(unit_resolution,[status(thm)],[3578, 21154])).
% 4.44/4.66 tff(21156,plain,
% 4.44/4.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 4.44/4.66 inference(rewrite,[status(thm)],[])).
% 4.44/4.66 tff(21157,plain,
% 4.44/4.66 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 4.44/4.66 inference(rewrite,[status(thm)],[])).
% 4.44/4.66 tff(21158,plain,
% 4.44/4.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))))),
% 4.44/4.66 inference(monotonicity,[status(thm)],[21157])).
% 4.44/4.66 tff(21159,plain,
% 4.44/4.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 4.44/4.67 inference(transitivity,[status(thm)],[21158, 21156])).
% 4.44/4.67 tff(21160,plain,
% 4.44/4.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 4.44/4.67 inference(quant_inst,[status(thm)],[])).
% 4.44/4.67 tff(21161,plain,
% 4.44/4.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))),
% 4.44/4.67 inference(modus_ponens,[status(thm)],[21160, 21159])).
% 4.44/4.67 tff(21162,plain,
% 4.44/4.67 (~b(s(s(s(z))), s(s(z)))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[21161, 178, 5619, 21151, 21071, 21074])).
% 4.44/4.67 tff(21163,plain,
% 4.44/4.67 (r(s(s(s(z))), s(s(z)))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[4966, 21162])).
% 4.44/4.67 tff(21164,plain,
% 4.44/4.67 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[8218, 21163, 21155])).
% 4.44/4.67 tff(21165,plain,
% 4.44/4.67 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[20667, 21164])).
% 4.44/4.67 tff(21166,plain,
% 4.44/4.67 (~b(z, s(s(s(elem!1))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[20791, 21165, 273, 928, 21153, 104, 5619, 47])).
% 4.44/4.67 tff(21167,plain,
% 4.44/4.67 (r(z, s(s(s(elem!1))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[2095, 21166])).
% 4.44/4.67 tff(21168,plain,
% 4.44/4.67 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[10799, 21153, 47])).
% 4.44/4.67 tff(21169,plain,
% 4.44/4.67 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[4173, 21168, 10731])).
% 4.44/4.67 tff(21170,plain,
% 4.44/4.67 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[20942, 21165, 928])).
% 4.44/4.67 tff(21171,plain,
% 4.44/4.67 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[4103, 21170, 104, 20996, 21169])).
% 4.44/4.67 tff(21172,plain,
% 4.44/4.67 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[10664, 21171, 20640])).
% 4.44/4.67 tff(21173,plain,
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% 4.44/4.67 inference(unit_resolution,[status(thm)],[19720, 21172, 21167, 47])).
% 4.44/4.67 tff(21174,plain,(r(s(s(s(z))), z) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~(elem!1 = z)) | b(z, s(s(s(s(z))))) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 4.44/4.67 tff(21175,plain,
% 4.44/4.67 (r(s(s(s(z))), z)),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[21174, 20636, 144, 104, 1, 10792])).
% 4.44/4.67 tff(21176,plain,
% 4.44/4.67 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[20734, 10793, 144, 47, 20636, 104])).
% 4.44/4.67 tff(21177,plain,
% 4.44/4.67 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[222, 21176])).
% 4.44/4.67 tff(21178,plain,
% 4.44/4.67 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[21069, 20636, 144, 104, 1, 10792])).
% 4.44/4.67 tff(21179,plain,
% 4.44/4.67 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[271, 21178])).
% 4.44/4.67 tff(21180,plain,
% 4.44/4.67 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[20797, 21175, 47])).
% 4.44/4.67 tff(21181,plain,
% 4.44/4.67 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[10755, 21180])).
% 4.44/4.67 tff(21182,plain,
% 4.44/4.67 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[20784, 19773, 16062])).
% 4.44/4.67 tff(21183,plain,
% 4.44/4.67 (b(s(s(s(s(z)))), s(s(s(z))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[11185, 21182])).
% 4.44/4.67 tff(21184,plain,
% 4.44/4.67 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[15816, 21183])).
% 4.44/4.67 tff(21185,plain,
% 4.44/4.67 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[20667, 21184])).
% 4.44/4.67 tff(21186,plain,
% 4.44/4.67 (~r(s(s(s(z))), s(s(z)))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[8218, 18207, 21185])).
% 4.44/4.67 tff(21187,plain,
% 4.44/4.67 (b(s(s(s(z))), s(s(z)))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[4966, 21186])).
% 4.44/4.67 tff(21188,plain,
% 4.44/4.67 (~r(s(s(z)), s(s(s(z))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[10533, 118, 18061, 21185])).
% 4.44/4.67 tff(21189,plain,
% 4.44/4.67 (b(s(s(z)), s(s(s(z))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[5088, 21188])).
% 4.44/4.67 tff(21190,plain,
% 4.44/4.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.44/4.67 inference(rewrite,[status(thm)],[])).
% 4.44/4.67 tff(21191,plain,
% 4.44/4.67 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(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(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(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.44/4.67 inference(rewrite,[status(thm)],[])).
% 4.44/4.67 tff(21192,plain,
% 4.44/4.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(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(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))))),
% 4.44/4.67 inference(monotonicity,[status(thm)],[21191])).
% 4.44/4.67 tff(21193,plain,
% 4.44/4.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(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(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.44/4.67 inference(transitivity,[status(thm)],[21192, 21190])).
% 4.44/4.67 tff(21194,plain,
% 4.44/4.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(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(z))), s(s(z)))))),
% 4.44/4.67 inference(quant_inst,[status(thm)],[])).
% 4.44/4.67 tff(21195,plain,
% 4.44/4.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 4.44/4.67 inference(modus_ponens,[status(thm)],[21194, 21193])).
% 4.44/4.67 tff(21196,plain,
% 4.44/4.67 ($false),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[21195, 178, 167, 1126, 21183, 21189, 21187])).
% 4.44/4.67 tff(21197,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(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(z))), z)) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.67 tff(21198,plain,
% 4.44/4.67 (~b(s(s(z)), s(s(s(s(z)))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[21197, 21181, 144, 104, 21179, 21177, 21175, 10793])).
% 4.44/4.67 tff(21199,plain,
% 4.44/4.67 (r(s(s(z)), s(s(s(s(z)))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[164, 21198])).
% 4.44/4.67 tff(21200,plain,
% 4.44/4.67 (r(elem!1, s(s(elem!1))) <=> r(z, s(s(elem!1)))),
% 4.44/4.67 inference(monotonicity,[status(thm)],[20636])).
% 4.44/4.67 tff(21201,plain,
% 4.44/4.67 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 4.44/4.67 inference(symmetry,[status(thm)],[21200])).
% 4.44/4.67 tff(21202,plain,
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% 4.44/4.67 inference(monotonicity,[status(thm)],[20636])).
% 4.44/4.67 tff(21203,plain,
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% 4.44/4.67 inference(monotonicity,[status(thm)],[21202])).
% 4.44/4.67 tff(21204,plain,
% 4.44/4.67 (r(z, s(s(elem!1))) <=> r(z, s(s(z)))),
% 4.44/4.67 inference(monotonicity,[status(thm)],[21203])).
% 4.44/4.67 tff(21205,plain,
% 4.44/4.67 (r(z, s(s(z))) <=> r(z, s(s(elem!1)))),
% 4.44/4.67 inference(symmetry,[status(thm)],[21204])).
% 4.44/4.67 tff(21206,plain,
% 4.44/4.67 (r(z, s(s(z))) <=> r(elem!1, s(s(elem!1)))),
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% 4.44/4.67 tff(21207,plain,
% 4.44/4.67 ((~r(z, s(s(z)))) <=> (~r(elem!1, s(s(elem!1))))),
% 4.44/4.67 inference(monotonicity,[status(thm)],[21206])).
% 4.44/4.67 tff(21208,plain,
% 4.44/4.67 (~r(elem!1, s(s(elem!1)))),
% 4.44/4.67 inference(modus_ponens,[status(thm)],[48, 21207])).
% 4.44/4.67 tff(21209,plain,
% 4.44/4.67 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), z)),
% 4.44/4.67 inference(monotonicity,[status(thm)],[928])).
% 4.44/4.67 tff(21210,plain,
% 4.44/4.67 (~b(elem!1, s(s(s(s(z)))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[5204, 928, 1])).
% 4.44/4.67 tff(21211,plain,
% 4.44/4.67 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[18185, 21210, 104])).
% 4.44/4.67 tff(21212,plain,
% 4.44/4.67 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[703, 21211])).
% 4.44/4.67 tff(21213,plain,
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% 4.44/4.67 tff(21214,plain,
% 4.44/4.67 (r(s(s(s(elem!1))), elem!1)),
% 4.44/4.67 inference(modus_ponens,[status(thm)],[21213, 20873])).
% 4.44/4.67 tff(21215,plain,
% 4.44/4.67 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.67 inference(monotonicity,[status(thm)],[931])).
% 4.44/4.67 tff(21216,plain,
% 4.44/4.67 (r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.67 inference(symmetry,[status(thm)],[21215])).
% 4.44/4.67 tff(21217,plain,
% 4.44/4.67 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.67 inference(modus_ponens,[status(thm)],[8216, 21216])).
% 4.44/4.67 tff(21218,plain,
% 4.44/4.67 ($false),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[19935, 21217])).
% 4.44/4.67 tff(21219,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.67 tff(21220,plain,
% 4.44/4.67 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[21219, 8216, 928])).
% 4.44/4.67 tff(21221,plain,
% 4.44/4.67 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
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% 4.44/4.67 tff(21222,plain,
% 4.44/4.67 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
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% 4.44/4.67 tff(21223,plain,
% 4.44/4.67 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.44/4.67 inference(modus_ponens,[status(thm)],[21222, 21209])).
% 4.44/4.67 tff(21224,plain,
% 4.44/4.67 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[4091, 178, 5619, 273, 21071, 21223])).
% 4.44/4.67 tff(21225,plain,
% 4.44/4.67 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[3578, 21224])).
% 4.44/4.67 tff(21226,plain,
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% 4.44/4.67 inference(unit_resolution,[status(thm)],[8218, 21225, 8216])).
% 4.44/4.67 tff(21227,plain,
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% 4.44/4.67 tff(21228,plain,
% 4.44/4.67 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 4.44/4.67 inference(modus_ponens,[status(thm)],[21227, 12040])).
% 4.44/4.67 tff(21229,plain,
% 4.44/4.67 (b(s(s(elem!1)), elem!1)),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[5878, 12064, 5619])).
% 4.44/4.67 tff(21230,plain,
% 4.44/4.67 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.44/4.67 inference(symmetry,[status(thm)],[15336])).
% 4.44/4.67 tff(21231,plain,
% 4.44/4.67 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
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% 4.44/4.67 tff(21232,plain,
% 4.44/4.67 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
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% 4.44/4.67 tff(21233,plain,
% 4.44/4.67 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
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% 4.44/4.67 tff(21234,plain,
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% 4.44/4.67 tff(21235,plain,
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% 4.44/4.67 tff(21236,plain,
% 4.44/4.67 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.44/4.67 inference(modus_ponens,[status(thm)],[21235, 21231])).
% 4.44/4.67 tff(21237,plain,
% 4.44/4.67 (~b(elem!1, s(s(s(elem!1))))),
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% 4.44/4.67 tff(21238,plain,
% 4.44/4.67 (r(elem!1, s(s(s(elem!1))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[2054, 21237, 12085])).
% 4.44/4.67 tff(21239,plain,
% 4.44/4.67 (b(z, s(z)) <=> b(z, s(elem!1))),
% 4.44/4.67 inference(monotonicity,[status(thm)],[6683])).
% 4.44/4.67 tff(21240,plain,
% 4.44/4.67 (b(z, s(z)) <=> b(elem!1, s(elem!1))),
% 4.44/4.67 inference(transitivity,[status(thm)],[21239, 12051])).
% 4.44/4.67 tff(21241,plain,
% 4.44/4.67 ((~b(z, s(z))) <=> (~b(elem!1, s(elem!1)))),
% 4.44/4.67 inference(monotonicity,[status(thm)],[21240])).
% 4.44/4.67 tff(21242,plain,
% 4.44/4.67 (~b(s(s(s(s(z)))), z)),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[10705, 178, 104, 20996, 21071, 21223])).
% 4.44/4.67 tff(21243,plain,
% 4.44/4.67 (r(s(s(s(s(z)))), z)),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[191, 21242])).
% 4.44/4.67 tff(21244,plain,
% 4.44/4.67 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[20784, 21243, 21213])).
% 4.44/4.67 tff(21245,plain,
% 4.44/4.67 (r(s(s(s(s(z)))), elem!1)),
% 4.44/4.67 inference(modus_ponens,[status(thm)],[21243, 20852])).
% 4.44/4.67 tff(21246,plain,
% 4.44/4.67 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[7220, 21245, 21244])).
% 4.44/4.67 tff(21247,plain,
% 4.44/4.67 (~(s(s(s(s(z)))) = s(elem!1))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[2168, 21246])).
% 4.44/4.67 tff(21248,plain,
% 4.44/4.67 (b(s(s(s(s(z)))), s(s(s(z))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[11185, 21244])).
% 4.44/4.67 tff(21249,plain,
% 4.44/4.67 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[20797, 21213, 47])).
% 4.44/4.67 tff(21250,plain,
% 4.44/4.67 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[10755, 21249])).
% 4.44/4.67 tff(21251,plain,
% 4.44/4.67 (~b(s(s(z)), s(s(s(s(z)))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[21197, 21250, 273, 104, 21071, 20996, 21213, 5619])).
% 4.44/4.67 tff(21252,plain,
% 4.44/4.67 (r(s(s(z)), s(s(s(s(z)))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[164, 21251])).
% 4.44/4.67 tff(21253,plain,
% 4.44/4.67 (~b(s(s(s(s(z)))), s(s(z)))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[9457, 178, 21250, 21248, 21235, 21227])).
% 4.44/4.67 tff(21254,plain,
% 4.44/4.67 (b(s(elem!1), s(s(z)))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[16105, 21253, 1, 21025, 21252, 21024, 5618])).
% 4.44/4.67 tff(21255,plain,
% 4.44/4.67 (b(s(z), s(s(z)))),
% 4.44/4.67 inference(modus_ponens,[status(thm)],[21254, 14161])).
% 4.44/4.67 tff(21256,plain,
% 4.44/4.67 (~r(s(s(s(elem!1))), s(elem!1))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[1576, 1426, 556])).
% 4.44/4.67 tff(21257,plain,
% 4.44/4.67 (b(s(s(s(elem!1))), s(elem!1))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[373, 21256, 12049])).
% 4.44/4.67 tff(21258,plain,
% 4.44/4.67 (b(s(s(s(z))), s(z))),
% 4.44/4.67 inference(modus_ponens,[status(thm)],[21257, 12043])).
% 4.44/4.67 tff(21259,plain,
% 4.44/4.67 (b(s(s(s(s(z)))), s(elem!1))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[2173, 20864, 2508])).
% 4.44/4.67 tff(21260,plain,
% 4.44/4.67 (b(s(s(s(s(z)))), s(z))),
% 4.44/4.67 inference(modus_ponens,[status(thm)],[21259, 12849])).
% 4.44/4.67 tff(21261,plain,
% 4.44/4.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.44/4.67 inference(rewrite,[status(thm)],[])).
% 4.44/4.67 tff(21262,plain,
% 4.44/4.67 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.44/4.67 inference(rewrite,[status(thm)],[])).
% 4.44/4.67 tff(21263,plain,
% 4.44/4.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))))),
% 4.44/4.67 inference(monotonicity,[status(thm)],[21262])).
% 4.44/4.67 tff(21264,plain,
% 4.44/4.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.44/4.67 inference(transitivity,[status(thm)],[21263, 21261])).
% 4.44/4.67 tff(21265,plain,
% 4.44/4.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 4.44/4.67 inference(quant_inst,[status(thm)],[])).
% 4.44/4.67 tff(21266,plain,
% 4.44/4.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))),
% 4.44/4.67 inference(modus_ponens,[status(thm)],[21265, 21264])).
% 4.44/4.67 tff(21267,plain,
% 4.44/4.67 ($false),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[21266, 178, 10110, 21260, 6170, 4932, 21258])).
% 4.44/4.67 tff(21268,plain,((~r(s(elem!1), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~(elem!1 = z)) | (s(s(s(s(z)))) = s(elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.67 tff(21269,plain,
% 4.44/4.67 (~r(s(elem!1), elem!1)),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[21268, 21255, 21248, 21227, 928, 21247, 21243, 21214])).
% 4.44/4.67 tff(21270,plain,
% 4.44/4.67 (b(s(elem!1), elem!1)),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[677, 21269, 20662])).
% 4.44/4.67 tff(21271,plain,
% 4.44/4.67 (b(s(z), z)),
% 4.44/4.67 inference(modus_ponens,[status(thm)],[21270, 21089])).
% 4.44/4.67 tff(21272,plain,
% 4.44/4.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(z))))),
% 4.44/4.67 inference(rewrite,[status(thm)],[])).
% 4.44/4.67 tff(21273,plain,
% 4.44/4.67 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z)))) <=> ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(z))))),
% 4.44/4.67 inference(rewrite,[status(thm)],[])).
% 4.44/4.67 tff(21274,plain,
% 4.44/4.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(z)))))),
% 4.44/4.67 inference(monotonicity,[status(thm)],[21273])).
% 4.44/4.67 tff(21275,plain,
% 4.44/4.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(z))))),
% 4.44/4.67 inference(transitivity,[status(thm)],[21274, 21272])).
% 4.44/4.67 tff(21276,plain,
% 4.44/4.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))),
% 4.44/4.67 inference(quant_inst,[status(thm)],[])).
% 4.44/4.67 tff(21277,plain,
% 4.44/4.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(z)))),
% 4.44/4.67 inference(modus_ponens,[status(thm)],[21276, 21275])).
% 4.44/4.67 tff(21278,plain,
% 4.44/4.67 (~b(z, s(z))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[21277, 178, 5619, 273, 21255, 21271])).
% 4.44/4.67 tff(21279,plain,
% 4.44/4.67 (~b(elem!1, s(elem!1))),
% 4.44/4.67 inference(modus_ponens,[status(thm)],[21278, 21241])).
% 4.44/4.67 tff(21280,plain,
% 4.44/4.67 (r(elem!1, s(elem!1))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[756, 21279, 20655])).
% 4.44/4.67 tff(21281,plain,
% 4.44/4.67 (~b(s(s(s(z))), s(z))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[12340, 178, 5619, 21255, 21271, 21227])).
% 4.44/4.67 tff(21282,plain,
% 4.44/4.67 (~b(s(s(s(elem!1))), s(elem!1))),
% 4.44/4.67 inference(modus_ponens,[status(thm)],[21281, 12295])).
% 4.44/4.67 tff(21283,plain,
% 4.44/4.67 (r(s(s(s(elem!1))), s(elem!1))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[373, 21282, 12049])).
% 4.44/4.67 tff(21284,plain,
% 4.44/4.67 ($false),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[1591, 21283, 21280, 21238])).
% 4.44/4.67 tff(21285,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = z)) | (~b(z, s(s(z)))) | b(z, s(s(s(s(z))))) | r(s(s(z)), z) | r(elem!1, s(s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.67 tff(21286,plain,
% 4.44/4.67 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[21285, 20636, 144, 1, 10792, 21208, 104])).
% 4.44/4.67 tff(21287,plain,
% 4.44/4.67 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[20667, 21286])).
% 4.44/4.67 tff(21288,plain,
% 4.44/4.67 (~b(z, s(s(s(elem!1))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[20791, 21287, 144, 20636, 21199, 104, 10793, 47])).
% 4.44/4.67 tff(21289,plain,
% 4.44/4.67 (r(z, s(s(s(elem!1))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[2095, 21288])).
% 4.44/4.67 tff(21290,plain,
% 4.44/4.67 (s(s(s(elem!1))) = s(s(s(z)))),
% 4.44/4.67 inference(monotonicity,[status(thm)],[21203])).
% 4.44/4.67 tff(21291,plain,
% 4.44/4.67 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(z))) = s(s(s(s(z)))))),
% 4.44/4.67 inference(monotonicity,[status(thm)],[21290])).
% 4.44/4.67 tff(21292,plain,
% 4.44/4.67 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 4.44/4.67 inference(transitivity,[status(thm)],[21291, 4936])).
% 4.44/4.67 tff(21293,plain,
% 4.44/4.67 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.44/4.67 inference(symmetry,[status(thm)],[21292])).
% 4.44/4.67 tff(21294,plain,
% 4.44/4.67 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 4.44/4.67 inference(transitivity,[status(thm)],[21293, 4164])).
% 4.44/4.67 tff(21295,plain,
% 4.44/4.67 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(s(z)))) = s(s(s(elem!1)))))),
% 4.44/4.67 inference(monotonicity,[status(thm)],[21294])).
% 4.44/4.67 tff(21296,plain,
% 4.44/4.67 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 4.44/4.67 inference(modus_ponens,[status(thm)],[4938, 21295])).
% 4.44/4.67 tff(21297,plain,
% 4.44/4.67 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(z))))))),
% 4.44/4.67 inference(monotonicity,[status(thm)],[21293])).
% 4.44/4.67 tff(21298,plain,
% 4.44/4.67 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.44/4.67 inference(modus_ponens,[status(thm)],[4938, 21297])).
% 4.44/4.67 tff(21299,plain,
% 4.44/4.67 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[20823, 21180, 20636])).
% 4.44/4.67 tff(21300,plain,
% 4.44/4.67 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[4173, 21299, 21298])).
% 4.44/4.67 tff(21301,plain,
% 4.44/4.67 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[20942, 21287, 20636])).
% 4.44/4.67 tff(21302,plain,
% 4.44/4.67 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[4103, 21301, 104, 21177, 21300])).
% 4.44/4.67 tff(21303,plain,
% 4.44/4.67 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[10664, 21302, 21296])).
% 4.44/4.67 tff(21304,plain,
% 4.44/4.67 ($false),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[19720, 21303, 21289, 47])).
% 4.44/4.67 tff(21305,plain,(b(z, s(s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | r(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.67 tff(21306,plain,
% 4.44/4.67 (b(z, s(s(s(s(z)))))),
% 4.44/4.67 inference(unit_resolution,[status(thm)],[21305, 48, 104])).
% 4.44/4.68 tff(21307,plain,
% 4.44/4.68 ($false),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[1809, 118, 106, 194, 147])).
% 4.44/4.68 tff(21308,plain,((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.68 tff(21309,plain,
% 4.44/4.68 (~r(s(s(z)), s(s(s(s(z)))))),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[21308, 194, 106])).
% 4.44/4.68 tff(21310,plain,
% 4.44/4.68 (b(s(s(z)), s(s(s(s(z)))))),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[164, 21309])).
% 4.44/4.68 tff(21311,plain,
% 4.44/4.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, 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))))))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, 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))))))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 4.44/4.68 inference(rewrite,[status(thm)],[])).
% 4.44/4.68 tff(21312,plain,
% 4.44/4.68 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z))) <=> ((~b(z, 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))))))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 4.44/4.68 inference(rewrite,[status(thm)],[])).
% 4.44/4.68 tff(21313,plain,
% 4.44/4.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, 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))))))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))))),
% 4.44/4.68 inference(monotonicity,[status(thm)],[21312])).
% 4.44/4.68 tff(21314,plain,
% 4.44/4.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, 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))))))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 4.44/4.68 inference(transitivity,[status(thm)],[21313, 21311])).
% 4.44/4.68 tff(21315,plain,
% 4.44/4.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 4.44/4.68 inference(quant_inst,[status(thm)],[])).
% 4.44/4.68 tff(21316,plain,
% 4.44/4.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, 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))))))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))),
% 4.44/4.68 inference(modus_ponens,[status(thm)],[21315, 21314])).
% 4.44/4.68 tff(21317,plain,
% 4.44/4.68 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[21316, 178, 273, 104, 1687, 202])).
% 4.44/4.68 tff(21318,plain,
% 4.44/4.68 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[133, 21317])).
% 4.44/4.68 tff(21319,plain,
% 4.44/4.68 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[123, 21318, 106])).
% 4.44/4.68 tff(21320,plain,
% 4.44/4.68 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[3578, 21319])).
% 4.44/4.68 tff(21321,plain,
% 4.44/4.68 ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[7840, 178, 273, 104, 167])).
% 4.44/4.68 tff(21322,plain,
% 4.44/4.68 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[21321, 21320])).
% 4.44/4.68 tff(21323,plain,
% 4.44/4.68 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[271, 21322])).
% 4.44/4.68 tff(21324,plain,
% 4.44/4.68 (~b(s(s(s(s(z)))), z)),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[1736, 178, 273, 1687, 167, 202])).
% 4.44/4.68 tff(21325,plain,
% 4.44/4.68 (r(s(s(s(s(z)))), z)),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[191, 21324])).
% 4.44/4.68 tff(21326,plain,
% 4.44/4.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.44/4.68 inference(rewrite,[status(thm)],[])).
% 4.44/4.68 tff(21327,plain,
% 4.44/4.68 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.44/4.68 inference(rewrite,[status(thm)],[])).
% 4.44/4.68 tff(21328,plain,
% 4.44/4.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 4.44/4.68 inference(monotonicity,[status(thm)],[21327])).
% 4.44/4.68 tff(21329,plain,
% 4.44/4.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.44/4.68 inference(transitivity,[status(thm)],[21328, 21326])).
% 4.44/4.68 tff(21330,plain,
% 4.44/4.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), z)))),
% 4.44/4.68 inference(quant_inst,[status(thm)],[])).
% 4.44/4.68 tff(21331,plain,
% 4.44/4.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 4.44/4.68 inference(modus_ponens,[status(thm)],[21330, 21329])).
% 4.44/4.68 tff(21332,plain,
% 4.44/4.68 ($false),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[21331, 118, 21325, 204, 21323])).
% 4.44/4.68 tff(21333,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.68 tff(21334,plain,
% 4.44/4.68 ($false),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[21333, 21310, 10714, 273, 104, 204, 106, 1687])).
% 4.44/4.68 tff(21335,plain,((~r(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.68 tff(21336,plain,
% 4.44/4.68 (~r(s(s(s(s(z)))), z)),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[21335, 204, 104, 273, 106, 1687])).
% 4.44/4.68 tff(21337,plain,
% 4.44/4.68 (b(s(s(s(s(z)))), z)),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[191, 21336])).
% 4.44/4.68 tff(21338,plain,
% 4.44/4.68 (~b(s(s(s(s(z)))), s(s(z)))),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[298, 134, 104, 273, 168])).
% 4.44/4.68 tff(21339,plain,
% 4.44/4.68 (r(s(s(s(s(z)))), s(s(z)))),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[102, 21338])).
% 4.44/4.68 tff(21340,plain,
% 4.44/4.68 ($false),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[3920, 118, 204, 21339, 107])).
% 4.44/4.68 tff(21341,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(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(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.68 tff(21342,plain,
% 4.44/4.68 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[21341, 21337, 104, 273, 204, 106])).
% 4.44/4.68 tff(21343,plain,
% 4.44/4.68 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[3578, 21342])).
% 4.44/4.68 tff(21344,plain,
% 4.44/4.68 (~r(s(s(s(s(z)))), s(s(z)))),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[3559, 224, 204])).
% 4.44/4.68 tff(21345,plain,
% 4.44/4.68 (b(s(s(s(s(z)))), s(s(z)))),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[102, 21344])).
% 4.44/4.68 tff(21346,plain,
% 4.44/4.68 ($false),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[21333, 20670, 21345, 273, 104, 204, 106, 1687])).
% 4.44/4.68 tff(21347,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.68 tff(21348,plain,
% 4.44/4.68 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[21347, 204, 104, 273, 106, 1687])).
% 4.44/4.68 tff(21349,plain,
% 4.44/4.68 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[249, 21348])).
% 4.44/4.68 tff(21350,plain,
% 4.44/4.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 4.44/4.68 inference(rewrite,[status(thm)],[])).
% 4.44/4.68 tff(21351,plain,
% 4.44/4.68 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 4.44/4.68 inference(rewrite,[status(thm)],[])).
% 4.44/4.68 tff(21352,plain,
% 4.44/4.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))))),
% 4.44/4.68 inference(monotonicity,[status(thm)],[21351])).
% 4.44/4.68 tff(21353,plain,
% 4.44/4.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 4.44/4.68 inference(transitivity,[status(thm)],[21352, 21350])).
% 4.44/4.68 tff(21354,plain,
% 4.44/4.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)))),
% 4.44/4.68 inference(quant_inst,[status(thm)],[])).
% 4.44/4.68 tff(21355,plain,
% 4.44/4.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))),
% 4.44/4.68 inference(modus_ponens,[status(thm)],[21354, 21353])).
% 4.44/4.68 tff(21356,plain,
% 4.44/4.68 ($false),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[21355, 178, 273, 1687, 167, 1127, 4932])).
% 4.44/4.68 tff(21357,plain,((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.68 tff(21358,plain,
% 4.44/4.68 (~b(s(s(s(z))), s(s(z)))),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[21357, 167, 1687, 273, 1127])).
% 4.44/4.68 tff(21359,plain,
% 4.44/4.68 (r(s(s(s(z))), s(s(z)))),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[4966, 21358])).
% 4.44/4.68 tff(21360,plain,
% 4.44/4.68 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[8218, 8216, 1125])).
% 4.44/4.68 tff(21361,plain,
% 4.44/4.68 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[3578, 21360])).
% 4.44/4.68 tff(21362,plain,
% 4.44/4.68 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[21321, 21361])).
% 4.44/4.68 tff(21363,plain,
% 4.44/4.68 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[271, 21362])).
% 4.44/4.68 tff(21364,plain,
% 4.44/4.68 (~r(s(s(s(s(z)))), z)),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[21331, 118, 204, 21363])).
% 4.44/4.68 tff(21365,plain,
% 4.44/4.68 (b(s(s(s(s(z)))), z)),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[191, 21364])).
% 4.44/4.68 tff(21366,plain,
% 4.44/4.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 4.44/4.68 inference(rewrite,[status(thm)],[])).
% 4.44/4.68 tff(21367,plain,
% 4.44/4.68 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 4.44/4.68 inference(rewrite,[status(thm)],[])).
% 4.44/4.68 tff(21368,plain,
% 4.44/4.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z))))),
% 4.44/4.68 inference(monotonicity,[status(thm)],[21367])).
% 4.44/4.68 tff(21369,plain,
% 4.44/4.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 4.44/4.68 inference(transitivity,[status(thm)],[21368, 21366])).
% 4.44/4.68 tff(21370,plain,
% 4.44/4.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 4.44/4.68 inference(quant_inst,[status(thm)],[])).
% 4.44/4.68 tff(21371,plain,
% 4.44/4.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z))),
% 4.44/4.68 inference(modus_ponens,[status(thm)],[21370, 21369])).
% 4.44/4.68 tff(21372,plain,
% 4.44/4.68 ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[21371, 178, 1687, 168, 1126])).
% 4.44/4.68 tff(21373,plain,
% 4.44/4.68 (~b(s(s(s(z))), z)),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[21372, 17894])).
% 4.44/4.68 tff(21374,plain,
% 4.44/4.68 ($false),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[4903, 41, 77, 21373, 11273])).
% 4.44/4.68 tff(21375,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.68 tff(21376,plain,
% 4.44/4.68 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[21375, 21365, 1687, 204, 8216, 21363])).
% 4.44/4.68 tff(21377,plain,
% 4.44/4.68 (r(s(s(s(z))), s(s(s(s(z)))))),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[10755, 21376])).
% 4.44/4.68 tff(21378,plain,
% 4.44/4.68 (~r(s(s(s(s(z)))), s(s(z)))),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[20838, 21377, 1125])).
% 4.44/4.68 tff(21379,plain,
% 4.44/4.68 (b(s(s(s(s(z)))), s(s(z)))),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[102, 21378])).
% 4.44/4.68 tff(21380,plain,
% 4.44/4.68 ($false),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[1736, 178, 273, 1687, 21365, 167, 21379])).
% 4.44/4.68 tff(21381,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(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))))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.68 tff(21382,plain,
% 4.44/4.68 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[21381, 167, 1687, 273, 21359, 204, 104])).
% 4.44/4.68 tff(21383,plain,
% 4.44/4.68 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[20667, 21382])).
% 4.44/4.68 tff(21384,plain,
% 4.44/4.68 (~b(s(s(s(s(z)))), s(s(z)))),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[21333, 167, 273, 104, 204, 106, 1687])).
% 4.44/4.68 tff(21385,plain,
% 4.44/4.68 (r(s(s(s(s(z)))), s(s(z)))),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[102, 21384])).
% 4.44/4.68 tff(21386,plain,
% 4.44/4.68 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[20838, 21385, 21359])).
% 4.44/4.68 tff(21387,plain,
% 4.44/4.68 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[10755, 21386])).
% 4.44/4.68 tff(21388,plain,
% 4.44/4.68 (~r(s(s(s(s(z)))), z)),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[199, 21385, 106])).
% 4.44/4.68 tff(21389,plain,
% 4.44/4.68 (b(s(s(s(s(z)))), z)),
% 4.44/4.68 inference(unit_resolution,[status(thm)],[191, 21388])).
% 4.44/4.68 tff(21390,plain,
% 4.44/4.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)))),
% 4.44/4.68 inference(rewrite,[status(thm)],[])).
% 4.44/4.68 tff(21391,plain,
% 4.44/4.68 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)))),
% 4.44/4.68 inference(rewrite,[status(thm)],[])).
% 4.44/4.68 tff(21392,plain,
% 4.44/4.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(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)))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z))))),
% 4.44/4.68 inference(monotonicity,[status(thm)],[21391])).
% 4.44/4.68 tff(21393,plain,
% 4.44/4.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(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)))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)))),
% 4.44/4.69 inference(transitivity,[status(thm)],[21392, 21390])).
% 4.44/4.69 tff(21394,plain,
% 4.44/4.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(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)))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 4.44/4.69 inference(quant_inst,[status(thm)],[])).
% 4.44/4.69 tff(21395,plain,
% 4.44/4.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z))),
% 4.44/4.69 inference(modus_ponens,[status(thm)],[21394, 21393])).
% 4.44/4.69 tff(21396,plain,
% 4.44/4.69 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[21395, 178, 104, 1687, 21389, 21387, 1127, 21383])).
% 4.44/4.69 tff(21397,plain,
% 4.44/4.69 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[8696, 118, 21385, 21359])).
% 4.44/4.69 tff(21398,plain,
% 4.44/4.69 ($false),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[11185, 21397, 21396])).
% 4.44/4.69 tff(21399,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.69 tff(21400,plain,
% 4.44/4.69 (~b(s(s(z)), s(s(s(s(z)))))),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[21399, 1127, 1687, 104, 106, 273, 204])).
% 4.44/4.69 tff(21401,plain,
% 4.44/4.69 (r(s(s(z)), s(s(s(s(z)))))),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[164, 21400])).
% 4.44/4.69 tff(21402,plain,
% 4.44/4.69 (~r(s(s(s(s(z)))), z)),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[21308, 21401, 106])).
% 4.44/4.69 tff(21403,plain,
% 4.44/4.69 (b(s(s(s(s(z)))), z)),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[191, 21402])).
% 4.44/4.69 tff(21404,plain,
% 4.44/4.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 4.44/4.69 inference(rewrite,[status(thm)],[])).
% 4.44/4.69 tff(21405,plain,
% 4.44/4.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 4.44/4.69 inference(quant_inst,[status(thm)],[])).
% 4.44/4.69 tff(21406,plain,
% 4.44/4.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 4.44/4.69 inference(modus_ponens,[status(thm)],[21405, 21404])).
% 4.44/4.69 tff(21407,plain,
% 4.44/4.69 ($false),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[21406, 118, 204, 4891, 8216])).
% 4.44/4.69 tff(21408,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.69 tff(21409,plain,
% 4.44/4.69 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[21408, 8216, 204])).
% 4.44/4.69 tff(21410,plain,
% 4.44/4.69 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[10755, 21409])).
% 4.44/4.69 tff(21411,plain,
% 4.44/4.69 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[21371, 178, 1687, 168, 21410, 1127])).
% 4.44/4.69 tff(21412,plain,
% 4.44/4.69 ($false),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[11185, 21411, 17893])).
% 4.44/4.69 tff(21413,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.69 tff(21414,plain,
% 4.44/4.69 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[21413, 21403, 1687, 1127, 204])).
% 4.44/4.69 tff(21415,plain,
% 4.44/4.69 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[20667, 21414])).
% 4.44/4.69 tff(21416,plain,
% 4.44/4.69 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[21341, 21403, 104, 273, 204, 106])).
% 4.44/4.69 tff(21417,plain,
% 4.44/4.69 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[3578, 21416])).
% 4.44/4.69 tff(21418,plain,
% 4.44/4.69 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[5624, 21401, 204])).
% 4.44/4.69 tff(21419,plain,
% 4.44/4.69 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[249, 21418])).
% 4.44/4.69 tff(21420,plain,
% 4.44/4.69 (~b(s(s(z)), s(s(s(z))))),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[1227, 178, 104, 166, 1126, 3002])).
% 4.44/4.69 tff(21421,plain,
% 4.44/4.69 (r(s(s(z)), s(s(s(z))))),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[5088, 21420])).
% 4.44/4.69 tff(21422,plain,
% 4.44/4.69 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[21395, 178, 104, 1687, 168, 1126, 1127, 3002])).
% 4.44/4.69 tff(21423,plain,
% 4.44/4.69 (r(s(s(s(s(z)))), s(s(s(z))))),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[11185, 21422])).
% 4.44/4.69 tff(21424,plain,
% 4.44/4.69 ($false),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[7239, 118, 147, 21423, 21421])).
% 4.44/4.69 tff(21425,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.69 tff(21426,plain,
% 4.44/4.69 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[21425, 21401, 104, 1687, 21403, 1127, 21415, 21419])).
% 4.44/4.69 tff(21427,plain,
% 4.44/4.69 (r(s(s(s(z))), s(s(s(s(z)))))),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[10755, 21426])).
% 4.44/4.69 tff(21428,plain,
% 4.44/4.69 (~r(s(s(s(z))), s(s(z)))),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[5071, 118, 21401, 21427])).
% 4.44/4.69 tff(21429,plain,
% 4.44/4.69 (b(s(s(s(z))), s(s(z)))),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[4966, 21428])).
% 4.44/4.69 tff(21430,plain,
% 4.44/4.69 (~r(s(s(z)), s(s(s(z))))),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[5079, 118, 21401, 21427])).
% 4.44/4.69 tff(21431,plain,
% 4.44/4.69 (b(s(s(z)), s(s(s(z))))),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[5088, 21430])).
% 4.44/4.69 tff(21432,plain,
% 4.44/4.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.44/4.69 inference(rewrite,[status(thm)],[])).
% 4.44/4.69 tff(21433,plain,
% 4.44/4.69 (((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(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(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.44/4.69 inference(rewrite,[status(thm)],[])).
% 4.44/4.69 tff(21434,plain,
% 4.44/4.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(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(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))))),
% 4.44/4.69 inference(monotonicity,[status(thm)],[21433])).
% 4.44/4.69 tff(21435,plain,
% 4.44/4.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(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(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.44/4.69 inference(transitivity,[status(thm)],[21434, 21432])).
% 4.44/4.69 tff(21436,plain,
% 4.44/4.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(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(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))))),
% 4.44/4.69 inference(quant_inst,[status(thm)],[])).
% 4.44/4.69 tff(21437,plain,
% 4.44/4.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 4.44/4.69 inference(modus_ponens,[status(thm)],[21436, 21435])).
% 4.44/4.69 tff(21438,plain,
% 4.44/4.69 ($false),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[21437, 178, 166, 5090, 4932, 1146, 3002])).
% 4.44/4.69 tff(21439,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.69 tff(21440,plain,
% 4.44/4.69 ($false),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[21439, 21431, 21429, 21419, 21417, 21415])).
% 4.44/4.69 tff(21441,plain,((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.69 tff(21442,plain,
% 4.44/4.69 (~b(s(s(s(z))), z)),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[21441, 204, 1687, 104, 273, 106])).
% 4.44/4.69 tff(21443,plain,
% 4.44/4.69 (r(s(s(s(z))), z)),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[21073, 21442])).
% 4.44/4.69 tff(21444,plain,
% 4.44/4.69 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[20977, 8216, 16062])).
% 4.44/4.69 tff(21445,plain,
% 4.44/4.69 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[271, 21444])).
% 4.44/4.69 tff(21446,plain,
% 4.44/4.69 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[1154, 21445, 166, 1146, 273])).
% 4.44/4.69 tff(21447,plain,
% 4.44/4.69 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[133, 21446])).
% 4.44/4.69 tff(21448,plain,
% 4.44/4.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.44/4.69 inference(rewrite,[status(thm)],[])).
% 4.44/4.69 tff(21449,plain,
% 4.44/4.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.44/4.69 inference(quant_inst,[status(thm)],[])).
% 4.44/4.69 tff(21450,plain,
% 4.44/4.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 4.44/4.69 inference(modus_ponens,[status(thm)],[21449, 21448])).
% 4.44/4.69 tff(21451,plain,
% 4.44/4.69 ($false),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[21450, 118, 21447, 16062, 8216])).
% 4.44/4.69 tff(21452,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.69 tff(21453,plain,
% 4.44/4.69 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[21452, 21443, 21349, 21343, 273])).
% 4.44/4.69 tff(21454,plain,
% 4.44/4.69 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[20667, 21453])).
% 4.44/4.69 tff(21455,plain,
% 4.44/4.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 4.44/4.69 inference(rewrite,[status(thm)],[])).
% 4.44/4.69 tff(21456,plain,
% 4.44/4.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 4.44/4.69 inference(quant_inst,[status(thm)],[])).
% 4.44/4.69 tff(21457,plain,
% 4.44/4.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z))))),
% 4.44/4.69 inference(modus_ponens,[status(thm)],[21456, 21455])).
% 4.44/4.69 tff(21458,plain,
% 4.44/4.69 (~r(s(s(s(z))), s(s(z)))),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[21457, 118, 106, 21443])).
% 4.44/4.69 tff(21459,plain,
% 4.44/4.69 (b(s(s(s(z))), s(s(z)))),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[4966, 21458])).
% 4.44/4.69 tff(21460,plain,
% 4.44/4.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 4.44/4.69 inference(rewrite,[status(thm)],[])).
% 4.44/4.69 tff(21461,plain,
% 4.44/4.69 (((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 4.44/4.69 inference(rewrite,[status(thm)],[])).
% 4.44/4.69 tff(21462,plain,
% 4.44/4.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z)))))))),
% 4.44/4.69 inference(monotonicity,[status(thm)],[21461])).
% 4.44/4.69 tff(21463,plain,
% 4.44/4.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 4.44/4.69 inference(transitivity,[status(thm)],[21462, 21460])).
% 4.44/4.69 tff(21464,plain,
% 4.44/4.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 4.44/4.69 inference(quant_inst,[status(thm)],[])).
% 4.44/4.69 tff(21465,plain,
% 4.44/4.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z)))))),
% 4.44/4.69 inference(modus_ponens,[status(thm)],[21464, 21463])).
% 4.44/4.69 tff(21466,plain,
% 4.44/4.69 (~r(s(s(z)), s(s(s(z))))),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[21465, 118, 106, 21443])).
% 4.44/4.69 tff(21467,plain,
% 4.44/4.69 (b(s(s(z)), s(s(s(z))))),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[5088, 21466])).
% 4.44/4.69 tff(21468,plain,
% 4.44/4.69 ($false),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[21439, 21467, 21459, 21349, 21343, 21454])).
% 4.44/4.69 tff(21469,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.69 tff(21470,plain,
% 4.44/4.69 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[21469, 106, 273, 104, 1687])).
% 4.44/4.69 tff(21471,plain,
% 4.44/4.69 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[222, 21470])).
% 4.44/4.69 tff(21472,plain,
% 4.44/4.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(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(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(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(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 4.44/4.69 inference(rewrite,[status(thm)],[])).
% 4.44/4.69 tff(21473,plain,
% 4.44/4.69 (((~b(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))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, 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(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(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 4.44/4.69 inference(rewrite,[status(thm)],[])).
% 4.44/4.69 tff(21474,plain,
% 4.44/4.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(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(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z))))))))),
% 4.44/4.69 inference(monotonicity,[status(thm)],[21473])).
% 4.44/4.69 tff(21475,plain,
% 4.44/4.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(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(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 4.44/4.69 inference(transitivity,[status(thm)],[21474, 21472])).
% 4.44/4.69 tff(21476,plain,
% 4.44/4.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 4.44/4.69 inference(quant_inst,[status(thm)],[])).
% 4.44/4.69 tff(21477,plain,
% 4.44/4.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z))))))),
% 4.44/4.69 inference(modus_ponens,[status(thm)],[21476, 21475])).
% 4.44/4.69 tff(21478,plain,
% 4.44/4.69 ($false),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[21477, 178, 104, 1687, 251, 399, 17330])).
% 4.44/4.69 tff(21479,plain,((~r(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(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 4.44/4.69 tff(21480,plain,
% 4.44/4.69 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[21479, 21471, 1687, 104, 106])).
% 4.44/4.69 tff(21481,plain,
% 4.44/4.69 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.44/4.69 inference(unit_resolution,[status(thm)],[249, 21480])).
% 4.44/4.69 tff(21482,plain,
% 4.44/4.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(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))))))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(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))))))))) | (~b(z, s(s(s(s(z)))))))),
% 4.44/4.69 inference(rewrite,[status(thm)],[])).
% 4.44/4.69 tff(21483,plain,
% 4.44/4.69 (((~b(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))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(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(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))))),
% 4.44/4.69 inference(rewrite,[status(thm)],[])).
% 4.44/4.69 tff(21484,plain,
% 4.44/4.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(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))))))))) | (~b(z, s(s(s(s(z))))))))),
% 4.44/4.69 inference(monotonicity,[status(thm)],[21483])).
% 4.44/4.69 tff(21485,plain,
% 4.44/4.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(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))))))))) | (~b(z, s(s(s(s(z)))))))),
% 4.44/4.70 inference(transitivity,[status(thm)],[21484, 21482])).
% 4.44/4.70 tff(21486,plain,
% 4.44/4.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))))),
% 4.44/4.70 inference(quant_inst,[status(thm)],[])).
% 4.44/4.70 tff(21487,plain,
% 4.44/4.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(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))))))))) | (~b(z, s(s(s(s(z))))))),
% 4.44/4.70 inference(modus_ponens,[status(thm)],[21486, 21485])).
% 4.44/4.70 tff(21488,plain,
% 4.44/4.70 (~b(s(s(z)), s(s(s(s(z)))))),
% 4.44/4.70 inference(unit_resolution,[status(thm)],[21487, 178, 273, 1687, 21481, 21471])).
% 4.44/4.70 tff(21489,plain,
% 4.44/4.70 (r(s(s(z)), s(s(s(s(z)))))),
% 4.44/4.70 inference(unit_resolution,[status(thm)],[164, 21488])).
% 4.44/4.70 tff(21490,plain,
% 4.44/4.70 (~r(s(s(s(s(z)))), z)),
% 4.44/4.70 inference(unit_resolution,[status(thm)],[21308, 21489, 106])).
% 4.44/4.70 tff(21491,plain,
% 4.44/4.70 (b(s(s(s(s(z)))), z)),
% 4.44/4.70 inference(unit_resolution,[status(thm)],[191, 21490])).
% 4.44/4.70 tff(21492,plain,
% 4.44/4.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(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))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(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))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 4.44/4.70 inference(rewrite,[status(thm)],[])).
% 4.44/4.70 tff(21493,plain,
% 4.44/4.70 (((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(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))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(s(z)))) | (~b(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))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 4.44/4.70 inference(rewrite,[status(thm)],[])).
% 4.44/4.70 tff(21494,plain,
% 4.44/4.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(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))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(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))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))))),
% 4.44/4.70 inference(monotonicity,[status(thm)],[21493])).
% 4.44/4.70 tff(21495,plain,
% 4.44/4.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(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))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(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))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 4.54/4.70 inference(transitivity,[status(thm)],[21494, 21492])).
% 4.54/4.70 tff(21496,plain,
% 4.54/4.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(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))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 4.54/4.70 inference(quant_inst,[status(thm)],[])).
% 4.54/4.70 tff(21497,plain,
% 4.54/4.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(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))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))),
% 4.54/4.70 inference(modus_ponens,[status(thm)],[21496, 21495])).
% 4.54/4.70 tff(21498,plain,
% 4.54/4.70 (~b(s(s(s(s(z)))), s(s(z)))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[21497, 178, 273, 1687, 21481, 21471])).
% 4.54/4.70 tff(21499,plain,
% 4.54/4.70 (r(s(s(s(s(z)))), s(s(z)))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[102, 21498])).
% 4.54/4.70 tff(21500,plain,
% 4.54/4.70 ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[11920, 178, 104, 1687, 21471])).
% 4.54/4.70 tff(21501,plain,
% 4.54/4.70 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[21500, 21491])).
% 4.54/4.70 tff(21502,plain,
% 4.54/4.70 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[271, 21501])).
% 4.54/4.70 tff(21503,plain,
% 4.54/4.70 (~r(s(s(s(z))), z)),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[20977, 8216, 203])).
% 4.54/4.70 tff(21504,plain,
% 4.54/4.70 (b(s(s(s(z))), z)),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[21073, 21503])).
% 4.54/4.70 tff(21505,plain,
% 4.54/4.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z))))))),
% 4.54/4.70 inference(rewrite,[status(thm)],[])).
% 4.54/4.70 tff(21506,plain,
% 4.54/4.70 (((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z))))))),
% 4.54/4.70 inference(rewrite,[status(thm)],[])).
% 4.54/4.70 tff(21507,plain,
% 4.54/4.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z)))))))),
% 4.54/4.70 inference(monotonicity,[status(thm)],[21506])).
% 4.54/4.70 tff(21508,plain,
% 4.54/4.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z))))))),
% 4.54/4.70 inference(transitivity,[status(thm)],[21507, 21505])).
% 4.54/4.70 tff(21509,plain,
% 4.54/4.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z))))))),
% 4.54/4.70 inference(quant_inst,[status(thm)],[])).
% 4.54/4.70 tff(21510,plain,
% 4.54/4.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z)))))),
% 4.54/4.70 inference(modus_ponens,[status(thm)],[21509, 21508])).
% 4.54/4.70 tff(21511,plain,
% 4.54/4.70 (~r(z, s(s(s(z))))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[21510, 118, 203, 8216])).
% 4.54/4.70 tff(21512,plain,
% 4.54/4.70 (b(z, s(s(s(z))))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[4920, 21511])).
% 4.54/4.70 tff(21513,plain,
% 4.54/4.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 4.54/4.70 inference(rewrite,[status(thm)],[])).
% 4.54/4.70 tff(21514,plain,
% 4.54/4.70 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 4.54/4.70 inference(rewrite,[status(thm)],[])).
% 4.54/4.70 tff(21515,plain,
% 4.54/4.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~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(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 4.54/4.70 inference(monotonicity,[status(thm)],[21514])).
% 4.54/4.70 tff(21516,plain,
% 4.54/4.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~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(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 4.54/4.70 inference(transitivity,[status(thm)],[21515, 21513])).
% 4.54/4.70 tff(21517,plain,
% 4.54/4.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~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(z, s(s(s(z))))))),
% 4.54/4.70 inference(quant_inst,[status(thm)],[])).
% 4.54/4.70 tff(21518,plain,
% 4.54/4.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 4.54/4.70 inference(modus_ponens,[status(thm)],[21517, 21516])).
% 4.54/4.70 tff(21519,plain,
% 4.54/4.70 ($false),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[21518, 178, 1687, 168, 1126, 21512, 21504])).
% 4.54/4.70 tff(21520,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.70 tff(21521,plain,
% 4.54/4.70 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[21520, 8216, 168, 203, 1687])).
% 4.54/4.70 tff(21522,plain,
% 4.54/4.70 (r(s(s(s(z))), s(s(s(s(z)))))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[10755, 21521])).
% 4.54/4.70 tff(21523,plain,
% 4.54/4.70 (~r(s(s(s(z))), s(s(z)))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[20838, 21522, 193])).
% 4.54/4.70 tff(21524,plain,
% 4.54/4.70 (b(s(s(s(z))), s(s(z)))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[4966, 21523])).
% 4.54/4.70 tff(21525,plain,
% 4.54/4.70 (~r(s(s(z)), s(s(s(z))))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[5079, 118, 147, 21522])).
% 4.54/4.70 tff(21526,plain,
% 4.54/4.70 (b(s(s(z)), s(s(s(z))))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[5088, 21525])).
% 4.54/4.70 tff(21527,plain,
% 4.54/4.70 ($false),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[10770, 178, 273, 21512, 21526, 21504, 21524])).
% 4.54/4.70 tff(21528,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.70 tff(21529,plain,
% 4.54/4.70 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[21528, 21489, 273, 21502, 21499, 21491, 1687])).
% 4.54/4.70 tff(21530,plain,
% 4.54/4.70 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[20667, 21529])).
% 4.54/4.70 tff(21531,plain,
% 4.54/4.70 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[11893, 178, 104, 1687, 21491, 21471])).
% 4.54/4.70 tff(21532,plain,
% 4.54/4.70 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[133, 21531])).
% 4.54/4.70 tff(21533,plain,
% 4.54/4.70 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[123, 21532, 106])).
% 4.54/4.70 tff(21534,plain,
% 4.54/4.70 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[3578, 21533])).
% 4.54/4.70 tff(21535,plain,
% 4.54/4.70 ($false),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[21439, 5089, 5073, 166, 1146, 3002])).
% 4.54/4.70 tff(21536,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.70 tff(21537,plain,
% 4.54/4.70 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[21536, 21530, 21489, 21481, 21534])).
% 4.54/4.70 tff(21538,plain,
% 4.54/4.70 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[10755, 21537])).
% 4.54/4.70 tff(21539,plain,
% 4.54/4.70 (~b(s(s(z)), s(s(s(z))))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[1227, 178, 104, 21481, 21538, 21530])).
% 4.54/4.70 tff(21540,plain,
% 4.54/4.70 (r(s(s(z)), s(s(s(z))))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[5088, 21539])).
% 4.54/4.70 tff(21541,plain,
% 4.54/4.70 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[11182, 178, 104, 21471, 21538, 21530])).
% 4.54/4.70 tff(21542,plain,
% 4.54/4.70 (r(s(s(s(s(z)))), s(s(s(z))))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[11185, 21541])).
% 4.54/4.70 tff(21543,plain,
% 4.54/4.70 ($false),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[7239, 118, 21489, 21542, 21540])).
% 4.54/4.70 tff(21544,plain,((~r(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.70 tff(21545,plain,
% 4.54/4.70 (~r(s(s(z)), z)),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[21544, 273, 104, 1687])).
% 4.54/4.70 tff(21546,plain,
% 4.54/4.70 (b(s(s(z)), z)),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[3249, 21545])).
% 4.54/4.70 tff(21547,plain,
% 4.54/4.70 (~b(s(s(s(z))), z)),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[11287, 8216, 21546, 273, 224])).
% 4.54/4.70 tff(21548,plain,
% 4.54/4.70 (r(s(s(s(z))), z)),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[21073, 21547])).
% 4.54/4.70 tff(21549,plain,
% 4.54/4.70 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[11290, 8216, 21546, 273, 224])).
% 4.54/4.70 tff(21550,plain,
% 4.54/4.70 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[271, 21549])).
% 4.54/4.70 tff(21551,plain,
% 4.54/4.70 ($false),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[6228, 178, 3461, 273, 1687, 167, 202])).
% 4.54/4.70 tff(21552,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.70 tff(21553,plain,
% 4.54/4.70 (~b(s(s(s(s(z)))), s(s(z)))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[21552, 167, 273, 1687, 3461])).
% 4.54/4.70 tff(21554,plain,
% 4.54/4.70 (r(s(s(s(s(z)))), s(s(z)))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[102, 21553])).
% 4.54/4.70 tff(21555,plain,
% 4.54/4.70 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[3559, 21554, 224])).
% 4.54/4.70 tff(21556,plain,
% 4.54/4.70 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[222, 21555])).
% 4.54/4.70 tff(21557,plain,
% 4.54/4.70 ($false),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[14395, 178, 3461, 1687, 167, 21556, 595])).
% 4.54/4.70 tff(21558,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.70 tff(21559,plain,
% 4.54/4.70 (~b(s(s(z)), s(s(s(s(z)))))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[21558, 21550, 1687, 21546, 224, 273])).
% 4.54/4.70 tff(21560,plain,
% 4.54/4.70 (r(s(s(z)), s(s(s(s(z)))))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[164, 21559])).
% 4.54/4.70 tff(21561,plain,
% 4.54/4.70 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[5624, 21560, 224])).
% 4.54/4.70 tff(21562,plain,
% 4.54/4.70 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[222, 21561])).
% 4.54/4.70 tff(21563,plain,
% 4.54/4.70 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[21477, 178, 104, 1687, 21562, 21550])).
% 4.54/4.70 tff(21564,plain,
% 4.54/4.70 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[133, 21563])).
% 4.54/4.70 tff(21565,plain,
% 4.54/4.70 ($false),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[21450, 118, 21564, 21548, 8216])).
% 4.54/4.70 tff(21566,plain,((~r(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(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.70 tff(21567,plain,
% 4.54/4.70 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[21566, 287, 1687, 104, 273])).
% 4.54/4.70 tff(21568,plain,
% 4.54/4.70 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[20667, 21567])).
% 4.54/4.70 tff(21569,plain,
% 4.54/4.70 (~b(s(s(s(s(z)))), s(s(z)))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[21552, 167, 273, 1687, 21546])).
% 4.54/4.70 tff(21570,plain,
% 4.54/4.70 (r(s(s(s(s(z)))), s(s(z)))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[102, 21569])).
% 4.54/4.70 tff(21571,plain,
% 4.54/4.70 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[3559, 21570, 224])).
% 4.54/4.70 tff(21572,plain,
% 4.54/4.70 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[222, 21571])).
% 4.54/4.70 tff(21573,plain,
% 4.54/4.70 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[16623, 21572, 224, 3002, 167, 104])).
% 4.54/4.70 tff(21574,plain,
% 4.54/4.70 (r(s(s(s(z))), s(s(s(s(z)))))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[10755, 21573])).
% 4.54/4.70 tff(21575,plain,
% 4.54/4.70 (~r(s(s(s(z))), s(s(z)))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[20838, 21574, 21570])).
% 4.54/4.70 tff(21576,plain,
% 4.54/4.70 (b(s(s(s(z))), s(s(z)))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[4966, 21575])).
% 4.54/4.70 tff(21577,plain,
% 4.54/4.70 (~b(s(s(s(z))), z)),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[21357, 21576, 1687, 273, 167])).
% 4.54/4.70 tff(21578,plain,
% 4.54/4.70 (r(s(s(s(z))), z)),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[21073, 21577])).
% 4.54/4.70 tff(21579,plain,
% 4.54/4.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 4.54/4.70 inference(rewrite,[status(thm)],[])).
% 4.54/4.70 tff(21580,plain,
% 4.54/4.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 4.54/4.70 inference(quant_inst,[status(thm)],[])).
% 4.54/4.70 tff(21581,plain,
% 4.54/4.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 4.54/4.70 inference(modus_ponens,[status(thm)],[21580, 21579])).
% 4.54/4.70 tff(21582,plain,
% 4.54/4.70 ($false),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[21581, 118, 194, 21574, 21578])).
% 4.54/4.70 tff(21583,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.70 tff(21584,plain,
% 4.54/4.70 (~b(s(s(z)), s(s(s(s(z)))))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[21583, 194, 1687, 273, 224, 3002, 104])).
% 4.54/4.70 tff(21585,plain,
% 4.54/4.70 (r(s(s(z)), s(s(s(s(z)))))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[164, 21584])).
% 4.54/4.70 tff(21586,plain,
% 4.54/4.70 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[5624, 21585, 224])).
% 4.54/4.70 tff(21587,plain,
% 4.54/4.70 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[222, 21586])).
% 4.54/4.70 tff(21588,plain,
% 4.54/4.70 (~r(s(s(s(z))), s(s(z)))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[20838, 4891, 193])).
% 4.54/4.70 tff(21589,plain,
% 4.54/4.70 (b(s(s(s(z))), s(s(z)))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[4966, 21588])).
% 4.54/4.70 tff(21590,plain,
% 4.54/4.70 ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[11284, 178, 3461, 273, 21589])).
% 4.54/4.70 tff(21591,plain,
% 4.54/4.70 (~b(s(s(s(z))), z)),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[21590, 5089])).
% 4.54/4.70 tff(21592,plain,
% 4.54/4.70 (r(s(s(s(z))), z)),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[21073, 21591])).
% 4.54/4.70 tff(21593,plain,
% 4.54/4.70 ($false),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[21581, 118, 194, 4891, 21592])).
% 4.54/4.70 tff(21594,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.70 tff(21595,plain,
% 4.54/4.70 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[21594, 193, 21546, 273, 147, 194])).
% 4.54/4.70 tff(21596,plain,
% 4.54/4.70 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[10755, 21595])).
% 4.54/4.70 tff(21597,plain,
% 4.54/4.70 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[11182, 178, 104, 251, 21596, 3002])).
% 4.54/4.70 tff(21598,plain,
% 4.54/4.70 (r(s(s(s(s(z)))), s(s(s(z))))),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[11185, 21597])).
% 4.54/4.70 tff(21599,plain,
% 4.54/4.70 (~r(s(s(s(z))), z)),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[20784, 21598, 194])).
% 4.54/4.70 tff(21600,plain,
% 4.54/4.70 (b(s(s(s(z))), z)),
% 4.54/4.70 inference(unit_resolution,[status(thm)],[21073, 21599])).
% 4.54/4.70 tff(21601,plain,
% 4.54/4.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 4.54/4.70 inference(rewrite,[status(thm)],[])).
% 4.54/4.70 tff(21602,plain,
% 4.54/4.70 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 4.54/4.70 inference(rewrite,[status(thm)],[])).
% 4.54/4.70 tff(21603,plain,
% 4.54/4.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(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(z)), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 4.54/4.71 inference(monotonicity,[status(thm)],[21602])).
% 4.54/4.71 tff(21604,plain,
% 4.54/4.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(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(z)), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 4.54/4.71 inference(transitivity,[status(thm)],[21603, 21601])).
% 4.54/4.71 tff(21605,plain,
% 4.54/4.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(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(z)), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))))),
% 4.54/4.71 inference(quant_inst,[status(thm)],[])).
% 4.54/4.71 tff(21606,plain,
% 4.54/4.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 4.54/4.71 inference(modus_ponens,[status(thm)],[21605, 21604])).
% 4.54/4.71 tff(21607,plain,
% 4.54/4.71 ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 4.54/4.71 inference(unit_resolution,[status(thm)],[21606, 178, 21546, 104, 1687, 21596, 3002])).
% 4.54/4.71 tff(21608,plain,
% 4.54/4.71 (~b(s(s(z)), s(s(s(z))))),
% 4.54/4.71 inference(unit_resolution,[status(thm)],[21607, 21600])).
% 4.54/4.71 tff(21609,plain,
% 4.54/4.71 (r(s(s(z)), s(s(s(z))))),
% 4.54/4.71 inference(unit_resolution,[status(thm)],[5088, 21608])).
% 4.54/4.71 tff(21610,plain,
% 4.54/4.71 ($false),
% 4.54/4.71 inference(unit_resolution,[status(thm)],[17129, 118, 193, 21598, 21609])).
% 4.54/4.71 tff(21611,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.71 tff(21612,plain,
% 4.54/4.71 (~r(s(s(s(s(z)))), s(s(z)))),
% 4.54/4.71 inference(unit_resolution,[status(thm)],[21611, 194, 1687, 3002, 104, 21587, 273, 21585])).
% 4.54/4.71 tff(21613,plain,
% 4.54/4.71 (b(s(s(s(s(z)))), s(s(z)))),
% 4.54/4.71 inference(unit_resolution,[status(thm)],[102, 21612])).
% 4.54/4.71 tff(21614,plain,
% 4.54/4.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), 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)))),
% 4.54/4.71 inference(rewrite,[status(thm)],[])).
% 4.54/4.71 tff(21615,plain,
% 4.54/4.71 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), 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)))),
% 4.54/4.71 inference(rewrite,[status(thm)],[])).
% 4.54/4.71 tff(21616,plain,
% 4.54/4.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), 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))))),
% 4.54/4.71 inference(monotonicity,[status(thm)],[21615])).
% 4.54/4.71 tff(21617,plain,
% 4.54/4.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), 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)))),
% 4.54/4.71 inference(transitivity,[status(thm)],[21616, 21614])).
% 4.54/4.71 tff(21618,plain,
% 4.54/4.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 4.54/4.71 inference(quant_inst,[status(thm)],[])).
% 4.54/4.71 tff(21619,plain,
% 4.54/4.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z))),
% 4.54/4.71 inference(modus_ponens,[status(thm)],[21618, 21617])).
% 4.54/4.71 tff(21620,plain,
% 4.54/4.71 (~b(s(s(s(z))), z)),
% 4.54/4.71 inference(unit_resolution,[status(thm)],[21619, 178, 273, 1687, 202, 1126])).
% 4.54/4.71 tff(21621,plain,
% 4.54/4.71 (r(s(s(s(z))), z)),
% 4.54/4.71 inference(unit_resolution,[status(thm)],[21073, 21620])).
% 4.54/4.71 tff(21622,plain,
% 4.54/4.71 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 4.54/4.71 inference(unit_resolution,[status(thm)],[11182, 178, 104, 251, 1126, 3002])).
% 4.54/4.71 tff(21623,plain,
% 4.54/4.71 (r(s(s(s(s(z)))), s(s(s(z))))),
% 4.54/4.71 inference(unit_resolution,[status(thm)],[11185, 21622])).
% 4.54/4.71 tff(21624,plain,
% 4.54/4.71 ($false),
% 4.54/4.71 inference(unit_resolution,[status(thm)],[20784, 21623, 21621, 194])).
% 4.54/4.71 tff(21625,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.71 tff(21626,plain,
% 4.54/4.71 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 4.54/4.71 inference(unit_resolution,[status(thm)],[21625, 194, 104, 21587, 3002, 273, 1687, 21613])).
% 4.54/4.71 tff(21627,plain,
% 4.54/4.71 (r(s(s(s(z))), s(s(s(s(z)))))),
% 4.54/4.71 inference(unit_resolution,[status(thm)],[10755, 21626])).
% 4.54/4.71 tff(21628,plain,
% 4.54/4.71 (~r(s(s(z)), s(s(s(z))))),
% 4.54/4.71 inference(unit_resolution,[status(thm)],[5079, 118, 21585, 21627])).
% 4.54/4.71 tff(21629,plain,
% 4.54/4.71 (b(s(s(z)), s(s(s(z))))),
% 4.54/4.71 inference(unit_resolution,[status(thm)],[5088, 21628])).
% 4.54/4.71 tff(21630,plain,
% 4.54/4.71 (~r(s(s(s(z))), s(s(z)))),
% 4.54/4.71 inference(unit_resolution,[status(thm)],[5071, 118, 21585, 21627])).
% 4.54/4.71 tff(21631,plain,
% 4.54/4.71 (b(s(s(s(z))), s(s(z)))),
% 4.54/4.71 inference(unit_resolution,[status(thm)],[4966, 21630])).
% 4.54/4.71 tff(21632,plain,
% 4.54/4.71 (~b(s(s(s(z))), z)),
% 4.54/4.71 inference(unit_resolution,[status(thm)],[11284, 178, 21546, 273, 21629, 21631])).
% 4.54/4.71 tff(21633,plain,
% 4.54/4.71 (r(s(s(s(z))), z)),
% 4.54/4.71 inference(unit_resolution,[status(thm)],[21073, 21632])).
% 4.54/4.71 tff(21634,plain,
% 4.54/4.71 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 4.54/4.71 inference(unit_resolution,[status(thm)],[20784, 21633, 194])).
% 4.54/4.71 tff(21635,plain,
% 4.54/4.71 (b(s(s(s(s(z)))), s(s(s(z))))),
% 4.54/4.71 inference(unit_resolution,[status(thm)],[11185, 21634])).
% 4.54/4.71 tff(21636,plain,
% 4.54/4.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 4.54/4.71 inference(rewrite,[status(thm)],[])).
% 4.54/4.71 tff(21637,plain,
% 4.54/4.71 (((~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(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 4.54/4.71 inference(rewrite,[status(thm)],[])).
% 4.54/4.71 tff(21638,plain,
% 4.54/4.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 4.54/4.71 inference(monotonicity,[status(thm)],[21637])).
% 4.54/4.71 tff(21639,plain,
% 4.54/4.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 4.54/4.71 inference(transitivity,[status(thm)],[21638, 21636])).
% 4.54/4.71 tff(21640,plain,
% 4.54/4.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 4.54/4.71 inference(quant_inst,[status(thm)],[])).
% 4.54/4.71 tff(21641,plain,
% 4.54/4.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))),
% 4.54/4.71 inference(modus_ponens,[status(thm)],[21640, 21639])).
% 4.54/4.71 tff(21642,plain,
% 4.54/4.71 ($false),
% 4.54/4.71 inference(unit_resolution,[status(thm)],[21641, 178, 273, 1687, 21613, 21635, 21629])).
% 4.54/4.71 tff(21643,plain,((~r(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.71 tff(21644,plain,
% 4.54/4.71 (~r(s(s(s(s(z)))), z)),
% 4.54/4.71 inference(unit_resolution,[status(thm)],[21643, 21568, 1687, 104, 273, 287])).
% 4.54/4.71 tff(21645,plain,
% 4.54/4.71 (b(s(s(s(s(z)))), z)),
% 4.54/4.71 inference(unit_resolution,[status(thm)],[191, 21644])).
% 4.54/4.71 tff(21646,plain,
% 4.54/4.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)) | (~b(z, s(s(s(s(z)))))))),
% 4.54/4.71 inference(rewrite,[status(thm)],[])).
% 4.54/4.71 tff(21647,plain,
% 4.54/4.71 (((~b(s(s(s(s(z)))), 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(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, 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)) | (~b(z, s(s(s(s(z)))))))),
% 4.54/4.71 inference(rewrite,[status(thm)],[])).
% 4.54/4.71 tff(21648,plain,
% 4.54/4.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)) | (~b(z, s(s(s(s(z))))))))),
% 4.54/4.71 inference(monotonicity,[status(thm)],[21647])).
% 4.54/4.71 tff(21649,plain,
% 4.54/4.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)) | (~b(z, s(s(s(s(z)))))))),
% 4.54/4.71 inference(transitivity,[status(thm)],[21648, 21646])).
% 4.54/4.71 tff(21650,plain,
% 4.54/4.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))))),
% 4.54/4.71 inference(quant_inst,[status(thm)],[])).
% 4.54/4.71 tff(21651,plain,
% 4.54/4.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))),
% 4.54/4.71 inference(modus_ponens,[status(thm)],[21650, 21649])).
% 4.54/4.71 tff(21652,plain,
% 4.54/4.71 ($false),
% 4.54/4.71 inference(unit_resolution,[status(thm)],[21651, 178, 3461, 273, 1687, 168, 167])).
% 4.54/4.71 tff(21653,plain,((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.71 tff(21654,plain,
% 4.54/4.71 (~b(s(s(z)), s(s(s(s(z)))))),
% 4.54/4.71 inference(unit_resolution,[status(thm)],[21653, 21645, 273, 1687, 21546])).
% 4.54/4.71 tff(21655,plain,
% 4.54/4.71 (r(s(s(z)), s(s(s(s(z)))))),
% 4.54/4.71 inference(unit_resolution,[status(thm)],[164, 21654])).
% 4.54/4.71 tff(21656,plain,
% 4.54/4.71 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.71 inference(unit_resolution,[status(thm)],[5624, 21655, 287])).
% 4.54/4.71 tff(21657,plain,
% 4.54/4.71 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.71 inference(unit_resolution,[status(thm)],[222, 21656])).
% 4.54/4.71 tff(21658,plain,
% 4.54/4.71 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.54/4.71 inference(unit_resolution,[status(thm)],[11893, 178, 104, 1687, 21645, 21657])).
% 4.54/4.71 tff(21659,plain,
% 4.54/4.71 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.54/4.71 inference(unit_resolution,[status(thm)],[133, 21658])).
% 4.54/4.71 tff(21660,plain,
% 4.54/4.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.54/4.71 inference(rewrite,[status(thm)],[])).
% 4.54/4.71 tff(21661,plain,
% 4.54/4.71 (((~b(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))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.54/4.71 inference(rewrite,[status(thm)],[])).
% 4.54/4.71 tff(21662,plain,
% 4.54/4.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 4.54/4.71 inference(monotonicity,[status(thm)],[21661])).
% 4.54/4.71 tff(21663,plain,
% 4.54/4.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.54/4.71 inference(transitivity,[status(thm)],[21662, 21660])).
% 4.54/4.71 tff(21664,plain,
% 4.54/4.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 4.54/4.71 inference(quant_inst,[status(thm)],[])).
% 4.54/4.71 tff(21665,plain,
% 4.54/4.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 4.54/4.71 inference(modus_ponens,[status(thm)],[21664, 21663])).
% 4.54/4.71 tff(21666,plain,
% 4.54/4.71 ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))),
% 4.54/4.71 inference(unit_resolution,[status(thm)],[21665, 178, 1687, 251, 3002])).
% 4.54/4.71 tff(21667,plain,
% 4.54/4.71 (~b(z, s(s(s(z))))),
% 4.54/4.71 inference(unit_resolution,[status(thm)],[21666, 1126])).
% 4.54/4.71 tff(21668,plain,
% 4.54/4.71 (r(z, s(s(s(z))))),
% 4.54/4.71 inference(unit_resolution,[status(thm)],[4920, 21667])).
% 4.54/4.71 tff(21669,plain,
% 4.54/4.71 ($false),
% 4.54/4.71 inference(unit_resolution,[status(thm)],[15390, 118, 108, 21668, 16606])).
% 4.54/4.71 tff(21670,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.71 tff(21671,plain,
% 4.54/4.71 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 4.54/4.71 inference(unit_resolution,[status(thm)],[21670, 21659, 1687, 21657, 21568, 104])).
% 4.54/4.71 tff(21672,plain,
% 4.54/4.71 (r(s(s(s(z))), s(s(s(s(z)))))),
% 4.54/4.71 inference(unit_resolution,[status(thm)],[10755, 21671])).
% 4.54/4.71 tff(21673,plain,
% 4.54/4.71 (~r(s(s(z)), s(s(s(z))))),
% 4.54/4.71 inference(unit_resolution,[status(thm)],[5079, 118, 21655, 21672])).
% 4.54/4.71 tff(21674,plain,
% 4.54/4.71 (b(s(s(z)), s(s(s(z))))),
% 4.54/4.71 inference(unit_resolution,[status(thm)],[5088, 21673])).
% 4.54/4.71 tff(21675,plain,
% 4.54/4.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(s(s(z)))))))),
% 4.54/4.72 inference(rewrite,[status(thm)],[])).
% 4.54/4.72 tff(21676,plain,
% 4.54/4.72 (((~b(s(s(z)), 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(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(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(s(s(z)))))))),
% 4.54/4.72 inference(rewrite,[status(thm)],[])).
% 4.54/4.72 tff(21677,plain,
% 4.54/4.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(s(s(z))))))))),
% 4.54/4.72 inference(monotonicity,[status(thm)],[21676])).
% 4.54/4.72 tff(21678,plain,
% 4.54/4.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(s(s(z)))))))),
% 4.54/4.72 inference(transitivity,[status(thm)],[21677, 21675])).
% 4.54/4.72 tff(21679,plain,
% 4.54/4.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 4.54/4.72 inference(quant_inst,[status(thm)],[])).
% 4.54/4.72 tff(21680,plain,
% 4.54/4.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(s(s(z))))))),
% 4.54/4.72 inference(modus_ponens,[status(thm)],[21679, 21678])).
% 4.54/4.72 tff(21681,plain,
% 4.54/4.72 (~b(s(s(s(s(z)))), s(s(z)))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[21680, 178, 21546, 273, 1687, 21645])).
% 4.54/4.72 tff(21682,plain,
% 4.54/4.72 (r(s(s(s(s(z)))), s(s(z)))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[102, 21681])).
% 4.54/4.72 tff(21683,plain,
% 4.54/4.72 (~r(s(s(s(z))), s(s(z)))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[20838, 21672, 21682])).
% 4.54/4.72 tff(21684,plain,
% 4.54/4.72 (b(s(s(s(z))), s(s(z)))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[4966, 21683])).
% 4.54/4.72 tff(21685,plain,
% 4.54/4.72 ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[11284, 178, 21546, 273, 21684])).
% 4.54/4.72 tff(21686,plain,
% 4.54/4.72 (~b(s(s(s(z))), z)),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[21685, 21674])).
% 4.54/4.72 tff(21687,plain,
% 4.54/4.72 (r(s(s(s(z))), z)),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[21073, 21686])).
% 4.54/4.72 tff(21688,plain,
% 4.54/4.72 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[20758, 21687, 21659])).
% 4.54/4.72 tff(21689,plain,
% 4.54/4.72 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 21688])).
% 4.54/4.72 tff(21690,plain,
% 4.54/4.72 (~r(s(s(s(s(z)))), z)),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[21643, 3002, 1687, 104, 273, 287])).
% 4.54/4.72 tff(21691,plain,
% 4.54/4.72 (b(s(s(s(s(z)))), z)),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[191, 21690])).
% 4.54/4.72 tff(21692,plain,
% 4.54/4.72 (~b(s(s(z)), s(s(s(s(z)))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[21653, 21691, 273, 1687, 21546])).
% 4.54/4.72 tff(21693,plain,
% 4.54/4.72 (r(s(s(z)), s(s(s(s(z)))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[164, 21692])).
% 4.54/4.72 tff(21694,plain,
% 4.54/4.72 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[5624, 21693, 287])).
% 4.54/4.72 tff(21695,plain,
% 4.54/4.72 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[222, 21694])).
% 4.54/4.72 tff(21696,plain,
% 4.54/4.72 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[11920, 178, 104, 1687, 21691, 21695])).
% 4.54/4.72 tff(21697,plain,
% 4.54/4.72 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[11893, 178, 104, 1687, 21691, 21695])).
% 4.54/4.72 tff(21698,plain,
% 4.54/4.72 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[133, 21697])).
% 4.54/4.72 tff(21699,plain,
% 4.54/4.72 (~b(s(s(s(s(z)))), s(s(z)))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[21680, 178, 21546, 273, 1687, 21691])).
% 4.54/4.72 tff(21700,plain,
% 4.54/4.72 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[20758, 21592, 108])).
% 4.54/4.72 tff(21701,plain,
% 4.54/4.72 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 21700])).
% 4.54/4.72 tff(21702,plain,
% 4.54/4.72 (~r(z, elem!1)),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[3319, 3311, 3243])).
% 4.54/4.72 tff(21703,plain,
% 4.54/4.72 (b(z, elem!1)),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[585, 21702, 318])).
% 4.54/4.72 tff(21704,plain,
% 4.54/4.72 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[4243, 21703, 4235])).
% 4.54/4.72 tff(21705,plain,
% 4.54/4.72 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[691, 21704, 644])).
% 4.54/4.72 tff(21706,plain,
% 4.54/4.72 (~(s(s(z)) = elem!1)),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[11305, 644, 224])).
% 4.54/4.72 tff(21707,plain,
% 4.54/4.72 (~b(s(s(z)), elem!1)),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[19407, 21703, 3461, 3240, 290, 3242, 273])).
% 4.54/4.72 tff(21708,plain,
% 4.54/4.72 (r(s(s(z)), elem!1)),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[448, 21707, 21706])).
% 4.54/4.72 tff(21709,plain,
% 4.54/4.72 (~r(elem!1, s(s(s(s(z)))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[8763, 21708, 147])).
% 4.54/4.72 tff(21710,plain,
% 4.54/4.72 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[5624, 147, 224])).
% 4.54/4.72 tff(21711,plain,
% 4.54/4.72 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[222, 21710])).
% 4.54/4.72 tff(21712,plain,
% 4.54/4.72 (~r(s(s(s(s(z)))), elem!1)),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[3329, 21708, 193])).
% 4.54/4.72 tff(21713,plain,
% 4.54/4.72 (elem!1 = s(s(s(s(z))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[8548, 21712, 104, 21711, 21709, 21705])).
% 4.54/4.72 tff(21714,plain,
% 4.54/4.72 (s(elem!1) = s(s(s(s(s(z)))))),
% 4.54/4.72 inference(monotonicity,[status(thm)],[21713])).
% 4.54/4.72 tff(21715,plain,
% 4.54/4.72 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 4.54/4.72 inference(monotonicity,[status(thm)],[21714])).
% 4.54/4.72 tff(21716,plain,
% 4.54/4.72 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 4.54/4.72 inference(monotonicity,[status(thm)],[21715])).
% 4.54/4.72 tff(21717,plain,
% 4.54/4.72 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.72 inference(monotonicity,[status(thm)],[21716])).
% 4.54/4.72 tff(21718,plain,
% 4.54/4.72 (r(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 4.54/4.72 inference(symmetry,[status(thm)],[21717])).
% 4.54/4.72 tff(21719,plain,
% 4.54/4.72 (r(s(s(z)), s(s(s(elem!1))))),
% 4.54/4.72 inference(modus_ponens,[status(thm)],[224, 21718])).
% 4.54/4.72 tff(21720,plain,
% 4.54/4.72 (~r(s(s(z)), s(s(s(elem!1))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[7973, 21708, 3311])).
% 4.54/4.72 tff(21721,plain,
% 4.54/4.72 ($false),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[21720, 21719])).
% 4.54/4.72 tff(21722,plain,((~r(elem!1, s(s(s(elem!1))))) | (~r(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)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)) | b(elem!1, s(s(s(elem!1)))) | (elem!1 = z) | b(z, s(s(s(elem!1)))) | (~b(z, s(s(z)))) | b(z, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.72 tff(21723,plain,
% 4.54/4.72 (~r(elem!1, s(s(s(elem!1))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[21722, 644, 104, 193, 147, 224, 3461, 3240, 290, 3242, 273, 4235])).
% 4.54/4.72 tff(21724,plain,
% 4.54/4.72 (elem!1 = s(s(s(elem!1)))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[2054, 21723, 3240])).
% 4.54/4.72 tff(21725,plain,
% 4.54/4.72 (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))))),
% 4.54/4.72 inference(monotonicity,[status(thm)],[21724])).
% 4.54/4.72 tff(21726,plain,
% 4.54/4.72 (~b(z, elem!1)),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[4187, 21724, 3242])).
% 4.54/4.72 tff(21727,plain,
% 4.54/4.72 (r(z, elem!1)),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[585, 21726, 318])).
% 4.54/4.72 tff(21728,plain,
% 4.54/4.72 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[11027, 21727, 108])).
% 4.54/4.72 tff(21729,plain,
% 4.54/4.72 (s(elem!1) = s(s(s(s(elem!1))))),
% 4.54/4.72 inference(monotonicity,[status(thm)],[21724])).
% 4.54/4.72 tff(21730,plain,
% 4.54/4.72 ((s(elem!1) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(z)))),
% 4.54/4.72 inference(monotonicity,[status(thm)],[21729])).
% 4.54/4.72 tff(21731,plain,
% 4.54/4.72 ((s(elem!1) = s(s(z))) <=> (s(s(z)) = s(s(s(s(elem!1)))))),
% 4.54/4.72 inference(transitivity,[status(thm)],[21730, 2129])).
% 4.54/4.72 tff(21732,plain,
% 4.54/4.72 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(elem!1) = s(s(z)))),
% 4.54/4.72 inference(symmetry,[status(thm)],[21731])).
% 4.54/4.72 tff(21733,plain,
% 4.54/4.72 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(s(elem!1) = s(s(z))))),
% 4.54/4.72 inference(monotonicity,[status(thm)],[21732])).
% 4.54/4.72 tff(21734,plain,
% 4.54/4.72 (~(s(elem!1) = s(s(z)))),
% 4.54/4.72 inference(modus_ponens,[status(thm)],[2131, 21733])).
% 4.54/4.72 tff(21735,plain,
% 4.54/4.72 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[2840, 21734])).
% 4.54/4.72 tff(21736,plain,
% 4.54/4.72 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[2859, 21735, 21724])).
% 4.54/4.72 tff(21737,plain,
% 4.54/4.72 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[703, 21736])).
% 4.54/4.72 tff(21738,plain,
% 4.54/4.72 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[3444, 21737, 21728])).
% 4.54/4.72 tff(21739,plain,
% 4.54/4.72 (b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.54/4.72 inference(modus_ponens,[status(thm)],[21738, 21725])).
% 4.54/4.72 tff(21740,plain,
% 4.54/4.72 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.72 inference(monotonicity,[status(thm)],[21724])).
% 4.54/4.72 tff(21741,plain,
% 4.54/4.72 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[691, 21736, 644])).
% 4.54/4.72 tff(21742,plain,
% 4.54/4.72 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.72 inference(modus_ponens,[status(thm)],[21741, 21740])).
% 4.54/4.72 tff(21743,plain,
% 4.54/4.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(z))))) | (~b(s(s(s(z))), 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(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(z))))) | (~b(s(s(s(z))), 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(z))), s(s(s(elem!1))))))),
% 4.54/4.72 inference(rewrite,[status(thm)],[])).
% 4.54/4.72 tff(21744,plain,
% 4.54/4.72 (((~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(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), 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(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 4.54/4.72 inference(rewrite,[status(thm)],[])).
% 4.54/4.72 tff(21745,plain,
% 4.54/4.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(z))))) | (~b(s(s(s(z))), 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(z))), s(s(s(elem!1)))))))),
% 4.54/4.72 inference(monotonicity,[status(thm)],[21744])).
% 4.54/4.72 tff(21746,plain,
% 4.54/4.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(z))))) | (~b(s(s(s(z))), 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(z))), s(s(s(elem!1))))))),
% 4.54/4.72 inference(transitivity,[status(thm)],[21745, 21743])).
% 4.54/4.72 tff(21747,plain,
% 4.54/4.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 4.54/4.72 inference(quant_inst,[status(thm)],[])).
% 4.54/4.72 tff(21748,plain,
% 4.54/4.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(z))))) | (~b(s(s(s(z))), 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(z))), s(s(s(elem!1)))))),
% 4.54/4.72 inference(modus_ponens,[status(thm)],[21747, 21746])).
% 4.54/4.72 tff(21749,plain,
% 4.54/4.72 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[21748, 178, 3002, 21742, 21739, 21701])).
% 4.54/4.72 tff(21750,plain,
% 4.54/4.72 (r(s(s(s(z))), s(s(s(elem!1))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[9126, 21749, 11613])).
% 4.54/4.72 tff(21751,plain,
% 4.54/4.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 4.54/4.72 inference(rewrite,[status(thm)],[])).
% 4.54/4.72 tff(21752,plain,
% 4.54/4.72 (((~b(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))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(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(elem!1))), 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(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(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 4.54/4.72 inference(rewrite,[status(thm)],[])).
% 4.54/4.72 tff(21753,plain,
% 4.54/4.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(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(elem!1))), s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))))),
% 4.54/4.72 inference(monotonicity,[status(thm)],[21752])).
% 4.54/4.72 tff(21754,plain,
% 4.54/4.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(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(elem!1))), s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 4.54/4.72 inference(transitivity,[status(thm)],[21753, 21751])).
% 4.54/4.72 tff(21755,plain,
% 4.54/4.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(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(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 4.54/4.72 inference(quant_inst,[status(thm)],[])).
% 4.54/4.72 tff(21756,plain,
% 4.54/4.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 4.54/4.72 inference(modus_ponens,[status(thm)],[21755, 21754])).
% 4.54/4.72 tff(21757,plain,
% 4.54/4.72 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[21756, 178, 104, 21711, 21742, 21739])).
% 4.54/4.72 tff(21758,plain,
% 4.54/4.72 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[4173, 21757, 21735])).
% 4.54/4.72 tff(21759,plain,
% 4.54/4.72 ($false),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[8197, 118, 21758, 4891, 21750])).
% 4.54/4.72 tff(21760,plain,(r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | b(z, s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (elem!1 = z) | (~b(z, s(s(z)))) | b(z, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.72 tff(21761,plain,
% 4.54/4.72 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[21760, 3240, 3002, 104, 108, 3242, 4891, 103, 147, 287, 3461, 290, 273, 4235])).
% 4.54/4.72 tff(21762,plain,
% 4.54/4.72 (~r(s(s(z)), elem!1)),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[2803, 21761, 287])).
% 4.54/4.72 tff(21763,plain,
% 4.54/4.72 (~r(z, elem!1)),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[3818, 21761, 4236])).
% 4.54/4.72 tff(21764,plain,
% 4.54/4.72 (b(z, elem!1)),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[585, 21763, 318])).
% 4.54/4.72 tff(21765,plain,
% 4.54/4.72 (~b(s(s(z)), elem!1)),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[19407, 21764, 3461, 3240, 290, 3242, 273])).
% 4.54/4.72 tff(21766,plain,
% 4.54/4.72 (s(s(z)) = elem!1),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[448, 21765, 21762])).
% 4.54/4.72 tff(21767,plain,
% 4.54/4.72 (s(s(s(z))) = s(elem!1)),
% 4.54/4.72 inference(monotonicity,[status(thm)],[21766])).
% 4.54/4.72 tff(21768,plain,
% 4.54/4.72 (s(s(s(s(z)))) = s(s(elem!1))),
% 4.54/4.72 inference(monotonicity,[status(thm)],[21767])).
% 4.54/4.72 tff(21769,plain,
% 4.54/4.72 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 4.54/4.72 inference(monotonicity,[status(thm)],[21768])).
% 4.54/4.72 tff(21770,plain,
% 4.54/4.72 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 4.54/4.72 inference(transitivity,[status(thm)],[21769, 3400])).
% 4.54/4.72 tff(21771,plain,
% 4.54/4.72 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 4.54/4.72 inference(transitivity,[status(thm)],[21770, 12033])).
% 4.54/4.72 tff(21772,plain,
% 4.54/4.72 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 4.54/4.72 inference(monotonicity,[status(thm)],[21771])).
% 4.54/4.72 tff(21773,plain,
% 4.54/4.72 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[5361, 21766])).
% 4.54/4.72 tff(21774,plain,
% 4.54/4.72 (~(elem!1 = s(s(s(elem!1))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[4187, 21764, 3242])).
% 4.54/4.72 tff(21775,plain,
% 4.54/4.72 (~(s(s(s(elem!1))) = elem!1)),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[2489, 21774])).
% 4.54/4.72 tff(21776,plain,
% 4.54/4.72 (~(s(elem!1) = elem!1)),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[2150, 21775])).
% 4.54/4.72 tff(21777,plain,
% 4.54/4.72 (~(elem!1 = s(elem!1))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[748, 21776])).
% 4.54/4.72 tff(21778,plain,
% 4.54/4.72 (~r(elem!1, z)),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[10809, 21761, 4236])).
% 4.54/4.72 tff(21779,plain,
% 4.54/4.72 (b(elem!1, z)),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[498, 21778, 290])).
% 4.54/4.72 tff(21780,plain,
% 4.54/4.72 (elem!1 = s(s(z))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[3230, 21766])).
% 4.54/4.72 tff(21781,plain,
% 4.54/4.72 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[10945, 21780, 287, 4236, 21779, 21764, 21777, 21776, 21761])).
% 4.54/4.72 tff(21782,plain,
% 4.54/4.72 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[395, 21781, 21773])).
% 4.54/4.72 tff(21783,plain,
% 4.54/4.72 (~(s(elem!1) = s(s(z)))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[2239, 21782, 286])).
% 4.54/4.72 tff(21784,plain,
% 4.54/4.72 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[2840, 21783])).
% 4.54/4.72 tff(21785,plain,
% 4.54/4.72 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 4.54/4.72 inference(modus_ponens,[status(thm)],[21784, 21772])).
% 4.54/4.72 tff(21786,plain,
% 4.54/4.72 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.54/4.72 inference(monotonicity,[status(thm)],[21768])).
% 4.54/4.72 tff(21787,plain,
% 4.54/4.72 (r(elem!1, s(s(s(elem!1))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[2054, 21774, 3240])).
% 4.54/4.72 tff(21788,plain,
% 4.54/4.72 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[8811, 21766, 21787, 3340, 86])).
% 4.54/4.72 tff(21789,plain,
% 4.54/4.72 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.54/4.72 inference(modus_ponens,[status(thm)],[21788, 21786])).
% 4.54/4.72 tff(21790,plain,
% 4.54/4.72 (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)))),
% 4.54/4.72 inference(monotonicity,[status(thm)],[21768])).
% 4.54/4.72 tff(21791,plain,
% 4.54/4.72 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.54/4.72 inference(modus_ponens,[status(thm)],[104, 21790])).
% 4.54/4.72 tff(21792,plain,
% 4.54/4.72 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.72 inference(monotonicity,[status(thm)],[21768])).
% 4.54/4.72 tff(21793,plain,
% 4.54/4.72 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[5624, 147, 287])).
% 4.54/4.72 tff(21794,plain,
% 4.54/4.72 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[222, 21793])).
% 4.54/4.72 tff(21795,plain,
% 4.54/4.72 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.72 inference(modus_ponens,[status(thm)],[21794, 21792])).
% 4.54/4.72 tff(21796,plain,
% 4.54/4.72 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[5130, 3243, 108])).
% 4.54/4.72 tff(21797,plain,
% 4.54/4.72 ((s(s(z)) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(z)))))),
% 4.54/4.72 inference(monotonicity,[status(thm)],[21766])).
% 4.54/4.72 tff(21798,plain,
% 4.54/4.72 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 4.54/4.72 inference(transitivity,[status(thm)],[21797, 321])).
% 4.54/4.72 tff(21799,plain,
% 4.54/4.72 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 4.54/4.72 inference(monotonicity,[status(thm)],[21798])).
% 4.54/4.72 tff(21800,plain,
% 4.54/4.72 (~(s(s(s(s(z)))) = elem!1)),
% 4.54/4.72 inference(modus_ponens,[status(thm)],[159, 21799])).
% 4.54/4.72 tff(21801,plain,
% 4.54/4.72 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[3502, 21800])).
% 4.54/4.72 tff(21802,plain,
% 4.54/4.72 (b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[5118, 21801, 21796])).
% 4.54/4.72 tff(21803,plain,
% 4.54/4.72 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[18367, 21802, 21795, 21791, 21789])).
% 4.54/4.72 tff(21804,plain,
% 4.54/4.72 (r(elem!1, s(s(elem!1)))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[9352, 21766, 147])).
% 4.54/4.72 tff(21805,plain,
% 4.54/4.72 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(elem!1))),
% 4.54/4.72 inference(monotonicity,[status(thm)],[21767])).
% 4.54/4.72 tff(21806,plain,
% 4.54/4.72 (b(s(s(z)), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 4.54/4.72 inference(monotonicity,[status(thm)],[21766])).
% 4.54/4.72 tff(21807,plain,
% 4.54/4.72 (b(elem!1, s(s(s(z))))),
% 4.54/4.72 inference(modus_ponens,[status(thm)],[5089, 21806])).
% 4.54/4.72 tff(21808,plain,
% 4.54/4.72 (b(elem!1, s(elem!1))),
% 4.54/4.72 inference(modus_ponens,[status(thm)],[21807, 21805])).
% 4.54/4.72 tff(21809,plain,
% 4.54/4.72 (b(s(s(s(z))), elem!1) <=> b(s(elem!1), elem!1)),
% 4.54/4.72 inference(monotonicity,[status(thm)],[21767])).
% 4.54/4.72 tff(21810,plain,
% 4.54/4.72 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), elem!1)),
% 4.54/4.72 inference(monotonicity,[status(thm)],[21766])).
% 4.54/4.72 tff(21811,plain,
% 4.54/4.72 (~r(s(s(s(z))), s(s(z)))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[20838, 4891, 103])).
% 4.54/4.72 tff(21812,plain,
% 4.54/4.72 (b(s(s(s(z))), s(s(z)))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[4966, 21811])).
% 4.54/4.72 tff(21813,plain,
% 4.54/4.72 (b(s(s(s(z))), elem!1)),
% 4.54/4.72 inference(modus_ponens,[status(thm)],[21812, 21810])).
% 4.54/4.72 tff(21814,plain,
% 4.54/4.72 (b(s(elem!1), elem!1)),
% 4.54/4.72 inference(modus_ponens,[status(thm)],[21813, 21809])).
% 4.54/4.72 tff(21815,plain,
% 4.54/4.72 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 4.54/4.72 inference(monotonicity,[status(thm)],[21767])).
% 4.54/4.72 tff(21816,plain,
% 4.54/4.72 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 4.54/4.72 inference(transitivity,[status(thm)],[21815, 3881])).
% 4.54/4.72 tff(21817,plain,
% 4.54/4.72 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 4.54/4.72 inference(monotonicity,[status(thm)],[21816])).
% 4.54/4.72 tff(21818,plain,
% 4.54/4.72 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.54/4.72 inference(modus_ponens,[status(thm)],[11613, 21817])).
% 4.54/4.72 tff(21819,plain,
% 4.54/4.72 (r(z, s(s(s(z)))) <=> r(z, s(elem!1))),
% 4.54/4.72 inference(monotonicity,[status(thm)],[21767])).
% 4.54/4.72 tff(21820,plain,
% 4.54/4.72 (~b(z, s(s(s(z))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[8742, 178, 3461, 273, 5089, 21812])).
% 4.54/4.72 tff(21821,plain,
% 4.54/4.72 (r(z, s(s(s(z))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[4920, 21820])).
% 4.54/4.72 tff(21822,plain,
% 4.54/4.72 (r(z, s(elem!1))),
% 4.54/4.72 inference(modus_ponens,[status(thm)],[21821, 21819])).
% 4.54/4.72 tff(21823,plain,
% 4.54/4.72 (~b(s(s(s(elem!1))), elem!1)),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[7389, 21822, 3243, 21818, 21814, 21808])).
% 4.54/4.72 tff(21824,plain,
% 4.54/4.72 (r(s(s(s(elem!1))), elem!1)),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[570, 21823, 21775])).
% 4.54/4.72 tff(21825,plain,
% 4.54/4.72 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[10206, 21824, 21804])).
% 4.54/4.72 tff(21826,plain,
% 4.54/4.72 ($false),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[3409, 21825, 21803, 21785])).
% 4.54/4.72 tff(21827,plain,(b(elem!1, s(s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(z)))), s(s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (elem!1 = z) | b(z, s(s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | b(z, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.72 tff(21828,plain,
% 4.54/4.72 (b(elem!1, s(s(s(elem!1))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[21827, 3242, 286, 21699, 21693, 21546, 290, 104, 273, 3002, 21698, 4891, 21696])).
% 4.54/4.72 tff(21829,plain,
% 4.54/4.72 (~(s(s(z)) = elem!1)),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[11305, 644, 287])).
% 4.54/4.72 tff(21830,plain,
% 4.54/4.72 (r(s(s(s(s(z)))), s(s(z)))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[102, 21699])).
% 4.54/4.72 tff(21831,plain,
% 4.54/4.72 (~r(s(s(z)), s(s(s(z))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[5079, 118, 21693, 4891])).
% 4.54/4.72 tff(21832,plain,
% 4.54/4.72 (b(s(s(z)), s(s(s(z))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[5088, 21831])).
% 4.54/4.72 tff(21833,plain,
% 4.54/4.72 (~r(s(s(s(z))), s(s(z)))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[20838, 4891, 21830])).
% 4.54/4.72 tff(21834,plain,
% 4.54/4.72 (b(s(s(s(z))), s(s(z)))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[4966, 21833])).
% 4.54/4.72 tff(21835,plain,
% 4.54/4.72 ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[11284, 178, 21546, 273, 21834])).
% 4.54/4.72 tff(21836,plain,
% 4.54/4.72 (~b(s(s(s(z))), z)),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[21835, 21832])).
% 4.54/4.72 tff(21837,plain,
% 4.54/4.72 (r(s(s(s(z))), z)),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[21073, 21836])).
% 4.54/4.72 tff(21838,plain,
% 4.54/4.72 (b(s(elem!1), elem!1) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 4.54/4.72 inference(transitivity,[status(thm)],[13354, 2693])).
% 4.54/4.72 tff(21839,plain,
% 4.54/4.72 (~b(s(s(z)), elem!1)),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[17684, 319, 21692])).
% 4.54/4.72 tff(21840,plain,
% 4.54/4.72 (r(s(s(z)), elem!1)),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[448, 21839, 12])).
% 4.54/4.72 tff(21841,plain,
% 4.54/4.72 (r(s(s(s(s(s(s(s(z))))))), z) <=> r(s(s(s(elem!1))), z)),
% 4.54/4.72 inference(symmetry,[status(thm)],[18709])).
% 4.54/4.72 tff(21842,plain,
% 4.54/4.72 (r(s(s(s(elem!1))), z)),
% 4.54/4.72 inference(modus_ponens,[status(thm)],[21698, 21841])).
% 4.54/4.72 tff(21843,plain,
% 4.54/4.72 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[20758, 21837, 21698])).
% 4.54/4.72 tff(21844,plain,
% 4.54/4.72 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 21843])).
% 4.54/4.72 tff(21845,plain,
% 4.54/4.72 (r(s(elem!1), elem!1) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 4.54/4.72 inference(transitivity,[status(thm)],[11428, 13567])).
% 4.54/4.72 tff(21846,plain,
% 4.54/4.72 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 4.54/4.72 inference(modus_ponens,[status(thm)],[1426, 21845])).
% 4.54/4.72 tff(21847,plain,
% 4.54/4.72 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[17073, 118, 21846, 4891])).
% 4.54/4.72 tff(21848,plain,
% 4.54/4.72 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 4.54/4.72 inference(unit_resolution,[status(thm)],[9830, 41, 11413, 21847])).
% 4.54/4.73 tff(21849,plain,
% 4.54/4.73 (~b(s(elem!1), z)),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[6776, 11429, 273, 11439, 147, 3461])).
% 4.54/4.73 tff(21850,plain,
% 4.54/4.73 (r(s(elem!1), z)),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[774, 21849])).
% 4.54/4.73 tff(21851,plain,
% 4.54/4.73 (~r(s(s(s(elem!1))), s(elem!1))),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[1557, 21850, 1552])).
% 4.54/4.73 tff(21852,plain,
% 4.54/4.73 (b(s(s(s(elem!1))), s(elem!1))),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[373, 21851, 356])).
% 4.54/4.73 tff(21853,plain,
% 4.54/4.73 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.54/4.73 inference(modus_ponens,[status(thm)],[21852, 17016])).
% 4.54/4.73 tff(21854,plain,
% 4.54/4.73 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 4.54/4.73 inference(modus_ponens,[status(thm)],[21853, 17015])).
% 4.54/4.73 tff(21855,assumption,(b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))), introduced(assumption)).
% 4.54/4.73 tff(21856,plain,
% 4.54/4.73 (~r(s(elem!1), s(s(z)))),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[2249, 1426, 438])).
% 4.54/4.73 tff(21857,plain,
% 4.54/4.73 (b(s(elem!1), s(s(z)))),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[421, 21856, 11439])).
% 4.54/4.73 tff(21858,plain,
% 4.54/4.73 (b(s(s(s(s(s(z))))), s(s(z)))),
% 4.54/4.73 inference(modus_ponens,[status(thm)],[21857, 2747])).
% 4.54/4.73 tff(21859,plain,
% 4.54/4.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(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(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(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(s(z))), s(s(s(s(s(z))))))))),
% 4.54/4.73 inference(rewrite,[status(thm)],[])).
% 4.54/4.73 tff(21860,plain,
% 4.54/4.73 (((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(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(s(z))))))) | (~b(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(s(z))), s(s(s(s(s(z))))))))),
% 4.54/4.73 inference(rewrite,[status(thm)],[])).
% 4.54/4.73 tff(21861,plain,
% 4.54/4.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(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(s(z))), s(s(s(s(s(z)))))))))),
% 4.54/4.73 inference(monotonicity,[status(thm)],[21860])).
% 4.54/4.73 tff(21862,plain,
% 4.54/4.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(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(s(z))), s(s(s(s(s(z))))))))),
% 4.54/4.73 inference(transitivity,[status(thm)],[21861, 21859])).
% 4.54/4.73 tff(21863,plain,
% 4.54/4.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 4.54/4.73 inference(quant_inst,[status(thm)],[])).
% 4.54/4.73 tff(21864,plain,
% 4.54/4.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 4.54/4.73 inference(modus_ponens,[status(thm)],[21863, 21862])).
% 4.54/4.73 tff(21865,plain,
% 4.54/4.73 ($false),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[21864, 178, 21858, 4932, 21855, 21854, 21848])).
% 4.54/4.73 tff(21866,plain,((~r(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~(elem!1 = s(s(s(s(z)))))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.73 tff(21867,plain,
% 4.54/4.73 (~r(s(elem!1), elem!1)),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[21866, 319, 21844, 21834, 349, 21842, 273, 21693, 21546, 4891, 21840])).
% 4.54/4.73 tff(21868,plain,
% 4.54/4.73 (b(s(elem!1), elem!1)),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[677, 21867, 20092])).
% 4.54/4.73 tff(21869,plain,
% 4.54/4.73 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 4.54/4.73 inference(modus_ponens,[status(thm)],[21868, 21838])).
% 4.54/4.73 tff(21870,plain,
% 4.54/4.73 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 4.54/4.73 inference(monotonicity,[status(thm)],[352])).
% 4.54/4.73 tff(21871,plain,
% 4.54/4.73 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.54/4.73 inference(symmetry,[status(thm)],[21870])).
% 4.54/4.73 tff(21872,plain,
% 4.54/4.73 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), elem!1)),
% 4.54/4.73 inference(transitivity,[status(thm)],[21871, 16932])).
% 4.54/4.73 tff(21873,plain,
% 4.54/4.73 (b(s(s(s(elem!1))), elem!1)),
% 4.54/4.73 inference(modus_ponens,[status(thm)],[104, 21872])).
% 4.54/4.73 tff(21874,plain,
% 4.54/4.73 (~(s(elem!1) = s(s(s(elem!1))))),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[5395, 349])).
% 4.54/4.73 tff(21875,plain,
% 4.54/4.73 ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(s(z)), s(s(s(elem!1)))))),
% 4.54/4.73 inference(monotonicity,[status(thm)],[18712])).
% 4.54/4.73 tff(21876,plain,
% 4.54/4.73 (~b(s(s(z)), s(s(s(elem!1))))),
% 4.54/4.73 inference(modus_ponens,[status(thm)],[286, 21875])).
% 4.54/4.73 tff(21877,plain,
% 4.54/4.73 (~r(s(s(z)), s(elem!1))),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[18732, 21868, 2042, 319, 20190, 21876, 21874, 21873, 21693])).
% 4.54/4.73 tff(21878,plain,
% 4.54/4.73 (b(s(s(z)), s(elem!1))),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[1067, 21877, 17020])).
% 4.54/4.73 tff(21879,plain,
% 4.54/4.73 (b(s(s(z)), s(s(s(s(s(z))))))),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[2330, 21878, 319])).
% 4.54/4.73 tff(21880,plain,
% 4.54/4.73 (~b(s(s(s(s(s(z))))), z)),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[13363, 178, 21546, 1687, 21879, 21869])).
% 4.54/4.73 tff(21881,plain,
% 4.54/4.73 (r(s(s(s(s(s(z))))), z)),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[410, 41, 242, 21880])).
% 4.54/4.73 tff(21882,plain,
% 4.54/4.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 4.54/4.73 inference(rewrite,[status(thm)],[])).
% 4.54/4.73 tff(21883,plain,
% 4.54/4.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 4.54/4.73 inference(quant_inst,[status(thm)],[])).
% 4.54/4.73 tff(21884,plain,
% 4.54/4.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 4.54/4.73 inference(modus_ponens,[status(thm)],[21883, 21882])).
% 4.54/4.73 tff(21885,plain,
% 4.54/4.73 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[21884, 118, 21881, 21837])).
% 4.54/4.73 tff(21886,plain,
% 4.54/4.73 (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 4.54/4.73 inference(modus_ponens,[status(thm)],[349, 18746])).
% 4.54/4.73 tff(21887,plain,
% 4.54/4.73 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[13204, 118, 21698, 21881])).
% 4.54/4.73 tff(21888,plain,
% 4.54/4.73 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[18762, 21887, 21886])).
% 4.54/4.73 tff(21889,plain,
% 4.54/4.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 4.54/4.73 inference(rewrite,[status(thm)],[])).
% 4.54/4.73 tff(21890,plain,
% 4.54/4.73 (((~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(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 4.54/4.73 inference(rewrite,[status(thm)],[])).
% 4.54/4.73 tff(21891,plain,
% 4.54/4.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 4.54/4.73 inference(monotonicity,[status(thm)],[21890])).
% 4.54/4.73 tff(21892,plain,
% 4.54/4.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 4.54/4.73 inference(transitivity,[status(thm)],[21891, 21889])).
% 4.54/4.73 tff(21893,plain,
% 4.54/4.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 4.54/4.73 inference(quant_inst,[status(thm)],[])).
% 4.54/4.73 tff(21894,plain,
% 4.54/4.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 4.54/4.73 inference(modus_ponens,[status(thm)],[21893, 21892])).
% 4.54/4.73 tff(21895,plain,
% 4.54/4.73 ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[21894, 178, 104, 21869, 3002])).
% 4.54/4.73 tff(21896,plain,
% 4.54/4.73 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[21895, 21888])).
% 4.54/4.73 tff(21897,plain,
% 4.54/4.73 ($false),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[9830, 41, 11413, 21896, 21885])).
% 4.54/4.73 tff(21898,plain,((~(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(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.54/4.73 tff(21899,plain,
% 4.54/4.73 (~(elem!1 = s(s(s(s(z)))))),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[21898, 21829, 3002, 1687, 2042, 273, 4891, 286, 104])).
% 4.54/4.73 tff(21900,plain,
% 4.54/4.73 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[691, 11145, 644])).
% 4.54/4.73 tff(21901,plain,
% 4.54/4.73 (~r(z, elem!1)),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[17868, 11249, 108, 949, 4254, 557, 21900, 1585])).
% 4.54/4.73 tff(21902,plain,
% 4.54/4.73 (b(z, elem!1)),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[585, 21901, 507])).
% 4.54/4.73 tff(21903,plain,
% 4.54/4.73 (~b(elem!1, s(s(s(s(z)))))),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[11955, 21902, 1687, 3461, 817])).
% 4.54/4.73 tff(21904,plain,
% 4.54/4.73 (r(elem!1, s(s(s(s(z)))))),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[483, 21903, 469])).
% 4.54/4.73 tff(21905,plain,
% 4.54/4.73 (~(elem!1 = s(s(z)))),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[311, 21829])).
% 4.54/4.73 tff(21906,plain,
% 4.54/4.73 (~b(elem!1, s(s(z)))),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[10893, 21902, 273, 3461, 817])).
% 4.54/4.73 tff(21907,plain,
% 4.54/4.73 (r(elem!1, s(s(z)))),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[467, 21906, 21905])).
% 4.54/4.73 tff(21908,plain,
% 4.54/4.73 ($false),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[3785, 21907, 21904, 193])).
% 4.54/4.73 tff(21909,plain,((~b(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))) | (elem!1 = s(s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (z = elem!1) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (s(s(s(elem!1))) = elem!1) | (~r(z, s(s(s(elem!1))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | b(s(s(z)), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.73 tff(21910,plain,
% 4.54/4.73 (~b(s(s(z)), elem!1)),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[21909, 21899, 21830, 273, 21546, 1687, 507, 21698, 19901, 557, 644, 286])).
% 4.54/4.73 tff(21911,plain,
% 4.54/4.73 (r(s(s(z)), elem!1)),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[448, 21910, 21829])).
% 4.54/4.73 tff(21912,plain,
% 4.54/4.73 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[11351, 21911, 287])).
% 4.54/4.73 tff(21913,plain,
% 4.54/4.73 (~r(elem!1, s(s(s(s(z)))))),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[8763, 21911, 21693])).
% 4.54/4.73 tff(21914,plain,
% 4.54/4.73 (b(elem!1, s(s(s(s(z)))))),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[483, 21913, 21899])).
% 4.54/4.73 tff(21915,plain,
% 4.54/4.73 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[11098, 21914, 21695, 21912, 104, 644])).
% 4.54/4.73 tff(21916,plain,
% 4.54/4.73 (~(s(s(s(s(z)))) = elem!1)),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[504, 21899])).
% 4.54/4.73 tff(21917,plain,
% 4.54/4.73 (~r(s(s(s(s(z)))), elem!1)),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[3329, 21911, 21830])).
% 4.54/4.73 tff(21918,plain,
% 4.54/4.73 (b(s(s(s(s(z)))), elem!1)),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[3142, 21917, 21916])).
% 4.54/4.73 tff(21919,plain,
% 4.54/4.73 ($false),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[11965, 178, 818, 3771, 1687, 168, 1301])).
% 4.54/4.73 tff(21920,plain,((~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.73 tff(21921,plain,
% 4.54/4.73 (~b(z, elem!1)),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[21920, 21918, 1687, 21691, 21914])).
% 4.54/4.73 tff(21922,plain,
% 4.54/4.73 (r(z, elem!1)),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[585, 21921, 507])).
% 4.54/4.73 tff(21923,plain,
% 4.54/4.73 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.73 inference(monotonicity,[status(thm)],[11730])).
% 4.54/4.73 tff(21924,plain,
% 4.54/4.73 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.73 inference(symmetry,[status(thm)],[21923])).
% 4.54/4.73 tff(21925,plain,
% 4.54/4.73 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.73 inference(monotonicity,[status(thm)],[679])).
% 4.54/4.73 tff(21926,plain,
% 4.54/4.73 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.73 inference(modus_ponens,[status(thm)],[1426, 21925])).
% 4.54/4.73 tff(21927,plain,
% 4.54/4.73 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.73 inference(modus_ponens,[status(thm)],[21926, 21924])).
% 4.54/4.73 tff(21928,plain,
% 4.54/4.73 (b(z, s(s(s(s(s(s(s(s(z)))))))))),
% 4.54/4.73 inference(modus_ponens,[status(thm)],[855, 16109])).
% 4.54/4.73 tff(21929,plain,
% 4.54/4.73 (b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 4.54/4.73 inference(modus_ponens,[status(thm)],[12197, 16232])).
% 4.54/4.73 tff(21930,plain,
% 4.54/4.73 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 4.54/4.73 inference(symmetry,[status(thm)],[19259])).
% 4.54/4.73 tff(21931,plain,
% 4.54/4.73 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 4.54/4.73 inference(modus_ponens,[status(thm)],[12196, 21930])).
% 4.54/4.73 tff(21932,plain,
% 4.54/4.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))))),
% 4.54/4.73 inference(rewrite,[status(thm)],[])).
% 4.54/4.73 tff(21933,plain,
% 4.54/4.73 (((~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))))),
% 4.54/4.73 inference(rewrite,[status(thm)],[])).
% 4.54/4.73 tff(21934,plain,
% 4.54/4.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), z)) | (~b(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z))))))))))))),
% 4.54/4.73 inference(monotonicity,[status(thm)],[21933])).
% 4.54/4.73 tff(21935,plain,
% 4.54/4.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), z)) | (~b(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))))),
% 4.54/4.73 inference(transitivity,[status(thm)],[21934, 21932])).
% 4.54/4.73 tff(21936,plain,
% 4.54/4.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))))),
% 4.54/4.73 inference(quant_inst,[status(thm)],[])).
% 4.54/4.73 tff(21937,plain,
% 4.54/4.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z))))))))))),
% 4.54/4.73 inference(modus_ponens,[status(thm)],[21936, 21935])).
% 4.54/4.73 tff(21938,plain,
% 4.54/4.73 ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z))))))))))),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[21937, 178, 3461])).
% 4.54/4.73 tff(21939,plain,
% 4.54/4.73 ($false),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[21938, 15440, 21931, 21929, 21928])).
% 4.54/4.73 tff(21940,plain,((s(elem!1) = s(s(z))) | (~b(s(s(z)), z)) | (~b(z, s(elem!1))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), z)) | r(s(s(z)), s(elem!1)) | r(s(elem!1), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.73 tff(21941,plain,
% 4.54/4.73 (s(elem!1) = s(s(z))),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[21940, 679, 855, 3461, 853, 1062, 927])).
% 4.54/4.73 tff(21942,plain,
% 4.54/4.73 (s(s(z)) = s(elem!1)),
% 4.54/4.73 inference(symmetry,[status(thm)],[21941])).
% 4.54/4.73 tff(21943,plain,
% 4.54/4.73 (s(s(z)) = s(s(s(s(s(s(s(s(z))))))))),
% 4.54/4.73 inference(transitivity,[status(thm)],[21942, 2823])).
% 4.54/4.73 tff(21944,plain,
% 4.54/4.73 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(s(s(s(z)))))))))),
% 4.54/4.73 inference(monotonicity,[status(thm)],[21943])).
% 4.54/4.73 tff(21945,plain,
% 4.54/4.73 (inj_0(s(s(s(s(s(s(s(s(z))))))))) = inj_0(s(s(z)))),
% 4.54/4.73 inference(symmetry,[status(thm)],[21944])).
% 4.54/4.73 tff(21946,plain,
% 4.54/4.73 (s(s(s(s(s(s(s(z))))))) = s(z)),
% 4.54/4.73 inference(transitivity,[status(thm)],[2829, 21945, 70])).
% 4.54/4.73 tff(21947,plain,
% 4.54/4.73 ($false),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[612, 21946])).
% 4.54/4.73 tff(21948,plain,((~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | r(s(s(z)), s(elem!1)) | r(s(elem!1), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.73 tff(21949,plain,
% 4.54/4.73 (r(s(s(z)), s(elem!1))),
% 4.54/4.73 inference(unit_resolution,[status(thm)],[21948, 11441, 3461, 679, 16111, 21856])).
% 4.54/4.73 tff(21950,plain,
% 4.54/4.73 (r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 4.54/4.73 inference(modus_ponens,[status(thm)],[21949, 16249])).
% 4.54/4.73 tff(21951,plain,
% 4.54/4.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 4.54/4.73 inference(rewrite,[status(thm)],[])).
% 4.54/4.73 tff(21952,plain,
% 4.54/4.73 (((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 4.54/4.74 inference(rewrite,[status(thm)],[])).
% 4.54/4.74 tff(21953,plain,
% 4.54/4.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))))),
% 4.54/4.74 inference(monotonicity,[status(thm)],[21952])).
% 4.54/4.74 tff(21954,plain,
% 4.54/4.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 4.54/4.74 inference(transitivity,[status(thm)],[21953, 21951])).
% 4.54/4.74 tff(21955,plain,
% 4.54/4.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))),
% 4.54/4.74 inference(quant_inst,[status(thm)],[])).
% 4.54/4.74 tff(21956,plain,
% 4.54/4.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))),
% 4.54/4.74 inference(modus_ponens,[status(thm)],[21955, 21954])).
% 4.54/4.74 tff(21957,plain,
% 4.54/4.74 ((~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[21956, 118, 224])).
% 4.54/4.74 tff(21958,plain,
% 4.54/4.74 ($false),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[21957, 21950, 21927])).
% 4.54/4.74 tff(21959,plain,((~r(s(elem!1), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.74 tff(21960,plain,
% 4.54/4.74 (~r(s(elem!1), elem!1)),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[21959, 21922, 21915, 21546, 21911, 287])).
% 4.54/4.74 tff(21961,plain,
% 4.54/4.74 (b(s(elem!1), elem!1)),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[677, 21960, 20092])).
% 4.54/4.74 tff(21962,plain,
% 4.54/4.74 (~r(elem!1, s(s(s(elem!1))))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[3319, 21922, 557])).
% 4.54/4.74 tff(21963,plain,
% 4.54/4.74 (~r(s(s(s(elem!1))), elem!1)),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[565, 21922, 557])).
% 4.54/4.74 tff(21964,plain,
% 4.54/4.74 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[16181, 21915])).
% 4.54/4.74 tff(21965,plain,
% 4.54/4.74 (~(s(s(s(s(z)))) = s(elem!1))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[2168, 21964])).
% 4.54/4.74 tff(21966,plain,
% 4.54/4.74 (~(s(s(elem!1)) = elem!1)),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[2510, 21965, 21915])).
% 4.54/4.74 tff(21967,plain,
% 4.54/4.74 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[348, 21966])).
% 4.54/4.74 tff(21968,plain,
% 4.54/4.74 (~(s(elem!1) = s(s(z)))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[18217, 21914, 21918, 104, 21912, 644])).
% 4.54/4.74 tff(21969,plain,
% 4.54/4.74 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[2840, 21968])).
% 4.54/4.74 tff(21970,plain,
% 4.54/4.74 (~(elem!1 = s(s(s(elem!1))))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[1530, 19901])).
% 4.54/4.74 tff(21971,plain,
% 4.54/4.74 (~r(s(elem!1), s(s(z)))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[16202, 21915, 21830, 104, 107])).
% 4.54/4.74 tff(21972,plain,
% 4.54/4.74 (r(elem!1, s(s(z))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.54/4.74 inference(monotonicity,[status(thm)],[21915])).
% 4.54/4.74 tff(21973,plain,
% 4.54/4.74 (r(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> r(elem!1, s(s(z)))),
% 4.54/4.74 inference(symmetry,[status(thm)],[21972])).
% 4.54/4.74 tff(21974,plain,
% 4.54/4.74 (r(elem!1, s(s(z)))),
% 4.54/4.74 inference(modus_ponens,[status(thm)],[107, 21973])).
% 4.54/4.74 tff(21975,plain,
% 4.54/4.74 (r(elem!1, z) <=> r(s(s(s(s(s(s(s(z))))))), z)),
% 4.54/4.74 inference(monotonicity,[status(thm)],[21915])).
% 4.54/4.74 tff(21976,plain,
% 4.54/4.74 (r(s(s(s(s(s(s(s(z))))))), z) <=> r(elem!1, z)),
% 4.54/4.74 inference(symmetry,[status(thm)],[21975])).
% 4.54/4.74 tff(21977,plain,
% 4.54/4.74 (r(elem!1, z)),
% 4.54/4.74 inference(modus_ponens,[status(thm)],[21698, 21976])).
% 4.54/4.74 tff(21978,plain,
% 4.54/4.74 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 4.54/4.74 inference(monotonicity,[status(thm)],[21915])).
% 4.54/4.74 tff(21979,plain,
% 4.54/4.74 (s(s(s(s(s(s(s(s(z)))))))) = s(elem!1)),
% 4.54/4.74 inference(symmetry,[status(thm)],[21978])).
% 4.54/4.74 tff(21980,plain,
% 4.54/4.74 (b(s(s(s(s(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))))))))),
% 4.54/4.74 inference(monotonicity,[status(thm)],[21979])).
% 4.54/4.74 tff(21981,plain,
% 4.54/4.74 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.74 inference(symmetry,[status(thm)],[21980])).
% 4.54/4.74 tff(21982,plain,
% 4.54/4.74 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[686, 21961, 21915])).
% 4.54/4.74 tff(21983,plain,
% 4.54/4.74 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.74 inference(modus_ponens,[status(thm)],[21982, 21981])).
% 4.54/4.74 tff(21984,plain,
% 4.54/4.74 (~r(s(s(z)), s(elem!1))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[16259, 21983, 21695, 104, 21693, 21915])).
% 4.54/4.74 tff(21985,plain,
% 4.54/4.74 (~r(s(s(z)), z)),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[458, 437, 450])).
% 4.54/4.74 tff(21986,plain,
% 4.54/4.74 (b(s(s(z)), z)),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[3249, 21985])).
% 4.54/4.74 tff(21987,plain,
% 4.54/4.74 ($false),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[6767, 21986, 15559, 1056, 273, 1062, 927])).
% 4.54/4.74 tff(21988,plain,((~r(elem!1, z)) | (s(elem!1) = s(s(z))) | (~b(z, s(s(z)))) | r(s(s(z)), s(elem!1)) | r(s(elem!1), s(s(z))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.74 tff(21989,plain,
% 4.54/4.74 (~r(elem!1, s(elem!1))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[21988, 21984, 21968, 273, 21977, 21974, 21971])).
% 4.54/4.74 tff(21990,plain,
% 4.54/4.74 (b(elem!1, s(elem!1))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[756, 21989, 20190])).
% 4.54/4.74 tff(21991,plain,
% 4.54/4.74 (b(s(elem!1), s(s(z)))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[421, 21971, 21968])).
% 4.54/4.74 tff(21992,plain,
% 4.54/4.74 (b(s(s(s(elem!1))), elem!1)),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[570, 21963, 19901])).
% 4.54/4.74 tff(21993,plain,
% 4.54/4.74 (~r(z, s(elem!1))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[16948, 21977, 21992, 21967, 557, 20190, 21961])).
% 4.54/4.74 tff(21994,plain,
% 4.54/4.74 (b(z, s(elem!1))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[2351, 21993])).
% 4.54/4.74 tff(21995,plain,
% 4.54/4.74 (~b(s(s(s(s(z)))), s(elem!1))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[10985, 21994, 273, 21691, 21991])).
% 4.54/4.74 tff(21996,plain,
% 4.54/4.74 (r(s(s(s(s(z)))), s(elem!1))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[2173, 21995, 21965])).
% 4.54/4.74 tff(21997,plain,
% 4.54/4.74 ($false),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[6432, 21996, 21990, 21914, 21970, 21969, 21967, 21963, 21962, 21918, 21961])).
% 4.54/4.74 tff(21998,plain,(r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (z = elem!1) | (~b(z, s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.74 tff(21999,plain,
% 4.54/4.74 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[21998, 3243, 104, 273, 107, 318, 1687, 286, 3002, 21828, 4891])).
% 4.54/4.74 tff(22000,plain,
% 4.54/4.74 (~r(s(s(z)), elem!1)),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[2803, 21999, 287])).
% 4.54/4.74 tff(22001,plain,
% 4.54/4.74 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[271, 21696])).
% 4.54/4.74 tff(22002,plain,
% 4.54/4.74 (~r(z, elem!1)),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[3818, 21999, 22001])).
% 4.54/4.74 tff(22003,plain,
% 4.54/4.74 (b(z, elem!1)),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[585, 22002, 318])).
% 4.54/4.74 tff(22004,plain,
% 4.54/4.74 (~r(elem!1, z)),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[10809, 21999, 22001])).
% 4.54/4.74 tff(22005,plain,
% 4.54/4.74 (b(elem!1, z)),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[498, 22004, 290])).
% 4.54/4.74 tff(22006,plain,
% 4.54/4.74 (~b(s(s(z)), elem!1)),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[11004, 22005, 21546, 273, 22003])).
% 4.54/4.74 tff(22007,plain,
% 4.54/4.74 (s(s(z)) = elem!1),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[448, 22006, 22000])).
% 4.54/4.74 tff(22008,plain,
% 4.54/4.74 (s(s(s(z))) = s(elem!1)),
% 4.54/4.74 inference(monotonicity,[status(thm)],[22007])).
% 4.54/4.74 tff(22009,plain,
% 4.54/4.74 (s(s(s(s(z)))) = s(s(elem!1))),
% 4.54/4.74 inference(monotonicity,[status(thm)],[22008])).
% 4.54/4.74 tff(22010,plain,
% 4.54/4.74 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 4.54/4.74 inference(monotonicity,[status(thm)],[22009])).
% 4.54/4.74 tff(22011,plain,
% 4.54/4.74 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 4.54/4.74 inference(transitivity,[status(thm)],[22010, 3400])).
% 4.54/4.74 tff(22012,plain,
% 4.54/4.74 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 4.54/4.74 inference(transitivity,[status(thm)],[22011, 12033])).
% 4.54/4.74 tff(22013,plain,
% 4.54/4.74 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 4.54/4.74 inference(monotonicity,[status(thm)],[22012])).
% 4.54/4.74 tff(22014,plain,
% 4.54/4.74 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[5361, 22007])).
% 4.54/4.74 tff(22015,plain,
% 4.54/4.74 (~(s(s(s(elem!1))) = elem!1)),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[16438, 21828])).
% 4.54/4.74 tff(22016,plain,
% 4.54/4.74 (~(s(elem!1) = elem!1)),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[2150, 22015])).
% 4.54/4.74 tff(22017,plain,
% 4.54/4.74 (~(elem!1 = s(elem!1))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[748, 22016])).
% 4.54/4.74 tff(22018,plain,
% 4.54/4.74 (elem!1 = s(s(z))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[3230, 22007])).
% 4.54/4.74 tff(22019,plain,
% 4.54/4.74 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[10945, 22018, 287, 22001, 22005, 22003, 22017, 22016, 21999])).
% 4.54/4.74 tff(22020,plain,
% 4.54/4.74 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[395, 22019, 22014])).
% 4.54/4.74 tff(22021,plain,
% 4.54/4.74 (~(s(elem!1) = s(s(z)))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[2239, 22020, 286])).
% 4.54/4.74 tff(22022,plain,
% 4.54/4.74 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[2840, 22021])).
% 4.54/4.74 tff(22023,plain,
% 4.54/4.74 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 4.54/4.74 inference(modus_ponens,[status(thm)],[22022, 22013])).
% 4.54/4.74 tff(22024,plain,
% 4.54/4.74 (r(elem!1, s(s(elem!1)))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[9352, 22007, 21693])).
% 4.54/4.74 tff(22025,plain,
% 4.54/4.74 (b(s(s(s(z))), elem!1) <=> b(s(elem!1), elem!1)),
% 4.54/4.74 inference(monotonicity,[status(thm)],[22008])).
% 4.54/4.74 tff(22026,plain,
% 4.54/4.74 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), elem!1)),
% 4.54/4.74 inference(monotonicity,[status(thm)],[22007])).
% 4.54/4.74 tff(22027,plain,
% 4.54/4.74 (b(s(s(s(z))), elem!1)),
% 4.54/4.74 inference(modus_ponens,[status(thm)],[21834, 22026])).
% 4.54/4.74 tff(22028,plain,
% 4.54/4.74 (b(s(elem!1), elem!1)),
% 4.54/4.74 inference(modus_ponens,[status(thm)],[22027, 22025])).
% 4.54/4.74 tff(22029,plain,
% 4.54/4.74 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(elem!1))),
% 4.54/4.74 inference(monotonicity,[status(thm)],[22008])).
% 4.54/4.74 tff(22030,plain,
% 4.54/4.74 (b(s(s(z)), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 4.54/4.74 inference(monotonicity,[status(thm)],[22007])).
% 4.54/4.74 tff(22031,plain,
% 4.54/4.74 (b(elem!1, s(s(s(z))))),
% 4.54/4.74 inference(modus_ponens,[status(thm)],[21832, 22030])).
% 4.54/4.74 tff(22032,plain,
% 4.54/4.74 (b(elem!1, s(elem!1))),
% 4.54/4.74 inference(modus_ponens,[status(thm)],[22031, 22029])).
% 4.54/4.74 tff(22033,plain,
% 4.54/4.74 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 4.54/4.74 inference(monotonicity,[status(thm)],[22008])).
% 4.54/4.74 tff(22034,plain,
% 4.54/4.74 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 4.54/4.74 inference(transitivity,[status(thm)],[22033, 3881])).
% 4.54/4.74 tff(22035,plain,
% 4.54/4.74 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 4.54/4.74 inference(monotonicity,[status(thm)],[22034])).
% 4.54/4.74 tff(22036,plain,
% 4.54/4.74 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.54/4.74 inference(modus_ponens,[status(thm)],[11613, 22035])).
% 4.54/4.74 tff(22037,plain,
% 4.54/4.74 (r(z, s(s(s(z)))) <=> r(z, s(elem!1))),
% 4.54/4.74 inference(monotonicity,[status(thm)],[22008])).
% 4.54/4.74 tff(22038,plain,
% 4.54/4.74 (~b(z, s(s(s(z))))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[8742, 178, 21546, 273, 21832, 21834])).
% 4.54/4.74 tff(22039,plain,
% 4.54/4.74 (r(z, s(s(s(z))))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[4920, 22038])).
% 4.54/4.74 tff(22040,plain,
% 4.54/4.74 (r(z, s(elem!1))),
% 4.54/4.74 inference(modus_ponens,[status(thm)],[22039, 22037])).
% 4.54/4.74 tff(22041,plain,
% 4.54/4.74 (~b(s(s(s(elem!1))), elem!1)),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[7389, 22040, 3243, 22036, 22032, 22028])).
% 4.54/4.74 tff(22042,plain,
% 4.54/4.74 (r(s(s(s(elem!1))), elem!1)),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[570, 22041, 22015])).
% 4.54/4.74 tff(22043,plain,
% 4.54/4.74 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[10206, 22042, 22024])).
% 4.54/4.74 tff(22044,plain,
% 4.54/4.74 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 4.54/4.74 inference(monotonicity,[status(thm)],[22009])).
% 4.54/4.74 tff(22045,plain,
% 4.54/4.74 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(z)))), elem!1)),
% 4.54/4.74 inference(monotonicity,[status(thm)],[22007])).
% 4.54/4.74 tff(22046,plain,
% 4.54/4.74 (r(s(s(s(s(z)))), elem!1)),
% 4.54/4.74 inference(modus_ponens,[status(thm)],[21830, 22045])).
% 4.54/4.74 tff(22047,plain,
% 4.54/4.74 (r(s(s(elem!1)), elem!1)),
% 4.54/4.74 inference(modus_ponens,[status(thm)],[22046, 22044])).
% 4.54/4.74 tff(22048,plain,
% 4.54/4.74 (r(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.54/4.74 inference(monotonicity,[status(thm)],[22007])).
% 4.54/4.74 tff(22049,plain,
% 4.54/4.74 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.54/4.74 inference(modus_ponens,[status(thm)],[107, 22048])).
% 4.54/4.74 tff(22050,plain,
% 4.54/4.74 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 4.54/4.74 inference(monotonicity,[status(thm)],[22011])).
% 4.54/4.74 tff(22051,plain,
% 4.54/4.74 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 4.54/4.74 inference(modus_ponens,[status(thm)],[22022, 22050])).
% 4.54/4.74 tff(22052,plain,
% 4.54/4.74 ((s(s(z)) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(z)))))),
% 4.54/4.74 inference(monotonicity,[status(thm)],[22007])).
% 4.54/4.74 tff(22053,plain,
% 4.54/4.74 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 4.54/4.74 inference(transitivity,[status(thm)],[22052, 321])).
% 4.54/4.74 tff(22054,plain,
% 4.54/4.74 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 4.54/4.74 inference(monotonicity,[status(thm)],[22053])).
% 4.54/4.74 tff(22055,plain,
% 4.54/4.74 (~(s(s(s(s(z)))) = elem!1)),
% 4.54/4.74 inference(modus_ponens,[status(thm)],[159, 22054])).
% 4.54/4.74 tff(22056,plain,
% 4.54/4.74 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[3502, 22055])).
% 4.54/4.74 tff(22057,plain,
% 4.54/4.74 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.74 inference(monotonicity,[status(thm)],[22009])).
% 4.54/4.74 tff(22058,plain,
% 4.54/4.74 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.74 inference(modus_ponens,[status(thm)],[21695, 22057])).
% 4.54/4.74 tff(22059,plain,
% 4.54/4.74 (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)))),
% 4.54/4.74 inference(monotonicity,[status(thm)],[22009])).
% 4.54/4.74 tff(22060,plain,
% 4.54/4.74 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.54/4.74 inference(modus_ponens,[status(thm)],[104, 22059])).
% 4.54/4.74 tff(22061,plain,
% 4.54/4.74 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[18369, 22042, 22060, 22058, 22056, 22051, 22049, 22047])).
% 4.54/4.74 tff(22062,plain,
% 4.54/4.74 ($false),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[3409, 22061, 22043, 22023])).
% 4.54/4.74 tff(22063,plain,(b(z, s(s(s(elem!1)))) | (~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(z)))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | (~b(z, s(s(z)))) | (elem!1 = z) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.74 tff(22064,plain,
% 4.54/4.74 (b(z, s(s(s(elem!1))))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[22063, 290, 107, 286, 273, 104, 1687, 3002, 4891])).
% 4.54/4.74 tff(22065,plain,
% 4.54/4.74 (~(elem!1 = s(s(s(s(z)))))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[11477, 22064, 21696])).
% 4.54/4.74 tff(22066,plain,
% 4.54/4.74 (~(elem!1 = s(s(s(s(z)))))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[11477, 2043, 21696])).
% 4.54/4.74 tff(22067,plain,
% 4.54/4.74 (~b(s(s(s(s(z)))), s(s(z)))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[21680, 178, 3461, 273, 1687, 168])).
% 4.54/4.74 tff(22068,plain,
% 4.54/4.74 (r(s(s(s(s(z)))), s(s(z)))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[102, 22067])).
% 4.54/4.74 tff(22069,plain,
% 4.54/4.74 (r(s(s(s(s(z)))), elem!1)),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[3142, 3278, 551])).
% 4.54/4.74 tff(22070,plain,
% 4.54/4.74 (~r(s(s(z)), elem!1)),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[3329, 22069, 193])).
% 4.54/4.74 tff(22071,plain,
% 4.54/4.74 (b(s(s(z)), elem!1)),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[448, 22070, 12])).
% 4.54/4.74 tff(22072,plain,
% 4.54/4.74 (~(z = elem!1)),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[20730, 3278, 168])).
% 4.54/4.74 tff(22073,plain,
% 4.54/4.74 (b(z, elem!1)),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[585, 22072, 2811])).
% 4.54/4.74 tff(22074,plain,
% 4.54/4.74 (~b(elem!1, s(s(z)))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[10893, 22073, 3461, 273, 22071])).
% 4.54/4.74 tff(22075,plain,
% 4.54/4.74 (r(elem!1, s(s(z)))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[467, 22074, 312])).
% 4.54/4.74 tff(22076,plain,
% 4.54/4.74 (~b(elem!1, s(s(s(s(z)))))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[11955, 22073, 3461, 1687, 22071])).
% 4.54/4.74 tff(22077,plain,
% 4.54/4.74 (r(elem!1, s(s(s(s(z)))))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[483, 22076, 469])).
% 4.54/4.74 tff(22078,plain,
% 4.54/4.74 ($false),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[3785, 22077, 22075, 193])).
% 4.54/4.74 tff(22079,plain,(b(s(s(s(s(z)))), elem!1) | (~r(s(s(s(s(z)))), s(s(z)))) | (elem!1 = s(s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | r(z, elem!1) | (~b(s(s(s(s(z)))), z)) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.54/4.74 tff(22080,plain,
% 4.54/4.74 (b(s(s(s(s(z)))), elem!1)),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[22079, 2811, 1687, 273, 3461, 168, 22068, 12, 469])).
% 4.54/4.74 tff(22081,plain,
% 4.54/4.74 (~b(elem!1, s(s(s(s(z)))))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[21920, 22080, 1687, 168, 3123])).
% 4.54/4.74 tff(22082,plain,
% 4.54/4.74 (r(elem!1, s(s(s(s(z)))))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[483, 22081, 469])).
% 4.54/4.74 tff(22083,plain,
% 4.54/4.74 (~r(elem!1, s(s(z)))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[3785, 22082, 22068])).
% 4.54/4.74 tff(22084,plain,
% 4.54/4.74 (b(elem!1, s(s(z)))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[467, 22083, 312])).
% 4.54/4.74 tff(22085,plain,
% 4.54/4.74 (~b(s(s(z)), s(s(s(s(z)))))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[21653, 168, 273, 1687, 3461])).
% 4.54/4.74 tff(22086,plain,
% 4.54/4.74 (r(s(s(z)), s(s(s(s(z)))))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[164, 22085])).
% 4.54/4.74 tff(22087,plain,
% 4.54/4.74 (~r(s(s(z)), elem!1)),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[8763, 22082, 22086])).
% 4.54/4.74 tff(22088,plain,
% 4.54/4.74 (b(s(s(z)), elem!1)),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[448, 22087, 12])).
% 4.54/4.74 tff(22089,plain,
% 4.54/4.74 ($false),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[10893, 22088, 22084, 273, 3461, 3123])).
% 4.54/4.74 tff(22090,plain,(r(z, elem!1) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (s(s(z)) = elem!1) | (elem!1 = s(s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.54/4.74 tff(22091,plain,
% 4.54/4.74 (r(z, elem!1)),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[22090, 21829, 21546, 273, 22066, 1687, 21691, 507])).
% 4.54/4.74 tff(22092,plain,
% 4.54/4.74 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[11027, 521, 21698])).
% 4.54/4.74 tff(22093,plain,
% 4.54/4.74 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[16380, 438, 273, 21711, 104, 469, 644, 521, 9308])).
% 4.54/4.74 tff(22094,plain,
% 4.54/4.74 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 4.54/4.74 inference(monotonicity,[status(thm)],[22093])).
% 4.54/4.74 tff(22095,plain,
% 4.54/4.74 (s(s(s(s(s(s(s(s(z)))))))) = s(elem!1)),
% 4.54/4.74 inference(symmetry,[status(thm)],[22094])).
% 4.54/4.74 tff(22096,plain,
% 4.54/4.74 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z))))))))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 4.54/4.74 inference(monotonicity,[status(thm)],[22095])).
% 4.54/4.74 tff(22097,plain,
% 4.54/4.74 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.54/4.74 inference(symmetry,[status(thm)],[22096])).
% 4.54/4.74 tff(22098,plain,
% 4.54/4.74 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[16181, 22093])).
% 4.54/4.74 tff(22099,plain,
% 4.54/4.74 (~(s(s(s(s(z)))) = s(elem!1))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[2168, 22098])).
% 4.54/4.74 tff(22100,plain,
% 4.54/4.74 (~r(s(elem!1), elem!1)),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[21959, 22093, 521, 3461, 438, 224])).
% 4.54/4.74 tff(22101,plain,
% 4.54/4.74 (b(s(elem!1), elem!1)),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[677, 22100, 725])).
% 4.54/4.74 tff(22102,plain,
% 4.54/4.74 (b(s(s(s(s(z)))), elem!1)),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[3142, 8690, 551])).
% 4.54/4.74 tff(22103,plain,
% 4.54/4.74 (r(elem!1, z) <=> r(s(s(s(s(s(s(s(z))))))), z)),
% 4.54/4.74 inference(monotonicity,[status(thm)],[22093])).
% 4.54/4.74 tff(22104,plain,
% 4.54/4.74 (r(s(s(s(s(s(s(s(z))))))), z) <=> r(elem!1, z)),
% 4.54/4.74 inference(symmetry,[status(thm)],[22103])).
% 4.54/4.74 tff(22105,plain,
% 4.54/4.74 (r(elem!1, z)),
% 4.54/4.74 inference(modus_ponens,[status(thm)],[108, 22104])).
% 4.54/4.74 tff(22106,plain,
% 4.54/4.74 (~r(elem!1, s(s(s(elem!1))))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[10847, 22105, 3461, 273, 438, 521])).
% 4.54/4.74 tff(22107,plain,
% 4.54/4.74 (~r(s(s(s(elem!1))), elem!1)),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[6388, 438, 521, 3461, 273])).
% 4.54/4.74 tff(22108,plain,
% 4.54/4.74 (~(s(s(elem!1)) = elem!1)),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[2510, 22099, 22093])).
% 4.54/4.74 tff(22109,plain,
% 4.54/4.74 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[348, 22108])).
% 4.54/4.74 tff(22110,plain,
% 4.54/4.74 (~(s(elem!1) = s(s(z)))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[2832, 22093])).
% 4.54/4.74 tff(22111,plain,
% 4.54/4.74 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[2840, 22110])).
% 4.54/4.74 tff(22112,plain,
% 4.54/4.74 (~r(s(elem!1), s(s(z)))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[16202, 22093, 193, 104, 107])).
% 4.54/4.74 tff(22113,plain,
% 4.54/4.74 (r(elem!1, s(s(z))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.54/4.74 inference(monotonicity,[status(thm)],[22093])).
% 4.54/4.74 tff(22114,plain,
% 4.54/4.74 (r(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> r(elem!1, s(s(z)))),
% 4.54/4.74 inference(symmetry,[status(thm)],[22113])).
% 4.54/4.74 tff(22115,plain,
% 4.54/4.74 (r(elem!1, s(s(z)))),
% 4.54/4.74 inference(modus_ponens,[status(thm)],[107, 22114])).
% 4.54/4.74 tff(22116,plain,
% 4.54/4.74 (b(s(s(s(s(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))))))))),
% 4.54/4.74 inference(monotonicity,[status(thm)],[22095])).
% 4.54/4.74 tff(22117,plain,
% 4.54/4.74 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.74 inference(symmetry,[status(thm)],[22116])).
% 4.54/4.74 tff(22118,plain,
% 4.54/4.74 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[686, 22101, 22093])).
% 4.54/4.74 tff(22119,plain,
% 4.54/4.74 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.74 inference(modus_ponens,[status(thm)],[22118, 22117])).
% 4.54/4.74 tff(22120,plain,
% 4.54/4.74 (~r(s(s(z)), s(elem!1))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[16259, 22119, 21711, 104, 147, 22093])).
% 4.54/4.74 tff(22121,plain,
% 4.54/4.74 (~r(elem!1, s(elem!1))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[21988, 22120, 22110, 273, 22105, 22115, 22112])).
% 4.54/4.74 tff(22122,plain,
% 4.54/4.74 (b(elem!1, s(elem!1))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[756, 22121, 749])).
% 4.54/4.74 tff(22123,plain,
% 4.54/4.74 (~r(s(s(s(s(z)))), s(elem!1))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[6432, 22122, 11957, 1586, 22111, 22109, 22107, 22106, 22102, 22101])).
% 4.54/4.74 tff(22124,plain,
% 4.54/4.74 (b(s(s(s(s(z)))), s(elem!1))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[2173, 22123, 22099])).
% 4.54/4.74 tff(22125,plain,
% 4.54/4.74 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.54/4.74 inference(modus_ponens,[status(thm)],[22124, 22097])).
% 4.54/4.74 tff(22126,plain,
% 4.54/4.74 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))) <=> r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.54/4.74 inference(monotonicity,[status(thm)],[22095])).
% 4.54/4.74 tff(22127,plain,
% 4.54/4.74 (r(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.54/4.74 inference(symmetry,[status(thm)],[22126])).
% 4.54/4.74 tff(22128,plain,
% 4.54/4.74 ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) <=> (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))),
% 4.54/4.74 inference(monotonicity,[status(thm)],[22127])).
% 4.54/4.74 tff(22129,plain,
% 4.54/4.74 (r(elem!1, s(elem!1)) <=> r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.54/4.74 inference(monotonicity,[status(thm)],[22093])).
% 4.54/4.74 tff(22130,plain,
% 4.54/4.74 ((~r(elem!1, s(elem!1))) <=> (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 4.54/4.74 inference(monotonicity,[status(thm)],[22129])).
% 4.54/4.74 tff(22131,plain,
% 4.54/4.74 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.54/4.74 inference(modus_ponens,[status(thm)],[22121, 22130])).
% 4.54/4.74 tff(22132,plain,
% 4.54/4.74 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.54/4.74 inference(modus_ponens,[status(thm)],[22131, 22128])).
% 4.54/4.74 tff(22133,plain,
% 4.54/4.74 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 4.54/4.74 inference(monotonicity,[status(thm)],[22095])).
% 4.54/4.74 tff(22134,plain,
% 4.54/4.74 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.54/4.74 inference(transitivity,[status(thm)],[22133, 377])).
% 4.54/4.74 tff(22135,plain,
% 4.54/4.74 ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z)))))))))),
% 4.54/4.74 inference(symmetry,[status(thm)],[22134])).
% 4.54/4.74 tff(22136,plain,
% 4.54/4.74 ((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z))))))))))),
% 4.54/4.74 inference(monotonicity,[status(thm)],[22135])).
% 4.54/4.74 tff(22137,plain,
% 4.54/4.74 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.54/4.74 inference(monotonicity,[status(thm)],[22093])).
% 4.54/4.74 tff(22138,plain,
% 4.54/4.74 ((~(s(elem!1) = elem!1)) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 4.54/4.74 inference(monotonicity,[status(thm)],[22137])).
% 4.54/4.74 tff(22139,plain,
% 4.54/4.74 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.54/4.74 inference(modus_ponens,[status(thm)],[725, 22138])).
% 4.54/4.74 tff(22140,plain,
% 4.54/4.74 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z)))))))))),
% 4.54/4.74 inference(modus_ponens,[status(thm)],[22139, 22136])).
% 4.54/4.74 tff(22141,plain,
% 4.54/4.74 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[19275, 22140, 22132])).
% 4.54/4.74 tff(22142,plain,
% 4.54/4.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(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(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(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(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 4.54/4.74 inference(rewrite,[status(thm)],[])).
% 4.54/4.74 tff(22143,plain,
% 4.54/4.74 (((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(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))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(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(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(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 4.54/4.74 inference(rewrite,[status(thm)],[])).
% 4.54/4.74 tff(22144,plain,
% 4.54/4.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(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))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(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(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))))),
% 4.54/4.74 inference(monotonicity,[status(thm)],[22143])).
% 4.54/4.74 tff(22145,plain,
% 4.54/4.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(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))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(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(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 4.54/4.74 inference(transitivity,[status(thm)],[22144, 22142])).
% 4.54/4.74 tff(22146,plain,
% 4.54/4.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(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))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 4.54/4.74 inference(quant_inst,[status(thm)],[])).
% 4.54/4.74 tff(22147,plain,
% 4.54/4.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))),
% 4.54/4.74 inference(modus_ponens,[status(thm)],[22146, 22145])).
% 4.54/4.74 tff(22148,plain,
% 4.54/4.74 ($false),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[22147, 178, 104, 21711, 22141, 22119, 22125])).
% 4.54/4.74 tff(22149,plain,((~r(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (elem!1 = s(s(s(elem!1)))) | (~b(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (s(elem!1) = elem!1) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (elem!1 = s(s(s(s(z))))) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.74 tff(22150,plain,
% 4.54/4.74 (~r(s(s(z)), elem!1)),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[22149, 1585, 104, 273, 21693, 21546, 521, 107, 5283, 21698, 287, 21830, 22066, 644])).
% 4.54/4.74 tff(22151,plain,
% 4.54/4.74 (b(s(s(z)), elem!1)),
% 4.54/4.74 inference(unit_resolution,[status(thm)],[448, 22150, 21829])).
% 4.54/4.74 tff(22152,plain,
% 4.54/4.74 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 4.54/4.75 inference(unit_resolution,[status(thm)],[10835, 22151, 286])).
% 4.54/4.75 tff(22153,plain,
% 4.54/4.75 (~b(elem!1, s(s(s(s(z)))))),
% 4.54/4.75 inference(unit_resolution,[status(thm)],[11098, 22152, 21695, 22092, 104, 644])).
% 4.54/4.75 tff(22154,plain,
% 4.54/4.75 (r(elem!1, s(s(s(s(z)))))),
% 4.54/4.75 inference(unit_resolution,[status(thm)],[483, 22153, 22066])).
% 4.54/4.75 tff(22155,plain,
% 4.54/4.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)))),
% 4.54/4.75 inference(rewrite,[status(thm)],[])).
% 4.54/4.75 tff(22156,plain,
% 4.54/4.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)))),
% 4.54/4.75 inference(quant_inst,[status(thm)],[])).
% 4.54/4.75 tff(22157,plain,
% 4.54/4.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1))),
% 4.54/4.75 inference(modus_ponens,[status(thm)],[22156, 22155])).
% 4.54/4.75 tff(22158,plain,
% 4.54/4.75 (~r(s(s(s(z))), elem!1)),
% 4.54/4.75 inference(unit_resolution,[status(thm)],[22157, 118, 22154, 4891])).
% 4.54/4.75 tff(22159,plain,
% 4.54/4.75 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.54/4.75 inference(unit_resolution,[status(thm)],[691, 22152, 644])).
% 4.54/4.75 tff(22160,plain,
% 4.54/4.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 4.54/4.75 inference(rewrite,[status(thm)],[])).
% 4.54/4.75 tff(22161,plain,
% 4.54/4.75 (((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 4.54/4.75 inference(rewrite,[status(thm)],[])).
% 4.54/4.75 tff(22162,plain,
% 4.54/4.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 4.54/4.75 inference(monotonicity,[status(thm)],[22161])).
% 4.54/4.75 tff(22163,plain,
% 4.54/4.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 4.54/4.75 inference(transitivity,[status(thm)],[22162, 22160])).
% 4.54/4.75 tff(22164,plain,
% 4.54/4.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 4.54/4.75 inference(quant_inst,[status(thm)],[])).
% 4.54/4.75 tff(22165,plain,
% 4.54/4.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 4.54/4.75 inference(modus_ponens,[status(thm)],[22164, 22163])).
% 4.54/4.75 tff(22166,plain,
% 4.54/4.75 (~b(s(s(s(z))), elem!1)),
% 4.54/4.75 inference(unit_resolution,[status(thm)],[22165, 178, 22151, 22159, 21832, 3002])).
% 4.54/4.75 tff(22167,plain,
% 4.54/4.75 (s(s(s(z))) = elem!1),
% 4.54/4.75 inference(unit_resolution,[status(thm)],[4981, 22166, 22158])).
% 4.54/4.75 tff(22168,plain,
% 4.54/4.75 (s(s(s(s(z)))) = s(elem!1)),
% 4.54/4.75 inference(monotonicity,[status(thm)],[22167])).
% 4.54/4.75 tff(22169,plain,
% 4.54/4.75 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 4.54/4.75 inference(monotonicity,[status(thm)],[22168])).
% 4.54/4.75 tff(22170,plain,
% 4.54/4.75 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 4.54/4.75 inference(monotonicity,[status(thm)],[22169])).
% 4.54/4.75 tff(22171,plain,
% 4.54/4.75 (s(s(s(s(s(s(s(z))))))) = s(s(s(s(elem!1))))),
% 4.54/4.75 inference(monotonicity,[status(thm)],[22170])).
% 4.54/4.75 tff(22172,plain,
% 4.54/4.75 ((s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 4.54/4.75 inference(monotonicity,[status(thm)],[22171])).
% 4.54/4.75 tff(22173,plain,
% 4.54/4.75 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(elem!1)))))),
% 4.54/4.75 inference(monotonicity,[status(thm)],[22172])).
% 4.54/4.75 tff(22174,plain,
% 4.54/4.75 (~(s(s(s(s(z)))) = elem!1)),
% 4.54/4.75 inference(unit_resolution,[status(thm)],[504, 22066])).
% 4.54/4.75 tff(22175,plain,
% 4.54/4.75 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 4.54/4.75 inference(unit_resolution,[status(thm)],[3502, 22174])).
% 4.54/4.75 tff(22176,plain,
% 4.54/4.75 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 4.54/4.75 inference(modus_ponens,[status(thm)],[22175, 22173])).
% 4.54/4.75 tff(22177,plain,
% 4.54/4.75 (r(s(s(s(s(s(s(s(z))))))), z) <=> r(s(s(s(s(elem!1)))), z)),
% 4.54/4.75 inference(monotonicity,[status(thm)],[22171])).
% 4.54/4.75 tff(22178,plain,
% 4.54/4.75 (r(s(s(s(s(elem!1)))), z)),
% 4.54/4.75 inference(modus_ponens,[status(thm)],[21698, 22177])).
% 4.54/4.75 tff(22179,plain,
% 4.54/4.75 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 4.54/4.75 inference(monotonicity,[status(thm)],[22168])).
% 4.54/4.75 tff(22180,plain,
% 4.54/4.75 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.54/4.75 inference(symmetry,[status(thm)],[22179])).
% 4.54/4.75 tff(22181,plain,
% 4.54/4.75 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 4.54/4.75 inference(monotonicity,[status(thm)],[22168, 22170])).
% 4.54/4.75 tff(22182,plain,
% 4.54/4.75 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 4.54/4.75 inference(transitivity,[status(thm)],[22181, 3881])).
% 4.54/4.75 tff(22183,plain,
% 4.54/4.75 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.54/4.75 inference(transitivity,[status(thm)],[22182, 22180])).
% 4.54/4.75 tff(22184,plain,
% 4.54/4.75 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(z))))))),
% 4.54/4.75 inference(monotonicity,[status(thm)],[22183])).
% 4.54/4.75 tff(22185,plain,
% 4.54/4.75 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.54/4.75 inference(modus_ponens,[status(thm)],[3698, 22184])).
% 4.54/4.75 tff(22186,plain,
% 4.54/4.75 (~r(elem!1, s(s(z)))),
% 4.54/4.75 inference(unit_resolution,[status(thm)],[3785, 22154, 21830])).
% 4.54/4.75 tff(22187,plain,
% 4.54/4.75 (b(elem!1, s(s(z)))),
% 4.54/4.75 inference(unit_resolution,[status(thm)],[467, 22186, 21905])).
% 4.54/4.75 tff(22188,plain,
% 4.54/4.75 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(z)), s(elem!1))),
% 4.54/4.75 inference(monotonicity,[status(thm)],[22168])).
% 4.54/4.75 tff(22189,plain,
% 4.54/4.75 (r(s(s(z)), s(elem!1))),
% 4.54/4.75 inference(modus_ponens,[status(thm)],[21693, 22188])).
% 4.54/4.75 tff(22190,plain,
% 4.54/4.75 (b(z, s(s(s(s(z))))) <=> b(z, s(elem!1))),
% 4.54/4.75 inference(monotonicity,[status(thm)],[22168])).
% 4.54/4.75 tff(22191,plain,
% 4.54/4.75 (b(z, s(elem!1))),
% 4.54/4.75 inference(modus_ponens,[status(thm)],[1687, 22190])).
% 4.54/4.75 tff(22192,plain,
% 4.54/4.75 (b(s(s(s(s(z)))), z) <=> b(s(elem!1), z)),
% 4.54/4.75 inference(monotonicity,[status(thm)],[22168])).
% 4.54/4.75 tff(22193,plain,
% 4.54/4.75 (b(s(elem!1), z)),
% 4.54/4.75 inference(modus_ponens,[status(thm)],[21691, 22192])).
% 4.54/4.75 tff(22194,plain,
% 4.54/4.75 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 4.54/4.75 inference(transitivity,[status(thm)],[22182, 7104])).
% 4.54/4.75 tff(22195,plain,
% 4.54/4.75 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 4.54/4.75 inference(monotonicity,[status(thm)],[22194])).
% 4.54/4.75 tff(22196,plain,
% 4.54/4.75 (~(s(elem!1) = s(s(s(elem!1))))),
% 4.54/4.75 inference(modus_ponens,[status(thm)],[3698, 22195])).
% 4.54/4.75 tff(22197,plain,
% 4.54/4.75 (r(s(s(s(z))), z) <=> r(elem!1, z)),
% 4.54/4.75 inference(monotonicity,[status(thm)],[22167])).
% 4.54/4.75 tff(22198,plain,
% 4.54/4.75 (r(elem!1, z)),
% 4.54/4.75 inference(modus_ponens,[status(thm)],[21837, 22197])).
% 4.54/4.75 tff(22199,plain,
% 4.54/4.75 (~r(elem!1, s(s(s(elem!1))))),
% 4.54/4.75 inference(unit_resolution,[status(thm)],[6352, 22198, 273, 21546, 22196, 22193, 22191, 22189])).
% 4.54/4.75 tff(22200,plain,
% 4.54/4.75 (b(elem!1, s(s(s(elem!1))))),
% 4.54/4.75 inference(unit_resolution,[status(thm)],[2054, 22199, 1585])).
% 4.54/4.75 tff(22201,plain,
% 4.54/4.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 4.54/4.75 inference(rewrite,[status(thm)],[])).
% 4.54/4.75 tff(22202,plain,
% 4.54/4.75 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z))))) <=> ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 4.54/4.75 inference(rewrite,[status(thm)],[])).
% 4.54/4.75 tff(22203,plain,
% 4.54/4.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 4.54/4.75 inference(monotonicity,[status(thm)],[22202])).
% 4.54/4.75 tff(22204,plain,
% 4.54/4.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 4.54/4.75 inference(transitivity,[status(thm)],[22203, 22201])).
% 4.54/4.75 tff(22205,plain,
% 4.54/4.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 4.54/4.75 inference(quant_inst,[status(thm)],[])).
% 4.54/4.75 tff(22206,plain,
% 4.54/4.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 4.54/4.75 inference(modus_ponens,[status(thm)],[22205, 22204])).
% 4.54/4.75 tff(22207,plain,
% 4.54/4.75 (~r(s(s(s(elem!1))), s(s(z)))),
% 4.54/4.75 inference(unit_resolution,[status(thm)],[22206, 118, 147, 3251])).
% 4.54/4.75 tff(22208,plain,
% 4.54/4.75 (b(s(s(s(elem!1))), s(s(z)))),
% 4.54/4.75 inference(unit_resolution,[status(thm)],[4209, 41, 22207, 4181])).
% 4.54/4.75 tff(22209,plain,
% 4.54/4.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 4.54/4.75 inference(rewrite,[status(thm)],[])).
% 4.54/4.75 tff(22210,plain,
% 4.54/4.75 (((~r(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(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 4.54/4.75 inference(rewrite,[status(thm)],[])).
% 4.54/4.75 tff(22211,plain,
% 4.54/4.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 4.54/4.75 inference(monotonicity,[status(thm)],[22210])).
% 4.54/4.75 tff(22212,plain,
% 4.54/4.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 4.54/4.75 inference(transitivity,[status(thm)],[22211, 22209])).
% 4.54/4.75 tff(22213,plain,
% 4.54/4.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 4.54/4.75 inference(quant_inst,[status(thm)],[])).
% 4.54/4.75 tff(22214,plain,
% 4.54/4.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 4.54/4.75 inference(modus_ponens,[status(thm)],[22213, 22212])).
% 4.54/4.75 tff(22215,plain,
% 4.54/4.75 (~r(s(s(s(elem!1))), elem!1)),
% 4.54/4.75 inference(unit_resolution,[status(thm)],[22214, 118, 470, 3251])).
% 4.54/4.75 tff(22216,plain,
% 4.54/4.75 (b(s(s(s(elem!1))), elem!1)),
% 4.54/4.75 inference(unit_resolution,[status(thm)],[570, 22215, 949])).
% 4.54/4.75 tff(22217,plain,
% 4.54/4.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 4.54/4.75 inference(rewrite,[status(thm)],[])).
% 4.54/4.75 tff(22218,plain,
% 4.54/4.75 (((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 4.54/4.75 inference(rewrite,[status(thm)],[])).
% 4.54/4.75 tff(22219,plain,
% 4.54/4.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(elem!1))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 4.54/4.75 inference(monotonicity,[status(thm)],[22218])).
% 4.54/4.75 tff(22220,plain,
% 4.54/4.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(elem!1))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 4.54/4.75 inference(transitivity,[status(thm)],[22219, 22217])).
% 4.54/4.75 tff(22221,plain,
% 4.54/4.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(elem!1, s(s(s(elem!1))))))),
% 4.54/4.75 inference(quant_inst,[status(thm)],[])).
% 4.54/4.75 tff(22222,plain,
% 4.54/4.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 4.54/4.75 inference(modus_ponens,[status(thm)],[22221, 22220])).
% 4.54/4.75 tff(22223,plain,
% 4.54/4.75 ($false),
% 4.54/4.75 inference(unit_resolution,[status(thm)],[22222, 178, 22216, 817, 812, 2042, 22208])).
% 4.54/4.75 tff(22224,plain,((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.75 tff(22225,plain,
% 4.54/4.75 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.54/4.75 inference(unit_resolution,[status(thm)],[22224, 22200, 21693, 22151, 949, 22187, 22154])).
% 4.54/4.75 tff(22226,plain,
% 4.54/4.75 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.54/4.75 inference(unit_resolution,[status(thm)],[4173, 22225, 22185])).
% 4.54/4.75 tff(22227,plain,
% 4.54/4.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 4.54/4.75 inference(rewrite,[status(thm)],[])).
% 4.54/4.75 tff(22228,plain,
% 4.54/4.75 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 4.54/4.75 inference(rewrite,[status(thm)],[])).
% 4.54/4.75 tff(22229,plain,
% 4.54/4.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 4.54/4.75 inference(monotonicity,[status(thm)],[22228])).
% 4.54/4.75 tff(22230,plain,
% 4.54/4.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 4.54/4.75 inference(transitivity,[status(thm)],[22229, 22227])).
% 4.54/4.75 tff(22231,plain,
% 4.54/4.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))))),
% 4.54/4.75 inference(quant_inst,[status(thm)],[])).
% 4.54/4.75 tff(22232,plain,
% 4.54/4.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 4.54/4.75 inference(modus_ponens,[status(thm)],[22231, 22230])).
% 4.54/4.75 tff(22233,plain,
% 4.54/4.75 ($false),
% 4.54/4.75 inference(unit_resolution,[status(thm)],[22232, 178, 2043, 7976, 1687, 168, 3831])).
% 4.54/4.75 tff(22234,plain,((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.75 tff(22235,plain,
% 4.54/4.75 (~b(s(s(s(elem!1))), z)),
% 4.54/4.75 inference(unit_resolution,[status(thm)],[22234, 22226, 1687, 21691, 2043])).
% 4.54/4.75 tff(22236,plain,
% 4.54/4.75 (r(s(s(s(elem!1))), z)),
% 4.54/4.75 inference(unit_resolution,[status(thm)],[1565, 22235])).
% 4.54/4.75 tff(22237,plain,
% 4.54/4.75 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 4.54/4.75 inference(unit_resolution,[status(thm)],[4736, 118, 22236, 22178])).
% 4.54/4.75 tff(22238,plain,
% 4.54/4.75 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 4.54/4.75 inference(unit_resolution,[status(thm)],[1988, 22237, 22176])).
% 4.54/4.75 tff(22239,plain,
% 4.54/4.75 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 4.54/4.75 inference(unit_resolution,[status(thm)],[4745, 118, 22236, 22178])).
% 4.54/4.75 tff(22240,plain,
% 4.54/4.75 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 4.54/4.75 inference(unit_resolution,[status(thm)],[1750, 22239, 8397])).
% 4.54/4.75 tff(22241,plain,
% 4.54/4.75 (s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(z)))))))),
% 4.54/4.75 inference(symmetry,[status(thm)],[22171])).
% 4.54/4.75 tff(22242,plain,
% 4.54/4.75 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.54/4.75 inference(monotonicity,[status(thm)],[22241])).
% 4.54/4.75 tff(22243,plain,
% 4.54/4.75 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 4.54/4.75 inference(symmetry,[status(thm)],[22242])).
% 4.54/4.75 tff(22244,plain,
% 4.54/4.75 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 4.54/4.75 inference(unit_resolution,[status(thm)],[703, 22152])).
% 4.54/4.75 tff(22245,plain,
% 4.54/4.75 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.54/4.75 inference(unit_resolution,[status(thm)],[3444, 22244, 22092])).
% 4.54/4.75 tff(22246,plain,
% 4.54/4.75 (b(s(s(s(s(elem!1)))), elem!1)),
% 4.54/4.75 inference(modus_ponens,[status(thm)],[22245, 22243])).
% 4.54/4.75 tff(22247,plain,
% 4.54/4.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 4.54/4.75 inference(rewrite,[status(thm)],[])).
% 4.54/4.75 tff(22248,plain,
% 4.54/4.75 (((~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 4.54/4.75 inference(rewrite,[status(thm)],[])).
% 4.54/4.75 tff(22249,plain,
% 4.54/4.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1))))),
% 4.54/4.75 inference(monotonicity,[status(thm)],[22248])).
% 4.54/4.75 tff(22250,plain,
% 4.54/4.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 4.54/4.75 inference(transitivity,[status(thm)],[22249, 22247])).
% 4.54/4.75 tff(22251,plain,
% 4.54/4.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 4.54/4.75 inference(quant_inst,[status(thm)],[])).
% 4.54/4.75 tff(22252,plain,
% 4.54/4.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1))),
% 4.54/4.75 inference(modus_ponens,[status(thm)],[22251, 22250])).
% 4.54/4.75 tff(22253,plain,
% 4.54/4.75 (~r(s(s(s(elem!1))), elem!1)),
% 4.54/4.75 inference(unit_resolution,[status(thm)],[22252, 118, 22198, 22236])).
% 4.54/4.75 tff(22254,plain,
% 4.54/4.75 (b(s(s(s(elem!1))), elem!1)),
% 4.54/4.75 inference(unit_resolution,[status(thm)],[570, 22253, 949])).
% 4.54/4.75 tff(22255,plain,
% 4.54/4.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 4.54/4.76 inference(rewrite,[status(thm)],[])).
% 4.54/4.76 tff(22256,plain,
% 4.54/4.76 (((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 4.54/4.76 inference(rewrite,[status(thm)],[])).
% 4.54/4.76 tff(22257,plain,
% 4.54/4.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))))),
% 4.54/4.76 inference(monotonicity,[status(thm)],[22256])).
% 4.54/4.76 tff(22258,plain,
% 4.54/4.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 4.54/4.76 inference(transitivity,[status(thm)],[22257, 22255])).
% 4.54/4.76 tff(22259,plain,
% 4.54/4.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 4.54/4.76 inference(quant_inst,[status(thm)],[])).
% 4.54/4.76 tff(22260,plain,
% 4.54/4.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))),
% 4.54/4.76 inference(modus_ponens,[status(thm)],[22259, 22258])).
% 4.54/4.76 tff(22261,plain,
% 4.54/4.76 ($false),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[22260, 178, 22254, 22200, 22246, 22240, 22238])).
% 4.54/4.76 tff(22262,plain,((s(s(s(elem!1))) = elem!1) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.76 tff(22263,plain,
% 4.54/4.76 (s(s(s(elem!1))) = elem!1),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[22262, 644, 2043, 273, 3002, 4891, 104, 1687, 286, 22091, 107])).
% 4.54/4.76 tff(22264,plain,
% 4.54/4.76 (b(z, elem!1)),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[17579, 22263, 2043])).
% 4.54/4.76 tff(22265,plain,
% 4.54/4.76 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[11027, 22091, 21698])).
% 4.54/4.76 tff(22266,plain,
% 4.54/4.76 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[4243, 22264, 21696])).
% 4.54/4.76 tff(22267,plain,
% 4.54/4.76 (~b(elem!1, s(s(s(s(z)))))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[11098, 22266, 21695, 22265, 104, 644])).
% 4.54/4.76 tff(22268,plain,
% 4.54/4.76 (r(elem!1, s(s(s(s(z)))))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[483, 22267, 22066])).
% 4.54/4.76 tff(22269,plain,
% 4.54/4.76 (~r(elem!1, s(s(z)))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[3785, 22268, 21830])).
% 4.54/4.76 tff(22270,plain,
% 4.54/4.76 (b(elem!1, s(s(z)))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[467, 22269, 21905])).
% 4.54/4.76 tff(22271,plain,
% 4.54/4.76 (~r(s(s(z)), elem!1)),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[8763, 22268, 21693])).
% 4.54/4.76 tff(22272,plain,
% 4.54/4.76 (b(s(s(z)), elem!1)),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[448, 22271, 21829])).
% 4.54/4.76 tff(22273,plain,
% 4.54/4.76 ($false),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[10893, 22272, 22270, 273, 21546, 22264])).
% 4.54/4.76 tff(22274,plain,(r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.54/4.76 tff(22275,plain,
% 4.54/4.76 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[22274, 22064, 104, 273, 3002, 4891, 1687, 286, 107, 318])).
% 4.54/4.76 tff(22276,plain,
% 4.54/4.76 (~r(z, elem!1)),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[3818, 22275, 22001])).
% 4.54/4.76 tff(22277,plain,
% 4.54/4.76 (s(s(z)) = elem!1),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[22090, 22276, 21546, 273, 22065, 1687, 21691, 318])).
% 4.54/4.76 tff(22278,plain,
% 4.54/4.76 (s(s(s(z))) = s(elem!1)),
% 4.54/4.76 inference(monotonicity,[status(thm)],[22277])).
% 4.54/4.76 tff(22279,plain,
% 4.54/4.76 (s(s(s(s(z)))) = s(s(elem!1))),
% 4.54/4.76 inference(monotonicity,[status(thm)],[22278])).
% 4.54/4.76 tff(22280,plain,
% 4.54/4.76 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 4.54/4.76 inference(monotonicity,[status(thm)],[22279])).
% 4.54/4.76 tff(22281,plain,
% 4.54/4.76 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 4.54/4.76 inference(transitivity,[status(thm)],[22280, 3400])).
% 4.54/4.76 tff(22282,plain,
% 4.54/4.76 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 4.54/4.76 inference(transitivity,[status(thm)],[22281, 12033])).
% 4.54/4.76 tff(22283,plain,
% 4.54/4.76 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 4.54/4.76 inference(monotonicity,[status(thm)],[22282])).
% 4.54/4.76 tff(22284,plain,
% 4.54/4.76 (elem!1 = s(s(z))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[3230, 22277])).
% 4.54/4.76 tff(22285,plain,
% 4.54/4.76 (~b(s(elem!1), z)),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[7042, 22284, 21836])).
% 4.54/4.76 tff(22286,plain,
% 4.54/4.76 (r(s(elem!1), z)),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[774, 22285])).
% 4.54/4.76 tff(22287,plain,
% 4.54/4.76 (~(s(s(z)) = s(elem!1))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[11742, 22286, 21545])).
% 4.54/4.76 tff(22288,plain,
% 4.54/4.76 (~(s(elem!1) = s(s(z)))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[1362, 22287])).
% 4.54/4.76 tff(22289,plain,
% 4.54/4.76 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[2840, 22288])).
% 4.54/4.76 tff(22290,plain,
% 4.54/4.76 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 4.54/4.76 inference(modus_ponens,[status(thm)],[22289, 22283])).
% 4.54/4.76 tff(22291,plain,
% 4.54/4.76 (r(elem!1, s(s(elem!1)))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[9352, 22277, 21693])).
% 4.54/4.76 tff(22292,plain,
% 4.54/4.76 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 4.54/4.76 inference(monotonicity,[status(thm)],[22277])).
% 4.54/4.76 tff(22293,plain,
% 4.54/4.76 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 4.54/4.76 inference(transitivity,[status(thm)],[22292, 1526])).
% 4.54/4.76 tff(22294,plain,
% 4.54/4.76 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 4.54/4.76 inference(monotonicity,[status(thm)],[22293])).
% 4.54/4.76 tff(22295,plain,
% 4.54/4.76 (~(s(s(s(elem!1))) = elem!1)),
% 4.54/4.76 inference(modus_ponens,[status(thm)],[1683, 22294])).
% 4.54/4.76 tff(22296,plain,
% 4.54/4.76 (b(z, elem!1)),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[585, 22276, 318])).
% 4.54/4.76 tff(22297,plain,
% 4.54/4.76 (~r(elem!1, z)),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[10809, 22275, 22001])).
% 4.54/4.76 tff(22298,plain,
% 4.54/4.76 (b(elem!1, z)),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[498, 22297, 290])).
% 4.54/4.76 tff(22299,plain,
% 4.54/4.76 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 4.54/4.76 inference(transitivity,[status(thm)],[22293, 2486])).
% 4.54/4.76 tff(22300,plain,
% 4.54/4.76 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 4.54/4.76 inference(monotonicity,[status(thm)],[22299])).
% 4.54/4.76 tff(22301,plain,
% 4.54/4.76 (~(elem!1 = s(s(s(elem!1))))),
% 4.54/4.76 inference(modus_ponens,[status(thm)],[1683, 22300])).
% 4.54/4.76 tff(22302,plain,
% 4.54/4.76 ((s(s(elem!1)) = s(s(z))) <=> (s(s(elem!1)) = elem!1)),
% 4.54/4.76 inference(monotonicity,[status(thm)],[22277])).
% 4.54/4.76 tff(22303,plain,
% 4.54/4.76 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(elem!1)) = elem!1))),
% 4.54/4.76 inference(monotonicity,[status(thm)],[22302])).
% 4.54/4.76 tff(22304,plain,
% 4.54/4.76 (~(s(s(elem!1)) = elem!1)),
% 4.54/4.76 inference(modus_ponens,[status(thm)],[3340, 22303])).
% 4.54/4.76 tff(22305,plain,
% 4.54/4.76 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 4.54/4.76 inference(monotonicity,[status(thm)],[22279])).
% 4.54/4.76 tff(22306,plain,
% 4.54/4.76 ((~b(s(s(s(s(z)))), elem!1)) <=> (~b(s(s(elem!1)), elem!1))),
% 4.54/4.76 inference(monotonicity,[status(thm)],[22305])).
% 4.54/4.76 tff(22307,plain,
% 4.54/4.76 (~b(s(s(s(s(z)))), elem!1)),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[3774, 22277, 21699])).
% 4.54/4.76 tff(22308,plain,
% 4.54/4.76 (~b(s(s(elem!1)), elem!1)),
% 4.54/4.76 inference(modus_ponens,[status(thm)],[22307, 22306])).
% 4.54/4.76 tff(22309,plain,
% 4.54/4.76 (b(s(s(s(s(z)))), z) <=> b(s(s(elem!1)), z)),
% 4.54/4.76 inference(monotonicity,[status(thm)],[22279])).
% 4.54/4.76 tff(22310,plain,
% 4.54/4.76 (b(s(s(elem!1)), z)),
% 4.54/4.76 inference(modus_ponens,[status(thm)],[21691, 22309])).
% 4.54/4.76 tff(22311,plain,
% 4.54/4.76 (b(z, s(s(s(s(z))))) <=> b(z, s(s(elem!1)))),
% 4.54/4.76 inference(monotonicity,[status(thm)],[22279])).
% 4.54/4.76 tff(22312,plain,
% 4.54/4.76 (b(z, s(s(elem!1)))),
% 4.54/4.76 inference(modus_ponens,[status(thm)],[1687, 22311])).
% 4.54/4.76 tff(22313,plain,
% 4.54/4.76 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[3377, 3311, 3358, 346])).
% 4.54/4.76 tff(22314,plain,
% 4.54/4.76 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[18614, 22313, 2043, 6477, 6604])).
% 4.54/4.76 tff(22315,plain,
% 4.54/4.76 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[3409, 22314, 5222])).
% 4.54/4.76 tff(22316,plain,
% 4.54/4.76 ($false),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[12160, 118, 3311, 22315, 5816])).
% 4.54/4.76 tff(22317,plain,((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | b(s(s(elem!1)), elem!1) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.54/4.76 tff(22318,plain,
% 4.54/4.76 (~r(elem!1, s(s(s(elem!1))))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[22317, 22291, 22290, 22064, 22312, 22310, 22308, 22304])).
% 4.54/4.76 tff(22319,plain,
% 4.54/4.76 (b(elem!1, s(s(s(elem!1))))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[2054, 22318, 22301])).
% 4.54/4.76 tff(22320,plain,
% 4.54/4.76 (~b(s(s(s(elem!1))), elem!1)),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[12925, 22319, 22064, 22298, 22296])).
% 4.54/4.76 tff(22321,plain,
% 4.54/4.76 (r(s(s(s(elem!1))), elem!1)),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[570, 22320, 22295])).
% 4.54/4.76 tff(22322,plain,
% 4.54/4.76 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[10206, 22321, 22291])).
% 4.54/4.76 tff(22323,plain,
% 4.54/4.76 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 4.54/4.76 inference(monotonicity,[status(thm)],[22279])).
% 4.54/4.76 tff(22324,plain,
% 4.54/4.76 (~(s(s(s(s(z)))) = elem!1)),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[504, 22065])).
% 4.54/4.76 tff(22325,plain,
% 4.54/4.76 (r(s(s(s(s(z)))), elem!1)),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[3142, 22307, 22324])).
% 4.54/4.76 tff(22326,plain,
% 4.54/4.76 (r(s(s(elem!1)), elem!1)),
% 4.54/4.76 inference(modus_ponens,[status(thm)],[22325, 22323])).
% 4.54/4.76 tff(22327,plain,
% 4.54/4.76 (r(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.54/4.76 inference(monotonicity,[status(thm)],[22277])).
% 4.54/4.76 tff(22328,plain,
% 4.54/4.76 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.54/4.76 inference(modus_ponens,[status(thm)],[107, 22327])).
% 4.54/4.76 tff(22329,plain,
% 4.54/4.76 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 4.54/4.76 inference(monotonicity,[status(thm)],[22281])).
% 4.54/4.76 tff(22330,plain,
% 4.54/4.76 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 4.54/4.76 inference(modus_ponens,[status(thm)],[22289, 22329])).
% 4.54/4.76 tff(22331,plain,
% 4.54/4.76 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[3502, 22324])).
% 4.54/4.76 tff(22332,plain,
% 4.54/4.76 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.76 inference(monotonicity,[status(thm)],[22279])).
% 4.54/4.76 tff(22333,plain,
% 4.54/4.76 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.76 inference(modus_ponens,[status(thm)],[21695, 22332])).
% 4.54/4.76 tff(22334,plain,
% 4.54/4.76 (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)))),
% 4.54/4.76 inference(monotonicity,[status(thm)],[22279])).
% 4.54/4.76 tff(22335,plain,
% 4.54/4.76 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.54/4.76 inference(modus_ponens,[status(thm)],[104, 22334])).
% 4.54/4.76 tff(22336,plain,
% 4.54/4.76 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[18369, 22321, 22335, 22333, 22331, 22330, 22328, 22326])).
% 4.54/4.76 tff(22337,plain,
% 4.54/4.76 ($false),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[3409, 22336, 22322, 22290])).
% 4.54/4.76 tff(22338,plain,((elem!1 = z) | (~b(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(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.76 tff(22339,plain,
% 4.54/4.76 (elem!1 = z),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[22338, 4891, 104, 107, 273, 3002, 1687, 286])).
% 4.54/4.76 tff(22340,plain,
% 4.54/4.76 (z = elem!1),
% 4.54/4.76 inference(symmetry,[status(thm)],[22339])).
% 4.54/4.76 tff(22341,plain,
% 4.54/4.76 (s(z) = s(elem!1)),
% 4.54/4.76 inference(monotonicity,[status(thm)],[22340])).
% 4.54/4.76 tff(22342,plain,
% 4.54/4.76 (s(elem!1) = s(z)),
% 4.54/4.76 inference(symmetry,[status(thm)],[22341])).
% 4.54/4.76 tff(22343,plain,
% 4.54/4.76 (s(s(elem!1)) = s(s(z))),
% 4.54/4.76 inference(monotonicity,[status(thm)],[22342])).
% 4.54/4.76 tff(22344,plain,
% 4.54/4.76 (s(s(s(elem!1))) = s(s(s(z)))),
% 4.54/4.76 inference(monotonicity,[status(thm)],[22343])).
% 4.54/4.76 tff(22345,plain,
% 4.54/4.76 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 4.54/4.76 inference(monotonicity,[status(thm)],[22344])).
% 4.54/4.76 tff(22346,plain,
% 4.54/4.76 ((s(elem!1) = s(s(s(s(elem!1))))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 4.54/4.76 inference(monotonicity,[status(thm)],[22345])).
% 4.54/4.76 tff(22347,plain,
% 4.54/4.76 ((s(elem!1) = s(s(s(s(elem!1))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 4.54/4.76 inference(transitivity,[status(thm)],[22346, 2163])).
% 4.54/4.76 tff(22348,plain,
% 4.54/4.76 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 4.54/4.76 inference(symmetry,[status(thm)],[22347])).
% 4.54/4.76 tff(22349,plain,
% 4.54/4.76 (b(s(elem!1), elem!1) <=> b(s(elem!1), z)),
% 4.54/4.76 inference(monotonicity,[status(thm)],[22339])).
% 4.54/4.76 tff(22350,plain,
% 4.54/4.76 ((s(elem!1) = elem!1) <=> (s(elem!1) = z)),
% 4.54/4.76 inference(monotonicity,[status(thm)],[22339])).
% 4.54/4.76 tff(22351,plain,
% 4.54/4.76 ((s(elem!1) = z) <=> (s(elem!1) = elem!1)),
% 4.54/4.76 inference(symmetry,[status(thm)],[22350])).
% 4.54/4.76 tff(22352,plain,
% 4.54/4.76 ((~(s(elem!1) = z)) <=> (~(s(elem!1) = elem!1))),
% 4.54/4.76 inference(monotonicity,[status(thm)],[22351])).
% 4.54/4.76 tff(22353,plain,
% 4.54/4.76 (~(s(elem!1) = elem!1)),
% 4.54/4.76 inference(modus_ponens,[status(thm)],[769, 22352])).
% 4.54/4.76 tff(22354,plain,
% 4.54/4.76 (r(elem!1, s(s(s(elem!1)))) <=> r(z, s(s(s(elem!1))))),
% 4.54/4.76 inference(monotonicity,[status(thm)],[22339])).
% 4.54/4.76 tff(22355,plain,
% 4.54/4.76 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 4.54/4.76 inference(symmetry,[status(thm)],[22354])).
% 4.54/4.76 tff(22356,plain,
% 4.54/4.76 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(z))))),
% 4.54/4.76 inference(monotonicity,[status(thm)],[22344])).
% 4.54/4.76 tff(22357,plain,
% 4.54/4.76 (r(z, s(s(s(z)))) <=> r(z, s(s(s(elem!1))))),
% 4.54/4.76 inference(symmetry,[status(thm)],[22356])).
% 4.54/4.76 tff(22358,plain,
% 4.54/4.76 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 4.54/4.76 inference(transitivity,[status(thm)],[22357, 22355])).
% 4.54/4.76 tff(22359,plain,
% 4.54/4.76 (r(elem!1, s(s(s(elem!1))))),
% 4.54/4.76 inference(modus_ponens,[status(thm)],[22039, 22358])).
% 4.54/4.76 tff(22360,plain,
% 4.54/4.76 (b(elem!1, s(s(z)))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[3276, 22339, 273])).
% 4.54/4.76 tff(22361,plain,
% 4.54/4.76 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(z)), s(s(z)))),
% 4.54/4.76 inference(monotonicity,[status(thm)],[22343])).
% 4.54/4.76 tff(22362,plain,
% 4.54/4.76 (b(s(s(z)), s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 4.54/4.76 inference(symmetry,[status(thm)],[22361])).
% 4.54/4.76 tff(22363,plain,
% 4.54/4.76 ((~b(s(s(z)), s(s(z)))) <=> (~b(s(s(elem!1)), s(s(z))))),
% 4.54/4.76 inference(monotonicity,[status(thm)],[22362])).
% 4.54/4.76 tff(22364,plain,
% 4.54/4.76 (~b(s(s(z)), s(s(z)))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[16833, 178, 21546, 273])).
% 4.54/4.76 tff(22365,plain,
% 4.54/4.76 (~b(s(s(elem!1)), s(s(z)))),
% 4.54/4.76 inference(modus_ponens,[status(thm)],[22364, 22363])).
% 4.54/4.76 tff(22366,plain,
% 4.54/4.76 (~(s(elem!1) = s(s(s(elem!1))))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[20889, 22365, 22360])).
% 4.54/4.76 tff(22367,plain,
% 4.54/4.76 (~r(s(elem!1), s(s(s(elem!1))))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[9138, 1426, 3311])).
% 4.54/4.76 tff(22368,plain,
% 4.54/4.76 (b(s(elem!1), s(s(s(elem!1))))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[5432, 22367, 5425])).
% 4.54/4.76 tff(22369,plain,
% 4.54/4.76 (b(s(z), s(s(s(z))))),
% 4.54/4.76 inference(modus_ponens,[status(thm)],[22368, 12745])).
% 4.54/4.76 tff(22370,plain,
% 4.54/4.76 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[14155, 118, 108, 20848])).
% 4.54/4.76 tff(22371,plain,
% 4.54/4.76 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.76 inference(modus_ponens,[status(thm)],[22370, 14149])).
% 4.54/4.76 tff(22372,plain,
% 4.54/4.76 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[395, 22371, 14147])).
% 4.54/4.76 tff(22373,plain,
% 4.54/4.76 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.76 inference(modus_ponens,[status(thm)],[22372, 20647])).
% 4.54/4.76 tff(22374,plain,
% 4.54/4.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))))),
% 4.54/4.76 inference(rewrite,[status(thm)],[])).
% 4.54/4.76 tff(22375,plain,
% 4.54/4.76 (((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))))),
% 4.54/4.76 inference(rewrite,[status(thm)],[])).
% 4.54/4.76 tff(22376,plain,
% 4.54/4.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z)))))))),
% 4.54/4.76 inference(monotonicity,[status(thm)],[22375])).
% 4.54/4.76 tff(22377,plain,
% 4.54/4.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))))),
% 4.54/4.76 inference(transitivity,[status(thm)],[22376, 22374])).
% 4.54/4.76 tff(22378,plain,
% 4.54/4.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 4.54/4.76 inference(quant_inst,[status(thm)],[])).
% 4.54/4.76 tff(22379,plain,
% 4.54/4.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z)))))),
% 4.54/4.76 inference(modus_ponens,[status(thm)],[22378, 22377])).
% 4.54/4.76 tff(22380,plain,
% 4.54/4.76 ($false),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[22379, 178, 3002, 22373, 21855, 22369, 20850])).
% 4.54/4.76 tff(22381,plain,((~r(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~(elem!1 = z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (s(elem!1) = s(s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.76 tff(22382,plain,
% 4.54/4.76 (~r(s(elem!1), elem!1)),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[22381, 21844, 3002, 22339, 21698, 22366, 22359])).
% 4.54/4.76 tff(22383,plain,
% 4.54/4.76 (b(s(elem!1), elem!1)),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[677, 22382, 22353])).
% 4.54/4.76 tff(22384,plain,
% 4.54/4.76 (b(s(elem!1), z)),
% 4.54/4.76 inference(modus_ponens,[status(thm)],[22383, 22349])).
% 4.54/4.76 tff(22385,plain,
% 4.54/4.76 (s(s(s(z))) = s(s(s(elem!1)))),
% 4.54/4.76 inference(symmetry,[status(thm)],[22344])).
% 4.54/4.76 tff(22386,plain,
% 4.54/4.76 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 4.54/4.76 inference(monotonicity,[status(thm)],[22385])).
% 4.54/4.76 tff(22387,plain,
% 4.54/4.76 ((~r(s(s(z)), s(s(s(z))))) <=> (~r(s(s(z)), s(s(s(elem!1)))))),
% 4.54/4.76 inference(monotonicity,[status(thm)],[22386])).
% 4.54/4.76 tff(22388,plain,
% 4.54/4.76 (~r(s(s(z)), s(s(s(elem!1))))),
% 4.54/4.76 inference(modus_ponens,[status(thm)],[21831, 22387])).
% 4.54/4.76 tff(22389,plain,
% 4.54/4.76 (~(s(elem!1) = s(s(z)))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[1838, 22388, 21693])).
% 4.54/4.76 tff(22390,plain,
% 4.54/4.76 (r(z, s(s(s(elem!1))))),
% 4.54/4.76 inference(modus_ponens,[status(thm)],[22039, 22357])).
% 4.54/4.76 tff(22391,plain,
% 4.54/4.76 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(z), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.76 inference(monotonicity,[status(thm)],[22342])).
% 4.54/4.76 tff(22392,plain,
% 4.54/4.76 ((s(s(s(s(s(s(s(z))))))) = s(z)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 4.54/4.76 inference(monotonicity,[status(thm)],[22341])).
% 4.54/4.76 tff(22393,plain,
% 4.54/4.76 ((s(s(s(s(s(s(s(z))))))) = s(z)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.54/4.76 inference(transitivity,[status(thm)],[22392, 377])).
% 4.54/4.76 tff(22394,plain,
% 4.54/4.76 ((~(s(s(s(s(s(s(s(z))))))) = s(z))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 4.54/4.76 inference(monotonicity,[status(thm)],[22393])).
% 4.54/4.76 tff(22395,plain,
% 4.54/4.76 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.54/4.76 inference(modus_ponens,[status(thm)],[612, 22394])).
% 4.54/4.76 tff(22396,plain,
% 4.54/4.76 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(z, s(s(s(s(s(s(s(z))))))))),
% 4.54/4.76 inference(monotonicity,[status(thm)],[22339])).
% 4.54/4.76 tff(22397,plain,
% 4.54/4.76 (r(z, s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.54/4.76 inference(symmetry,[status(thm)],[22396])).
% 4.54/4.76 tff(22398,plain,
% 4.54/4.76 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.54/4.76 inference(modus_ponens,[status(thm)],[22001, 22397])).
% 4.54/4.76 tff(22399,plain,
% 4.54/4.76 (b(s(elem!1), s(s(z)))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[421, 10931, 1056])).
% 4.54/4.76 tff(22400,plain,
% 4.54/4.76 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[12552, 22399, 86])).
% 4.54/4.76 tff(22401,plain,
% 4.54/4.76 (~r(z, s(elem!1))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[6201, 10934, 928])).
% 4.54/4.76 tff(22402,plain,
% 4.54/4.76 (b(z, s(elem!1))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[2351, 22401])).
% 4.54/4.76 tff(22403,plain,
% 4.54/4.76 (~b(s(elem!1), s(s(s(s(z)))))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[11770, 178, 855, 853, 1687, 168])).
% 4.54/4.76 tff(22404,plain,
% 4.54/4.76 (r(s(elem!1), s(s(s(s(z)))))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[1084, 22403, 1369])).
% 4.54/4.76 tff(22405,plain,
% 4.54/4.76 (~r(s(elem!1), s(s(z)))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[3949, 22404, 193])).
% 4.54/4.76 tff(22406,plain,
% 4.54/4.76 (b(s(elem!1), s(s(z)))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[421, 22405, 1056])).
% 4.54/4.76 tff(22407,plain,
% 4.54/4.76 (~b(s(s(z)), s(elem!1))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[2776, 22406, 273, 855, 853])).
% 4.54/4.76 tff(22408,plain,
% 4.54/4.76 (r(s(s(z)), s(elem!1))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[1067, 22407, 2311])).
% 4.54/4.76 tff(22409,plain,
% 4.54/4.76 (~r(s(s(z)), s(s(s(s(z)))))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[5758, 22408, 22404])).
% 4.54/4.76 tff(22410,plain,
% 4.54/4.76 (b(s(s(z)), s(s(s(s(z)))))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[164, 22409])).
% 4.54/4.76 tff(22411,plain,
% 4.54/4.76 ($false),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[9606, 178, 853, 273, 22406, 1687, 22410])).
% 4.54/4.76 tff(22412,plain,((~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(z, s(elem!1))) | (s(elem!1) = s(s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (s(elem!1) = s(s(s(s(z))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.76 tff(22413,plain,
% 4.54/4.76 ($false),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[22412, 22402, 22400, 1687, 273, 1056, 103, 853, 168])).
% 4.54/4.76 tff(22414,plain,((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (s(elem!1) = s(s(z))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | b(s(s(s(s(z)))), s(s(z))) | (~(elem!1 = z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.76 tff(22415,plain,
% 4.54/4.76 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[22414, 22389, 273, 1687, 22384, 21691, 21699, 22339, 22398, 287])).
% 4.54/4.76 tff(22416,plain,
% 4.54/4.76 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[395, 22415, 22395])).
% 4.54/4.76 tff(22417,plain,
% 4.54/4.76 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.76 inference(modus_ponens,[status(thm)],[22416, 22391])).
% 4.54/4.76 tff(22418,plain,
% 4.54/4.76 (~b(s(s(s(s(z)))), s(s(z)))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[21680, 178, 21546, 273, 1687, 168])).
% 4.54/4.76 tff(22419,plain,
% 4.54/4.76 (r(s(s(s(s(z)))), s(s(z)))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[102, 22418])).
% 4.54/4.76 tff(22420,plain,
% 4.54/4.76 (~b(z, s(elem!1))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[22412, 1369, 1687, 273, 1056, 22419, 853, 168])).
% 4.54/4.76 tff(22421,plain,
% 4.54/4.76 (r(z, s(elem!1))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[2351, 22420])).
% 4.54/4.76 tff(22422,plain,
% 4.54/4.76 (~r(s(s(s(elem!1))), s(elem!1))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[5447, 22421, 557])).
% 4.54/4.76 tff(22423,plain,
% 4.54/4.76 (b(s(s(s(elem!1))), s(elem!1))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[373, 22422, 12049])).
% 4.54/4.76 tff(22424,plain,
% 4.54/4.76 (b(s(s(s(z))), s(z))),
% 4.54/4.76 inference(modus_ponens,[status(thm)],[22423, 12043])).
% 4.54/4.76 tff(22425,plain,
% 4.54/4.76 (~b(s(s(z)), s(s(s(s(z)))))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[21653, 168, 273, 1687, 21546])).
% 4.54/4.76 tff(22426,plain,
% 4.54/4.76 (r(s(s(z)), s(s(s(s(z)))))),
% 4.54/4.76 inference(unit_resolution,[status(thm)],[164, 22425])).
% 4.54/4.76 tff(22427,plain,
% 4.54/4.76 (~r(s(elem!1), s(s(s(s(z)))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[6776, 853, 273, 1056, 22426, 21546])).
% 4.54/4.77 tff(22428,plain,
% 4.54/4.77 (b(s(elem!1), s(s(s(s(z)))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[1084, 1369, 22427])).
% 4.54/4.77 tff(22429,plain,
% 4.54/4.77 (b(s(z), s(s(s(s(z)))))),
% 4.54/4.77 inference(modus_ponens,[status(thm)],[22428, 14888])).
% 4.54/4.77 tff(22430,plain,
% 4.54/4.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))))),
% 4.54/4.77 inference(rewrite,[status(thm)],[])).
% 4.54/4.77 tff(22431,plain,
% 4.54/4.77 (((~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(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))))),
% 4.54/4.77 inference(rewrite,[status(thm)],[])).
% 4.54/4.77 tff(22432,plain,
% 4.54/4.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z)))))),
% 4.54/4.77 inference(monotonicity,[status(thm)],[22431])).
% 4.54/4.77 tff(22433,plain,
% 4.54/4.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))))),
% 4.54/4.77 inference(transitivity,[status(thm)],[22432, 22430])).
% 4.54/4.77 tff(22434,plain,
% 4.54/4.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))))),
% 4.54/4.77 inference(quant_inst,[status(thm)],[])).
% 4.54/4.77 tff(22435,plain,
% 4.54/4.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z)))),
% 4.54/4.77 inference(modus_ponens,[status(thm)],[22434, 22433])).
% 4.54/4.77 tff(22436,plain,
% 4.54/4.77 ($false),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[22435, 178, 104, 22429, 3002, 4669, 22424])).
% 4.54/4.77 tff(22437,plain,((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(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = z)) | (~r(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (s(elem!1) = s(s(z))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.77 tff(22438,plain,
% 4.54/4.77 (s(elem!1) = s(s(s(s(z))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[22437, 22417, 3002, 104, 22339, 22390, 1687, 273, 22389, 22384, 21691])).
% 4.54/4.77 tff(22439,plain,
% 4.54/4.77 (s(s(s(s(z)))) = s(elem!1)),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[13963, 22438])).
% 4.54/4.77 tff(22440,plain,
% 4.54/4.77 (s(elem!1) = s(s(s(s(elem!1))))),
% 4.54/4.77 inference(modus_ponens,[status(thm)],[22439, 22348])).
% 4.54/4.77 tff(22441,plain,
% 4.54/4.77 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = z)),
% 4.54/4.77 inference(monotonicity,[status(thm)],[22339])).
% 4.54/4.77 tff(22442,plain,
% 4.54/4.77 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 4.54/4.77 inference(symmetry,[status(thm)],[22441])).
% 4.54/4.77 tff(22443,plain,
% 4.54/4.77 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 4.54/4.77 inference(monotonicity,[status(thm)],[22442])).
% 4.54/4.77 tff(22444,plain,
% 4.54/4.77 (~(s(s(s(elem!1))) = elem!1)),
% 4.54/4.77 inference(modus_ponens,[status(thm)],[940, 22443])).
% 4.54/4.77 tff(22445,plain,
% 4.54/4.77 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[951, 22444])).
% 4.54/4.77 tff(22446,plain,
% 4.54/4.77 ($false),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[22445, 22440])).
% 4.54/4.77 tff(22447,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | b(s(s(z)), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.77 tff(22448,plain,
% 4.54/4.77 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[22447, 3002, 104, 1687, 273, 107, 286])).
% 4.54/4.77 tff(22449,plain,
% 4.54/4.77 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[10755, 22448])).
% 4.54/4.77 tff(22450,plain,
% 4.54/4.77 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[8227, 178, 104, 21695, 22449, 3002])).
% 4.54/4.77 tff(22451,plain,
% 4.54/4.77 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 22450])).
% 4.54/4.77 tff(22452,plain,
% 4.54/4.77 (~r(s(s(s(z))), z)),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[20758, 22451, 21698])).
% 4.54/4.77 tff(22453,plain,
% 4.54/4.77 (b(s(s(s(z))), z)),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[21073, 22452])).
% 4.54/4.77 tff(22454,plain,
% 4.54/4.77 ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[21606, 178, 21546, 104, 1687, 22449, 3002])).
% 4.54/4.77 tff(22455,plain,
% 4.54/4.77 (~b(s(s(z)), s(s(s(z))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[22454, 22453])).
% 4.54/4.77 tff(22456,plain,
% 4.54/4.77 (r(s(s(z)), s(s(s(z))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[5088, 22455])).
% 4.54/4.77 tff(22457,plain,
% 4.54/4.77 ($false),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[16016, 118, 22456, 107, 22451])).
% 4.54/4.77 tff(22458,plain,((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | b(s(s(z)), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.77 tff(22459,plain,
% 4.54/4.77 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[22458, 21568, 104, 1687, 273, 286])).
% 4.54/4.77 tff(22460,plain,
% 4.54/4.77 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[3578, 22459])).
% 4.54/4.77 tff(22461,plain,
% 4.54/4.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.54/4.77 inference(rewrite,[status(thm)],[])).
% 4.54/4.77 tff(22462,plain,
% 4.54/4.77 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(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(s(z))), 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))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.54/4.77 inference(rewrite,[status(thm)],[])).
% 4.54/4.77 tff(22463,plain,
% 4.54/4.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(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(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))))),
% 4.54/4.77 inference(monotonicity,[status(thm)],[22462])).
% 4.54/4.77 tff(22464,plain,
% 4.54/4.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(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(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.54/4.77 inference(transitivity,[status(thm)],[22463, 22461])).
% 4.54/4.77 tff(22465,plain,
% 4.54/4.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(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(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.54/4.77 inference(quant_inst,[status(thm)],[])).
% 4.54/4.77 tff(22466,plain,
% 4.54/4.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 4.54/4.77 inference(modus_ponens,[status(thm)],[22465, 22464])).
% 4.54/4.77 tff(22467,plain,
% 4.54/4.77 ($false),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[22466, 178, 21674, 21684, 22460, 21568, 21689])).
% 4.54/4.77 tff(22468,plain,(b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.77 tff(22469,plain,
% 4.54/4.77 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[22468, 144, 21306, 104])).
% 4.54/4.77 tff(22470,plain,
% 4.54/4.77 (~r(s(s(z)), z)),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[21544, 144, 104, 21306])).
% 4.54/4.77 tff(22471,plain,
% 4.54/4.77 (b(s(s(z)), z)),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[3249, 22470])).
% 4.54/4.77 tff(22472,plain,
% 4.54/4.77 ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[11879, 178, 22471, 104, 21306])).
% 4.54/4.77 tff(22473,plain,
% 4.54/4.77 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[22472, 22469])).
% 4.54/4.77 tff(22474,plain,
% 4.54/4.77 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[133, 22473])).
% 4.54/4.77 tff(22475,plain,
% 4.54/4.77 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[22468, 273, 1687, 104])).
% 4.54/4.77 tff(22476,plain,
% 4.54/4.77 ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[11879, 178, 21546, 104, 1687])).
% 4.54/4.77 tff(22477,plain,
% 4.54/4.77 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[22476, 22475])).
% 4.54/4.77 tff(22478,plain,
% 4.54/4.77 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[133, 22477])).
% 4.54/4.77 tff(22479,plain,
% 4.54/4.77 (~b(s(s(s(s(z)))), z)),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[21653, 167, 273, 1687, 3461])).
% 4.54/4.77 tff(22480,plain,
% 4.54/4.77 (r(s(s(s(s(z)))), z)),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[191, 22479])).
% 4.54/4.77 tff(22481,plain,
% 4.54/4.77 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[14923, 118, 22480, 108])).
% 4.54/4.77 tff(22482,plain,
% 4.54/4.77 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[222, 22481])).
% 4.54/4.77 tff(22483,plain,
% 4.54/4.77 ($false),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[21487, 178, 273, 1687, 166, 167, 22482])).
% 4.54/4.77 tff(22484,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.77 tff(22485,plain,
% 4.54/4.77 (~b(s(s(z)), s(s(s(s(z)))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[22484, 273, 1687, 22475, 22478, 21546])).
% 4.54/4.77 tff(22486,plain,
% 4.54/4.77 (r(s(s(z)), s(s(s(s(z)))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[164, 22485])).
% 4.54/4.77 tff(22487,plain,
% 4.54/4.77 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[12281, 178, 21546, 104, 1687, 22475])).
% 4.54/4.77 tff(22488,plain,
% 4.54/4.77 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[271, 22487])).
% 4.54/4.77 tff(22489,plain,
% 4.54/4.77 (~r(s(s(s(s(z)))), z)),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[21331, 118, 204, 22488])).
% 4.54/4.77 tff(22490,plain,
% 4.54/4.77 (b(s(s(s(s(z)))), z)),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[191, 22489])).
% 4.54/4.77 tff(22491,plain,
% 4.54/4.77 (~b(s(s(s(s(z)))), s(s(z)))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[21680, 178, 21546, 273, 1687, 22490])).
% 4.54/4.77 tff(22492,plain,
% 4.54/4.77 (r(s(s(s(s(z)))), s(s(z)))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[102, 22491])).
% 4.54/4.77 tff(22493,plain,
% 4.54/4.77 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[21528, 22492, 273, 22488, 22486, 22490, 1687])).
% 4.54/4.77 tff(22494,plain,
% 4.54/4.77 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[20667, 22493])).
% 4.54/4.77 tff(22495,plain,
% 4.54/4.77 (~b(s(s(s(z))), z)),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[21425, 1126, 104, 1687, 166, 147, 168, 3002])).
% 4.54/4.77 tff(22496,plain,
% 4.54/4.77 (r(s(s(s(z))), z)),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[21073, 22495])).
% 4.54/4.77 tff(22497,plain,
% 4.54/4.77 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[20758, 22496, 108])).
% 4.54/4.77 tff(22498,plain,
% 4.54/4.77 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 22497])).
% 4.54/4.77 tff(22499,plain,
% 4.54/4.77 ($false),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[8278, 178, 104, 1126, 6170, 3002, 21855])).
% 4.54/4.77 tff(22500,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.77 tff(22501,plain,
% 4.54/4.77 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[22500, 1126, 104, 3002, 22498])).
% 4.54/4.77 tff(22502,plain,
% 4.54/4.77 (r(s(s(s(s(z)))), s(s(s(z))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[11185, 22501])).
% 4.54/4.77 tff(22503,plain,
% 4.54/4.77 ($false),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[17129, 118, 193, 22502, 21421])).
% 4.54/4.77 tff(22504,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.77 tff(22505,plain,
% 4.54/4.77 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[22504, 22492, 104, 22494, 22475, 22478, 1687, 22486, 22490])).
% 4.54/4.77 tff(22506,plain,
% 4.54/4.77 (r(s(s(s(z))), s(s(s(s(z)))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[10755, 22505])).
% 4.54/4.77 tff(22507,plain,
% 4.54/4.77 (~b(s(s(z)), s(s(s(z))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[21439, 21589, 166, 1146, 3002])).
% 4.54/4.77 tff(22508,plain,
% 4.54/4.77 (r(s(s(z)), s(s(s(z))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[5088, 22507])).
% 4.54/4.77 tff(22509,plain,
% 4.54/4.77 ($false),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[5079, 118, 147, 22508, 4891])).
% 4.54/4.77 tff(22510,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.77 tff(22511,plain,
% 4.54/4.77 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[22510, 22506, 22475, 22492, 22494, 22486])).
% 4.54/4.77 tff(22512,plain,
% 4.54/4.77 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[3578, 22511])).
% 4.54/4.77 tff(22513,plain,
% 4.54/4.77 ($false),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[3920, 118, 204, 22492, 22512])).
% 4.54/4.77 tff(22514,plain,((~r(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(z, s(s(s(s(z)))))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.77 tff(22515,plain,
% 4.54/4.77 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[22514, 21306, 104, 144])).
% 4.54/4.77 tff(22516,plain,
% 4.54/4.77 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[222, 22515])).
% 4.54/4.77 tff(22517,plain,
% 4.54/4.77 (~b(s(s(z)), s(s(s(s(z)))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[22484, 144, 21306, 22469, 22474, 22471])).
% 4.54/4.77 tff(22518,plain,
% 4.54/4.77 (r(s(s(z)), s(s(s(s(z)))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[164, 22517])).
% 4.54/4.77 tff(22519,plain,
% 4.54/4.77 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[12281, 178, 22471, 104, 21306, 22469])).
% 4.54/4.77 tff(22520,plain,
% 4.54/4.77 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[271, 22519])).
% 4.54/4.77 tff(22521,plain,
% 4.54/4.77 (~b(s(s(s(s(z)))), s(s(z)))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[21497, 178, 144, 21306, 22469, 22516])).
% 4.54/4.77 tff(22522,plain,
% 4.54/4.77 (r(s(s(s(s(z)))), s(s(z)))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[102, 22521])).
% 4.54/4.77 tff(22523,plain,
% 4.54/4.77 (~b(s(s(s(z))), s(s(z)))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[20992, 21512, 273, 3461, 21503])).
% 4.54/4.77 tff(22524,plain,
% 4.54/4.77 (r(s(s(s(z))), s(s(z)))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[4966, 22523])).
% 4.54/4.77 tff(22525,plain,
% 4.54/4.77 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[8696, 118, 193, 22524])).
% 4.54/4.77 tff(22526,plain,
% 4.54/4.77 (b(s(s(s(s(z)))), s(s(s(z))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[11185, 22525])).
% 4.54/4.77 tff(22527,plain,
% 4.54/4.77 (~b(s(s(s(s(z)))), z)),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[21528, 8216, 273, 203, 147, 193, 1687])).
% 4.54/4.77 tff(22528,plain,
% 4.54/4.77 (r(s(s(s(s(z)))), z)),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[191, 22527])).
% 4.54/4.77 tff(22529,plain,
% 4.54/4.77 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[21594, 22528, 3461, 273, 147, 193])).
% 4.54/4.77 tff(22530,plain,
% 4.54/4.77 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[10755, 22529])).
% 4.54/4.77 tff(22531,plain,
% 4.54/4.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 4.54/4.77 inference(rewrite,[status(thm)],[])).
% 4.54/4.77 tff(22532,plain,
% 4.54/4.77 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 4.54/4.77 inference(rewrite,[status(thm)],[])).
% 4.54/4.77 tff(22533,plain,
% 4.54/4.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 4.54/4.77 inference(monotonicity,[status(thm)],[22532])).
% 4.54/4.77 tff(22534,plain,
% 4.54/4.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 4.54/4.77 inference(transitivity,[status(thm)],[22533, 22531])).
% 4.54/4.77 tff(22535,plain,
% 4.54/4.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 4.54/4.77 inference(quant_inst,[status(thm)],[])).
% 4.54/4.77 tff(22536,plain,
% 4.54/4.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 4.54/4.77 inference(modus_ponens,[status(thm)],[22535, 22534])).
% 4.54/4.77 tff(22537,plain,
% 4.54/4.77 ($false),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[22536, 178, 1687, 22530, 21512, 22526, 21504])).
% 4.54/4.77 tff(22538,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.77 tff(22539,plain,
% 4.54/4.77 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[22538, 21306, 22522, 144, 22471, 22520, 22518])).
% 4.54/4.77 tff(22540,plain,
% 4.54/4.77 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[20667, 22539])).
% 4.54/4.77 tff(22541,plain,
% 4.54/4.77 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[21670, 22540, 21306, 22474, 22516, 104])).
% 4.54/4.77 tff(22542,plain,
% 4.54/4.77 (r(s(s(s(z))), s(s(s(s(z)))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[10755, 22541])).
% 4.54/4.77 tff(22543,plain,
% 4.54/4.77 (~r(s(s(z)), s(s(s(z))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[5079, 118, 22518, 22542])).
% 4.54/4.77 tff(22544,plain,
% 4.54/4.77 (b(s(s(z)), s(s(s(z))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[5088, 22543])).
% 4.54/4.77 tff(22545,plain,
% 4.54/4.77 (~r(s(s(s(z))), s(s(z)))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[20838, 22542, 22522])).
% 4.54/4.77 tff(22546,plain,
% 4.54/4.77 (b(s(s(s(z))), s(s(z)))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[4966, 22545])).
% 4.54/4.77 tff(22547,plain,
% 4.54/4.77 ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[11284, 178, 22471, 144, 22546])).
% 4.54/4.77 tff(22548,plain,
% 4.54/4.77 (~b(s(s(s(z))), z)),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[22547, 22544])).
% 4.54/4.77 tff(22549,plain,
% 4.54/4.77 (r(s(s(s(z))), z)),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[21073, 22548])).
% 4.54/4.77 tff(22550,plain,
% 4.54/4.77 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[20758, 22549, 22474])).
% 4.54/4.77 tff(22551,plain,
% 4.54/4.77 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.54/4.77 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 22550])).
% 4.54/4.78 tff(22552,plain,
% 4.54/4.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.54/4.78 inference(rewrite,[status(thm)],[])).
% 4.54/4.78 tff(22553,plain,
% 4.54/4.78 (((~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(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.54/4.78 inference(rewrite,[status(thm)],[])).
% 4.54/4.78 tff(22554,plain,
% 4.54/4.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))))),
% 4.54/4.78 inference(monotonicity,[status(thm)],[22553])).
% 4.54/4.78 tff(22555,plain,
% 4.54/4.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.54/4.78 inference(transitivity,[status(thm)],[22554, 22552])).
% 4.54/4.78 tff(22556,plain,
% 4.54/4.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.54/4.78 inference(quant_inst,[status(thm)],[])).
% 4.54/4.78 tff(22557,plain,
% 4.54/4.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 4.54/4.78 inference(modus_ponens,[status(thm)],[22556, 22555])).
% 4.54/4.78 tff(22558,plain,
% 4.54/4.78 ($false),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[22557, 178, 22469, 22544, 22546, 22540, 22551])).
% 4.54/4.78 tff(22559,plain,(r(z, s(s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.78 tff(22560,plain,
% 4.54/4.78 (r(z, s(s(z)))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[22559, 104])).
% 4.54/4.78 tff(22561,plain,
% 4.54/4.78 (~r(s(s(s(s(z)))), z)),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[9569, 103, 22560])).
% 4.54/4.78 tff(22562,plain,
% 4.54/4.78 (b(s(s(s(s(z)))), z)),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[191, 22561])).
% 4.54/4.78 tff(22563,plain,
% 4.54/4.78 (~r(s(s(z)), s(s(s(s(z)))))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[3478, 47, 22560])).
% 4.54/4.78 tff(22564,plain,
% 4.54/4.78 (b(s(s(z)), s(s(s(s(z)))))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[164, 22563])).
% 4.54/4.78 tff(22565,plain,
% 4.54/4.78 (~r(s(s(s(s(z)))), s(s(z)))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[3269, 47, 22560])).
% 4.54/4.78 tff(22566,plain,
% 4.54/4.78 (b(s(s(s(s(z)))), s(s(z)))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[102, 22565])).
% 4.54/4.78 tff(22567,plain,
% 4.54/4.78 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[8067, 22566, 22560, 104, 47])).
% 4.54/4.78 tff(22568,plain,
% 4.54/4.78 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[271, 22567])).
% 4.54/4.78 tff(22569,plain,
% 4.54/4.78 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[21408, 204, 8216])).
% 4.54/4.78 tff(22570,plain,
% 4.54/4.78 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[10755, 22569])).
% 4.54/4.78 tff(22571,plain,
% 4.54/4.78 ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[4944, 178, 167, 202, 22570])).
% 4.54/4.78 tff(22572,plain,
% 4.54/4.78 (~b(s(s(s(z))), s(s(z)))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[22571, 17894])).
% 4.54/4.78 tff(22573,plain,
% 4.54/4.78 (r(s(s(s(z))), s(s(z)))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[4966, 22572])).
% 4.54/4.78 tff(22574,plain,
% 4.54/4.78 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[8218, 22573, 8216])).
% 4.54/4.78 tff(22575,plain,
% 4.54/4.78 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[3578, 22574])).
% 4.54/4.78 tff(22576,plain,
% 4.54/4.78 (~r(z, s(s(s(z))))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[10452, 118, 22560, 22573])).
% 4.54/4.78 tff(22577,plain,
% 4.54/4.78 (b(z, s(s(s(z))))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[4920, 22576])).
% 4.54/4.78 tff(22578,plain,
% 4.54/4.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(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(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(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(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 4.54/4.78 inference(rewrite,[status(thm)],[])).
% 4.54/4.78 tff(22579,plain,
% 4.54/4.78 (((~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(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(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(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 4.54/4.78 inference(rewrite,[status(thm)],[])).
% 4.54/4.78 tff(22580,plain,
% 4.54/4.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(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(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(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(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))))),
% 4.54/4.78 inference(monotonicity,[status(thm)],[22579])).
% 4.54/4.78 tff(22581,plain,
% 4.54/4.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(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(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(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(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 4.54/4.78 inference(transitivity,[status(thm)],[22580, 22578])).
% 4.54/4.78 tff(22582,plain,
% 4.54/4.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(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(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 4.54/4.78 inference(quant_inst,[status(thm)],[])).
% 4.54/4.78 tff(22583,plain,
% 4.54/4.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 4.54/4.78 inference(modus_ponens,[status(thm)],[22582, 22581])).
% 4.54/4.78 tff(22584,plain,
% 4.54/4.78 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[22583, 178, 104, 167, 595, 22570, 22577, 22575])).
% 4.54/4.78 tff(22585,plain,
% 4.54/4.78 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 22584])).
% 4.54/4.78 tff(22586,plain,
% 4.54/4.78 (~b(s(s(z)), s(s(s(z))))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[1293, 178, 167, 202, 22570, 17894])).
% 4.54/4.78 tff(22587,plain,
% 4.54/4.78 (r(s(s(z)), s(s(s(z))))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[5088, 22586])).
% 4.54/4.78 tff(22588,plain,
% 4.54/4.78 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[16621, 118, 22587, 22585])).
% 4.54/4.78 tff(22589,plain,
% 4.54/4.78 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[249, 22588])).
% 4.54/4.78 tff(22590,plain,
% 4.54/4.78 ($false),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[1259, 178, 104, 22589, 167, 202, 22575])).
% 4.54/4.78 tff(22591,plain,((~r(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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.78 tff(22592,plain,
% 4.54/4.78 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[22591, 8216, 22564, 22566, 22568, 104])).
% 4.54/4.78 tff(22593,plain,
% 4.54/4.78 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[222, 22592])).
% 4.54/4.78 tff(22594,plain,
% 4.54/4.78 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[259, 22593, 104, 22566, 22564])).
% 4.54/4.78 tff(22595,plain,
% 4.54/4.78 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[249, 22594])).
% 4.54/4.78 tff(22596,plain,
% 4.54/4.78 (~r(s(s(z)), s(s(s(z))))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[10533, 118, 22595, 8216])).
% 4.54/4.78 tff(22597,plain,
% 4.54/4.78 (b(s(s(z)), s(s(s(z))))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[5088, 22596])).
% 4.54/4.78 tff(22598,plain,
% 4.54/4.78 ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[8089, 178, 104, 22564, 22566])).
% 4.54/4.78 tff(22599,plain,
% 4.54/4.78 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[22598, 22593])).
% 4.54/4.78 tff(22600,plain,
% 4.54/4.78 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[3578, 22599])).
% 4.54/4.78 tff(22601,plain,
% 4.54/4.78 (~r(s(s(s(z))), s(s(z)))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[8218, 22600, 8216])).
% 4.54/4.78 tff(22602,plain,
% 4.54/4.78 (b(s(s(s(z))), s(s(z)))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[4966, 22601])).
% 4.54/4.78 tff(22603,plain,
% 4.54/4.78 ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[5253, 178, 22564, 22566, 22602])).
% 4.54/4.78 tff(22604,plain,
% 4.54/4.78 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[22603, 22597])).
% 4.54/4.78 tff(22605,plain,
% 4.54/4.78 (r(s(s(s(z))), s(s(s(s(z)))))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[10755, 22604])).
% 4.54/4.78 tff(22606,plain,
% 4.54/4.78 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[3102, 22595, 106])).
% 4.54/4.78 tff(22607,plain,
% 4.54/4.78 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[133, 22606])).
% 4.54/4.78 tff(22608,plain,
% 4.54/4.78 (~b(s(s(s(s(z)))), z)),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[10705, 178, 104, 22593, 22568, 22607])).
% 4.54/4.78 tff(22609,plain,
% 4.54/4.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.54/4.78 inference(rewrite,[status(thm)],[])).
% 4.54/4.78 tff(22610,plain,
% 4.54/4.78 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(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(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.54/4.78 inference(rewrite,[status(thm)],[])).
% 4.54/4.78 tff(22611,plain,
% 4.54/4.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))))),
% 4.54/4.78 inference(monotonicity,[status(thm)],[22610])).
% 4.54/4.78 tff(22612,plain,
% 4.54/4.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.54/4.78 inference(transitivity,[status(thm)],[22611, 22609])).
% 4.54/4.78 tff(22613,plain,
% 4.54/4.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 4.54/4.78 inference(quant_inst,[status(thm)],[])).
% 4.54/4.78 tff(22614,plain,
% 4.54/4.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 4.54/4.78 inference(modus_ponens,[status(thm)],[22613, 22612])).
% 4.54/4.78 tff(22615,plain,
% 4.54/4.78 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[22614, 178, 22564, 22566, 22597, 22602])).
% 4.54/4.78 tff(22616,plain,
% 4.54/4.78 (r(s(s(s(s(z)))), s(s(s(z))))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[11185, 22615])).
% 4.54/4.78 tff(22617,plain,
% 4.54/4.78 (b(z, s(s(s(z)))) <=> b(z, s(s(s(elem!1))))),
% 4.54/4.78 inference(symmetry,[status(thm)],[20676])).
% 4.54/4.78 tff(22618,plain,
% 4.54/4.78 (~r(z, s(s(s(z))))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[4910, 118, 47, 4891])).
% 4.54/4.78 tff(22619,plain,
% 4.54/4.78 (b(z, s(s(s(z))))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[4920, 22618])).
% 4.54/4.78 tff(22620,plain,
% 4.54/4.78 (b(z, s(s(s(elem!1))))),
% 4.54/4.78 inference(modus_ponens,[status(thm)],[22619, 22617])).
% 4.54/4.78 tff(22621,plain,
% 4.54/4.78 (~(s(elem!1) = s(s(z)))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[17598, 22620, 1])).
% 4.54/4.78 tff(22622,plain,
% 4.54/4.78 ((~r(s(elem!1), elem!1)) <=> (~r(s(elem!1), z))),
% 4.54/4.78 inference(monotonicity,[status(thm)],[12732])).
% 4.54/4.78 tff(22623,plain,
% 4.54/4.78 (r(s(s(s(s(z)))), elem!1)),
% 4.54/4.78 inference(modus_ponens,[status(thm)],[3244, 20852])).
% 4.54/4.78 tff(22624,plain,
% 4.54/4.78 (~r(s(s(z)), s(s(s(s(z)))))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[3478, 47, 3261])).
% 4.54/4.78 tff(22625,plain,
% 4.54/4.78 (b(s(s(z)), s(s(s(s(z)))))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[164, 22624])).
% 4.54/4.78 tff(22626,plain,
% 4.54/4.78 (~r(s(s(s(s(z)))), s(s(z)))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[3269, 47, 3261])).
% 4.54/4.78 tff(22627,plain,
% 4.54/4.78 (b(s(s(s(s(z)))), s(s(z)))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[102, 22626])).
% 4.54/4.78 tff(22628,plain,
% 4.54/4.78 (r(s(elem!1), z)),
% 4.54/4.78 inference(modus_ponens,[status(thm)],[1426, 12732])).
% 4.54/4.78 tff(22629,plain,
% 4.54/4.78 (~r(s(elem!1), s(s(s(s(z)))))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[7010, 1426, 3132])).
% 4.54/4.78 tff(22630,plain,
% 4.54/4.78 (~r(s(elem!1), s(s(z)))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[2249, 1426, 10721])).
% 4.54/4.78 tff(22631,plain,
% 4.54/4.78 (~r(s(elem!1), z)),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[1038, 22630, 106, 928, 202, 22629, 167])).
% 4.54/4.78 tff(22632,plain,
% 4.54/4.78 ($false),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[22631, 22628])).
% 4.54/4.78 tff(22633,plain,((~r(s(elem!1), elem!1)) | (~(elem!1 = z)) | (~r(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.78 tff(22634,plain,
% 4.54/4.78 (~r(s(elem!1), elem!1)),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[22633, 928, 106, 22627, 22625, 22623])).
% 4.54/4.78 tff(22635,plain,
% 4.54/4.78 (~r(s(elem!1), z)),
% 4.54/4.78 inference(modus_ponens,[status(thm)],[22634, 22622])).
% 4.54/4.78 tff(22636,plain,
% 4.54/4.78 (b(s(elem!1), elem!1)),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[677, 22634, 20662])).
% 4.54/4.78 tff(22637,plain,
% 4.54/4.78 ((~r(z, s(s(s(z))))) <=> (~r(elem!1, s(s(s(elem!1)))))),
% 4.54/4.78 inference(monotonicity,[status(thm)],[10724])).
% 4.54/4.78 tff(22638,plain,
% 4.54/4.78 (~r(elem!1, s(s(s(elem!1))))),
% 4.54/4.78 inference(modus_ponens,[status(thm)],[22618, 22637])).
% 4.54/4.78 tff(22639,plain,
% 4.54/4.78 (b(s(s(s(elem!1))), z) <=> b(s(s(s(z))), z)),
% 4.54/4.78 inference(monotonicity,[status(thm)],[931])).
% 4.54/4.78 tff(22640,plain,
% 4.54/4.78 (b(s(s(s(z))), z) <=> b(s(s(s(elem!1))), z)),
% 4.54/4.78 inference(symmetry,[status(thm)],[22639])).
% 4.54/4.78 tff(22641,plain,
% 4.54/4.78 (~r(s(s(s(z))), z)),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[20797, 4891, 47])).
% 4.54/4.78 tff(22642,plain,
% 4.54/4.78 (b(s(s(s(z))), z)),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[21073, 22641])).
% 4.54/4.78 tff(22643,plain,
% 4.54/4.78 (b(s(s(s(elem!1))), z)),
% 4.54/4.78 inference(modus_ponens,[status(thm)],[22642, 22640])).
% 4.54/4.78 tff(22644,plain,
% 4.54/4.78 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 4.54/4.78 inference(monotonicity,[status(thm)],[931])).
% 4.54/4.78 tff(22645,plain,
% 4.54/4.78 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.54/4.78 inference(symmetry,[status(thm)],[22644])).
% 4.54/4.78 tff(22646,plain,
% 4.54/4.78 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.54/4.78 inference(modus_ponens,[status(thm)],[4953, 22645])).
% 4.54/4.78 tff(22647,plain,
% 4.54/4.78 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.54/4.78 inference(modus_ponens,[status(thm)],[4891, 20805])).
% 4.54/4.78 tff(22648,plain,
% 4.54/4.78 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(s(s(s(z))))))), z)),
% 4.54/4.78 inference(monotonicity,[status(thm)],[1120])).
% 4.54/4.78 tff(22649,plain,
% 4.54/4.78 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.54/4.78 inference(modus_ponens,[status(thm)],[3988, 22648])).
% 4.54/4.78 tff(22650,plain,
% 4.54/4.78 ($false),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[126, 22649])).
% 4.54/4.78 tff(22651,plain,((~r(s(s(s(s(elem!1)))), z)) | r(s(s(s(s(s(s(s(z))))))), z) | (~(s(elem!1) = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.78 tff(22652,plain,
% 4.54/4.78 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[22651, 15305, 17329])).
% 4.54/4.78 tff(22653,plain,
% 4.54/4.78 (b(s(z), s(s(z))) <=> b(s(elem!1), s(s(z)))),
% 4.54/4.78 inference(symmetry,[status(thm)],[14161])).
% 4.54/4.78 tff(22654,plain,
% 4.54/4.78 ((~b(s(z), s(s(z)))) <=> (~b(s(elem!1), s(s(z))))),
% 4.54/4.78 inference(monotonicity,[status(thm)],[22653])).
% 4.54/4.78 tff(22655,plain,
% 4.54/4.78 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(z))), s(z))),
% 4.54/4.78 inference(monotonicity,[status(thm)],[931, 929])).
% 4.54/4.78 tff(22656,plain,
% 4.54/4.78 (b(elem!1, s(elem!1))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[12054, 855, 928])).
% 4.54/4.78 tff(22657,plain,
% 4.54/4.78 (~b(s(s(s(elem!1))), s(elem!1))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[10046, 22656, 2043, 7976, 4512, 683, 767])).
% 4.54/4.78 tff(22658,plain,
% 4.54/4.78 (r(s(s(s(elem!1))), s(elem!1))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[373, 22657, 12049])).
% 4.54/4.78 tff(22659,plain,
% 4.54/4.78 (r(s(s(s(z))), s(z))),
% 4.54/4.78 inference(modus_ponens,[status(thm)],[22658, 22655])).
% 4.54/4.78 tff(22660,plain,
% 4.54/4.78 (r(s(s(s(z))), s(s(s(s(z)))))),
% 4.54/4.78 inference(modus_ponens,[status(thm)],[3251, 5213])).
% 4.54/4.78 tff(22661,assumption,(r(s(s(s(z))), s(z))), introduced(assumption)).
% 4.54/4.78 tff(22662,plain,
% 4.54/4.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 4.54/4.78 inference(rewrite,[status(thm)],[])).
% 4.54/4.78 tff(22663,plain,
% 4.54/4.78 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 4.54/4.78 inference(rewrite,[status(thm)],[])).
% 4.54/4.78 tff(22664,plain,
% 4.54/4.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 4.54/4.78 inference(monotonicity,[status(thm)],[22663])).
% 4.54/4.78 tff(22665,plain,
% 4.54/4.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 4.54/4.78 inference(transitivity,[status(thm)],[22664, 22662])).
% 4.54/4.78 tff(22666,plain,
% 4.54/4.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))),
% 4.54/4.78 inference(quant_inst,[status(thm)],[])).
% 4.54/4.78 tff(22667,plain,
% 4.54/4.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 4.54/4.78 inference(modus_ponens,[status(thm)],[22666, 22665])).
% 4.54/4.78 tff(22668,plain,
% 4.54/4.78 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[22667, 118, 4554, 22661])).
% 4.54/4.78 tff(22669,plain,
% 4.54/4.78 ($false),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[22668, 22660])).
% 4.54/4.78 tff(22670,plain,((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~(elem!1 = z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.78 tff(22671,plain,
% 4.54/4.78 (~r(s(z), s(s(s(s(z)))))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[22670, 22659, 3251, 928])).
% 4.54/4.78 tff(22672,plain,
% 4.54/4.78 (~r(s(elem!1), s(s(s(s(z)))))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[6689, 22671, 928])).
% 4.54/4.78 tff(22673,plain,
% 4.54/4.78 (b(s(elem!1), s(s(s(s(z)))))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[1084, 22672, 1369])).
% 4.54/4.78 tff(22674,plain,
% 4.54/4.78 (b(s(z), s(s(s(s(z)))))),
% 4.54/4.78 inference(modus_ponens,[status(thm)],[22673, 14888])).
% 4.54/4.78 tff(22675,plain,
% 4.54/4.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 4.54/4.78 inference(rewrite,[status(thm)],[])).
% 4.54/4.78 tff(22676,plain,
% 4.54/4.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 4.54/4.78 inference(quant_inst,[status(thm)],[])).
% 4.54/4.78 tff(22677,plain,
% 4.54/4.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 4.54/4.78 inference(modus_ponens,[status(thm)],[22676, 22675])).
% 4.54/4.78 tff(22678,plain,
% 4.54/4.78 ($false),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[22677, 118, 1551, 6400, 3279])).
% 4.54/4.78 tff(22679,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.78 tff(22680,plain,
% 4.54/4.78 (~r(s(s(s(s(z)))), s(elem!1))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[22679, 22658, 3279])).
% 4.54/4.78 tff(22681,plain,
% 4.54/4.78 (b(s(s(s(s(z)))), s(elem!1))),
% 4.54/4.78 inference(unit_resolution,[status(thm)],[2173, 22680, 2169])).
% 4.54/4.78 tff(22682,plain,
% 4.54/4.78 (b(s(s(s(s(z)))), s(z))),
% 4.54/4.78 inference(modus_ponens,[status(thm)],[22681, 12849])).
% 4.54/4.78 tff(22683,plain,
% 4.54/4.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 4.54/4.79 inference(rewrite,[status(thm)],[])).
% 4.54/4.79 tff(22684,plain,
% 4.54/4.79 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), 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)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 4.54/4.79 inference(rewrite,[status(thm)],[])).
% 4.54/4.79 tff(22685,plain,
% 4.54/4.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(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(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))))),
% 4.54/4.79 inference(monotonicity,[status(thm)],[22684])).
% 4.54/4.79 tff(22686,plain,
% 4.54/4.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(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(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 4.54/4.79 inference(transitivity,[status(thm)],[22685, 22683])).
% 4.54/4.79 tff(22687,plain,
% 4.54/4.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(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(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 4.54/4.79 inference(quant_inst,[status(thm)],[])).
% 4.54/4.79 tff(22688,plain,
% 4.54/4.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))),
% 4.54/4.79 inference(modus_ponens,[status(thm)],[22687, 22686])).
% 4.54/4.79 tff(22689,plain,
% 4.54/4.79 (~b(s(z), s(s(z)))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[22688, 178, 167, 202, 22682, 22674])).
% 4.54/4.79 tff(22690,plain,
% 4.54/4.79 (~b(s(elem!1), s(s(z)))),
% 4.54/4.79 inference(modus_ponens,[status(thm)],[22689, 22654])).
% 4.54/4.79 tff(22691,plain,
% 4.54/4.79 (b(s(z), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.79 inference(symmetry,[status(thm)],[20647])).
% 4.54/4.79 tff(22692,plain,
% 4.54/4.79 ((~b(s(z), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 4.54/4.79 inference(monotonicity,[status(thm)],[22691])).
% 4.54/4.79 tff(22693,plain,
% 4.54/4.79 (b(z, s(elem!1)) <=> b(z, s(z))),
% 4.54/4.79 inference(symmetry,[status(thm)],[21239])).
% 4.54/4.79 tff(22694,plain,
% 4.54/4.79 (b(z, s(z))),
% 4.54/4.79 inference(modus_ponens,[status(thm)],[855, 22693])).
% 4.54/4.79 tff(22695,plain,
% 4.54/4.79 (b(s(z), z)),
% 4.54/4.79 inference(modus_ponens,[status(thm)],[683, 21089])).
% 4.54/4.79 tff(22696,plain,
% 4.54/4.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 4.54/4.79 inference(rewrite,[status(thm)],[])).
% 4.54/4.79 tff(22697,plain,
% 4.54/4.79 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z)))) <=> ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 4.54/4.79 inference(rewrite,[status(thm)],[])).
% 4.54/4.79 tff(22698,plain,
% 4.54/4.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 4.54/4.79 inference(monotonicity,[status(thm)],[22697])).
% 4.54/4.79 tff(22699,plain,
% 4.54/4.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 4.54/4.79 inference(transitivity,[status(thm)],[22698, 22696])).
% 4.54/4.79 tff(22700,plain,
% 4.54/4.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))))),
% 4.54/4.79 inference(quant_inst,[status(thm)],[])).
% 4.54/4.79 tff(22701,plain,
% 4.54/4.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 4.54/4.79 inference(modus_ponens,[status(thm)],[22700, 22699])).
% 4.54/4.79 tff(22702,plain,
% 4.54/4.79 ((~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[22701, 178, 595, 22695, 146])).
% 4.54/4.79 tff(22703,plain,
% 4.54/4.79 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[22702, 22694])).
% 4.54/4.79 tff(22704,plain,
% 4.54/4.79 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.79 inference(modus_ponens,[status(thm)],[22703, 22692])).
% 4.54/4.79 tff(22705,plain,
% 4.54/4.79 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[395, 22704, 14147])).
% 4.54/4.79 tff(22706,plain,
% 4.54/4.79 (~r(s(elem!1), s(s(z)))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[390, 22705, 224])).
% 4.54/4.79 tff(22707,plain,
% 4.54/4.79 (b(s(elem!1), s(s(z)))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[421, 22706, 1056])).
% 4.54/4.79 tff(22708,plain,
% 4.54/4.79 ($false),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[22707, 22690])).
% 4.54/4.79 tff(22709,plain,((~b(z, s(elem!1))) | (~(elem!1 = z)) | (s(elem!1) = s(s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (s(elem!1) = s(s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | r(elem!1, s(s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | r(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 4.54/4.79 tff(22710,plain,
% 4.54/4.79 (~b(z, s(elem!1))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[22709, 928, 22621, 224, 22625, 22627, 22652, 22647, 595, 17330, 22646, 22620, 22643, 22638, 22636, 22635])).
% 4.54/4.79 tff(22711,plain,
% 4.54/4.79 (r(z, s(elem!1))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[2351, 22710])).
% 4.54/4.79 tff(22712,plain,
% 4.54/4.79 (~r(s(elem!1), s(s(z)))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[11762, 22711, 3261])).
% 4.54/4.79 tff(22713,plain,
% 4.54/4.79 (b(s(elem!1), s(s(z)))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[421, 22712, 22621])).
% 4.54/4.79 tff(22714,plain,
% 4.54/4.79 (r(elem!1, s(s(z))) <=> r(z, s(s(z)))),
% 4.54/4.79 inference(monotonicity,[status(thm)],[928])).
% 4.54/4.79 tff(22715,plain,
% 4.54/4.79 (r(z, s(s(z))) <=> r(elem!1, s(s(z)))),
% 4.54/4.79 inference(symmetry,[status(thm)],[22714])).
% 4.54/4.79 tff(22716,plain,
% 4.54/4.79 (r(elem!1, s(s(z)))),
% 4.54/4.79 inference(modus_ponens,[status(thm)],[3261, 22715])).
% 4.54/4.79 tff(22717,plain,
% 4.54/4.79 (r(elem!1, s(elem!1))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[6201, 22711, 928])).
% 4.54/4.79 tff(22718,plain,
% 4.54/4.79 (~(s(s(z)) = s(elem!1))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[1058, 22621])).
% 4.54/4.79 tff(22719,plain,
% 4.54/4.79 (~r(s(s(z)), s(elem!1))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[12114, 22711, 3261])).
% 4.54/4.79 tff(22720,plain,
% 4.54/4.79 (b(s(s(z)), s(elem!1))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[1067, 22719, 22718])).
% 4.54/4.79 tff(22721,plain,
% 4.54/4.79 (~r(s(s(s(s(z)))), s(s(z)))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[3785, 470, 450])).
% 4.54/4.79 tff(22722,plain,
% 4.54/4.79 (b(s(s(s(s(z)))), s(s(z)))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[101, 22721, 97])).
% 4.54/4.79 tff(22723,plain,
% 4.54/4.79 (~r(s(elem!1), s(s(s(s(z)))))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[14364, 470, 1587])).
% 4.54/4.79 tff(22724,plain,
% 4.54/4.79 (b(s(elem!1), s(s(s(s(z)))))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[1084, 22723, 1369])).
% 4.54/4.79 tff(22725,plain,
% 4.54/4.79 (~b(s(s(z)), s(s(s(s(z)))))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[1079, 22724, 1070, 1071, 22722])).
% 4.54/4.79 tff(22726,plain,
% 4.54/4.79 (r(s(s(z)), s(s(s(s(z)))))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[163, 22725, 159])).
% 4.54/4.79 tff(22727,plain,
% 4.54/4.79 ($false),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[5668, 118, 450, 470, 22726])).
% 4.54/4.79 tff(22728,plain,((~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (s(elem!1) = s(s(s(s(z))))) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.79 tff(22729,plain,
% 4.54/4.79 ($false),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[22728, 22720, 22717, 22716, 21041, 22652, 22713])).
% 4.54/4.79 tff(22730,plain,((~(elem!1 = z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)) | b(z, s(s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 4.54/4.79 tff(22731,plain,
% 4.54/4.79 (~(elem!1 = z)),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[22730, 22595, 22560, 22568, 106, 1, 22605, 22616, 22608])).
% 4.54/4.79 tff(22732,plain,
% 4.54/4.79 (~r(elem!1, z)),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[493, 18301, 106, 22566, 21829, 47, 22564])).
% 4.54/4.79 tff(22733,plain,
% 4.54/4.79 (b(elem!1, z)),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[498, 22732, 290])).
% 4.54/4.79 tff(22734,plain,
% 4.54/4.79 (r(elem!1, z)),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[2820, 869, 595, 2811, 146, 507])).
% 4.54/4.79 tff(22735,plain,
% 4.54/4.79 (~b(elem!1, s(s(s(s(z)))))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[1309, 869, 104, 2812, 595])).
% 4.54/4.79 tff(22736,plain,
% 4.54/4.79 (r(elem!1, s(s(s(s(z)))))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[483, 22735, 469])).
% 4.54/4.79 tff(22737,plain,
% 4.54/4.79 ($false),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[478, 22736, 22734, 145])).
% 4.54/4.79 tff(22738,plain,((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(z)))))) | (elem!1 = s(s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | r(z, elem!1) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (z = elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.79 tff(22739,plain,
% 4.54/4.79 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[22738, 18301, 47, 3104, 22568, 318, 2811, 104])).
% 4.54/4.79 tff(22740,plain,
% 4.54/4.79 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[691, 22739, 644])).
% 4.54/4.79 tff(22741,plain,
% 4.54/4.79 (r(elem!1, s(s(z))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.54/4.79 inference(monotonicity,[status(thm)],[22740])).
% 4.54/4.79 tff(22742,plain,
% 4.54/4.79 (r(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> r(elem!1, s(s(z)))),
% 4.54/4.79 inference(symmetry,[status(thm)],[22741])).
% 4.54/4.79 tff(22743,plain,
% 4.54/4.79 (r(elem!1, s(s(z)))),
% 4.54/4.79 inference(modus_ponens,[status(thm)],[15765, 22742])).
% 4.54/4.79 tff(22744,plain,
% 4.54/4.79 (b(s(elem!1), s(s(z)))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[809, 22743, 106, 15765, 287, 22733, 318, 22566, 21829, 47])).
% 4.54/4.79 tff(22745,plain,
% 4.54/4.79 (~b(s(s(z)), elem!1)),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[10835, 22740, 286])).
% 4.54/4.79 tff(22746,plain,
% 4.54/4.79 (b(elem!1, s(s(z))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.54/4.79 inference(monotonicity,[status(thm)],[22740])).
% 4.54/4.79 tff(22747,plain,
% 4.54/4.79 (b(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> b(elem!1, s(s(z)))),
% 4.54/4.79 inference(symmetry,[status(thm)],[22746])).
% 4.54/4.79 tff(22748,plain,
% 4.54/4.79 ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) <=> (~b(elem!1, s(s(z))))),
% 4.54/4.79 inference(monotonicity,[status(thm)],[22747])).
% 4.54/4.79 tff(22749,plain,
% 4.54/4.79 (~b(elem!1, s(s(z)))),
% 4.54/4.79 inference(modus_ponens,[status(thm)],[3576, 22748])).
% 4.54/4.79 tff(22750,plain,
% 4.54/4.79 (b(elem!1, s(s(s(elem!1))))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[10659, 22749, 1, 3170, 22745])).
% 4.54/4.79 tff(22751,plain,
% 4.54/4.79 (~r(s(s(s(s(z)))), s(s(z)))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[3269, 145, 3261])).
% 4.54/4.79 tff(22752,plain,
% 4.54/4.79 (b(s(s(s(s(z)))), s(s(z)))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[102, 22751])).
% 4.54/4.79 tff(22753,plain,
% 4.54/4.79 ($false),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[19484, 3288, 557, 3261, 22752, 145, 2857])).
% 4.54/4.79 tff(22754,plain,((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.79 tff(22755,plain,
% 4.54/4.79 (~r(z, s(s(s(elem!1))))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[22754, 13192, 47, 22560, 3244])).
% 4.54/4.79 tff(22756,plain,
% 4.54/4.79 (b(z, s(s(s(elem!1))))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[2095, 22755])).
% 4.54/4.79 tff(22757,plain,
% 4.54/4.79 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[16181, 22740])).
% 4.54/4.79 tff(22758,plain,
% 4.54/4.79 (~(s(s(s(s(z)))) = s(elem!1))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[2168, 22757])).
% 4.54/4.79 tff(22759,plain,
% 4.54/4.79 (~(s(s(elem!1)) = elem!1)),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[2510, 22758, 22740])).
% 4.54/4.79 tff(22760,plain,
% 4.54/4.79 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[348, 22759])).
% 4.54/4.79 tff(22761,plain,
% 4.54/4.79 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 4.54/4.79 inference(monotonicity,[status(thm)],[22740])).
% 4.54/4.79 tff(22762,plain,
% 4.54/4.79 (s(s(s(s(s(s(s(s(z)))))))) = s(elem!1)),
% 4.54/4.79 inference(symmetry,[status(thm)],[22761])).
% 4.54/4.79 tff(22763,plain,
% 4.54/4.79 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 4.54/4.79 inference(monotonicity,[status(thm)],[22762])).
% 4.54/4.79 tff(22764,plain,
% 4.54/4.79 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.54/4.79 inference(transitivity,[status(thm)],[22763, 377])).
% 4.54/4.79 tff(22765,plain,
% 4.54/4.79 ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z)))))))))),
% 4.54/4.79 inference(symmetry,[status(thm)],[22764])).
% 4.54/4.79 tff(22766,plain,
% 4.54/4.79 ((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z))))))))))),
% 4.54/4.79 inference(monotonicity,[status(thm)],[22765])).
% 4.54/4.79 tff(22767,plain,
% 4.54/4.79 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.54/4.79 inference(monotonicity,[status(thm)],[22740])).
% 4.54/4.79 tff(22768,plain,
% 4.54/4.79 ((~(s(elem!1) = elem!1)) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 4.54/4.79 inference(monotonicity,[status(thm)],[22767])).
% 4.54/4.79 tff(22769,plain,
% 4.54/4.79 (~(elem!1 = s(s(s(elem!1))))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[2859, 22740, 13192])).
% 4.54/4.79 tff(22770,plain,
% 4.54/4.79 (~(s(s(s(elem!1))) = elem!1)),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[2489, 22769])).
% 4.54/4.79 tff(22771,plain,
% 4.54/4.79 (~(s(elem!1) = elem!1)),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[2150, 22770])).
% 4.54/4.79 tff(22772,plain,
% 4.54/4.79 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.54/4.79 inference(modus_ponens,[status(thm)],[22771, 22768])).
% 4.54/4.79 tff(22773,plain,
% 4.54/4.79 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z)))))))))),
% 4.54/4.79 inference(modus_ponens,[status(thm)],[22772, 22766])).
% 4.54/4.79 tff(22774,plain,
% 4.54/4.79 (b(s(s(s(s(s(s(s(s(z)))))))), z) <=> b(s(elem!1), z)),
% 4.54/4.79 inference(monotonicity,[status(thm)],[22762])).
% 4.54/4.79 tff(22775,plain,
% 4.54/4.79 (b(s(elem!1), z) <=> b(s(s(s(s(s(s(s(s(z)))))))), z)),
% 4.54/4.79 inference(symmetry,[status(thm)],[22774])).
% 4.54/4.79 tff(22776,plain,
% 4.54/4.79 (~b(s(s(s(elem!1))), elem!1)),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[12925, 22750, 22756, 22733, 18256])).
% 4.54/4.79 tff(22777,plain,
% 4.54/4.79 (r(s(s(s(elem!1))), elem!1)),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[570, 22776, 22770])).
% 4.54/4.79 tff(22778,plain,
% 4.54/4.79 (b(elem!1, s(s(s(s(z)))))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[18185, 22740, 104])).
% 4.54/4.79 tff(22779,plain,
% 4.54/4.79 (~r(s(elem!1), s(s(s(s(z)))))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[916, 12569, 194])).
% 4.54/4.79 tff(22780,plain,
% 4.54/4.79 (b(s(elem!1), s(s(s(s(z)))))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[1084, 22779, 1369])).
% 4.54/4.79 tff(22781,plain,
% 4.54/4.79 (~b(s(s(z)), s(elem!1))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[1079, 22780, 202, 167, 1070])).
% 4.54/4.79 tff(22782,plain,
% 4.54/4.79 (r(s(s(z)), s(elem!1))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[1067, 22781, 2311])).
% 4.54/4.79 tff(22783,plain,
% 4.54/4.79 (~r(z, s(elem!1))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[12114, 22782, 3261])).
% 4.54/4.79 tff(22784,plain,
% 4.54/4.79 (b(z, s(elem!1))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[2351, 22783])).
% 4.54/4.79 tff(22785,plain,
% 4.54/4.79 (r(s(elem!1), z)),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[772, 41, 769, 766])).
% 4.54/4.79 tff(22786,plain,
% 4.54/4.79 (~r(s(elem!1), s(s(z)))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[2256, 118, 22785, 106])).
% 4.54/4.79 tff(22787,plain,
% 4.54/4.79 (b(s(elem!1), s(s(z)))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[420, 41, 1056, 22786])).
% 4.54/4.79 tff(22788,plain,
% 4.54/4.79 (r(s(elem!1), elem!1)),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[677, 19339, 2141])).
% 4.54/4.79 tff(22789,plain,
% 4.54/4.79 (~r(s(elem!1), s(s(s(elem!1))))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[2108, 118, 22788, 556])).
% 4.54/4.79 tff(22790,plain,
% 4.54/4.79 ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1))))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[5430, 41, 22789])).
% 4.54/4.79 tff(22791,plain,
% 4.54/4.79 (b(s(elem!1), s(s(s(elem!1))))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[22790, 7106])).
% 4.54/4.79 tff(22792,plain,
% 4.54/4.79 (~r(s(s(z)), s(elem!1))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[1052, 118, 22785, 106])).
% 4.54/4.79 tff(22793,plain,
% 4.54/4.79 ((s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[1065, 41, 22792])).
% 4.54/4.79 tff(22794,plain,
% 4.54/4.79 (b(s(s(z)), s(elem!1))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[22793, 12967])).
% 4.54/4.79 tff(22795,plain,
% 4.54/4.79 (~r(s(s(s(elem!1))), s(elem!1))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[1576, 22788, 556])).
% 4.54/4.79 tff(22796,plain,
% 4.54/4.79 (b(s(s(s(elem!1))), s(elem!1))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[373, 22795, 356])).
% 4.54/4.79 tff(22797,plain,
% 4.54/4.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 4.54/4.79 inference(rewrite,[status(thm)],[])).
% 4.54/4.79 tff(22798,plain,
% 4.54/4.79 (((~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(s(z)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 4.54/4.79 inference(rewrite,[status(thm)],[])).
% 4.54/4.79 tff(22799,plain,
% 4.54/4.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(elem!1))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 4.54/4.79 inference(monotonicity,[status(thm)],[22798])).
% 4.54/4.79 tff(22800,plain,
% 4.54/4.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(elem!1))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 4.54/4.79 inference(transitivity,[status(thm)],[22799, 22797])).
% 4.54/4.79 tff(22801,plain,
% 4.54/4.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 4.54/4.79 inference(quant_inst,[status(thm)],[])).
% 4.54/4.79 tff(22802,plain,
% 4.54/4.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 4.54/4.79 inference(modus_ponens,[status(thm)],[22801, 22800])).
% 4.54/4.79 tff(22803,plain,
% 4.54/4.79 (~b(s(s(s(elem!1))), s(s(z)))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[22802, 178, 22796, 22794, 22791, 22787])).
% 4.54/4.79 tff(22804,plain,
% 4.54/4.79 ((s(s(s(elem!1))) = s(s(z))) | r(s(s(s(elem!1))), s(s(z)))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[4209, 41, 22803])).
% 4.54/4.79 tff(22805,plain,
% 4.54/4.79 (r(s(s(s(elem!1))), s(s(z)))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[22804, 12790])).
% 4.54/4.79 tff(22806,plain,
% 4.54/4.79 (~b(s(s(z)), s(s(s(elem!1))))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[13023, 178, 22796, 22794, 22791, 22787])).
% 4.54/4.79 tff(22807,plain,
% 4.54/4.79 (r(s(s(z)), s(s(s(elem!1))))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[4221, 41, 1683, 22806])).
% 4.54/4.79 tff(22808,plain,
% 4.54/4.79 (~r(z, s(s(s(elem!1))))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[1831, 22807, 106])).
% 4.54/4.79 tff(22809,plain,
% 4.54/4.79 (b(z, s(s(s(elem!1))))),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[2095, 22808])).
% 4.54/4.79 tff(22810,plain,
% 4.54/4.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 4.54/4.79 inference(rewrite,[status(thm)],[])).
% 4.54/4.79 tff(22811,plain,
% 4.54/4.79 (((~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(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 4.54/4.79 inference(rewrite,[status(thm)],[])).
% 4.54/4.79 tff(22812,plain,
% 4.54/4.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 4.54/4.79 inference(monotonicity,[status(thm)],[22811])).
% 4.54/4.79 tff(22813,plain,
% 4.54/4.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 4.54/4.79 inference(transitivity,[status(thm)],[22812, 22810])).
% 4.54/4.79 tff(22814,plain,
% 4.54/4.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)))),
% 4.54/4.79 inference(quant_inst,[status(thm)],[])).
% 4.54/4.79 tff(22815,plain,
% 4.54/4.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 4.54/4.79 inference(modus_ponens,[status(thm)],[22814, 22813])).
% 4.54/4.79 tff(22816,plain,
% 4.54/4.79 (~b(s(s(s(elem!1))), z)),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[22815, 178, 22796, 855, 22809, 22791])).
% 4.54/4.79 tff(22817,plain,
% 4.54/4.79 (r(s(s(s(elem!1))), z)),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[1563, 41, 940, 22816])).
% 4.54/4.79 tff(22818,plain,
% 4.54/4.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 4.54/4.79 inference(rewrite,[status(thm)],[])).
% 4.54/4.79 tff(22819,plain,
% 4.54/4.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 4.54/4.79 inference(quant_inst,[status(thm)],[])).
% 4.54/4.79 tff(22820,plain,
% 4.54/4.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z))))),
% 4.54/4.79 inference(modus_ponens,[status(thm)],[22819, 22818])).
% 4.54/4.79 tff(22821,plain,
% 4.54/4.79 ($false),
% 4.54/4.79 inference(unit_resolution,[status(thm)],[22820, 118, 22817, 106, 22805])).
% 4.54/4.79 tff(22822,plain,(b(s(elem!1), z) | (~r(s(s(z)), z)) | (~b(z, s(elem!1))) | (s(elem!1) = s(s(z))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | b(s(elem!1), elem!1) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.80 tff(22823,plain,
% 4.54/4.80 (b(s(elem!1), elem!1)),
% 4.54/4.80 inference(unit_resolution,[status(thm)],[22822, 22784, 106, 556, 506, 1056, 356, 766])).
% 4.54/4.80 tff(22824,plain,
% 4.54/4.80 ($false),
% 4.54/4.80 inference(unit_resolution,[status(thm)],[20257, 22823, 22784, 818, 1301, 22780])).
% 4.54/4.80 tff(22825,plain,(b(s(elem!1), z) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (s(elem!1) = s(s(z))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z)))) | (s(elem!1) = s(s(s(s(z))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.80 tff(22826,plain,
% 4.54/4.80 (b(s(elem!1), z)),
% 4.54/4.80 inference(unit_resolution,[status(thm)],[22825, 18256, 22778, 106, 22777, 22733, 1056, 22760, 22560, 22566, 22564, 22744, 22757, 3244])).
% 4.54/4.80 tff(22827,plain,
% 4.54/4.80 (b(s(s(s(s(s(s(s(s(z)))))))), z)),
% 4.54/4.80 inference(modus_ponens,[status(thm)],[22826, 22775])).
% 4.54/4.80 tff(22828,plain,
% 4.54/4.80 (b(s(s(s(s(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))))))))),
% 4.54/4.80 inference(monotonicity,[status(thm)],[22762])).
% 4.54/4.80 tff(22829,plain,
% 4.54/4.80 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.80 inference(symmetry,[status(thm)],[22828])).
% 4.54/4.80 tff(22830,plain,
% 4.54/4.80 (s(s(elem!1)) = s(s(s(s(s(s(s(s(s(z)))))))))),
% 4.54/4.80 inference(monotonicity,[status(thm)],[22761])).
% 4.54/4.80 tff(22831,plain,
% 4.54/4.80 (s(s(s(elem!1))) = s(s(s(s(s(s(s(s(s(s(z))))))))))),
% 4.54/4.80 inference(monotonicity,[status(thm)],[22830])).
% 4.54/4.80 tff(22832,plain,
% 4.54/4.80 (s(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(s(elem!1)))),
% 4.54/4.80 inference(symmetry,[status(thm)],[22831])).
% 4.54/4.80 tff(22833,plain,
% 4.54/4.80 (r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.80 inference(monotonicity,[status(thm)],[22832])).
% 4.54/4.80 tff(22834,plain,
% 4.54/4.80 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.80 inference(symmetry,[status(thm)],[22833])).
% 4.54/4.80 tff(22835,plain,
% 4.54/4.80 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.80 inference(unit_resolution,[status(thm)],[19937, 22777, 22740])).
% 4.54/4.80 tff(22836,plain,
% 4.54/4.80 (r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.80 inference(modus_ponens,[status(thm)],[22835, 22834])).
% 4.54/4.80 tff(22837,plain,
% 4.54/4.80 (~r(s(s(z)), s(s(s(elem!1))))),
% 4.54/4.80 inference(unit_resolution,[status(thm)],[19952, 22836, 287, 22740])).
% 4.54/4.80 tff(22838,plain,
% 4.54/4.80 (r(s(s(z)), elem!1)),
% 4.54/4.80 inference(unit_resolution,[status(thm)],[448, 22745, 21829])).
% 4.54/4.80 tff(22839,plain,
% 4.54/4.80 (b(s(s(s(elem!1))), s(elem!1))),
% 4.54/4.80 inference(unit_resolution,[status(thm)],[373, 21256, 356])).
% 4.54/4.80 tff(22840,plain,
% 4.54/4.80 (~r(s(elem!1), s(s(s(elem!1))))),
% 4.54/4.80 inference(unit_resolution,[status(thm)],[2110, 1426, 556])).
% 4.54/4.80 tff(22841,plain,
% 4.54/4.80 (b(s(elem!1), s(s(s(elem!1))))),
% 4.54/4.80 inference(unit_resolution,[status(thm)],[5432, 22840, 5396])).
% 4.54/4.80 tff(22842,plain,
% 4.54/4.80 ($false),
% 4.54/4.80 inference(unit_resolution,[status(thm)],[12989, 22841, 22839, 438, 556, 1056, 1426, 1836])).
% 4.54/4.80 tff(22843,plain,((~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (s(elem!1) = s(s(z))) | r(s(s(z)), s(s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.54/4.80 tff(22844,plain,
% 4.54/4.80 (~r(s(elem!1), elem!1)),
% 4.54/4.80 inference(unit_resolution,[status(thm)],[22843, 22838, 22777, 1056, 22837, 22760])).
% 4.54/4.80 tff(22845,plain,
% 4.54/4.80 (b(s(elem!1), elem!1)),
% 4.54/4.80 inference(unit_resolution,[status(thm)],[677, 22844, 22771])).
% 4.54/4.80 tff(22846,plain,
% 4.54/4.80 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.80 inference(unit_resolution,[status(thm)],[686, 22845, 22740])).
% 4.54/4.80 tff(22847,plain,
% 4.54/4.80 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 4.54/4.80 inference(modus_ponens,[status(thm)],[22846, 22829])).
% 4.54/4.80 tff(22848,plain,
% 4.54/4.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 4.64/4.80 inference(rewrite,[status(thm)],[])).
% 4.64/4.80 tff(22849,plain,
% 4.64/4.80 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 4.64/4.80 inference(rewrite,[status(thm)],[])).
% 4.64/4.80 tff(22850,plain,
% 4.64/4.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))))),
% 4.64/4.80 inference(monotonicity,[status(thm)],[22849])).
% 4.64/4.80 tff(22851,plain,
% 4.64/4.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 4.64/4.80 inference(transitivity,[status(thm)],[22850, 22848])).
% 4.64/4.80 tff(22852,plain,
% 4.64/4.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 4.64/4.80 inference(quant_inst,[status(thm)],[])).
% 4.64/4.80 tff(22853,plain,
% 4.64/4.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))),
% 4.64/4.80 inference(modus_ponens,[status(thm)],[22852, 22851])).
% 4.64/4.80 tff(22854,plain,
% 4.64/4.80 ((~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))),
% 4.64/4.80 inference(unit_resolution,[status(thm)],[22853, 178, 22568, 3104, 22847])).
% 4.64/4.80 tff(22855,plain,
% 4.64/4.80 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.64/4.80 inference(unit_resolution,[status(thm)],[22854, 22827])).
% 4.64/4.80 tff(22856,plain,
% 4.64/4.80 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.64/4.80 inference(unit_resolution,[status(thm)],[16349, 41, 22855])).
% 4.64/4.80 tff(22857,plain,
% 4.64/4.80 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.64/4.80 inference(unit_resolution,[status(thm)],[22856, 22773])).
% 4.64/4.80 tff(22858,plain,
% 4.64/4.80 (r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z))))))))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 4.64/4.80 inference(monotonicity,[status(thm)],[4345, 11730])).
% 4.64/4.80 tff(22859,plain,
% 4.64/4.80 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.64/4.80 inference(symmetry,[status(thm)],[22858])).
% 4.64/4.80 tff(22860,plain,
% 4.64/4.80 (r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.64/4.80 inference(modus_ponens,[status(thm)],[1551, 22859])).
% 4.64/4.80 tff(22861,assumption,(r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))), introduced(assumption)).
% 4.64/4.80 tff(22862,plain,
% 4.64/4.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))))),
% 4.64/4.80 inference(rewrite,[status(thm)],[])).
% 4.64/4.80 tff(22863,plain,
% 4.64/4.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))))),
% 4.64/4.80 inference(quant_inst,[status(thm)],[])).
% 4.64/4.80 tff(22864,plain,
% 4.64/4.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z)))))))))),
% 4.64/4.80 inference(modus_ponens,[status(thm)],[22863, 22862])).
% 4.64/4.80 tff(22865,plain,
% 4.64/4.80 (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.64/4.80 inference(unit_resolution,[status(thm)],[22864, 118, 19940, 22861])).
% 4.64/4.80 tff(22866,plain,
% 4.64/4.80 ($false),
% 4.64/4.80 inference(unit_resolution,[status(thm)],[22865, 22860])).
% 4.64/4.80 tff(22867,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.80 tff(22868,plain,
% 4.64/4.80 (~r(s(s(s(elem!1))), s(elem!1))),
% 4.64/4.80 inference(unit_resolution,[status(thm)],[22867, 22740, 22836, 22857])).
% 4.64/4.80 tff(22869,plain,
% 4.64/4.80 (b(s(s(s(elem!1))), s(elem!1))),
% 4.64/4.80 inference(unit_resolution,[status(thm)],[373, 22868, 22760])).
% 4.64/4.80 tff(22870,plain,
% 4.64/4.80 (~b(z, s(elem!1))),
% 4.64/4.80 inference(unit_resolution,[status(thm)],[2052, 22869, 22756, 22733, 22750])).
% 4.64/4.80 tff(22871,plain,
% 4.64/4.80 (r(z, s(elem!1))),
% 4.64/4.80 inference(unit_resolution,[status(thm)],[2351, 22870])).
% 4.64/4.80 tff(22872,plain,
% 4.64/4.80 (~r(s(s(z)), s(elem!1))),
% 4.64/4.80 inference(unit_resolution,[status(thm)],[12114, 22871, 22560])).
% 4.64/4.80 tff(22873,plain,
% 4.64/4.80 (b(s(s(z)), s(elem!1))),
% 4.64/4.80 inference(unit_resolution,[status(thm)],[1067, 22872, 2311])).
% 4.64/4.80 tff(22874,plain,
% 4.64/4.80 (~r(s(elem!1), s(s(s(s(z)))))),
% 4.64/4.80 inference(unit_resolution,[status(thm)],[2766, 22871, 47])).
% 4.64/4.80 tff(22875,plain,
% 4.64/4.80 (b(s(elem!1), s(s(s(s(z)))))),
% 4.64/4.80 inference(unit_resolution,[status(thm)],[1084, 22874, 22757])).
% 4.64/4.80 tff(22876,plain,
% 4.64/4.80 ($false),
% 4.64/4.80 inference(unit_resolution,[status(thm)],[1079, 22875, 22873, 22566, 22564, 22744])).
% 4.64/4.80 tff(22877,plain,(r(z, elem!1) | (s(elem!1) = s(s(z))) | (~r(s(s(z)), z)) | b(z, s(s(s(s(z))))) | b(s(s(s(s(z)))), z) | b(s(s(s(s(s(s(s(z))))))), s(s(z))) | b(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)))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 4.64/4.80 tff(22878,plain,
% 4.64/4.80 (r(z, elem!1)),
% 4.64/4.80 inference(unit_resolution,[status(thm)],[22877, 1056, 106, 1, 3170, 3576, 286, 104, 644, 290])).
% 4.64/4.80 tff(22879,plain,
% 4.64/4.80 (~r(elem!1, s(s(z)))),
% 4.64/4.80 inference(unit_resolution,[status(thm)],[4862, 22878, 22560])).
% 4.64/4.80 tff(22880,plain,
% 4.64/4.80 (b(elem!1, s(s(z)))),
% 4.64/4.80 inference(unit_resolution,[status(thm)],[467, 22879, 21905])).
% 4.64/4.80 tff(22881,plain,
% 4.64/4.80 (elem!1 = s(s(s(s(z))))),
% 4.64/4.80 inference(unit_resolution,[status(thm)],[814, 22880, 106, 22564, 22878, 21829, 47, 22566])).
% 4.64/4.80 tff(22882,plain,
% 4.64/4.80 (s(elem!1) = s(s(s(s(s(z)))))),
% 4.64/4.80 inference(monotonicity,[status(thm)],[22881])).
% 4.64/4.80 tff(22883,plain,
% 4.64/4.80 (s(s(s(s(s(z))))) = s(elem!1)),
% 4.64/4.80 inference(symmetry,[status(thm)],[22882])).
% 4.64/4.80 tff(22884,plain,
% 4.64/4.80 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 4.64/4.80 inference(monotonicity,[status(thm)],[22883])).
% 4.64/4.80 tff(22885,plain,
% 4.64/4.80 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 4.64/4.80 inference(symmetry,[status(thm)],[22884])).
% 4.64/4.80 tff(22886,plain,
% 4.64/4.80 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(s(s(z)))))),
% 4.64/4.80 inference(monotonicity,[status(thm)],[22881])).
% 4.64/4.80 tff(22887,plain,
% 4.64/4.80 (r(s(elem!1), elem!1) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 4.64/4.80 inference(transitivity,[status(thm)],[22886, 22885])).
% 4.64/4.80 tff(22888,plain,
% 4.64/4.80 (~r(s(s(z)), elem!1)),
% 4.64/4.80 inference(unit_resolution,[status(thm)],[8412, 22878, 22560])).
% 4.64/4.80 tff(22889,plain,
% 4.64/4.80 (b(s(s(z)), elem!1)),
% 4.64/4.80 inference(unit_resolution,[status(thm)],[448, 22888, 21829])).
% 4.64/4.80 tff(22890,plain,
% 4.64/4.80 (s(s(s(s(z)))) = elem!1),
% 4.64/4.80 inference(unit_resolution,[status(thm)],[3151, 22889, 22566, 22564, 22878, 3244, 47])).
% 4.64/4.80 tff(22891,plain,
% 4.64/4.80 (~(s(s(elem!1)) = elem!1)),
% 4.64/4.80 inference(unit_resolution,[status(thm)],[338, 22890, 21829])).
% 4.64/4.80 tff(22892,plain,
% 4.64/4.80 (~(s(elem!1) = elem!1)),
% 4.64/4.80 inference(unit_resolution,[status(thm)],[672, 22891])).
% 4.64/4.80 tff(22893,plain,
% 4.64/4.80 (b(s(elem!1), s(s(z)))),
% 4.64/4.80 inference(unit_resolution,[status(thm)],[435, 22881, 106, 15765, 287, 21829])).
% 4.64/4.80 tff(22894,plain,
% 4.64/4.80 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.64/4.80 inference(unit_resolution,[status(thm)],[348, 22891])).
% 4.64/4.80 tff(22895,plain,
% 4.64/4.80 (~(s(elem!1) = s(s(s(elem!1))))),
% 4.64/4.80 inference(unit_resolution,[status(thm)],[5395, 22894])).
% 4.64/4.80 tff(22896,plain,
% 4.64/4.80 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 4.64/4.80 inference(monotonicity,[status(thm)],[22882])).
% 4.64/4.80 tff(22897,plain,
% 4.64/4.80 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 4.64/4.80 inference(monotonicity,[status(thm)],[22896])).
% 4.64/4.80 tff(22898,plain,
% 4.64/4.80 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.80 inference(monotonicity,[status(thm)],[22897])).
% 4.64/4.80 tff(22899,plain,
% 4.64/4.80 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 4.64/4.80 inference(symmetry,[status(thm)],[22898])).
% 4.64/4.80 tff(22900,plain,
% 4.64/4.80 ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(s(z)), s(s(s(elem!1)))))),
% 4.64/4.80 inference(monotonicity,[status(thm)],[22899])).
% 4.64/4.80 tff(22901,plain,
% 4.64/4.80 (~b(s(s(z)), s(s(s(elem!1))))),
% 4.64/4.80 inference(modus_ponens,[status(thm)],[286, 22900])).
% 4.64/4.80 tff(22902,plain,
% 4.64/4.80 ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(elem!1), s(s(s(elem!1)))))),
% 4.64/4.80 inference(monotonicity,[status(thm)],[18685])).
% 4.64/4.80 tff(22903,plain,
% 4.64/4.80 (~b(s(s(z)), s(elem!1))),
% 4.64/4.80 inference(unit_resolution,[status(thm)],[13708, 683, 817, 812, 1070])).
% 4.64/4.80 tff(22904,plain,
% 4.64/4.80 (r(s(s(z)), s(elem!1))),
% 4.64/4.80 inference(unit_resolution,[status(thm)],[1067, 22903, 1060])).
% 4.64/4.80 tff(22905,plain,
% 4.64/4.80 (~r(z, s(elem!1))),
% 4.64/4.80 inference(unit_resolution,[status(thm)],[12114, 22904, 22560])).
% 4.64/4.80 tff(22906,plain,
% 4.64/4.80 (b(z, s(elem!1))),
% 4.64/4.80 inference(unit_resolution,[status(thm)],[2351, 22905])).
% 4.64/4.80 tff(22907,plain,
% 4.64/4.80 (b(z, s(s(s(s(s(z))))))),
% 4.64/4.80 inference(modus_ponens,[status(thm)],[22906, 2310])).
% 4.64/4.80 tff(22908,plain,
% 4.64/4.80 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 4.64/4.80 inference(modus_ponens,[status(thm)],[683, 21838])).
% 4.64/4.80 tff(22909,plain,
% 4.64/4.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(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(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(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(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 4.64/4.80 inference(rewrite,[status(thm)],[])).
% 4.64/4.80 tff(22910,plain,
% 4.64/4.80 (((~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(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(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(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 4.64/4.80 inference(rewrite,[status(thm)],[])).
% 4.64/4.80 tff(22911,plain,
% 4.64/4.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(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(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 4.64/4.80 inference(monotonicity,[status(thm)],[22910])).
% 4.64/4.80 tff(22912,plain,
% 4.64/4.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(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(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 4.64/4.80 inference(transitivity,[status(thm)],[22911, 22909])).
% 4.64/4.80 tff(22913,plain,
% 4.64/4.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 4.64/4.80 inference(quant_inst,[status(thm)],[])).
% 4.64/4.80 tff(22914,plain,
% 4.64/4.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 4.64/4.80 inference(modus_ponens,[status(thm)],[22913, 22912])).
% 4.64/4.80 tff(22915,plain,
% 4.64/4.80 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.80 inference(unit_resolution,[status(thm)],[22914, 178, 104, 595, 22908, 22907])).
% 4.64/4.80 tff(22916,plain,
% 4.64/4.80 (~b(s(elem!1), s(s(s(elem!1))))),
% 4.64/4.80 inference(modus_ponens,[status(thm)],[22915, 22902])).
% 4.64/4.80 tff(22917,plain,
% 4.64/4.80 (b(s(elem!1), s(s(s(elem!1))))),
% 4.64/4.80 inference(unit_resolution,[status(thm)],[6127, 22904, 4218, 5425])).
% 4.64/4.80 tff(22918,plain,
% 4.64/4.80 ($false),
% 4.64/4.80 inference(unit_resolution,[status(thm)],[22917, 22916])).
% 4.64/4.80 tff(22919,plain,((~b(s(elem!1), elem!1)) | (~(elem!1 = s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | b(s(s(z)), s(s(s(elem!1)))) | (s(elem!1) = s(s(s(elem!1)))) | (s(s(z)) = s(elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.80 tff(22920,plain,
% 4.64/4.80 (~b(s(elem!1), elem!1)),
% 4.64/4.80 inference(unit_resolution,[status(thm)],[22919, 22881, 104, 22568, 22901, 22895, 2311, 22889, 22880, 22893])).
% 4.64/4.80 tff(22921,plain,
% 4.64/4.80 (r(s(elem!1), elem!1)),
% 4.64/4.80 inference(unit_resolution,[status(thm)],[677, 22920, 22892])).
% 4.64/4.80 tff(22922,plain,
% 4.64/4.80 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 4.64/4.80 inference(modus_ponens,[status(thm)],[22921, 22887])).
% 4.64/4.80 tff(22923,plain,
% 4.64/4.80 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 4.64/4.80 inference(unit_resolution,[status(thm)],[17073, 118, 22922, 4891])).
% 4.64/4.80 tff(22924,plain,
% 4.64/4.80 (b(z, s(elem!1)) <=> b(z, s(s(s(s(s(z))))))),
% 4.64/4.80 inference(monotonicity,[status(thm)],[22882])).
% 4.64/4.80 tff(22925,plain,
% 4.64/4.80 (~r(z, s(elem!1))),
% 4.64/4.80 inference(unit_resolution,[status(thm)],[7070, 22921, 22878])).
% 4.64/4.80 tff(22926,plain,
% 4.64/4.80 (b(z, s(elem!1))),
% 4.64/4.80 inference(unit_resolution,[status(thm)],[2351, 22925])).
% 4.64/4.80 tff(22927,plain,
% 4.64/4.80 (b(z, s(s(s(s(s(z))))))),
% 4.64/4.80 inference(modus_ponens,[status(thm)],[22926, 22924])).
% 4.64/4.80 tff(22928,plain,
% 4.64/4.80 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 4.64/4.80 inference(monotonicity,[status(thm)],[22882])).
% 4.64/4.80 tff(22929,plain,
% 4.64/4.80 (b(s(s(s(s(s(z))))), s(s(z)))),
% 4.64/4.80 inference(modus_ponens,[status(thm)],[22893, 22928])).
% 4.64/4.80 tff(22930,plain,
% 4.64/4.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 4.64/4.80 inference(rewrite,[status(thm)],[])).
% 4.64/4.80 tff(22931,plain,
% 4.64/4.80 (((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 4.64/4.80 inference(rewrite,[status(thm)],[])).
% 4.64/4.80 tff(22932,plain,
% 4.64/4.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 4.64/4.80 inference(monotonicity,[status(thm)],[22931])).
% 4.64/4.80 tff(22933,plain,
% 4.64/4.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 4.64/4.81 inference(transitivity,[status(thm)],[22932, 22930])).
% 4.64/4.81 tff(22934,plain,
% 4.64/4.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))))),
% 4.64/4.81 inference(quant_inst,[status(thm)],[])).
% 4.64/4.81 tff(22935,plain,
% 4.64/4.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 4.64/4.81 inference(modus_ponens,[status(thm)],[22934, 22933])).
% 4.64/4.81 tff(22936,plain,
% 4.64/4.81 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[22935, 178, 22929, 22927, 22619, 4932])).
% 4.64/4.81 tff(22937,plain,
% 4.64/4.81 ($false),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[9830, 41, 11413, 22936, 22923])).
% 4.64/4.81 tff(22938,plain,((s(elem!1) = s(s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), z)) | b(z, s(s(s(s(z))))) | b(s(s(s(s(z)))), z) | b(s(s(s(s(s(s(s(z))))))), s(s(z))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 4.64/4.81 tff(22939,plain,
% 4.64/4.81 (s(elem!1) = s(s(z))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[22938, 290, 4932, 104, 286, 106, 1, 3170, 3576, 644, 4891])).
% 4.64/4.81 tff(22940,plain,
% 4.64/4.81 (~(elem!1 = s(s(s(s(z)))))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[11438, 22939])).
% 4.64/4.81 tff(22941,plain,
% 4.64/4.81 (~r(z, elem!1)),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[580, 22939, 106, 21829, 22566, 47, 22940])).
% 4.64/4.81 tff(22942,plain,
% 4.64/4.81 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[2832, 22939])).
% 4.64/4.81 tff(22943,plain,
% 4.64/4.81 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[691, 22942, 644])).
% 4.64/4.81 tff(22944,plain,
% 4.64/4.81 ($false),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[22738, 22943, 22940, 47, 3104, 22568, 318, 22941, 104])).
% 4.64/4.81 tff(22945,plain,((elem!1 = z) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | b(z, s(s(s(s(z))))) | b(s(s(s(s(z)))), z) | b(s(s(s(s(s(s(s(z))))))), s(s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.81 tff(22946,plain,
% 4.64/4.81 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[22945, 22731, 104, 106, 22602, 22594, 1, 22608, 22599, 22605])).
% 4.64/4.81 tff(22947,plain,
% 4.64/4.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), elem!1)))),
% 4.64/4.81 inference(rewrite,[status(thm)],[])).
% 4.64/4.81 tff(22948,plain,
% 4.64/4.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), elem!1)))),
% 4.64/4.81 inference(quant_inst,[status(thm)],[])).
% 4.64/4.81 tff(22949,plain,
% 4.64/4.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), elem!1))),
% 4.64/4.81 inference(modus_ponens,[status(thm)],[22948, 22947])).
% 4.64/4.81 tff(22950,plain,
% 4.64/4.81 (~r(s(s(s(z))), elem!1)),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[22949, 118, 22946, 8216])).
% 4.64/4.81 tff(22951,plain,
% 4.64/4.81 (~(z = elem!1)),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[317, 22731])).
% 4.64/4.81 tff(22952,plain,
% 4.64/4.81 (~(s(s(elem!1)) = s(s(z)))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[2386, 22951])).
% 4.64/4.81 tff(22953,plain,
% 4.64/4.81 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[8244, 22952])).
% 4.64/4.81 tff(22954,plain,
% 4.64/4.81 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[16628, 22953, 47, 22605])).
% 4.64/4.81 tff(22955,plain,
% 4.64/4.81 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[4173, 13192, 22954])).
% 4.64/4.81 tff(22956,plain,
% 4.64/4.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z))))))),
% 4.64/4.81 inference(rewrite,[status(thm)],[])).
% 4.64/4.81 tff(22957,plain,
% 4.64/4.81 (((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z))))))),
% 4.64/4.81 inference(rewrite,[status(thm)],[])).
% 4.64/4.81 tff(22958,plain,
% 4.64/4.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z)))))))),
% 4.64/4.81 inference(monotonicity,[status(thm)],[22957])).
% 4.64/4.81 tff(22959,plain,
% 4.64/4.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z))))))),
% 4.64/4.81 inference(transitivity,[status(thm)],[22958, 22956])).
% 4.64/4.81 tff(22960,plain,
% 4.64/4.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z))))))),
% 4.64/4.81 inference(quant_inst,[status(thm)],[])).
% 4.64/4.81 tff(22961,plain,
% 4.64/4.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(z)))))),
% 4.64/4.81 inference(modus_ponens,[status(thm)],[22960, 22959])).
% 4.64/4.81 tff(22962,plain,
% 4.64/4.81 (~r(elem!1, s(s(s(z))))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[22961, 118, 22946, 8216])).
% 4.64/4.81 tff(22963,plain,
% 4.64/4.81 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 4.64/4.81 inference(monotonicity,[status(thm)],[331])).
% 4.64/4.81 tff(22964,plain,
% 4.64/4.81 (r(elem!1, s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 4.64/4.81 inference(symmetry,[status(thm)],[22963])).
% 4.64/4.81 tff(22965,plain,
% 4.64/4.81 ((~r(elem!1, s(s(s(z))))) <=> (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 4.64/4.81 inference(monotonicity,[status(thm)],[22964])).
% 4.64/4.81 tff(22966,assumption,(~r(elem!1, s(s(s(z))))), introduced(assumption)).
% 4.64/4.81 tff(22967,plain,
% 4.64/4.81 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 4.64/4.81 inference(modus_ponens,[status(thm)],[22966, 22965])).
% 4.64/4.81 tff(22968,plain,
% 4.64/4.81 ($false),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[4953, 22967])).
% 4.64/4.81 tff(22969,plain,((~(s(s(s(s(z)))) = elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | r(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.81 tff(22970,plain,
% 4.64/4.81 (~(s(s(s(s(z)))) = elem!1)),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[22969, 22616, 22962])).
% 4.64/4.81 tff(22971,plain,
% 4.64/4.81 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[3502, 22970])).
% 4.64/4.81 tff(22972,plain,
% 4.64/4.81 (~r(s(s(z)), elem!1)),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[2803, 22946, 22595])).
% 4.64/4.81 tff(22973,plain,
% 4.64/4.81 (~(elem!1 = s(s(s(s(z)))))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[325, 22970])).
% 4.64/4.81 tff(22974,plain,
% 4.64/4.81 (~r(s(s(s(z))), z)),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[20797, 22605, 47])).
% 4.64/4.81 tff(22975,plain,
% 4.64/4.81 (b(s(s(s(z))), z)),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[21073, 22974])).
% 4.64/4.81 tff(22976,plain,
% 4.64/4.81 (~r(elem!1, s(s(z)))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[20457, 22946, 22600])).
% 4.64/4.81 tff(22977,plain,
% 4.64/4.81 (r(s(s(s(s(z)))), z)),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[191, 22608])).
% 4.64/4.81 tff(22978,plain,
% 4.64/4.81 (~r(elem!1, s(s(z)))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[20457, 1265, 107])).
% 4.64/4.81 tff(22979,assumption,(~r(s(s(s(z))), elem!1)), introduced(assumption)).
% 4.64/4.81 tff(22980,plain,
% 4.64/4.81 ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[5253, 178, 22564, 22566, 4932])).
% 4.64/4.81 tff(22981,plain,
% 4.64/4.81 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[22980, 5090])).
% 4.64/4.81 tff(22982,plain,
% 4.64/4.81 (r(s(s(s(z))), s(s(s(s(z)))))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[10755, 22981])).
% 4.64/4.81 tff(22983,plain,
% 4.64/4.81 (~r(s(s(s(z))), z)),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[20797, 22982, 47])).
% 4.64/4.81 tff(22984,plain,
% 4.64/4.81 (b(s(s(s(z))), z)),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[21073, 22983])).
% 4.64/4.81 tff(22985,plain,
% 4.64/4.81 (~r(z, s(s(s(z))))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[4910, 118, 47, 22982])).
% 4.64/4.81 tff(22986,plain,
% 4.64/4.81 (b(z, s(s(s(z))))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[4920, 22985])).
% 4.64/4.81 tff(22987,plain,
% 4.64/4.81 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[2944, 178, 22568, 17330, 22986, 22984])).
% 4.64/4.81 tff(22988,plain,
% 4.64/4.81 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 22987])).
% 4.64/4.81 tff(22989,plain,
% 4.64/4.81 (~r(z, s(s(s(elem!1))))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[22754, 13192, 47, 22560, 194])).
% 4.64/4.81 tff(22990,plain,
% 4.64/4.81 (b(z, s(s(s(elem!1))))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[2095, 22989])).
% 4.64/4.81 tff(22991,plain,
% 4.64/4.81 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[16628, 11613, 47, 22982])).
% 4.64/4.81 tff(22992,plain,
% 4.64/4.81 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[4173, 13192, 22991])).
% 4.64/4.81 tff(22993,plain,
% 4.64/4.81 (~r(s(elem!1), s(s(s(s(z)))))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[2766, 2333, 47])).
% 4.64/4.81 tff(22994,plain,
% 4.64/4.81 (~r(s(s(z)), s(elem!1))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[12114, 2333, 22560])).
% 4.64/4.81 tff(22995,plain,
% 4.64/4.81 (b(s(s(z)), s(elem!1))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[1067, 22994, 2311])).
% 4.64/4.81 tff(22996,plain,
% 4.64/4.81 (~r(s(elem!1), s(s(z)))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[11762, 2333, 22560])).
% 4.64/4.81 tff(22997,plain,
% 4.64/4.81 (b(s(elem!1), s(s(z)))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[421, 22996, 1056])).
% 4.64/4.81 tff(22998,plain,
% 4.64/4.81 (~b(s(elem!1), s(s(s(s(z)))))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[1079, 22997, 22566, 22564, 22995])).
% 4.64/4.81 tff(22999,plain,
% 4.64/4.81 (s(elem!1) = s(s(s(s(z))))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[1084, 22998, 22993])).
% 4.64/4.81 tff(23000,plain,
% 4.64/4.81 (~(elem!1 = s(s(s(elem!1))))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[2498, 22999, 2387])).
% 4.64/4.81 tff(23001,plain,
% 4.64/4.81 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 4.64/4.81 inference(monotonicity,[status(thm)],[22999])).
% 4.64/4.81 tff(23002,plain,
% 4.64/4.81 (elem!1 = s(s(s(z)))),
% 4.64/4.81 inference(transitivity,[status(thm)],[517, 23001, 11])).
% 4.64/4.81 tff(23003,plain,
% 4.64/4.81 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.64/4.81 inference(monotonicity,[status(thm)],[23002])).
% 4.64/4.81 tff(23004,plain,
% 4.64/4.81 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.64/4.81 inference(symmetry,[status(thm)],[23003])).
% 4.64/4.81 tff(23005,plain,
% 4.64/4.81 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.64/4.81 inference(modus_ponens,[status(thm)],[16063, 23004])).
% 4.64/4.81 tff(23006,plain,
% 4.64/4.81 (~(s(s(s(elem!1))) = elem!1)),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[2489, 23000])).
% 4.64/4.81 tff(23007,plain,
% 4.64/4.81 (~(s(elem!1) = elem!1)),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[2150, 23006])).
% 4.64/4.81 tff(23008,plain,
% 4.64/4.81 (r(s(elem!1), elem!1)),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[677, 23007, 2141])).
% 4.64/4.81 tff(23009,plain,
% 4.64/4.81 (~r(z, elem!1)),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[7070, 23008, 2333])).
% 4.64/4.81 tff(23010,plain,
% 4.64/4.81 (b(z, elem!1)),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[585, 23009, 507])).
% 4.64/4.81 tff(23011,plain,
% 4.64/4.81 (~(elem!1 = s(s(s(s(z)))))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[1846, 23010, 1])).
% 4.64/4.81 tff(23012,plain,
% 4.64/4.81 (~(s(s(s(s(z)))) = elem!1)),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[504, 23011])).
% 4.64/4.81 tff(23013,plain,
% 4.64/4.81 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[3502, 23012])).
% 4.64/4.81 tff(23014,plain,
% 4.64/4.81 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 4.64/4.81 inference(monotonicity,[status(thm)],[22999])).
% 4.64/4.81 tff(23015,plain,
% 4.64/4.81 (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))),
% 4.64/4.81 inference(monotonicity,[status(thm)],[23014])).
% 4.64/4.81 tff(23016,plain,
% 4.64/4.81 (b(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(s(s(s(z)))))))),
% 4.64/4.81 inference(monotonicity,[status(thm)],[23015])).
% 4.64/4.81 tff(23017,plain,
% 4.64/4.81 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.64/4.81 inference(symmetry,[status(thm)],[23016])).
% 4.64/4.81 tff(23018,plain,
% 4.64/4.81 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) <=> (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 4.64/4.81 inference(monotonicity,[status(thm)],[23017])).
% 4.64/4.81 tff(23019,plain,
% 4.64/4.81 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 4.64/4.81 inference(symmetry,[status(thm)],[23015])).
% 4.64/4.81 tff(23020,plain,
% 4.64/4.81 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.64/4.81 inference(monotonicity,[status(thm)],[23019])).
% 4.64/4.81 tff(23021,plain,
% 4.64/4.81 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 4.64/4.81 inference(symmetry,[status(thm)],[23020])).
% 4.64/4.81 tff(23022,plain,
% 4.64/4.81 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 4.64/4.81 inference(modus_ponens,[status(thm)],[3831, 23021])).
% 4.64/4.81 tff(23023,plain,
% 4.64/4.81 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(s(s(s(z)))))))),
% 4.64/4.81 inference(monotonicity,[status(thm)],[23015])).
% 4.64/4.81 tff(23024,plain,
% 4.64/4.81 (b(z, s(s(s(s(s(s(z)))))))),
% 4.64/4.81 inference(modus_ponens,[status(thm)],[2043, 23023])).
% 4.64/4.81 tff(23025,plain,
% 4.64/4.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))),
% 4.64/4.81 inference(rewrite,[status(thm)],[])).
% 4.64/4.81 tff(23026,plain,
% 4.64/4.81 (((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(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(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(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(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))),
% 4.64/4.81 inference(rewrite,[status(thm)],[])).
% 4.64/4.81 tff(23027,plain,
% 4.64/4.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(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(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))))))),
% 4.64/4.81 inference(monotonicity,[status(thm)],[23026])).
% 4.64/4.81 tff(23028,plain,
% 4.64/4.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(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(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))),
% 4.64/4.81 inference(transitivity,[status(thm)],[23027, 23025])).
% 4.64/4.81 tff(23029,plain,
% 4.64/4.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(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(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 4.64/4.81 inference(quant_inst,[status(thm)],[])).
% 4.64/4.81 tff(23030,plain,
% 4.64/4.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))))),
% 4.64/4.81 inference(modus_ponens,[status(thm)],[23029, 23028])).
% 4.64/4.81 tff(23031,plain,
% 4.64/4.81 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[23030, 178, 104, 22568, 23024, 23022])).
% 4.64/4.81 tff(23032,plain,
% 4.64/4.81 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.64/4.81 inference(modus_ponens,[status(thm)],[23031, 23018])).
% 4.64/4.81 tff(23033,plain,
% 4.64/4.81 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[5118, 23032, 23013])).
% 4.64/4.81 tff(23034,plain,
% 4.64/4.81 (~r(elem!1, s(s(s(elem!1))))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[8969, 23033, 23005])).
% 4.64/4.81 tff(23035,plain,
% 4.64/4.81 (b(elem!1, s(s(s(elem!1))))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[2054, 23034, 23000])).
% 4.64/4.81 tff(23036,plain,
% 4.64/4.81 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[6974, 23035, 22999])).
% 4.64/4.81 tff(23037,plain,
% 4.64/4.81 (~(s(s(s(s(s(s(z)))))) = s(s(z)))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[6058, 22999])).
% 4.64/4.81 tff(23038,plain,
% 4.64/4.81 (~r(s(s(s(elem!1))), s(s(z)))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[10401, 23033, 107])).
% 4.64/4.81 tff(23039,plain,
% 4.64/4.81 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[6165, 23038, 22999])).
% 4.64/4.81 tff(23040,plain,
% 4.64/4.81 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[6139, 23039, 23037])).
% 4.64/4.81 tff(23041,plain,
% 4.64/4.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(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(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(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(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 4.64/4.81 inference(rewrite,[status(thm)],[])).
% 4.64/4.81 tff(23042,plain,
% 4.64/4.81 (((~b(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(s(s(z)))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(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(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 4.64/4.81 inference(rewrite,[status(thm)],[])).
% 4.64/4.81 tff(23043,plain,
% 4.64/4.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(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(s(z))), s(s(z)))) | (~b(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(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(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 4.64/4.81 inference(monotonicity,[status(thm)],[23042])).
% 4.64/4.81 tff(23044,plain,
% 4.64/4.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(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(s(z))), s(s(z)))) | (~b(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(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(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 4.64/4.81 inference(transitivity,[status(thm)],[23043, 23041])).
% 4.64/4.81 tff(23045,plain,
% 4.64/4.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(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(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 4.64/4.81 inference(quant_inst,[status(thm)],[])).
% 4.64/4.81 tff(23046,plain,
% 4.64/4.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))),
% 4.64/4.81 inference(modus_ponens,[status(thm)],[23045, 23044])).
% 4.64/4.81 tff(23047,plain,
% 4.64/4.81 ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[23046, 178, 22564, 23022, 4932])).
% 4.64/4.81 tff(23048,plain,
% 4.64/4.81 ($false),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[23047, 23040, 23036])).
% 4.64/4.81 tff(23049,plain,((~r(z, s(elem!1))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), 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(z)))))) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | b(z, s(s(s(s(z))))) | (z = elem!1) | b(s(elem!1), elem!1) | (s(elem!1) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.81 tff(23050,plain,
% 4.64/4.81 (~r(z, s(elem!1))),
% 4.64/4.81 inference(unit_resolution,[status(thm)],[23049, 2141, 107, 104, 22992, 22990, 22988, 1, 318, 4932, 1056])).
% 4.64/4.82 tff(23051,plain,
% 4.64/4.82 (b(z, s(elem!1))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[2351, 23050])).
% 4.64/4.82 tff(23052,plain,
% 4.64/4.82 (s(s(s(s(z)))) = s(elem!1)),
% 4.64/4.82 inference(monotonicity,[status(thm)],[4824])).
% 4.64/4.82 tff(23053,plain,
% 4.64/4.82 (b(z, s(s(s(s(z))))) <=> b(z, s(elem!1))),
% 4.64/4.82 inference(monotonicity,[status(thm)],[23052])).
% 4.64/4.82 tff(23054,plain,
% 4.64/4.82 (b(z, s(elem!1)) <=> b(z, s(s(s(s(z)))))),
% 4.64/4.82 inference(symmetry,[status(thm)],[23053])).
% 4.64/4.82 tff(23055,plain,
% 4.64/4.82 (b(z, s(s(s(s(z)))))),
% 4.64/4.82 inference(modus_ponens,[status(thm)],[855, 23054])).
% 4.64/4.82 tff(23056,plain,
% 4.64/4.82 ($false),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[1, 23055])).
% 4.64/4.82 tff(23057,plain,((~(s(s(s(z))) = elem!1)) | b(z, s(s(s(s(z))))) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.82 tff(23058,plain,
% 4.64/4.82 (~(s(s(s(z))) = elem!1)),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[23057, 23051, 1])).
% 4.64/4.82 tff(23059,plain,
% 4.64/4.82 (b(s(s(s(z))), elem!1)),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[4981, 23058, 22979])).
% 4.64/4.82 tff(23060,plain,
% 4.64/4.82 ((~(s(s(s(z))) = elem!1)) <=> (~(elem!1 = s(s(s(z)))))),
% 4.64/4.82 inference(monotonicity,[status(thm)],[10420])).
% 4.64/4.82 tff(23061,plain,
% 4.64/4.82 (~(elem!1 = s(s(s(z))))),
% 4.64/4.82 inference(modus_ponens,[status(thm)],[23058, 23060])).
% 4.64/4.82 tff(23062,plain,
% 4.64/4.82 (b(elem!1, s(s(s(z))))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[17275, 23061, 22966])).
% 4.64/4.82 tff(23063,plain,
% 4.64/4.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 4.64/4.82 inference(rewrite,[status(thm)],[])).
% 4.64/4.82 tff(23064,plain,
% 4.64/4.82 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 4.64/4.82 inference(rewrite,[status(thm)],[])).
% 4.64/4.82 tff(23065,plain,
% 4.64/4.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))))),
% 4.64/4.82 inference(monotonicity,[status(thm)],[23064])).
% 4.64/4.82 tff(23066,plain,
% 4.64/4.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 4.64/4.82 inference(transitivity,[status(thm)],[23065, 23063])).
% 4.64/4.82 tff(23067,plain,
% 4.64/4.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1)))),
% 4.64/4.82 inference(quant_inst,[status(thm)],[])).
% 4.64/4.82 tff(23068,plain,
% 4.64/4.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))),
% 4.64/4.82 inference(modus_ponens,[status(thm)],[23067, 23066])).
% 4.64/4.82 tff(23069,plain,
% 4.64/4.82 (~b(elem!1, s(s(z)))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[23068, 178, 5090, 4932, 23062, 23059])).
% 4.64/4.82 tff(23070,plain,
% 4.64/4.82 (elem!1 = s(s(z))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[467, 23069, 22978])).
% 4.64/4.82 tff(23071,plain,
% 4.64/4.82 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(z)))),
% 4.64/4.82 inference(monotonicity,[status(thm)],[23070])).
% 4.64/4.82 tff(23072,plain,
% 4.64/4.82 (b(s(elem!1), s(s(z))) <=> b(s(elem!1), elem!1)),
% 4.64/4.82 inference(symmetry,[status(thm)],[23071])).
% 4.64/4.82 tff(23073,plain,
% 4.64/4.82 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[22614, 178, 22564, 22566, 5090, 4932])).
% 4.64/4.82 tff(23074,plain,
% 4.64/4.82 (r(s(s(s(s(z)))), s(s(s(z))))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[11185, 23073])).
% 4.64/4.82 tff(23075,plain,
% 4.64/4.82 (~(s(s(s(s(z)))) = elem!1)),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[22969, 23074, 22966])).
% 4.64/4.82 tff(23076,plain,
% 4.64/4.82 (r(s(elem!1), s(s(z)))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[421, 305, 1056])).
% 4.64/4.82 tff(23077,plain,
% 4.64/4.82 (~r(s(elem!1), z)),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[8621, 23076, 3261])).
% 4.64/4.82 tff(23078,plain,
% 4.64/4.82 (b(s(elem!1), z)),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[774, 23077])).
% 4.64/4.82 tff(23079,plain,
% 4.64/4.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 4.64/4.82 inference(rewrite,[status(thm)],[])).
% 4.64/4.82 tff(23080,plain,
% 4.64/4.82 (((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 4.64/4.82 inference(rewrite,[status(thm)],[])).
% 4.64/4.82 tff(23081,plain,
% 4.64/4.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1)))))),
% 4.64/4.82 inference(monotonicity,[status(thm)],[23080])).
% 4.64/4.82 tff(23082,plain,
% 4.64/4.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 4.64/4.82 inference(transitivity,[status(thm)],[23081, 23079])).
% 4.64/4.82 tff(23083,plain,
% 4.64/4.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))))),
% 4.64/4.82 inference(quant_inst,[status(thm)],[])).
% 4.64/4.82 tff(23084,plain,
% 4.64/4.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1)))),
% 4.64/4.82 inference(modus_ponens,[status(thm)],[23083, 23082])).
% 4.64/4.82 tff(23085,plain,
% 4.64/4.82 (~b(s(s(s(z))), s(elem!1))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[23084, 178, 855, 23078, 3008, 1127])).
% 4.64/4.82 tff(23086,plain,
% 4.64/4.82 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), elem!1)),
% 4.64/4.82 inference(monotonicity,[status(thm)],[668])).
% 4.64/4.82 tff(23087,plain,
% 4.64/4.82 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(elem!1))),
% 4.64/4.82 inference(symmetry,[status(thm)],[23086])).
% 4.64/4.82 tff(23088,plain,
% 4.64/4.82 (~(s(s(s(z))) = elem!1)),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[4830, 13450, 2484])).
% 4.64/4.82 tff(23089,plain,
% 4.64/4.82 (b(s(s(s(z))), elem!1)),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[4981, 23088, 22979])).
% 4.64/4.82 tff(23090,plain,
% 4.64/4.82 (b(s(s(s(z))), s(elem!1))),
% 4.64/4.82 inference(modus_ponens,[status(thm)],[23089, 23087])).
% 4.64/4.82 tff(23091,assumption,(~b(s(s(s(z))), s(elem!1))), introduced(assumption)).
% 4.64/4.82 tff(23092,plain,
% 4.64/4.82 ($false),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[23091, 23090])).
% 4.64/4.82 tff(23093,plain,((~(s(elem!1) = elem!1)) | b(s(s(s(z))), s(elem!1)) | r(s(s(s(z))), elem!1) | (s(s(elem!1)) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.82 tff(23094,plain,
% 4.64/4.82 (~(s(elem!1) = elem!1)),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[23093, 23085, 22979, 3340])).
% 4.64/4.82 tff(23095,plain,
% 4.64/4.82 (r(s(elem!1), elem!1)),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[677, 23094, 2141])).
% 4.64/4.82 tff(23096,plain,
% 4.64/4.82 (~r(s(s(z)), s(s(s(s(z)))))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[3478, 145, 3261])).
% 4.64/4.82 tff(23097,plain,
% 4.64/4.82 (b(s(s(z)), s(s(s(s(z)))))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[164, 23096])).
% 4.64/4.82 tff(23098,plain,
% 4.64/4.82 (~r(s(s(z)), elem!1)),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[2803, 1265, 224])).
% 4.64/4.82 tff(23099,plain,
% 4.64/4.82 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[390, 23076, 224])).
% 4.64/4.82 tff(23100,plain,
% 4.64/4.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~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))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~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))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 4.64/4.82 inference(rewrite,[status(thm)],[])).
% 4.64/4.82 tff(23101,plain,
% 4.64/4.82 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), 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(z, s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~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))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 4.64/4.82 inference(rewrite,[status(thm)],[])).
% 4.64/4.82 tff(23102,plain,
% 4.64/4.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1), z)) | (~b(s(elem!1), 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(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~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))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 4.64/4.82 inference(monotonicity,[status(thm)],[23101])).
% 4.64/4.82 tff(23103,plain,
% 4.64/4.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1), z)) | (~b(s(elem!1), 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(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~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))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 4.64/4.82 inference(transitivity,[status(thm)],[23102, 23100])).
% 4.64/4.82 tff(23104,plain,
% 4.64/4.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1), z)) | (~b(s(elem!1), 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(z, s(elem!1))))),
% 4.64/4.82 inference(quant_inst,[status(thm)],[])).
% 4.64/4.82 tff(23105,plain,
% 4.64/4.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~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))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 4.64/4.82 inference(modus_ponens,[status(thm)],[23104, 23103])).
% 4.64/4.82 tff(23106,plain,
% 4.64/4.82 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[23105, 178, 855, 23078, 595, 17330])).
% 4.64/4.82 tff(23107,plain,
% 4.64/4.82 (s(elem!1) = s(s(s(s(s(s(s(z)))))))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[395, 23106, 23099])).
% 4.64/4.82 tff(23108,plain,
% 4.64/4.82 (~(s(s(z)) = elem!1)),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[5361, 23107])).
% 4.64/4.82 tff(23109,plain,
% 4.64/4.82 (b(s(s(z)), elem!1)),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[448, 23108, 23098])).
% 4.64/4.82 tff(23110,plain,
% 4.64/4.82 (~r(z, elem!1)),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[3151, 23109, 22752, 23097, 323, 194, 145])).
% 4.64/4.82 tff(23111,plain,
% 4.64/4.82 (b(z, elem!1)),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[585, 23110, 318])).
% 4.64/4.82 tff(23112,plain,
% 4.64/4.82 (~r(elem!1, z)),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[493, 23108, 106, 22752, 3130, 145, 23097])).
% 4.64/4.82 tff(23113,plain,
% 4.64/4.82 (b(elem!1, z)),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[498, 23112, 290])).
% 4.64/4.82 tff(23114,plain,
% 4.64/4.82 (~b(elem!1, s(elem!1))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[863, 23113, 855, 23111, 23078])).
% 4.64/4.82 tff(23115,plain,
% 4.64/4.82 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.82 inference(monotonicity,[status(thm)],[23107])).
% 4.64/4.82 tff(23116,plain,
% 4.64/4.82 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 4.64/4.82 inference(symmetry,[status(thm)],[23115])).
% 4.64/4.82 tff(23117,plain,
% 4.64/4.82 (~r(z, s(s(s(elem!1))))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[22754, 13192, 145, 3261, 194])).
% 4.64/4.82 tff(23118,plain,
% 4.64/4.82 (b(z, s(s(s(elem!1))))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[2095, 23117])).
% 4.64/4.82 tff(23119,plain,
% 4.64/4.82 (~(elem!1 = s(s(z)))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[311, 23108])).
% 4.64/4.82 tff(23120,plain,
% 4.64/4.82 (b(elem!1, s(s(z)))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[467, 23119, 22978])).
% 4.64/4.82 tff(23121,plain,
% 4.64/4.82 (~(elem!1 = s(s(s(s(z)))))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[435, 23108, 106, 107, 224, 305])).
% 4.64/4.82 tff(23122,plain,
% 4.64/4.82 (~r(z, elem!1)),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[814, 23121, 106, 23097, 23120, 23108, 145, 22752])).
% 4.64/4.82 tff(23123,plain,
% 4.64/4.82 (b(z, elem!1)),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[585, 23122, 318])).
% 4.64/4.82 tff(23124,plain,
% 4.64/4.82 (~r(elem!1, z)),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[493, 23121, 106, 22752, 23108, 145, 23097])).
% 4.64/4.82 tff(23125,plain,
% 4.64/4.82 (b(elem!1, z)),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[498, 23124, 290])).
% 4.64/4.82 tff(23126,plain,
% 4.64/4.82 (~(s(s(s(s(z)))) = elem!1)),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[504, 23121])).
% 4.64/4.82 tff(23127,plain,
% 4.64/4.82 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[3502, 23126])).
% 4.64/4.82 tff(23128,plain,
% 4.64/4.82 (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[8403, 23127])).
% 4.64/4.82 tff(23129,plain,
% 4.64/4.82 ((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))))))))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[3612, 41, 8928])).
% 4.64/4.82 tff(23130,plain,
% 4.64/4.82 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[23129, 23128])).
% 4.64/4.82 tff(23131,plain,
% 4.64/4.82 (~r(elem!1, s(s(s(elem!1))))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[3623, 23130, 1265])).
% 4.64/4.82 tff(23132,plain,
% 4.64/4.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~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)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~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)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 4.64/4.82 inference(rewrite,[status(thm)],[])).
% 4.64/4.82 tff(23133,plain,
% 4.64/4.82 (((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, s(elem!1))) | (~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)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 4.64/4.82 inference(rewrite,[status(thm)],[])).
% 4.64/4.82 tff(23134,plain,
% 4.64/4.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~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)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 4.64/4.82 inference(monotonicity,[status(thm)],[23133])).
% 4.64/4.82 tff(23135,plain,
% 4.64/4.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~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)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 4.64/4.82 inference(transitivity,[status(thm)],[23134, 23132])).
% 4.64/4.82 tff(23136,plain,
% 4.64/4.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 4.64/4.82 inference(quant_inst,[status(thm)],[])).
% 4.64/4.82 tff(23137,plain,
% 4.64/4.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~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)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 4.64/4.82 inference(modus_ponens,[status(thm)],[23136, 23135])).
% 4.64/4.82 tff(23138,plain,
% 4.64/4.82 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[23137, 178, 855, 23078, 595, 17330])).
% 4.64/4.82 tff(23139,plain,
% 4.64/4.82 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[802, 118, 23076, 107])).
% 4.64/4.82 tff(23140,plain,
% 4.64/4.82 ((s(s(s(s(s(s(s(z))))))) = s(elem!1)) | b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[806, 41, 23139])).
% 4.64/4.82 tff(23141,plain,
% 4.64/4.82 (s(s(s(s(s(s(s(z))))))) = s(elem!1)),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[23140, 23138])).
% 4.64/4.82 tff(23142,plain,
% 4.64/4.82 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))),
% 4.64/4.82 inference(monotonicity,[status(thm)],[23107])).
% 4.64/4.82 tff(23143,plain,
% 4.64/4.82 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(z)))))),
% 4.64/4.82 inference(transitivity,[status(thm)],[23142, 214])).
% 4.64/4.82 tff(23144,plain,
% 4.64/4.82 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 4.64/4.82 inference(symmetry,[status(thm)],[23143])).
% 4.64/4.82 tff(23145,plain,
% 4.64/4.82 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 4.64/4.82 inference(monotonicity,[status(thm)],[23144])).
% 4.64/4.82 tff(23146,plain,
% 4.64/4.82 (~(s(s(s(s(z)))) = s(elem!1))),
% 4.64/4.82 inference(modus_ponens,[status(thm)],[79, 23145])).
% 4.64/4.82 tff(23147,plain,
% 4.64/4.82 (~(elem!1 = s(s(s(elem!1))))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[4015, 23146, 23141])).
% 4.64/4.82 tff(23148,plain,
% 4.64/4.82 (b(elem!1, s(s(s(elem!1))))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[2054, 23147, 23131])).
% 4.64/4.82 tff(23149,plain,
% 4.64/4.82 (~(s(s(elem!1)) = elem!1)),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[666, 23126, 23141])).
% 4.64/4.82 tff(23150,plain,
% 4.64/4.82 (~(s(elem!1) = elem!1)),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[672, 23149])).
% 4.64/4.82 tff(23151,plain,
% 4.64/4.82 (r(s(elem!1), elem!1)),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[677, 23150, 2141])).
% 4.64/4.82 tff(23152,plain,
% 4.64/4.82 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.82 inference(monotonicity,[status(thm)],[23107])).
% 4.64/4.82 tff(23153,plain,
% 4.64/4.82 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 4.64/4.82 inference(symmetry,[status(thm)],[23152])).
% 4.64/4.82 tff(23154,plain,
% 4.64/4.82 (r(s(s(s(elem!1))), s(elem!1))),
% 4.64/4.82 inference(modus_ponens,[status(thm)],[23130, 23153])).
% 4.64/4.82 tff(23155,plain,
% 4.64/4.82 (~r(s(s(s(elem!1))), elem!1)),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[1576, 23154, 23151])).
% 4.64/4.82 tff(23156,plain,
% 4.64/4.82 (~(s(s(s(elem!1))) = elem!1)),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[2489, 23147])).
% 4.64/4.82 tff(23157,plain,
% 4.64/4.82 (b(s(s(s(elem!1))), elem!1)),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[570, 23156, 23155])).
% 4.64/4.82 tff(23158,plain,
% 4.64/4.82 ($false),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[12925, 23157, 23148, 2043, 23125, 23123])).
% 4.64/4.82 tff(23159,plain,(b(s(elem!1), s(s(z))) | (~b(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | b(s(elem!1), elem!1) | b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))) | (elem!1 = z) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (s(elem!1) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.82 tff(23160,plain,
% 4.64/4.82 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[23159, 305, 1265, 23118, 2141, 290, 106, 145, 107, 224, 855, 595, 3261, 1056])).
% 4.64/4.82 tff(23161,plain,
% 4.64/4.82 (b(s(s(s(elem!1))), s(elem!1))),
% 4.64/4.82 inference(modus_ponens,[status(thm)],[23160, 23116])).
% 4.64/4.82 tff(23162,plain,
% 4.64/4.82 (b(elem!1, s(elem!1))),
% 4.64/4.82 inference(modus_ponens,[status(thm)],[2044, 3867])).
% 4.64/4.82 tff(23163,plain,
% 4.64/4.82 ($false),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[751, 23162])).
% 4.64/4.82 tff(23164,plain,((~b(s(s(s(elem!1))), s(elem!1))) | b(elem!1, s(elem!1)) | (~(elem!1 = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.82 tff(23165,plain,
% 4.64/4.82 (~(elem!1 = s(s(s(elem!1))))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[23164, 23161, 23114])).
% 4.64/4.82 tff(23166,plain,
% 4.64/4.82 (~b(elem!1, s(s(s(elem!1))))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[2052, 23161, 23118, 855, 23113])).
% 4.64/4.82 tff(23167,plain,
% 4.64/4.82 (r(elem!1, s(s(s(elem!1))))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[2054, 23166, 23165])).
% 4.64/4.82 tff(23168,plain,
% 4.64/4.82 (~(s(s(elem!1)) = elem!1)),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[666, 23141, 323])).
% 4.64/4.82 tff(23169,plain,
% 4.64/4.82 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[348, 23168])).
% 4.64/4.82 tff(23170,plain,
% 4.64/4.82 (~(s(elem!1) = s(s(s(elem!1))))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[5395, 23169])).
% 4.64/4.82 tff(23171,plain,
% 4.64/4.82 (~b(s(elem!1), s(s(s(elem!1))))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[6736, 23161, 23118, 23078, 855])).
% 4.64/4.82 tff(23172,plain,
% 4.64/4.82 (r(s(elem!1), s(s(s(elem!1))))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[5432, 23171, 23170])).
% 4.64/4.82 tff(23173,plain,
% 4.64/4.82 ($false),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[9138, 23172, 23167, 23095])).
% 4.64/4.82 tff(23174,plain,(b(s(elem!1), s(s(z))) | (~b(z, s(elem!1))) | (elem!1 = z) | (s(s(s(s(z)))) = elem!1) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | b(s(elem!1), elem!1) | r(s(s(s(z))), elem!1) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.82 tff(23175,plain,
% 4.64/4.82 (b(s(elem!1), s(s(z)))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[23174, 23051, 290, 23075, 194, 47, 106, 2141, 22979, 22986, 22984, 22568, 107, 224, 22560, 1265, 1056])).
% 4.64/4.82 tff(23176,plain,
% 4.64/4.82 (b(s(elem!1), elem!1)),
% 4.64/4.82 inference(modus_ponens,[status(thm)],[23175, 23072])).
% 4.64/4.82 tff(23177,plain,
% 4.64/4.82 ($false),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[2141, 23176])).
% 4.64/4.82 tff(23178,plain,(b(s(elem!1), elem!1) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | r(elem!1, s(s(s(z)))) | r(s(s(s(z))), elem!1) | b(z, s(s(s(s(z))))) | (elem!1 = z) | (~r(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)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.82 tff(23179,plain,
% 4.64/4.82 (b(s(elem!1), elem!1)),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[23178, 1056, 22602, 22962, 22950, 1, 22731, 22977, 106, 22600, 22595, 22946, 22597, 104])).
% 4.64/4.82 tff(23180,plain,
% 4.64/4.82 (b(s(elem!1), s(s(z)))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[421, 12729, 1056])).
% 4.64/4.82 tff(23181,plain,
% 4.64/4.82 (b(s(s(z)), s(elem!1))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[1067, 13326, 2311])).
% 4.64/4.82 tff(23182,plain,
% 4.64/4.82 (~r(s(elem!1), s(s(s(s(z)))))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[2766, 2333, 145])).
% 4.64/4.82 tff(23183,plain,
% 4.64/4.82 (~b(s(elem!1), s(s(s(s(z)))))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[1079, 23181, 22752, 23097, 23180])).
% 4.64/4.82 tff(23184,plain,
% 4.64/4.82 (s(elem!1) = s(s(s(s(z))))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[1084, 23183, 23182])).
% 4.64/4.82 tff(23185,plain,
% 4.64/4.82 (~(elem!1 = s(s(z)))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[1353, 23184, 323])).
% 4.64/4.82 tff(23186,plain,
% 4.64/4.82 (b(elem!1, s(s(z)))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[467, 23185, 460])).
% 4.64/4.82 tff(23187,plain,
% 4.64/4.82 (~(s(s(z)) = elem!1)),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[3230, 23185])).
% 4.64/4.82 tff(23188,plain,
% 4.64/4.82 (b(s(s(z)), elem!1)),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[448, 23187, 10828])).
% 4.64/4.82 tff(23189,plain,
% 4.64/4.82 ($false),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[13708, 23188, 23186, 683, 23181, 23180])).
% 4.64/4.82 tff(23190,plain,((~r(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | r(s(s(z)), elem!1) | r(elem!1, s(s(z))) | (s(s(s(s(z)))) = elem!1) | (s(elem!1) = s(s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.82 tff(23191,plain,
% 4.64/4.82 (~r(z, s(elem!1))),
% 4.64/4.82 inference(unit_resolution,[status(thm)],[23190, 23179, 22972, 22976, 22970, 1056, 47, 22560])).
% 4.64/4.83 tff(23192,plain,
% 4.64/4.83 (b(z, s(elem!1))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[2351, 23191])).
% 4.64/4.83 tff(23193,plain,
% 4.64/4.83 (~(s(s(s(z))) = elem!1)),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[23057, 23192, 1])).
% 4.64/4.83 tff(23194,plain,
% 4.64/4.83 (b(s(s(s(z))), elem!1)),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[4981, 23193, 22950])).
% 4.64/4.83 tff(23195,assumption,(b(s(s(s(z))), elem!1)), introduced(assumption)).
% 4.64/4.83 tff(23196,plain,
% 4.64/4.83 (b(s(s(z)), elem!1)),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[448, 12, 10828])).
% 4.64/4.83 tff(23197,plain,
% 4.64/4.83 (~r(elem!1, z)),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[493, 12, 106, 202, 469, 145, 167])).
% 4.64/4.83 tff(23198,plain,
% 4.64/4.83 (b(elem!1, z)),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[498, 23197, 290])).
% 4.64/4.83 tff(23199,plain,
% 4.64/4.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 4.64/4.83 inference(rewrite,[status(thm)],[])).
% 4.64/4.83 tff(23200,plain,
% 4.64/4.83 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 4.64/4.83 inference(rewrite,[status(thm)],[])).
% 4.64/4.83 tff(23201,plain,
% 4.64/4.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))))),
% 4.64/4.83 inference(monotonicity,[status(thm)],[23200])).
% 4.64/4.83 tff(23202,plain,
% 4.64/4.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 4.64/4.83 inference(transitivity,[status(thm)],[23201, 23199])).
% 4.64/4.83 tff(23203,plain,
% 4.64/4.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 4.64/4.83 inference(quant_inst,[status(thm)],[])).
% 4.64/4.83 tff(23204,plain,
% 4.64/4.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))),
% 4.64/4.83 inference(modus_ponens,[status(thm)],[23203, 23202])).
% 4.64/4.83 tff(23205,plain,
% 4.64/4.83 ($false),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[23204, 178, 23198, 23196, 5090, 1127, 23195])).
% 4.64/4.83 tff(23206,plain,((s(s(z)) = elem!1) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (elem!1 = z) | (~r(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (elem!1 = s(s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | r(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.64/4.83 tff(23207,plain,
% 4.64/4.83 (s(s(z)) = elem!1),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[23206, 23194, 22975, 22597, 22731, 106, 22566, 22973, 47, 22564, 22972])).
% 4.64/4.83 tff(23208,plain,
% 4.64/4.83 (s(s(s(z))) = s(elem!1)),
% 4.64/4.83 inference(monotonicity,[status(thm)],[23207])).
% 4.64/4.83 tff(23209,plain,
% 4.64/4.83 (s(s(s(s(z)))) = s(s(elem!1))),
% 4.64/4.83 inference(monotonicity,[status(thm)],[23208])).
% 4.64/4.83 tff(23210,plain,
% 4.64/4.83 (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)))),
% 4.64/4.83 inference(monotonicity,[status(thm)],[23209])).
% 4.64/4.83 tff(23211,plain,
% 4.64/4.83 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.64/4.83 inference(modus_ponens,[status(thm)],[104, 23210])).
% 4.64/4.83 tff(23212,plain,
% 4.64/4.83 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[10679, 23207, 22955])).
% 4.64/4.83 tff(23213,plain,
% 4.64/4.83 (~r(z, s(s(s(elem!1))))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[22754, 13192, 47, 22560, 22977])).
% 4.64/4.83 tff(23214,plain,
% 4.64/4.83 (b(z, s(s(s(elem!1))))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[2095, 23213])).
% 4.64/4.83 tff(23215,plain,
% 4.64/4.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(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(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(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(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 4.64/4.83 inference(rewrite,[status(thm)],[])).
% 4.64/4.83 tff(23216,plain,
% 4.64/4.83 (((~b(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)))) | (~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(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(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(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 4.64/4.83 inference(rewrite,[status(thm)],[])).
% 4.64/4.83 tff(23217,plain,
% 4.64/4.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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)))) | (~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(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(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(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 4.64/4.83 inference(monotonicity,[status(thm)],[23216])).
% 4.64/4.83 tff(23218,plain,
% 4.64/4.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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)))) | (~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(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(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(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 4.64/4.83 inference(transitivity,[status(thm)],[23217, 23215])).
% 4.64/4.83 tff(23219,plain,
% 4.64/4.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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)))) | (~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(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(elem!1))))))),
% 4.64/4.83 inference(quant_inst,[status(thm)],[])).
% 4.64/4.83 tff(23220,plain,
% 4.64/4.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(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(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 4.64/4.83 inference(modus_ponens,[status(thm)],[23219, 23218])).
% 4.64/4.83 tff(23221,plain,
% 4.64/4.83 (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[23220, 178, 23214, 23212, 22568, 23211])).
% 4.64/4.83 tff(23222,plain,
% 4.64/4.83 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[17549, 178, 23214, 23212, 22568, 23211])).
% 4.64/4.83 tff(23223,plain,
% 4.64/4.83 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[23129, 11632])).
% 4.64/4.83 tff(23224,plain,
% 4.64/4.83 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[5059, 118, 8216, 23223])).
% 4.64/4.83 tff(23225,plain,
% 4.64/4.83 (b(s(s(s(z))), s(s(s(elem!1))))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[9126, 23224, 8246])).
% 4.64/4.83 tff(23226,plain,
% 4.64/4.83 (~r(s(s(s(z))), s(s(z)))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[8218, 107, 8216])).
% 4.64/4.83 tff(23227,plain,
% 4.64/4.83 (b(s(s(s(z))), s(s(z)))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[4966, 23226])).
% 4.64/4.83 tff(23228,plain,
% 4.64/4.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(z))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 4.64/4.83 inference(rewrite,[status(thm)],[])).
% 4.64/4.83 tff(23229,plain,
% 4.64/4.83 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 4.64/4.83 inference(rewrite,[status(thm)],[])).
% 4.64/4.83 tff(23230,plain,
% 4.64/4.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 4.64/4.83 inference(monotonicity,[status(thm)],[23229])).
% 4.64/4.83 tff(23231,plain,
% 4.64/4.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 4.64/4.83 inference(transitivity,[status(thm)],[23230, 23228])).
% 4.64/4.83 tff(23232,plain,
% 4.64/4.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 4.64/4.83 inference(quant_inst,[status(thm)],[])).
% 4.64/4.83 tff(23233,plain,
% 4.64/4.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 4.64/4.83 inference(modus_ponens,[status(thm)],[23232, 23231])).
% 4.64/4.83 tff(23234,plain,
% 4.64/4.83 ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[23233, 178, 167, 23227, 3831])).
% 4.64/4.83 tff(23235,plain,
% 4.64/4.83 (~b(s(s(s(elem!1))), s(s(z)))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[23234, 23225])).
% 4.64/4.83 tff(23236,plain,
% 4.64/4.83 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[5118, 3521, 5116])).
% 4.64/4.83 tff(23237,plain,
% 4.64/4.83 (~r(s(s(s(elem!1))), s(s(z)))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[10401, 23236, 107])).
% 4.64/4.83 tff(23238,plain,
% 4.64/4.83 ($false),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[4209, 41, 23237, 23235, 4181])).
% 4.64/4.83 tff(23239,plain,((s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), 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(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.83 tff(23240,plain,
% 4.64/4.83 ($false),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[23239, 23222, 23221, 22971, 22953, 8216, 22600, 22564, 22955])).
% 4.64/4.83 tff(23241,plain,((s(elem!1) = s(s(z))) | (~r(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)))))) | (~r(s(s(z)), z)) | b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.83 tff(23242,plain,
% 4.64/4.83 (s(elem!1) = s(s(z))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[23241, 8216, 104, 106, 1])).
% 4.64/4.83 tff(23243,plain,
% 4.64/4.83 (s(s(elem!1)) = s(s(s(z)))),
% 4.64/4.83 inference(monotonicity,[status(thm)],[23242])).
% 4.64/4.83 tff(23244,plain,
% 4.64/4.83 ((s(s(elem!1)) = elem!1) <=> (s(s(s(z))) = elem!1)),
% 4.64/4.83 inference(monotonicity,[status(thm)],[23243])).
% 4.64/4.83 tff(23245,plain,
% 4.64/4.83 ((s(s(elem!1)) = elem!1) <=> (elem!1 = s(s(s(z))))),
% 4.64/4.83 inference(transitivity,[status(thm)],[23244, 10420])).
% 4.64/4.83 tff(23246,plain,
% 4.64/4.83 ((s(s(elem!1)) = elem!1) <=> (s(s(s(z))) = elem!1)),
% 4.64/4.83 inference(transitivity,[status(thm)],[23245, 10421])).
% 4.64/4.83 tff(23247,plain,
% 4.64/4.83 ((~(s(s(elem!1)) = elem!1)) <=> (~(s(s(s(z))) = elem!1))),
% 4.64/4.83 inference(monotonicity,[status(thm)],[23246])).
% 4.64/4.83 tff(23248,plain,
% 4.64/4.83 (~(elem!1 = s(s(s(s(elem!1)))))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[1422, 23242])).
% 4.64/4.83 tff(23249,plain,
% 4.64/4.83 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[1509, 23248])).
% 4.64/4.83 tff(23250,plain,
% 4.64/4.83 (~(elem!1 = s(s(elem!1)))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[1539, 23249])).
% 4.64/4.83 tff(23251,plain,
% 4.64/4.83 (~(s(s(elem!1)) = elem!1)),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[1546, 23250])).
% 4.64/4.83 tff(23252,plain,
% 4.64/4.83 (~(s(s(s(z))) = elem!1)),
% 4.64/4.83 inference(modus_ponens,[status(thm)],[23251, 23247])).
% 4.64/4.83 tff(23253,plain,
% 4.64/4.83 ((s(elem!1) = elem!1) <=> (s(s(z)) = elem!1)),
% 4.64/4.83 inference(monotonicity,[status(thm)],[23242])).
% 4.64/4.83 tff(23254,plain,
% 4.64/4.83 ((~(s(elem!1) = elem!1)) <=> (~(s(s(z)) = elem!1))),
% 4.64/4.83 inference(monotonicity,[status(thm)],[23253])).
% 4.64/4.83 tff(23255,plain,
% 4.64/4.83 (~(s(elem!1) = elem!1)),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[672, 23251])).
% 4.64/4.83 tff(23256,plain,
% 4.64/4.83 (~(s(s(z)) = elem!1)),
% 4.64/4.83 inference(modus_ponens,[status(thm)],[23255, 23254])).
% 4.64/4.83 tff(23257,plain,
% 4.64/4.83 (~b(s(s(s(z))), elem!1)),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[23206, 23256, 22975, 22597, 22731, 106, 22566, 22973, 47, 22564, 22972])).
% 4.64/4.83 tff(23258,plain,
% 4.64/4.83 ($false),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[4981, 23257, 23252, 22950])).
% 4.64/4.83 tff(23259,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.83 tff(23260,plain,
% 4.64/4.83 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[23259, 106, 104, 1])).
% 4.64/4.83 tff(23261,plain,
% 4.64/4.83 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[20667, 23260])).
% 4.64/4.83 tff(23262,plain,
% 4.64/4.83 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[20797, 16062, 145])).
% 4.64/4.83 tff(23263,plain,
% 4.64/4.83 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[10755, 23262])).
% 4.64/4.83 tff(23264,plain,
% 4.64/4.83 (~r(s(s(z)), s(s(s(s(z)))))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[3478, 145, 22560])).
% 4.64/4.83 tff(23265,plain,
% 4.64/4.83 (b(s(s(z)), s(s(s(s(z)))))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[164, 23264])).
% 4.64/4.83 tff(23266,plain,
% 4.64/4.83 (~r(s(s(s(s(z)))), s(s(z)))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[3269, 145, 22560])).
% 4.64/4.83 tff(23267,plain,
% 4.64/4.83 (b(s(s(s(s(z)))), s(s(z)))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[102, 23266])).
% 4.64/4.83 tff(23268,plain,
% 4.64/4.83 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[8067, 23267, 22560, 104, 145])).
% 4.64/4.83 tff(23269,plain,
% 4.64/4.83 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[271, 23268])).
% 4.64/4.83 tff(23270,plain,
% 4.64/4.83 (~b(z, s(s(s(z))))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[8267, 178, 104, 23269, 23263, 3002])).
% 4.64/4.83 tff(23271,plain,
% 4.64/4.83 (r(z, s(s(s(z))))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[4920, 23270])).
% 4.64/4.83 tff(23272,plain,
% 4.64/4.83 (~r(s(s(s(s(z)))), z)),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[10454, 23271, 22560, 23267, 23265, 23263])).
% 4.64/4.83 tff(23273,plain,
% 4.64/4.83 (b(s(s(s(s(z)))), z)),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[191, 23272])).
% 4.64/4.83 tff(23274,plain,
% 4.64/4.83 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[20754, 23273, 104, 3002, 23263])).
% 4.64/4.83 tff(23275,plain,
% 4.64/4.83 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[133, 23274])).
% 4.64/4.83 tff(23276,plain,
% 4.64/4.83 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[3102, 23275, 106])).
% 4.64/4.83 tff(23277,plain,
% 4.64/4.83 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[249, 23276])).
% 4.64/4.83 tff(23278,plain,
% 4.64/4.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.64/4.83 inference(rewrite,[status(thm)],[])).
% 4.64/4.83 tff(23279,plain,
% 4.64/4.83 (((~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(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(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(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.64/4.83 inference(rewrite,[status(thm)],[])).
% 4.64/4.83 tff(23280,plain,
% 4.64/4.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(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(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z))))))),
% 4.64/4.83 inference(monotonicity,[status(thm)],[23279])).
% 4.64/4.83 tff(23281,plain,
% 4.64/4.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(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(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.64/4.83 inference(transitivity,[status(thm)],[23280, 23278])).
% 4.64/4.83 tff(23282,plain,
% 4.64/4.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(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(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.64/4.83 inference(quant_inst,[status(thm)],[])).
% 4.64/4.83 tff(23283,plain,
% 4.64/4.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z))))),
% 4.64/4.83 inference(modus_ponens,[status(thm)],[23282, 23281])).
% 4.64/4.83 tff(23284,plain,
% 4.64/4.83 ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z))))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[23283, 178, 104, 23265, 3002])).
% 4.64/4.83 tff(23285,plain,
% 4.64/4.83 (~b(s(s(s(z))), s(s(z)))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[23284, 23277])).
% 4.64/4.83 tff(23286,plain,
% 4.64/4.83 (r(s(s(s(z))), s(s(z)))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[4966, 23285])).
% 4.64/4.83 tff(23287,plain,
% 4.64/4.83 ($false),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[6019, 118, 22560, 23286, 16062])).
% 4.64/4.83 tff(23288,plain,((~r(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.83 tff(23289,plain,
% 4.64/4.83 (~r(s(s(s(z))), z)),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[23288, 23261, 104, 106, 47])).
% 4.64/4.83 tff(23290,plain,
% 4.64/4.83 (b(s(s(s(z))), z)),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[21073, 23289])).
% 4.64/4.83 tff(23291,plain,
% 4.64/4.83 ($false),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[1259, 178, 104, 166, 167, 202, 1146])).
% 4.64/4.83 tff(23292,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.83 tff(23293,plain,
% 4.64/4.83 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[23292, 166, 104, 167, 202])).
% 4.64/4.83 tff(23294,plain,
% 4.64/4.83 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[3578, 23293])).
% 4.64/4.83 tff(23295,plain,
% 4.64/4.83 ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z))))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[23283, 178, 104, 167, 3002])).
% 4.64/4.83 tff(23296,plain,
% 4.64/4.83 (~b(s(s(s(z))), s(s(z)))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[23295, 166])).
% 4.64/4.83 tff(23297,plain,
% 4.64/4.83 (r(s(s(s(z))), s(s(z)))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[4966, 23296])).
% 4.64/4.83 tff(23298,plain,
% 4.64/4.83 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[1175, 118, 23297, 23294])).
% 4.64/4.83 tff(23299,plain,
% 4.64/4.83 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 23298])).
% 4.64/4.83 tff(23300,plain,
% 4.64/4.83 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[123, 23294, 106])).
% 4.64/4.83 tff(23301,plain,
% 4.64/4.83 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[133, 23300])).
% 4.64/4.83 tff(23302,plain,
% 4.64/4.83 ($false),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[1207, 178, 595, 23301, 1127, 3002, 23299])).
% 4.64/4.83 tff(23303,plain,((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)) | (~b(s(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(z))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.83 tff(23304,plain,
% 4.64/4.83 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[23303, 23290, 22568, 23261, 106, 104, 22564, 22566])).
% 4.64/4.83 tff(23305,plain,
% 4.64/4.83 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[249, 23304])).
% 4.64/4.83 tff(23306,plain,
% 4.64/4.83 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[3102, 23305, 106])).
% 4.64/4.83 tff(23307,plain,
% 4.64/4.83 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[133, 23306])).
% 4.64/4.83 tff(23308,plain,
% 4.64/4.83 ($false),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[4910, 118, 145, 4952, 4891])).
% 4.64/4.83 tff(23309,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.83 tff(23310,plain,
% 4.64/4.83 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[23309, 4952, 145])).
% 4.64/4.83 tff(23311,plain,
% 4.64/4.83 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[10755, 23310])).
% 4.64/4.83 tff(23312,plain,
% 4.64/4.83 (~b(s(s(s(s(z)))), z)),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[20754, 23311, 104, 3002, 146])).
% 4.64/4.83 tff(23313,plain,
% 4.64/4.83 (~r(s(s(s(s(z)))), z)),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[10454, 23311, 22560, 23267, 23265, 4952])).
% 4.64/4.83 tff(23314,plain,
% 4.64/4.83 ($false),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[191, 23313, 23312])).
% 4.64/4.83 tff(23315,plain,((~r(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.83 tff(23316,plain,
% 4.64/4.83 (~r(z, s(s(s(z))))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[23315, 23261, 104, 23307, 47])).
% 4.64/4.83 tff(23317,plain,
% 4.64/4.83 (b(z, s(s(s(z))))),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[4920, 23316])).
% 4.64/4.83 tff(23318,plain,
% 4.64/4.83 ($false),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[1319, 178, 22568, 23307, 23317, 23290, 23261])).
% 4.64/4.83 tff(23319,plain,((~r(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.83 tff(23320,plain,
% 4.64/4.83 (~r(s(s(z)), z)),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[23319, 1, 104])).
% 4.64/4.83 tff(23321,plain,
% 4.64/4.83 (b(s(s(z)), z)),
% 4.64/4.83 inference(unit_resolution,[status(thm)],[3249, 23320])).
% 4.64/4.83 tff(23322,plain,
% 4.64/4.83 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[22591, 8216, 167, 202, 595, 104])).
% 4.64/4.84 tff(23323,plain,
% 4.64/4.84 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[222, 23322])).
% 4.64/4.84 tff(23324,plain,
% 4.64/4.84 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[17447, 23323])).
% 4.64/4.84 tff(23325,plain,
% 4.64/4.84 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[3578, 23324])).
% 4.64/4.84 tff(23326,plain,
% 4.64/4.84 (~r(s(s(s(z))), s(s(z)))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[8218, 23325, 8216])).
% 4.64/4.84 tff(23327,plain,
% 4.64/4.84 (b(s(s(s(z))), s(s(z)))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[4966, 23326])).
% 4.64/4.84 tff(23328,plain,
% 4.64/4.84 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[4945, 23327])).
% 4.64/4.84 tff(23329,plain,
% 4.64/4.84 (r(s(s(s(s(z)))), s(s(s(z))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[11185, 23328])).
% 4.64/4.84 tff(23330,plain,
% 4.64/4.84 (~r(s(s(s(s(z)))), z)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[20784, 23329, 16062])).
% 4.64/4.84 tff(23331,plain,
% 4.64/4.84 (b(s(s(s(s(z)))), z)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[191, 23330])).
% 4.64/4.84 tff(23332,plain,
% 4.64/4.84 ($false),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[14128, 178, 3461, 23331, 167, 23323, 595])).
% 4.64/4.84 tff(23333,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.84 tff(23334,plain,
% 4.64/4.84 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[23333, 16062, 23265, 23269, 3461, 23267, 23263, 104])).
% 4.64/4.84 tff(23335,plain,
% 4.64/4.84 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[20667, 23334])).
% 4.64/4.84 tff(23336,plain,
% 4.64/4.84 ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[8267, 178, 104, 23269, 23263])).
% 4.64/4.84 tff(23337,plain,
% 4.64/4.84 (~b(z, s(s(s(z))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[23336, 23335])).
% 4.64/4.84 tff(23338,plain,
% 4.64/4.84 (r(z, s(s(s(z))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[4920, 23337])).
% 4.64/4.84 tff(23339,plain,
% 4.64/4.84 (~r(s(s(s(s(z)))), z)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[10454, 23338, 22560, 23267, 23265, 23263])).
% 4.64/4.84 tff(23340,plain,
% 4.64/4.84 (b(s(s(s(s(z)))), z)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[191, 23339])).
% 4.64/4.84 tff(23341,plain,
% 4.64/4.84 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[14852, 23340, 104, 23265, 3461])).
% 4.64/4.84 tff(23342,plain,
% 4.64/4.84 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[3578, 23341])).
% 4.64/4.84 tff(23343,plain,
% 4.64/4.84 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[23315, 23338, 104, 23335, 145])).
% 4.64/4.84 tff(23344,plain,
% 4.64/4.84 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[133, 23343])).
% 4.64/4.84 tff(23345,plain,
% 4.64/4.84 ($false),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[11826, 118, 22560, 23344, 23342])).
% 4.64/4.84 tff(23346,plain,((~r(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.84 tff(23347,plain,
% 4.64/4.84 (~r(s(s(s(z))), z)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[23346, 3461, 104, 145])).
% 4.64/4.84 tff(23348,plain,
% 4.64/4.84 (b(s(s(s(z))), z)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[21073, 23347])).
% 4.64/4.84 tff(23349,plain,
% 4.64/4.84 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[10454, 4952, 3261, 22752, 23097, 194])).
% 4.64/4.84 tff(23350,plain,
% 4.64/4.84 ($false),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[10755, 23349, 23310])).
% 4.64/4.84 tff(23351,plain,((~r(z, s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.84 tff(23352,plain,
% 4.64/4.84 (~r(z, s(s(s(z))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[23351, 194, 22560, 145])).
% 4.64/4.84 tff(23353,plain,
% 4.64/4.84 (b(z, s(s(s(z))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[4920, 23352])).
% 4.64/4.84 tff(23354,plain,
% 4.64/4.84 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[1319, 178, 595, 12395, 3008, 1127])).
% 4.64/4.84 tff(23355,plain,
% 4.64/4.84 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[20667, 23354])).
% 4.64/4.84 tff(23356,plain,
% 4.64/4.84 (~r(s(s(s(z))), s(s(z)))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[8218, 23355, 107])).
% 4.64/4.84 tff(23357,plain,
% 4.64/4.84 ($false),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[2944, 178, 595, 146, 3008, 1127, 21855])).
% 4.64/4.84 tff(23358,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.84 tff(23359,plain,
% 4.64/4.84 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[23358, 12395, 595, 3008, 1127])).
% 4.64/4.84 tff(23360,plain,
% 4.64/4.84 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 23359])).
% 4.64/4.84 tff(23361,plain,
% 4.64/4.84 ($false),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[16016, 118, 7670, 107, 16063])).
% 4.64/4.84 tff(23362,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.84 tff(23363,plain,
% 4.64/4.84 (~r(s(s(z)), s(s(s(z))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[23362, 23360, 107])).
% 4.64/4.84 tff(23364,plain,
% 4.64/4.84 (b(s(s(z)), s(s(s(z))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[5088, 23363])).
% 4.64/4.84 tff(23365,plain,
% 4.64/4.84 (~b(s(s(s(z))), s(s(z)))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[5098, 23364, 3461, 1127, 3008])).
% 4.64/4.84 tff(23366,plain,
% 4.64/4.84 ($false),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[4966, 23365, 23356])).
% 4.64/4.84 tff(23367,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.84 tff(23368,plain,
% 4.64/4.84 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[23367, 23353, 23348, 3461, 23269, 22560])).
% 4.64/4.84 tff(23369,plain,
% 4.64/4.84 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[3578, 23368])).
% 4.64/4.84 tff(23370,plain,
% 4.64/4.84 ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[8089, 178, 104, 23265, 23267])).
% 4.64/4.84 tff(23371,plain,
% 4.64/4.84 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[23370, 23369])).
% 4.64/4.84 tff(23372,plain,
% 4.64/4.84 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[222, 23371])).
% 4.64/4.84 tff(23373,plain,
% 4.64/4.84 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[22591, 23372, 23265, 23267, 23269, 104])).
% 4.64/4.84 tff(23374,plain,
% 4.64/4.84 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[20667, 23373])).
% 4.64/4.84 tff(23375,plain,
% 4.64/4.84 ($false),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[14923, 118, 194, 204, 108])).
% 4.64/4.84 tff(23376,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.84 tff(23377,plain,
% 4.64/4.84 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[23376, 194, 23372])).
% 4.64/4.84 tff(23378,plain,
% 4.64/4.84 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[133, 23377])).
% 4.64/4.84 tff(23379,plain,
% 4.64/4.84 ($false),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[1319, 178, 23269, 23378, 23353, 23348, 23374])).
% 4.64/4.84 tff(23380,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.84 tff(23381,plain,
% 4.64/4.84 (~r(s(s(s(s(z)))), z)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[23380, 23321, 104, 47])).
% 4.64/4.84 tff(23382,plain,
% 4.64/4.84 (b(s(s(s(s(z)))), z)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[191, 23381])).
% 4.64/4.84 tff(23383,plain,
% 4.64/4.84 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[14852, 23382, 104, 22564, 23321])).
% 4.64/4.84 tff(23384,plain,
% 4.64/4.84 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[3578, 23383])).
% 4.64/4.84 tff(23385,plain,
% 4.64/4.84 (~r(s(s(s(z))), z)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[23346, 23321, 104, 47])).
% 4.64/4.84 tff(23386,plain,
% 4.64/4.84 (b(s(s(s(z))), z)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[21073, 23385])).
% 4.64/4.84 tff(23387,plain,
% 4.64/4.84 (~b(z, s(s(s(z))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[23367, 23384, 23386, 23321, 22568, 22560])).
% 4.64/4.84 tff(23388,plain,
% 4.64/4.84 (r(z, s(s(s(z))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[4920, 23387])).
% 4.64/4.84 tff(23389,plain,
% 4.64/4.84 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[23309, 23388, 47])).
% 4.64/4.84 tff(23390,plain,
% 4.64/4.84 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[10755, 23389])).
% 4.64/4.84 tff(23391,plain,
% 4.64/4.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.64/4.84 inference(rewrite,[status(thm)],[])).
% 4.64/4.84 tff(23392,plain,
% 4.64/4.84 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(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(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.64/4.84 inference(rewrite,[status(thm)],[])).
% 4.64/4.84 tff(23393,plain,
% 4.64/4.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(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(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z))))))),
% 4.64/4.84 inference(monotonicity,[status(thm)],[23392])).
% 4.64/4.84 tff(23394,plain,
% 4.64/4.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(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(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.64/4.84 inference(transitivity,[status(thm)],[23393, 23391])).
% 4.64/4.84 tff(23395,plain,
% 4.64/4.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(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(z))), s(s(z)))))),
% 4.64/4.84 inference(quant_inst,[status(thm)],[])).
% 4.64/4.84 tff(23396,plain,
% 4.64/4.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z))))),
% 4.64/4.84 inference(modus_ponens,[status(thm)],[23395, 23394])).
% 4.64/4.84 tff(23397,plain,
% 4.64/4.84 (~b(s(s(s(z))), s(s(z)))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[23396, 178, 23321, 23382, 22564, 23390])).
% 4.64/4.84 tff(23398,plain,
% 4.64/4.84 (r(s(s(s(z))), s(s(z)))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[4966, 23397])).
% 4.64/4.84 tff(23399,plain,
% 4.64/4.84 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[8218, 23398, 23384])).
% 4.64/4.84 tff(23400,plain,
% 4.64/4.84 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[20667, 23399])).
% 4.64/4.84 tff(23401,plain,
% 4.64/4.84 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[23315, 23400, 104, 23388, 47])).
% 4.64/4.84 tff(23402,plain,
% 4.64/4.84 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[133, 23401])).
% 4.64/4.84 tff(23403,plain,
% 4.64/4.84 ($false),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[11826, 118, 22560, 23402, 23384])).
% 4.64/4.84 tff(23404,plain,(b(z, s(s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.84 tff(23405,plain,
% 4.64/4.84 (b(z, s(s(s(s(z)))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[23404, 104])).
% 4.64/4.84 tff(23406,plain,
% 4.64/4.84 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[11893, 178, 104, 23405, 22562])).
% 4.64/4.84 tff(23407,plain,
% 4.64/4.84 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[23406, 251])).
% 4.64/4.84 tff(23408,plain,
% 4.64/4.84 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[133, 23407])).
% 4.64/4.84 tff(23409,plain,
% 4.64/4.84 (~r(s(s(s(z))), z)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[20977, 8216, 4236])).
% 4.64/4.84 tff(23410,plain,
% 4.64/4.84 (b(s(s(s(z))), z)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[21073, 23409])).
% 4.64/4.84 tff(23411,plain,
% 4.64/4.84 (~r(z, s(s(s(z))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[21510, 118, 4236, 8216])).
% 4.64/4.84 tff(23412,plain,
% 4.64/4.84 (b(z, s(s(s(z))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[4920, 23411])).
% 4.64/4.84 tff(23413,plain,
% 4.64/4.84 (~r(s(s(s(s(z)))), z)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[9569, 193, 22560])).
% 4.64/4.84 tff(23414,plain,
% 4.64/4.84 (b(s(s(s(s(z)))), z)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[191, 23413])).
% 4.64/4.84 tff(23415,plain,
% 4.64/4.84 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[21520, 8216, 23414, 4236, 23405])).
% 4.64/4.84 tff(23416,plain,
% 4.64/4.84 (r(s(s(s(z))), s(s(s(s(z)))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[10755, 23415])).
% 4.64/4.84 tff(23417,plain,
% 4.64/4.84 (~r(s(s(z)), s(s(s(z))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[5079, 118, 147, 23416])).
% 4.64/4.84 tff(23418,plain,
% 4.64/4.84 (b(s(s(z)), s(s(s(z))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[5088, 23417])).
% 4.64/4.84 tff(23419,plain,
% 4.64/4.84 (~r(s(s(s(z))), s(s(z)))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[20838, 23416, 193])).
% 4.64/4.84 tff(23420,plain,
% 4.64/4.84 (b(s(s(s(z))), s(s(z)))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[4966, 23419])).
% 4.64/4.84 tff(23421,plain,
% 4.64/4.84 (~b(s(s(z)), z)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[5098, 23412, 23420, 23410, 23418])).
% 4.64/4.84 tff(23422,plain,
% 4.64/4.84 (r(s(s(z)), z)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[3249, 23421])).
% 4.64/4.84 tff(23423,plain,
% 4.64/4.84 (~(s(s(z)) = elem!1)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[1345, 1342, 106])).
% 4.64/4.84 tff(23424,plain,
% 4.64/4.84 (~r(s(s(z)), elem!1)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[12239, 5284, 1687, 147, 469, 551, 318, 3261])).
% 4.64/4.84 tff(23425,plain,
% 4.64/4.84 ($false),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[448, 23424, 23423, 3241])).
% 4.64/4.84 tff(23426,plain,(r(elem!1, z) | b(s(s(z)), elem!1) | (~b(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (elem!1 = s(s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 4.64/4.84 tff(23427,plain,
% 4.64/4.84 (r(elem!1, z)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[23426, 3241, 3261, 1687, 290, 147, 106, 469])).
% 4.64/4.84 tff(23428,plain,
% 4.64/4.84 ($false),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[443, 23427, 19826, 106])).
% 4.64/4.84 tff(23429,plain,(b(s(s(z)), elem!1) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (elem!1 = z) | (~r(s(s(z)), s(s(s(s(z)))))) | (elem!1 = s(s(s(s(z))))) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.64/4.84 tff(23430,plain,
% 4.64/4.84 (b(s(s(z)), elem!1)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[23429, 12, 22560, 23405, 290, 147, 469, 23422])).
% 4.64/4.84 tff(23431,assumption,(s(elem!1) = s(s(s(z)))), introduced(assumption)).
% 4.64/4.84 tff(23432,plain,
% 4.64/4.84 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 4.64/4.84 inference(monotonicity,[status(thm)],[23431])).
% 4.64/4.84 tff(23433,plain,
% 4.64/4.84 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 4.64/4.84 inference(symmetry,[status(thm)],[23432])).
% 4.64/4.84 tff(23434,plain,
% 4.64/4.84 (s(s(z)) = elem!1),
% 4.64/4.84 inference(transitivity,[status(thm)],[66, 23433, 304])).
% 4.64/4.84 tff(23435,plain,
% 4.64/4.84 ($false),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[12, 23434])).
% 4.64/4.84 tff(23436,plain,((~(s(elem!1) = s(s(s(z))))) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.64/4.84 tff(23437,plain,
% 4.64/4.84 (~(s(elem!1) = s(s(s(z))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[23436, 12])).
% 4.64/4.84 tff(23438,plain,
% 4.64/4.84 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[11893, 178, 104, 23405, 23414])).
% 4.64/4.84 tff(23439,plain,
% 4.64/4.84 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[23438, 251])).
% 4.64/4.84 tff(23440,plain,
% 4.64/4.84 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[133, 23439])).
% 4.64/4.84 tff(23441,plain,
% 4.64/4.84 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[13684, 147, 22560, 23414])).
% 4.64/4.84 tff(23442,plain,
% 4.64/4.84 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[249, 23441])).
% 4.64/4.84 tff(23443,plain,
% 4.64/4.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 4.64/4.84 inference(rewrite,[status(thm)],[])).
% 4.64/4.84 tff(23444,plain,
% 4.64/4.84 (((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 4.64/4.84 inference(rewrite,[status(thm)],[])).
% 4.64/4.84 tff(23445,plain,
% 4.64/4.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))))),
% 4.64/4.84 inference(monotonicity,[status(thm)],[23444])).
% 4.64/4.84 tff(23446,plain,
% 4.64/4.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 4.64/4.84 inference(transitivity,[status(thm)],[23445, 23443])).
% 4.64/4.84 tff(23447,plain,
% 4.64/4.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 4.64/4.84 inference(quant_inst,[status(thm)],[])).
% 4.64/4.84 tff(23448,plain,
% 4.64/4.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 4.64/4.84 inference(modus_ponens,[status(thm)],[23447, 23446])).
% 4.64/4.84 tff(23449,plain,
% 4.64/4.84 ($false),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[23448, 118, 3261, 203, 107])).
% 4.64/4.84 tff(23450,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.84 tff(23451,plain,
% 4.64/4.84 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[23450, 4236, 22560])).
% 4.64/4.84 tff(23452,plain,
% 4.64/4.84 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[3578, 23451])).
% 4.64/4.84 tff(23453,plain,
% 4.64/4.84 (~r(elem!1, z)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[458, 450, 106])).
% 4.64/4.84 tff(23454,plain,
% 4.64/4.84 (b(elem!1, z)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[498, 23453, 290])).
% 4.64/4.84 tff(23455,plain,
% 4.64/4.84 (~r(s(s(s(s(z)))), z)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[199, 193, 106])).
% 4.64/4.84 tff(23456,plain,
% 4.64/4.84 (b(s(s(s(s(z)))), z)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[191, 23455])).
% 4.64/4.84 tff(23457,plain,
% 4.64/4.84 (~r(elem!1, s(s(s(s(z)))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[3785, 450, 193])).
% 4.64/4.84 tff(23458,plain,
% 4.64/4.84 (b(elem!1, s(s(s(s(z)))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[483, 23457, 469])).
% 4.64/4.84 tff(23459,plain,
% 4.64/4.84 (~r(s(s(s(s(z)))), elem!1)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[10883, 450, 193])).
% 4.64/4.84 tff(23460,plain,
% 4.64/4.84 (b(s(s(s(s(z)))), elem!1)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[3142, 23459, 551])).
% 4.64/4.84 tff(23461,plain,
% 4.64/4.84 ($false),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[16429, 23460, 23458, 23456, 23454, 818])).
% 4.64/4.84 tff(23462,plain,((~r(elem!1, s(s(z)))) | (~b(z, elem!1)) | (elem!1 = z) | (elem!1 = s(s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.84 tff(23463,plain,
% 4.64/4.84 (~r(elem!1, s(s(z)))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[23462, 818, 193, 106, 290, 469])).
% 4.64/4.84 tff(23464,plain,
% 4.64/4.84 (b(elem!1, s(s(z)))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[467, 23463, 462])).
% 4.64/4.84 tff(23465,plain,
% 4.64/4.84 ($false),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[11859, 23464, 11615, 166, 1146, 817])).
% 4.64/4.84 tff(23466,plain,((~b(z, elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (elem!1 = s(s(z))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), z)) | (elem!1 = z) | (elem!1 = s(s(s(s(z))))) | b(z, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.84 tff(23467,plain,
% 4.64/4.84 (~b(z, elem!1)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[23466, 644, 23452, 817, 462, 23442, 193, 23422, 290, 469, 4235])).
% 4.64/4.84 tff(23468,plain,
% 4.64/4.84 (r(z, elem!1)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[585, 23467, 318])).
% 4.64/4.84 tff(23469,plain,
% 4.64/4.84 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[11027, 23468, 23440])).
% 4.64/4.84 tff(23470,plain,
% 4.64/4.84 (~r(elem!1, s(s(z)))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[4862, 23468, 22560])).
% 4.64/4.84 tff(23471,plain,
% 4.64/4.84 (b(elem!1, s(s(z)))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[467, 23470, 462])).
% 4.64/4.84 tff(23472,plain,
% 4.64/4.84 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[14184, 23471, 23442, 23452, 644, 23469])).
% 4.64/4.84 tff(23473,plain,
% 4.64/4.84 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 4.64/4.84 inference(monotonicity,[status(thm)],[23472])).
% 4.64/4.84 tff(23474,plain,
% 4.64/4.84 (s(s(s(s(s(s(s(s(z)))))))) = s(elem!1)),
% 4.64/4.84 inference(symmetry,[status(thm)],[23473])).
% 4.64/4.84 tff(23475,plain,
% 4.64/4.84 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.84 inference(monotonicity,[status(thm)],[23474])).
% 4.64/4.84 tff(23476,plain,
% 4.64/4.84 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.84 inference(symmetry,[status(thm)],[23475])).
% 4.64/4.84 tff(23477,plain,
% 4.64/4.84 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.84 inference(monotonicity,[status(thm)],[23472])).
% 4.64/4.84 tff(23478,plain,
% 4.64/4.84 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[16181, 23472])).
% 4.64/4.84 tff(23479,plain,
% 4.64/4.84 (~(s(s(s(s(z)))) = s(elem!1))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[2168, 23478])).
% 4.64/4.84 tff(23480,plain,
% 4.64/4.84 (~(s(s(elem!1)) = elem!1)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[2510, 23479, 23472])).
% 4.64/4.84 tff(23481,plain,
% 4.64/4.84 (~(s(elem!1) = elem!1)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[672, 23480])).
% 4.64/4.84 tff(23482,plain,
% 4.64/4.84 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[686, 683, 679])).
% 4.64/4.84 tff(23483,plain,
% 4.64/4.84 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.84 inference(modus_ponens,[status(thm)],[23482, 11735])).
% 4.64/4.84 tff(23484,plain,
% 4.64/4.84 (~r(s(s(z)), s(elem!1))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[16259, 23483, 147, 104, 251, 679])).
% 4.64/4.84 tff(23485,plain,
% 4.64/4.84 (b(s(s(z)), s(elem!1))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[1067, 23484, 16233])).
% 4.64/4.84 tff(23486,plain,
% 4.64/4.84 (~b(s(elem!1), s(s(z)))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[13708, 23485, 817, 683, 812])).
% 4.64/4.84 tff(23487,plain,
% 4.64/4.84 (r(s(elem!1), s(s(z)))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[421, 23486, 10483])).
% 4.64/4.84 tff(23488,plain,
% 4.64/4.84 (~b(s(elem!1), s(s(s(s(z)))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[2529, 23485, 104, 23442, 23482])).
% 4.64/4.84 tff(23489,plain,
% 4.64/4.84 (r(s(elem!1), s(s(s(s(z)))))),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[1084, 23488, 16182])).
% 4.64/4.84 tff(23490,plain,
% 4.64/4.84 ($false),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[3949, 23489, 23487, 193])).
% 4.64/4.84 tff(23491,plain,((~b(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.84 tff(23492,plain,
% 4.64/4.84 (~b(s(elem!1), elem!1)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[23491, 23471, 104, 817, 193, 147, 251, 23472])).
% 4.64/4.84 tff(23493,plain,
% 4.64/4.84 (r(s(elem!1), elem!1)),
% 4.64/4.84 inference(unit_resolution,[status(thm)],[677, 23492, 23481])).
% 4.64/4.84 tff(23494,plain,
% 4.64/4.84 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.84 inference(modus_ponens,[status(thm)],[23493, 23477])).
% 4.64/4.84 tff(23495,plain,
% 4.64/4.84 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.84 inference(modus_ponens,[status(thm)],[23494, 23476])).
% 4.64/4.84 tff(23496,plain,
% 4.64/4.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 4.64/4.84 inference(rewrite,[status(thm)],[])).
% 4.64/4.84 tff(23497,plain,
% 4.64/4.84 (((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 4.64/4.84 inference(rewrite,[status(thm)],[])).
% 4.64/4.84 tff(23498,plain,
% 4.64/4.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))))),
% 4.64/4.84 inference(monotonicity,[status(thm)],[23497])).
% 4.64/4.84 tff(23499,plain,
% 4.64/4.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 4.64/4.84 inference(transitivity,[status(thm)],[23498, 23496])).
% 4.64/4.84 tff(23500,plain,
% 4.64/4.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 4.64/4.84 inference(quant_inst,[status(thm)],[])).
% 4.64/4.84 tff(23501,plain,
% 4.64/4.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))),
% 4.64/4.84 inference(modus_ponens,[status(thm)],[23500, 23499])).
% 4.64/4.84 tff(23502,plain,
% 4.64/4.84 ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))),
% 4.64/4.85 inference(unit_resolution,[status(thm)],[23501, 118, 8216])).
% 4.64/4.85 tff(23503,plain,
% 4.64/4.85 (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.64/4.85 inference(unit_resolution,[status(thm)],[23502, 23495])).
% 4.64/4.85 tff(23504,plain,
% 4.64/4.85 (b(z, s(s(s(s(s(s(s(s(z))))))))) <=> b(z, s(elem!1))),
% 4.64/4.85 inference(monotonicity,[status(thm)],[23474])).
% 4.64/4.85 tff(23505,plain,
% 4.64/4.85 (b(z, s(elem!1)) <=> b(z, s(s(s(s(s(s(s(s(z)))))))))),
% 4.64/4.85 inference(symmetry,[status(thm)],[23504])).
% 4.64/4.85 tff(23506,plain,
% 4.64/4.85 (~r(z, s(elem!1))),
% 4.64/4.85 inference(unit_resolution,[status(thm)],[7070, 23493, 23468])).
% 4.64/4.85 tff(23507,plain,
% 4.64/4.85 (b(z, s(elem!1))),
% 4.64/4.85 inference(unit_resolution,[status(thm)],[2351, 23506])).
% 4.64/4.85 tff(23508,plain,
% 4.64/4.85 (b(z, s(s(s(s(s(s(s(s(z)))))))))),
% 4.64/4.85 inference(modus_ponens,[status(thm)],[23507, 23505])).
% 4.64/4.85 tff(23509,plain,
% 4.64/4.85 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 4.64/4.85 inference(monotonicity,[status(thm)],[23473])).
% 4.64/4.85 tff(23510,plain,
% 4.64/4.85 (~r(s(elem!1), z)),
% 4.64/4.85 inference(unit_resolution,[status(thm)],[1284, 23493, 23468])).
% 4.64/4.85 tff(23511,plain,
% 4.64/4.85 (b(s(elem!1), z)),
% 4.64/4.85 inference(unit_resolution,[status(thm)],[774, 23510])).
% 4.64/4.85 tff(23512,plain,
% 4.64/4.85 (b(s(elem!1), s(s(z)))),
% 4.64/4.85 inference(unit_resolution,[status(thm)],[11783, 23511, 22560, 23405, 147, 23414, 23472])).
% 4.64/4.85 tff(23513,plain,
% 4.64/4.85 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 4.64/4.85 inference(modus_ponens,[status(thm)],[23512, 23509])).
% 4.64/4.85 tff(23514,plain,
% 4.64/4.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 4.64/4.85 inference(rewrite,[status(thm)],[])).
% 4.64/4.85 tff(23515,plain,
% 4.64/4.85 (((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(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(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 4.64/4.85 inference(rewrite,[status(thm)],[])).
% 4.64/4.85 tff(23516,plain,
% 4.64/4.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(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(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))))),
% 4.64/4.85 inference(monotonicity,[status(thm)],[23515])).
% 4.64/4.85 tff(23517,plain,
% 4.64/4.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(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(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 4.64/4.85 inference(transitivity,[status(thm)],[23516, 23514])).
% 4.64/4.85 tff(23518,plain,
% 4.64/4.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(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(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(z))))))),
% 4.64/4.85 inference(quant_inst,[status(thm)],[])).
% 4.64/4.85 tff(23519,plain,
% 4.64/4.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))),
% 4.64/4.85 inference(modus_ponens,[status(thm)],[23518, 23517])).
% 4.64/4.85 tff(23520,plain,
% 4.64/4.85 ((~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))),
% 4.64/4.85 inference(unit_resolution,[status(thm)],[23519, 178, 23412, 23420, 23513])).
% 4.64/4.85 tff(23521,plain,
% 4.64/4.85 (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.64/4.85 inference(unit_resolution,[status(thm)],[23520, 23508])).
% 4.64/4.85 tff(23522,plain,
% 4.64/4.85 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))),
% 4.64/4.85 inference(rewrite,[status(thm)],[])).
% 4.64/4.85 tff(23523,plain,
% 4.64/4.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))),
% 4.64/4.85 inference(quant_inst,[status(thm)],[])).
% 4.64/4.85 tff(23524,plain,
% 4.64/4.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.64/4.85 inference(modus_ponens,[status(thm)],[23523, 23522])).
% 4.64/4.85 tff(23525,plain,
% 4.64/4.85 (s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))),
% 4.64/4.85 inference(unit_resolution,[status(thm)],[23524, 41, 23521, 23503])).
% 4.64/4.85 tff(23526,plain,
% 4.64/4.85 (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z)))),
% 4.64/4.85 inference(symmetry,[status(thm)],[23525])).
% 4.64/4.85 tff(23527,plain,
% 4.64/4.85 (s(elem!1) = s(s(s(z)))),
% 4.64/4.85 inference(transitivity,[status(thm)],[23473, 23526])).
% 4.64/4.85 tff(23528,assumption,(~(s(elem!1) = s(s(s(z))))), introduced(assumption)).
% 4.64/4.85 tff(23529,plain,
% 4.64/4.85 ($false),
% 4.64/4.85 inference(unit_resolution,[status(thm)],[23528, 23527])).
% 4.64/4.85 tff(23530,plain,(r(elem!1, s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(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(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(s(z))) | (elem!1 = z) | (elem!1 = s(s(s(s(z))))) | b(z, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.85 tff(23531,plain,
% 4.64/4.85 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.64/4.85 inference(unit_resolution,[status(thm)],[23530, 23437, 8216, 147, 104, 23430, 193, 251, 312, 290, 469, 4235])).
% 4.64/4.85 tff(23532,plain,
% 4.64/4.85 (~r(elem!1, z)),
% 4.64/4.85 inference(unit_resolution,[status(thm)],[10809, 23531, 4236])).
% 4.64/4.85 tff(23533,plain,
% 4.64/4.85 (b(elem!1, z)),
% 4.64/4.85 inference(unit_resolution,[status(thm)],[498, 23532, 290])).
% 4.64/4.85 tff(23534,plain,
% 4.64/4.85 (~r(z, elem!1)),
% 4.64/4.85 inference(unit_resolution,[status(thm)],[3818, 23531, 4236])).
% 4.64/4.85 tff(23535,plain,
% 4.64/4.85 (b(z, elem!1)),
% 4.64/4.85 inference(unit_resolution,[status(thm)],[585, 23534, 318])).
% 4.64/4.85 tff(23536,plain,
% 4.64/4.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 4.64/4.85 inference(rewrite,[status(thm)],[])).
% 4.64/4.85 tff(23537,plain,
% 4.64/4.85 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 4.64/4.85 inference(rewrite,[status(thm)],[])).
% 4.64/4.85 tff(23538,plain,
% 4.64/4.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))))),
% 4.64/4.85 inference(monotonicity,[status(thm)],[23537])).
% 4.64/4.85 tff(23539,plain,
% 4.64/4.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 4.64/4.85 inference(transitivity,[status(thm)],[23538, 23536])).
% 4.64/4.85 tff(23540,plain,
% 4.64/4.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)))),
% 4.64/4.85 inference(quant_inst,[status(thm)],[])).
% 4.64/4.85 tff(23541,plain,
% 4.64/4.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))),
% 4.64/4.85 inference(modus_ponens,[status(thm)],[23540, 23539])).
% 4.64/4.85 tff(23542,plain,
% 4.64/4.85 (~b(elem!1, s(s(s(z))))),
% 4.64/4.85 inference(unit_resolution,[status(thm)],[23541, 178, 23535, 23533, 23412, 23410])).
% 4.64/4.85 tff(23543,plain,
% 4.64/4.85 (~r(elem!1, s(s(s(z))))),
% 4.64/4.85 inference(unit_resolution,[status(thm)],[22961, 118, 23531, 8216])).
% 4.64/4.85 tff(23544,plain,
% 4.64/4.85 (elem!1 = s(s(s(z)))),
% 4.64/4.85 inference(unit_resolution,[status(thm)],[17275, 23543, 23542])).
% 4.64/4.85 tff(23545,plain,
% 4.64/4.85 (s(elem!1) = s(s(s(s(z))))),
% 4.64/4.85 inference(monotonicity,[status(thm)],[23544])).
% 4.64/4.85 tff(23546,plain,
% 4.64/4.85 (s(s(s(s(z)))) = s(elem!1)),
% 4.64/4.85 inference(symmetry,[status(thm)],[23545])).
% 4.64/4.85 tff(23547,plain,
% 4.64/4.85 (s(elem!1) = s(s(s(s(z))))),
% 4.64/4.85 inference(unit_resolution,[status(thm)],[2168, 23546])).
% 4.64/4.85 tff(23548,plain,
% 4.64/4.85 (r(elem!1, s(elem!1)) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 4.64/4.85 inference(monotonicity,[status(thm)],[23544, 23545])).
% 4.64/4.85 tff(23549,plain,
% 4.64/4.85 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(elem!1, s(elem!1))),
% 4.64/4.85 inference(symmetry,[status(thm)],[23548])).
% 4.64/4.85 tff(23550,plain,
% 4.64/4.85 (r(elem!1, s(elem!1))),
% 4.64/4.85 inference(modus_ponens,[status(thm)],[23416, 23549])).
% 4.64/4.85 tff(23551,plain,
% 4.64/4.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 4.64/4.85 inference(rewrite,[status(thm)],[])).
% 4.64/4.85 tff(23552,plain,
% 4.64/4.85 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z)))))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 4.64/4.85 inference(rewrite,[status(thm)],[])).
% 4.64/4.85 tff(23553,plain,
% 4.64/4.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))))),
% 4.64/4.85 inference(monotonicity,[status(thm)],[23552])).
% 4.64/4.85 tff(23554,plain,
% 4.64/4.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 4.64/4.85 inference(transitivity,[status(thm)],[23553, 23551])).
% 4.64/4.85 tff(23555,plain,
% 4.64/4.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))),
% 4.64/4.85 inference(quant_inst,[status(thm)],[])).
% 4.64/4.85 tff(23556,plain,
% 4.64/4.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))),
% 4.64/4.85 inference(modus_ponens,[status(thm)],[23555, 23554])).
% 4.64/4.85 tff(23557,plain,
% 4.64/4.85 (~b(s(s(s(z))), elem!1)),
% 4.64/4.85 inference(unit_resolution,[status(thm)],[23556, 178, 23535, 23533, 23412, 23410])).
% 4.64/4.85 tff(23558,plain,
% 4.64/4.85 (~r(s(s(s(z))), elem!1)),
% 4.64/4.85 inference(unit_resolution,[status(thm)],[22949, 118, 23531, 8216])).
% 4.64/4.85 tff(23559,plain,
% 4.64/4.85 (s(s(s(z))) = elem!1),
% 4.64/4.85 inference(unit_resolution,[status(thm)],[4981, 23558, 23557])).
% 4.64/4.85 tff(23560,plain,
% 4.64/4.85 (~(elem!1 = s(s(s(elem!1))))),
% 4.64/4.85 inference(unit_resolution,[status(thm)],[4830, 23559, 3340])).
% 4.64/4.85 tff(23561,plain,
% 4.64/4.85 (~b(elem!1, s(s(s(s(z)))))),
% 4.64/4.85 inference(unit_resolution,[status(thm)],[12519, 178, 23535, 23533, 23405, 23414])).
% 4.64/4.85 tff(23562,plain,
% 4.64/4.85 (r(elem!1, s(s(s(s(z)))))),
% 4.64/4.85 inference(unit_resolution,[status(thm)],[483, 23561, 469])).
% 4.64/4.85 tff(23563,plain,
% 4.64/4.85 (~r(elem!1, s(s(z)))),
% 4.64/4.85 inference(unit_resolution,[status(thm)],[23462, 23535, 193, 23422, 290, 469])).
% 4.64/4.85 tff(23564,plain,
% 4.64/4.85 (b(elem!1, s(s(z)))),
% 4.64/4.85 inference(unit_resolution,[status(thm)],[467, 23563, 312])).
% 4.64/4.85 tff(23565,assumption,(elem!1 = s(s(s(z)))), introduced(assumption)).
% 4.64/4.85 tff(23566,plain,
% 4.64/4.85 (s(elem!1) = s(s(s(s(z))))),
% 4.64/4.85 inference(monotonicity,[status(thm)],[23565])).
% 4.64/4.85 tff(23567,plain,
% 4.64/4.85 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 4.64/4.85 inference(monotonicity,[status(thm)],[23566])).
% 4.64/4.85 tff(23568,plain,
% 4.64/4.85 (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))),
% 4.64/4.85 inference(monotonicity,[status(thm)],[23567])).
% 4.64/4.85 tff(23569,plain,
% 4.64/4.85 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 4.64/4.85 inference(symmetry,[status(thm)],[23568])).
% 4.64/4.85 tff(23570,plain,
% 4.64/4.85 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.64/4.85 inference(monotonicity,[status(thm)],[23569])).
% 4.64/4.85 tff(23571,plain,
% 4.64/4.85 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 4.64/4.85 inference(symmetry,[status(thm)],[23570])).
% 4.64/4.85 tff(23572,plain,
% 4.64/4.85 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 4.64/4.85 inference(monotonicity,[status(thm)],[23569])).
% 4.64/4.85 tff(23573,plain,
% 4.64/4.85 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.64/4.85 inference(transitivity,[status(thm)],[23572, 3289])).
% 4.64/4.85 tff(23574,plain,
% 4.64/4.85 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(z))))))),
% 4.64/4.85 inference(monotonicity,[status(thm)],[23573])).
% 4.64/4.85 tff(23575,plain,
% 4.64/4.85 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.64/4.85 inference(modus_ponens,[status(thm)],[3698, 23574])).
% 4.64/4.85 tff(23576,plain,
% 4.64/4.85 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.85 inference(monotonicity,[status(thm)],[23568])).
% 4.64/4.85 tff(23577,plain,
% 4.64/4.85 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.85 inference(symmetry,[status(thm)],[23576])).
% 4.64/4.85 tff(23578,plain,
% 4.64/4.85 (s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(z)))))))),
% 4.64/4.85 inference(monotonicity,[status(thm)],[23568])).
% 4.64/4.85 tff(23579,plain,
% 4.64/4.85 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.85 inference(monotonicity,[status(thm)],[23568, 23578])).
% 4.64/4.85 tff(23580,plain,
% 4.64/4.85 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.85 inference(transitivity,[status(thm)],[23579, 23577])).
% 4.64/4.85 tff(23581,plain,
% 4.64/4.85 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.85 inference(monotonicity,[status(thm)],[23568, 23578])).
% 4.64/4.85 tff(23582,plain,
% 4.64/4.85 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 4.64/4.85 inference(symmetry,[status(thm)],[23581])).
% 4.64/4.85 tff(23583,plain,
% 4.64/4.85 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 4.64/4.85 inference(monotonicity,[status(thm)],[23582])).
% 4.64/4.85 tff(23584,plain,
% 4.64/4.85 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.64/4.85 inference(monotonicity,[status(thm)],[23566])).
% 4.64/4.85 tff(23585,plain,
% 4.64/4.85 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 4.64/4.85 inference(transitivity,[status(thm)],[23584, 23571])).
% 4.64/4.85 tff(23586,plain,
% 4.64/4.85 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.64/4.85 inference(monotonicity,[status(thm)],[23566])).
% 4.64/4.85 tff(23587,plain,
% 4.64/4.85 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 4.64/4.85 inference(symmetry,[status(thm)],[23586])).
% 4.64/4.85 tff(23588,plain,
% 4.64/4.85 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 4.64/4.85 inference(transitivity,[status(thm)],[23573, 23587])).
% 4.64/4.85 tff(23589,plain,
% 4.64/4.85 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 4.64/4.85 inference(monotonicity,[status(thm)],[23588])).
% 4.64/4.85 tff(23590,plain,
% 4.64/4.85 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.64/4.85 inference(modus_ponens,[status(thm)],[3698, 23589])).
% 4.64/4.85 tff(23591,plain,
% 4.64/4.85 (~r(s(s(s(elem!1))), s(elem!1))),
% 4.64/4.85 inference(unit_resolution,[status(thm)],[1591, 3311, 1587])).
% 4.64/4.85 tff(23592,plain,
% 4.64/4.85 (b(s(s(s(elem!1))), s(elem!1))),
% 4.64/4.85 inference(unit_resolution,[status(thm)],[373, 23591, 23590])).
% 4.64/4.85 tff(23593,plain,
% 4.64/4.85 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 4.64/4.85 inference(modus_ponens,[status(thm)],[23592, 23585])).
% 4.64/4.85 tff(23594,plain,
% 4.64/4.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(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(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(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(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 4.64/4.85 inference(rewrite,[status(thm)],[])).
% 4.64/4.85 tff(23595,plain,
% 4.64/4.85 (((~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(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(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(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 4.64/4.85 inference(rewrite,[status(thm)],[])).
% 4.64/4.85 tff(23596,plain,
% 4.64/4.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(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(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 4.64/4.85 inference(monotonicity,[status(thm)],[23595])).
% 4.64/4.85 tff(23597,plain,
% 4.64/4.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(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(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 4.64/4.85 inference(transitivity,[status(thm)],[23596, 23594])).
% 4.64/4.85 tff(23598,plain,
% 4.64/4.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 4.64/4.85 inference(quant_inst,[status(thm)],[])).
% 4.64/4.85 tff(23599,plain,
% 4.64/4.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 4.64/4.85 inference(modus_ponens,[status(thm)],[23598, 23597])).
% 4.64/4.85 tff(23600,plain,
% 4.64/4.85 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.85 inference(unit_resolution,[status(thm)],[23599, 178, 104, 166, 23593, 18564])).
% 4.64/4.85 tff(23601,plain,
% 4.64/4.85 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 4.64/4.85 inference(modus_ponens,[status(thm)],[23600, 23583])).
% 4.64/4.86 tff(23602,plain,
% 4.64/4.86 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 4.64/4.86 inference(unit_resolution,[status(thm)],[1750, 23601, 1858])).
% 4.64/4.86 tff(23603,plain,
% 4.64/4.86 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.86 inference(modus_ponens,[status(thm)],[23602, 23580])).
% 4.64/4.86 tff(23604,plain,
% 4.64/4.86 (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.86 inference(unit_resolution,[status(thm)],[3623, 3311, 1265])).
% 4.64/4.86 tff(23605,plain,
% 4.64/4.86 ($false),
% 4.64/4.86 inference(unit_resolution,[status(thm)],[23604, 23603])).
% 4.64/4.86 tff(23606,plain,((~r(elem!1, s(s(s(elem!1))))) | (~(elem!1 = s(s(s(z))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.86 tff(23607,plain,
% 4.64/4.86 (~r(elem!1, s(s(s(elem!1))))),
% 4.64/4.86 inference(unit_resolution,[status(thm)],[23606, 18564, 9198, 104, 166, 23565, 1587, 1265])).
% 4.64/4.86 tff(23608,plain,
% 4.64/4.86 (b(elem!1, s(s(s(elem!1))))),
% 4.64/4.86 inference(unit_resolution,[status(thm)],[2054, 23607, 1586])).
% 4.64/4.86 tff(23609,plain,
% 4.64/4.86 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.64/4.86 inference(unit_resolution,[status(thm)],[22224, 23608, 147, 817, 6403, 812, 470])).
% 4.64/4.86 tff(23610,plain,
% 4.64/4.86 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.64/4.86 inference(unit_resolution,[status(thm)],[4173, 23609, 23575])).
% 4.64/4.86 tff(23611,plain,
% 4.64/4.86 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 4.64/4.86 inference(modus_ponens,[status(thm)],[23610, 23571])).
% 4.64/4.86 tff(23612,plain,
% 4.64/4.86 (s(s(s(s(z)))) = s(elem!1)),
% 4.64/4.86 inference(symmetry,[status(thm)],[23566])).
% 4.64/4.86 tff(23613,plain,
% 4.64/4.86 (s(elem!1) = s(s(s(s(z))))),
% 4.64/4.86 inference(unit_resolution,[status(thm)],[2168, 23612])).
% 4.64/4.86 tff(23614,plain,
% 4.64/4.86 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 4.64/4.86 inference(unit_resolution,[status(thm)],[6974, 23608, 23613])).
% 4.64/4.86 tff(23615,plain,
% 4.64/4.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)))),
% 4.64/4.86 inference(rewrite,[status(thm)],[])).
% 4.64/4.86 tff(23616,plain,
% 4.64/4.86 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)))),
% 4.64/4.86 inference(rewrite,[status(thm)],[])).
% 4.64/4.86 tff(23617,plain,
% 4.64/4.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z))))),
% 4.64/4.86 inference(monotonicity,[status(thm)],[23616])).
% 4.64/4.86 tff(23618,plain,
% 4.64/4.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)))),
% 4.64/4.86 inference(transitivity,[status(thm)],[23617, 23615])).
% 4.64/4.86 tff(23619,plain,
% 4.64/4.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 4.64/4.86 inference(quant_inst,[status(thm)],[])).
% 4.64/4.86 tff(23620,plain,
% 4.64/4.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z))),
% 4.64/4.86 inference(modus_ponens,[status(thm)],[23619, 23618])).
% 4.64/4.86 tff(23621,plain,
% 4.64/4.86 (~b(s(s(s(s(s(s(z)))))), z)),
% 4.64/4.86 inference(unit_resolution,[status(thm)],[23620, 178, 23405, 6154, 6155, 1127])).
% 4.64/4.86 tff(23622,plain,
% 4.64/4.86 (r(s(s(s(s(s(s(z)))))), z)),
% 4.64/4.86 inference(unit_resolution,[status(thm)],[18523, 41, 433, 23621])).
% 4.64/4.86 tff(23623,plain,
% 4.64/4.86 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.86 inference(unit_resolution,[status(thm)],[23599, 178, 104, 166, 6154, 18564])).
% 4.64/4.86 tff(23624,plain,
% 4.64/4.86 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 4.64/4.86 inference(modus_ponens,[status(thm)],[23623, 23583])).
% 4.64/4.86 tff(23625,plain,
% 4.64/4.86 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 4.64/4.86 inference(unit_resolution,[status(thm)],[1750, 23624, 1858])).
% 4.64/4.86 tff(23626,plain,
% 4.64/4.86 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.86 inference(modus_ponens,[status(thm)],[23625, 23579])).
% 4.64/4.86 tff(23627,plain,
% 4.64/4.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 4.64/4.86 inference(rewrite,[status(thm)],[])).
% 4.64/4.86 tff(23628,plain,
% 4.64/4.86 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(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(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 4.64/4.86 inference(rewrite,[status(thm)],[])).
% 4.64/4.86 tff(23629,plain,
% 4.64/4.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))))),
% 4.64/4.86 inference(monotonicity,[status(thm)],[23628])).
% 4.64/4.86 tff(23630,plain,
% 4.64/4.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 4.64/4.86 inference(transitivity,[status(thm)],[23629, 23627])).
% 4.64/4.86 tff(23631,plain,
% 4.64/4.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 4.64/4.86 inference(quant_inst,[status(thm)],[])).
% 4.64/4.86 tff(23632,plain,
% 4.64/4.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))),
% 4.64/4.86 inference(modus_ponens,[status(thm)],[23631, 23630])).
% 4.64/4.86 tff(23633,plain,
% 4.64/4.86 ($false),
% 4.64/4.86 inference(unit_resolution,[status(thm)],[23632, 118, 203, 23626, 23622])).
% 4.64/4.86 tff(23634,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(s(s(z))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.86 tff(23635,plain,
% 4.64/4.86 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 4.64/4.86 inference(unit_resolution,[status(thm)],[23634, 23614, 23565, 9198, 203, 1127, 104, 166, 18564])).
% 4.64/4.86 tff(23636,plain,
% 4.64/4.86 ($false),
% 4.64/4.86 inference(unit_resolution,[status(thm)],[23635, 23611])).
% 4.64/4.86 tff(23637,plain,((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~(elem!1 = s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), 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(z)))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))) | (elem!1 = s(s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.86 tff(23638,plain,
% 4.64/4.86 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 4.64/4.86 inference(unit_resolution,[status(thm)],[23637, 23544, 4236, 23410, 104, 23442, 147, 23430, 23564, 23562, 23560, 23550, 23531])).
% 4.64/4.86 tff(23639,plain,
% 4.64/4.86 (~b(s(s(z)), s(s(s(elem!1))))),
% 4.64/4.86 inference(unit_resolution,[status(thm)],[7268, 23638, 23547])).
% 4.64/4.86 tff(23640,plain,
% 4.64/4.86 (r(s(s(z)), s(s(s(elem!1))))),
% 4.64/4.86 inference(unit_resolution,[status(thm)],[4223, 23639])).
% 4.64/4.86 tff(23641,plain,
% 4.64/4.86 (~r(z, s(s(s(elem!1))))),
% 4.64/4.86 inference(unit_resolution,[status(thm)],[4808, 23640, 22560])).
% 4.64/4.86 tff(23642,plain,
% 4.64/4.86 (b(z, s(s(s(elem!1))))),
% 4.64/4.86 inference(unit_resolution,[status(thm)],[2095, 23641])).
% 4.64/4.86 tff(23643,plain,
% 4.64/4.86 (~(s(s(s(elem!1))) = elem!1)),
% 4.64/4.86 inference(unit_resolution,[status(thm)],[2489, 23560])).
% 4.64/4.86 tff(23644,plain,
% 4.64/4.86 (r(s(elem!1), elem!1) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 4.64/4.86 inference(monotonicity,[status(thm)],[23545, 23544])).
% 4.64/4.86 tff(23645,plain,
% 4.64/4.86 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(elem!1), elem!1)),
% 4.64/4.86 inference(symmetry,[status(thm)],[23644])).
% 4.64/4.86 tff(23646,plain,
% 4.64/4.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 4.64/4.86 inference(rewrite,[status(thm)],[])).
% 4.64/4.86 tff(23647,plain,
% 4.64/4.86 (((~b(s(s(s(z))), 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(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 4.64/4.86 inference(rewrite,[status(thm)],[])).
% 4.64/4.86 tff(23648,plain,
% 4.64/4.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 4.64/4.86 inference(monotonicity,[status(thm)],[23647])).
% 4.64/4.86 tff(23649,plain,
% 4.64/4.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 4.64/4.86 inference(transitivity,[status(thm)],[23648, 23646])).
% 4.64/4.86 tff(23650,plain,
% 4.64/4.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 4.64/4.86 inference(quant_inst,[status(thm)],[])).
% 4.64/4.86 tff(23651,plain,
% 4.64/4.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 4.64/4.86 inference(modus_ponens,[status(thm)],[23650, 23649])).
% 4.64/4.86 tff(23652,plain,
% 4.64/4.86 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 4.64/4.86 inference(unit_resolution,[status(thm)],[23651, 178, 23405, 23414, 23412, 23410])).
% 4.64/4.86 tff(23653,plain,
% 4.64/4.86 (r(s(s(s(s(z)))), s(s(s(z))))),
% 4.64/4.86 inference(unit_resolution,[status(thm)],[11185, 23652])).
% 4.64/4.86 tff(23654,plain,
% 4.64/4.86 (r(s(elem!1), elem!1)),
% 4.64/4.86 inference(modus_ponens,[status(thm)],[23653, 23645])).
% 4.64/4.86 tff(23655,plain,
% 4.64/4.86 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.64/4.86 inference(monotonicity,[status(thm)],[23545])).
% 4.64/4.86 tff(23656,plain,
% 4.64/4.86 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 4.64/4.86 inference(symmetry,[status(thm)],[23655])).
% 4.64/4.86 tff(23657,plain,
% 4.64/4.86 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 4.64/4.86 inference(monotonicity,[status(thm)],[23545])).
% 4.64/4.86 tff(23658,plain,
% 4.64/4.86 (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))),
% 4.64/4.86 inference(monotonicity,[status(thm)],[23657])).
% 4.64/4.86 tff(23659,plain,
% 4.64/4.86 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 4.64/4.86 inference(symmetry,[status(thm)],[23658])).
% 4.64/4.86 tff(23660,plain,
% 4.64/4.86 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 4.64/4.86 inference(monotonicity,[status(thm)],[23659])).
% 4.64/4.86 tff(23661,plain,
% 4.64/4.86 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.64/4.86 inference(transitivity,[status(thm)],[23660, 3289])).
% 4.64/4.86 tff(23662,plain,
% 4.64/4.86 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 4.64/4.86 inference(transitivity,[status(thm)],[23661, 23656])).
% 4.64/4.86 tff(23663,plain,
% 4.64/4.86 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 4.64/4.86 inference(monotonicity,[status(thm)],[23662])).
% 4.64/4.86 tff(23664,plain,
% 4.64/4.86 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.64/4.86 inference(modus_ponens,[status(thm)],[3698, 23663])).
% 4.64/4.86 tff(23665,plain,
% 4.64/4.86 (b(s(elem!1), z) <=> b(s(s(s(s(z)))), z)),
% 4.64/4.86 inference(monotonicity,[status(thm)],[23545])).
% 4.64/4.86 tff(23666,plain,
% 4.64/4.86 (b(s(s(s(s(z)))), z) <=> b(s(elem!1), z)),
% 4.64/4.86 inference(symmetry,[status(thm)],[23665])).
% 4.64/4.86 tff(23667,plain,
% 4.64/4.86 (b(s(elem!1), z)),
% 4.64/4.86 inference(modus_ponens,[status(thm)],[23414, 23666])).
% 4.64/4.86 tff(23668,plain,
% 4.64/4.86 (b(z, s(elem!1)) <=> b(z, s(s(s(s(z)))))),
% 4.64/4.86 inference(monotonicity,[status(thm)],[23545])).
% 4.64/4.86 tff(23669,plain,
% 4.64/4.86 (b(z, s(s(s(s(z))))) <=> b(z, s(elem!1))),
% 4.64/4.86 inference(symmetry,[status(thm)],[23668])).
% 4.64/4.86 tff(23670,plain,
% 4.64/4.86 (b(z, s(elem!1))),
% 4.64/4.86 inference(modus_ponens,[status(thm)],[23405, 23669])).
% 4.64/4.86 tff(23671,plain,
% 4.64/4.86 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 4.64/4.86 inference(transitivity,[status(thm)],[23661, 23656, 7104])).
% 4.64/4.86 tff(23672,plain,
% 4.64/4.86 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 4.64/4.86 inference(monotonicity,[status(thm)],[23671])).
% 4.64/4.86 tff(23673,plain,
% 4.64/4.86 (~(s(elem!1) = s(s(s(elem!1))))),
% 4.64/4.86 inference(modus_ponens,[status(thm)],[3698, 23672])).
% 4.64/4.86 tff(23674,plain,
% 4.64/4.86 (r(s(s(z)), s(elem!1)) <=> r(s(s(z)), s(s(s(s(z)))))),
% 4.64/4.86 inference(monotonicity,[status(thm)],[23545])).
% 4.64/4.86 tff(23675,plain,
% 4.64/4.86 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(z)), s(elem!1))),
% 4.64/4.86 inference(symmetry,[status(thm)],[23674])).
% 4.64/4.86 tff(23676,plain,
% 4.64/4.86 (r(s(s(z)), s(elem!1))),
% 4.64/4.86 inference(modus_ponens,[status(thm)],[147, 23675])).
% 4.64/4.86 tff(23677,plain,
% 4.64/4.86 (b(s(elem!1), s(s(s(elem!1))))),
% 4.64/4.86 inference(unit_resolution,[status(thm)],[6127, 23639, 23676, 23673])).
% 4.64/4.86 tff(23678,plain,
% 4.64/4.86 (~b(s(s(s(elem!1))), s(elem!1))),
% 4.64/4.86 inference(unit_resolution,[status(thm)],[6736, 23642, 23677, 23670, 23667])).
% 4.64/4.86 tff(23679,plain,
% 4.64/4.86 (r(s(s(s(elem!1))), s(elem!1))),
% 4.64/4.86 inference(unit_resolution,[status(thm)],[373, 23678, 23664])).
% 4.64/4.86 tff(23680,plain,
% 4.64/4.86 (~r(s(s(s(elem!1))), elem!1)),
% 4.64/4.86 inference(unit_resolution,[status(thm)],[1576, 23679, 23654])).
% 4.64/4.86 tff(23681,plain,
% 4.64/4.86 (b(s(s(s(elem!1))), elem!1)),
% 4.64/4.86 inference(unit_resolution,[status(thm)],[570, 23680, 23643])).
% 4.64/4.86 tff(23682,plain,
% 4.64/4.86 (~r(elem!1, s(s(s(elem!1))))),
% 4.64/4.86 inference(unit_resolution,[status(thm)],[1591, 23679, 23550])).
% 4.64/4.86 tff(23683,plain,
% 4.64/4.86 (b(elem!1, s(s(s(elem!1))))),
% 4.64/4.86 inference(unit_resolution,[status(thm)],[2054, 23682, 23560])).
% 4.64/4.86 tff(23684,plain,
% 4.64/4.86 ($false),
% 4.64/4.86 inference(unit_resolution,[status(thm)],[12925, 23683, 23681, 23533, 23535, 23642])).
% 4.64/4.86 tff(23685,plain,((s(s(z)) = elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (elem!1 = s(s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (elem!1 = z) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | b(z, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.86 tff(23686,plain,
% 4.64/4.86 (s(s(z)) = elem!1),
% 4.64/4.86 inference(unit_resolution,[status(thm)],[23685, 3130, 10794, 104, 8216, 103, 290, 251, 4235])).
% 4.64/4.86 tff(23687,plain,
% 4.64/4.86 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 4.64/4.86 inference(monotonicity,[status(thm)],[23686])).
% 4.64/4.86 tff(23688,plain,
% 4.64/4.86 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 4.64/4.86 inference(transitivity,[status(thm)],[23687, 1526])).
% 4.64/4.86 tff(23689,plain,
% 4.64/4.86 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 4.64/4.86 inference(monotonicity,[status(thm)],[23688])).
% 4.64/4.86 tff(23690,plain,
% 4.64/4.86 (~(s(s(s(elem!1))) = elem!1)),
% 4.64/4.86 inference(modus_ponens,[status(thm)],[1683, 23689])).
% 4.64/4.86 tff(23691,plain,
% 4.64/4.86 (s(s(s(z))) = s(elem!1)),
% 4.64/4.86 inference(monotonicity,[status(thm)],[23686])).
% 4.64/4.86 tff(23692,plain,
% 4.64/4.86 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 4.64/4.86 inference(monotonicity,[status(thm)],[23691])).
% 4.64/4.86 tff(23693,plain,
% 4.64/4.86 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 4.64/4.86 inference(transitivity,[status(thm)],[23692, 3881])).
% 4.64/4.86 tff(23694,plain,
% 4.64/4.86 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 4.64/4.86 inference(monotonicity,[status(thm)],[23693])).
% 4.64/4.86 tff(23695,plain,
% 4.64/4.86 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.64/4.86 inference(modus_ponens,[status(thm)],[11613, 23694])).
% 4.64/4.86 tff(23696,plain,
% 4.64/4.86 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 4.64/4.86 inference(unit_resolution,[status(thm)],[1649, 23695])).
% 4.64/4.86 tff(23697,plain,
% 4.64/4.86 (r(z, elem!1)),
% 4.64/4.86 inference(unit_resolution,[status(thm)],[7053, 23686, 22560])).
% 4.64/4.86 tff(23698,plain,
% 4.64/4.86 (s(s(s(s(z)))) = s(s(elem!1))),
% 4.64/4.86 inference(monotonicity,[status(thm)],[23691])).
% 4.64/4.86 tff(23699,plain,
% 4.64/4.86 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 4.64/4.86 inference(monotonicity,[status(thm)],[23698])).
% 4.64/4.86 tff(23700,plain,
% 4.64/4.86 (~b(s(s(s(s(z)))), elem!1)),
% 4.64/4.86 inference(unit_resolution,[status(thm)],[3774, 23686, 86])).
% 4.64/4.86 tff(23701,plain,
% 4.64/4.86 (r(s(s(s(s(z)))), elem!1)),
% 4.64/4.86 inference(unit_resolution,[status(thm)],[3142, 23700, 323])).
% 4.64/4.86 tff(23702,plain,
% 4.64/4.86 (r(s(s(elem!1)), elem!1)),
% 4.64/4.86 inference(modus_ponens,[status(thm)],[23701, 23699])).
% 4.64/4.86 tff(23703,plain,
% 4.64/4.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 4.64/4.86 inference(rewrite,[status(thm)],[])).
% 4.64/4.86 tff(23704,plain,
% 4.64/4.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 4.64/4.86 inference(quant_inst,[status(thm)],[])).
% 4.64/4.86 tff(23705,plain,
% 4.64/4.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 4.64/4.86 inference(modus_ponens,[status(thm)],[23704, 23703])).
% 4.64/4.86 tff(23706,plain,
% 4.64/4.86 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 4.64/4.86 inference(unit_resolution,[status(thm)],[23705, 118, 556, 3365])).
% 4.64/4.86 tff(23707,plain,
% 4.64/4.86 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 4.64/4.86 inference(unit_resolution,[status(thm)],[3409, 23706, 6444])).
% 4.64/4.86 tff(23708,plain,
% 4.64/4.86 (~r(s(s(elem!1)), z)),
% 4.64/4.86 inference(unit_resolution,[status(thm)],[6591, 118, 521, 3365])).
% 4.64/4.86 tff(23709,plain,
% 4.64/4.86 (b(s(s(elem!1)), z)),
% 4.64/4.86 inference(unit_resolution,[status(thm)],[6600, 23708])).
% 4.64/4.86 tff(23710,plain,
% 4.64/4.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 4.64/4.86 inference(rewrite,[status(thm)],[])).
% 4.64/4.86 tff(23711,plain,
% 4.64/4.86 (((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 4.64/4.86 inference(rewrite,[status(thm)],[])).
% 4.64/4.86 tff(23712,plain,
% 4.64/4.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 4.64/4.86 inference(monotonicity,[status(thm)],[23711])).
% 4.64/4.86 tff(23713,plain,
% 4.64/4.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 4.64/4.86 inference(transitivity,[status(thm)],[23712, 23710])).
% 4.64/4.86 tff(23714,plain,
% 4.64/4.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 4.64/4.87 inference(quant_inst,[status(thm)],[])).
% 4.64/4.87 tff(23715,plain,
% 4.64/4.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 4.64/4.87 inference(modus_ponens,[status(thm)],[23714, 23713])).
% 4.64/4.87 tff(23716,plain,
% 4.64/4.87 ($false),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[23715, 178, 6382, 6380, 23709, 23707, 18363])).
% 4.64/4.87 tff(23717,plain,((~r(s(s(elem!1)), elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.87 tff(23718,plain,
% 4.64/4.87 (~r(s(s(s(elem!1))), elem!1)),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[23717, 23702, 23697, 23696])).
% 4.64/4.87 tff(23719,plain,
% 4.64/4.87 (b(s(s(s(elem!1))), elem!1)),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[570, 23718, 23690])).
% 4.64/4.87 tff(23720,plain,
% 4.64/4.87 (b(s(s(s(z))), elem!1) <=> b(s(elem!1), elem!1)),
% 4.64/4.87 inference(monotonicity,[status(thm)],[23691])).
% 4.64/4.87 tff(23721,plain,
% 4.64/4.87 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), elem!1)),
% 4.64/4.87 inference(monotonicity,[status(thm)],[23686])).
% 4.64/4.87 tff(23722,plain,
% 4.64/4.87 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[21520, 8216, 22562, 4236, 23405])).
% 4.64/4.87 tff(23723,plain,
% 4.64/4.87 (r(s(s(s(z))), s(s(s(s(z)))))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[10755, 23722])).
% 4.64/4.87 tff(23724,plain,
% 4.64/4.87 (~r(s(s(s(z))), s(s(z)))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[20838, 23723, 103])).
% 4.64/4.87 tff(23725,plain,
% 4.64/4.87 (b(s(s(s(z))), s(s(z)))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[4966, 23724])).
% 4.64/4.87 tff(23726,plain,
% 4.64/4.87 (b(s(s(s(z))), elem!1)),
% 4.64/4.87 inference(modus_ponens,[status(thm)],[23725, 23721])).
% 4.64/4.87 tff(23727,plain,
% 4.64/4.87 (b(s(elem!1), elem!1)),
% 4.64/4.87 inference(modus_ponens,[status(thm)],[23726, 23720])).
% 4.64/4.87 tff(23728,plain,
% 4.64/4.87 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 4.64/4.87 inference(transitivity,[status(thm)],[23688, 2486])).
% 4.64/4.87 tff(23729,plain,
% 4.64/4.87 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 4.64/4.87 inference(monotonicity,[status(thm)],[23728])).
% 4.64/4.87 tff(23730,plain,
% 4.64/4.87 (~(elem!1 = s(s(s(elem!1))))),
% 4.64/4.87 inference(modus_ponens,[status(thm)],[1683, 23729])).
% 4.64/4.87 tff(23731,plain,
% 4.64/4.87 (~b(elem!1, s(s(s(s(z)))))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[17698, 23686, 105])).
% 4.64/4.87 tff(23732,plain,
% 4.64/4.87 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[18185, 23731, 104])).
% 4.64/4.87 tff(23733,plain,
% 4.64/4.87 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[3818, 23697, 4236])).
% 4.64/4.87 tff(23734,plain,
% 4.64/4.87 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[691, 23733, 23732])).
% 4.64/4.87 tff(23735,plain,
% 4.64/4.87 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[703, 23732])).
% 4.64/4.87 tff(23736,plain,
% 4.64/4.87 (~r(z, s(s(s(elem!1))))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[17868, 23690, 23408, 23697, 9310, 23735, 23734, 23730])).
% 4.64/4.87 tff(23737,plain,
% 4.64/4.87 (b(z, s(s(s(elem!1))))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[2095, 23736])).
% 4.64/4.87 tff(23738,plain,
% 4.64/4.87 (b(z, s(s(s(z)))) <=> b(z, s(elem!1))),
% 4.64/4.87 inference(monotonicity,[status(thm)],[23691])).
% 4.64/4.87 tff(23739,plain,
% 4.64/4.87 (b(z, s(elem!1))),
% 4.64/4.87 inference(modus_ponens,[status(thm)],[23412, 23738])).
% 4.64/4.87 tff(23740,plain,
% 4.64/4.87 (s(s(elem!1)) = s(s(s(s(z))))),
% 4.64/4.87 inference(symmetry,[status(thm)],[23698])).
% 4.64/4.87 tff(23741,plain,
% 4.64/4.87 (r(s(elem!1), s(s(elem!1))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 4.64/4.87 inference(monotonicity,[status(thm)],[23740])).
% 4.64/4.87 tff(23742,plain,
% 4.64/4.87 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(elem!1), s(s(elem!1)))),
% 4.64/4.87 inference(symmetry,[status(thm)],[23741])).
% 4.64/4.87 tff(23743,plain,
% 4.64/4.87 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 4.64/4.87 inference(monotonicity,[status(thm)],[23691])).
% 4.64/4.87 tff(23744,plain,
% 4.64/4.87 (r(s(elem!1), s(s(s(s(z)))))),
% 4.64/4.87 inference(modus_ponens,[status(thm)],[23723, 23743])).
% 4.64/4.87 tff(23745,plain,
% 4.64/4.87 (r(s(elem!1), s(s(elem!1)))),
% 4.64/4.87 inference(modus_ponens,[status(thm)],[23744, 23742])).
% 4.64/4.87 tff(23746,plain,
% 4.64/4.87 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[3404, 23696])).
% 4.64/4.87 tff(23747,plain,
% 4.64/4.87 (b(s(s(s(s(z)))), z) <=> b(s(s(elem!1)), z)),
% 4.64/4.87 inference(monotonicity,[status(thm)],[23698])).
% 4.64/4.87 tff(23748,plain,
% 4.64/4.87 (b(s(s(elem!1)), z)),
% 4.64/4.87 inference(modus_ponens,[status(thm)],[22562, 23747])).
% 4.64/4.87 tff(23749,plain,
% 4.64/4.87 (b(z, s(s(s(s(z))))) <=> b(z, s(s(elem!1)))),
% 4.64/4.87 inference(monotonicity,[status(thm)],[23698])).
% 4.64/4.87 tff(23750,plain,
% 4.64/4.87 (b(z, s(s(elem!1)))),
% 4.64/4.87 inference(modus_ponens,[status(thm)],[23405, 23749])).
% 4.64/4.87 tff(23751,plain,
% 4.64/4.87 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 4.64/4.87 inference(transitivity,[status(thm)],[23693, 7104])).
% 4.64/4.87 tff(23752,plain,
% 4.64/4.87 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 4.64/4.87 inference(monotonicity,[status(thm)],[23751])).
% 4.64/4.87 tff(23753,plain,
% 4.64/4.87 (~(s(elem!1) = s(s(s(elem!1))))),
% 4.64/4.87 inference(modus_ponens,[status(thm)],[11613, 23752])).
% 4.64/4.87 tff(23754,plain,
% 4.64/4.87 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(elem!1))),
% 4.64/4.87 inference(monotonicity,[status(thm)],[23691])).
% 4.64/4.87 tff(23755,plain,
% 4.64/4.87 (b(s(s(z)), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 4.64/4.87 inference(monotonicity,[status(thm)],[23686])).
% 4.64/4.87 tff(23756,plain,
% 4.64/4.87 (~r(s(s(z)), s(s(s(z))))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[5079, 118, 10794, 23723])).
% 4.64/4.87 tff(23757,plain,
% 4.64/4.87 (b(s(s(z)), s(s(s(z))))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[5088, 23756])).
% 4.64/4.87 tff(23758,plain,
% 4.64/4.87 (b(elem!1, s(s(s(z))))),
% 4.64/4.87 inference(modus_ponens,[status(thm)],[23757, 23755])).
% 4.64/4.87 tff(23759,plain,
% 4.64/4.87 (b(elem!1, s(elem!1))),
% 4.64/4.87 inference(modus_ponens,[status(thm)],[23758, 23754])).
% 4.64/4.87 tff(23760,plain,
% 4.64/4.87 ((s(elem!1) = s(s(z))) <=> (s(elem!1) = elem!1)),
% 4.64/4.87 inference(monotonicity,[status(thm)],[23686])).
% 4.64/4.87 tff(23761,plain,
% 4.64/4.87 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(z)))),
% 4.64/4.87 inference(symmetry,[status(thm)],[23760])).
% 4.64/4.87 tff(23762,plain,
% 4.64/4.87 ((elem!1 = s(s(s(z)))) <=> (elem!1 = s(elem!1))),
% 4.64/4.87 inference(monotonicity,[status(thm)],[23691])).
% 4.64/4.87 tff(23763,plain,
% 4.64/4.87 ((elem!1 = s(s(s(z)))) <=> (s(elem!1) = elem!1)),
% 4.64/4.87 inference(transitivity,[status(thm)],[23762, 3190])).
% 4.64/4.87 tff(23764,plain,
% 4.64/4.87 ((elem!1 = s(s(s(z)))) <=> (s(elem!1) = s(s(z)))),
% 4.64/4.87 inference(transitivity,[status(thm)],[23763, 23761])).
% 4.64/4.87 tff(23765,plain,
% 4.64/4.87 ((~(elem!1 = s(s(s(z))))) <=> (~(s(elem!1) = s(s(z))))),
% 4.64/4.87 inference(monotonicity,[status(thm)],[23764])).
% 4.64/4.87 tff(23766,plain,
% 4.64/4.87 ((s(s(z)) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 4.64/4.87 inference(monotonicity,[status(thm)],[23686])).
% 4.64/4.87 tff(23767,plain,
% 4.64/4.87 ((~(s(s(z)) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 4.64/4.87 inference(monotonicity,[status(thm)],[23766])).
% 4.64/4.87 tff(23768,plain,
% 4.64/4.87 (~(elem!1 = s(s(s(z))))),
% 4.64/4.87 inference(modus_ponens,[status(thm)],[3205, 23767])).
% 4.64/4.87 tff(23769,plain,
% 4.64/4.87 (~(s(elem!1) = s(s(z)))),
% 4.64/4.87 inference(modus_ponens,[status(thm)],[23768, 23765])).
% 4.64/4.87 tff(23770,plain,
% 4.64/4.87 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[2840, 23769])).
% 4.64/4.87 tff(23771,plain,
% 4.64/4.87 (~b(s(s(z)), z)),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[5098, 23412, 23725, 23410, 23757])).
% 4.64/4.87 tff(23772,plain,
% 4.64/4.87 (r(s(s(z)), z)),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[3249, 23771])).
% 4.64/4.87 tff(23773,plain,
% 4.64/4.87 (r(elem!1, z)),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[1345, 23686, 23772])).
% 4.64/4.87 tff(23774,plain,
% 4.64/4.87 (r(elem!1, s(s(s(s(z)))))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[483, 23731, 3130])).
% 4.64/4.87 tff(23775,plain,
% 4.64/4.87 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[22232, 178, 2043, 6073, 1687, 168])).
% 4.64/4.87 tff(23776,plain,
% 4.64/4.87 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[3825, 41, 2857, 23775])).
% 4.64/4.87 tff(23777,plain,
% 4.64/4.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 4.64/4.87 inference(rewrite,[status(thm)],[])).
% 4.64/4.87 tff(23778,plain,
% 4.64/4.87 (((~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)))))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 4.64/4.87 inference(rewrite,[status(thm)],[])).
% 4.64/4.87 tff(23779,plain,
% 4.64/4.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 4.64/4.87 inference(monotonicity,[status(thm)],[23778])).
% 4.64/4.87 tff(23780,plain,
% 4.64/4.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 4.64/4.87 inference(transitivity,[status(thm)],[23779, 23777])).
% 4.64/4.87 tff(23781,plain,
% 4.64/4.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 4.64/4.87 inference(quant_inst,[status(thm)],[])).
% 4.64/4.87 tff(23782,plain,
% 4.64/4.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 4.64/4.87 inference(modus_ponens,[status(thm)],[23781, 23780])).
% 4.64/4.87 tff(23783,plain,
% 4.64/4.87 ($false),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[23782, 118, 3311, 470, 23776])).
% 4.64/4.87 tff(23784,plain,((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.87 tff(23785,plain,
% 4.64/4.87 (~r(elem!1, s(s(s(elem!1))))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[23784, 23737, 23405, 23774, 23773, 22562, 23770])).
% 4.64/4.87 tff(23786,plain,
% 4.64/4.87 (b(elem!1, s(s(s(elem!1))))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[2054, 23785, 23730])).
% 4.64/4.87 tff(23787,plain,
% 4.64/4.87 (~b(s(elem!1), s(s(s(elem!1))))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[6834, 23786, 23727, 23759, 23719])).
% 4.64/4.87 tff(23788,plain,
% 4.64/4.87 (r(s(elem!1), s(s(s(elem!1))))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[5432, 23787, 23753])).
% 4.64/4.87 tff(23789,plain,
% 4.64/4.87 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[5994, 23788, 23745])).
% 4.64/4.87 tff(23790,plain,
% 4.64/4.87 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[3375, 23789, 23696])).
% 4.64/4.87 tff(23791,plain,
% 4.64/4.87 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[18614, 23790, 23750, 23737, 23748])).
% 4.64/4.87 tff(23792,plain,
% 4.64/4.87 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[3409, 23791, 23746])).
% 4.64/4.87 tff(23793,plain,
% 4.64/4.87 (~r(s(s(s(elem!1))), s(elem!1))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[5980, 23792, 23745])).
% 4.64/4.87 tff(23794,plain,
% 4.64/4.87 (b(s(s(s(elem!1))), s(elem!1))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[373, 23793, 23695])).
% 4.64/4.87 tff(23795,plain,
% 4.64/4.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 4.64/4.87 inference(rewrite,[status(thm)],[])).
% 4.64/4.87 tff(23796,plain,
% 4.64/4.87 (((~b(s(elem!1), 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(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 4.64/4.87 inference(rewrite,[status(thm)],[])).
% 4.64/4.87 tff(23797,plain,
% 4.64/4.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))))),
% 4.64/4.87 inference(monotonicity,[status(thm)],[23796])).
% 4.64/4.87 tff(23798,plain,
% 4.64/4.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 4.64/4.87 inference(transitivity,[status(thm)],[23797, 23795])).
% 4.64/4.87 tff(23799,plain,
% 4.64/4.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))))),
% 4.64/4.87 inference(quant_inst,[status(thm)],[])).
% 4.64/4.87 tff(23800,plain,
% 4.64/4.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))),
% 4.64/4.87 inference(modus_ponens,[status(thm)],[23799, 23798])).
% 4.64/4.87 tff(23801,plain,
% 4.64/4.87 ($false),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[23800, 178, 23794, 23739, 23737, 23727, 23719])).
% 4.64/4.87 tff(23802,plain,((s(s(s(s(z)))) = elem!1) | (~b(s(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(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (elem!1 = z) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | b(z, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.87 tff(23803,plain,
% 4.64/4.87 (s(s(s(s(z)))) = elem!1),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[23802, 290, 105, 86, 8216, 104, 251, 4235])).
% 4.64/4.87 tff(23804,plain,
% 4.64/4.87 (s(s(s(s(s(z))))) = s(elem!1)),
% 4.64/4.87 inference(monotonicity,[status(thm)],[23803])).
% 4.64/4.87 tff(23805,plain,
% 4.64/4.87 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(elem!1), s(s(z)))),
% 4.64/4.87 inference(monotonicity,[status(thm)],[23804])).
% 4.64/4.87 tff(23806,plain,
% 4.64/4.87 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 4.64/4.87 inference(symmetry,[status(thm)],[23805])).
% 4.64/4.87 tff(23807,plain,
% 4.64/4.87 (elem!1 = s(s(s(s(z))))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[504, 23803])).
% 4.64/4.87 tff(23808,plain,
% 4.64/4.87 (~(s(elem!1) = s(s(z)))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[11438, 23807])).
% 4.64/4.87 tff(23809,plain,
% 4.64/4.87 (~b(s(s(z)), elem!1)),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[17684, 23807, 105])).
% 4.64/4.87 tff(23810,plain,
% 4.64/4.87 (b(elem!1, z)),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[12557, 23807, 22562])).
% 4.64/4.87 tff(23811,plain,
% 4.64/4.87 (b(elem!1, z) <=> b(s(s(z)), z)),
% 4.64/4.87 inference(monotonicity,[status(thm)],[308])).
% 4.64/4.87 tff(23812,plain,
% 4.64/4.87 (b(s(s(z)), z) <=> b(elem!1, z)),
% 4.64/4.87 inference(symmetry,[status(thm)],[23811])).
% 4.64/4.87 tff(23813,plain,
% 4.64/4.87 ((~b(s(s(z)), z)) <=> (~b(elem!1, z))),
% 4.64/4.87 inference(monotonicity,[status(thm)],[23812])).
% 4.64/4.87 tff(23814,assumption,(~b(s(s(z)), z)), introduced(assumption)).
% 4.64/4.87 tff(23815,plain,
% 4.64/4.87 (~b(elem!1, z)),
% 4.64/4.87 inference(modus_ponens,[status(thm)],[23814, 23813])).
% 4.64/4.87 tff(23816,plain,
% 4.64/4.87 ($false),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[506, 23815])).
% 4.64/4.87 tff(23817,plain,((~(elem!1 = s(s(z)))) | (~b(elem!1, z)) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 4.64/4.87 tff(23818,plain,
% 4.64/4.87 (~(elem!1 = s(s(z)))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[23817, 23810, 23771])).
% 4.64/4.87 tff(23819,plain,
% 4.64/4.87 (~(s(s(z)) = elem!1)),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[3230, 23818])).
% 4.64/4.87 tff(23820,plain,
% 4.64/4.87 (r(s(s(z)), elem!1)),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[448, 23819, 23809])).
% 4.64/4.87 tff(23821,plain,
% 4.64/4.87 (~r(z, elem!1)),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[8412, 23820, 22560])).
% 4.64/4.87 tff(23822,plain,
% 4.64/4.87 (b(z, elem!1)),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[585, 23821, 318])).
% 4.64/4.87 tff(23823,plain,
% 4.64/4.87 (~(s(s(elem!1)) = elem!1)),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[338, 23819, 23803])).
% 4.64/4.87 tff(23824,plain,
% 4.64/4.87 (~(s(elem!1) = elem!1)),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[672, 23823])).
% 4.64/4.87 tff(23825,plain,
% 4.64/4.87 (r(s(s(s(s(z)))), s(s(z))) <=> r(elem!1, s(s(z)))),
% 4.64/4.87 inference(monotonicity,[status(thm)],[23803])).
% 4.64/4.87 tff(23826,plain,
% 4.64/4.87 (r(elem!1, s(s(z)))),
% 4.64/4.87 inference(modus_ponens,[status(thm)],[103, 23825])).
% 4.64/4.87 tff(23827,plain,
% 4.64/4.87 (~r(s(elem!1), s(s(z)))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[17418, 23826, 23772, 23824, 23810, 23822])).
% 4.64/4.87 tff(23828,plain,
% 4.64/4.87 (b(s(elem!1), s(s(z)))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[421, 23827, 23808])).
% 4.64/4.87 tff(23829,plain,
% 4.64/4.87 (b(s(s(s(s(s(z))))), s(s(z)))),
% 4.64/4.87 inference(modus_ponens,[status(thm)],[23828, 23806])).
% 4.64/4.87 tff(23830,plain,
% 4.64/4.87 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[13684, 10794, 22560, 22562])).
% 4.64/4.87 tff(23831,plain,
% 4.64/4.87 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[249, 23830])).
% 4.64/4.87 tff(23832,plain,
% 4.64/4.87 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.64/4.87 inference(monotonicity,[status(thm)],[23804])).
% 4.64/4.87 tff(23833,plain,
% 4.64/4.87 ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 4.64/4.87 inference(symmetry,[status(thm)],[23832])).
% 4.64/4.87 tff(23834,plain,
% 4.64/4.87 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 4.64/4.87 inference(monotonicity,[status(thm)],[23804])).
% 4.64/4.87 tff(23835,plain,
% 4.64/4.87 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 4.64/4.87 inference(monotonicity,[status(thm)],[23834])).
% 4.64/4.87 tff(23836,plain,
% 4.64/4.87 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 4.64/4.87 inference(symmetry,[status(thm)],[23835])).
% 4.64/4.87 tff(23837,plain,
% 4.64/4.87 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 4.64/4.87 inference(monotonicity,[status(thm)],[23836])).
% 4.64/4.87 tff(23838,plain,
% 4.64/4.87 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.64/4.87 inference(transitivity,[status(thm)],[23837, 377])).
% 4.64/4.87 tff(23839,plain,
% 4.64/4.87 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 4.64/4.87 inference(transitivity,[status(thm)],[23838, 23833])).
% 4.64/4.87 tff(23840,plain,
% 4.64/4.87 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))))),
% 4.64/4.87 inference(monotonicity,[status(thm)],[23839])).
% 4.64/4.87 tff(23841,plain,
% 4.64/4.87 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[348, 23823])).
% 4.64/4.87 tff(23842,plain,
% 4.64/4.87 (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 4.64/4.87 inference(modus_ponens,[status(thm)],[23841, 23840])).
% 4.64/4.87 tff(23843,plain,
% 4.64/4.87 (r(z, s(s(s(s(s(z)))))) <=> r(z, s(elem!1))),
% 4.64/4.87 inference(monotonicity,[status(thm)],[12866])).
% 4.64/4.87 tff(23844,plain,
% 4.64/4.87 (r(z, s(elem!1)) <=> r(z, s(s(s(s(s(z))))))),
% 4.64/4.87 inference(symmetry,[status(thm)],[23843])).
% 4.64/4.87 tff(23845,plain,
% 4.64/4.87 (r(z, s(s(s(s(s(z))))))),
% 4.64/4.87 inference(modus_ponens,[status(thm)],[2333, 23844])).
% 4.64/4.87 tff(23846,plain,
% 4.64/4.87 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[23450, 203, 3261])).
% 4.64/4.87 tff(23847,plain,
% 4.64/4.87 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[3578, 23846])).
% 4.64/4.87 tff(23848,plain,
% 4.64/4.87 (elem!1 = s(s(s(s(z))))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[504, 331])).
% 4.64/4.87 tff(23849,plain,
% 4.64/4.87 (~(s(elem!1) = s(s(z)))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[11438, 23848])).
% 4.64/4.87 tff(23850,plain,
% 4.64/4.87 (~(s(s(z)) = s(elem!1))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[1058, 23849])).
% 4.64/4.87 tff(23851,plain,
% 4.64/4.87 (b(s(s(z)), s(elem!1))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[1067, 13326, 23850])).
% 4.64/4.87 tff(23852,plain,
% 4.64/4.87 (b(s(s(z)), s(s(s(s(s(z))))))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[2330, 23851, 23848])).
% 4.64/4.87 tff(23853,plain,
% 4.64/4.87 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[14448, 23852, 166, 23847, 1851])).
% 4.64/4.87 tff(23854,plain,
% 4.64/4.87 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[18762, 23853, 18756])).
% 4.64/4.87 tff(23855,assumption,(r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 4.64/4.87 tff(23856,assumption,(r(z, s(s(s(s(s(z))))))), introduced(assumption)).
% 4.64/4.87 tff(23857,plain,
% 4.64/4.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 4.64/4.87 inference(rewrite,[status(thm)],[])).
% 4.64/4.87 tff(23858,plain,
% 4.64/4.87 (((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 4.64/4.87 inference(rewrite,[status(thm)],[])).
% 4.64/4.87 tff(23859,plain,
% 4.64/4.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 4.64/4.87 inference(monotonicity,[status(thm)],[23858])).
% 4.64/4.87 tff(23860,plain,
% 4.64/4.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 4.64/4.87 inference(transitivity,[status(thm)],[23859, 23857])).
% 4.64/4.87 tff(23861,plain,
% 4.64/4.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 4.64/4.87 inference(quant_inst,[status(thm)],[])).
% 4.64/4.87 tff(23862,plain,
% 4.64/4.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 4.64/4.87 inference(modus_ponens,[status(thm)],[23861, 23860])).
% 4.64/4.87 tff(23863,plain,
% 4.64/4.87 ($false),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[23862, 118, 203, 23856, 23855])).
% 4.64/4.87 tff(23864,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.87 tff(23865,plain,
% 4.64/4.87 (~r(z, s(s(s(s(s(z))))))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[23864, 23854, 203])).
% 4.64/4.87 tff(23866,plain,
% 4.64/4.87 ($false),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[23865, 23845])).
% 4.64/4.87 tff(23867,plain,((~r(z, s(elem!1))) | (~(s(s(s(s(z)))) = elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.87 tff(23868,plain,
% 4.64/4.87 (~r(z, s(elem!1))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[23867, 23803, 4236, 23842, 23831, 23829, 22560])).
% 4.64/4.87 tff(23869,plain,
% 4.64/4.87 (b(z, s(elem!1))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[2351, 23868])).
% 4.64/4.87 tff(23870,plain,
% 4.64/4.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))))),
% 4.64/4.87 inference(rewrite,[status(thm)],[])).
% 4.64/4.87 tff(23871,plain,
% 4.64/4.87 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))))),
% 4.64/4.87 inference(rewrite,[status(thm)],[])).
% 4.64/4.87 tff(23872,plain,
% 4.64/4.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(s(z)))))))),
% 4.64/4.87 inference(monotonicity,[status(thm)],[23871])).
% 4.64/4.87 tff(23873,plain,
% 4.64/4.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))))),
% 4.64/4.87 inference(transitivity,[status(thm)],[23872, 23870])).
% 4.64/4.87 tff(23874,plain,
% 4.64/4.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(elem!1))))),
% 4.64/4.87 inference(quant_inst,[status(thm)],[])).
% 4.64/4.87 tff(23875,plain,
% 4.64/4.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(s(z)))))),
% 4.64/4.87 inference(modus_ponens,[status(thm)],[23874, 23873])).
% 4.64/4.87 tff(23876,plain,
% 4.64/4.87 ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(z)))))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[23875, 178, 23828, 23412, 23725])).
% 4.64/4.87 tff(23877,plain,
% 4.64/4.87 (~b(s(elem!1), s(s(s(z))))),
% 4.64/4.87 inference(unit_resolution,[status(thm)],[23876, 23869])).
% 4.64/4.88 tff(23878,plain,
% 4.64/4.88 (~(s(elem!1) = s(s(s(z))))),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[23436, 23819])).
% 4.64/4.88 tff(23879,plain,
% 4.64/4.88 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | r(s(elem!1), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | r(s(elem!1), s(s(s(z)))))),
% 4.64/4.88 inference(rewrite,[status(thm)],[])).
% 4.64/4.88 tff(23880,plain,
% 4.64/4.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | r(s(elem!1), s(s(s(z)))))),
% 4.64/4.88 inference(quant_inst,[status(thm)],[])).
% 4.64/4.88 tff(23881,plain,
% 4.64/4.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | r(s(elem!1), s(s(s(z))))),
% 4.64/4.88 inference(modus_ponens,[status(thm)],[23880, 23879])).
% 4.64/4.88 tff(23882,plain,
% 4.64/4.88 (r(s(elem!1), s(s(s(z))))),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[23881, 41, 23878, 23877])).
% 4.64/4.88 tff(23883,plain,
% 4.64/4.88 (r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 4.64/4.88 inference(monotonicity,[status(thm)],[23835])).
% 4.64/4.88 tff(23884,plain,
% 4.64/4.88 (r(s(s(s(z))), s(s(s(elem!1))))),
% 4.64/4.88 inference(modus_ponens,[status(thm)],[8216, 23883])).
% 4.64/4.88 tff(23885,plain,
% 4.64/4.88 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 4.64/4.88 inference(monotonicity,[status(thm)],[23838])).
% 4.64/4.88 tff(23886,plain,
% 4.64/4.88 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.64/4.88 inference(modus_ponens,[status(thm)],[23841, 23885])).
% 4.64/4.88 tff(23887,plain,
% 4.64/4.88 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(elem!1))))),
% 4.64/4.88 inference(monotonicity,[status(thm)],[23835])).
% 4.64/4.88 tff(23888,plain,
% 4.64/4.88 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.64/4.88 inference(monotonicity,[status(thm)],[23803])).
% 4.64/4.88 tff(23889,plain,
% 4.64/4.88 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.64/4.88 inference(modus_ponens,[status(thm)],[251, 23888])).
% 4.64/4.88 tff(23890,plain,
% 4.64/4.88 (b(elem!1, s(s(s(elem!1))))),
% 4.64/4.88 inference(modus_ponens,[status(thm)],[23889, 23887])).
% 4.64/4.88 tff(23891,plain,
% 4.64/4.88 (~(elem!1 = s(elem!1))),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[748, 23824])).
% 4.64/4.88 tff(23892,plain,
% 4.64/4.88 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 4.64/4.88 inference(monotonicity,[status(thm)],[23835])).
% 4.64/4.88 tff(23893,plain,
% 4.64/4.88 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.64/4.88 inference(monotonicity,[status(thm)],[23803])).
% 4.64/4.88 tff(23894,plain,
% 4.64/4.88 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.64/4.88 inference(modus_ponens,[status(thm)],[104, 23893])).
% 4.64/4.88 tff(23895,plain,
% 4.64/4.88 (b(s(s(s(elem!1))), elem!1)),
% 4.64/4.88 inference(modus_ponens,[status(thm)],[23894, 23892])).
% 4.64/4.88 tff(23896,plain,
% 4.64/4.88 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(z))), elem!1)),
% 4.64/4.88 inference(monotonicity,[status(thm)],[23803])).
% 4.64/4.88 tff(23897,plain,
% 4.64/4.88 (r(s(s(s(z))), elem!1)),
% 4.64/4.88 inference(modus_ponens,[status(thm)],[23723, 23896])).
% 4.64/4.88 tff(23898,assumption,(r(s(elem!1), s(s(s(z))))), introduced(assumption)).
% 4.64/4.88 tff(23899,plain,
% 4.64/4.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))))),
% 4.64/4.88 inference(rewrite,[status(thm)],[])).
% 4.64/4.88 tff(23900,plain,
% 4.64/4.88 (((~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z)))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))))),
% 4.64/4.88 inference(rewrite,[status(thm)],[])).
% 4.64/4.88 tff(23901,plain,
% 4.64/4.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z)))))))),
% 4.64/4.88 inference(monotonicity,[status(thm)],[23900])).
% 4.64/4.88 tff(23902,plain,
% 4.64/4.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))))),
% 4.64/4.88 inference(transitivity,[status(thm)],[23901, 23899])).
% 4.64/4.88 tff(23903,plain,
% 4.64/4.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))))),
% 4.64/4.88 inference(quant_inst,[status(thm)],[])).
% 4.64/4.88 tff(23904,plain,
% 4.64/4.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z)))))),
% 4.64/4.88 inference(modus_ponens,[status(thm)],[23903, 23902])).
% 4.64/4.88 tff(23905,plain,
% 4.64/4.88 ($false),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[23904, 118, 1426, 18022, 23898])).
% 4.64/4.88 tff(23906,plain,((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.88 tff(23907,plain,
% 4.64/4.88 (~r(s(elem!1), elem!1)),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[23906, 23897, 23882])).
% 4.64/4.88 tff(23908,plain,
% 4.64/4.88 (b(s(elem!1), elem!1)),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[677, 23907, 23824])).
% 4.64/4.88 tff(23909,plain,
% 4.64/4.88 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[18695, 23908, 23831, 23807, 23895, 23891, 23890, 104, 10794])).
% 4.64/4.88 tff(23910,plain,
% 4.64/4.88 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[395, 23909, 23886])).
% 4.64/4.88 tff(23911,plain,
% 4.64/4.88 (r(s(elem!1), s(s(s(elem!1))))),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[14608, 23910, 23807])).
% 4.64/4.88 tff(23912,plain,
% 4.64/4.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(z))))))),
% 4.64/4.88 inference(rewrite,[status(thm)],[])).
% 4.64/4.88 tff(23913,plain,
% 4.64/4.88 (((~r(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(z)))))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(z))))))),
% 4.64/4.88 inference(rewrite,[status(thm)],[])).
% 4.64/4.88 tff(23914,plain,
% 4.64/4.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(z)))))))),
% 4.64/4.88 inference(monotonicity,[status(thm)],[23913])).
% 4.64/4.88 tff(23915,plain,
% 4.64/4.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(z))))))),
% 4.64/4.88 inference(transitivity,[status(thm)],[23914, 23912])).
% 4.64/4.88 tff(23916,plain,
% 4.64/4.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(z))))))),
% 4.64/4.88 inference(quant_inst,[status(thm)],[])).
% 4.64/4.88 tff(23917,plain,
% 4.64/4.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(z)))))),
% 4.64/4.88 inference(modus_ponens,[status(thm)],[23916, 23915])).
% 4.64/4.88 tff(23918,plain,
% 4.64/4.88 ($false),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[23917, 118, 23911, 23884, 23882])).
% 4.64/4.88 tff(23919,plain,((elem!1 = z) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | b(s(s(z)), s(s(s(s(z))))) | b(s(s(s(s(z)))), s(s(z))) | b(z, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.88 tff(23920,plain,
% 4.64/4.88 (elem!1 = z),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[23919, 8216, 104, 251, 105, 86, 4235])).
% 4.64/4.88 tff(23921,plain,
% 4.64/4.88 (r(s(elem!1), elem!1) <=> r(s(elem!1), z)),
% 4.64/4.88 inference(monotonicity,[status(thm)],[23920])).
% 4.64/4.88 tff(23922,plain,
% 4.64/4.88 ((s(elem!1) = elem!1) <=> (s(elem!1) = z)),
% 4.64/4.88 inference(monotonicity,[status(thm)],[23920])).
% 4.64/4.88 tff(23923,plain,
% 4.64/4.88 ((s(elem!1) = z) <=> (s(elem!1) = elem!1)),
% 4.64/4.88 inference(symmetry,[status(thm)],[23922])).
% 4.64/4.88 tff(23924,plain,
% 4.64/4.88 ((~(s(elem!1) = z)) <=> (~(s(elem!1) = elem!1))),
% 4.64/4.88 inference(monotonicity,[status(thm)],[23923])).
% 4.64/4.88 tff(23925,plain,
% 4.64/4.88 (~(s(elem!1) = elem!1)),
% 4.64/4.88 inference(modus_ponens,[status(thm)],[769, 23924])).
% 4.64/4.88 tff(23926,plain,
% 4.64/4.88 (b(elem!1, s(s(s(elem!1)))) <=> b(z, s(s(s(elem!1))))),
% 4.64/4.88 inference(monotonicity,[status(thm)],[23920])).
% 4.64/4.88 tff(23927,plain,
% 4.64/4.88 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 4.64/4.88 inference(symmetry,[status(thm)],[23926])).
% 4.64/4.88 tff(23928,plain,
% 4.64/4.88 (s(elem!1) = s(z)),
% 4.64/4.88 inference(monotonicity,[status(thm)],[23920])).
% 4.64/4.88 tff(23929,plain,
% 4.64/4.88 (s(s(elem!1)) = s(s(z))),
% 4.64/4.88 inference(monotonicity,[status(thm)],[23928])).
% 4.64/4.88 tff(23930,plain,
% 4.64/4.88 (s(s(s(elem!1))) = s(s(s(z)))),
% 4.64/4.88 inference(monotonicity,[status(thm)],[23929])).
% 4.64/4.88 tff(23931,plain,
% 4.64/4.88 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(z))))),
% 4.64/4.88 inference(monotonicity,[status(thm)],[23930])).
% 4.64/4.88 tff(23932,plain,
% 4.64/4.88 (b(z, s(s(s(z)))) <=> b(z, s(s(s(elem!1))))),
% 4.64/4.88 inference(symmetry,[status(thm)],[23931])).
% 4.64/4.88 tff(23933,plain,
% 4.64/4.88 (b(z, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 4.64/4.88 inference(transitivity,[status(thm)],[23932, 23927])).
% 4.64/4.88 tff(23934,plain,
% 4.64/4.88 (b(elem!1, s(s(s(elem!1))))),
% 4.64/4.88 inference(modus_ponens,[status(thm)],[23412, 23933])).
% 4.64/4.88 tff(23935,plain,
% 4.64/4.88 (s(s(s(z))) = s(s(s(elem!1)))),
% 4.64/4.88 inference(symmetry,[status(thm)],[23930])).
% 4.64/4.88 tff(23936,plain,
% 4.64/4.88 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 4.64/4.88 inference(monotonicity,[status(thm)],[23935])).
% 4.64/4.88 tff(23937,plain,
% 4.64/4.88 ((~r(s(s(z)), s(s(s(z))))) <=> (~r(s(s(z)), s(s(s(elem!1)))))),
% 4.64/4.88 inference(monotonicity,[status(thm)],[23936])).
% 4.64/4.88 tff(23938,plain,
% 4.64/4.88 (~r(s(s(z)), s(s(s(elem!1))))),
% 4.64/4.88 inference(modus_ponens,[status(thm)],[23756, 23937])).
% 4.64/4.88 tff(23939,plain,
% 4.64/4.88 (~(s(elem!1) = s(s(z)))),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[1838, 23938, 10794])).
% 4.64/4.88 tff(23940,plain,
% 4.64/4.88 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(z, s(s(s(s(s(s(s(z))))))))),
% 4.64/4.88 inference(monotonicity,[status(thm)],[23920])).
% 4.64/4.88 tff(23941,plain,
% 4.64/4.88 (r(z, s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.64/4.88 inference(symmetry,[status(thm)],[23940])).
% 4.64/4.88 tff(23942,plain,
% 4.64/4.88 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.64/4.88 inference(modus_ponens,[status(thm)],[4236, 23941])).
% 4.64/4.88 tff(23943,plain,
% 4.64/4.88 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), z)),
% 4.64/4.88 inference(monotonicity,[status(thm)],[23920])).
% 4.64/4.88 tff(23944,plain,
% 4.64/4.88 (r(s(s(s(s(s(s(s(z))))))), z) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.64/4.88 inference(symmetry,[status(thm)],[23943])).
% 4.64/4.88 tff(23945,plain,
% 4.64/4.88 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.64/4.88 inference(modus_ponens,[status(thm)],[23408, 23944])).
% 4.64/4.88 tff(23946,plain,
% 4.64/4.88 (r(s(s(z)), elem!1) <=> r(s(s(z)), z)),
% 4.64/4.88 inference(monotonicity,[status(thm)],[23920])).
% 4.64/4.88 tff(23947,plain,
% 4.64/4.88 (r(s(s(z)), z) <=> r(s(s(z)), elem!1)),
% 4.64/4.88 inference(symmetry,[status(thm)],[23946])).
% 4.64/4.88 tff(23948,plain,
% 4.64/4.88 (r(s(s(z)), elem!1)),
% 4.64/4.88 inference(modus_ponens,[status(thm)],[23772, 23947])).
% 4.64/4.88 tff(23949,plain,
% 4.64/4.88 (r(elem!1, s(elem!1))),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[6201, 2333, 928])).
% 4.64/4.88 tff(23950,plain,
% 4.64/4.88 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[2935, 23949, 1265])).
% 4.64/4.88 tff(23951,plain,
% 4.64/4.88 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[2979, 23181, 438, 2953, 23180])).
% 4.64/4.88 tff(23952,plain,
% 4.64/4.88 ($false),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[395, 23951, 23950, 14147])).
% 4.64/4.88 tff(23953,plain,((~r(z, s(elem!1))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(s(z))) | (~(elem!1 = z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.88 tff(23954,plain,
% 4.64/4.88 (~r(z, s(elem!1))),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[23953, 23948, 23945, 23942, 23939, 23920, 22560])).
% 4.64/4.88 tff(23955,plain,
% 4.64/4.88 (b(z, s(elem!1))),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[2351, 23954])).
% 4.64/4.88 tff(23956,plain,
% 4.64/4.88 (b(elem!1, s(elem!1))),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[12054, 23955, 23920])).
% 4.64/4.88 tff(23957,plain,
% 4.64/4.88 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 4.64/4.88 inference(monotonicity,[status(thm)],[23930])).
% 4.64/4.88 tff(23958,plain,
% 4.64/4.88 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 4.64/4.88 inference(monotonicity,[status(thm)],[23957, 23930])).
% 4.64/4.88 tff(23959,plain,
% 4.64/4.88 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 4.64/4.88 inference(symmetry,[status(thm)],[23958])).
% 4.64/4.88 tff(23960,plain,
% 4.64/4.88 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(elem!1)))))),
% 4.64/4.88 inference(monotonicity,[status(thm)],[23959])).
% 4.64/4.88 tff(23961,plain,
% 4.64/4.88 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 4.64/4.88 inference(modus_ponens,[status(thm)],[4938, 23960])).
% 4.64/4.88 tff(23962,plain,
% 4.64/4.88 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = z)),
% 4.64/4.88 inference(monotonicity,[status(thm)],[23920])).
% 4.64/4.88 tff(23963,plain,
% 4.64/4.88 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 4.64/4.88 inference(symmetry,[status(thm)],[23962])).
% 4.64/4.88 tff(23964,plain,
% 4.64/4.88 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 4.64/4.88 inference(monotonicity,[status(thm)],[23963])).
% 4.64/4.88 tff(23965,plain,
% 4.64/4.88 (~(s(s(s(elem!1))) = elem!1)),
% 4.64/4.88 inference(modus_ponens,[status(thm)],[940, 23964])).
% 4.64/4.88 tff(23966,plain,
% 4.64/4.88 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[951, 23965])).
% 4.64/4.88 tff(23967,plain,
% 4.64/4.88 (b(elem!1, s(s(s(s(elem!1))))) <=> b(z, s(s(s(s(elem!1)))))),
% 4.64/4.88 inference(monotonicity,[status(thm)],[23920])).
% 4.64/4.88 tff(23968,plain,
% 4.64/4.88 (b(z, s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 4.64/4.88 inference(symmetry,[status(thm)],[23967])).
% 4.64/4.88 tff(23969,plain,
% 4.64/4.88 (b(z, s(s(s(s(elem!1))))) <=> b(z, s(s(s(s(z)))))),
% 4.64/4.88 inference(monotonicity,[status(thm)],[23957])).
% 4.64/4.88 tff(23970,plain,
% 4.64/4.88 (b(z, s(s(s(s(z))))) <=> b(z, s(s(s(s(elem!1)))))),
% 4.64/4.88 inference(symmetry,[status(thm)],[23969])).
% 4.64/4.88 tff(23971,plain,
% 4.64/4.88 (b(z, s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 4.64/4.88 inference(transitivity,[status(thm)],[23970, 23968])).
% 4.64/4.88 tff(23972,plain,
% 4.64/4.88 (b(elem!1, s(s(s(s(elem!1)))))),
% 4.64/4.88 inference(modus_ponens,[status(thm)],[23405, 23971])).
% 4.64/4.88 tff(23973,plain,
% 4.64/4.88 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), z)),
% 4.64/4.88 inference(monotonicity,[status(thm)],[23920])).
% 4.64/4.88 tff(23974,plain,
% 4.64/4.88 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 4.64/4.88 inference(symmetry,[status(thm)],[23973])).
% 4.64/4.88 tff(23975,plain,
% 4.64/4.88 (b(s(s(s(elem!1))), z) <=> b(s(s(s(z))), z)),
% 4.64/4.88 inference(monotonicity,[status(thm)],[23930])).
% 4.64/4.88 tff(23976,plain,
% 4.64/4.88 (b(s(s(s(z))), z) <=> b(s(s(s(elem!1))), z)),
% 4.64/4.88 inference(symmetry,[status(thm)],[23975])).
% 4.64/4.88 tff(23977,plain,
% 4.64/4.88 (b(s(s(s(z))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 4.64/4.88 inference(transitivity,[status(thm)],[23976, 23974])).
% 4.64/4.88 tff(23978,plain,
% 4.64/4.88 (b(s(s(s(elem!1))), elem!1)),
% 4.64/4.88 inference(modus_ponens,[status(thm)],[23410, 23977])).
% 4.64/4.88 tff(23979,plain,
% 4.64/4.88 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(elem!1)))), z)),
% 4.64/4.88 inference(monotonicity,[status(thm)],[23920])).
% 4.64/4.88 tff(23980,plain,
% 4.64/4.88 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 4.64/4.88 inference(symmetry,[status(thm)],[23979])).
% 4.64/4.88 tff(23981,plain,
% 4.64/4.88 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(z)))), z)),
% 4.64/4.88 inference(monotonicity,[status(thm)],[23957])).
% 4.64/4.88 tff(23982,plain,
% 4.64/4.88 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(elem!1)))), z)),
% 4.64/4.88 inference(symmetry,[status(thm)],[23981])).
% 4.64/4.88 tff(23983,plain,
% 4.64/4.88 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 4.64/4.88 inference(transitivity,[status(thm)],[23982, 23980])).
% 4.64/4.88 tff(23984,plain,
% 4.64/4.88 (b(s(s(s(s(elem!1)))), elem!1)),
% 4.64/4.88 inference(modus_ponens,[status(thm)],[22562, 23983])).
% 4.64/4.88 tff(23985,plain,
% 4.64/4.88 ((s(elem!1) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 4.64/4.88 inference(monotonicity,[status(thm)],[23935])).
% 4.64/4.88 tff(23986,plain,
% 4.64/4.88 ((s(elem!1) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 4.64/4.88 inference(transitivity,[status(thm)],[23985, 3881])).
% 4.64/4.88 tff(23987,plain,
% 4.64/4.88 ((s(elem!1) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 4.64/4.88 inference(transitivity,[status(thm)],[23986, 7104])).
% 4.64/4.88 tff(23988,plain,
% 4.64/4.88 ((~(s(elem!1) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 4.64/4.88 inference(monotonicity,[status(thm)],[23987])).
% 4.64/4.88 tff(23989,plain,
% 4.64/4.88 (z = elem!1),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[2808, 23920])).
% 4.64/4.88 tff(23990,plain,
% 4.64/4.88 (b(s(s(s(s(z)))), elem!1)),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[20730, 23989, 22562])).
% 4.64/4.88 tff(23991,plain,
% 4.64/4.88 (~(s(s(z)) = elem!1)),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[3774, 23990, 86])).
% 4.64/4.88 tff(23992,plain,
% 4.64/4.88 (~(s(elem!1) = s(s(s(z))))),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[23436, 23991])).
% 4.64/4.88 tff(23993,plain,
% 4.64/4.88 (~(s(elem!1) = s(s(s(elem!1))))),
% 4.64/4.88 inference(modus_ponens,[status(thm)],[23992, 23988])).
% 4.64/4.88 tff(23994,plain,
% 4.64/4.88 (~b(s(elem!1), s(s(s(elem!1))))),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[6834, 683, 2042, 854, 1597])).
% 4.64/4.88 tff(23995,plain,
% 4.64/4.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 4.64/4.88 inference(rewrite,[status(thm)],[])).
% 4.64/4.88 tff(23996,plain,
% 4.64/4.88 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 4.64/4.88 inference(rewrite,[status(thm)],[])).
% 4.64/4.88 tff(23997,plain,
% 4.64/4.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 4.64/4.88 inference(monotonicity,[status(thm)],[23996])).
% 4.64/4.88 tff(23998,plain,
% 4.64/4.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 4.64/4.88 inference(transitivity,[status(thm)],[23997, 23995])).
% 4.64/4.88 tff(23999,plain,
% 4.64/4.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))))),
% 4.64/4.88 inference(quant_inst,[status(thm)],[])).
% 4.64/4.88 tff(24000,plain,
% 4.64/4.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 4.64/4.88 inference(modus_ponens,[status(thm)],[23999, 23998])).
% 4.64/4.88 tff(24001,plain,
% 4.64/4.88 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[24000, 178, 5818, 683, 854, 3710])).
% 4.64/4.88 tff(24002,plain,
% 4.64/4.88 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[962, 41, 4341, 24001])).
% 4.64/4.88 tff(24003,plain,
% 4.64/4.88 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[12168, 178, 5818, 1597, 2042, 3710])).
% 4.64/4.88 tff(24004,plain,
% 4.64/4.88 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[1987, 41, 1693, 24003])).
% 4.64/4.88 tff(24005,plain,
% 4.64/4.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 4.64/4.88 inference(rewrite,[status(thm)],[])).
% 4.64/4.88 tff(24006,plain,
% 4.64/4.88 (((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 4.64/4.88 inference(rewrite,[status(thm)],[])).
% 4.64/4.88 tff(24007,plain,
% 4.64/4.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1))))))))),
% 4.64/4.88 inference(monotonicity,[status(thm)],[24006])).
% 4.64/4.88 tff(24008,plain,
% 4.64/4.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 4.64/4.88 inference(transitivity,[status(thm)],[24007, 24005])).
% 4.64/4.88 tff(24009,plain,
% 4.64/4.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 4.64/4.88 inference(quant_inst,[status(thm)],[])).
% 4.64/4.88 tff(24010,plain,
% 4.64/4.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1))))))),
% 4.64/4.88 inference(modus_ponens,[status(thm)],[24009, 24008])).
% 4.64/4.88 tff(24011,plain,
% 4.64/4.88 ($false),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[24010, 118, 2102, 24004, 24002])).
% 4.64/4.88 tff(24012,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (s(elem!1) = s(s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(elem!1, s(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(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.88 tff(24013,plain,
% 4.64/4.88 (~r(s(elem!1), s(s(s(elem!1))))),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[24012, 683, 3710, 1597, 5818, 4341, 1693, 854, 2042])).
% 4.64/4.88 tff(24014,plain,
% 4.64/4.88 ($false),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[5432, 24013, 23994, 5425])).
% 4.64/4.88 tff(24015,plain,((~b(s(elem!1), elem!1)) | (s(elem!1) = s(s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (s(elem!1) = s(s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.88 tff(24016,plain,
% 4.64/4.88 (~b(s(elem!1), elem!1)),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[24015, 23993, 23984, 23978, 23972, 23966, 23961, 23956, 23934])).
% 4.64/4.88 tff(24017,plain,
% 4.64/4.88 (r(s(elem!1), elem!1)),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[677, 24016, 23925])).
% 4.64/4.88 tff(24018,plain,
% 4.64/4.88 (r(s(elem!1), z)),
% 4.64/4.88 inference(modus_ponens,[status(thm)],[24017, 23921])).
% 4.64/4.88 tff(24019,plain,
% 4.64/4.88 (~r(s(elem!1), s(s(z)))),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[2249, 24017, 23948])).
% 4.64/4.88 tff(24020,plain,
% 4.64/4.88 (b(s(elem!1), s(s(z)))),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[421, 24019, 23939])).
% 4.64/4.88 tff(24021,plain,
% 4.64/4.88 (~r(s(elem!1), z)),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[14170, 24020, 23831, 23452, 23920, 23408])).
% 4.64/4.88 tff(24022,plain,
% 4.64/4.88 ($false),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[24021, 24018])).
% 4.64/4.88 tff(24023,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(z)))), 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(z)), s(s(s(s(z))))) | b(z, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.88 tff(24024,plain,
% 4.64/4.88 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[24023, 251, 104, 86, 105, 4235])).
% 4.64/4.88 tff(24025,plain,
% 4.64/4.88 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[20667, 24024])).
% 4.64/4.88 tff(24026,plain,
% 4.64/4.88 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[21670, 24025, 23405, 23408, 251, 104])).
% 4.64/4.88 tff(24027,plain,
% 4.64/4.88 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[22510, 24025, 103, 23831, 23452, 10794])).
% 4.64/4.88 tff(24028,plain,
% 4.64/4.88 ($false),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[10755, 24027, 24026])).
% 4.64/4.88 tff(24029,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(z))) | b(s(s(z)), s(s(s(s(z))))) | b(z, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.88 tff(24030,plain,
% 4.64/4.88 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[24029, 4235, 86, 105, 104])).
% 4.64/4.88 tff(24031,plain,
% 4.64/4.88 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[222, 24030])).
% 4.64/4.88 tff(24032,plain,
% 4.64/4.88 ($false),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[10755, 21521, 21409])).
% 4.64/4.88 tff(24033,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.88 tff(24034,plain,
% 4.64/4.88 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[24033, 24031, 4236, 23405, 22562])).
% 4.64/4.88 tff(24035,plain,
% 4.64/4.88 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[20667, 24034])).
% 4.64/4.88 tff(24036,plain,
% 4.64/4.88 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[22510, 24035, 103, 23831, 23452, 10794])).
% 4.64/4.88 tff(24037,plain,
% 4.64/4.88 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[10755, 24036])).
% 4.64/4.88 tff(24038,plain,
% 4.64/4.88 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[22504, 24037, 104, 103, 23831, 24035, 23405, 10794, 22562])).
% 4.64/4.88 tff(24039,plain,
% 4.64/4.88 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[20754, 24037, 104, 22562, 24035])).
% 4.64/4.88 tff(24040,plain,
% 4.64/4.88 ($false),
% 4.64/4.88 inference(unit_resolution,[status(thm)],[133, 24039, 24038])).
% 4.64/4.88 tff(24041,plain,(b(z, s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(z))) | b(s(s(z)), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.89 tff(24042,plain,
% 4.64/4.89 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[24041, 105, 86, 104])).
% 4.64/4.89 tff(24043,plain,
% 4.64/4.89 ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[12281, 178, 104, 23405, 23831])).
% 4.64/4.89 tff(24044,plain,
% 4.64/4.89 (~b(s(s(z)), z)),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[24043, 24042])).
% 4.64/4.89 tff(24045,plain,
% 4.64/4.89 (r(s(s(z)), z)),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[3249, 24044])).
% 4.64/4.89 tff(24046,plain,
% 4.64/4.89 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[20754, 146, 104, 23414, 3002])).
% 4.64/4.89 tff(24047,plain,
% 4.64/4.89 (r(s(s(s(z))), s(s(s(s(z)))))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[10755, 24046])).
% 4.64/4.89 tff(24048,plain,
% 4.64/4.89 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[22510, 24047, 193, 23442, 3002, 147])).
% 4.64/4.89 tff(24049,plain,
% 4.64/4.89 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[3578, 24048])).
% 4.64/4.89 tff(24050,plain,
% 4.64/4.89 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[23438, 146])).
% 4.64/4.89 tff(24051,plain,
% 4.64/4.89 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[222, 24050])).
% 4.64/4.89 tff(24052,plain,
% 4.64/4.89 ($false),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[3920, 118, 24051, 193, 24049])).
% 4.64/4.89 tff(24053,plain,((~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.89 tff(24054,plain,
% 4.64/4.89 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[24053, 3002, 193, 147, 104])).
% 4.64/4.89 tff(24055,plain,
% 4.64/4.89 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[133, 24054])).
% 4.64/4.89 tff(24056,plain,
% 4.64/4.89 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[22504, 24055, 104, 193, 23442, 3002, 23405, 147, 23414])).
% 4.64/4.89 tff(24057,plain,
% 4.64/4.89 (r(s(s(s(z))), s(s(s(s(z)))))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[10755, 24056])).
% 4.64/4.89 tff(24058,plain,
% 4.64/4.89 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[123, 24055, 106])).
% 4.64/4.89 tff(24059,plain,
% 4.64/4.89 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[3578, 24058])).
% 4.64/4.89 tff(24060,plain,
% 4.64/4.89 ($false),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[22510, 24059, 24057, 193, 23442, 3002, 147])).
% 4.64/4.89 tff(24061,plain,((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.89 tff(24062,plain,
% 4.64/4.89 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[24061, 10794, 103, 24045, 104])).
% 4.64/4.89 tff(24063,plain,
% 4.64/4.89 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[20667, 24062])).
% 4.64/4.89 tff(24064,plain,
% 4.64/4.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 4.64/4.89 inference(rewrite,[status(thm)],[])).
% 4.64/4.89 tff(24065,plain,
% 4.64/4.89 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(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(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 4.64/4.89 inference(rewrite,[status(thm)],[])).
% 4.64/4.89 tff(24066,plain,
% 4.64/4.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z))))))))),
% 4.64/4.89 inference(monotonicity,[status(thm)],[24065])).
% 4.64/4.89 tff(24067,plain,
% 4.64/4.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 4.64/4.89 inference(transitivity,[status(thm)],[24066, 24064])).
% 4.64/4.89 tff(24068,plain,
% 4.64/4.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 4.64/4.89 inference(quant_inst,[status(thm)],[])).
% 4.64/4.89 tff(24069,plain,
% 4.64/4.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z))))))),
% 4.64/4.89 inference(modus_ponens,[status(thm)],[24068, 24067])).
% 4.64/4.89 tff(24070,plain,
% 4.64/4.89 ($false),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[24069, 178, 104, 23405, 168, 595, 146])).
% 4.64/4.89 tff(24071,plain,((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.89 tff(24072,plain,
% 4.64/4.89 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[24071, 24042, 22562, 104])).
% 4.64/4.89 tff(24073,plain,
% 4.64/4.89 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[133, 24072])).
% 4.64/4.89 tff(24074,plain,
% 4.64/4.89 ($false),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[21450, 118, 108, 16062, 8216])).
% 4.64/4.89 tff(24075,plain,((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.89 tff(24076,plain,
% 4.64/4.89 (~r(s(s(s(z))), z)),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[24075, 24073, 24063])).
% 4.64/4.89 tff(24077,plain,
% 4.64/4.89 (b(s(s(s(z))), z)),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[21073, 24076])).
% 4.64/4.89 tff(24078,plain,
% 4.64/4.89 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[21413, 24077, 23405, 24063, 22562])).
% 4.64/4.89 tff(24079,plain,
% 4.64/4.89 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[222, 24078])).
% 4.64/4.89 tff(24080,plain,
% 4.64/4.89 ($false),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[11920, 178, 104, 23405, 22562, 24079, 24042])).
% 4.64/4.89 tff(24081,plain,(b(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(z)))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.89 tff(24082,plain,
% 4.64/4.89 (b(s(s(z)), s(s(s(s(z)))))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[24081, 86, 104])).
% 4.64/4.89 tff(24083,plain,
% 4.64/4.89 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[23450, 203, 22560])).
% 4.64/4.89 tff(24084,plain,
% 4.64/4.89 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[3578, 24083])).
% 4.64/4.89 tff(24085,plain,
% 4.64/4.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.64/4.89 inference(rewrite,[status(thm)],[])).
% 4.64/4.89 tff(24086,plain,
% 4.64/4.89 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(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(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(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(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(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.64/4.89 inference(rewrite,[status(thm)],[])).
% 4.64/4.89 tff(24087,plain,
% 4.64/4.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(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(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(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z))))))),
% 4.64/4.89 inference(monotonicity,[status(thm)],[24086])).
% 4.64/4.89 tff(24088,plain,
% 4.64/4.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(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(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(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.64/4.89 inference(transitivity,[status(thm)],[24087, 24085])).
% 4.64/4.89 tff(24089,plain,
% 4.64/4.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(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(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(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.64/4.89 inference(quant_inst,[status(thm)],[])).
% 4.64/4.89 tff(24090,plain,
% 4.64/4.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z))))),
% 4.64/4.89 inference(modus_ponens,[status(thm)],[24089, 24088])).
% 4.64/4.89 tff(24091,plain,
% 4.64/4.89 ($false),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[24090, 178, 104, 167, 4932, 1146, 3002])).
% 4.64/4.89 tff(24092,plain,((~b(s(s(s(z))), s(s(z)))) | (~b(s(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(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.89 tff(24093,plain,
% 4.64/4.89 (~b(s(s(s(z))), s(s(z)))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[24092, 3002, 167, 104, 1146])).
% 4.64/4.89 tff(24094,plain,
% 4.64/4.89 (r(s(s(s(z))), s(s(z)))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[4966, 24093])).
% 4.64/4.89 tff(24095,plain,
% 4.64/4.89 (~r(s(s(s(z))), z)),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[6019, 118, 22560, 24094])).
% 4.64/4.89 tff(24096,plain,
% 4.64/4.89 (b(s(s(s(z))), z)),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[21073, 24095])).
% 4.64/4.89 tff(24097,plain,
% 4.64/4.89 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[8696, 118, 193, 24094])).
% 4.64/4.89 tff(24098,plain,
% 4.64/4.89 (b(s(s(s(s(z)))), s(s(s(z))))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[11185, 24097])).
% 4.64/4.89 tff(24099,plain,
% 4.64/4.89 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[20838, 24094, 193])).
% 4.64/4.89 tff(24100,plain,
% 4.64/4.89 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[10755, 24099])).
% 4.64/4.89 tff(24101,plain,
% 4.64/4.89 ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[21395, 178, 104, 23405, 23414, 24100, 3002])).
% 4.64/4.89 tff(24102,plain,
% 4.64/4.89 ($false),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[24101, 24098, 24096])).
% 4.64/4.89 tff(24103,plain,((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.89 tff(24104,plain,
% 4.64/4.89 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[24103, 24084, 193, 167, 104])).
% 4.64/4.89 tff(24105,plain,
% 4.64/4.89 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[20667, 24104])).
% 4.64/4.89 tff(24106,plain,
% 4.64/4.89 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[24033, 24105, 203, 23405, 23414])).
% 4.64/4.89 tff(24107,plain,
% 4.64/4.89 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[222, 24106])).
% 4.64/4.89 tff(24108,plain,
% 4.64/4.89 (~b(s(s(z)), z)),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[14130, 224, 22560, 193, 167])).
% 4.64/4.89 tff(24109,plain,
% 4.64/4.89 ($false),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[11920, 178, 104, 1687, 168, 14122, 399])).
% 4.64/4.89 tff(24110,plain,((~r(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(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.89 tff(24111,plain,
% 4.64/4.89 (~r(s(s(z)), z)),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[24110, 224, 104, 23405, 23414, 193])).
% 4.64/4.89 tff(24112,plain,
% 4.64/4.89 ($false),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[3249, 24111, 24108])).
% 4.64/4.89 tff(24113,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.89 tff(24114,plain,
% 4.64/4.89 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[24113, 193, 104, 167])).
% 4.64/4.89 tff(24115,plain,
% 4.64/4.89 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[249, 24114])).
% 4.64/4.89 tff(24116,plain,
% 4.64/4.89 ($false),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[9047, 178, 104, 24115, 167, 24107, 24084])).
% 4.64/4.89 tff(24117,plain,((~r(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(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.89 tff(24118,plain,
% 4.64/4.89 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[24117, 24082, 104, 103])).
% 4.64/4.89 tff(24119,plain,
% 4.64/4.89 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[271, 24118])).
% 4.64/4.89 tff(24120,plain,
% 4.64/4.89 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[24113, 103, 104, 24082])).
% 4.64/4.89 tff(24121,plain,
% 4.64/4.89 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[249, 24120])).
% 4.64/4.89 tff(24122,plain,
% 4.64/4.89 ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[12281, 178, 104, 23405, 24121])).
% 4.64/4.89 tff(24123,plain,
% 4.64/4.89 (~b(s(s(z)), z)),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[24122, 24119])).
% 4.64/4.89 tff(24124,plain,
% 4.64/4.89 (r(s(s(z)), z)),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[3249, 24123])).
% 4.64/4.89 tff(24125,plain,
% 4.64/4.89 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[23438, 134])).
% 4.64/4.89 tff(24126,plain,
% 4.64/4.89 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[222, 24125])).
% 4.64/4.89 tff(24127,plain,
% 4.64/4.89 ($false),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[3920, 118, 24126, 193, 107])).
% 4.64/4.89 tff(24128,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.89 tff(24129,plain,
% 4.64/4.89 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[24128, 24124, 104, 103])).
% 4.64/4.89 tff(24130,plain,
% 4.64/4.89 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[3578, 24129])).
% 4.64/4.89 tff(24131,plain,
% 4.64/4.89 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[24103, 24130, 103, 24082, 104])).
% 4.64/4.89 tff(24132,plain,
% 4.64/4.89 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[20667, 24131])).
% 4.64/4.89 tff(24133,plain,
% 4.64/4.89 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[186, 24121, 104, 24082, 22562])).
% 4.64/4.89 tff(24134,plain,
% 4.64/4.89 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[133, 24133])).
% 4.64/4.89 tff(24135,plain,
% 4.64/4.89 (~r(s(s(s(z))), z)),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[24075, 24132, 24134])).
% 4.64/4.89 tff(24136,plain,
% 4.64/4.89 (b(s(s(s(z))), z)),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[21073, 24135])).
% 4.64/4.89 tff(24137,plain,
% 4.64/4.89 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[21413, 24136, 23405, 24132, 22562])).
% 4.64/4.89 tff(24138,plain,
% 4.64/4.89 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[222, 24137])).
% 4.64/4.89 tff(24139,plain,
% 4.64/4.89 ($false),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[11920, 178, 104, 23405, 22562, 24138, 24119])).
% 4.64/4.89 tff(24140,plain,(b(s(s(s(s(z)))), s(s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.89 tff(24141,plain,
% 4.64/4.89 (b(s(s(s(s(z)))), s(s(z)))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[24140, 85])).
% 4.64/4.89 tff(24142,plain,
% 4.64/4.89 (r(z, s(s(z)))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[22559, 85])).
% 4.64/4.89 tff(24143,plain,
% 4.64/4.89 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[4690, 224, 22560])).
% 4.64/4.89 tff(24144,plain,
% 4.64/4.89 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[271, 24143])).
% 4.64/4.89 tff(24145,plain,
% 4.64/4.89 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[21477, 178, 104, 23405, 251, 595])).
% 4.64/4.89 tff(24146,plain,
% 4.64/4.89 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[133, 24145])).
% 4.64/4.89 tff(24147,plain,
% 4.64/4.89 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[21670, 1126, 23405, 251, 24146, 104])).
% 4.64/4.89 tff(24148,plain,
% 4.64/4.89 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[20667, 24147])).
% 4.64/4.89 tff(24149,plain,
% 4.64/4.89 (~r(s(s(s(z))), z)),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[24075, 24148, 24146])).
% 4.64/4.89 tff(24150,plain,
% 4.64/4.89 (b(s(s(s(z))), z)),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[21073, 24149])).
% 4.64/4.89 tff(24151,plain,
% 4.64/4.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(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(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(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(z))), z)))),
% 4.64/4.89 inference(rewrite,[status(thm)],[])).
% 4.64/4.89 tff(24152,plain,
% 4.64/4.89 (((~b(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))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(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(z))), z)))),
% 4.64/4.89 inference(rewrite,[status(thm)],[])).
% 4.64/4.89 tff(24153,plain,
% 4.64/4.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(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(z))), z))))),
% 4.64/4.89 inference(monotonicity,[status(thm)],[24152])).
% 4.64/4.89 tff(24154,plain,
% 4.64/4.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(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(z))), z)))),
% 4.64/4.89 inference(transitivity,[status(thm)],[24153, 24151])).
% 4.64/4.89 tff(24155,plain,
% 4.64/4.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 4.64/4.89 inference(quant_inst,[status(thm)],[])).
% 4.64/4.89 tff(24156,plain,
% 4.64/4.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z))),
% 4.64/4.89 inference(modus_ponens,[status(thm)],[24155, 24154])).
% 4.64/4.89 tff(24157,plain,
% 4.64/4.89 ($false),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[24156, 178, 23405, 251, 595, 1126, 24150])).
% 4.64/4.89 tff(24158,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.89 tff(24159,plain,
% 4.64/4.89 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[24158, 21711, 24144, 104])).
% 4.64/4.89 tff(24160,plain,
% 4.64/4.89 (r(s(s(s(z))), s(s(s(s(z)))))),
% 4.64/4.89 inference(unit_resolution,[status(thm)],[10755, 24159])).
% 4.64/4.89 tff(24161,plain,
% 4.64/4.90 (~r(s(s(s(z))), s(s(z)))),
% 4.64/4.90 inference(unit_resolution,[status(thm)],[5071, 118, 147, 24160])).
% 4.64/4.90 tff(24162,plain,
% 4.64/4.90 (b(s(s(s(z))), s(s(z)))),
% 4.64/4.90 inference(unit_resolution,[status(thm)],[4966, 24161])).
% 4.64/4.90 tff(24163,plain,
% 4.64/4.90 ($false),
% 4.64/4.90 inference(unit_resolution,[status(thm)],[21581, 118, 194, 4891, 16062])).
% 4.64/4.90 tff(24164,plain,((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.64/4.90 tff(24165,plain,
% 4.64/4.90 (~r(s(s(s(z))), z)),
% 4.64/4.90 inference(unit_resolution,[status(thm)],[24164, 24160, 194])).
% 4.64/4.90 tff(24166,plain,
% 4.64/4.90 (b(s(s(s(z))), z)),
% 4.64/4.90 inference(unit_resolution,[status(thm)],[21073, 24165])).
% 4.64/4.90 tff(24167,plain,
% 4.64/4.90 (~r(s(s(z)), s(s(s(z))))),
% 4.64/4.90 inference(unit_resolution,[status(thm)],[5079, 118, 147, 24160])).
% 4.64/4.90 tff(24168,plain,
% 4.64/4.90 (b(s(s(z)), s(s(s(z))))),
% 4.64/4.90 inference(unit_resolution,[status(thm)],[5088, 24167])).
% 4.64/4.90 tff(24169,plain,
% 4.64/4.90 (~r(s(s(z)), z)),
% 4.64/4.90 inference(unit_resolution,[status(thm)],[21308, 147, 194])).
% 4.64/4.90 tff(24170,plain,
% 4.64/4.90 (b(s(s(z)), z)),
% 4.64/4.90 inference(unit_resolution,[status(thm)],[3249, 24169])).
% 4.64/4.90 tff(24171,plain,
% 4.64/4.90 (~b(z, s(s(s(z))))),
% 4.64/4.90 inference(unit_resolution,[status(thm)],[5098, 24162, 24170, 24166, 24168])).
% 4.64/4.90 tff(24172,plain,
% 4.64/4.90 (r(z, s(s(s(z))))),
% 4.64/4.90 inference(unit_resolution,[status(thm)],[4920, 24171])).
% 4.64/4.90 tff(24173,plain,
% 4.64/4.90 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 4.64/4.90 inference(unit_resolution,[status(thm)],[4961, 24172, 194])).
% 4.64/4.90 tff(24174,plain,
% 4.64/4.90 (b(s(s(s(s(z)))), s(s(s(z))))),
% 4.64/4.90 inference(unit_resolution,[status(thm)],[11185, 24173])).
% 4.64/4.90 tff(24175,plain,
% 4.64/4.90 (b(s(s(s(s(z)))), s(s(z)))),
% 4.64/4.90 inference(unit_resolution,[status(thm)],[24140, 104])).
% 4.64/4.90 tff(24176,plain,
% 4.64/4.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 4.64/4.90 inference(rewrite,[status(thm)],[])).
% 4.64/4.90 tff(24177,plain,
% 4.64/4.90 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(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(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 4.64/4.90 inference(rewrite,[status(thm)],[])).
% 4.64/4.90 tff(24178,plain,
% 4.64/4.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(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(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))))),
% 4.64/4.90 inference(monotonicity,[status(thm)],[24177])).
% 4.64/4.90 tff(24179,plain,
% 4.64/4.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(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(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 4.64/4.90 inference(transitivity,[status(thm)],[24178, 24176])).
% 4.74/4.90 tff(24180,plain,
% 4.74/4.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(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(s(s(z)))), s(s(s(z))))))),
% 4.74/4.90 inference(quant_inst,[status(thm)],[])).
% 4.74/4.90 tff(24181,plain,
% 4.74/4.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))),
% 4.74/4.90 inference(modus_ponens,[status(thm)],[24180, 24179])).
% 4.74/4.90 tff(24182,plain,
% 4.74/4.90 ($false),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[24181, 178, 24170, 24175, 24174, 24166, 24162])).
% 4.74/4.90 tff(24183,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.90 tff(24184,plain,
% 4.74/4.90 (~r(s(s(z)), s(s(s(s(z)))))),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[24183, 224, 104, 194])).
% 4.74/4.90 tff(24185,plain,
% 4.74/4.90 (b(s(s(z)), s(s(s(s(z)))))),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[164, 24184])).
% 4.74/4.90 tff(24186,plain,
% 4.74/4.90 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[12409, 5619, 23405, 24185, 146])).
% 4.74/4.90 tff(24187,plain,
% 4.74/4.90 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[3578, 24186])).
% 4.74/4.90 tff(24188,plain,
% 4.74/4.90 (b(elem!1, z)),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[11793, 461, 22560, 5618, 290])).
% 4.74/4.90 tff(24189,plain,
% 4.74/4.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(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(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(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(z)))))))),
% 4.74/4.90 inference(rewrite,[status(thm)],[])).
% 4.74/4.90 tff(24190,plain,
% 4.74/4.90 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(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(z)))))))),
% 4.74/4.90 inference(rewrite,[status(thm)],[])).
% 4.74/4.90 tff(24191,plain,
% 4.74/4.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(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(z))))))))),
% 4.74/4.90 inference(monotonicity,[status(thm)],[24190])).
% 4.74/4.90 tff(24192,plain,
% 4.74/4.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(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(z)))))))),
% 4.74/4.90 inference(transitivity,[status(thm)],[24191, 24189])).
% 4.74/4.90 tff(24193,plain,
% 4.74/4.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.74/4.90 inference(quant_inst,[status(thm)],[])).
% 4.74/4.90 tff(24194,plain,
% 4.74/4.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z))))))),
% 4.74/4.90 inference(modus_ponens,[status(thm)],[24193, 24192])).
% 4.74/4.90 tff(24195,plain,
% 4.74/4.90 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[24194, 178, 24188, 104, 23405, 146])).
% 4.74/4.90 tff(24196,plain,
% 4.74/4.90 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[3113, 450, 224])).
% 4.74/4.90 tff(24197,plain,
% 4.74/4.90 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[691, 24196, 4289])).
% 4.74/4.90 tff(24198,plain,
% 4.74/4.90 (~(s(elem!1) = s(s(z)))),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[2832, 24197])).
% 4.74/4.90 tff(24199,plain,
% 4.74/4.90 (~(s(s(z)) = s(elem!1))),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[1058, 24198])).
% 4.74/4.90 tff(24200,plain,
% 4.74/4.90 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[16181, 24197])).
% 4.74/4.90 tff(24201,plain,
% 4.74/4.90 (~r(s(elem!1), z)),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[14209, 24200, 3261, 1687, 194, 167, 24199])).
% 4.74/4.90 tff(24202,plain,
% 4.74/4.90 (b(s(elem!1), z)),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[774, 24201])).
% 4.74/4.90 tff(24203,assumption,(~b(s(s(s(s(s(s(s(s(z)))))))), z)), introduced(assumption)).
% 4.74/4.90 tff(24204,plain,
% 4.74/4.90 ($false),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[24203, 15440])).
% 4.74/4.90 tff(24205,plain,(b(s(s(s(s(s(s(s(s(z)))))))), z) | (~b(s(elem!1), z)) | (~(elem!1 = s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.90 tff(24206,plain,
% 4.74/4.90 (b(s(s(s(s(s(s(s(s(z)))))))), z)),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[24205, 24202, 24197])).
% 4.74/4.90 tff(24207,plain,
% 4.74/4.90 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 4.74/4.90 inference(monotonicity,[status(thm)],[24197])).
% 4.74/4.90 tff(24208,plain,
% 4.74/4.90 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 4.74/4.90 inference(monotonicity,[status(thm)],[24207])).
% 4.74/4.90 tff(24209,plain,
% 4.74/4.90 (b(z, elem!1)),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[585, 7203, 507])).
% 4.74/4.90 tff(24210,plain,
% 4.74/4.90 (~(s(s(s(s(z)))) = s(elem!1))),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[2168, 24200])).
% 4.74/4.90 tff(24211,plain,
% 4.74/4.90 (~(s(s(elem!1)) = elem!1)),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[2510, 24210, 24197])).
% 4.74/4.90 tff(24212,plain,
% 4.74/4.90 (~(s(elem!1) = elem!1)),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[672, 24211])).
% 4.74/4.90 tff(24213,plain,
% 4.74/4.90 (~r(s(elem!1), s(s(z)))),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[2550, 24212, 506, 450, 24202, 24209])).
% 4.74/4.90 tff(24214,plain,
% 4.74/4.90 (b(s(elem!1), s(s(z)))),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[421, 24213, 24198])).
% 4.74/4.90 tff(24215,plain,
% 4.74/4.90 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 4.74/4.90 inference(modus_ponens,[status(thm)],[24214, 24208])).
% 4.74/4.90 tff(24216,plain,
% 4.74/4.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)))),
% 4.74/4.90 inference(rewrite,[status(thm)],[])).
% 4.74/4.90 tff(24217,plain,
% 4.74/4.90 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)))),
% 4.74/4.90 inference(rewrite,[status(thm)],[])).
% 4.74/4.90 tff(24218,plain,
% 4.74/4.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), z)) | (~b(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z))))),
% 4.74/4.90 inference(monotonicity,[status(thm)],[24217])).
% 4.74/4.90 tff(24219,plain,
% 4.74/4.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), z)) | (~b(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)))),
% 4.74/4.90 inference(transitivity,[status(thm)],[24218, 24216])).
% 4.74/4.90 tff(24220,plain,
% 4.74/4.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))))),
% 4.74/4.90 inference(quant_inst,[status(thm)],[])).
% 4.74/4.90 tff(24221,plain,
% 4.74/4.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z))),
% 4.74/4.90 inference(modus_ponens,[status(thm)],[24220, 24219])).
% 4.74/4.90 tff(24222,plain,
% 4.74/4.90 ($false),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[24221, 178, 3461, 1687, 167, 24215, 24206])).
% 4.74/4.90 tff(24223,plain,((~r(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (z = elem!1) | b(elem!1, s(s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.90 tff(24224,plain,
% 4.74/4.90 (~r(elem!1, s(s(z)))),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[24223, 24188, 23405, 24185, 5619, 22560, 194, 318, 24195, 224])).
% 4.74/4.90 tff(24225,plain,
% 4.74/4.90 (elem!1 = s(s(z))),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[467, 24224, 461])).
% 4.74/4.90 tff(24226,plain,
% 4.74/4.90 (s(elem!1) = s(s(s(z)))),
% 4.74/4.90 inference(monotonicity,[status(thm)],[24225])).
% 4.74/4.90 tff(24227,plain,
% 4.74/4.90 (r(z, s(elem!1)) <=> r(z, s(s(s(z))))),
% 4.74/4.90 inference(monotonicity,[status(thm)],[24226])).
% 4.74/4.90 tff(24228,plain,
% 4.74/4.90 (r(z, s(s(s(z)))) <=> r(z, s(elem!1))),
% 4.74/4.90 inference(symmetry,[status(thm)],[24227])).
% 4.74/4.90 tff(24229,plain,
% 4.74/4.90 (~(s(s(s(s(z)))) = elem!1)),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[4509, 461, 24175])).
% 4.74/4.90 tff(24230,plain,
% 4.74/4.90 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[1353, 24225, 24229])).
% 4.74/4.90 tff(24231,plain,
% 4.74/4.90 ((s(elem!1) = s(s(z))) <=> (s(s(s(z))) = s(s(z)))),
% 4.74/4.90 inference(monotonicity,[status(thm)],[24226])).
% 4.74/4.90 tff(24232,plain,
% 4.74/4.90 ((s(elem!1) = s(s(z))) <=> (s(s(z)) = s(s(s(z))))),
% 4.74/4.90 inference(transitivity,[status(thm)],[24231, 3003])).
% 4.74/4.90 tff(24233,plain,
% 4.74/4.90 ((s(s(z)) = s(s(s(z)))) <=> (s(elem!1) = s(s(z)))),
% 4.74/4.90 inference(symmetry,[status(thm)],[24232])).
% 4.74/4.90 tff(24234,plain,
% 4.74/4.90 ((s(s(z)) = s(s(s(z)))) <=> (s(s(z)) = s(elem!1))),
% 4.74/4.90 inference(transitivity,[status(thm)],[24233, 1359])).
% 4.74/4.90 tff(24235,plain,
% 4.74/4.90 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(z)) = s(elem!1)))),
% 4.74/4.90 inference(monotonicity,[status(thm)],[24234])).
% 4.74/4.90 tff(24236,plain,
% 4.74/4.90 (~(s(s(z)) = s(elem!1))),
% 4.74/4.90 inference(modus_ponens,[status(thm)],[3205, 24235])).
% 4.74/4.90 tff(24237,plain,
% 4.74/4.90 (~r(s(elem!1), z)),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[14209, 24236, 22560, 23405, 194, 24185, 24230])).
% 4.74/4.90 tff(24238,plain,
% 4.74/4.90 (b(s(elem!1), z)),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[774, 24237])).
% 4.74/4.90 tff(24239,plain,
% 4.74/4.90 (b(s(s(s(z))), z)),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[7042, 24238, 24225])).
% 4.74/4.90 tff(24240,plain,
% 4.74/4.90 (~b(z, s(s(s(z))))),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[23367, 24239, 24187, 5619, 24144, 22560])).
% 4.74/4.90 tff(24241,plain,
% 4.74/4.90 (r(z, s(s(s(z))))),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[4920, 24240])).
% 4.74/4.90 tff(24242,plain,
% 4.74/4.90 (r(z, s(elem!1))),
% 4.74/4.90 inference(modus_ponens,[status(thm)],[24241, 24228])).
% 4.74/4.90 tff(24243,plain,
% 4.74/4.90 (s(s(z)) = elem!1),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[311, 24225])).
% 4.74/4.90 tff(24244,plain,
% 4.74/4.90 (~(s(s(s(s(z)))) = s(elem!1))),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[2168, 24230])).
% 4.74/4.90 tff(24245,plain,
% 4.74/4.90 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[5361, 24243])).
% 4.74/4.90 tff(24246,plain,
% 4.74/4.90 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[395, 391, 2286])).
% 4.74/4.90 tff(24247,plain,
% 4.74/4.90 (~r(s(elem!1), z)),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[8621, 363, 3261])).
% 4.74/4.90 tff(24248,plain,
% 4.74/4.90 (b(s(elem!1), z)),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[774, 24247])).
% 4.74/4.90 tff(24249,plain,
% 4.74/4.90 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[797, 178, 24248, 24246, 595, 146])).
% 4.74/4.90 tff(24250,plain,
% 4.74/4.90 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 4.74/4.90 inference(modus_ponens,[status(thm)],[2286, 2561])).
% 4.74/4.90 tff(24251,plain,
% 4.74/4.90 ($false),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[806, 41, 3912, 24250, 24249])).
% 4.74/4.90 tff(24252,plain,((~r(s(elem!1), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.90 tff(24253,plain,
% 4.74/4.90 (~r(s(elem!1), s(s(z)))),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[24252, 24245, 224, 146, 24144, 24187, 22560])).
% 4.74/4.90 tff(24254,plain,
% 4.74/4.90 (~r(s(elem!1), elem!1)),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[7028, 24253, 24225])).
% 4.74/4.90 tff(24255,plain,
% 4.74/4.90 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(z)))),
% 4.74/4.90 inference(monotonicity,[status(thm)],[24225])).
% 4.74/4.90 tff(24256,plain,
% 4.74/4.90 ((s(elem!1) = s(s(z))) <=> (s(elem!1) = elem!1)),
% 4.74/4.90 inference(symmetry,[status(thm)],[24255])).
% 4.74/4.90 tff(24257,plain,
% 4.74/4.90 ((s(s(z)) = s(s(s(z)))) <=> (s(elem!1) = elem!1)),
% 4.74/4.90 inference(transitivity,[status(thm)],[24233, 24256])).
% 4.74/4.90 tff(24258,plain,
% 4.74/4.90 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(elem!1) = elem!1))),
% 4.74/4.90 inference(monotonicity,[status(thm)],[24257])).
% 4.74/4.90 tff(24259,plain,
% 4.74/4.90 (~(s(elem!1) = elem!1)),
% 4.74/4.90 inference(modus_ponens,[status(thm)],[3205, 24258])).
% 4.74/4.90 tff(24260,plain,
% 4.74/4.90 (b(s(elem!1), elem!1)),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[677, 24259, 24254])).
% 4.74/4.90 tff(24261,plain,
% 4.74/4.90 (r(elem!1, s(elem!1))),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[10007, 24238, 24175, 5619, 24225, 24259, 24260, 24244, 194])).
% 4.74/4.90 tff(24262,plain,
% 4.74/4.90 (r(s(s(z)), s(elem!1))),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[13127, 24261, 24243])).
% 4.74/4.90 tff(24263,plain,
% 4.74/4.90 (~r(z, s(elem!1))),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[12114, 24262, 22560])).
% 4.74/4.90 tff(24264,plain,
% 4.74/4.90 ($false),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[24263, 24242])).
% 4.74/4.90 tff(24265,plain,(b(elem!1, s(s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | r(s(s(z)), z) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 4.74/4.90 tff(24266,plain,
% 4.74/4.90 (b(elem!1, s(s(z)))),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[24265, 290, 224, 146, 104, 5618, 194])).
% 4.74/4.90 tff(24267,plain,
% 4.74/4.90 (~(s(s(z)) = elem!1)),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[3223, 24266])).
% 4.74/4.90 tff(24268,plain,
% 4.74/4.90 (~(s(elem!1) = elem!1)),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[672, 339])).
% 4.74/4.90 tff(24269,plain,
% 4.74/4.90 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.74/4.90 inference(modus_ponens,[status(thm)],[24268, 16927])).
% 4.74/4.90 tff(24270,plain,
% 4.74/4.90 (~r(s(elem!1), z)),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[14209, 24269, 3261, 1687, 194, 167, 17020])).
% 4.74/4.90 tff(24271,plain,
% 4.74/4.90 (~r(s(s(s(s(s(z))))), z)),
% 4.74/4.90 inference(modus_ponens,[status(thm)],[24270, 2313])).
% 4.74/4.90 tff(24272,plain,
% 4.74/4.90 (b(s(s(s(s(s(z))))), z)),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[410, 41, 242, 24271])).
% 4.74/4.90 tff(24273,plain,
% 4.74/4.90 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[12409, 3461, 1687, 167, 146])).
% 4.74/4.90 tff(24274,plain,
% 4.74/4.90 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[3578, 24273])).
% 4.74/4.90 tff(24275,plain,
% 4.74/4.90 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.74/4.90 inference(modus_ponens,[status(thm)],[349, 16940])).
% 4.74/4.90 tff(24276,plain,
% 4.74/4.90 (~r(s(elem!1), s(s(z)))),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[24252, 24275, 224, 146, 14120, 24274, 3261])).
% 4.74/4.90 tff(24277,plain,
% 4.74/4.90 (b(s(elem!1), s(s(z)))),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[421, 24276, 11439])).
% 4.74/4.90 tff(24278,plain,
% 4.74/4.90 (b(s(s(s(s(s(z))))), s(s(z)))),
% 4.74/4.90 inference(modus_ponens,[status(thm)],[24277, 2747])).
% 4.74/4.90 tff(24279,plain,
% 4.74/4.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 4.74/4.90 inference(rewrite,[status(thm)],[])).
% 4.74/4.90 tff(24280,plain,
% 4.74/4.90 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 4.74/4.90 inference(rewrite,[status(thm)],[])).
% 4.74/4.90 tff(24281,plain,
% 4.74/4.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(z))))))))),
% 4.74/4.90 inference(monotonicity,[status(thm)],[24280])).
% 4.74/4.90 tff(24282,plain,
% 4.74/4.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 4.74/4.90 inference(transitivity,[status(thm)],[24281, 24279])).
% 4.74/4.90 tff(24283,plain,
% 4.74/4.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 4.74/4.90 inference(quant_inst,[status(thm)],[])).
% 4.74/4.90 tff(24284,plain,
% 4.74/4.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(z))))))),
% 4.74/4.90 inference(modus_ponens,[status(thm)],[24283, 24282])).
% 4.74/4.90 tff(24285,plain,
% 4.74/4.90 ($false),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[24284, 178, 3461, 1687, 167, 24278, 24272])).
% 4.74/4.90 tff(24286,plain,((~(elem!1 = s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.74/4.90 tff(24287,plain,
% 4.74/4.90 (~(elem!1 = s(s(s(s(z)))))),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[24286, 24267, 23405, 24185, 224, 146, 22560, 194, 5619])).
% 4.74/4.90 tff(24288,plain,
% 4.74/4.90 (~r(elem!1, s(s(s(s(z)))))),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[9980, 437, 194])).
% 4.74/4.90 tff(24289,plain,
% 4.74/4.90 (~(s(s(z)) = elem!1)),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[3223, 812])).
% 4.74/4.90 tff(24290,plain,
% 4.74/4.90 (~(elem!1 = s(s(z)))),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[311, 24289])).
% 4.74/4.90 tff(24291,plain,
% 4.74/4.90 (b(z, elem!1)),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[13524, 437, 3261, 1687, 194, 24290, 24289, 507])).
% 4.74/4.90 tff(24292,plain,
% 4.74/4.90 ((~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z))))))),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[11975, 178, 812, 1687, 202])).
% 4.74/4.90 tff(24293,plain,
% 4.74/4.90 (~b(elem!1, s(s(s(s(z)))))),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[24292, 24291])).
% 4.74/4.90 tff(24294,plain,
% 4.74/4.90 ($false),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[483, 24293, 24288, 469])).
% 4.74/4.90 tff(24295,plain,((~r(elem!1, z)) | (elem!1 = s(s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.74/4.90 tff(24296,plain,
% 4.74/4.90 (~r(elem!1, z)),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[24295, 24287, 24266, 23405, 24175, 194, 22560, 318])).
% 4.74/4.90 tff(24297,plain,
% 4.74/4.90 (b(elem!1, z)),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[498, 24296, 290])).
% 4.74/4.90 tff(24298,plain,
% 4.74/4.90 ($false),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[12506, 178, 24297, 5619, 24266, 23405, 24185])).
% 4.74/4.90 tff(24299,plain,((elem!1 = z) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 4.74/4.90 tff(24300,plain,
% 4.74/4.90 (elem!1 = z),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[24299, 5618, 224, 146, 104, 194])).
% 4.74/4.90 tff(24301,plain,
% 4.74/4.90 ($false),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[10452, 118, 3261, 1125, 4952])).
% 4.74/4.90 tff(24302,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.90 tff(24303,plain,
% 4.74/4.90 (~r(s(s(s(z))), s(s(z)))),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[24302, 4952, 3261])).
% 4.74/4.90 tff(24304,plain,
% 4.74/4.90 (b(s(s(s(z))), s(s(z)))),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[4966, 24303])).
% 4.74/4.90 tff(24305,plain,
% 4.74/4.90 (~r(s(s(z)), s(s(s(elem!1))))),
% 4.74/4.90 inference(unit_resolution,[status(thm)],[4808, 10732, 3261])).
% 4.74/4.90 tff(24306,plain,
% 4.74/4.91 (b(s(s(z)), s(s(s(elem!1))))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[4223, 24305])).
% 4.74/4.91 tff(24307,plain,
% 4.74/4.91 (b(s(s(z)), s(s(s(z))))),
% 4.74/4.91 inference(modus_ponens,[status(thm)],[24306, 5240])).
% 4.74/4.91 tff(24308,plain,
% 4.74/4.91 (b(s(s(s(s(z)))), s(s(s(z))))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[11185, 10443])).
% 4.74/4.91 tff(24309,plain,
% 4.74/4.91 ($false),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[22614, 178, 167, 202, 24308, 24307, 24304])).
% 4.74/4.91 tff(24310,plain,((~r(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~(elem!1 = z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.91 tff(24311,plain,
% 4.74/4.91 (~r(z, s(s(s(z))))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[24310, 24300, 24175, 24185, 22560, 194])).
% 4.74/4.91 tff(24312,plain,
% 4.74/4.91 (b(z, s(s(s(z))))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[4920, 24311])).
% 4.74/4.91 tff(24313,plain,
% 4.74/4.91 (~b(s(s(s(z))), z)),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[23367, 24312, 24187, 5619, 24144, 22560])).
% 4.74/4.91 tff(24314,plain,
% 4.74/4.91 (r(s(s(s(z))), z)),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[21073, 24313])).
% 4.74/4.91 tff(24315,plain,
% 4.74/4.91 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[20784, 24314, 194])).
% 4.74/4.91 tff(24316,plain,
% 4.74/4.91 (b(s(s(s(s(z)))), s(s(s(z))))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[11185, 24315])).
% 4.74/4.91 tff(24317,plain,
% 4.74/4.91 ($false),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[12696, 178, 1687, 202, 3008, 6170, 4932])).
% 4.74/4.91 tff(24318,plain,((~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.91 tff(24319,plain,
% 4.74/4.91 (~b(s(s(s(z))), s(s(z)))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[24318, 24316, 24175, 23405, 24312])).
% 4.74/4.91 tff(24320,plain,
% 4.74/4.91 (r(s(s(s(z))), s(s(z)))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[4966, 24319])).
% 4.74/4.91 tff(24321,plain,
% 4.74/4.91 ($false),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[6019, 118, 22560, 24320, 24314])).
% 4.74/4.91 tff(24322,plain,(r(s(s(z)), z) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.91 tff(24323,plain,
% 4.74/4.91 (r(s(s(z)), z)),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[24322, 146, 224, 194, 104])).
% 4.74/4.91 tff(24324,plain,
% 4.74/4.91 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[21479, 24323, 23405, 104, 224])).
% 4.74/4.91 tff(24325,plain,
% 4.74/4.91 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[222, 24324])).
% 4.74/4.91 tff(24326,plain,
% 4.74/4.91 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[22591, 24325, 24175, 24185, 24144, 104])).
% 4.74/4.91 tff(24327,plain,
% 4.74/4.91 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[20667, 24326])).
% 4.74/4.91 tff(24328,plain,
% 4.74/4.91 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[20784, 16062, 194])).
% 4.74/4.91 tff(24329,plain,
% 4.74/4.91 (b(s(s(s(s(z)))), s(s(s(z))))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[11185, 24328])).
% 4.74/4.91 tff(24330,plain,
% 4.74/4.91 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[24164, 16062, 194])).
% 4.74/4.91 tff(24331,plain,
% 4.74/4.91 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[10755, 24330])).
% 4.74/4.91 tff(24332,plain,
% 4.74/4.91 (~r(z, s(s(s(z))))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[10454, 24331, 22560, 24175, 194, 167])).
% 4.74/4.91 tff(24333,plain,
% 4.74/4.91 (b(z, s(s(s(z))))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[4920, 24332])).
% 4.74/4.91 tff(24334,plain,
% 4.74/4.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 4.74/4.91 inference(rewrite,[status(thm)],[])).
% 4.74/4.91 tff(24335,plain,
% 4.74/4.91 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z))) <=> ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 4.74/4.91 inference(rewrite,[status(thm)],[])).
% 4.74/4.91 tff(24336,plain,
% 4.74/4.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))))),
% 4.74/4.91 inference(monotonicity,[status(thm)],[24335])).
% 4.74/4.91 tff(24337,plain,
% 4.74/4.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 4.74/4.91 inference(transitivity,[status(thm)],[24336, 24334])).
% 4.74/4.91 tff(24338,plain,
% 4.74/4.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 4.74/4.91 inference(quant_inst,[status(thm)],[])).
% 4.74/4.91 tff(24339,plain,
% 4.74/4.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))),
% 4.74/4.91 inference(modus_ponens,[status(thm)],[24338, 24337])).
% 4.74/4.91 tff(24340,plain,
% 4.74/4.91 ($false),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[24339, 178, 104, 23405, 146, 24333, 24329])).
% 4.74/4.91 tff(24341,plain,((~r(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.91 tff(24342,plain,
% 4.74/4.91 (~r(s(s(s(z))), z)),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[24341, 146, 104, 194, 24185])).
% 4.74/4.91 tff(24343,plain,
% 4.74/4.91 (b(s(s(s(z))), z)),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[21073, 24342])).
% 4.74/4.91 tff(24344,plain,
% 4.74/4.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)))),
% 4.74/4.91 inference(rewrite,[status(thm)],[])).
% 4.74/4.91 tff(24345,plain,
% 4.74/4.91 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)))),
% 4.74/4.91 inference(rewrite,[status(thm)],[])).
% 4.74/4.91 tff(24346,plain,
% 4.74/4.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z))))),
% 4.74/4.91 inference(monotonicity,[status(thm)],[24345])).
% 4.74/4.91 tff(24347,plain,
% 4.74/4.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)))),
% 4.74/4.91 inference(transitivity,[status(thm)],[24346, 24344])).
% 4.74/4.91 tff(24348,plain,
% 4.74/4.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.74/4.91 inference(quant_inst,[status(thm)],[])).
% 4.74/4.91 tff(24349,plain,
% 4.74/4.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z))),
% 4.74/4.91 inference(modus_ponens,[status(thm)],[24348, 24347])).
% 4.74/4.91 tff(24350,plain,
% 4.74/4.91 ($false),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[24349, 178, 104, 23405, 146, 24343, 24327])).
% 4.74/4.91 tff(24351,plain,((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.91 tff(24352,plain,
% 4.74/4.91 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[24351, 224, 194, 104])).
% 4.74/4.91 tff(24353,plain,
% 4.74/4.91 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[133, 24352])).
% 4.74/4.91 tff(24354,plain,
% 4.74/4.91 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[23376, 24353, 194])).
% 4.74/4.91 tff(24355,plain,
% 4.74/4.91 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[222, 24354])).
% 4.74/4.91 tff(24356,plain,
% 4.74/4.91 (~r(s(s(z)), z)),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[3102, 24353, 224])).
% 4.74/4.91 tff(24357,plain,
% 4.74/4.91 (b(s(s(z)), z)),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[3249, 24356])).
% 4.74/4.91 tff(24358,plain,
% 4.74/4.91 ($false),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[14395, 178, 24357, 23405, 24185, 24355, 24144])).
% 4.74/4.91 tff(24359,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.91 tff(24360,plain,
% 4.74/4.91 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[24359, 3244, 85])).
% 4.74/4.91 tff(24361,plain,
% 4.74/4.91 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[249, 24360])).
% 4.74/4.91 tff(24362,plain,
% 4.74/4.91 (b(z, s(s(s(s(z)))))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[23404, 85])).
% 4.74/4.91 tff(24363,plain,
% 4.74/4.91 (~r(s(s(z)), z)),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[21308, 10794, 3244])).
% 4.74/4.91 tff(24364,plain,
% 4.74/4.91 (b(s(s(z)), z)),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[3249, 24363])).
% 4.74/4.91 tff(24365,plain,
% 4.74/4.91 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[11879, 178, 24364, 85, 24362, 24361])).
% 4.74/4.91 tff(24366,plain,
% 4.74/4.91 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[133, 24365])).
% 4.74/4.91 tff(24367,plain,
% 4.74/4.91 ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[12281, 178, 85, 24362, 24361])).
% 4.74/4.91 tff(24368,plain,
% 4.74/4.91 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[24367, 24364])).
% 4.74/4.91 tff(24369,plain,
% 4.74/4.91 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[271, 24368])).
% 4.74/4.91 tff(24370,plain,
% 4.74/4.91 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[23376, 24366, 3244])).
% 4.74/4.91 tff(24371,plain,
% 4.74/4.91 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[222, 24370])).
% 4.74/4.91 tff(24372,plain,
% 4.74/4.91 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.91 inference(monotonicity,[status(thm)],[3506])).
% 4.74/4.91 tff(24373,plain,
% 4.74/4.91 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.91 inference(modus_ponens,[status(thm)],[251, 24372])).
% 4.74/4.91 tff(24374,plain,
% 4.74/4.91 (r(z, elem!1)),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[7053, 1324, 22560])).
% 4.74/4.91 tff(24375,plain,
% 4.74/4.91 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[11027, 24374, 108])).
% 4.74/4.91 tff(24376,plain,
% 4.74/4.91 (~b(elem!1, s(s(s(s(z)))))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[17698, 1324, 105])).
% 4.74/4.91 tff(24377,plain,
% 4.74/4.91 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[18185, 24376, 104])).
% 4.74/4.91 tff(24378,plain,
% 4.74/4.91 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[703, 24377])).
% 4.74/4.91 tff(24379,plain,
% 4.74/4.91 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[3444, 24378, 24375])).
% 4.74/4.91 tff(24380,plain,
% 4.74/4.91 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[3818, 24374, 203])).
% 4.74/4.91 tff(24381,plain,
% 4.74/4.91 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[691, 24377, 24380])).
% 4.74/4.91 tff(24382,plain,
% 4.74/4.91 (b(s(s(s(s(z)))), elem!1)),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[8526, 1324, 24175])).
% 4.74/4.91 tff(24383,plain,
% 4.74/4.91 (b(s(s(elem!1)), elem!1)),
% 4.74/4.91 inference(modus_ponens,[status(thm)],[24382, 8522])).
% 4.74/4.91 tff(24384,plain,
% 4.74/4.91 ($false),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[9399, 178, 24383, 24381, 24379, 8176, 24373])).
% 4.74/4.91 tff(24385,plain,((~(s(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)))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | b(s(s(z)), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.91 tff(24386,plain,
% 4.74/4.91 (~(s(s(z)) = elem!1)),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[24385, 24371, 85, 24369, 24366, 105])).
% 4.74/4.91 tff(24387,plain,
% 4.74/4.91 (~r(s(s(z)), z)),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[21308, 147, 3244])).
% 4.74/4.91 tff(24388,plain,
% 4.74/4.91 (b(s(s(z)), z)),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[3249, 24387])).
% 4.74/4.91 tff(24389,plain,
% 4.74/4.91 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[11879, 178, 24388, 85, 24362, 24361])).
% 4.74/4.91 tff(24390,plain,
% 4.74/4.91 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[24367, 24388])).
% 4.74/4.91 tff(24391,plain,
% 4.74/4.91 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[271, 24390])).
% 4.74/4.91 tff(24392,plain,
% 4.74/4.91 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[133, 125])).
% 4.74/4.91 tff(24393,plain,
% 4.74/4.91 (b(elem!1, z)),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[11793, 461, 3261, 5618, 290])).
% 4.74/4.91 tff(24394,plain,
% 4.74/4.91 (~r(s(s(z)), elem!1)),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[12239, 24393, 3261, 1687, 147, 13054, 318, 13055])).
% 4.74/4.91 tff(24395,plain,
% 4.74/4.91 (b(s(s(z)), elem!1)),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[448, 24394, 12])).
% 4.74/4.91 tff(24396,plain,
% 4.74/4.91 ($false),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[12263, 14552, 24395, 1687, 5619, 24393, 13055, 147, 312])).
% 4.74/4.91 tff(24397,plain,(b(elem!1, s(s(z))) | (~b(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (s(s(z)) = elem!1) | (~r(z, s(s(z)))) | r(s(s(z)), z) | (elem!1 = z) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.91 tff(24398,plain,
% 4.74/4.91 (b(elem!1, s(s(z)))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[24397, 12, 147, 1687, 3261, 24169, 290, 202])).
% 4.74/4.91 tff(24399,plain,
% 4.74/4.91 (~r(elem!1, z)),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[24295, 469, 24398, 1687, 202, 194, 3261, 318])).
% 4.74/4.91 tff(24400,plain,
% 4.74/4.91 (b(elem!1, z)),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[498, 24399, 290])).
% 4.74/4.91 tff(24401,plain,
% 4.74/4.91 (b(z, elem!1)),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[585, 12234, 318])).
% 4.74/4.91 tff(24402,plain,
% 4.74/4.91 (~b(elem!1, s(s(z)))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[11977, 469, 3261, 1687, 147, 438, 551, 24401])).
% 4.74/4.91 tff(24403,plain,
% 4.74/4.91 (~b(elem!1, z)),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[12239, 551, 3261, 1687, 147, 438, 318, 469])).
% 4.74/4.91 tff(24404,plain,
% 4.74/4.91 ($false),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[11793, 24403, 24402, 3261, 5618, 290])).
% 4.74/4.91 tff(24405,plain,((elem!1 = s(s(s(s(z))))) | (~r(z, s(s(z)))) | r(s(s(z)), z) | (elem!1 = z) | (~b(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.91 tff(24406,plain,
% 4.74/4.91 (~r(s(s(z)), elem!1)),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[24405, 469, 24169, 147, 1687, 290, 3261])).
% 4.74/4.91 tff(24407,plain,
% 4.74/4.91 (b(s(s(z)), elem!1)),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[448, 24406, 12])).
% 4.74/4.91 tff(24408,plain,
% 4.74/4.91 (~b(z, elem!1)),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[12263, 24407, 1687, 24170, 24400, 469, 147, 312])).
% 4.74/4.91 tff(24409,plain,
% 4.74/4.91 (r(z, elem!1)),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[585, 24408, 318])).
% 4.74/4.91 tff(24410,plain,
% 4.74/4.91 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[11027, 24409, 24392])).
% 4.74/4.91 tff(24411,plain,
% 4.74/4.91 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[3818, 24409, 203])).
% 4.74/4.91 tff(24412,plain,
% 4.74/4.91 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[14184, 24411, 166, 23847, 24398, 24410])).
% 4.74/4.91 tff(24413,plain,
% 4.74/4.91 (b(elem!1, z) <=> b(s(s(s(s(s(s(s(z))))))), z)),
% 4.74/4.91 inference(monotonicity,[status(thm)],[24412])).
% 4.74/4.91 tff(24414,plain,
% 4.74/4.91 (b(s(s(s(s(s(s(s(z))))))), z) <=> b(elem!1, z)),
% 4.74/4.91 inference(symmetry,[status(thm)],[24413])).
% 4.74/4.91 tff(24415,plain,
% 4.74/4.91 ((~b(s(s(s(s(s(s(s(z))))))), z)) <=> (~b(elem!1, z))),
% 4.74/4.91 inference(monotonicity,[status(thm)],[24414])).
% 4.74/4.91 tff(24416,plain,
% 4.74/4.91 (~b(elem!1, z)),
% 4.74/4.91 inference(modus_ponens,[status(thm)],[125, 24415])).
% 4.74/4.91 tff(24417,plain,
% 4.74/4.91 ($false),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[24400, 24416])).
% 4.74/4.91 tff(24418,plain,((elem!1 = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(z))))))), z) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (elem!1 = z) | (s(s(z)) = elem!1) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.91 tff(24419,plain,
% 4.74/4.91 (elem!1 = s(s(s(s(z))))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[24418, 12, 24361, 24391, 24362, 147, 290, 24389, 24141, 3244, 24142])).
% 4.74/4.91 tff(24420,plain,
% 4.74/4.91 (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)))))),
% 4.74/4.91 inference(monotonicity,[status(thm)],[24419])).
% 4.74/4.91 tff(24421,plain,
% 4.74/4.91 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.74/4.91 inference(symmetry,[status(thm)],[24420])).
% 4.74/4.91 tff(24422,plain,
% 4.74/4.91 ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) <=> (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 4.74/4.91 inference(monotonicity,[status(thm)],[24421])).
% 4.74/4.91 tff(24423,plain,
% 4.74/4.91 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.74/4.91 inference(modus_ponens,[status(thm)],[49, 24422])).
% 4.74/4.91 tff(24424,plain,
% 4.74/4.91 (~b(elem!1, z)),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[3172, 24419, 3170])).
% 4.74/4.91 tff(24425,plain,
% 4.74/4.91 (r(elem!1, z)),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[498, 24424, 290])).
% 4.74/4.91 tff(24426,plain,
% 4.74/4.91 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[10809, 24425, 24391])).
% 4.74/4.91 tff(24427,plain,
% 4.74/4.91 (b(elem!1, s(s(z)))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[24397, 12, 147, 24362, 24142, 24387, 290, 24141])).
% 4.74/4.91 tff(24428,plain,
% 4.74/4.91 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[23450, 24391, 24142])).
% 4.74/4.91 tff(24429,plain,
% 4.74/4.91 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[3578, 24428])).
% 4.74/4.91 tff(24430,plain,
% 4.74/4.91 (b(z, elem!1)),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[13524, 24425, 24142, 24362, 3244, 312, 12, 318])).
% 4.74/4.91 tff(24431,plain,
% 4.74/4.91 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[4243, 24430, 24390])).
% 4.74/4.91 tff(24432,plain,
% 4.74/4.91 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[14184, 24431, 24361, 24429, 24427, 24426])).
% 4.74/4.91 tff(24433,plain,
% 4.74/4.91 ($false),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[24432, 24423])).
% 4.74/4.91 tff(24434,plain,((s(s(z)) = elem!1) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | (elem!1 = z) | b(s(s(s(s(z)))), z) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.91 tff(24435,plain,
% 4.74/4.91 (elem!1 = z),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[24434, 24386, 49, 3170, 10794])).
% 4.74/4.91 tff(24436,plain,
% 4.74/4.91 (s(elem!1) = s(z)),
% 4.74/4.91 inference(monotonicity,[status(thm)],[24435])).
% 4.74/4.91 tff(24437,plain,
% 4.74/4.91 (s(s(elem!1)) = s(s(z))),
% 4.74/4.91 inference(monotonicity,[status(thm)],[24436])).
% 4.74/4.91 tff(24438,plain,
% 4.74/4.91 (s(s(s(elem!1))) = s(s(s(z)))),
% 4.74/4.91 inference(monotonicity,[status(thm)],[24437])).
% 4.74/4.91 tff(24439,plain,
% 4.74/4.91 ((s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(z))))),
% 4.74/4.91 inference(monotonicity,[status(thm)],[24438])).
% 4.74/4.91 tff(24440,plain,
% 4.74/4.91 ((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))))),
% 4.74/4.91 inference(symmetry,[status(thm)],[24439])).
% 4.74/4.91 tff(24441,plain,
% 4.74/4.91 ((~(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)))))),
% 4.74/4.91 inference(monotonicity,[status(thm)],[24440])).
% 4.74/4.91 tff(24442,plain,
% 4.74/4.91 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 4.74/4.91 inference(modus_ponens,[status(thm)],[1104, 24441])).
% 4.74/4.91 tff(24443,plain,
% 4.74/4.91 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[23450, 24369, 24142])).
% 4.74/4.91 tff(24444,plain,
% 4.74/4.91 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.74/4.91 inference(unit_resolution,[status(thm)],[3578, 24443])).
% 4.74/4.91 tff(24445,plain,
% 4.74/4.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 4.74/4.91 inference(rewrite,[status(thm)],[])).
% 4.74/4.91 tff(24446,plain,
% 4.74/4.91 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(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(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(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(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 4.74/4.92 inference(rewrite,[status(thm)],[])).
% 4.74/4.92 tff(24447,plain,
% 4.74/4.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))))),
% 4.74/4.92 inference(monotonicity,[status(thm)],[24446])).
% 4.74/4.92 tff(24448,plain,
% 4.74/4.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 4.74/4.92 inference(transitivity,[status(thm)],[24447, 24445])).
% 4.74/4.92 tff(24449,plain,
% 4.74/4.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 4.74/4.92 inference(quant_inst,[status(thm)],[])).
% 4.74/4.92 tff(24450,plain,
% 4.74/4.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))),
% 4.74/4.92 inference(modus_ponens,[status(thm)],[24449, 24448])).
% 4.74/4.92 tff(24451,plain,
% 4.74/4.92 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[24450, 178, 104, 1687, 202, 1146])).
% 4.74/4.92 tff(24452,plain,
% 4.74/4.92 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[271, 24451])).
% 4.74/4.92 tff(24453,plain,
% 4.74/4.92 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[20977, 24452, 16062])).
% 4.74/4.92 tff(24454,plain,
% 4.74/4.92 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[20667, 24453])).
% 4.74/4.92 tff(24455,plain,
% 4.74/4.92 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[21536, 24454, 1146, 166, 147])).
% 4.74/4.92 tff(24456,plain,
% 4.74/4.92 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[10755, 24455])).
% 4.74/4.92 tff(24457,plain,
% 4.74/4.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.74/4.92 inference(rewrite,[status(thm)],[])).
% 4.74/4.92 tff(24458,plain,
% 4.74/4.92 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(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(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(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(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.74/4.92 inference(rewrite,[status(thm)],[])).
% 4.74/4.92 tff(24459,plain,
% 4.74/4.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 4.74/4.92 inference(monotonicity,[status(thm)],[24458])).
% 4.74/4.92 tff(24460,plain,
% 4.74/4.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.74/4.92 inference(transitivity,[status(thm)],[24459, 24457])).
% 4.74/4.92 tff(24461,plain,
% 4.74/4.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.74/4.92 inference(quant_inst,[status(thm)],[])).
% 4.74/4.92 tff(24462,plain,
% 4.74/4.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 4.74/4.92 inference(modus_ponens,[status(thm)],[24461, 24460])).
% 4.74/4.92 tff(24463,plain,
% 4.74/4.92 ($false),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[24462, 178, 104, 202, 24456, 1146, 24454])).
% 4.74/4.92 tff(24464,plain,((~b(s(s(s(s(z)))), 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(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.92 tff(24465,plain,
% 4.74/4.92 (~r(s(s(s(z))), z)),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[24464, 24444, 24141, 24361, 85, 10794, 24362])).
% 4.74/4.92 tff(24466,plain,
% 4.74/4.92 (b(s(s(s(z))), z)),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[21073, 24465])).
% 4.74/4.92 tff(24467,plain,
% 4.74/4.92 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 4.74/4.92 inference(symmetry,[status(thm)],[1690])).
% 4.74/4.92 tff(24468,plain,
% 4.74/4.92 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 4.74/4.92 inference(transitivity,[status(thm)],[15340, 24467])).
% 4.74/4.92 tff(24469,plain,
% 4.74/4.92 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))),
% 4.74/4.92 inference(monotonicity,[status(thm)],[24468])).
% 4.74/4.92 tff(24470,plain,
% 4.74/4.92 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 4.74/4.92 inference(modus_ponens,[status(thm)],[4938, 24469])).
% 4.74/4.92 tff(24471,plain,
% 4.74/4.92 (b(s(s(s(elem!1))), z)),
% 4.74/4.92 inference(modus_ponens,[status(thm)],[1127, 22640])).
% 4.74/4.92 tff(24472,plain,
% 4.74/4.92 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[12809, 2043, 3461, 12068, 24471])).
% 4.74/4.92 tff(24473,plain,
% 4.74/4.92 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[1750, 24472, 24470])).
% 4.74/4.92 tff(24474,plain,
% 4.74/4.92 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.74/4.92 inference(modus_ponens,[status(thm)],[24473, 5215])).
% 4.74/4.92 tff(24475,plain,
% 4.74/4.92 (~b(s(s(z)), s(s(s(z))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[7229, 178, 3461, 1687, 24474, 1127])).
% 4.74/4.92 tff(24476,plain,
% 4.74/4.92 (r(s(s(z)), s(s(s(z))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[5088, 24475])).
% 4.74/4.92 tff(24477,plain,
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% 4.74/4.92 inference(unit_resolution,[status(thm)],[7239, 118, 147, 4953, 7670])).
% 4.74/4.92 tff(24478,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.92 tff(24479,plain,
% 4.74/4.92 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[24478, 24476, 147])).
% 4.74/4.92 tff(24480,plain,
% 4.74/4.92 (b(s(s(s(s(z)))), s(s(s(z))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[11185, 24479])).
% 4.74/4.92 tff(24481,plain,
% 4.74/4.92 ($false),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[22536, 178, 1687, 24474, 20787, 24480, 1127])).
% 4.74/4.92 tff(24482,plain,((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.92 tff(24483,plain,
% 4.74/4.92 (~b(z, s(s(s(elem!1))))),
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% 4.74/4.92 tff(24484,plain,
% 4.74/4.92 (r(z, s(s(s(elem!1))))),
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% 4.74/4.92 tff(24485,plain,
% 4.74/4.92 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
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% 4.74/4.92 tff(24486,plain,
% 4.74/4.92 (b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[5118, 24485, 24442])).
% 4.74/4.92 tff(24487,plain,
% 4.74/4.92 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.74/4.92 inference(monotonicity,[status(thm)],[24437])).
% 4.74/4.92 tff(24488,plain,
% 4.74/4.92 (b(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.74/4.92 inference(symmetry,[status(thm)],[24487])).
% 4.74/4.92 tff(24489,plain,
% 4.74/4.92 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.74/4.92 inference(modus_ponens,[status(thm)],[24444, 24488])).
% 4.74/4.92 tff(24490,plain,
% 4.74/4.92 (b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.92 inference(monotonicity,[status(thm)],[24437])).
% 4.74/4.92 tff(24491,plain,
% 4.74/4.92 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.92 inference(symmetry,[status(thm)],[24490])).
% 4.74/4.92 tff(24492,plain,
% 4.74/4.92 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.92 inference(modus_ponens,[status(thm)],[24361, 24491])).
% 4.74/4.92 tff(24493,plain,
% 4.74/4.92 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(s(elem!1))))),
% 4.74/4.92 inference(monotonicity,[status(thm)],[24437])).
% 4.74/4.92 tff(24494,plain,
% 4.74/4.92 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
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% 4.74/4.92 tff(24495,plain,
% 4.74/4.92 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
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% 4.74/4.92 tff(24496,plain,
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% 4.74/4.92 tff(24497,plain,
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% 4.74/4.92 tff(24498,plain,
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% 4.74/4.92 tff(24499,plain,
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% 4.74/4.92 tff(24500,plain,
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% 4.74/4.92 tff(24501,plain,
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% 4.74/4.92 inference(unit_resolution,[status(thm)],[5235, 24484, 24500])).
% 4.74/4.92 tff(24502,plain,
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% 4.74/4.92 tff(24503,plain,
% 4.74/4.92 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 4.74/4.92 inference(monotonicity,[status(thm)],[24494])).
% 4.74/4.92 tff(24504,plain,
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% 4.74/4.92 tff(24505,plain,
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% 4.74/4.92 tff(24506,plain,
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% 4.74/4.92 tff(24507,plain,
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% 4.74/4.92 tff(24508,plain,
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% 4.74/4.92 inference(modus_ponens,[status(thm)],[24142, 24507])).
% 4.74/4.92 tff(24509,plain,
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% 4.74/4.92 inference(unit_resolution,[status(thm)],[4850, 24484, 24435])).
% 4.74/4.92 tff(24510,plain,
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% 4.74/4.92 inference(unit_resolution,[status(thm)],[5845, 24509, 24508])).
% 4.74/4.92 tff(24511,plain,
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% 4.74/4.92 tff(24513,plain,(b(s(s(z)), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 4.74/4.92 tff(24514,plain,
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% 4.74/4.92 tff(24518,plain,
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% 4.74/4.92 tff(24519,plain,
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% 4.74/4.92 inference(unit_resolution,[status(thm)],[24367, 24518])).
% 4.74/4.92 tff(24520,plain,
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% 4.74/4.92 inference(unit_resolution,[status(thm)],[3249, 24519])).
% 4.74/4.92 tff(24521,plain,
% 4.74/4.92 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
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% 4.74/4.92 tff(24522,plain,
% 4.74/4.92 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[222, 24521])).
% 4.74/4.92 tff(24523,plain,
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% 4.74/4.92 inference(unit_resolution,[status(thm)],[23376, 24522, 3244])).
% 4.74/4.92 tff(24524,plain,
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% 4.74/4.92 inference(unit_resolution,[status(thm)],[133, 24523])).
% 4.74/4.92 tff(24525,plain,
% 4.74/4.92 (~r(s(s(s(z))), z)),
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% 4.74/4.92 tff(24526,plain,
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% 4.74/4.92 inference(unit_resolution,[status(thm)],[21073, 24525])).
% 4.74/4.92 tff(24527,plain,
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% 4.74/4.92 inference(unit_resolution,[status(thm)],[20667, 24527])).
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% 4.74/4.92 tff(24530,plain,(b(s(s(s(s(z)))), z) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.92 tff(24531,plain,
% 4.74/4.92 (b(s(s(s(s(z)))), z)),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[24530, 49])).
% 4.74/4.92 tff(24532,plain,
% 4.74/4.92 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[13684, 147, 22560, 168])).
% 4.74/4.92 tff(24533,plain,
% 4.74/4.92 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[249, 24532])).
% 4.74/4.92 tff(24534,plain,
% 4.74/4.92 (~r(s(s(s(z))), z)),
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% 4.74/4.92 tff(24535,plain,
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% 4.74/4.92 inference(unit_resolution,[status(thm)],[21073, 24534])).
% 4.74/4.92 tff(24536,plain,
% 4.74/4.92 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[21425, 3002, 104, 23405, 168, 147, 24533, 24535])).
% 4.74/4.92 tff(24537,plain,
% 4.74/4.92 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[21536, 3002, 24533, 147, 1146])).
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% 4.74/4.92 inference(unit_resolution,[status(thm)],[10755, 24537, 24536])).
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% 4.74/4.92 tff(24540,plain,
% 4.74/4.92 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[24539, 1146, 147, 104, 168])).
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% 4.74/4.92 inference(unit_resolution,[status(thm)],[20667, 24540])).
% 4.74/4.92 tff(24542,plain,
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% 4.74/4.92 inference(unit_resolution,[status(thm)],[21413, 24541, 23405, 24535, 168])).
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% 4.74/4.92 inference(unit_resolution,[status(thm)],[222, 24542])).
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% 4.74/4.92 tff(24545,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.92 tff(24546,plain,
% 4.74/4.92 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[24545, 147, 168, 104])).
% 4.74/4.92 tff(24547,plain,
% 4.74/4.92 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[3578, 24546])).
% 4.74/4.92 tff(24548,plain,
% 4.74/4.92 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[23450, 24547, 22560])).
% 4.74/4.92 tff(24549,plain,
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% 4.74/4.92 inference(unit_resolution,[status(thm)],[271, 24548])).
% 4.74/4.92 tff(24550,plain,
% 4.74/4.92 ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[12281, 178, 104, 23405, 24533])).
% 4.74/4.92 tff(24551,plain,
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% 4.74/4.92 inference(unit_resolution,[status(thm)],[24550, 3461])).
% 4.74/4.92 tff(24552,plain,
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% 4.74/4.92 inference(unit_resolution,[status(thm)],[271, 24551])).
% 4.74/4.92 tff(24553,plain,
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% 4.74/4.92 inference(unit_resolution,[status(thm)],[23450, 24552, 22560])).
% 4.74/4.92 tff(24554,plain,
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% 4.74/4.92 inference(unit_resolution,[status(thm)],[3578, 24553])).
% 4.74/4.92 tff(24555,plain,
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% 4.74/4.92 inference(unit_resolution,[status(thm)],[24539, 24554, 147, 104, 168])).
% 4.74/4.92 tff(24556,plain,
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% 4.74/4.92 inference(unit_resolution,[status(thm)],[20667, 24555])).
% 4.74/4.92 tff(24557,plain,
% 4.74/4.92 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[21520, 24556, 168, 24552, 23405])).
% 4.74/4.92 tff(24558,plain,
% 4.74/4.92 (r(s(s(s(z))), s(s(s(s(z)))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[10755, 24557])).
% 4.74/4.92 tff(24559,plain,
% 4.74/4.92 (~r(s(s(s(z))), s(s(z)))),
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% 4.74/4.92 tff(24560,plain,
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% 4.74/4.92 tff(24561,plain,
% 4.74/4.92 (~r(s(s(s(z))), z)),
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% 4.74/4.92 tff(24562,plain,
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% 4.74/4.92 tff(24563,plain,
% 4.74/4.92 (~r(s(s(z)), s(s(s(z))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[5079, 118, 147, 24558])).
% 4.74/4.92 tff(24564,plain,
% 4.74/4.92 (b(s(s(z)), s(s(s(z))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[5088, 24563])).
% 4.74/4.92 tff(24565,plain,
% 4.74/4.92 (~b(z, s(s(s(z))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[5098, 24564, 3461, 24562, 24560])).
% 4.74/4.92 tff(24566,plain,
% 4.74/4.92 (r(z, s(s(s(z))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[4920, 24565])).
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% 4.74/4.92 tff(24569,plain,
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% 4.74/4.92 inference(unit_resolution,[status(thm)],[24568, 147, 168, 104])).
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% 4.74/4.92 inference(unit_resolution,[status(thm)],[3249, 24569])).
% 4.74/4.92 tff(24571,plain,
% 4.74/4.92 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[123, 24547, 24570])).
% 4.74/4.92 tff(24572,plain,
% 4.74/4.92 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[133, 24571])).
% 4.74/4.92 tff(24573,plain,
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% 4.74/4.92 inference(unit_resolution,[status(thm)],[24071, 24572, 24549, 168, 104])).
% 4.74/4.92 tff(24574,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.92 tff(24575,plain,
% 4.74/4.92 (~r(s(s(z)), s(s(s(s(z)))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[24574, 24531, 85])).
% 4.74/4.92 tff(24576,plain,
% 4.74/4.92 (b(s(s(z)), s(s(s(s(z)))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[164, 24575])).
% 4.74/4.92 tff(24577,plain,
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% 4.74/4.92 tff(24578,plain,
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% 4.74/4.92 inference(unit_resolution,[status(thm)],[3249, 24577])).
% 4.74/4.92 tff(24579,plain,
% 4.74/4.92 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[4690, 203, 22560])).
% 4.74/4.92 tff(24580,plain,
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% 4.74/4.92 inference(unit_resolution,[status(thm)],[249, 24579])).
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% 4.74/4.92 tff(24582,plain,((~r(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(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.92 tff(24583,plain,
% 4.74/4.92 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[24582, 85, 24576])).
% 4.74/4.92 tff(24584,plain,
% 4.74/4.92 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[271, 24583])).
% 4.74/4.92 tff(24585,plain,
% 4.74/4.92 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[24071, 24584, 24531, 85])).
% 4.74/4.92 tff(24586,plain,
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% 4.74/4.92 tff(24587,plain,
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% 4.74/4.92 inference(unit_resolution,[status(thm)],[3102, 24586, 24578])).
% 4.74/4.92 tff(24588,plain,
% 4.74/4.92 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[249, 24587])).
% 4.74/4.92 tff(24589,plain,
% 4.74/4.92 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[123, 24586, 24578])).
% 4.74/4.92 tff(24590,plain,
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% 4.74/4.92 inference(unit_resolution,[status(thm)],[3578, 24589])).
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% 4.74/4.92 tff(24592,plain,(r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.92 tff(24593,plain,
% 4.74/4.92 ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[1138, 24592])).
% 4.74/4.92 tff(24594,plain,
% 4.74/4.92 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[24593, 47])).
% 4.74/4.92 tff(24595,plain,
% 4.74/4.92 ((~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~r(z, s(s(s(s(z))))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[8677, 24592])).
% 4.74/4.92 tff(24596,plain,
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% 4.74/4.92 tff(24599,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.92 tff(24600,plain,
% 4.74/4.92 (~r(s(s(s(z))), s(s(z)))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[24599, 16062, 106])).
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% 4.74/4.92 tff(24602,plain,
% 4.74/4.92 ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))),
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% 4.74/4.92 tff(24603,plain,
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% 4.74/4.92 inference(unit_resolution,[status(thm)],[24602, 145])).
% 4.74/4.92 tff(24604,plain,
% 4.74/4.92 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[10755, 24603])).
% 4.74/4.92 tff(24605,plain,
% 4.74/4.92 ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[9102, 24592])).
% 4.74/4.92 tff(24606,plain,
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% 4.74/4.92 inference(unit_resolution,[status(thm)],[24605, 145])).
% 4.74/4.92 tff(24607,plain,
% 4.74/4.92 (b(s(s(z)), s(s(s(s(z)))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[164, 24606])).
% 4.74/4.92 tff(24608,plain,
% 4.74/4.92 ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[2213, 178, 273, 24607, 24604])).
% 4.74/4.92 tff(24609,plain,
% 4.74/4.92 (~b(z, s(s(s(z))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[24608, 24601])).
% 4.74/4.92 tff(24610,plain,
% 4.74/4.92 (r(z, s(s(s(z))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[4920, 24609])).
% 4.74/4.92 tff(24611,plain,
% 4.74/4.92 (~r(s(s(z)), s(s(s(z))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[21465, 118, 106, 16062])).
% 4.74/4.92 tff(24612,plain,
% 4.74/4.92 (b(s(s(z)), s(s(s(z))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[5088, 24611])).
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% 4.74/4.92 tff(24614,plain,((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.92 tff(24615,plain,
% 4.74/4.92 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[24614, 24601, 24604, 24607, 106, 16062])).
% 4.74/4.92 tff(24616,plain,
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% 4.74/4.92 tff(24618,plain,((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.92 tff(24619,plain,
% 4.74/4.92 (~r(s(s(s(z))), z)),
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% 4.74/4.92 tff(24620,plain,
% 4.74/4.92 (b(s(s(s(z))), z)),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[21073, 24619])).
% 4.74/4.92 tff(24621,plain,
% 4.74/4.92 ((~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[4843, 24592])).
% 4.74/4.92 tff(24622,plain,
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% 4.74/4.92 inference(unit_resolution,[status(thm)],[24621, 145])).
% 4.74/4.92 tff(24623,plain,
% 4.74/4.92 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[271, 24622])).
% 4.74/4.92 tff(24624,plain,
% 4.74/4.92 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[24593, 145])).
% 4.74/4.92 tff(24625,plain,
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% 4.74/4.92 inference(unit_resolution,[status(thm)],[133, 24624])).
% 4.74/4.92 tff(24626,plain,
% 4.74/4.92 ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[3891, 24592])).
% 4.74/4.92 tff(24627,plain,
% 4.74/4.92 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[24626, 193])).
% 4.74/4.92 tff(24628,plain,
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% 4.74/4.92 inference(unit_resolution,[status(thm)],[3578, 24627])).
% 4.74/4.92 tff(24629,plain,
% 4.74/4.92 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[1154, 24628, 24625, 24623, 273])).
% 4.74/4.92 tff(24630,plain,
% 4.74/4.92 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[249, 24629])).
% 4.74/4.92 tff(24631,plain,
% 4.74/4.92 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[3559, 24630, 193])).
% 4.74/4.92 tff(24632,plain,
% 4.74/4.92 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[222, 24631])).
% 4.74/4.92 tff(24633,plain,
% 4.74/4.92 ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[18875, 24592])).
% 4.74/4.92 tff(24634,plain,
% 4.74/4.92 (~r(s(s(s(s(z)))), z)),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[24633, 193, 145])).
% 4.74/4.92 tff(24635,plain,
% 4.74/4.92 (b(s(s(s(s(z)))), z)),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[191, 24634])).
% 4.74/4.92 tff(24636,plain,
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% 4.74/4.92 inference(unit_resolution,[status(thm)],[21084, 178, 24635, 24632, 24623, 24604, 24620])).
% 4.74/4.92 tff(24637,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.92 tff(24638,plain,
% 4.74/4.92 (~r(s(s(s(s(z)))), s(s(z)))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[24637, 144, 47])).
% 4.74/4.92 tff(24639,plain,
% 4.74/4.92 (b(s(s(s(s(z)))), s(s(z)))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[102, 24638])).
% 4.74/4.92 tff(24640,plain,
% 4.74/4.92 (~r(s(s(z)), s(s(s(s(z)))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[24605, 47])).
% 4.74/4.92 tff(24641,plain,
% 4.74/4.92 (b(s(s(z)), s(s(s(s(z)))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[164, 24640])).
% 4.74/4.92 tff(24642,plain,
% 4.74/4.92 (~b(s(s(s(s(z)))), z)),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[16647, 178, 5619, 144, 24641, 24639])).
% 4.74/4.92 tff(24643,plain,
% 4.74/4.92 (~r(s(s(s(s(z)))), s(s(z)))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[24637, 273, 47])).
% 4.74/4.92 tff(24644,plain,
% 4.74/4.92 (b(s(s(s(s(z)))), s(s(z)))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[102, 24643])).
% 4.74/4.92 tff(24645,plain,
% 4.74/4.92 (~b(s(s(s(s(z)))), z)),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[16647, 178, 5619, 273, 24641, 24644])).
% 4.74/4.92 tff(24646,plain,
% 4.74/4.92 (r(s(s(s(s(z)))), z)),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[191, 24645])).
% 4.74/4.92 tff(24647,plain,
% 4.74/4.92 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[133, 24594])).
% 4.74/4.92 tff(24648,plain,
% 4.74/4.92 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[24621, 47])).
% 4.74/4.92 tff(24649,plain,
% 4.74/4.92 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[271, 24648])).
% 4.74/4.92 tff(24650,plain,
% 4.74/4.92 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[4091, 178, 5619, 273, 24649, 24647])).
% 4.74/4.92 tff(24651,plain,
% 4.74/4.92 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[20718, 5619, 24649, 24647, 273])).
% 4.74/4.92 tff(24652,plain,
% 4.74/4.92 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[249, 24651])).
% 4.74/4.92 tff(24653,plain,
% 4.74/4.92 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[3113, 14548, 24652])).
% 4.74/4.92 tff(24654,plain,
% 4.74/4.92 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[24602, 47])).
% 4.74/4.92 tff(24655,plain,
% 4.74/4.92 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[10755, 24654])).
% 4.74/4.92 tff(24656,plain,
% 4.74/4.92 (~b(s(s(s(z))), s(s(z)))),
% 4.74/4.92 inference(unit_resolution,[status(thm)],[4963, 24646, 273, 24641, 24655, 24644])).
% 4.74/4.92 tff(24657,plain,
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% 4.74/4.92 inference(unit_resolution,[status(thm)],[4966, 24656])).
% 4.74/4.92 tff(24658,plain,
% 4.74/4.92 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), elem!1)))),
% 4.74/4.92 inference(rewrite,[status(thm)],[])).
% 4.74/4.92 tff(24659,plain,
% 4.74/4.92 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), elem!1)))),
% 4.74/4.93 inference(quant_inst,[status(thm)],[])).
% 4.74/4.93 tff(24660,plain,
% 4.74/4.93 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), elem!1))),
% 4.74/4.93 inference(modus_ponens,[status(thm)],[24659, 24658])).
% 4.74/4.93 tff(24661,plain,
% 4.74/4.93 (~r(s(s(s(z))), elem!1)),
% 4.74/4.93 inference(unit_resolution,[status(thm)],[24660, 118, 14548, 24657])).
% 4.74/4.93 tff(24662,plain,
% 4.74/4.93 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.74/4.93 inference(unit_resolution,[status(thm)],[3578, 24650])).
% 4.74/4.93 tff(24663,plain,
% 4.74/4.93 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.74/4.93 inference(unit_resolution,[status(thm)],[1175, 118, 24657, 24662])).
% 4.74/4.93 tff(24664,plain,
% 4.74/4.93 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.74/4.93 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 24663])).
% 4.74/4.93 tff(24665,plain,
% 4.74/4.93 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.93 inference(unit_resolution,[status(thm)],[8218, 24657, 24662])).
% 4.74/4.93 tff(24666,plain,
% 4.74/4.93 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.93 inference(unit_resolution,[status(thm)],[20667, 24665])).
% 4.74/4.93 tff(24667,plain,
% 4.74/4.93 (~b(s(s(s(z))), z)),
% 4.74/4.93 inference(unit_resolution,[status(thm)],[1207, 178, 24649, 24647, 24666, 24664])).
% 4.74/4.93 tff(24668,plain,
% 4.74/4.93 (~(s(s(s(s(z)))) = elem!1)),
% 4.74/4.93 inference(unit_resolution,[status(thm)],[4509, 461, 24644])).
% 4.74/4.93 tff(24669,plain,
% 4.74/4.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.74/4.93 inference(rewrite,[status(thm)],[])).
% 4.74/4.93 tff(24670,plain,
% 4.74/4.93 (((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, 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(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.74/4.93 inference(rewrite,[status(thm)],[])).
% 4.74/4.93 tff(24671,plain,
% 4.74/4.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 4.74/4.93 inference(monotonicity,[status(thm)],[24670])).
% 4.74/4.93 tff(24672,plain,
% 4.74/4.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.74/4.93 inference(transitivity,[status(thm)],[24671, 24669])).
% 4.74/4.93 tff(24673,plain,
% 4.74/4.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 4.74/4.93 inference(quant_inst,[status(thm)],[])).
% 4.74/4.93 tff(24674,plain,
% 4.74/4.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 4.74/4.93 inference(modus_ponens,[status(thm)],[24673, 24672])).
% 4.74/4.93 tff(24675,plain,
% 4.74/4.93 (~b(z, s(s(s(z))))),
% 4.74/4.93 inference(unit_resolution,[status(thm)],[24674, 178, 24649, 24647, 24666, 24664])).
% 4.74/4.93 tff(24676,plain,
% 4.74/4.93 (r(z, s(s(s(z))))),
% 4.74/4.93 inference(unit_resolution,[status(thm)],[4920, 24675])).
% 4.74/4.93 tff(24677,plain,
% 4.74/4.93 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 4.74/4.93 inference(unit_resolution,[status(thm)],[4961, 24676, 24646])).
% 4.74/4.93 tff(24678,plain,
% 4.74/4.93 (b(s(s(s(s(z)))), s(s(s(z))))),
% 4.74/4.93 inference(unit_resolution,[status(thm)],[11185, 24677])).
% 4.74/4.93 tff(24679,plain,
% 4.74/4.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(z))))))),
% 4.74/4.93 inference(rewrite,[status(thm)],[])).
% 4.74/4.93 tff(24680,plain,
% 4.74/4.93 (((~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(z))))))),
% 4.74/4.93 inference(rewrite,[status(thm)],[])).
% 4.74/4.93 tff(24681,plain,
% 4.74/4.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(z)))))))),
% 4.74/4.93 inference(monotonicity,[status(thm)],[24680])).
% 4.74/4.93 tff(24682,plain,
% 4.74/4.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(z))))))),
% 4.74/4.93 inference(transitivity,[status(thm)],[24681, 24679])).
% 4.74/4.93 tff(24683,plain,
% 4.74/4.93 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(z))))))),
% 4.74/4.93 inference(quant_inst,[status(thm)],[])).
% 4.74/4.93 tff(24684,plain,
% 4.74/4.93 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(z)))))),
% 4.74/4.93 inference(modus_ponens,[status(thm)],[24683, 24682])).
% 4.74/4.93 tff(24685,plain,
% 4.74/4.93 (~r(elem!1, s(s(s(z))))),
% 4.74/4.93 inference(unit_resolution,[status(thm)],[24684, 118, 14548, 24657])).
% 4.74/4.93 tff(24686,plain,
% 4.74/4.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 4.74/4.93 inference(rewrite,[status(thm)],[])).
% 4.74/4.93 tff(24687,plain,
% 4.74/4.93 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(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(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 4.74/4.93 inference(rewrite,[status(thm)],[])).
% 4.74/4.93 tff(24688,plain,
% 4.74/4.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(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(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 4.74/4.93 inference(monotonicity,[status(thm)],[24687])).
% 4.74/4.93 tff(24689,plain,
% 4.74/4.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(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(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 4.74/4.93 inference(transitivity,[status(thm)],[24688, 24686])).
% 4.74/4.93 tff(24690,plain,
% 4.74/4.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(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(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 4.74/4.93 inference(quant_inst,[status(thm)],[])).
% 4.74/4.93 tff(24691,plain,
% 4.74/4.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 4.74/4.93 inference(modus_ponens,[status(thm)],[24690, 24689])).
% 4.74/4.93 tff(24692,plain,
% 4.74/4.93 (~b(s(s(s(s(z)))), s(s(s(s(z)))))),
% 4.74/4.93 inference(unit_resolution,[status(thm)],[24691, 178, 24641, 24644])).
% 4.74/4.93 tff(24693,plain,
% 4.74/4.93 (~r(elem!1, s(s(s(s(z)))))),
% 4.74/4.93 inference(unit_resolution,[status(thm)],[478, 437, 47])).
% 4.74/4.93 tff(24694,plain,
% 4.74/4.93 (b(elem!1, s(s(s(s(z)))))),
% 4.74/4.93 inference(unit_resolution,[status(thm)],[483, 24693, 3130])).
% 4.74/4.93 tff(24695,plain,
% 4.74/4.93 (~r(s(s(s(s(z)))), elem!1)),
% 4.74/4.93 inference(unit_resolution,[status(thm)],[6033, 437, 3244])).
% 4.74/4.93 tff(24696,plain,
% 4.74/4.93 (b(s(s(s(s(z)))), elem!1)),
% 4.74/4.93 inference(unit_resolution,[status(thm)],[3142, 24695, 323])).
% 4.74/4.93 tff(24697,plain,
% 4.74/4.93 (~b(s(s(s(z))), elem!1)),
% 4.74/4.93 inference(unit_resolution,[status(thm)],[17846, 178, 24696, 24694, 24655, 6170])).
% 4.74/4.93 tff(24698,plain,
% 4.74/4.93 (s(s(s(z))) = elem!1),
% 4.74/4.93 inference(unit_resolution,[status(thm)],[4981, 24697, 22979])).
% 4.74/4.93 tff(24699,plain,
% 4.74/4.93 (~b(z, s(elem!1))),
% 4.74/4.93 inference(unit_resolution,[status(thm)],[23057, 24698, 1])).
% 4.74/4.93 tff(24700,plain,
% 4.74/4.93 (r(z, s(elem!1))),
% 4.74/4.93 inference(unit_resolution,[status(thm)],[2351, 24699])).
% 4.74/4.93 tff(24701,plain,
% 4.74/4.93 (~r(elem!1, s(elem!1))),
% 4.74/4.93 inference(unit_resolution,[status(thm)],[12189, 24700, 437])).
% 4.74/4.93 tff(24702,plain,
% 4.74/4.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), 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(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), 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(z))))))),
% 4.74/4.93 inference(rewrite,[status(thm)],[])).
% 4.74/4.93 tff(24703,plain,
% 4.74/4.93 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))))),
% 4.74/4.93 inference(rewrite,[status(thm)],[])).
% 4.74/4.93 tff(24704,plain,
% 4.74/4.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), 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(z)))))))),
% 4.74/4.93 inference(monotonicity,[status(thm)],[24703])).
% 4.74/4.93 tff(24705,plain,
% 4.74/4.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), 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(z))))))),
% 4.74/4.93 inference(transitivity,[status(thm)],[24704, 24702])).
% 4.74/4.93 tff(24706,plain,
% 4.74/4.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 4.74/4.93 inference(quant_inst,[status(thm)],[])).
% 4.74/4.93 tff(24707,plain,
% 4.74/4.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), 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(z)))))),
% 4.74/4.93 inference(modus_ponens,[status(thm)],[24706, 24705])).
% 4.74/4.93 tff(24708,plain,
% 4.74/4.93 (~b(elem!1, s(s(s(z))))),
% 4.74/4.93 inference(unit_resolution,[status(thm)],[24707, 178, 24696, 24694, 24655, 6170])).
% 4.74/4.93 tff(24709,plain,
% 4.74/4.93 (elem!1 = s(s(s(z)))),
% 4.74/4.93 inference(unit_resolution,[status(thm)],[17275, 24708, 22966])).
% 4.74/4.93 tff(24710,plain,
% 4.74/4.93 (s(elem!1) = s(s(s(s(z))))),
% 4.74/4.93 inference(monotonicity,[status(thm)],[24709])).
% 4.74/4.93 tff(24711,plain,
% 4.74/4.93 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.74/4.93 inference(monotonicity,[status(thm)],[24710])).
% 4.74/4.93 tff(24712,plain,
% 4.74/4.93 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 4.74/4.93 inference(symmetry,[status(thm)],[24711])).
% 4.74/4.93 tff(24713,plain,
% 4.74/4.93 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 4.74/4.93 inference(monotonicity,[status(thm)],[24712])).
% 4.74/4.93 tff(24714,plain,
% 4.74/4.93 (~(s(elem!1) = s(s(z)))),
% 4.74/4.93 inference(unit_resolution,[status(thm)],[1047, 24701, 450])).
% 4.74/4.93 tff(24715,plain,
% 4.74/4.93 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.74/4.93 inference(unit_resolution,[status(thm)],[2840, 24714])).
% 4.74/4.93 tff(24716,plain,
% 4.74/4.93 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.74/4.93 inference(modus_ponens,[status(thm)],[24715, 24713])).
% 4.74/4.93 tff(24717,plain,
% 4.74/4.93 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(s(s(z)))), s(s(s(s(z)))))),
% 4.74/4.93 inference(monotonicity,[status(thm)],[24710])).
% 4.74/4.93 tff(24718,plain,
% 4.74/4.93 (b(s(s(s(s(z)))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 4.74/4.93 inference(symmetry,[status(thm)],[24717])).
% 4.74/4.93 tff(24719,plain,
% 4.74/4.93 ((~b(s(s(s(s(z)))), s(s(s(s(z)))))) <=> (~b(s(elem!1), s(s(s(s(z))))))),
% 4.74/4.93 inference(monotonicity,[status(thm)],[24718])).
% 4.74/4.93 tff(24720,assumption,(~b(s(s(s(s(z)))), s(s(s(s(z)))))), introduced(assumption)).
% 4.74/4.93 tff(24721,plain,
% 4.74/4.93 (~b(s(elem!1), s(s(s(s(z)))))),
% 4.74/4.93 inference(modus_ponens,[status(thm)],[24720, 24719])).
% 4.74/4.93 tff(24722,plain,
% 4.74/4.93 ($false),
% 4.74/4.93 inference(unit_resolution,[status(thm)],[10314, 24721, 24716, 5618, 3170, 461, 24701])).
% 4.74/4.93 tff(24723,plain,((~r(elem!1, z)) | r(s(s(z)), z) | b(s(s(s(s(z)))), z) | b(elem!1, s(s(z))) | b(s(s(s(s(z)))), s(s(s(s(z))))) | (~r(elem!1, s(s(z)))) | b(z, s(s(s(s(z))))) | r(s(s(s(z))), elem!1) | r(elem!1, s(s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.74/4.93 tff(24724,plain,
% 4.74/4.93 (~r(elem!1, z)),
% 4.74/4.93 inference(unit_resolution,[status(thm)],[24723, 461, 24645, 5618, 24692, 14548, 1, 24661, 24685, 24678, 24668])).
% 4.74/4.93 tff(24725,plain,
% 4.74/4.93 (b(elem!1, z)),
% 4.74/4.93 inference(unit_resolution,[status(thm)],[498, 24724, 290])).
% 4.74/4.93 tff(24726,plain,
% 4.74/4.93 (b(s(s(s(z))), z) <=> b(elem!1, z)),
% 4.74/4.93 inference(monotonicity,[status(thm)],[4824])).
% 4.74/4.93 tff(24727,plain,
% 4.74/4.93 (b(elem!1, z) <=> b(s(s(s(z))), z)),
% 4.74/4.93 inference(symmetry,[status(thm)],[24726])).
% 4.74/4.93 tff(24728,plain,
% 4.74/4.93 (b(s(s(s(z))), z)),
% 4.74/4.93 inference(modus_ponens,[status(thm)],[506, 24727])).
% 4.74/4.93 tff(24729,plain,
% 4.74/4.93 ($false),
% 4.74/4.93 inference(unit_resolution,[status(thm)],[7040, 24728])).
% 4.74/4.93 tff(24730,plain,((~(s(s(s(z))) = elem!1)) | b(s(s(s(z))), z) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.93 tff(24731,plain,
% 4.74/4.93 (~(s(s(s(z))) = elem!1)),
% 4.74/4.93 inference(unit_resolution,[status(thm)],[24730, 24725, 24667])).
% 4.74/4.93 tff(24732,plain,
% 4.74/4.93 (b(s(s(s(z))), elem!1)),
% 4.74/4.93 inference(unit_resolution,[status(thm)],[4981, 24731, 24661])).
% 4.74/4.93 tff(24733,plain,
% 4.74/4.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)))),
% 4.74/4.93 inference(rewrite,[status(thm)],[])).
% 4.74/4.93 tff(24734,plain,
% 4.74/4.93 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)))),
% 4.74/4.93 inference(rewrite,[status(thm)],[])).
% 4.74/4.93 tff(24735,plain,
% 4.74/4.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1))))),
% 4.74/4.93 inference(monotonicity,[status(thm)],[24734])).
% 4.74/4.93 tff(24736,plain,
% 4.74/4.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)))),
% 4.74/4.93 inference(transitivity,[status(thm)],[24735, 24733])).
% 4.74/4.93 tff(24737,plain,
% 4.74/4.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)))),
% 4.74/4.93 inference(quant_inst,[status(thm)],[])).
% 4.74/4.93 tff(24738,plain,
% 4.74/4.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1))),
% 4.74/4.93 inference(modus_ponens,[status(thm)],[24737, 24736])).
% 4.74/4.93 tff(24739,plain,
% 4.74/4.93 ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1))),
% 4.74/4.93 inference(unit_resolution,[status(thm)],[24738, 178, 24725, 24647, 24666])).
% 4.74/4.93 tff(24740,plain,
% 4.74/4.93 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.74/4.93 inference(unit_resolution,[status(thm)],[24739, 24732])).
% 4.74/4.93 tff(24741,plain,
% 4.74/4.93 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 4.74/4.93 inference(unit_resolution,[status(thm)],[691, 24740, 24653])).
% 4.74/4.93 tff(24742,plain,
% 4.74/4.93 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.93 inference(monotonicity,[status(thm)],[24741])).
% 4.74/4.93 tff(24743,plain,
% 4.74/4.93 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(z)))), elem!1)),
% 4.74/4.93 inference(symmetry,[status(thm)],[24742])).
% 4.74/4.93 tff(24744,plain,
% 4.74/4.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(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(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(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(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.74/4.93 inference(rewrite,[status(thm)],[])).
% 4.74/4.93 tff(24745,plain,
% 4.74/4.93 (((~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(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(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(z))))) | (~b(s(s(s(s(z)))), s(s(s(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(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.74/4.93 inference(rewrite,[status(thm)],[])).
% 4.74/4.93 tff(24746,plain,
% 4.74/4.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(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(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(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(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 4.74/4.94 inference(monotonicity,[status(thm)],[24745])).
% 4.74/4.94 tff(24747,plain,
% 4.74/4.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(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(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(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(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.74/4.94 inference(transitivity,[status(thm)],[24746, 24744])).
% 4.74/4.94 tff(24748,plain,
% 4.74/4.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(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(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 4.74/4.94 inference(quant_inst,[status(thm)],[])).
% 4.74/4.94 tff(24749,plain,
% 4.74/4.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(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(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 4.74/4.94 inference(modus_ponens,[status(thm)],[24748, 24747])).
% 4.74/4.94 tff(24750,plain,
% 4.74/4.94 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.94 inference(unit_resolution,[status(thm)],[24749, 178, 24655, 24678, 24666, 24664])).
% 4.74/4.94 tff(24751,plain,
% 4.74/4.94 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.94 inference(unit_resolution,[status(thm)],[222, 24750])).
% 4.74/4.94 tff(24752,plain,
% 4.74/4.94 (r(s(s(s(s(z)))), elem!1)),
% 4.74/4.94 inference(modus_ponens,[status(thm)],[24751, 24743])).
% 4.74/4.94 tff(24753,plain,
% 4.74/4.94 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.74/4.94 inference(unit_resolution,[status(thm)],[16181, 24741])).
% 4.74/4.94 tff(24754,plain,
% 4.74/4.94 (~(s(s(s(s(z)))) = s(elem!1))),
% 4.74/4.94 inference(unit_resolution,[status(thm)],[2168, 24753])).
% 4.74/4.94 tff(24755,plain,
% 4.74/4.94 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 4.74/4.94 inference(monotonicity,[status(thm)],[24741])).
% 4.74/4.94 tff(24756,plain,
% 4.74/4.94 (s(s(s(s(s(s(s(s(z)))))))) = s(elem!1)),
% 4.74/4.94 inference(symmetry,[status(thm)],[24755])).
% 4.74/4.94 tff(24757,plain,
% 4.74/4.94 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z))))))))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 4.74/4.94 inference(monotonicity,[status(thm)],[24756])).
% 4.74/4.94 tff(24758,plain,
% 4.74/4.94 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) <=> (~b(s(s(s(s(z)))), s(elem!1)))),
% 4.74/4.94 inference(monotonicity,[status(thm)],[24757])).
% 4.74/4.94 tff(24759,plain,
% 4.74/4.94 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 4.74/4.94 inference(monotonicity,[status(thm)],[24756])).
% 4.74/4.94 tff(24760,plain,
% 4.74/4.94 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 4.74/4.94 inference(symmetry,[status(thm)],[24759])).
% 4.74/4.94 tff(24761,plain,
% 4.74/4.94 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 4.74/4.94 inference(unit_resolution,[status(thm)],[23404, 1])).
% 4.74/4.94 tff(24762,plain,
% 4.74/4.94 (b(elem!1, s(s(s(elem!1))))),
% 4.74/4.94 inference(unit_resolution,[status(thm)],[19038, 461, 1, 24761, 24645])).
% 4.74/4.94 tff(24763,plain,
% 4.74/4.94 (~(s(s(s(elem!1))) = elem!1)),
% 4.74/4.94 inference(unit_resolution,[status(thm)],[16438, 24762])).
% 4.74/4.94 tff(24764,plain,
% 4.74/4.94 (~(s(elem!1) = elem!1)),
% 4.74/4.94 inference(unit_resolution,[status(thm)],[2150, 24763])).
% 4.74/4.94 tff(24765,plain,
% 4.74/4.94 (~b(elem!1, s(s(s(s(z)))))),
% 4.74/4.94 inference(unit_resolution,[status(thm)],[3434, 679, 3428])).
% 4.74/4.94 tff(24766,plain,
% 4.74/4.94 (elem!1 = s(s(s(s(z))))),
% 4.74/4.94 inference(unit_resolution,[status(thm)],[483, 24765, 5721])).
% 4.74/4.94 tff(24767,plain,
% 4.74/4.94 (s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))),
% 4.74/4.94 inference(transitivity,[status(thm)],[680, 24766])).
% 4.74/4.94 tff(24768,plain,
% 4.74/4.94 ($false),
% 4.74/4.94 inference(unit_resolution,[status(thm)],[79, 24767])).
% 4.74/4.94 tff(24769,plain,((~(elem!1 = s(s(s(s(s(s(s(z))))))))) | r(elem!1, s(s(s(s(z))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.94 tff(24770,plain,
% 4.74/4.94 (r(elem!1, s(s(s(s(z)))))),
% 4.74/4.94 inference(unit_resolution,[status(thm)],[24769, 24741, 24761])).
% 4.74/4.94 tff(24771,plain,
% 4.74/4.94 (~r(s(elem!1), s(s(s(s(z)))))),
% 4.74/4.94 inference(unit_resolution,[status(thm)],[17654, 24770, 47, 5619, 24725, 24764, 273, 24646, 461])).
% 4.74/4.94 tff(24772,plain,
% 4.74/4.94 (b(s(elem!1), s(s(s(s(z)))))),
% 4.74/4.94 inference(unit_resolution,[status(thm)],[1084, 24771, 24753])).
% 4.74/4.94 tff(24773,plain,
% 4.74/4.94 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 4.74/4.94 inference(modus_ponens,[status(thm)],[24772, 24760])).
% 4.74/4.94 tff(24774,assumption,(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z)))), introduced(assumption)).
% 4.74/4.94 tff(24775,plain,
% 4.74/4.94 (s(elem!1) = s(s(s(z)))),
% 4.74/4.94 inference(transitivity,[status(thm)],[2823, 24774])).
% 4.74/4.94 tff(24776,plain,
% 4.74/4.94 ($false),
% 4.74/4.94 inference(unit_resolution,[status(thm)],[23528, 24775])).
% 4.74/4.94 tff(24777,plain,((~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z))))) | (s(elem!1) = s(s(s(z)))) | (~(elem!1 = s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.94 tff(24778,plain,
% 4.74/4.94 (~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z))))),
% 4.74/4.94 inference(unit_resolution,[status(thm)],[24777, 24741, 23437])).
% 4.74/4.94 tff(24779,plain,
% 4.74/4.94 (~b(s(s(z)), elem!1)),
% 4.74/4.94 inference(unit_resolution,[status(thm)],[10835, 24741, 24651])).
% 4.74/4.94 tff(24780,plain,
% 4.74/4.94 (r(s(s(z)), elem!1)),
% 4.74/4.94 inference(unit_resolution,[status(thm)],[448, 24779, 12])).
% 4.74/4.94 tff(24781,plain,
% 4.74/4.94 (~r(z, elem!1)),
% 4.74/4.94 inference(unit_resolution,[status(thm)],[529, 24770, 47])).
% 4.74/4.94 tff(24782,plain,
% 4.74/4.94 (b(z, elem!1)),
% 4.74/4.94 inference(unit_resolution,[status(thm)],[585, 24781, 318])).
% 4.74/4.94 tff(24783,plain,
% 4.74/4.94 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(z))) <=> b(s(elem!1), s(s(z)))),
% 4.74/4.94 inference(symmetry,[status(thm)],[11737])).
% 4.74/4.94 tff(24784,plain,
% 4.74/4.94 ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) <=> (~b(s(elem!1), s(s(z))))),
% 4.74/4.94 inference(monotonicity,[status(thm)],[24783])).
% 4.74/4.94 tff(24785,assumption,(b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))), introduced(assumption)).
% 4.74/4.94 tff(24786,plain,
% 4.74/4.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 4.74/4.94 inference(rewrite,[status(thm)],[])).
% 4.74/4.94 tff(24787,plain,
% 4.74/4.94 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(s(z))))))))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 4.74/4.94 inference(rewrite,[status(thm)],[])).
% 4.74/4.94 tff(24788,plain,
% 4.74/4.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))))),
% 4.74/4.94 inference(monotonicity,[status(thm)],[24787])).
% 4.74/4.94 tff(24789,plain,
% 4.74/4.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 4.74/4.94 inference(transitivity,[status(thm)],[24788, 24786])).
% 4.74/4.94 tff(24790,plain,
% 4.74/4.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))))),
% 4.74/4.94 inference(quant_inst,[status(thm)],[])).
% 4.74/4.94 tff(24791,plain,
% 4.74/4.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))),
% 4.74/4.94 inference(modus_ponens,[status(thm)],[24790, 24789])).
% 4.74/4.94 tff(24792,plain,
% 4.74/4.94 ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))),
% 4.74/4.94 inference(unit_resolution,[status(thm)],[24791, 178, 273, 167])).
% 4.74/4.94 tff(24793,plain,
% 4.74/4.94 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 4.74/4.94 inference(unit_resolution,[status(thm)],[24792, 21928, 24785])).
% 4.74/4.94 tff(24794,plain,
% 4.74/4.94 (~b(s(elem!1), s(s(z)))),
% 4.74/4.94 inference(modus_ponens,[status(thm)],[24793, 24784])).
% 4.74/4.94 tff(24795,plain,
% 4.74/4.94 (r(s(elem!1), s(s(z)))),
% 4.74/4.94 inference(unit_resolution,[status(thm)],[421, 24794, 10483])).
% 4.74/4.94 tff(24796,plain,
% 4.74/4.94 (~r(s(elem!1), elem!1)),
% 4.74/4.94 inference(unit_resolution,[status(thm)],[2249, 24795, 438])).
% 4.74/4.94 tff(24797,plain,
% 4.74/4.94 (b(s(elem!1), elem!1)),
% 4.74/4.94 inference(unit_resolution,[status(thm)],[677, 24796, 725])).
% 4.74/4.94 tff(24798,plain,
% 4.74/4.94 (~b(elem!1, s(elem!1))),
% 4.74/4.94 inference(unit_resolution,[status(thm)],[1396, 24797, 506, 818, 855])).
% 4.74/4.94 tff(24799,plain,
% 4.74/4.94 (r(elem!1, s(elem!1))),
% 4.74/4.94 inference(unit_resolution,[status(thm)],[756, 24798, 749])).
% 4.74/4.94 tff(24800,plain,
% 4.74/4.94 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.74/4.94 inference(modus_ponens,[status(thm)],[24799, 19264])).
% 4.74/4.94 tff(24801,plain,
% 4.74/4.94 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 4.74/4.94 inference(modus_ponens,[status(thm)],[24795, 16192])).
% 4.74/4.94 tff(24802,plain,
% 4.74/4.94 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.74/4.94 inference(unit_resolution,[status(thm)],[19321, 24801, 679, 107])).
% 4.74/4.94 tff(24803,plain,
% 4.74/4.94 ($false),
% 4.74/4.94 inference(unit_resolution,[status(thm)],[24802, 24800])).
% 4.74/4.94 tff(24804,plain,((~b(z, s(elem!1))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (s(elem!1) = elem!1) | (~r(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.94 tff(24805,plain,
% 4.74/4.94 (~b(z, s(elem!1))),
% 4.74/4.94 inference(unit_resolution,[status(thm)],[24804, 24741, 24662, 24725, 24782, 24764, 24780, 24773, 273, 24641])).
% 4.74/4.94 tff(24806,plain,
% 4.74/4.94 (r(z, s(elem!1))),
% 4.74/4.94 inference(unit_resolution,[status(thm)],[2351, 24805])).
% 4.74/4.94 tff(24807,plain,
% 4.74/4.94 (r(z, s(s(s(s(s(s(s(s(z))))))))) <=> r(z, s(elem!1))),
% 4.74/4.94 inference(monotonicity,[status(thm)],[11730])).
% 4.74/4.94 tff(24808,plain,
% 4.74/4.94 (r(z, s(elem!1)) <=> r(z, s(s(s(s(s(s(s(s(z)))))))))),
% 4.74/4.94 inference(symmetry,[status(thm)],[24807])).
% 4.74/4.94 tff(24809,plain,
% 4.74/4.94 (r(z, s(s(s(s(s(s(s(s(z)))))))))),
% 4.74/4.94 inference(modus_ponens,[status(thm)],[2333, 24808])).
% 4.74/4.94 tff(24810,assumption,(~r(z, s(s(s(s(s(s(s(s(z)))))))))), introduced(assumption)).
% 4.74/4.94 tff(24811,plain,
% 4.74/4.94 ($false),
% 4.74/4.94 inference(unit_resolution,[status(thm)],[24810, 24809])).
% 4.74/4.94 tff(24812,plain,(r(z, s(s(s(s(s(s(s(s(z))))))))) | (~r(z, s(elem!1))) | (~(elem!1 = s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.94 tff(24813,plain,
% 4.74/4.94 (r(z, s(s(s(s(s(s(s(s(z)))))))))),
% 4.74/4.94 inference(unit_resolution,[status(thm)],[24812, 24806, 24741])).
% 4.74/4.94 tff(24814,assumption,(r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))), introduced(assumption)).
% 4.74/4.94 tff(24815,assumption,(r(z, s(s(s(s(s(s(s(s(z)))))))))), introduced(assumption)).
% 4.74/4.94 tff(24816,plain,
% 4.74/4.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 4.74/4.94 inference(rewrite,[status(thm)],[])).
% 4.74/4.94 tff(24817,plain,
% 4.74/4.94 (((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 4.74/4.94 inference(rewrite,[status(thm)],[])).
% 4.74/4.94 tff(24818,plain,
% 4.74/4.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))))),
% 4.74/4.94 inference(monotonicity,[status(thm)],[24817])).
% 4.74/4.94 tff(24819,plain,
% 4.74/4.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 4.74/4.94 inference(transitivity,[status(thm)],[24818, 24816])).
% 4.74/4.94 tff(24820,plain,
% 4.74/4.94 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))))),
% 4.74/4.94 inference(quant_inst,[status(thm)],[])).
% 4.74/4.94 tff(24821,plain,
% 4.74/4.94 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 4.74/4.94 inference(modus_ponens,[status(thm)],[24820, 24819])).
% 4.74/4.94 tff(24822,plain,
% 4.74/4.94 ($false),
% 4.74/4.94 inference(unit_resolution,[status(thm)],[24821, 118, 4952, 24815, 24814])).
% 4.74/4.94 tff(24823,plain,((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(s(z))))))))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.94 tff(24824,plain,
% 4.74/4.94 (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 4.74/4.94 inference(unit_resolution,[status(thm)],[24823, 24813, 24676])).
% 4.74/4.94 tff(24825,assumption,(~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z))))), introduced(assumption)).
% 4.74/4.94 tff(24826,assumption,(~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))), introduced(assumption)).
% 4.74/4.94 tff(24827,assumption,(~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))), introduced(assumption)).
% 4.74/4.94 tff(24828,plain,
% 4.74/4.94 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z)))) | b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))) | r(s(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(s(z)))))))) = s(s(s(z)))) | b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))) | r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 4.74/4.94 inference(rewrite,[status(thm)],[])).
% 4.74/4.94 tff(24829,plain,
% 4.74/4.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z)))) | b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))) | r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 4.74/4.94 inference(quant_inst,[status(thm)],[])).
% 4.74/4.94 tff(24830,plain,
% 4.74/4.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z)))) | b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))) | r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 4.74/4.94 inference(modus_ponens,[status(thm)],[24829, 24828])).
% 4.74/4.94 tff(24831,plain,
% 4.74/4.94 ($false),
% 4.74/4.94 inference(unit_resolution,[status(thm)],[24830, 41, 24827, 24826, 24825])).
% 4.74/4.94 tff(24832,plain,(b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))) | r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))) | (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.94 tff(24833,plain,
% 4.74/4.94 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 4.74/4.94 inference(unit_resolution,[status(thm)],[24832, 24824, 24778])).
% 4.74/4.94 tff(24834,plain,
% 4.74/4.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 4.74/4.94 inference(rewrite,[status(thm)],[])).
% 4.74/4.94 tff(24835,plain,
% 4.74/4.94 (((~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(s(z)))))))), s(s(s(s(z)))))) | (~b(s(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(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 4.74/4.94 inference(rewrite,[status(thm)],[])).
% 4.74/4.94 tff(24836,plain,
% 4.74/4.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(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(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))))),
% 4.74/4.94 inference(monotonicity,[status(thm)],[24835])).
% 4.74/4.94 tff(24837,plain,
% 4.74/4.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(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(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 4.74/4.94 inference(transitivity,[status(thm)],[24836, 24834])).
% 4.74/4.94 tff(24838,plain,
% 4.74/4.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(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(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))))),
% 4.74/4.94 inference(quant_inst,[status(thm)],[])).
% 4.74/4.94 tff(24839,plain,
% 4.74/4.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 4.74/4.94 inference(modus_ponens,[status(thm)],[24838, 24837])).
% 4.74/4.94 tff(24840,plain,
% 4.74/4.94 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 4.74/4.94 inference(unit_resolution,[status(thm)],[24839, 178, 24655, 24678])).
% 4.74/4.94 tff(24841,plain,
% 4.74/4.94 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.74/4.94 inference(unit_resolution,[status(thm)],[24840, 24833, 24773])).
% 4.74/4.94 tff(24842,plain,
% 4.74/4.94 (~b(s(s(s(s(z)))), s(elem!1))),
% 4.74/4.94 inference(modus_ponens,[status(thm)],[24841, 24758])).
% 4.74/4.94 tff(24843,plain,
% 4.74/4.94 (r(s(s(s(s(z)))), s(elem!1))),
% 4.74/4.94 inference(unit_resolution,[status(thm)],[2173, 24842, 24754])).
% 4.74/4.94 tff(24844,plain,
% 4.74/4.94 (~(elem!1 = s(elem!1))),
% 4.74/4.94 inference(unit_resolution,[status(thm)],[748, 24764])).
% 4.74/4.94 tff(24845,plain,
% 4.74/4.94 (b(elem!1, s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.74/4.94 inference(monotonicity,[status(thm)],[24741])).
% 4.74/4.94 tff(24846,plain,
% 4.74/4.94 (b(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 4.74/4.94 inference(symmetry,[status(thm)],[24845])).
% 4.74/4.94 tff(24847,plain,
% 4.74/4.94 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.74/4.94 inference(monotonicity,[status(thm)],[24756])).
% 4.74/4.94 tff(24848,plain,
% 4.74/4.94 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))) <=> b(elem!1, s(elem!1))),
% 4.74/4.94 inference(transitivity,[status(thm)],[24847, 24846])).
% 4.74/4.94 tff(24849,plain,
% 4.74/4.94 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) <=> (~b(elem!1, s(elem!1)))),
% 4.74/4.94 inference(monotonicity,[status(thm)],[24848])).
% 4.74/4.94 tff(24850,plain,
% 4.74/4.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 4.74/4.94 inference(rewrite,[status(thm)],[])).
% 4.74/4.94 tff(24851,plain,
% 4.74/4.94 (((~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(s(z)))))))), s(s(s(s(z)))))) | (~b(s(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))))) | (~b(s(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(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(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 4.74/4.95 inference(rewrite,[status(thm)],[])).
% 4.74/4.95 tff(24852,plain,
% 4.74/4.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(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))))) | (~b(s(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(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))))),
% 4.74/4.95 inference(monotonicity,[status(thm)],[24851])).
% 4.74/4.95 tff(24853,plain,
% 4.74/4.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(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))))) | (~b(s(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(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 4.74/4.95 inference(transitivity,[status(thm)],[24852, 24850])).
% 4.74/4.95 tff(24854,plain,
% 4.74/4.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(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))))) | (~b(s(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(s(s(s(s(z)))))))))))),
% 4.74/4.95 inference(quant_inst,[status(thm)],[])).
% 4.74/4.95 tff(24855,plain,
% 4.74/4.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 4.74/4.95 inference(modus_ponens,[status(thm)],[24854, 24853])).
% 4.74/4.95 tff(24856,plain,
% 4.74/4.95 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[24855, 178, 24655, 24664])).
% 4.74/4.95 tff(24857,plain,
% 4.74/4.95 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[24856, 24833, 24773])).
% 4.74/4.95 tff(24858,plain,
% 4.74/4.95 (~b(elem!1, s(elem!1))),
% 4.74/4.95 inference(modus_ponens,[status(thm)],[24857, 24849])).
% 4.74/4.95 tff(24859,plain,
% 4.74/4.95 (r(elem!1, s(elem!1))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[756, 24858, 24844])).
% 4.74/4.95 tff(24860,plain,
% 4.74/4.95 ($false),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[10992, 24859, 24843, 24752])).
% 4.74/4.95 tff(24861,plain,(b(elem!1, s(s(z))) | (~b(z, s(s(z)))) | (s(s(z)) = elem!1) | (elem!1 = z) | r(s(s(z)), z) | b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.95 tff(24862,plain,
% 4.74/4.95 (b(elem!1, s(s(z)))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[24861, 12, 273, 290, 5618, 1])).
% 4.74/4.95 tff(24863,plain,
% 4.74/4.95 (b(s(s(s(s(z)))), elem!1)),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[3142, 323, 5369])).
% 4.74/4.95 tff(24864,plain,
% 4.74/4.95 (b(elem!1, s(s(s(s(z)))))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[483, 3130, 5721])).
% 4.74/4.95 tff(24865,plain,
% 4.74/4.95 ($false),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[16667, 24864, 24863, 202, 167, 812])).
% 4.74/4.95 tff(24866,plain,((s(s(s(s(z)))) = elem!1) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | r(elem!1, s(s(s(s(z))))) | r(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.74/4.95 tff(24867,plain,
% 4.74/4.95 (s(s(s(s(z)))) = elem!1),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[24866, 24693, 24641, 812, 24644, 14934])).
% 4.74/4.95 tff(24868,plain,
% 4.74/4.95 (~(s(s(elem!1)) = elem!1)),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[338, 24867, 12])).
% 4.74/4.95 tff(24869,plain,
% 4.74/4.95 (~(s(elem!1) = elem!1)),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[672, 24868])).
% 4.74/4.95 tff(24870,plain,
% 4.74/4.95 (~(elem!1 = s(elem!1))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[748, 24869])).
% 4.74/4.95 tff(24871,plain,
% 4.74/4.95 (elem!1 = s(s(s(s(z))))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[504, 24867])).
% 4.74/4.95 tff(24872,plain,
% 4.74/4.95 (~r(s(s(z)), elem!1)),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[18181, 24871, 24640])).
% 4.74/4.95 tff(24873,plain,
% 4.74/4.95 (b(s(s(z)), elem!1)),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[448, 24872, 12])).
% 4.74/4.95 tff(24874,plain,
% 4.74/4.95 (s(s(s(s(s(z))))) = s(elem!1)),
% 4.74/4.95 inference(monotonicity,[status(thm)],[24867])).
% 4.74/4.95 tff(24875,plain,
% 4.74/4.95 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 4.74/4.95 inference(monotonicity,[status(thm)],[24874])).
% 4.74/4.95 tff(24876,plain,
% 4.74/4.95 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 4.74/4.95 inference(monotonicity,[status(thm)],[24875])).
% 4.74/4.95 tff(24877,plain,
% 4.74/4.95 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 4.74/4.95 inference(monotonicity,[status(thm)],[24876])).
% 4.74/4.95 tff(24878,plain,
% 4.74/4.95 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.74/4.95 inference(monotonicity,[status(thm)],[24867])).
% 4.74/4.95 tff(24879,plain,
% 4.74/4.95 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.74/4.95 inference(modus_ponens,[status(thm)],[24592, 24878])).
% 4.74/4.95 tff(24880,plain,
% 4.74/4.95 (r(s(s(s(elem!1))), elem!1)),
% 4.74/4.95 inference(modus_ponens,[status(thm)],[24879, 24877])).
% 4.74/4.95 tff(24881,plain,
% 4.74/4.95 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[348, 24868])).
% 4.74/4.95 tff(24882,plain,
% 4.74/4.95 (b(z, s(s(s(elem!1))))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[17717, 24871, 24649])).
% 4.74/4.95 tff(24883,plain,
% 4.74/4.95 (~b(z, elem!1)),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[1846, 24871, 1])).
% 4.74/4.95 tff(24884,plain,
% 4.74/4.95 (r(z, elem!1)),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[585, 24883, 507])).
% 4.74/4.95 tff(24885,plain,
% 4.74/4.95 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 4.74/4.95 inference(monotonicity,[status(thm)],[24876])).
% 4.74/4.95 tff(24886,plain,
% 4.74/4.95 ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) <=> (~b(s(s(s(elem!1))), elem!1))),
% 4.74/4.95 inference(monotonicity,[status(thm)],[24885])).
% 4.74/4.95 tff(24887,plain,
% 4.74/4.95 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.74/4.95 inference(monotonicity,[status(thm)],[24867])).
% 4.74/4.95 tff(24888,plain,
% 4.74/4.95 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) <=> (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 4.74/4.95 inference(monotonicity,[status(thm)],[24887])).
% 4.74/4.95 tff(24889,plain,
% 4.74/4.95 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.74/4.95 inference(modus_ponens,[status(thm)],[24761, 24888])).
% 4.74/4.95 tff(24890,plain,
% 4.74/4.95 (~b(s(s(s(elem!1))), elem!1)),
% 4.74/4.95 inference(modus_ponens,[status(thm)],[24889, 24886])).
% 4.74/4.95 tff(24891,plain,
% 4.74/4.95 (r(s(elem!1), elem!1)),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[677, 2141, 725])).
% 4.74/4.95 tff(24892,plain,
% 4.74/4.95 (~r(z, s(elem!1))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[7070, 24891, 521])).
% 4.74/4.95 tff(24893,plain,
% 4.74/4.95 (b(z, s(elem!1))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[2351, 24892])).
% 4.74/4.95 tff(24894,plain,
% 4.74/4.95 (~r(s(elem!1), z)),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[1284, 24891, 521])).
% 4.74/4.95 tff(24895,plain,
% 4.74/4.95 (b(s(elem!1), z)),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[774, 24894])).
% 4.74/4.95 tff(24896,plain,
% 4.74/4.95 (~r(s(s(s(elem!1))), s(elem!1))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[1576, 24891, 556])).
% 4.74/4.95 tff(24897,plain,
% 4.74/4.95 (b(s(s(s(elem!1))), s(elem!1))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[373, 24896, 356])).
% 4.74/4.95 tff(24898,plain,
% 4.74/4.95 ($false),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[7117, 24897, 24895, 2043, 356, 556, 2141, 24893, 5308])).
% 4.74/4.95 tff(24899,plain,(b(s(elem!1), elem!1) | (~b(z, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | b(s(s(s(elem!1))), elem!1) | (~r(z, elem!1)) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.74/4.95 tff(24900,plain,
% 4.74/4.95 (b(s(elem!1), elem!1)),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[24899, 24890, 24884, 24882, 24881, 24880, 24869])).
% 4.74/4.95 tff(24901,plain,
% 4.74/4.95 (r(s(s(s(elem!1))), s(s(z)))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[14415, 24871, 3576])).
% 4.74/4.95 tff(24902,plain,
% 4.74/4.95 (b(s(s(s(s(s(s(s(z))))))), z) <=> b(s(s(s(elem!1))), z)),
% 4.74/4.95 inference(monotonicity,[status(thm)],[24876])).
% 4.74/4.95 tff(24903,plain,
% 4.74/4.95 (b(s(s(s(elem!1))), z)),
% 4.74/4.95 inference(modus_ponens,[status(thm)],[24647, 24902])).
% 4.74/4.95 tff(24904,plain,
% 4.74/4.95 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.95 inference(monotonicity,[status(thm)],[12869])).
% 4.74/4.95 tff(24905,plain,
% 4.74/4.95 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 4.74/4.95 inference(symmetry,[status(thm)],[24904])).
% 4.74/4.95 tff(24906,plain,
% 4.74/4.95 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 4.74/4.95 inference(monotonicity,[status(thm)],[12869])).
% 4.74/4.95 tff(24907,plain,
% 4.74/4.95 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.74/4.95 inference(transitivity,[status(thm)],[24906, 377])).
% 4.74/4.95 tff(24908,plain,
% 4.74/4.95 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 4.74/4.95 inference(monotonicity,[status(thm)],[24907])).
% 4.74/4.95 tff(24909,plain,
% 4.74/4.95 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.74/4.95 inference(modus_ponens,[status(thm)],[356, 24908])).
% 4.74/4.95 tff(24910,plain,
% 4.74/4.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 4.74/4.95 inference(rewrite,[status(thm)],[])).
% 4.74/4.95 tff(24911,plain,
% 4.74/4.95 (((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 4.74/4.95 inference(rewrite,[status(thm)],[])).
% 4.74/4.95 tff(24912,plain,
% 4.74/4.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1))))),
% 4.74/4.95 inference(monotonicity,[status(thm)],[24911])).
% 4.74/4.95 tff(24913,plain,
% 4.74/4.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 4.74/4.95 inference(transitivity,[status(thm)],[24912, 24910])).
% 4.74/4.95 tff(24914,plain,
% 4.74/4.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))))),
% 4.74/4.95 inference(quant_inst,[status(thm)],[])).
% 4.74/4.95 tff(24915,plain,
% 4.74/4.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1))),
% 4.74/4.95 inference(modus_ponens,[status(thm)],[24914, 24913])).
% 4.74/4.95 tff(24916,plain,
% 4.74/4.95 ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(z))))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[24915, 178, 683, 817, 273])).
% 4.74/4.95 tff(24917,plain,
% 4.74/4.95 (~b(s(elem!1), s(s(z)))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[24916, 855])).
% 4.74/4.95 tff(24918,plain,
% 4.74/4.95 (r(s(elem!1), s(s(z)))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[421, 24917, 23849])).
% 4.74/4.95 tff(24919,plain,
% 4.74/4.95 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[390, 24918, 224])).
% 4.74/4.95 tff(24920,plain,
% 4.74/4.95 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[395, 24919, 24909])).
% 4.74/4.95 tff(24921,plain,
% 4.74/4.95 (b(s(elem!1), s(s(s(elem!1))))),
% 4.74/4.95 inference(modus_ponens,[status(thm)],[24920, 24905])).
% 4.74/4.95 tff(24922,plain,
% 4.74/4.95 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(elem!1), s(s(z)))))),
% 4.74/4.95 inference(rewrite,[status(thm)],[])).
% 4.74/4.95 tff(24923,plain,
% 4.74/4.95 (((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(elem!1), s(s(z)))))),
% 4.74/4.95 inference(rewrite,[status(thm)],[])).
% 4.74/4.95 tff(24924,plain,
% 4.74/4.95 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(elem!1), s(s(z))))))),
% 4.74/4.95 inference(monotonicity,[status(thm)],[24923])).
% 4.74/4.95 tff(24925,plain,
% 4.74/4.95 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(elem!1), s(s(z)))))),
% 4.74/4.95 inference(transitivity,[status(thm)],[24924, 24922])).
% 4.74/4.95 tff(24926,plain,
% 4.74/4.95 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 4.74/4.95 inference(quant_inst,[status(thm)],[])).
% 4.74/4.95 tff(24927,plain,
% 4.74/4.95 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(elem!1), s(s(z))))),
% 4.74/4.95 inference(modus_ponens,[status(thm)],[24926, 24925])).
% 4.74/4.95 tff(24928,plain,
% 4.74/4.95 (~r(s(s(s(elem!1))), s(elem!1))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[24927, 118, 24918, 3859])).
% 4.74/4.95 tff(24929,plain,
% 4.74/4.95 (b(s(s(s(elem!1))), s(elem!1))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[373, 24928, 356])).
% 4.74/4.95 tff(24930,plain,
% 4.74/4.95 ($false),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[22815, 178, 24929, 855, 2043, 7976, 24921])).
% 4.74/4.95 tff(24931,plain,((~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~(s(s(s(s(z)))) = elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.95 tff(24932,plain,
% 4.74/4.95 (~b(z, s(elem!1))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[24931, 24882, 24903, 24881, 24901, 24867, 224, 24900, 24873, 273])).
% 4.74/4.95 tff(24933,plain,
% 4.74/4.95 (r(z, s(elem!1))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[2351, 24932])).
% 4.74/4.95 tff(24934,plain,
% 4.74/4.95 (~r(elem!1, s(elem!1))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[12189, 24933, 437])).
% 4.74/4.95 tff(24935,plain,
% 4.74/4.95 (b(elem!1, s(elem!1))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[756, 24934, 24870])).
% 4.74/4.95 tff(24936,plain,
% 4.74/4.95 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(z))), elem!1)),
% 4.74/4.95 inference(monotonicity,[status(thm)],[24867])).
% 4.74/4.95 tff(24937,plain,
% 4.74/4.95 (b(s(s(s(z))), elem!1)),
% 4.74/4.95 inference(modus_ponens,[status(thm)],[24655, 24936])).
% 4.74/4.95 tff(24938,plain,
% 4.74/4.95 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 4.74/4.95 inference(monotonicity,[status(thm)],[24867])).
% 4.74/4.95 tff(24939,plain,
% 4.74/4.95 (~b(s(s(s(z))), s(s(z)))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[4963, 194, 273, 24641, 24655, 24644])).
% 4.74/4.95 tff(24940,plain,
% 4.74/4.95 (r(s(s(s(z))), s(s(z)))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[4966, 24939])).
% 4.74/4.95 tff(24941,plain,
% 4.74/4.95 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[1175, 118, 24940, 15765])).
% 4.74/4.95 tff(24942,plain,
% 4.74/4.95 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 24941])).
% 4.74/4.95 tff(24943,plain,
% 4.74/4.95 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[8218, 24940, 15765])).
% 4.74/4.95 tff(24944,plain,
% 4.74/4.95 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[20667, 24943])).
% 4.74/4.95 tff(24945,plain,
% 4.74/4.95 (~b(z, s(s(s(z))))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[24674, 178, 24649, 24647, 24944, 24942])).
% 4.74/4.95 tff(24946,plain,
% 4.74/4.95 (r(z, s(s(s(z))))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[4920, 24945])).
% 4.74/4.95 tff(24947,plain,
% 4.74/4.95 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[4961, 24946, 194])).
% 4.74/4.95 tff(24948,plain,
% 4.74/4.95 (b(s(s(s(s(z)))), s(s(s(z))))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[11185, 24947])).
% 4.74/4.95 tff(24949,plain,
% 4.74/4.95 (b(elem!1, s(s(s(z))))),
% 4.74/4.95 inference(modus_ponens,[status(thm)],[24948, 24938])).
% 4.74/4.95 tff(24950,plain,
% 4.74/4.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 4.74/4.95 inference(rewrite,[status(thm)],[])).
% 4.74/4.95 tff(24951,plain,
% 4.74/4.95 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 4.74/4.95 inference(rewrite,[status(thm)],[])).
% 4.74/4.95 tff(24952,plain,
% 4.74/4.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))))),
% 4.74/4.95 inference(monotonicity,[status(thm)],[24951])).
% 4.74/4.95 tff(24953,plain,
% 4.74/4.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 4.74/4.95 inference(transitivity,[status(thm)],[24952, 24950])).
% 4.74/4.95 tff(24954,plain,
% 4.74/4.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(elem!1))))),
% 4.74/4.95 inference(quant_inst,[status(thm)],[])).
% 4.74/4.95 tff(24955,plain,
% 4.74/4.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))),
% 4.74/4.95 inference(modus_ponens,[status(thm)],[24954, 24953])).
% 4.74/4.95 tff(24956,plain,
% 4.74/4.95 ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(z)))))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[24955, 178, 24900, 24949, 24937])).
% 4.74/4.95 tff(24957,plain,
% 4.74/4.95 (~b(s(elem!1), s(s(s(z))))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[24956, 24935])).
% 4.74/4.95 tff(24958,plain,
% 4.74/4.95 (r(s(elem!1), s(s(s(z))))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[23881, 41, 23437, 24957])).
% 4.74/4.95 tff(24959,plain,
% 4.74/4.95 (~(s(elem!1) = s(s(z)))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[11438, 24871])).
% 4.74/4.95 tff(24960,plain,
% 4.74/4.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))))),
% 4.74/4.95 inference(rewrite,[status(thm)],[])).
% 4.74/4.95 tff(24961,plain,
% 4.74/4.95 (((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))))),
% 4.74/4.95 inference(rewrite,[status(thm)],[])).
% 4.74/4.95 tff(24962,plain,
% 4.74/4.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z))))))),
% 4.74/4.95 inference(monotonicity,[status(thm)],[24961])).
% 4.74/4.95 tff(24963,plain,
% 4.74/4.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))))),
% 4.74/4.95 inference(transitivity,[status(thm)],[24962, 24960])).
% 4.74/4.95 tff(24964,plain,
% 4.74/4.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(elem!1))))),
% 4.74/4.95 inference(quant_inst,[status(thm)],[])).
% 4.74/4.95 tff(24965,plain,
% 4.74/4.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z))))),
% 4.74/4.95 inference(modus_ponens,[status(thm)],[24964, 24963])).
% 4.74/4.95 tff(24966,plain,
% 4.74/4.95 ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z))))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[24965, 178, 24900, 24873, 812])).
% 4.74/4.95 tff(24967,plain,
% 4.74/4.95 (~b(s(elem!1), s(s(z)))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[24966, 24935])).
% 4.74/4.95 tff(24968,plain,
% 4.74/4.95 (r(s(elem!1), s(s(z)))),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[421, 24967, 24959])).
% 4.74/4.95 tff(24969,plain,
% 4.74/4.95 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(elem!1), s(s(s(z))))))),
% 4.74/4.95 inference(rewrite,[status(thm)],[])).
% 4.74/4.95 tff(24970,plain,
% 4.74/4.95 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(s(s(z)))))) <=> ((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(elem!1), s(s(s(z))))))),
% 4.74/4.95 inference(rewrite,[status(thm)],[])).
% 4.74/4.95 tff(24971,plain,
% 4.74/4.95 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(elem!1), s(s(s(z)))))))),
% 4.74/4.95 inference(monotonicity,[status(thm)],[24970])).
% 4.74/4.95 tff(24972,plain,
% 4.74/4.95 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(elem!1), s(s(s(z))))))),
% 4.74/4.95 inference(transitivity,[status(thm)],[24971, 24969])).
% 4.74/4.95 tff(24973,plain,
% 4.74/4.95 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(s(s(z))))))),
% 4.74/4.95 inference(quant_inst,[status(thm)],[])).
% 4.74/4.95 tff(24974,plain,
% 4.74/4.95 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(elem!1), s(s(s(z)))))),
% 4.74/4.95 inference(modus_ponens,[status(thm)],[24973, 24972])).
% 4.74/4.95 tff(24975,plain,
% 4.74/4.95 ($false),
% 4.74/4.95 inference(unit_resolution,[status(thm)],[24974, 118, 24968, 24940, 24958])).
% 4.74/4.95 tff(24976,plain,((~r(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (z = elem!1) | (s(s(z)) = elem!1) | b(s(s(s(s(s(s(s(z))))))), s(s(z))) | b(z, s(s(s(s(z))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.95 tff(24977,plain,
% 4.74/4.95 (~r(elem!1, z)),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[24976, 24862, 24652, 273, 318, 12, 24650, 1, 24646])).
% 4.74/4.96 tff(24978,plain,
% 4.74/4.96 (b(elem!1, z)),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[498, 24977, 290])).
% 4.74/4.96 tff(24979,plain,
% 4.74/4.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 4.74/4.96 inference(rewrite,[status(thm)],[])).
% 4.74/4.96 tff(24980,plain,
% 4.74/4.96 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 4.74/4.96 inference(rewrite,[status(thm)],[])).
% 4.74/4.96 tff(24981,plain,
% 4.74/4.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 4.74/4.96 inference(monotonicity,[status(thm)],[24980])).
% 4.74/4.96 tff(24982,plain,
% 4.74/4.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 4.74/4.96 inference(transitivity,[status(thm)],[24981, 24979])).
% 4.74/4.96 tff(24983,plain,
% 4.74/4.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 4.74/4.96 inference(quant_inst,[status(thm)],[])).
% 4.74/4.96 tff(24984,plain,
% 4.74/4.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 4.74/4.96 inference(modus_ponens,[status(thm)],[24983, 24982])).
% 4.74/4.96 tff(24985,plain,
% 4.74/4.96 ((~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[24984, 178, 273, 24862, 24647])).
% 4.74/4.96 tff(24986,plain,
% 4.74/4.96 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[24985, 24978])).
% 4.74/4.96 tff(24987,plain,
% 4.74/4.96 ((~b(elem!1, z)) | (~b(s(s(z)), elem!1))),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[19870, 178, 5619, 273, 24862])).
% 4.74/4.96 tff(24988,plain,
% 4.74/4.96 (~b(s(s(z)), elem!1)),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[24987, 24978])).
% 4.74/4.96 tff(24989,plain,
% 4.74/4.96 (r(s(s(z)), elem!1)),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[448, 24988, 12])).
% 4.74/4.96 tff(24990,plain,
% 4.74/4.96 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[17566, 24989, 24662])).
% 4.74/4.96 tff(24991,plain,
% 4.74/4.96 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[3444, 24990, 24986])).
% 4.74/4.96 tff(24992,plain,
% 4.74/4.96 (b(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> b(elem!1, s(s(z)))),
% 4.74/4.96 inference(monotonicity,[status(thm)],[24991])).
% 4.74/4.96 tff(24993,plain,
% 4.74/4.96 (b(elem!1, s(s(z))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.74/4.96 inference(symmetry,[status(thm)],[24992])).
% 4.74/4.96 tff(24994,plain,
% 4.74/4.96 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.74/4.96 inference(modus_ponens,[status(thm)],[24862, 24993])).
% 4.74/4.96 tff(24995,plain,
% 4.74/4.96 ($false),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[24650, 24994])).
% 4.74/4.96 tff(24996,plain,((s(s(z)) = elem!1) | (~b(z, s(s(z)))) | (elem!1 = z) | b(z, s(s(s(s(z))))) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 4.74/4.96 tff(24997,plain,
% 4.74/4.96 (s(s(z)) = elem!1),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[24996, 290, 144, 1, 5618])).
% 4.74/4.96 tff(24998,plain,
% 4.74/4.96 (b(elem!1, s(s(s(s(z)))))),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[17989, 24997, 24641])).
% 4.74/4.96 tff(24999,plain,
% 4.74/4.96 (~r(z, elem!1)),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[18165, 24997, 48])).
% 4.74/4.96 tff(25000,plain,
% 4.74/4.96 (b(z, elem!1)),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[585, 24999, 318])).
% 4.74/4.96 tff(25001,plain,
% 4.74/4.96 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[20718, 5619, 24649, 24647, 144])).
% 4.74/4.96 tff(25002,plain,
% 4.74/4.96 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[249, 25001])).
% 4.74/4.96 tff(25003,plain,
% 4.74/4.96 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[11305, 24997, 25002])).
% 4.74/4.96 tff(25004,plain,
% 4.74/4.96 (~r(s(s(z)), elem!1)),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[2803, 25003, 25002])).
% 4.74/4.96 tff(25005,plain,
% 4.74/4.96 ($false),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[18160, 25004, 25000, 24649, 144, 24640, 24639, 24641, 5619, 1, 3340, 24998])).
% 4.74/4.96 tff(25006,plain,((elem!1 = z) | b(z, s(s(s(s(z))))) | r(z, s(s(z))) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 4.74/4.96 tff(25007,plain,
% 4.74/4.96 (elem!1 = z),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[25006, 5618, 48, 1])).
% 4.74/4.96 tff(25008,plain,
% 4.74/4.96 (z = elem!1),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[2808, 25007])).
% 4.74/4.96 tff(25009,plain,
% 4.74/4.96 (~b(s(s(s(s(elem!1)))), z)),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[5184, 25008, 24642])).
% 4.74/4.96 tff(25010,plain,
% 4.74/4.96 (r(s(s(s(s(elem!1)))), z)),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[1716, 25009])).
% 4.74/4.96 tff(25011,plain,
% 4.74/4.96 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[22651, 25010, 24594])).
% 4.74/4.96 tff(25012,plain,
% 4.74/4.96 (s(elem!1) = s(z)),
% 4.74/4.96 inference(monotonicity,[status(thm)],[25007])).
% 4.74/4.96 tff(25013,plain,
% 4.74/4.96 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(z), s(s(s(s(z)))))),
% 4.74/4.96 inference(monotonicity,[status(thm)],[25012])).
% 4.74/4.96 tff(25014,plain,
% 4.74/4.96 (b(s(z), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 4.74/4.96 inference(symmetry,[status(thm)],[25013])).
% 4.74/4.96 tff(25015,plain,
% 4.74/4.96 ((~b(s(z), s(s(s(s(z)))))) <=> (~b(s(elem!1), s(s(s(s(z))))))),
% 4.74/4.96 inference(monotonicity,[status(thm)],[25014])).
% 4.74/4.96 tff(25016,plain,
% 4.74/4.96 (s(z) = s(elem!1)),
% 4.74/4.96 inference(symmetry,[status(thm)],[25012])).
% 4.74/4.96 tff(25017,plain,
% 4.74/4.96 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), s(elem!1))),
% 4.74/4.96 inference(monotonicity,[status(thm)],[25016])).
% 4.74/4.96 tff(25018,plain,
% 4.74/4.96 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(z))),
% 4.74/4.96 inference(symmetry,[status(thm)],[25017])).
% 4.74/4.96 tff(25019,plain,
% 4.74/4.96 (s(s(elem!1)) = s(s(z))),
% 4.74/4.96 inference(monotonicity,[status(thm)],[25012])).
% 4.74/4.96 tff(25020,plain,
% 4.74/4.96 (s(s(s(elem!1))) = s(s(s(z)))),
% 4.74/4.96 inference(monotonicity,[status(thm)],[25019])).
% 4.74/4.96 tff(25021,plain,
% 4.74/4.96 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(elem!1))),
% 4.74/4.96 inference(monotonicity,[status(thm)],[25020])).
% 4.74/4.96 tff(25022,plain,
% 4.74/4.96 (s(s(s(z))) = s(s(s(elem!1)))),
% 4.74/4.96 inference(symmetry,[status(thm)],[25020])).
% 4.74/4.96 tff(25023,plain,
% 4.74/4.96 ((s(elem!1) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 4.74/4.96 inference(monotonicity,[status(thm)],[25022])).
% 4.74/4.96 tff(25024,plain,
% 4.74/4.96 ((s(elem!1) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 4.74/4.96 inference(transitivity,[status(thm)],[25023, 3881])).
% 4.74/4.96 tff(25025,plain,
% 4.74/4.96 ((~(s(elem!1) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 4.74/4.96 inference(monotonicity,[status(thm)],[25024])).
% 4.74/4.96 tff(25026,plain,
% 4.74/4.96 (~b(elem!1, s(s(s(s(z)))))),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[5204, 25007, 1])).
% 4.74/4.96 tff(25027,plain,
% 4.74/4.96 (~(s(s(z)) = elem!1)),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[17989, 25026, 24641])).
% 4.74/4.96 tff(25028,plain,
% 4.74/4.96 (~(s(elem!1) = s(s(s(z))))),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[23436, 25027])).
% 4.74/4.96 tff(25029,plain,
% 4.74/4.96 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.74/4.96 inference(modus_ponens,[status(thm)],[25028, 25025])).
% 4.74/4.96 tff(25030,plain,
% 4.74/4.96 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 4.74/4.96 inference(monotonicity,[status(thm)],[25019])).
% 4.74/4.96 tff(25031,plain,
% 4.74/4.96 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 4.74/4.96 inference(symmetry,[status(thm)],[25030])).
% 4.74/4.96 tff(25032,plain,
% 4.74/4.96 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 4.74/4.96 inference(monotonicity,[status(thm)],[25022])).
% 4.74/4.96 tff(25033,plain,
% 4.74/4.96 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 4.74/4.96 inference(transitivity,[status(thm)],[25032, 25031])).
% 4.74/4.96 tff(25034,plain,
% 4.74/4.96 (r(s(s(s(s(z)))), z)),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[191, 24642])).
% 4.74/4.96 tff(25035,plain,
% 4.74/4.96 (~b(s(s(s(z))), s(s(z)))),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[4963, 25034, 144, 24641, 24655, 24639])).
% 4.74/4.96 tff(25036,plain,
% 4.74/4.96 (r(s(s(s(z))), s(s(z)))),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[4966, 25035])).
% 4.74/4.96 tff(25037,plain,
% 4.74/4.96 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 4.74/4.96 inference(modus_ponens,[status(thm)],[25036, 25033])).
% 4.74/4.96 tff(25038,plain,
% 4.74/4.96 ((s(s(elem!1)) = elem!1) <=> (s(s(elem!1)) = z)),
% 4.74/4.96 inference(monotonicity,[status(thm)],[25007])).
% 4.74/4.96 tff(25039,plain,
% 4.74/4.96 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 4.74/4.96 inference(symmetry,[status(thm)],[25038])).
% 4.74/4.96 tff(25040,plain,
% 4.74/4.96 ((~(s(s(elem!1)) = z)) <=> (~(s(s(elem!1)) = elem!1))),
% 4.74/4.96 inference(monotonicity,[status(thm)],[25039])).
% 4.74/4.96 tff(25041,plain,
% 4.74/4.96 (~(s(s(elem!1)) = elem!1)),
% 4.74/4.96 inference(modus_ponens,[status(thm)],[970, 25040])).
% 4.74/4.96 tff(25042,plain,
% 4.74/4.96 (~(s(elem!1) = s(s(elem!1)))),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[979, 25041])).
% 4.74/4.96 tff(25043,plain,
% 4.74/4.96 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(z))))),
% 4.74/4.96 inference(monotonicity,[status(thm)],[25020])).
% 4.74/4.96 tff(25044,plain,
% 4.74/4.96 (r(z, s(s(s(z)))) <=> r(z, s(s(s(elem!1))))),
% 4.74/4.96 inference(symmetry,[status(thm)],[25043])).
% 4.74/4.96 tff(25045,plain,
% 4.74/4.96 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[4091, 178, 5619, 144, 24649, 24647])).
% 4.74/4.96 tff(25046,plain,
% 4.74/4.96 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[3578, 25045])).
% 4.74/4.96 tff(25047,plain,
% 4.74/4.96 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[1175, 118, 25036, 25046])).
% 4.74/4.96 tff(25048,plain,
% 4.74/4.96 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 25047])).
% 4.74/4.96 tff(25049,plain,
% 4.74/4.96 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[8218, 25036, 25046])).
% 4.74/4.96 tff(25050,plain,
% 4.74/4.96 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[20667, 25049])).
% 4.74/4.96 tff(25051,plain,
% 4.74/4.96 (~b(z, s(s(s(z))))),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[24674, 178, 24649, 24647, 25050, 25048])).
% 4.74/4.96 tff(25052,plain,
% 4.74/4.96 (r(z, s(s(s(z))))),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[4920, 25051])).
% 4.74/4.96 tff(25053,plain,
% 4.74/4.96 (r(z, s(s(s(elem!1))))),
% 4.74/4.96 inference(modus_ponens,[status(thm)],[25052, 25044])).
% 4.74/4.96 tff(25054,plain,
% 4.74/4.96 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 4.74/4.96 inference(monotonicity,[status(thm)],[25019])).
% 4.74/4.96 tff(25055,plain,
% 4.74/4.96 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.74/4.96 inference(symmetry,[status(thm)],[25054])).
% 4.74/4.96 tff(25056,plain,
% 4.74/4.96 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 4.74/4.96 inference(monotonicity,[status(thm)],[25022])).
% 4.74/4.96 tff(25057,plain,
% 4.74/4.96 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.74/4.96 inference(transitivity,[status(thm)],[25056, 25055])).
% 4.74/4.96 tff(25058,plain,
% 4.74/4.96 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[4961, 25052, 25034])).
% 4.74/4.96 tff(25059,plain,
% 4.74/4.96 (b(s(s(s(s(z)))), s(s(s(z))))),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[11185, 25058])).
% 4.74/4.96 tff(25060,plain,
% 4.74/4.96 (~b(s(s(z)), s(s(s(z))))),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[1293, 178, 24641, 24639, 24655, 25059])).
% 4.74/4.96 tff(25061,plain,
% 4.74/4.96 (r(s(s(z)), s(s(s(z))))),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[5088, 25060])).
% 4.74/4.96 tff(25062,plain,
% 4.74/4.96 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.74/4.96 inference(modus_ponens,[status(thm)],[25061, 25057])).
% 4.74/4.96 tff(25063,plain,
% 4.74/4.96 (~r(s(elem!1), s(s(elem!1)))),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[5980, 1551, 5227])).
% 4.74/4.96 tff(25064,plain,
% 4.74/4.96 (b(s(elem!1), s(s(elem!1)))),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[1028, 25063, 984])).
% 4.74/4.96 tff(25065,plain,
% 4.74/4.96 (~r(s(s(elem!1)), s(elem!1))),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[15350, 1551, 3364])).
% 4.74/4.96 tff(25066,plain,
% 4.74/4.96 (b(s(s(elem!1)), s(elem!1))),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[1006, 25065, 11563])).
% 4.74/4.96 tff(25067,plain,
% 4.74/4.96 (b(z, s(s(elem!1)))),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[6469, 41, 6466, 11578])).
% 4.74/4.96 tff(25068,plain,
% 4.74/4.96 (~r(z, s(elem!1))),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[5447, 1551, 557])).
% 4.74/4.96 tff(25069,plain,
% 4.74/4.96 (b(z, s(elem!1))),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[2351, 25068])).
% 4.74/4.96 tff(25070,plain,
% 4.74/4.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 4.74/4.96 inference(rewrite,[status(thm)],[])).
% 4.74/4.96 tff(25071,plain,
% 4.74/4.96 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 4.74/4.96 inference(rewrite,[status(thm)],[])).
% 4.74/4.96 tff(25072,plain,
% 4.74/4.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1))))))),
% 4.74/4.96 inference(monotonicity,[status(thm)],[25071])).
% 4.74/4.96 tff(25073,plain,
% 4.74/4.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 4.74/4.96 inference(transitivity,[status(thm)],[25072, 25070])).
% 4.74/4.96 tff(25074,plain,
% 4.74/4.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)))),
% 4.74/4.96 inference(quant_inst,[status(thm)],[])).
% 4.74/4.96 tff(25075,plain,
% 4.74/4.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1))))),
% 4.74/4.96 inference(modus_ponens,[status(thm)],[25074, 25073])).
% 4.74/4.96 tff(25076,plain,
% 4.74/4.96 ($false),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[25075, 178, 25069, 11588, 25067, 25066, 25064])).
% 4.74/4.96 tff(25077,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (s(elem!1) = s(s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.96 tff(25078,plain,
% 4.74/4.96 (~r(s(s(s(elem!1))), s(elem!1))),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[25077, 25062, 25053, 25042, 25037])).
% 4.74/4.96 tff(25079,plain,
% 4.74/4.96 (b(s(s(s(elem!1))), s(elem!1))),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[373, 25078, 25029])).
% 4.74/4.96 tff(25080,plain,
% 4.74/4.96 (b(s(s(s(z))), s(elem!1))),
% 4.74/4.96 inference(modus_ponens,[status(thm)],[25079, 25021])).
% 4.74/4.96 tff(25081,plain,
% 4.74/4.96 (b(s(s(s(z))), s(z))),
% 4.74/4.96 inference(modus_ponens,[status(thm)],[25080, 25018])).
% 4.74/4.96 tff(25082,plain,
% 4.74/4.96 ((s(elem!1) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 4.74/4.96 inference(transitivity,[status(thm)],[25024, 7104])).
% 4.74/4.96 tff(25083,plain,
% 4.74/4.96 ((~(s(elem!1) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 4.74/4.96 inference(monotonicity,[status(thm)],[25082])).
% 4.74/4.96 tff(25084,plain,
% 4.74/4.96 (~(s(elem!1) = s(s(s(elem!1))))),
% 4.74/4.96 inference(modus_ponens,[status(thm)],[25028, 25083])).
% 4.74/4.96 tff(25085,plain,
% 4.74/4.96 (~r(s(elem!1), s(s(s(elem!1))))),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[11597, 25062, 25053, 25042])).
% 4.74/4.96 tff(25086,plain,
% 4.74/4.96 (b(s(elem!1), s(s(s(elem!1))))),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[5432, 25085, 25084])).
% 4.74/4.96 tff(25087,plain,
% 4.74/4.96 (b(s(z), s(s(s(z))))),
% 4.74/4.96 inference(modus_ponens,[status(thm)],[5888, 12745])).
% 4.74/4.96 tff(25088,assumption,(~b(s(z), s(s(s(z))))), introduced(assumption)).
% 4.74/4.96 tff(25089,plain,
% 4.74/4.96 ($false),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[25088, 25087])).
% 4.74/4.96 tff(25090,plain,(b(s(z), s(s(s(z)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.96 tff(25091,plain,
% 4.74/4.96 (b(s(z), s(s(s(z))))),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[25090, 25086, 25007])).
% 4.74/4.96 tff(25092,plain,
% 4.74/4.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 4.74/4.96 inference(rewrite,[status(thm)],[])).
% 4.74/4.96 tff(25093,plain,
% 4.74/4.96 (((~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(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 4.74/4.96 inference(rewrite,[status(thm)],[])).
% 4.74/4.96 tff(25094,plain,
% 4.74/4.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 4.74/4.96 inference(monotonicity,[status(thm)],[25093])).
% 4.74/4.96 tff(25095,plain,
% 4.74/4.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 4.74/4.96 inference(transitivity,[status(thm)],[25094, 25092])).
% 4.74/4.96 tff(25096,plain,
% 4.74/4.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 4.74/4.96 inference(quant_inst,[status(thm)],[])).
% 4.74/4.96 tff(25097,plain,
% 4.74/4.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 4.74/4.96 inference(modus_ponens,[status(thm)],[25096, 25095])).
% 4.74/4.96 tff(25098,plain,
% 4.74/4.96 ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[25097, 178, 24655, 25059, 25091])).
% 4.74/4.96 tff(25099,plain,
% 4.74/4.96 (~b(s(z), s(s(s(s(z)))))),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[25098, 25081])).
% 4.74/4.96 tff(25100,plain,
% 4.74/4.96 (~b(s(elem!1), s(s(s(s(z)))))),
% 4.74/4.96 inference(modus_ponens,[status(thm)],[25099, 25015])).
% 4.74/4.96 tff(25101,plain,
% 4.74/4.96 (r(s(elem!1), s(s(s(s(z)))))),
% 4.74/4.96 inference(unit_resolution,[status(thm)],[1084, 25100, 25011])).
% 4.74/4.96 tff(25102,plain,
% 4.74/4.96 ((s(s(s(s(s(s(s(z))))))) = s(z)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 4.74/4.96 inference(monotonicity,[status(thm)],[25016])).
% 4.74/4.96 tff(25103,plain,
% 4.74/4.96 ((s(s(s(s(s(s(s(z))))))) = s(z)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.74/4.96 inference(transitivity,[status(thm)],[25102, 377])).
% 4.74/4.96 tff(25104,plain,
% 4.74/4.96 ((~(s(s(s(s(s(s(s(z))))))) = s(z))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 4.74/4.96 inference(monotonicity,[status(thm)],[25103])).
% 4.74/4.96 tff(25105,plain,
% 4.74/4.96 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.74/4.96 inference(modus_ponens,[status(thm)],[612, 25104])).
% 4.74/4.96 tff(25106,plain,
% 4.74/4.96 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(z), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.96 inference(monotonicity,[status(thm)],[25012])).
% 4.74/4.96 tff(25107,plain,
% 4.74/4.96 (b(s(z), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.96 inference(symmetry,[status(thm)],[25106])).
% 4.74/4.96 tff(25108,plain,
% 4.74/4.96 ((~b(s(z), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 4.74/4.96 inference(monotonicity,[status(thm)],[25107])).
% 4.74/4.96 tff(25109,plain,
% 4.74/4.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 4.74/4.96 inference(rewrite,[status(thm)],[])).
% 4.74/4.97 tff(25110,plain,
% 4.74/4.97 (((~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(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 4.74/4.97 inference(rewrite,[status(thm)],[])).
% 4.74/4.97 tff(25111,plain,
% 4.74/4.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 4.74/4.97 inference(monotonicity,[status(thm)],[25110])).
% 4.74/4.97 tff(25112,plain,
% 4.74/4.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 4.74/4.97 inference(transitivity,[status(thm)],[25111, 25109])).
% 4.74/4.97 tff(25113,plain,
% 4.74/4.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))))),
% 4.74/4.97 inference(quant_inst,[status(thm)],[])).
% 4.74/4.97 tff(25114,plain,
% 4.74/4.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 4.74/4.97 inference(modus_ponens,[status(thm)],[25113, 25112])).
% 4.74/4.97 tff(25115,plain,
% 4.74/4.97 ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z)))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[25114, 178, 25050, 25048, 25091])).
% 4.74/4.97 tff(25116,plain,
% 4.74/4.97 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[25115, 25081])).
% 4.74/4.97 tff(25117,plain,
% 4.74/4.97 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.97 inference(modus_ponens,[status(thm)],[25116, 25108])).
% 4.74/4.97 tff(25118,plain,
% 4.74/4.97 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[395, 25117, 25105])).
% 4.74/4.97 tff(25119,plain,
% 4.74/4.97 ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[5568, 24592])).
% 4.74/4.97 tff(25120,plain,
% 4.74/4.97 ($false),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[25119, 25118, 25101])).
% 4.74/4.97 tff(25121,plain,(r(s(s(z)), z) | b(z, s(s(s(s(z))))) | r(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.97 tff(25122,plain,
% 4.74/4.97 (r(s(s(z)), z)),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[25121, 48, 1])).
% 4.74/4.97 tff(25123,plain,
% 4.74/4.97 (~r(s(s(s(z))), z)),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[24618, 106, 145, 273])).
% 4.74/4.97 tff(25124,plain,
% 4.74/4.97 (b(s(s(s(z))), z)),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[21073, 25123])).
% 4.74/4.97 tff(25125,plain,
% 4.74/4.97 (~r(s(s(s(s(z)))), s(s(z)))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[24637, 273, 145])).
% 4.74/4.97 tff(25126,plain,
% 4.74/4.97 (b(s(s(s(s(z)))), s(s(z)))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[102, 25125])).
% 4.74/4.97 tff(25127,plain,
% 4.74/4.97 ($false),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[20778, 178, 273, 168, 202, 1126, 1127])).
% 4.74/4.97 tff(25128,plain,((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.97 tff(25129,plain,
% 4.74/4.97 (~b(s(s(s(s(z)))), z)),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[25128, 273, 25126, 24604, 25124])).
% 4.74/4.97 tff(25130,plain,
% 4.74/4.97 (r(s(s(s(s(z)))), z)),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[191, 25129])).
% 4.74/4.97 tff(25131,plain,
% 4.74/4.97 (r(s(s(z)), z) <=> r(s(s(z)), elem!1)),
% 4.74/4.97 inference(monotonicity,[status(thm)],[13])).
% 4.74/4.97 tff(25132,plain,
% 4.74/4.97 (r(s(s(z)), elem!1)),
% 4.74/4.97 inference(modus_ponens,[status(thm)],[106, 25131])).
% 4.74/4.97 tff(25133,plain,
% 4.74/4.97 (~r(z, s(s(s(z))))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[10735, 25132, 145, 25126, 5198, 24607, 25130])).
% 4.74/4.97 tff(25134,plain,
% 4.74/4.97 (b(z, s(s(s(z))))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[4920, 25133])).
% 4.74/4.97 tff(25135,plain,
% 4.74/4.97 ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[1319, 178, 24623, 24625, 25124])).
% 4.74/4.97 tff(25136,plain,
% 4.74/4.97 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[25135, 25134])).
% 4.74/4.97 tff(25137,plain,
% 4.74/4.97 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[20667, 25136])).
% 4.74/4.97 tff(25138,plain,
% 4.74/4.97 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[21219, 25137, 5198])).
% 4.74/4.97 tff(25139,plain,
% 4.74/4.97 (r(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.97 inference(monotonicity,[status(thm)],[15])).
% 4.74/4.97 tff(25140,plain,
% 4.74/4.97 (~b(s(s(s(z))), s(s(z)))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[4963, 25130, 273, 24607, 24604, 25126])).
% 4.74/4.97 tff(25141,plain,
% 4.74/4.97 (r(s(s(s(z))), s(s(z)))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[4966, 25140])).
% 4.74/4.97 tff(25142,plain,
% 4.74/4.97 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[8218, 25137, 25141])).
% 4.74/4.97 tff(25143,plain,
% 4.74/4.97 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[3578, 25142])).
% 4.74/4.97 tff(25144,plain,
% 4.74/4.97 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[1154, 25143, 24625, 24623, 273])).
% 4.74/4.97 tff(25145,plain,
% 4.74/4.97 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[249, 25144])).
% 4.74/4.97 tff(25146,plain,
% 4.74/4.97 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.97 inference(modus_ponens,[status(thm)],[25145, 25139])).
% 4.74/4.97 tff(25147,plain,
% 4.74/4.97 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 4.74/4.97 inference(monotonicity,[status(thm)],[16, 15])).
% 4.74/4.97 tff(25148,plain,
% 4.74/4.97 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 4.74/4.97 inference(modus_ponens,[status(thm)],[25141, 25147])).
% 4.74/4.97 tff(25149,plain,
% 4.74/4.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~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))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~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))))))))))),
% 4.74/4.97 inference(rewrite,[status(thm)],[])).
% 4.74/4.97 tff(25150,plain,
% 4.74/4.97 (((~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(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 4.74/4.97 inference(rewrite,[status(thm)],[])).
% 4.74/4.97 tff(25151,plain,
% 4.74/4.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~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)))))))))))),
% 4.74/4.97 inference(monotonicity,[status(thm)],[25150])).
% 4.74/4.97 tff(25152,plain,
% 4.74/4.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~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))))))))))),
% 4.74/4.97 inference(transitivity,[status(thm)],[25151, 25149])).
% 4.74/4.97 tff(25153,plain,
% 4.74/4.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(s(elem!1))), s(s(elem!1)))))),
% 4.74/4.97 inference(quant_inst,[status(thm)],[])).
% 4.74/4.97 tff(25154,plain,
% 4.74/4.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 4.74/4.97 inference(modus_ponens,[status(thm)],[25153, 25152])).
% 4.74/4.97 tff(25155,plain,
% 4.74/4.97 ($false),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[25154, 118, 25148, 25146, 25138])).
% 4.74/4.97 tff(25156,plain,((~(z = elem!1)) | (~b(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.97 tff(25157,plain,
% 4.74/4.97 (~(z = elem!1)),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[25156, 144, 47, 25122])).
% 4.74/4.97 tff(25158,plain,
% 4.74/4.97 (~b(s(elem!1), s(s(s(s(z)))))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[2756, 1060, 167, 319, 106, 273, 307, 1070])).
% 4.74/4.97 tff(25159,plain,
% 4.74/4.97 (r(s(elem!1), s(s(s(s(z)))))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[1084, 25158, 1369])).
% 4.74/4.97 tff(25160,plain,
% 4.74/4.97 (~r(z, s(elem!1))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[2766, 25159, 145])).
% 4.74/4.97 tff(25161,plain,
% 4.74/4.97 (b(z, s(elem!1))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[2351, 25160])).
% 4.74/4.97 tff(25162,plain,
% 4.74/4.97 (b(z, s(s(s(s(s(z))))))),
% 4.74/4.97 inference(modus_ponens,[status(thm)],[25161, 2310])).
% 4.74/4.97 tff(25163,plain,
% 4.74/4.97 (~r(s(elem!1), z)),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[916, 25159, 194])).
% 4.74/4.97 tff(25164,plain,
% 4.74/4.97 (~r(s(s(s(s(s(z))))), z)),
% 4.74/4.97 inference(modus_ponens,[status(thm)],[25163, 2313])).
% 4.74/4.97 tff(25165,plain,
% 4.74/4.97 (b(s(s(s(s(s(z))))), z)),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[410, 41, 242, 25164])).
% 4.74/4.97 tff(25166,plain,
% 4.74/4.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 4.74/4.97 inference(rewrite,[status(thm)],[])).
% 4.74/4.97 tff(25167,plain,
% 4.74/4.97 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 4.74/4.97 inference(rewrite,[status(thm)],[])).
% 4.74/4.97 tff(25168,plain,
% 4.74/4.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 4.74/4.97 inference(monotonicity,[status(thm)],[25167])).
% 4.74/4.97 tff(25169,plain,
% 4.74/4.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 4.74/4.97 inference(transitivity,[status(thm)],[25168, 25166])).
% 4.74/4.97 tff(25170,plain,
% 4.74/4.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 4.74/4.97 inference(quant_inst,[status(thm)],[])).
% 4.74/4.97 tff(25171,plain,
% 4.74/4.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 4.74/4.97 inference(modus_ponens,[status(thm)],[25170, 25169])).
% 4.74/4.97 tff(25172,plain,
% 4.74/4.97 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[25171, 178, 289, 25165, 25162, 146])).
% 4.74/4.97 tff(25173,plain,
% 4.74/4.97 (~b(s(elem!1), s(s(s(elem!1))))),
% 4.74/4.97 inference(modus_ponens,[status(thm)],[25172, 22902])).
% 4.74/4.97 tff(25174,plain,
% 4.74/4.97 (b(s(elem!1), z)),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[774, 25163])).
% 4.74/4.97 tff(25175,plain,
% 4.74/4.97 (~b(s(s(z)), s(elem!1))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[2776, 25161, 273, 1070, 25174])).
% 4.74/4.97 tff(25176,plain,
% 4.74/4.97 (r(s(s(z)), s(elem!1))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[1067, 25175, 1060])).
% 4.74/4.97 tff(25177,plain,
% 4.74/4.97 (b(s(elem!1), s(s(s(elem!1))))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[6127, 21876, 25176, 5425])).
% 4.74/4.97 tff(25178,plain,
% 4.74/4.97 ($false),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[25177, 25173])).
% 4.74/4.97 tff(25179,plain,((s(s(z)) = s(elem!1)) | (~(elem!1 = s(s(s(s(z)))))) | (s(elem!1) = s(s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (s(elem!1) = s(s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.97 tff(25180,plain,
% 4.74/4.97 (~b(s(elem!1), s(s(z)))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[25179, 24269, 145, 273, 106, 24625, 25130, 24607, 286, 319, 17020, 21874])).
% 4.74/4.97 tff(25181,plain,
% 4.74/4.97 (r(s(elem!1), s(s(z)))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[421, 25180, 11439])).
% 4.74/4.97 tff(25182,plain,
% 4.74/4.97 (r(s(s(s(s(s(z))))), s(s(z)))),
% 4.74/4.97 inference(modus_ponens,[status(thm)],[25181, 362])).
% 4.74/4.97 tff(25183,plain,
% 4.74/4.97 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[9826, 118, 25182, 25141])).
% 4.74/4.97 tff(25184,plain,
% 4.74/4.97 (~r(s(elem!1), z)),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[2258, 25181, 106])).
% 4.74/4.97 tff(25185,plain,
% 4.74/4.97 (~r(s(s(s(s(s(z))))), z)),
% 4.74/4.97 inference(modus_ponens,[status(thm)],[25184, 2313])).
% 4.74/4.97 tff(25186,plain,
% 4.74/4.97 (b(s(s(s(s(s(z))))), z)),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[410, 41, 242, 25185])).
% 4.74/4.97 tff(25187,plain,
% 4.74/4.97 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[390, 25181, 287])).
% 4.74/4.97 tff(25188,plain,
% 4.74/4.97 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[395, 25187, 24275])).
% 4.74/4.97 tff(25189,plain,
% 4.74/4.97 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.97 inference(modus_ponens,[status(thm)],[25188, 376])).
% 4.74/4.97 tff(25190,plain,
% 4.74/4.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 4.74/4.97 inference(rewrite,[status(thm)],[])).
% 4.74/4.97 tff(25191,plain,
% 4.74/4.97 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 4.74/4.97 inference(rewrite,[status(thm)],[])).
% 4.74/4.97 tff(25192,plain,
% 4.74/4.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 4.74/4.97 inference(monotonicity,[status(thm)],[25191])).
% 4.74/4.97 tff(25193,plain,
% 4.74/4.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 4.74/4.97 inference(transitivity,[status(thm)],[25192, 25190])).
% 4.74/4.97 tff(25194,plain,
% 4.74/4.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 4.74/4.97 inference(quant_inst,[status(thm)],[])).
% 4.74/4.97 tff(25195,plain,
% 4.74/4.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 4.74/4.97 inference(modus_ponens,[status(thm)],[25194, 25193])).
% 4.74/4.97 tff(25196,plain,
% 4.74/4.97 ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[25195, 178, 24623, 25124, 25189])).
% 4.74/4.97 tff(25197,plain,
% 4.74/4.97 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[25196, 25186])).
% 4.74/4.97 tff(25198,plain,
% 4.74/4.97 ($false),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[9830, 41, 11413, 25197, 25183])).
% 4.74/4.97 tff(25199,plain,((~(elem!1 = s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.74/4.97 tff(25200,plain,
% 4.74/4.97 (~(elem!1 = s(s(s(s(z)))))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[25199, 286, 47, 273, 106, 12])).
% 4.74/4.97 tff(25201,plain,
% 4.74/4.97 (~r(elem!1, z)),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[493, 25200, 24644, 106, 12, 47, 24641])).
% 4.74/4.97 tff(25202,plain,
% 4.74/4.97 (b(elem!1, z)),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[498, 25201, 2809])).
% 4.74/4.97 tff(25203,plain,
% 4.74/4.97 (~b(s(s(z)), elem!1)),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[3162, 25200, 47, 273, 24644, 106, 286, 2809, 12])).
% 4.74/4.97 tff(25204,plain,
% 4.74/4.97 (r(s(s(z)), elem!1)),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[448, 25203, 12])).
% 4.74/4.97 tff(25205,plain,
% 4.74/4.97 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[11351, 25204, 287])).
% 4.74/4.97 tff(25206,plain,
% 4.74/4.97 (~(s(elem!1) = s(s(z)))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[617, 25205, 24644, 106, 12, 24647, 507, 25200, 24649, 47, 25202])).
% 4.74/4.97 tff(25207,plain,
% 4.74/4.97 (~r(elem!1, z)),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[458, 14548, 106])).
% 4.74/4.97 tff(25208,plain,
% 4.74/4.97 (b(elem!1, z)),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[498, 25207, 14984])).
% 4.74/4.97 tff(25209,plain,
% 4.74/4.97 (~r(s(s(s(z))), z)),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[24618, 106, 47, 273])).
% 4.74/4.97 tff(25210,plain,
% 4.74/4.97 (b(s(s(s(z))), z)),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[21073, 25209])).
% 4.74/4.97 tff(25211,plain,
% 4.74/4.97 (~b(s(s(s(s(z)))), z)),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[25128, 273, 24644, 24655, 25210])).
% 4.74/4.97 tff(25212,plain,
% 4.74/4.97 (b(elem!1, s(s(s(elem!1))))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[19038, 461, 1, 24761, 25211])).
% 4.74/4.97 tff(25213,plain,
% 4.74/4.97 (~(s(s(s(elem!1))) = elem!1)),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[16438, 25212])).
% 4.74/4.97 tff(25214,plain,
% 4.74/4.97 (~(s(elem!1) = elem!1)),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[2150, 25213])).
% 4.74/4.97 tff(25215,plain,
% 4.74/4.97 (~(elem!1 = s(s(s(s(z)))))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[325, 24668])).
% 4.74/4.97 tff(25216,plain,
% 4.74/4.97 (b(s(elem!1), s(s(z)))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[2660, 107, 145, 273, 106, 25130, 24607, 12, 290])).
% 4.74/4.97 tff(25217,plain,
% 4.74/4.97 ($false),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[3089, 25216, 107, 145, 273, 106, 25130, 12, 469, 506, 725, 318, 24607])).
% 4.74/4.97 tff(25218,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~r(s(s(z)), z)) | (s(s(z)) = elem!1) | (elem!1 = s(s(s(s(z))))) | (~b(elem!1, z)) | (s(elem!1) = elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 4.74/4.97 tff(25219,plain,
% 4.74/4.97 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[25218, 25215, 273, 106, 12, 47, 25208, 25214, 14984])).
% 4.74/4.97 tff(25220,plain,
% 4.74/4.97 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[3578, 25219])).
% 4.74/4.97 tff(25221,plain,
% 4.74/4.97 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[1154, 25220, 24647, 24649, 273])).
% 4.74/4.97 tff(25222,plain,
% 4.74/4.97 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[249, 25221])).
% 4.74/4.97 tff(25223,plain,
% 4.74/4.97 (~b(s(s(z)), elem!1)),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[3162, 25221, 47, 273, 24644, 106, 25215, 14984, 12])).
% 4.74/4.97 tff(25224,plain,
% 4.74/4.97 (r(s(s(z)), elem!1)),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[448, 25223, 12])).
% 4.74/4.97 tff(25225,plain,
% 4.74/4.97 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[11351, 25224, 25222])).
% 4.74/4.97 tff(25226,plain,
% 4.74/4.97 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[3113, 25222, 14548])).
% 4.74/4.97 tff(25227,plain,
% 4.74/4.97 (~r(z, elem!1)),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[541, 25224, 106])).
% 4.74/4.97 tff(25228,plain,
% 4.74/4.97 (b(z, elem!1)),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[585, 25227, 15020])).
% 4.74/4.97 tff(25229,plain,
% 4.74/4.97 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[18193, 25228, 24649, 25226, 25225, 25208])).
% 4.74/4.97 tff(25230,plain,
% 4.74/4.97 (b(elem!1, s(s(z))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.74/4.97 inference(monotonicity,[status(thm)],[25229])).
% 4.74/4.97 tff(25231,plain,
% 4.74/4.97 (b(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> b(elem!1, s(s(z)))),
% 4.74/4.97 inference(symmetry,[status(thm)],[25230])).
% 4.74/4.97 tff(25232,plain,
% 4.74/4.97 (b(elem!1, s(s(z)))),
% 4.74/4.97 inference(modus_ponens,[status(thm)],[25220, 25231])).
% 4.74/4.97 tff(25233,plain,
% 4.74/4.97 ($false),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[461, 25232])).
% 4.74/4.97 tff(25234,plain,(b(elem!1, s(s(z))) | (~r(s(s(z)), z)) | (s(s(z)) = elem!1) | (~b(z, s(s(z)))) | b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.97 tff(25235,plain,
% 4.74/4.97 (b(elem!1, s(s(z)))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[25234, 12, 106, 273, 1])).
% 4.74/4.97 tff(25236,plain,
% 4.74/4.97 (~r(z, elem!1)),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[814, 25200, 24641, 106, 25235, 12, 47, 24644])).
% 4.74/4.97 tff(25237,plain,
% 4.74/4.97 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[2820, 25236, 24649, 24647, 507, 25201])).
% 4.74/4.97 tff(25238,plain,
% 4.74/4.97 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[2803, 25204, 287])).
% 4.74/4.97 tff(25239,plain,
% 4.74/4.97 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[691, 25238, 25237])).
% 4.74/4.97 tff(25240,plain,
% 4.74/4.97 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[16181, 25239])).
% 4.74/4.97 tff(25241,plain,
% 4.74/4.97 (r(s(s(s(s(z)))), z)),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[191, 25211])).
% 4.74/4.97 tff(25242,plain,
% 4.74/4.97 (~b(s(s(s(z))), s(s(z)))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[4963, 25241, 273, 24641, 24655, 24644])).
% 4.74/4.97 tff(25243,plain,
% 4.74/4.97 (r(s(s(s(z))), s(s(z)))),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[4966, 25242])).
% 4.74/4.97 tff(25244,plain,
% 4.74/4.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))),
% 4.74/4.97 inference(rewrite,[status(thm)],[])).
% 4.74/4.97 tff(25245,plain,
% 4.74/4.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))),
% 4.74/4.97 inference(quant_inst,[status(thm)],[])).
% 4.74/4.97 tff(25246,plain,
% 4.74/4.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z))))),
% 4.74/4.97 inference(modus_ponens,[status(thm)],[25245, 25244])).
% 4.74/4.97 tff(25247,plain,
% 4.74/4.97 ($false),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[25246, 118, 438, 1125, 18022])).
% 4.74/4.97 tff(25248,plain,((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.97 tff(25249,plain,
% 4.74/4.97 (~r(s(s(s(z))), elem!1)),
% 4.74/4.97 inference(unit_resolution,[status(thm)],[25248, 25204, 25243])).
% 4.74/4.97 tff(25250,plain,
% 4.74/4.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 4.74/4.98 inference(rewrite,[status(thm)],[])).
% 4.74/4.98 tff(25251,plain,
% 4.74/4.98 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1))) <=> ((~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 4.74/4.98 inference(rewrite,[status(thm)],[])).
% 4.74/4.98 tff(25252,plain,
% 4.74/4.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))))),
% 4.74/4.98 inference(monotonicity,[status(thm)],[25251])).
% 4.74/4.98 tff(25253,plain,
% 4.74/4.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 4.74/4.98 inference(transitivity,[status(thm)],[25252, 25250])).
% 4.74/4.98 tff(25254,plain,
% 4.74/4.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)))),
% 4.74/4.98 inference(quant_inst,[status(thm)],[])).
% 4.74/4.98 tff(25255,plain,
% 4.74/4.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))),
% 4.74/4.98 inference(modus_ponens,[status(thm)],[25254, 25253])).
% 4.74/4.98 tff(25256,plain,
% 4.74/4.98 ((~b(elem!1, z)) | (~b(s(s(s(z))), elem!1))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[25255, 178, 273, 25235, 25210])).
% 4.74/4.98 tff(25257,plain,
% 4.74/4.98 (~b(s(s(s(z))), elem!1)),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[25256, 25202])).
% 4.74/4.98 tff(25258,plain,
% 4.74/4.98 (s(s(s(z))) = elem!1),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[4981, 25257, 25249])).
% 4.74/4.98 tff(25259,plain,
% 4.74/4.98 (~b(z, s(elem!1))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[23057, 25258, 1])).
% 4.74/4.98 tff(25260,plain,
% 4.74/4.98 (r(z, s(elem!1))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[2351, 25259])).
% 4.74/4.98 tff(25261,plain,
% 4.74/4.98 (~r(s(elem!1), s(s(s(s(z)))))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[2766, 25260, 47])).
% 4.74/4.98 tff(25262,plain,
% 4.74/4.98 (b(s(elem!1), s(s(s(s(z)))))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[1084, 25261, 25240])).
% 4.74/4.98 tff(25263,plain,
% 4.74/4.98 (~(s(s(z)) = s(elem!1))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[1058, 25206])).
% 4.74/4.98 tff(25264,plain,
% 4.74/4.98 (~r(s(s(z)), s(elem!1))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[2341, 25260, 106])).
% 4.74/4.98 tff(25265,plain,
% 4.74/4.98 (b(s(s(z)), s(elem!1))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[1067, 25264, 25263])).
% 4.74/4.98 tff(25266,plain,
% 4.74/4.98 (~b(s(elem!1), s(s(z)))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[1079, 25265, 24644, 24641, 25262])).
% 4.74/4.98 tff(25267,plain,
% 4.74/4.98 (r(s(elem!1), s(s(z)))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[421, 25266, 25206])).
% 4.74/4.98 tff(25268,plain,
% 4.74/4.98 (~r(s(elem!1), z)),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[2258, 25267, 106])).
% 4.74/4.98 tff(25269,plain,
% 4.74/4.98 (~(elem!1 = s(s(s(elem!1))))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[4830, 25258, 2387])).
% 4.74/4.98 tff(25270,plain,
% 4.74/4.98 (~(s(s(s(elem!1))) = elem!1)),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[2489, 25269])).
% 4.74/4.98 tff(25271,plain,
% 4.74/4.98 (~(s(elem!1) = elem!1)),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[2150, 25270])).
% 4.74/4.98 tff(25272,plain,
% 4.74/4.98 (b(z, elem!1)),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[585, 25236, 507])).
% 4.74/4.98 tff(25273,plain,
% 4.74/4.98 (~b(s(elem!1), z)),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[2558, 25267, 273, 12, 25202, 25272, 25271])).
% 4.74/4.98 tff(25274,plain,
% 4.74/4.98 ($false),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[774, 25273, 25268])).
% 4.74/4.98 tff(25275,plain,(b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | (~b(z, s(s(z)))) | (s(s(z)) = elem!1) | (~r(s(s(z)), z)) | b(z, s(s(s(s(z))))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.74/4.98 tff(25276,plain,
% 4.74/4.98 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[25275, 507, 12, 106, 1, 273])).
% 4.74/4.98 tff(25277,plain,
% 4.74/4.98 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[1154, 25276, 24647, 24649, 273])).
% 4.74/4.98 tff(25278,plain,
% 4.74/4.98 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[3578, 25277])).
% 4.74/4.98 tff(25279,plain,
% 4.74/4.98 (b(elem!1, s(s(z))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.74/4.98 inference(monotonicity,[status(thm)],[679])).
% 4.74/4.98 tff(25280,plain,
% 4.74/4.98 (b(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> b(elem!1, s(s(z)))),
% 4.74/4.98 inference(symmetry,[status(thm)],[25279])).
% 4.74/4.98 tff(25281,plain,
% 4.74/4.98 ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) <=> (~b(elem!1, s(s(z))))),
% 4.74/4.98 inference(monotonicity,[status(thm)],[25280])).
% 4.74/4.98 tff(25282,plain,
% 4.74/4.98 (~b(elem!1, s(s(z)))),
% 4.74/4.98 inference(modus_ponens,[status(thm)],[3576, 25281])).
% 4.74/4.98 tff(25283,plain,
% 4.74/4.98 ($false),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[812, 25282])).
% 4.74/4.98 tff(25284,plain,((~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z)))) | b(s(s(s(s(s(s(s(z))))))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.98 tff(25285,plain,
% 4.74/4.98 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[25284, 25277, 25235])).
% 4.74/4.98 tff(25286,plain,
% 4.74/4.98 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[703, 25285])).
% 4.74/4.98 tff(25287,plain,
% 4.74/4.98 (b(s(elem!1), s(s(z)))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[2660, 25278, 47, 273, 106, 25241, 24641, 12, 2809])).
% 4.74/4.98 tff(25288,plain,
% 4.74/4.98 (~r(elem!1, z)),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[2792, 25287, 273, 106, 47, 24641, 25241, 12, 25278])).
% 4.74/4.98 tff(25289,plain,
% 4.74/4.98 (b(elem!1, z)),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[498, 25288, 2809])).
% 4.74/4.98 tff(25290,plain,
% 4.74/4.98 ((~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[24984, 178, 273, 25235, 24647])).
% 4.74/4.98 tff(25291,plain,
% 4.74/4.98 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[25290, 25289])).
% 4.74/4.98 tff(25292,plain,
% 4.74/4.98 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[3444, 25291, 25286])).
% 4.74/4.98 tff(25293,plain,
% 4.74/4.98 (~r(s(s(z)), elem!1)),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[17566, 25292, 25278])).
% 4.74/4.98 tff(25294,plain,
% 4.74/4.98 (~(elem!1 = s(s(s(s(z)))))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[3172, 25289, 25211])).
% 4.74/4.98 tff(25295,plain,
% 4.74/4.98 (~r(z, elem!1)),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[814, 25294, 24641, 106, 25235, 12, 47, 24644])).
% 4.74/4.98 tff(25296,plain,
% 4.74/4.98 (b(z, elem!1)),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[585, 25295, 507])).
% 4.74/4.98 tff(25297,plain,
% 4.74/4.98 (~b(s(s(z)), elem!1)),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[826, 25296, 273, 25235, 25289])).
% 4.74/4.98 tff(25298,plain,
% 4.74/4.98 ($false),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[448, 25297, 25293, 12])).
% 4.74/4.98 tff(25299,plain,((z = elem!1) | (s(s(z)) = elem!1) | (~b(z, s(s(z)))) | (~r(s(s(z)), z)) | b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.98 tff(25300,plain,
% 4.74/4.98 (s(s(z)) = elem!1),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[25299, 25157, 144, 25122, 1])).
% 4.74/4.98 tff(25301,plain,
% 4.74/4.98 (s(s(s(z))) = s(elem!1)),
% 4.74/4.98 inference(monotonicity,[status(thm)],[25300])).
% 4.74/4.98 tff(25302,plain,
% 4.74/4.98 (s(s(s(s(z)))) = s(s(elem!1))),
% 4.74/4.98 inference(monotonicity,[status(thm)],[25301])).
% 4.74/4.98 tff(25303,plain,
% 4.74/4.98 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(elem!1)))),
% 4.74/4.98 inference(monotonicity,[status(thm)],[25302])).
% 4.74/4.98 tff(25304,plain,
% 4.74/4.98 (b(elem!1, s(s(s(s(z)))))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[17989, 25300, 24641])).
% 4.74/4.98 tff(25305,plain,
% 4.74/4.98 (b(elem!1, s(s(elem!1)))),
% 4.74/4.98 inference(modus_ponens,[status(thm)],[25304, 25303])).
% 4.74/4.98 tff(25306,plain,
% 4.74/4.98 ((s(elem!1) = s(s(z))) <=> (s(elem!1) = elem!1)),
% 4.74/4.98 inference(monotonicity,[status(thm)],[25300])).
% 4.74/4.98 tff(25307,plain,
% 4.74/4.98 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(z)))),
% 4.74/4.98 inference(symmetry,[status(thm)],[25306])).
% 4.74/4.98 tff(25308,plain,
% 4.74/4.98 ((~(s(elem!1) = elem!1)) <=> (~(s(elem!1) = s(s(z))))),
% 4.74/4.98 inference(monotonicity,[status(thm)],[25307])).
% 4.74/4.98 tff(25309,plain,
% 4.74/4.98 (~r(s(s(s(z))), z)),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[24618, 25122, 47, 144])).
% 4.74/4.98 tff(25310,plain,
% 4.74/4.98 (b(s(s(s(z))), z)),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[21073, 25309])).
% 4.74/4.98 tff(25311,plain,
% 4.74/4.98 (~b(s(s(s(s(z)))), z)),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[25128, 144, 24639, 24655, 25310])).
% 4.74/4.98 tff(25312,plain,
% 4.74/4.98 (~b(elem!1, s(s(z)))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[3223, 25300])).
% 4.74/4.98 tff(25313,plain,
% 4.74/4.98 (b(elem!1, s(s(s(elem!1))))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[19038, 25312, 1, 24761, 25311])).
% 4.74/4.98 tff(25314,plain,
% 4.74/4.98 (~(s(s(s(elem!1))) = elem!1)),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[16438, 25313])).
% 4.74/4.98 tff(25315,plain,
% 4.74/4.98 (~(s(elem!1) = elem!1)),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[2150, 25314])).
% 4.74/4.98 tff(25316,plain,
% 4.74/4.98 (~(s(elem!1) = s(s(z)))),
% 4.74/4.98 inference(modus_ponens,[status(thm)],[25315, 25308])).
% 4.74/4.98 tff(25317,plain,
% 4.74/4.98 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[2840, 25316])).
% 4.74/4.98 tff(25318,plain,
% 4.74/4.98 (~(s(s(s(s(z)))) = elem!1)),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[4509, 25312, 24639])).
% 4.74/4.98 tff(25319,plain,
% 4.74/4.98 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[3502, 25318])).
% 4.74/4.98 tff(25320,plain,
% 4.74/4.98 (r(s(s(s(s(z)))), z)),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[191, 25311])).
% 4.74/4.98 tff(25321,plain,
% 4.74/4.98 (b(s(s(z)), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 4.74/4.98 inference(monotonicity,[status(thm)],[25300])).
% 4.74/4.98 tff(25322,plain,
% 4.74/4.98 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 4.74/4.98 inference(symmetry,[status(thm)],[25321])).
% 4.74/4.98 tff(25323,plain,
% 4.74/4.98 (b(s(s(z)), s(s(s(elem!1))))),
% 4.74/4.98 inference(modus_ponens,[status(thm)],[25313, 25322])).
% 4.74/4.98 tff(25324,plain,
% 4.74/4.98 (~r(z, s(s(s(elem!1))))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[10669, 25323, 47, 24641, 24639, 25320, 25317])).
% 4.74/4.98 tff(25325,plain,
% 4.74/4.98 (b(z, s(s(s(elem!1))))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[2095, 25324])).
% 4.74/4.98 tff(25326,plain,
% 4.74/4.98 ((~b(z, s(s(s(elem!1))))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[8061, 24592])).
% 4.74/4.98 tff(25327,plain,
% 4.74/4.98 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[25326, 25325, 47, 25319])).
% 4.74/4.98 tff(25328,plain,
% 4.74/4.98 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[4173, 25327, 25317])).
% 4.74/4.98 tff(25329,plain,
% 4.74/4.98 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[10679, 25328, 25300])).
% 4.74/4.98 tff(25330,plain,
% 4.74/4.98 (~r(z, elem!1)),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[18165, 25300, 48])).
% 4.74/4.98 tff(25331,plain,
% 4.74/4.98 (b(z, elem!1)),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[585, 25330, 25157])).
% 4.74/4.98 tff(25332,plain,
% 4.74/4.98 ($false),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[10686, 178, 25331, 25325, 25313, 25329, 25305])).
% 4.74/4.98 tff(25333,plain,(r(z, s(s(z))) | b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.98 tff(25334,plain,
% 4.74/4.98 (r(z, s(s(z)))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[25333, 1])).
% 4.74/4.98 tff(25335,plain,
% 4.74/4.98 (~r(s(s(s(s(z)))), s(s(z)))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[3269, 25334, 47])).
% 4.74/4.98 tff(25336,plain,
% 4.74/4.98 (b(s(s(s(s(z)))), s(s(z)))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[102, 25335])).
% 4.74/4.98 tff(25337,plain,
% 4.74/4.98 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 4.74/4.98 inference(modus_ponens,[status(thm)],[25336, 18])).
% 4.74/4.98 tff(25338,plain,
% 4.74/4.98 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 4.74/4.98 inference(monotonicity,[status(thm)],[15, 17])).
% 4.74/4.98 tff(25339,plain,
% 4.74/4.98 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 4.74/4.98 inference(modus_ponens,[status(thm)],[24641, 25338])).
% 4.74/4.98 tff(25340,plain,
% 4.74/4.98 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 4.74/4.98 inference(monotonicity,[status(thm)],[15])).
% 4.74/4.98 tff(25341,plain,
% 4.74/4.98 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 4.74/4.98 inference(monotonicity,[status(thm)],[25340])).
% 4.74/4.98 tff(25342,plain,
% 4.74/4.98 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 4.74/4.98 inference(modus_ponens,[status(thm)],[1683, 25341])).
% 4.74/4.98 tff(25343,plain,
% 4.74/4.98 ((s(elem!1) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 4.74/4.98 inference(monotonicity,[status(thm)],[16])).
% 4.74/4.98 tff(25344,plain,
% 4.74/4.98 ((s(elem!1) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 4.74/4.98 inference(transitivity,[status(thm)],[25343, 3881])).
% 4.74/4.98 tff(25345,plain,
% 4.74/4.98 ((s(elem!1) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 4.74/4.98 inference(transitivity,[status(thm)],[25344, 7104])).
% 4.74/4.98 tff(25346,plain,
% 4.74/4.98 ((~(s(elem!1) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 4.74/4.98 inference(monotonicity,[status(thm)],[25345])).
% 4.74/4.98 tff(25347,plain,
% 4.74/4.98 (~(s(s(z)) = elem!1)),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[17989, 5205, 24641])).
% 4.74/4.98 tff(25348,plain,
% 4.74/4.98 (~(s(elem!1) = s(s(s(z))))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[23436, 25347])).
% 4.74/4.98 tff(25349,plain,
% 4.74/4.98 (~(s(elem!1) = s(s(s(elem!1))))),
% 4.74/4.98 inference(modus_ponens,[status(thm)],[25348, 25346])).
% 4.74/4.98 tff(25350,plain,
% 4.74/4.98 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 4.74/4.98 inference(monotonicity,[status(thm)],[17])).
% 4.74/4.98 tff(25351,plain,
% 4.74/4.98 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 4.74/4.98 inference(commutativity,[status(thm)],[])).
% 4.74/4.98 tff(25352,plain,
% 4.74/4.98 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 4.74/4.98 inference(monotonicity,[status(thm)],[17])).
% 4.74/4.98 tff(25353,plain,
% 4.74/4.98 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 4.74/4.98 inference(transitivity,[status(thm)],[25352, 25351])).
% 4.74/4.98 tff(25354,plain,
% 4.74/4.98 ((s(elem!1) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 4.74/4.98 inference(transitivity,[status(thm)],[2163, 25353])).
% 4.74/4.98 tff(25355,plain,
% 4.74/4.98 (s(elem!1) = s(s(s(s(elem!1))))),
% 4.74/4.98 inference(modus_ponens,[status(thm)],[1117, 25354])).
% 4.74/4.98 tff(25356,plain,
% 4.74/4.98 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 4.74/4.98 inference(monotonicity,[status(thm)],[12146])).
% 4.74/4.98 tff(25357,plain,
% 4.74/4.98 (~(s(s(s(elem!1))) = elem!1)),
% 4.74/4.98 inference(modus_ponens,[status(thm)],[940, 25356])).
% 4.74/4.98 tff(25358,plain,
% 4.74/4.98 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[951, 25357])).
% 4.74/4.98 tff(25359,plain,
% 4.74/4.98 ($false),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[25358, 25355])).
% 4.74/4.98 tff(25360,plain,((~(s(elem!1) = s(s(s(s(z)))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.98 tff(25361,plain,
% 4.74/4.98 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[25360, 13])).
% 4.74/4.98 tff(25362,plain,
% 4.74/4.98 (b(z, s(z)) <=> b(elem!1, s(elem!1))),
% 4.74/4.98 inference(monotonicity,[status(thm)],[13, 14])).
% 4.74/4.98 tff(25363,plain,
% 4.74/4.98 (b(elem!1, s(elem!1)) <=> b(z, s(z))),
% 4.74/4.98 inference(symmetry,[status(thm)],[25362])).
% 4.74/4.98 tff(25364,plain,
% 4.74/4.98 (~b(s(s(s(z))), s(s(z)))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[23396, 178, 3461, 168, 167, 1126])).
% 4.74/4.98 tff(25365,plain,
% 4.74/4.98 (r(s(s(s(z))), s(s(z)))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[4966, 25364])).
% 4.74/4.98 tff(25366,plain,
% 4.74/4.98 (~r(s(s(s(z))), z)),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[6019, 118, 3261, 25365])).
% 4.74/4.98 tff(25367,plain,
% 4.74/4.98 (b(s(s(s(z))), z)),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[21073, 25366])).
% 4.74/4.98 tff(25368,plain,
% 4.74/4.98 (~r(z, s(s(s(z))))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[24302, 25365, 3261])).
% 4.74/4.98 tff(25369,plain,
% 4.74/4.98 (b(z, s(s(s(z))))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[4920, 25368])).
% 4.74/4.98 tff(25370,plain,
% 4.74/4.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)))),
% 4.74/4.98 inference(rewrite,[status(thm)],[])).
% 4.74/4.98 tff(25371,plain,
% 4.74/4.98 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)))),
% 4.74/4.98 inference(rewrite,[status(thm)],[])).
% 4.74/4.98 tff(25372,plain,
% 4.74/4.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z))))),
% 4.74/4.98 inference(monotonicity,[status(thm)],[25371])).
% 4.74/4.98 tff(25373,plain,
% 4.74/4.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)))),
% 4.74/4.98 inference(transitivity,[status(thm)],[25372, 25370])).
% 4.74/4.98 tff(25374,plain,
% 4.74/4.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 4.74/4.98 inference(quant_inst,[status(thm)],[])).
% 4.74/4.98 tff(25375,plain,
% 4.74/4.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z))),
% 4.74/4.98 inference(modus_ponens,[status(thm)],[25374, 25373])).
% 4.74/4.98 tff(25376,plain,
% 4.74/4.98 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[25375, 178, 168, 595, 146, 1126, 25369, 25367])).
% 4.74/4.98 tff(25377,plain,
% 4.74/4.98 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[20667, 25376])).
% 4.74/4.98 tff(25378,plain,
% 4.74/4.98 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[23367, 25367, 3461, 25369, 595, 3261])).
% 4.74/4.98 tff(25379,plain,
% 4.74/4.98 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[3578, 25378])).
% 4.74/4.98 tff(25380,plain,
% 4.74/4.98 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[13776, 25379, 146, 595, 3461])).
% 4.74/4.98 tff(25381,plain,
% 4.74/4.98 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[249, 25380])).
% 4.74/4.98 tff(25382,plain,
% 4.74/4.98 ($false),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[1269, 118, 25381, 25365, 25377])).
% 4.74/4.98 tff(25383,plain,((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~r(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.98 tff(25384,plain,
% 4.74/4.98 (~b(s(s(s(s(z)))), z)),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[25383, 5619, 24647, 24655, 24649, 25334, 24641])).
% 4.74/4.98 tff(25385,plain,
% 4.74/4.98 (r(s(s(s(s(z)))), z)),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[191, 25384])).
% 4.74/4.98 tff(25386,plain,
% 4.74/4.98 (~r(z, s(s(s(z))))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[23351, 25385, 47, 25334])).
% 4.74/4.98 tff(25387,plain,
% 4.74/4.98 (b(z, s(s(s(z))))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[4920, 25386])).
% 4.74/4.98 tff(25388,plain,
% 4.74/4.98 (~b(s(s(s(z))), s(s(z)))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[4945, 24329])).
% 4.74/4.98 tff(25389,plain,
% 4.74/4.98 (r(s(s(s(z))), s(s(z)))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[4966, 25388])).
% 4.74/4.98 tff(25390,plain,
% 4.74/4.98 ($false),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[6019, 118, 3261, 25389, 16062])).
% 4.74/4.98 tff(25391,plain,((~r(s(s(s(z))), z)) | (~r(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(s(s(z)))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.98 tff(25392,plain,
% 4.74/4.98 (~r(s(s(s(z))), z)),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[25391, 25385, 24641, 25336, 24655, 25334])).
% 4.74/4.98 tff(25393,plain,
% 4.74/4.98 (b(s(s(s(z))), z)),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[21073, 25392])).
% 4.74/4.98 tff(25394,plain,
% 4.74/4.98 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[23367, 25393, 5619, 25387, 24649, 25334])).
% 4.74/4.98 tff(25395,plain,
% 4.74/4.98 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[3578, 25394])).
% 4.74/4.98 tff(25396,plain,
% 4.74/4.98 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[13776, 25395, 24647, 24649, 5619])).
% 4.74/4.98 tff(25397,plain,
% 4.74/4.98 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[249, 25396])).
% 4.74/4.98 tff(25398,plain,
% 4.74/4.98 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 4.74/4.98 inference(monotonicity,[status(thm)],[16])).
% 4.74/4.98 tff(25399,plain,
% 4.74/4.98 (b(z, s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 4.74/4.98 inference(monotonicity,[status(thm)],[13])).
% 4.74/4.98 tff(25400,plain,
% 4.74/4.98 (b(elem!1, s(s(s(z))))),
% 4.74/4.98 inference(modus_ponens,[status(thm)],[3008, 25399])).
% 4.74/4.98 tff(25401,plain,
% 4.74/4.98 (b(elem!1, s(s(s(elem!1))))),
% 4.74/4.98 inference(modus_ponens,[status(thm)],[25400, 25398])).
% 4.74/4.98 tff(25402,plain,
% 4.74/4.98 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 4.74/4.98 inference(monotonicity,[status(thm)],[16])).
% 4.74/4.98 tff(25403,plain,
% 4.74/4.98 (b(s(s(s(z))), z) <=> b(s(s(s(z))), elem!1)),
% 4.74/4.98 inference(monotonicity,[status(thm)],[13])).
% 4.74/4.98 tff(25404,plain,
% 4.74/4.98 (b(s(s(s(z))), elem!1)),
% 4.74/4.98 inference(modus_ponens,[status(thm)],[1127, 25403])).
% 4.74/4.98 tff(25405,plain,
% 4.74/4.98 (b(s(s(s(elem!1))), elem!1)),
% 4.74/4.98 inference(modus_ponens,[status(thm)],[25404, 25402])).
% 4.74/4.98 tff(25406,plain,
% 4.74/4.98 (b(s(s(elem!1)), elem!1)),
% 4.74/4.98 inference(unit_resolution,[status(thm)],[5878, 13, 3461])).
% 4.74/4.98 tff(25407,plain,
% 4.74/4.98 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 4.74/4.98 inference(transitivity,[status(thm)],[25340, 12033])).
% 4.74/4.98 tff(25408,plain,
% 4.74/4.98 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 4.74/4.98 inference(monotonicity,[status(thm)],[25407])).
% 4.74/4.98 tff(25409,plain,
% 4.74/4.98 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 4.74/4.98 inference(modus_ponens,[status(thm)],[1683, 25408])).
% 4.74/4.98 tff(25410,plain,
% 4.74/4.98 (b(s(s(s(s(s(s(s(z))))))), z) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.74/4.98 inference(monotonicity,[status(thm)],[13])).
% 4.74/4.98 tff(25411,plain,
% 4.74/4.98 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.74/4.98 inference(modus_ponens,[status(thm)],[146, 25410])).
% 4.74/4.98 tff(25412,plain,
% 4.74/4.98 (b(z, s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.74/4.98 inference(monotonicity,[status(thm)],[13])).
% 4.74/4.98 tff(25413,plain,
% 4.74/4.98 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.74/4.98 inference(modus_ponens,[status(thm)],[595, 25412])).
% 4.74/4.98 tff(25414,plain,
% 4.74/4.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(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))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(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))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.74/4.98 inference(rewrite,[status(thm)],[])).
% 4.74/4.98 tff(25415,plain,
% 4.74/4.98 (((~b(s(s(s(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(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(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(elem!1, s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.74/4.98 inference(rewrite,[status(thm)],[])).
% 4.74/4.98 tff(25416,plain,
% 4.74/4.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(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(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(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))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 4.74/4.98 inference(monotonicity,[status(thm)],[25415])).
% 4.74/4.98 tff(25417,plain,
% 4.74/4.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(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(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(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))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.74/4.98 inference(transitivity,[status(thm)],[25416, 25414])).
% 4.74/4.98 tff(25418,plain,
% 4.74/4.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(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(elem!1, s(s(s(elem!1))))))),
% 4.74/4.98 inference(quant_inst,[status(thm)],[])).
% 4.74/4.98 tff(25419,plain,
% 4.74/4.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(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))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 4.74/4.99 inference(modus_ponens,[status(thm)],[25418, 25417])).
% 4.74/4.99 tff(25420,plain,
% 4.74/4.99 (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[25419, 178, 25405, 25401, 25413, 25411])).
% 4.74/4.99 tff(25421,plain,
% 4.74/4.99 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[20942, 25420, 5198])).
% 4.74/4.99 tff(25422,plain,
% 4.74/4.99 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[20667, 25421])).
% 4.74/4.99 tff(25423,plain,
% 4.74/4.99 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[21219, 25422, 5198])).
% 4.74/4.99 tff(25424,plain,
% 4.74/4.99 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.99 inference(modus_ponens,[status(thm)],[224, 25139])).
% 4.74/4.99 tff(25425,plain,
% 4.74/4.99 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[25154, 118, 25424, 25423])).
% 4.74/4.99 tff(25426,plain,
% 4.74/4.99 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[3409, 25425, 25409])).
% 4.74/4.99 tff(25427,plain,
% 4.74/4.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~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))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~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))))))))))),
% 4.74/4.99 inference(rewrite,[status(thm)],[])).
% 4.74/4.99 tff(25428,plain,
% 4.74/4.99 (((~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(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~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))))))))))),
% 4.74/4.99 inference(rewrite,[status(thm)],[])).
% 4.74/4.99 tff(25429,plain,
% 4.74/4.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(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(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~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)))))))))))),
% 4.74/4.99 inference(monotonicity,[status(thm)],[25428])).
% 4.74/4.99 tff(25430,plain,
% 4.74/4.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(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(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~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))))))))))),
% 4.74/4.99 inference(transitivity,[status(thm)],[25429, 25427])).
% 4.74/4.99 tff(25431,plain,
% 4.74/4.99 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(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(elem!1))))))),
% 4.74/4.99 inference(quant_inst,[status(thm)],[])).
% 4.74/4.99 tff(25432,plain,
% 4.74/4.99 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 4.74/4.99 inference(modus_ponens,[status(thm)],[25431, 25430])).
% 4.74/4.99 tff(25433,plain,
% 4.74/4.99 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[25432, 118, 25424, 25423])).
% 4.74/4.99 tff(25434,plain,
% 4.74/4.99 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[3375, 25433, 25342])).
% 4.74/4.99 tff(25435,plain,
% 4.74/4.99 ($false),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[5500, 25434, 25426, 25406, 25405, 25401])).
% 4.74/4.99 tff(25436,plain,((~(z = elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(z, 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(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.99 tff(25437,plain,
% 4.74/4.99 (~(z = elem!1)),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[25436, 25397, 25393, 25387, 24647, 24649, 5619])).
% 4.74/4.99 tff(25438,plain,
% 4.74/4.99 (~r(z, s(s(s(z))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[23351, 3244, 47, 25334])).
% 4.74/4.99 tff(25439,plain,
% 4.74/4.99 (b(z, s(s(s(z))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[4920, 25438])).
% 4.74/4.99 tff(25440,plain,
% 4.74/4.99 (~r(s(s(s(z))), z)),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[25391, 3244, 24641, 25336, 24655, 25334])).
% 4.74/4.99 tff(25441,plain,
% 4.74/4.99 (b(s(s(s(z))), z)),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[21073, 25440])).
% 4.74/4.99 tff(25442,plain,
% 4.74/4.99 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[23367, 25441, 5619, 25439, 24649, 25334])).
% 4.74/4.99 tff(25443,plain,
% 4.74/4.99 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[3578, 25442])).
% 4.74/4.99 tff(25444,plain,
% 4.74/4.99 (~r(z, elem!1)),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[4862, 13066, 25334])).
% 4.74/4.99 tff(25445,plain,
% 4.74/4.99 (~r(elem!1, z)),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[8416, 13066, 25334])).
% 4.74/4.99 tff(25446,plain,
% 4.74/4.99 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[2820, 25445, 24649, 24647, 507, 25444])).
% 4.74/4.99 tff(25447,plain,
% 4.74/4.99 (b(z, elem!1)),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[585, 25444, 507])).
% 4.74/4.99 tff(25448,plain,
% 4.74/4.99 (b(elem!1, z)),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[11793, 461, 25334, 5618, 2809])).
% 4.74/4.99 tff(25449,plain,
% 4.74/4.99 (b(elem!1, s(s(s(elem!1))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[19038, 461, 1, 24761, 3170])).
% 4.74/4.99 tff(25450,plain,
% 4.74/4.99 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[3113, 224, 450])).
% 4.74/4.99 tff(25451,plain,
% 4.74/4.99 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[691, 25450, 4289])).
% 4.74/4.99 tff(25452,plain,
% 4.74/4.99 (~(s(elem!1) = s(s(z)))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[2832, 25451])).
% 4.74/4.99 tff(25453,plain,
% 4.74/4.99 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[2840, 25452])).
% 4.74/4.99 tff(25454,plain,
% 4.74/4.99 ($false),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[19484, 19902, 557, 3261, 22752, 145, 2857])).
% 4.74/4.99 tff(25455,plain,((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (s(s(s(elem!1))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.99 tff(25456,plain,
% 4.74/4.99 (~r(z, s(s(s(elem!1))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[25455, 25453, 145, 3261])).
% 4.74/4.99 tff(25457,plain,
% 4.74/4.99 (b(z, s(s(s(elem!1))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[2095, 25456])).
% 4.74/4.99 tff(25458,plain,
% 4.74/4.99 (r(elem!1, s(s(z))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.74/4.99 inference(monotonicity,[status(thm)],[25451])).
% 4.74/4.99 tff(25459,plain,
% 4.74/4.99 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.74/4.99 inference(modus_ponens,[status(thm)],[450, 25458])).
% 4.74/4.99 tff(25460,plain,
% 4.74/4.99 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 4.74/4.99 inference(monotonicity,[status(thm)],[25451])).
% 4.74/4.99 tff(25461,plain,
% 4.74/4.99 (s(s(elem!1)) = s(s(s(s(s(s(s(s(s(z)))))))))),
% 4.74/4.99 inference(monotonicity,[status(thm)],[25460])).
% 4.74/4.99 tff(25462,plain,
% 4.74/4.99 (s(s(s(elem!1))) = s(s(s(s(s(s(s(s(s(s(z))))))))))),
% 4.74/4.99 inference(monotonicity,[status(thm)],[25461])).
% 4.74/4.99 tff(25463,plain,
% 4.74/4.99 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))),
% 4.74/4.99 inference(monotonicity,[status(thm)],[25462])).
% 4.74/4.99 tff(25464,plain,
% 4.74/4.99 ((~r(s(s(s(elem!1))), s(s(z)))) <=> (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z))))),
% 4.74/4.99 inference(monotonicity,[status(thm)],[25463])).
% 4.74/4.99 tff(25465,plain,
% 4.74/4.99 (~b(s(s(s(elem!1))), elem!1)),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[12925, 25457, 2042, 506, 818])).
% 4.74/4.99 tff(25466,plain,
% 4.74/4.99 (r(s(s(s(elem!1))), elem!1)),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[570, 25465, 19901])).
% 4.74/4.99 tff(25467,plain,
% 4.74/4.99 (~r(s(s(s(elem!1))), s(s(z)))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[4205, 25466, 450])).
% 4.74/4.99 tff(25468,plain,
% 4.74/4.99 (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))),
% 4.74/4.99 inference(modus_ponens,[status(thm)],[25467, 25464])).
% 4.74/4.99 tff(25469,plain,
% 4.74/4.99 ((~(elem!1 = s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1)))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[10514, 24592])).
% 4.74/4.99 tff(25470,plain,
% 4.74/4.99 (~b(s(s(z)), s(s(s(elem!1))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[25469, 25468, 25459, 25457, 145, 25451])).
% 4.74/4.99 tff(25471,plain,
% 4.74/4.99 (s(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(s(elem!1)))),
% 4.74/4.99 inference(symmetry,[status(thm)],[25462])).
% 4.74/4.99 tff(25472,plain,
% 4.74/4.99 (r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.99 inference(monotonicity,[status(thm)],[25471])).
% 4.74/4.99 tff(25473,plain,
% 4.74/4.99 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.99 inference(symmetry,[status(thm)],[25472])).
% 4.74/4.99 tff(25474,plain,
% 4.74/4.99 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[19937, 25466, 25451])).
% 4.74/4.99 tff(25475,plain,
% 4.74/4.99 (r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.99 inference(modus_ponens,[status(thm)],[25474, 25473])).
% 4.74/4.99 tff(25476,plain,
% 4.74/4.99 (~r(s(s(z)), s(s(s(elem!1))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[19952, 25475, 224, 25451])).
% 4.74/4.99 tff(25477,plain,
% 4.74/4.99 ($false),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[4223, 25476, 25470])).
% 4.74/4.99 tff(25478,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~r(z, s(s(z)))) | b(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.99 tff(25479,plain,
% 4.74/4.99 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[25478, 13066, 47, 25449, 25448, 25447, 25334, 25446])).
% 4.74/4.99 tff(25480,plain,
% 4.74/4.99 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[249, 25479])).
% 4.74/4.99 tff(25481,plain,
% 4.74/4.99 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[13776, 25480, 24647, 24649, 5619])).
% 4.74/4.99 tff(25482,plain,
% 4.74/4.99 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[3578, 25481])).
% 4.74/4.99 tff(25483,plain,
% 4.74/4.99 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[20457, 25482, 13066])).
% 4.74/4.99 tff(25484,plain,
% 4.74/4.99 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[691, 25483, 25446])).
% 4.74/4.99 tff(25485,plain,
% 4.74/4.99 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 4.74/4.99 inference(monotonicity,[status(thm)],[25484])).
% 4.74/4.99 tff(25486,plain,
% 4.74/4.99 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 4.74/4.99 inference(monotonicity,[status(thm)],[25485])).
% 4.74/4.99 tff(25487,plain,
% 4.74/4.99 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(z))) <=> b(s(elem!1), s(s(z)))),
% 4.74/4.99 inference(symmetry,[status(thm)],[25486])).
% 4.74/4.99 tff(25488,plain,
% 4.74/4.99 ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) <=> (~b(s(elem!1), s(s(z))))),
% 4.74/4.99 inference(monotonicity,[status(thm)],[25487])).
% 4.74/4.99 tff(25489,plain,
% 4.74/4.99 (~(s(s(s(elem!1))) = elem!1)),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[16438, 25449])).
% 4.74/4.99 tff(25490,plain,
% 4.74/4.99 (~(s(elem!1) = elem!1)),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[2150, 25489])).
% 4.74/4.99 tff(25491,plain,
% 4.74/4.99 (~(s(elem!1) = s(s(z)))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[2832, 25484])).
% 4.74/4.99 tff(25492,plain,
% 4.74/4.99 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[2840, 25491])).
% 4.74/4.99 tff(25493,plain,
% 4.74/4.99 (~r(z, s(s(s(elem!1))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[25455, 25492, 47, 25334])).
% 4.74/4.99 tff(25494,plain,
% 4.74/4.99 (b(z, s(s(s(elem!1))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[2095, 25493])).
% 4.74/4.99 tff(25495,plain,
% 4.74/4.99 (~b(s(s(s(elem!1))), elem!1)),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[12925, 25494, 25449, 25448, 25447])).
% 4.74/4.99 tff(25496,plain,
% 4.74/4.99 (r(s(s(s(elem!1))), elem!1)),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[570, 25495, 25489])).
% 4.74/4.99 tff(25497,plain,
% 4.74/4.99 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[16181, 25484])).
% 4.74/4.99 tff(25498,plain,
% 4.74/4.99 (~(s(s(s(s(z)))) = s(elem!1))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[2168, 25497])).
% 4.74/4.99 tff(25499,plain,
% 4.74/4.99 (~(s(s(elem!1)) = elem!1)),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[2510, 25498, 25484])).
% 4.74/4.99 tff(25500,plain,
% 4.74/4.99 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[348, 25499])).
% 4.74/4.99 tff(25501,plain,
% 4.74/4.99 (~(s(s(z)) = s(elem!1))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[1058, 25491])).
% 4.74/4.99 tff(25502,plain,
% 4.74/4.99 (r(elem!1, s(s(s(s(z)))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[24769, 25484, 24761])).
% 4.74/4.99 tff(25503,plain,
% 4.74/4.99 (r(s(elem!1), s(s(s(s(z)))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[1084, 5720, 1369])).
% 4.74/4.99 tff(25504,plain,
% 4.74/4.99 (r(elem!1, s(elem!1))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[10314, 5720, 461, 3170, 356, 5618])).
% 4.74/4.99 tff(25505,plain,
% 4.74/4.99 ($false),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[14364, 25504, 25503, 470])).
% 4.74/4.99 tff(25506,plain,(b(s(elem!1), s(s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))) | b(elem!1, s(s(z))) | b(s(s(s(s(z)))), z) | (s(s(s(elem!1))) = s(elem!1)) | r(s(s(z)), z) | (s(elem!1) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.99 tff(25507,plain,
% 4.74/4.99 (b(s(elem!1), s(s(s(s(z)))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[25506, 25500, 5618, 3170, 461, 25502, 25497])).
% 4.74/4.99 tff(25508,plain,
% 4.74/4.99 (~b(s(s(s(z))), z)),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[23367, 25482, 5619, 25439, 24649, 25334])).
% 4.74/4.99 tff(25509,plain,
% 4.74/4.99 (r(s(s(s(z))), z)),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[21073, 25508])).
% 4.74/4.99 tff(25510,plain,
% 4.74/4.99 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[20784, 25509, 3244])).
% 4.74/4.99 tff(25511,plain,
% 4.74/4.99 (b(s(s(s(s(z)))), s(s(s(z))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[11185, 25510])).
% 4.74/4.99 tff(25512,plain,
% 4.74/4.99 ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[4944, 178, 24641, 25336, 24655])).
% 4.74/4.99 tff(25513,plain,
% 4.74/4.99 (~b(s(s(s(z))), s(s(z)))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[25512, 25511])).
% 4.74/4.99 tff(25514,plain,
% 4.74/4.99 (r(s(s(s(z))), s(s(z)))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[4966, 25513])).
% 4.74/4.99 tff(25515,plain,
% 4.74/4.99 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[8218, 25514, 25482])).
% 4.74/4.99 tff(25516,plain,
% 4.74/4.99 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[20667, 25515])).
% 4.74/4.99 tff(25517,plain,
% 4.74/4.99 (~r(s(elem!1), s(s(s(z))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[24974, 118, 363, 1125])).
% 4.74/4.99 tff(25518,plain,
% 4.74/4.99 (b(s(elem!1), s(s(s(z))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[23881, 41, 23528, 25517])).
% 4.74/4.99 tff(25519,plain,
% 4.74/4.99 (~r(s(s(s(z))), z)),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[6019, 118, 3261, 1125])).
% 4.74/4.99 tff(25520,plain,
% 4.74/4.99 (b(s(s(s(z))), z)),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[21073, 25519])).
% 4.74/4.99 tff(25521,plain,
% 4.74/4.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z))))))),
% 4.74/4.99 inference(rewrite,[status(thm)],[])).
% 4.74/4.99 tff(25522,plain,
% 4.74/4.99 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(s(elem!1), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z))))))),
% 4.74/4.99 inference(rewrite,[status(thm)],[])).
% 4.74/4.99 tff(25523,plain,
% 4.74/4.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z)))))))),
% 4.74/4.99 inference(monotonicity,[status(thm)],[25522])).
% 4.74/4.99 tff(25524,plain,
% 4.74/4.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z))))))),
% 4.74/4.99 inference(transitivity,[status(thm)],[25523, 25521])).
% 4.74/4.99 tff(25525,plain,
% 4.74/4.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z))))))),
% 4.74/4.99 inference(quant_inst,[status(thm)],[])).
% 4.74/4.99 tff(25526,plain,
% 4.74/4.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z)))))),
% 4.74/4.99 inference(modus_ponens,[status(thm)],[25525, 25524])).
% 4.74/4.99 tff(25527,plain,
% 4.74/4.99 ($false),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[25526, 178, 24248, 595, 25520, 3002, 25518])).
% 4.74/4.99 tff(25528,plain,((~r(s(elem!1), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.99 tff(25529,plain,
% 4.74/4.99 (~r(s(elem!1), s(s(z)))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[25528, 25516, 25334, 23528, 25514, 24649])).
% 4.74/4.99 tff(25530,plain,
% 4.74/4.99 (b(s(elem!1), s(s(z)))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[421, 25529, 25491])).
% 4.74/4.99 tff(25531,plain,
% 4.74/4.99 (~b(s(s(z)), s(elem!1))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[1079, 25530, 25336, 24641, 25507])).
% 4.74/4.99 tff(25532,plain,
% 4.74/4.99 (r(s(s(z)), s(elem!1))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[1067, 25531, 25501])).
% 4.74/4.99 tff(25533,plain,
% 4.74/4.99 (~r(z, s(elem!1))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[12114, 25532, 25334])).
% 4.74/4.99 tff(25534,plain,
% 4.74/4.99 (b(z, s(elem!1))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[2351, 25533])).
% 4.74/4.99 tff(25535,plain,
% 4.74/4.99 (~b(s(s(s(elem!1))), s(elem!1))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[2052, 25534, 25448, 25494, 25449])).
% 4.74/4.99 tff(25536,plain,
% 4.74/4.99 (r(s(s(s(elem!1))), s(elem!1))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[373, 25535, 25500])).
% 4.74/4.99 tff(25537,plain,
% 4.74/4.99 (~r(s(elem!1), elem!1)),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[1576, 25536, 25496])).
% 4.74/4.99 tff(25538,plain,
% 4.74/4.99 (b(s(elem!1), elem!1)),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[677, 25537, 25490])).
% 4.74/4.99 tff(25539,plain,
% 4.74/4.99 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[686, 25538, 25484])).
% 4.74/4.99 tff(25540,plain,
% 4.74/4.99 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[16215, 25539, 25480, 5619, 25484, 24647])).
% 4.74/4.99 tff(25541,plain,
% 4.74/4.99 (~b(s(elem!1), s(s(z)))),
% 4.74/4.99 inference(modus_ponens,[status(thm)],[25540, 25488])).
% 4.74/4.99 tff(25542,plain,
% 4.74/4.99 ($false),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[25530, 25541])).
% 4.74/4.99 tff(25543,plain,(b(elem!1, s(s(z))) | (s(elem!1) = s(s(s(z)))) | r(s(s(z)), z) | b(s(s(s(s(z)))), z) | (z = elem!1) | (elem!1 = s(s(z))) | b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.74/4.99 tff(25544,plain,
% 4.74/4.99 (b(elem!1, s(s(z)))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[25543, 3170, 5618, 23437, 507, 312, 1])).
% 4.74/4.99 tff(25545,plain,
% 4.74/4.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 4.74/4.99 inference(rewrite,[status(thm)],[])).
% 4.74/4.99 tff(25546,plain,
% 4.74/4.99 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 4.74/4.99 inference(rewrite,[status(thm)],[])).
% 4.74/4.99 tff(25547,plain,
% 4.74/4.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 4.74/4.99 inference(monotonicity,[status(thm)],[25546])).
% 4.74/4.99 tff(25548,plain,
% 4.74/4.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 4.74/4.99 inference(transitivity,[status(thm)],[25547, 25545])).
% 4.74/4.99 tff(25549,plain,
% 4.74/4.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.74/4.99 inference(quant_inst,[status(thm)],[])).
% 4.74/4.99 tff(25550,plain,
% 4.74/4.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 4.74/4.99 inference(modus_ponens,[status(thm)],[25549, 25548])).
% 4.74/4.99 tff(25551,plain,
% 4.74/4.99 ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[25550, 178, 5619, 25544, 24647])).
% 4.74/4.99 tff(25552,plain,
% 4.74/4.99 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[25551, 25443])).
% 4.74/4.99 tff(25553,plain,
% 4.74/4.99 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[13776, 25443, 24647, 24649, 5619])).
% 4.74/4.99 tff(25554,plain,
% 4.74/4.99 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.74/4.99 inference(unit_resolution,[status(thm)],[249, 25553])).
% 4.74/4.99 tff(25555,plain,
% 4.74/4.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), 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))))))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), 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))))))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 4.74/4.99 inference(rewrite,[status(thm)],[])).
% 4.74/4.99 tff(25556,plain,
% 4.74/4.99 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), 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))))))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 4.74/4.99 inference(rewrite,[status(thm)],[])).
% 4.74/4.99 tff(25557,plain,
% 4.74/4.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), 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))))))), z)) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 4.74/4.99 inference(monotonicity,[status(thm)],[25556])).
% 4.74/4.99 tff(25558,plain,
% 4.74/4.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), 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))))))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 4.74/4.99 inference(transitivity,[status(thm)],[25557, 25555])).
% 4.74/4.99 tff(25559,plain,
% 4.74/4.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.74/4.99 inference(quant_inst,[status(thm)],[])).
% 4.74/4.99 tff(25560,plain,
% 4.74/4.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), 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))))))), z)) | (~b(s(s(s(s(z)))), s(s(z))))),
% 4.74/4.99 inference(modus_ponens,[status(thm)],[25559, 25558])).
% 4.74/4.99 tff(25561,plain,
% 4.74/4.99 ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[25560, 178, 5619, 25336, 24647])).
% 4.74/5.00 tff(25562,plain,
% 4.74/5.00 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[25561, 25443])).
% 4.74/5.00 tff(25563,plain,
% 4.74/5.00 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[222, 25562])).
% 4.74/5.00 tff(25564,plain,
% 4.74/5.00 (~r(s(s(s(s(z)))), elem!1)),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[20490, 521, 145])).
% 4.74/5.00 tff(25565,plain,
% 4.74/5.00 (~r(s(s(s(s(z)))), s(s(z)))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[3269, 3261, 145])).
% 4.74/5.00 tff(25566,plain,
% 4.74/5.00 (b(s(s(s(s(z)))), s(s(z)))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[102, 25565])).
% 4.74/5.00 tff(25567,plain,
% 4.74/5.00 (s(s(s(s(z)))) = elem!1),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[24866, 530, 24607, 812, 25566, 25564])).
% 4.74/5.00 tff(25568,plain,
% 4.74/5.00 (elem!1 = s(s(s(s(z))))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[504, 25567])).
% 4.74/5.00 tff(25569,plain,
% 4.74/5.00 (~(s(elem!1) = s(s(z)))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[11438, 25568])).
% 4.74/5.00 tff(25570,plain,
% 4.74/5.00 (~(s(s(z)) = s(elem!1))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[1058, 25569])).
% 4.74/5.00 tff(25571,plain,
% 4.74/5.00 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), elem!1)),
% 4.74/5.00 inference(monotonicity,[status(thm)],[25567])).
% 4.74/5.00 tff(25572,plain,
% 4.74/5.00 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(s(z)))))),
% 4.74/5.00 inference(symmetry,[status(thm)],[25571])).
% 4.74/5.00 tff(25573,plain,
% 4.74/5.00 (~(s(s(elem!1)) = elem!1)),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[338, 25567, 12])).
% 4.74/5.00 tff(25574,plain,
% 4.74/5.00 (~(s(elem!1) = elem!1)),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[672, 25573])).
% 4.74/5.00 tff(25575,plain,
% 4.74/5.00 (s(s(s(s(s(z))))) = s(elem!1)),
% 4.74/5.00 inference(monotonicity,[status(thm)],[25567])).
% 4.74/5.00 tff(25576,plain,
% 4.74/5.00 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 4.74/5.00 inference(monotonicity,[status(thm)],[25575])).
% 4.74/5.00 tff(25577,plain,
% 4.74/5.00 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 4.74/5.00 inference(monotonicity,[status(thm)],[25576])).
% 4.74/5.00 tff(25578,plain,
% 4.74/5.00 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 4.74/5.00 inference(monotonicity,[status(thm)],[25577])).
% 4.74/5.00 tff(25579,plain,
% 4.74/5.00 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.74/5.00 inference(monotonicity,[status(thm)],[25567])).
% 4.74/5.00 tff(25580,plain,
% 4.74/5.00 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.74/5.00 inference(modus_ponens,[status(thm)],[24592, 25579])).
% 4.74/5.00 tff(25581,plain,
% 4.74/5.00 (r(s(s(s(elem!1))), elem!1)),
% 4.74/5.00 inference(modus_ponens,[status(thm)],[25580, 25578])).
% 4.74/5.00 tff(25582,plain,
% 4.74/5.00 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[348, 25573])).
% 4.74/5.00 tff(25583,plain,
% 4.74/5.00 (b(z, s(s(s(elem!1))))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[17717, 25568, 24623])).
% 4.74/5.00 tff(25584,plain,
% 4.74/5.00 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 4.74/5.00 inference(monotonicity,[status(thm)],[25577])).
% 4.74/5.00 tff(25585,plain,
% 4.74/5.00 ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) <=> (~b(s(s(s(elem!1))), elem!1))),
% 4.74/5.00 inference(monotonicity,[status(thm)],[25584])).
% 4.74/5.00 tff(25586,plain,
% 4.74/5.00 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.74/5.00 inference(monotonicity,[status(thm)],[25567])).
% 4.74/5.00 tff(25587,plain,
% 4.74/5.00 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) <=> (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 4.74/5.00 inference(monotonicity,[status(thm)],[25586])).
% 4.74/5.00 tff(25588,plain,
% 4.74/5.00 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.74/5.00 inference(modus_ponens,[status(thm)],[3428, 25587])).
% 4.74/5.00 tff(25589,plain,
% 4.74/5.00 (~b(s(s(s(elem!1))), elem!1)),
% 4.74/5.00 inference(modus_ponens,[status(thm)],[25588, 25585])).
% 4.74/5.00 tff(25590,plain,
% 4.74/5.00 (b(s(elem!1), elem!1)),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[24899, 25589, 521, 25583, 25582, 25581, 25574])).
% 4.74/5.00 tff(25591,plain,
% 4.74/5.00 (b(s(elem!1), s(s(s(s(z)))))),
% 4.74/5.00 inference(modus_ponens,[status(thm)],[25590, 25572])).
% 4.74/5.00 tff(25592,plain,
% 4.74/5.00 (~r(z, s(s(s(z))))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[23351, 3244, 145, 3261])).
% 4.74/5.00 tff(25593,plain,
% 4.74/5.00 (b(z, s(s(s(z))))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[4920, 25592])).
% 4.74/5.00 tff(25594,plain,
% 4.74/5.00 (~r(s(s(s(z))), z)),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[25391, 3244, 24607, 25566, 24604, 3261])).
% 4.74/5.00 tff(25595,plain,
% 4.74/5.00 (b(s(s(s(z))), z)),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[21073, 25594])).
% 4.74/5.00 tff(25596,plain,
% 4.74/5.00 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[23367, 25595, 5619, 25593, 24623, 3261])).
% 4.74/5.00 tff(25597,plain,
% 4.74/5.00 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[3578, 25596])).
% 4.74/5.00 tff(25598,plain,
% 4.74/5.00 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[13776, 25597, 24625, 24623, 5619])).
% 4.74/5.00 tff(25599,plain,
% 4.74/5.00 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[249, 25598])).
% 4.74/5.00 tff(25600,plain,
% 4.74/5.00 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 4.74/5.00 inference(symmetry,[status(thm)],[25577])).
% 4.74/5.00 tff(25601,plain,
% 4.74/5.00 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 4.74/5.00 inference(monotonicity,[status(thm)],[25600])).
% 4.74/5.00 tff(25602,plain,
% 4.74/5.00 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.74/5.00 inference(transitivity,[status(thm)],[25601, 377])).
% 4.74/5.00 tff(25603,plain,
% 4.74/5.00 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 4.74/5.00 inference(monotonicity,[status(thm)],[25602])).
% 4.74/5.00 tff(25604,plain,
% 4.74/5.00 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.74/5.00 inference(modus_ponens,[status(thm)],[25582, 25603])).
% 4.74/5.00 tff(25605,plain,
% 4.74/5.00 (b(s(s(s(s(s(s(s(z))))))), z) <=> b(s(s(s(elem!1))), z)),
% 4.74/5.00 inference(monotonicity,[status(thm)],[25577])).
% 4.74/5.00 tff(25606,plain,
% 4.74/5.00 (b(s(s(s(elem!1))), z)),
% 4.74/5.00 inference(modus_ponens,[status(thm)],[24625, 25605])).
% 4.74/5.00 tff(25607,plain,
% 4.74/5.00 (r(s(elem!1), s(s(z)))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[421, 305, 23849])).
% 4.74/5.00 tff(25608,plain,
% 4.74/5.00 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[390, 25607, 224])).
% 4.74/5.00 tff(25609,plain,
% 4.74/5.00 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[395, 25608, 2286])).
% 4.74/5.00 tff(25610,plain,
% 4.74/5.00 (b(s(elem!1), s(s(s(elem!1))))),
% 4.74/5.00 inference(modus_ponens,[status(thm)],[25609, 24905])).
% 4.74/5.00 tff(25611,plain,
% 4.74/5.00 (~r(s(elem!1), z)),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[11747, 305, 3261, 5618])).
% 4.74/5.00 tff(25612,plain,
% 4.74/5.00 (b(s(elem!1), z)),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[774, 25611])).
% 4.74/5.00 tff(25613,plain,
% 4.74/5.00 (~r(z, s(elem!1))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[11762, 25607, 3261])).
% 4.74/5.00 tff(25614,plain,
% 4.74/5.00 (b(z, s(elem!1))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[2351, 25613])).
% 4.74/5.00 tff(25615,plain,
% 4.74/5.00 ($false),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[6348, 178, 25614, 2043, 7976, 25612, 25610])).
% 4.74/5.00 tff(25616,plain,(b(s(elem!1), s(s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~(s(s(s(s(z)))) = elem!1)) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 4.74/5.00 tff(25617,plain,
% 4.74/5.00 (b(s(elem!1), s(s(z)))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[25616, 25583, 25606, 25567, 25604, 25599, 3261, 5618])).
% 4.74/5.00 tff(25618,plain,
% 4.74/5.00 (~b(s(s(z)), s(elem!1))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[1079, 25617, 25566, 24607, 25591])).
% 4.74/5.00 tff(25619,plain,
% 4.74/5.00 (r(s(s(z)), s(elem!1))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[1067, 25618, 25570])).
% 4.74/5.00 tff(25620,plain,
% 4.74/5.00 (~r(z, s(elem!1))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[12114, 25619, 3261])).
% 4.74/5.00 tff(25621,plain,
% 4.74/5.00 (b(z, s(elem!1))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[2351, 25620])).
% 4.74/5.00 tff(25622,plain,
% 4.74/5.00 (~(s(elem!1) = s(s(s(elem!1))))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[5395, 25582])).
% 4.74/5.00 tff(25623,plain,
% 4.74/5.00 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 4.74/5.00 inference(monotonicity,[status(thm)],[25577])).
% 4.74/5.00 tff(25624,plain,
% 4.74/5.00 ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(s(z)), s(s(s(elem!1)))))),
% 4.74/5.00 inference(monotonicity,[status(thm)],[25623])).
% 4.74/5.00 tff(25625,plain,
% 4.74/5.00 (~b(s(s(z)), s(s(s(elem!1))))),
% 4.74/5.00 inference(modus_ponens,[status(thm)],[25598, 25624])).
% 4.74/5.00 tff(25626,plain,
% 4.74/5.00 (b(s(elem!1), s(s(s(elem!1))))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[6127, 25619, 25625, 25622])).
% 4.74/5.00 tff(25627,plain,
% 4.74/5.00 (~b(elem!1, z)),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[3172, 25568, 3170])).
% 4.74/5.00 tff(25628,plain,
% 4.74/5.00 (r(elem!1, z)),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[498, 25627, 290])).
% 4.74/5.00 tff(25629,plain,
% 4.74/5.00 (~(elem!1 = s(elem!1))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[748, 25574])).
% 4.74/5.00 tff(25630,plain,
% 4.74/5.00 ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z))))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[24965, 178, 25590, 11801, 812])).
% 4.74/5.00 tff(25631,plain,
% 4.74/5.00 (~b(elem!1, s(elem!1))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[25630, 25617])).
% 4.74/5.00 tff(25632,plain,
% 4.74/5.00 (r(elem!1, s(elem!1))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[756, 25631, 25629])).
% 4.74/5.00 tff(25633,plain,
% 4.74/5.00 (~r(s(elem!1), z)),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[2711, 25632, 25628])).
% 4.74/5.00 tff(25634,plain,
% 4.74/5.00 (b(s(elem!1), z)),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[774, 25633])).
% 4.74/5.00 tff(25635,plain,
% 4.74/5.00 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(elem!1))))),
% 4.74/5.00 inference(monotonicity,[status(thm)],[25577])).
% 4.74/5.00 tff(25636,plain,
% 4.74/5.00 ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[25550, 178, 5619, 812, 24625])).
% 4.74/5.00 tff(25637,plain,
% 4.74/5.00 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[25636, 25597])).
% 4.74/5.00 tff(25638,plain,
% 4.74/5.00 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[24769, 530, 3428])).
% 4.74/5.00 tff(25639,plain,
% 4.74/5.00 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[691, 25638, 25637])).
% 4.74/5.00 tff(25640,plain,
% 4.74/5.00 (r(elem!1, s(s(s(elem!1))))),
% 4.74/5.00 inference(modus_ponens,[status(thm)],[25639, 25635])).
% 4.74/5.00 tff(25641,plain,
% 4.74/5.00 (~r(s(s(s(elem!1))), s(elem!1))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[1591, 25632, 25640])).
% 4.74/5.00 tff(25642,plain,
% 4.74/5.00 (b(s(s(s(elem!1))), s(elem!1))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[373, 25641, 25582])).
% 4.74/5.00 tff(25643,plain,
% 4.74/5.00 ($false),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[6736, 25642, 25634, 25583, 25626, 25621])).
% 4.74/5.00 tff(25644,plain,((~r(z, elem!1)) | (~r(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | r(s(s(z)), z) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | (elem!1 = z) | b(s(s(s(s(z)))), z) | (s(s(z)) = elem!1) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.74/5.00 tff(25645,plain,
% 4.74/5.00 (~r(z, elem!1)),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[25644, 25544, 25334, 5618, 24761, 2809, 3170, 12, 47])).
% 4.74/5.00 tff(25646,plain,
% 4.74/5.00 (b(z, elem!1)),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[585, 25645, 507])).
% 4.74/5.00 tff(25647,plain,
% 4.74/5.00 (~(elem!1 = s(s(s(s(z)))))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[1846, 25646, 1])).
% 4.74/5.00 tff(25648,plain,
% 4.74/5.00 (~(s(s(s(s(z)))) = elem!1)),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[504, 25647])).
% 4.74/5.00 tff(25649,plain,
% 4.74/5.00 (~r(s(s(z)), elem!1)),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[2801, 118, 224, 1265])).
% 4.74/5.00 tff(25650,plain,
% 4.74/5.00 (~b(s(s(z)), elem!1)),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[17305, 1265, 167, 204, 202, 323])).
% 4.74/5.00 tff(25651,plain,
% 4.74/5.00 ($false),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[448, 25650, 25649, 12])).
% 4.74/5.00 tff(25652,plain,((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (s(s(z)) = elem!1) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (s(s(s(s(z)))) = elem!1) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.74/5.00 tff(25653,plain,
% 4.74/5.00 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[25652, 25648, 24641, 12, 25336, 25563, 25554])).
% 4.74/5.00 tff(25654,plain,
% 4.74/5.00 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[691, 25653, 25552])).
% 4.74/5.00 tff(25655,plain,
% 4.74/5.00 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 4.74/5.00 inference(monotonicity,[status(thm)],[25654])).
% 4.74/5.00 tff(25656,plain,
% 4.74/5.00 (r(s(s(z)), s(elem!1)) <=> r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 4.74/5.00 inference(monotonicity,[status(thm)],[25655])).
% 4.74/5.00 tff(25657,plain,
% 4.74/5.00 (r(s(s(z)), s(s(s(s(s(s(s(s(z))))))))) <=> r(s(s(z)), s(elem!1))),
% 4.74/5.00 inference(symmetry,[status(thm)],[25656])).
% 4.74/5.00 tff(25658,plain,
% 4.74/5.00 ((~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) <=> (~r(s(s(z)), s(elem!1)))),
% 4.74/5.00 inference(monotonicity,[status(thm)],[25657])).
% 4.74/5.00 tff(25659,plain,
% 4.74/5.00 (s(s(s(s(s(s(s(s(z)))))))) = s(elem!1)),
% 4.74/5.00 inference(symmetry,[status(thm)],[25655])).
% 4.74/5.00 tff(25660,plain,
% 4.74/5.00 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.74/5.00 inference(monotonicity,[status(thm)],[25659])).
% 4.74/5.00 tff(25661,plain,
% 4.74/5.00 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 4.74/5.00 inference(symmetry,[status(thm)],[25660])).
% 4.74/5.00 tff(25662,plain,
% 4.74/5.00 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.74/5.00 inference(monotonicity,[status(thm)],[25654])).
% 4.74/5.00 tff(25663,plain,
% 4.74/5.00 ((~(s(elem!1) = elem!1)) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 4.74/5.00 inference(monotonicity,[status(thm)],[25662])).
% 4.74/5.00 tff(25664,plain,
% 4.74/5.00 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[16181, 25654])).
% 4.74/5.00 tff(25665,plain,
% 4.74/5.00 (~(s(s(s(s(z)))) = s(elem!1))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[2168, 25664])).
% 4.74/5.00 tff(25666,plain,
% 4.74/5.00 (~(s(s(elem!1)) = elem!1)),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[2510, 25665, 25654])).
% 4.74/5.00 tff(25667,plain,
% 4.74/5.00 (~(s(elem!1) = elem!1)),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[672, 25666])).
% 4.74/5.00 tff(25668,plain,
% 4.74/5.00 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.74/5.00 inference(modus_ponens,[status(thm)],[25667, 25663])).
% 4.74/5.00 tff(25669,plain,
% 4.74/5.00 (b(s(s(s(s(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))))))))),
% 4.74/5.00 inference(monotonicity,[status(thm)],[25659])).
% 4.74/5.00 tff(25670,plain,
% 4.74/5.00 ((~b(s(s(s(s(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)))))))))),
% 4.74/5.00 inference(monotonicity,[status(thm)],[25669])).
% 4.74/5.00 tff(25671,plain,
% 4.74/5.00 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 4.74/5.00 inference(monotonicity,[status(thm)],[25655])).
% 4.74/5.00 tff(25672,plain,
% 4.74/5.00 (r(s(elem!1), s(s(z)))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[421, 305, 10483])).
% 4.74/5.00 tff(25673,plain,
% 4.74/5.00 (~r(z, s(elem!1))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[11762, 25672, 3261])).
% 4.74/5.00 tff(25674,plain,
% 4.74/5.00 (b(z, s(elem!1))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[2351, 25673])).
% 4.74/5.00 tff(25675,plain,
% 4.74/5.00 (b(z, s(s(s(s(s(s(s(s(z)))))))))),
% 4.74/5.00 inference(modus_ponens,[status(thm)],[25674, 16109])).
% 4.74/5.00 tff(25676,plain,
% 4.74/5.00 (b(s(s(s(s(s(s(s(s(z)))))))), z)),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[24205, 25612, 679])).
% 4.74/5.00 tff(25677,plain,
% 4.74/5.00 (~(s(elem!1) = elem!1)),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[672, 19974])).
% 4.74/5.00 tff(25678,plain,
% 4.74/5.00 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.74/5.00 inference(modus_ponens,[status(thm)],[25677, 19272])).
% 4.74/5.00 tff(25679,plain,
% 4.74/5.00 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[390, 25672, 224])).
% 4.74/5.00 tff(25680,plain,
% 4.74/5.00 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[395, 25679, 25678])).
% 4.74/5.00 tff(25681,plain,
% 4.74/5.00 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 4.74/5.00 inference(modus_ponens,[status(thm)],[25680, 11735])).
% 4.74/5.00 tff(25682,plain,
% 4.74/5.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 4.74/5.00 inference(rewrite,[status(thm)],[])).
% 4.74/5.00 tff(25683,plain,
% 4.74/5.00 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(s(z))))))))))) <=> ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 4.74/5.00 inference(rewrite,[status(thm)],[])).
% 4.74/5.00 tff(25684,plain,
% 4.74/5.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))))),
% 4.74/5.00 inference(monotonicity,[status(thm)],[25683])).
% 4.74/5.00 tff(25685,plain,
% 4.74/5.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 4.74/5.00 inference(transitivity,[status(thm)],[25684, 25682])).
% 4.74/5.00 tff(25686,plain,
% 4.74/5.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))))),
% 4.74/5.00 inference(quant_inst,[status(thm)],[])).
% 4.74/5.00 tff(25687,plain,
% 4.74/5.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))),
% 4.74/5.00 inference(modus_ponens,[status(thm)],[25686, 25685])).
% 4.74/5.00 tff(25688,plain,
% 4.74/5.00 ($false),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[25687, 178, 595, 146, 25681, 25676, 25675])).
% 4.74/5.00 tff(25689,plain,(b(s(elem!1), s(s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 4.74/5.00 tff(25690,plain,
% 4.74/5.00 (b(s(elem!1), s(s(z)))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[25689, 25654, 24647, 24649, 25554, 25334, 5618])).
% 4.74/5.00 tff(25691,plain,
% 4.74/5.00 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 4.74/5.00 inference(modus_ponens,[status(thm)],[25690, 25671])).
% 4.74/5.00 tff(25692,plain,
% 4.74/5.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), 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(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), 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(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 4.74/5.00 inference(rewrite,[status(thm)],[])).
% 4.74/5.00 tff(25693,plain,
% 4.74/5.00 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(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(s(z)))))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(z)), 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(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 4.74/5.00 inference(rewrite,[status(thm)],[])).
% 4.74/5.00 tff(25694,plain,
% 4.74/5.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(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(s(z)))))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), 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(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))))),
% 4.74/5.00 inference(monotonicity,[status(thm)],[25693])).
% 4.74/5.00 tff(25695,plain,
% 4.74/5.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(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(s(z)))))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), 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(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 4.74/5.00 inference(transitivity,[status(thm)],[25694, 25692])).
% 4.74/5.00 tff(25696,plain,
% 4.74/5.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(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(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 4.74/5.00 inference(quant_inst,[status(thm)],[])).
% 4.74/5.00 tff(25697,plain,
% 4.74/5.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), 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(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))),
% 4.74/5.00 inference(modus_ponens,[status(thm)],[25696, 25695])).
% 4.74/5.00 tff(25698,plain,
% 4.74/5.00 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[25697, 178, 5619, 24647, 25443, 25691])).
% 4.74/5.00 tff(25699,plain,
% 4.74/5.00 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.74/5.00 inference(modus_ponens,[status(thm)],[25698, 25670])).
% 4.74/5.00 tff(25700,plain,
% 4.74/5.00 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[395, 25699, 25668])).
% 4.74/5.00 tff(25701,plain,
% 4.74/5.00 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 4.74/5.00 inference(modus_ponens,[status(thm)],[25700, 25661])).
% 4.74/5.00 tff(25702,plain,
% 4.74/5.00 (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[21956, 118, 25554, 25701])).
% 4.74/5.00 tff(25703,plain,
% 4.74/5.00 (~r(s(s(z)), s(elem!1))),
% 4.74/5.00 inference(modus_ponens,[status(thm)],[25702, 25658])).
% 4.74/5.00 tff(25704,plain,
% 4.74/5.00 (~(s(elem!1) = s(s(z)))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[2832, 25654])).
% 4.74/5.00 tff(25705,plain,
% 4.74/5.00 (~(s(s(z)) = s(elem!1))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[1058, 25704])).
% 4.74/5.00 tff(25706,plain,
% 4.74/5.00 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.74/5.00 inference(monotonicity,[status(thm)],[25654])).
% 4.74/5.00 tff(25707,plain,
% 4.74/5.00 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(z)))), elem!1)),
% 4.74/5.00 inference(symmetry,[status(thm)],[25706])).
% 4.74/5.00 tff(25708,plain,
% 4.74/5.00 (r(s(s(s(s(z)))), elem!1)),
% 4.74/5.00 inference(modus_ponens,[status(thm)],[25563, 25707])).
% 4.74/5.00 tff(25709,plain,
% 4.74/5.00 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.74/5.00 inference(monotonicity,[status(thm)],[25654])).
% 4.74/5.00 tff(25710,plain,
% 4.74/5.00 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), elem!1)),
% 4.74/5.00 inference(symmetry,[status(thm)],[25709])).
% 4.74/5.00 tff(25711,plain,
% 4.74/5.00 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), elem!1)),
% 4.74/5.00 inference(transitivity,[status(thm)],[25669, 25710])).
% 4.74/5.00 tff(25712,plain,
% 4.74/5.00 ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(elem!1), elem!1))),
% 4.74/5.00 inference(monotonicity,[status(thm)],[25711])).
% 4.74/5.00 tff(25713,plain,
% 4.74/5.00 (~b(s(elem!1), elem!1)),
% 4.74/5.00 inference(modus_ponens,[status(thm)],[25698, 25712])).
% 4.74/5.00 tff(25714,plain,
% 4.74/5.00 (r(s(elem!1), elem!1)),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[677, 25713, 25667])).
% 4.74/5.00 tff(25715,plain,
% 4.74/5.00 (~r(s(elem!1), s(s(s(s(z)))))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[7010, 25714, 25708])).
% 4.74/5.00 tff(25716,plain,
% 4.74/5.00 (b(s(elem!1), s(s(s(s(z)))))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[1084, 25715, 25664])).
% 4.74/5.00 tff(25717,plain,
% 4.74/5.00 (~b(s(s(z)), s(elem!1))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[1079, 25716, 25336, 24641, 25690])).
% 4.74/5.00 tff(25718,plain,
% 4.74/5.00 (r(s(s(z)), s(elem!1))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[1067, 25717, 25705])).
% 4.74/5.00 tff(25719,plain,
% 4.74/5.00 ($false),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[25718, 25703])).
% 4.74/5.00 tff(25720,plain,(b(s(s(s(s(z)))), z) | r(s(s(z)), z) | (s(s(z)) = elem!1) | b(z, s(s(s(s(z))))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.74/5.00 tff(25721,plain,
% 4.74/5.00 (s(s(z)) = elem!1),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[25720, 25437, 25384, 1, 5618])).
% 4.74/5.00 tff(25722,plain,
% 4.74/5.00 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[11305, 25721, 25397])).
% 4.74/5.00 tff(25723,plain,
% 4.74/5.00 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[5361, 25721])).
% 4.74/5.00 tff(25724,plain,
% 4.74/5.00 (s(s(s(z))) = s(elem!1)),
% 4.74/5.00 inference(monotonicity,[status(thm)],[25721])).
% 4.74/5.00 tff(25725,plain,
% 4.74/5.00 (b(s(s(s(z))), z) <=> b(s(elem!1), z)),
% 4.74/5.00 inference(monotonicity,[status(thm)],[25724])).
% 4.74/5.00 tff(25726,plain,
% 4.74/5.00 (b(s(elem!1), z)),
% 4.74/5.00 inference(modus_ponens,[status(thm)],[25393, 25725])).
% 4.74/5.00 tff(25727,plain,
% 4.74/5.00 (b(z, s(s(s(z)))) <=> b(z, s(elem!1))),
% 4.74/5.00 inference(monotonicity,[status(thm)],[25724])).
% 4.74/5.00 tff(25728,plain,
% 4.74/5.00 (b(z, s(elem!1))),
% 4.74/5.00 inference(modus_ponens,[status(thm)],[25387, 25727])).
% 4.74/5.00 tff(25729,plain,
% 4.74/5.00 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[23105, 178, 25728, 25726, 24649, 24647])).
% 4.74/5.00 tff(25730,plain,
% 4.74/5.00 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[395, 25729, 25723])).
% 4.74/5.00 tff(25731,plain,
% 4.74/5.00 (~r(elem!1, s(elem!1))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[2935, 25730, 25722])).
% 4.74/5.00 tff(25732,plain,
% 4.74/5.00 ((s(elem!1) = s(s(z))) <=> (s(elem!1) = elem!1)),
% 4.74/5.00 inference(monotonicity,[status(thm)],[25721])).
% 4.74/5.00 tff(25733,plain,
% 4.74/5.00 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(z)))),
% 4.74/5.00 inference(symmetry,[status(thm)],[25732])).
% 4.74/5.00 tff(25734,plain,
% 4.74/5.00 ((~(s(elem!1) = elem!1)) <=> (~(s(elem!1) = s(s(z))))),
% 4.74/5.00 inference(monotonicity,[status(thm)],[25733])).
% 4.74/5.00 tff(25735,plain,
% 4.74/5.00 (~b(elem!1, s(s(z)))),
% 4.74/5.00 inference(unit_resolution,[status(thm)],[3223, 25721])).
% 4.74/5.01 tff(25736,plain,
% 4.74/5.01 (b(elem!1, s(s(s(elem!1))))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[19038, 25735, 1, 24761, 25384])).
% 4.74/5.01 tff(25737,plain,
% 4.74/5.01 (~(s(s(s(elem!1))) = elem!1)),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[16438, 25736])).
% 4.74/5.01 tff(25738,plain,
% 4.74/5.01 (~(s(elem!1) = elem!1)),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[2150, 25737])).
% 4.74/5.01 tff(25739,plain,
% 4.74/5.01 (~(s(elem!1) = s(s(z)))),
% 4.74/5.01 inference(modus_ponens,[status(thm)],[25738, 25734])).
% 4.74/5.01 tff(25740,plain,
% 4.74/5.01 (~r(s(elem!1), s(s(z)))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[390, 25730, 25397])).
% 4.74/5.01 tff(25741,plain,
% 4.74/5.01 (r(s(s(z)), s(elem!1))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[12205, 25740, 5619, 25739, 25728, 25726])).
% 4.74/5.01 tff(25742,plain,
% 4.74/5.01 ($false),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[1331, 25741, 25731, 25721])).
% 4.74/5.01 tff(25743,plain,(r(s(s(z)), z) | b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.74/5.01 tff(25744,plain,
% 4.74/5.01 (r(s(s(z)), z)),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[25743, 1])).
% 4.74/5.01 tff(25745,plain,
% 4.74/5.01 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 4.74/5.01 inference(monotonicity,[status(thm)],[16])).
% 4.74/5.01 tff(25746,plain,
% 4.74/5.01 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.74/5.01 inference(transitivity,[status(thm)],[25745, 3289])).
% 4.74/5.01 tff(25747,plain,
% 4.74/5.01 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(z))))))),
% 4.74/5.01 inference(monotonicity,[status(thm)],[25746])).
% 4.74/5.01 tff(25748,plain,
% 4.74/5.01 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.74/5.01 inference(modus_ponens,[status(thm)],[4938, 25747])).
% 4.74/5.01 tff(25749,plain,
% 4.74/5.01 (~r(z, s(s(s(elem!1))))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[25455, 25748, 47, 25334])).
% 4.74/5.01 tff(25750,plain,
% 4.74/5.01 (b(z, s(s(s(elem!1))))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[2095, 25749])).
% 4.74/5.01 tff(25751,plain,
% 4.74/5.01 (~(s(elem!1) = s(s(z)))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[17598, 25750, 1])).
% 4.74/5.01 tff(25752,plain,
% 4.74/5.01 (~r(s(s(z)), s(elem!1))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[2341, 2333, 106])).
% 4.74/5.01 tff(25753,plain,
% 4.74/5.01 (b(s(s(z)), s(elem!1))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[1067, 25752, 2311])).
% 4.74/5.01 tff(25754,plain,
% 4.74/5.01 ($false),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[1079, 23180, 25753, 202, 167, 1069])).
% 4.74/5.01 tff(25755,plain,((~r(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (s(elem!1) = s(s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 4.74/5.01 tff(25756,plain,
% 4.74/5.01 (~b(s(elem!1), s(s(s(s(z)))))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[25755, 2333, 24607, 25566, 1056, 3261, 106])).
% 4.74/5.01 tff(25757,plain,
% 4.74/5.01 ($false),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[1084, 25756, 23182, 1369])).
% 4.74/5.01 tff(25758,plain,((~r(z, s(elem!1))) | (s(elem!1) = s(s(s(s(z))))) | (s(elem!1) = s(s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.74/5.01 tff(25759,plain,
% 4.74/5.01 (~r(z, s(elem!1))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[25758, 25361, 25751, 25334, 25744, 47])).
% 4.74/5.01 tff(25760,plain,
% 4.74/5.01 (b(z, s(elem!1))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[2351, 25759])).
% 4.74/5.01 tff(25761,plain,
% 4.74/5.01 (b(elem!1, s(elem!1))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[12054, 25760, 5198])).
% 4.74/5.01 tff(25762,plain,
% 4.74/5.01 (b(z, s(z))),
% 4.74/5.01 inference(modus_ponens,[status(thm)],[25761, 25363])).
% 4.74/5.01 tff(25763,plain,
% 4.74/5.01 (b(s(z), z) <=> b(s(elem!1), elem!1)),
% 4.74/5.01 inference(monotonicity,[status(thm)],[14, 13])).
% 4.74/5.01 tff(25764,plain,
% 4.74/5.01 (b(s(elem!1), elem!1) <=> b(s(z), z)),
% 4.74/5.01 inference(symmetry,[status(thm)],[25763])).
% 4.74/5.01 tff(25765,plain,
% 4.74/5.01 ((s(elem!1) = z) <=> (s(elem!1) = elem!1)),
% 4.74/5.01 inference(monotonicity,[status(thm)],[13])).
% 4.74/5.01 tff(25766,plain,
% 4.74/5.01 ((~(s(elem!1) = z)) <=> (~(s(elem!1) = elem!1))),
% 4.74/5.01 inference(monotonicity,[status(thm)],[25765])).
% 4.74/5.01 tff(25767,plain,
% 4.74/5.01 (~(s(elem!1) = elem!1)),
% 4.74/5.01 inference(modus_ponens,[status(thm)],[769, 25766])).
% 4.74/5.01 tff(25768,plain,
% 4.74/5.01 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 4.74/5.01 inference(symmetry,[status(thm)],[17])).
% 4.74/5.01 tff(25769,plain,
% 4.74/5.01 (r(s(elem!1), s(s(s(s(elem!1))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 4.74/5.01 inference(monotonicity,[status(thm)],[25768])).
% 4.74/5.01 tff(25770,plain,
% 4.74/5.01 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(elem!1)))))),
% 4.74/5.01 inference(symmetry,[status(thm)],[25769])).
% 4.74/5.01 tff(25771,plain,
% 4.74/5.01 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 4.74/5.01 inference(modus_ponens,[status(thm)],[908, 25770])).
% 4.74/5.01 tff(25772,plain,
% 4.74/5.01 (r(elem!1, s(s(s(s(elem!1))))) <=> r(elem!1, s(s(s(s(z)))))),
% 4.74/5.01 inference(monotonicity,[status(thm)],[25768])).
% 4.74/5.01 tff(25773,plain,
% 4.74/5.01 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 4.74/5.01 inference(symmetry,[status(thm)],[25772])).
% 4.74/5.01 tff(25774,plain,
% 4.74/5.01 (r(z, s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 4.74/5.01 inference(monotonicity,[status(thm)],[13])).
% 4.74/5.01 tff(25775,plain,
% 4.74/5.01 (r(elem!1, s(s(s(s(z)))))),
% 4.74/5.01 inference(modus_ponens,[status(thm)],[145, 25774])).
% 4.74/5.01 tff(25776,plain,
% 4.74/5.01 (r(elem!1, s(s(s(s(elem!1)))))),
% 4.74/5.01 inference(modus_ponens,[status(thm)],[25775, 25773])).
% 4.74/5.01 tff(25777,plain,
% 4.74/5.01 (~r(s(elem!1), elem!1)),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[1458, 118, 25776, 25771])).
% 4.74/5.01 tff(25778,plain,
% 4.74/5.01 (b(s(elem!1), elem!1)),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[677, 25777, 25767])).
% 4.74/5.01 tff(25779,plain,
% 4.74/5.01 (b(s(z), z)),
% 4.74/5.01 inference(modus_ponens,[status(thm)],[25778, 25764])).
% 4.74/5.01 tff(25780,plain,
% 4.74/5.01 (r(s(z), s(s(s(s(z)))))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[6689, 908, 5198])).
% 4.74/5.01 tff(25781,plain,
% 4.74/5.01 ((~b(s(z), z)) | (~b(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[4564, 24592])).
% 4.74/5.01 tff(25782,plain,
% 4.74/5.01 (~b(s(z), z)),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[25781, 25780, 145, 1790])).
% 4.74/5.01 tff(25783,plain,
% 4.74/5.01 ($false),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[25782, 25779])).
% 4.74/5.01 tff(25784,plain,((~r(s(elem!1), s(s(s(s(z)))))) | (~(z = elem!1)) | (~r(z, s(s(s(s(z)))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.74/5.01 tff(25785,plain,
% 4.74/5.01 (~r(s(elem!1), s(s(s(s(z)))))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[25784, 13, 47, 25762])).
% 4.74/5.01 tff(25786,plain,
% 4.74/5.01 (b(s(elem!1), s(s(s(s(z)))))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[1084, 25785, 25361])).
% 4.74/5.01 tff(25787,plain,
% 4.74/5.01 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 4.74/5.01 inference(modus_ponens,[status(thm)],[25786, 25350])).
% 4.74/5.01 tff(25788,plain,
% 4.74/5.01 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.74/5.01 inference(monotonicity,[status(thm)],[25768])).
% 4.74/5.01 tff(25789,plain,
% 4.74/5.01 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 4.74/5.01 inference(symmetry,[status(thm)],[25788])).
% 4.74/5.01 tff(25790,plain,
% 4.74/5.01 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.74/5.01 inference(monotonicity,[status(thm)],[16])).
% 4.74/5.01 tff(25791,plain,
% 4.74/5.01 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.74/5.01 inference(modus_ponens,[status(thm)],[24655, 25790])).
% 4.74/5.01 tff(25792,plain,
% 4.74/5.01 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 4.74/5.01 inference(modus_ponens,[status(thm)],[25791, 25789])).
% 4.74/5.01 tff(25793,plain,
% 4.74/5.01 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 4.74/5.01 inference(monotonicity,[status(thm)],[25768])).
% 4.74/5.01 tff(25794,plain,
% 4.74/5.01 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.74/5.01 inference(transitivity,[status(thm)],[25793, 3289])).
% 4.74/5.01 tff(25795,plain,
% 4.74/5.01 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 4.74/5.01 inference(symmetry,[status(thm)],[25794])).
% 4.74/5.01 tff(25796,plain,
% 4.74/5.01 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 4.74/5.01 inference(transitivity,[status(thm)],[25795, 24467])).
% 4.74/5.01 tff(25797,plain,
% 4.74/5.01 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))),
% 4.74/5.01 inference(monotonicity,[status(thm)],[25796])).
% 4.74/5.01 tff(25798,plain,
% 4.74/5.01 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 4.74/5.01 inference(modus_ponens,[status(thm)],[25748, 25797])).
% 4.74/5.01 tff(25799,plain,
% 4.74/5.01 (r(elem!1, s(s(s(s(z)))))),
% 4.74/5.01 inference(modus_ponens,[status(thm)],[47, 25774])).
% 4.74/5.01 tff(25800,plain,
% 4.74/5.01 (~r(elem!1, s(s(s(elem!1))))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[5261, 25799, 25334, 5198, 25336, 25798, 25409])).
% 4.74/5.01 tff(25801,plain,
% 4.74/5.01 (b(elem!1, s(s(s(elem!1))))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[2054, 25800, 12149])).
% 4.74/5.01 tff(25802,plain,
% 4.74/5.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 4.74/5.01 inference(rewrite,[status(thm)],[])).
% 4.74/5.01 tff(25803,plain,
% 4.74/5.01 (((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(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(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 4.74/5.01 inference(rewrite,[status(thm)],[])).
% 4.74/5.01 tff(25804,plain,
% 4.74/5.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 4.74/5.01 inference(monotonicity,[status(thm)],[25803])).
% 4.74/5.01 tff(25805,plain,
% 4.74/5.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 4.74/5.01 inference(transitivity,[status(thm)],[25804, 25802])).
% 4.74/5.01 tff(25806,plain,
% 4.74/5.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))),
% 4.74/5.01 inference(quant_inst,[status(thm)],[])).
% 4.74/5.01 tff(25807,plain,
% 4.74/5.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1)))))),
% 4.74/5.01 inference(modus_ponens,[status(thm)],[25806, 25805])).
% 4.74/5.01 tff(25808,plain,
% 4.74/5.01 (~b(s(elem!1), s(s(s(elem!1))))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[25807, 178, 25761, 25801, 25792, 25787])).
% 4.74/5.01 tff(25809,plain,
% 4.74/5.01 (r(s(elem!1), s(s(s(elem!1))))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[5432, 25808, 25349])).
% 4.74/5.01 tff(25810,plain,
% 4.74/5.01 ((s(s(elem!1)) = s(s(z))) <=> (s(s(z)) = s(s(elem!1)))),
% 4.74/5.01 inference(symmetry,[status(thm)],[6456])).
% 4.74/5.01 tff(25811,plain,
% 4.74/5.01 (s(s(z)) = s(s(elem!1))),
% 4.74/5.01 inference(modus_ponens,[status(thm)],[2378, 25810])).
% 4.74/5.01 tff(25812,plain,
% 4.74/5.01 ($false),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[6472, 25811])).
% 4.74/5.01 tff(25813,plain,((s(s(z)) = s(s(elem!1))) | (~(s(s(elem!1)) = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.74/5.01 tff(25814,plain,
% 4.74/5.01 (s(s(z)) = s(s(elem!1))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[25813, 12139])).
% 4.74/5.01 tff(25815,plain,
% 4.74/5.01 (~(s(s(z)) = s(elem!1))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[1058, 25751])).
% 4.74/5.01 tff(25816,plain,
% 4.74/5.01 ((~(s(elem!1) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 4.74/5.01 inference(monotonicity,[status(thm)],[25344])).
% 4.74/5.01 tff(25817,plain,
% 4.74/5.01 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.74/5.01 inference(modus_ponens,[status(thm)],[25348, 25816])).
% 4.74/5.01 tff(25818,plain,
% 4.74/5.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 4.74/5.01 inference(rewrite,[status(thm)],[])).
% 4.74/5.01 tff(25819,plain,
% 4.74/5.01 (((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 4.74/5.01 inference(rewrite,[status(thm)],[])).
% 4.74/5.01 tff(25820,plain,
% 4.74/5.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 4.74/5.01 inference(monotonicity,[status(thm)],[25819])).
% 4.74/5.01 tff(25821,plain,
% 4.74/5.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 4.74/5.01 inference(transitivity,[status(thm)],[25820, 25818])).
% 4.74/5.01 tff(25822,plain,
% 4.74/5.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 4.74/5.01 inference(quant_inst,[status(thm)],[])).
% 4.74/5.01 tff(25823,plain,
% 4.74/5.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1)))))),
% 4.74/5.01 inference(modus_ponens,[status(thm)],[25822, 25821])).
% 4.74/5.01 tff(25824,plain,
% 4.74/5.01 (~b(s(s(s(elem!1))), s(elem!1))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[25823, 178, 25761, 25801, 25792, 25787])).
% 4.74/5.01 tff(25825,plain,
% 4.74/5.01 (r(s(s(s(elem!1))), s(elem!1))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[373, 25824, 25817])).
% 4.74/5.01 tff(25826,plain,
% 4.74/5.01 (b(s(elem!1), s(s(z))) <=> b(s(elem!1), s(s(elem!1)))),
% 4.74/5.01 inference(symmetry,[status(thm)],[13472])).
% 4.74/5.01 tff(25827,plain,
% 4.74/5.01 (b(s(elem!1), s(s(elem!1)))),
% 4.74/5.01 inference(modus_ponens,[status(thm)],[1070, 25826])).
% 4.74/5.01 tff(25828,plain,
% 4.74/5.01 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 4.74/5.01 inference(monotonicity,[status(thm)],[25768])).
% 4.74/5.01 tff(25829,plain,
% 4.74/5.01 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 4.74/5.01 inference(symmetry,[status(thm)],[25828])).
% 4.74/5.01 tff(25830,plain,
% 4.74/5.01 (~(s(s(s(s(z)))) = s(elem!1))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[2168, 25361])).
% 4.74/5.01 tff(25831,plain,
% 4.74/5.01 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 4.74/5.01 inference(transitivity,[status(thm)],[25746, 4164])).
% 4.74/5.01 tff(25832,plain,
% 4.74/5.01 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(s(z)))) = s(s(s(elem!1)))))),
% 4.74/5.01 inference(monotonicity,[status(thm)],[25831])).
% 4.74/5.01 tff(25833,plain,
% 4.74/5.01 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 4.74/5.01 inference(modus_ponens,[status(thm)],[4938, 25832])).
% 4.74/5.01 tff(25834,plain,
% 4.74/5.01 (~b(s(s(z)), s(elem!1))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[1079, 1070, 202, 167, 1069])).
% 4.74/5.01 tff(25835,plain,
% 4.74/5.01 (r(s(s(z)), s(elem!1))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[1067, 25834, 1060])).
% 4.74/5.01 tff(25836,plain,
% 4.74/5.01 (b(s(s(z)), s(s(s(elem!1))))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[6127, 25835, 5427, 5425])).
% 4.74/5.01 tff(25837,plain,
% 4.74/5.01 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[10667, 25836, 167, 202, 3831])).
% 4.74/5.01 tff(25838,plain,
% 4.74/5.01 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[10664, 25837, 25833])).
% 4.74/5.01 tff(25839,plain,
% 4.74/5.01 (~r(s(s(s(s(z)))), s(elem!1))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[22679, 25838, 1551])).
% 4.74/5.01 tff(25840,plain,
% 4.74/5.01 (b(s(s(s(s(z)))), s(elem!1))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[2173, 25839, 25830])).
% 4.74/5.01 tff(25841,plain,
% 4.74/5.01 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 4.74/5.01 inference(modus_ponens,[status(thm)],[25840, 25829])).
% 4.74/5.01 tff(25842,plain,
% 4.74/5.01 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 4.74/5.01 inference(modus_ponens,[status(thm)],[202, 18])).
% 4.74/5.01 tff(25843,plain,
% 4.74/5.01 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 4.74/5.01 inference(modus_ponens,[status(thm)],[167, 25338])).
% 4.74/5.01 tff(25844,plain,
% 4.74/5.01 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 4.74/5.01 inference(modus_ponens,[status(thm)],[1069, 25350])).
% 4.74/5.01 tff(25845,plain,
% 4.74/5.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 4.74/5.01 inference(rewrite,[status(thm)],[])).
% 4.74/5.01 tff(25846,plain,
% 4.74/5.01 (((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 4.74/5.01 inference(rewrite,[status(thm)],[])).
% 4.74/5.01 tff(25847,plain,
% 4.74/5.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 4.74/5.01 inference(monotonicity,[status(thm)],[25846])).
% 4.74/5.01 tff(25848,plain,
% 4.74/5.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 4.74/5.01 inference(transitivity,[status(thm)],[25847, 25845])).
% 4.74/5.01 tff(25849,plain,
% 4.74/5.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 4.74/5.01 inference(quant_inst,[status(thm)],[])).
% 4.74/5.01 tff(25850,plain,
% 4.74/5.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 4.74/5.01 inference(modus_ponens,[status(thm)],[25849, 25848])).
% 4.74/5.01 tff(25851,plain,
% 4.74/5.01 ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1))))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[25850, 178, 25844, 25843, 25842])).
% 4.74/5.01 tff(25852,plain,
% 4.74/5.01 ($false),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[25851, 25841, 25827])).
% 4.74/5.01 tff(25853,plain,((~b(s(elem!1), s(s(z)))) | (~(z = elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | b(s(elem!1), s(s(s(elem!1)))) | (s(elem!1) = s(s(s(elem!1)))) | (s(s(z)) = s(elem!1)) | (~b(s(elem!1), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.74/5.01 tff(25854,plain,
% 4.74/5.01 (~b(s(elem!1), s(s(z)))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[25853, 13, 25825, 24641, 25336, 25791, 25808, 25349, 25815, 25786])).
% 4.74/5.01 tff(25855,plain,
% 4.74/5.01 (r(s(elem!1), s(s(z)))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[421, 25854, 25751])).
% 4.74/5.01 tff(25856,plain,
% 4.74/5.01 (s(s(elem!1)) = s(s(z))),
% 4.74/5.01 inference(symmetry,[status(thm)],[6457])).
% 4.74/5.01 tff(25857,plain,
% 4.74/5.01 (r(s(elem!1), s(s(elem!1))) <=> r(s(elem!1), s(s(z)))),
% 4.74/5.01 inference(monotonicity,[status(thm)],[25856])).
% 4.74/5.01 tff(25858,plain,
% 4.74/5.01 (r(s(elem!1), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 4.74/5.01 inference(symmetry,[status(thm)],[25857])).
% 4.74/5.01 tff(25859,plain,
% 4.74/5.01 (r(s(elem!1), s(s(elem!1)))),
% 4.74/5.01 inference(modus_ponens,[status(thm)],[363, 25858])).
% 4.74/5.01 tff(25860,plain,
% 4.74/5.01 ($false),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[5388, 25859])).
% 4.74/5.01 tff(25861,plain,((~(s(s(z)) = s(s(elem!1)))) | r(s(elem!1), s(s(elem!1))) | (~r(s(elem!1), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.74/5.01 tff(25862,plain,
% 4.74/5.01 (r(s(elem!1), s(s(elem!1)))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[25861, 25855, 25814])).
% 4.74/5.01 tff(25863,plain,
% 4.74/5.01 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[5994, 25862, 25809])).
% 4.74/5.01 tff(25864,plain,
% 4.74/5.01 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[3375, 25863, 25342])).
% 4.74/5.01 tff(25865,plain,
% 4.74/5.01 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[5980, 25862, 25825])).
% 4.74/5.01 tff(25866,plain,
% 4.74/5.01 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[3409, 25865, 25409])).
% 4.74/5.01 tff(25867,plain,
% 4.74/5.01 ($false),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[5834, 178, 25866, 25792, 25864, 25339, 25337])).
% 4.74/5.01 tff(25868,plain,((~(z = elem!1)) | b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.74/5.01 tff(25869,plain,
% 4.74/5.01 (~(z = elem!1)),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[25868, 1])).
% 4.74/5.01 tff(25870,plain,
% 4.74/5.01 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[23358, 25441, 24649, 24647, 25439])).
% 4.74/5.01 tff(25871,assumption,(~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))), introduced(assumption)).
% 4.74/5.01 tff(25872,plain,
% 4.74/5.01 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 25871])).
% 4.74/5.01 tff(25873,plain,
% 4.74/5.01 (~(elem!1 = s(s(s(s(z)))))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[11438, 515])).
% 4.74/5.01 tff(25874,plain,
% 4.74/5.01 (~r(z, elem!1)),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[580, 515, 202, 106, 12, 145, 25873])).
% 4.74/5.01 tff(25875,plain,
% 4.74/5.01 (~(s(s(s(s(z)))) = elem!1)),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[504, 25873])).
% 4.74/5.01 tff(25876,plain,
% 4.74/5.01 (~r(elem!1, z)),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[493, 25873, 202, 106, 12, 145, 24607])).
% 4.74/5.01 tff(25877,plain,
% 4.74/5.01 (b(elem!1, z)),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[498, 25876, 2809])).
% 4.74/5.01 tff(25878,plain,
% 4.74/5.01 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[617, 25877, 202, 106, 507, 24625, 12, 25873, 24623, 145, 515])).
% 4.74/5.01 tff(25879,plain,
% 4.74/5.01 ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[3442, 24592])).
% 4.74/5.01 tff(25880,plain,
% 4.74/5.01 (~r(s(s(s(s(z)))), elem!1)),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[25879, 25878])).
% 4.74/5.01 tff(25881,plain,
% 4.74/5.01 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[2820, 25876, 24623, 24625, 507, 25874])).
% 4.74/5.01 tff(25882,plain,
% 4.74/5.01 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[691, 25881, 12393])).
% 4.74/5.01 tff(25883,plain,
% 4.74/5.01 ((~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[18983, 24592])).
% 4.74/5.01 tff(25884,plain,
% 4.74/5.01 (~r(elem!1, s(s(s(s(z)))))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[25883, 25882])).
% 4.74/5.01 tff(25885,plain,
% 4.74/5.01 (~b(elem!1, s(s(z)))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[24866, 25884, 24607, 25880, 202, 25875])).
% 4.74/5.01 tff(25886,plain,
% 4.74/5.01 (r(elem!1, s(s(z)))),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[467, 25885, 312])).
% 4.74/5.01 tff(25887,plain,
% 4.74/5.01 (~b(s(s(z)), elem!1)),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[18993, 25886, 3428, 202, 507, 145, 12393, 25875, 25874])).
% 4.74/5.01 tff(25888,plain,
% 4.74/5.01 (r(s(s(z)), elem!1)),
% 4.74/5.01 inference(unit_resolution,[status(thm)],[448, 25887, 12])).
% 4.74/5.01 tff(25889,plain,
% 4.74/5.01 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), elem!1)),
% 4.74/5.01 inference(monotonicity,[status(thm)],[534])).
% 4.74/5.01 tff(25890,plain,
% 4.74/5.01 ((~b(s(s(s(z))), s(z))) <=> (~b(s(s(s(z))), elem!1))),
% 4.74/5.01 inference(monotonicity,[status(thm)],[25889])).
% 4.74/5.02 tff(25891,plain,
% 4.74/5.02 (b(elem!1, s(s(s(s(z)))))),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[483, 25884, 25873])).
% 4.74/5.02 tff(25892,plain,
% 4.74/5.02 (b(s(z), s(s(s(s(z)))))),
% 4.74/5.02 inference(modus_ponens,[status(thm)],[25891, 520])).
% 4.74/5.02 tff(25893,plain,
% 4.74/5.02 (b(z, elem!1)),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[585, 25874, 507])).
% 4.74/5.02 tff(25894,plain,
% 4.74/5.02 (b(z, s(z))),
% 4.74/5.02 inference(modus_ponens,[status(thm)],[25893, 519])).
% 4.74/5.02 tff(25895,plain,
% 4.74/5.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 4.74/5.02 inference(rewrite,[status(thm)],[])).
% 4.74/5.02 tff(25896,plain,
% 4.74/5.02 (((~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(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 4.74/5.02 inference(rewrite,[status(thm)],[])).
% 4.74/5.02 tff(25897,plain,
% 4.74/5.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 4.74/5.02 inference(monotonicity,[status(thm)],[25896])).
% 4.74/5.02 tff(25898,plain,
% 4.74/5.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 4.74/5.02 inference(transitivity,[status(thm)],[25897, 25895])).
% 4.74/5.02 tff(25899,plain,
% 4.74/5.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 4.74/5.02 inference(quant_inst,[status(thm)],[])).
% 4.74/5.02 tff(25900,plain,
% 4.74/5.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 4.74/5.02 inference(modus_ponens,[status(thm)],[25899, 25898])).
% 4.74/5.02 tff(25901,plain,
% 4.74/5.02 (~b(s(s(s(z))), s(z))),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[25900, 178, 25894, 24604, 3008, 25892])).
% 4.74/5.02 tff(25902,plain,
% 4.74/5.02 (~b(s(s(s(z))), elem!1)),
% 4.74/5.02 inference(modus_ponens,[status(thm)],[25901, 25890])).
% 4.74/5.02 tff(25903,plain,
% 4.74/5.02 (r(s(s(s(z))), elem!1)),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[4981, 25902, 17825])).
% 4.74/5.02 tff(25904,plain,
% 4.74/5.02 (~r(s(s(s(z))), s(s(z)))),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[25248, 25903, 25888])).
% 4.74/5.02 tff(25905,plain,
% 4.74/5.02 (b(s(s(s(z))), s(s(z)))),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[4966, 25904])).
% 4.74/5.02 tff(25906,plain,
% 4.74/5.02 ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[4944, 178, 24607, 202, 24604])).
% 4.74/5.02 tff(25907,plain,
% 4.74/5.02 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[25906, 25905])).
% 4.74/5.02 tff(25908,plain,
% 4.74/5.02 (r(s(s(s(s(z)))), s(s(s(z))))),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[11185, 25907])).
% 4.74/5.02 tff(25909,plain,
% 4.74/5.02 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 4.74/5.02 inference(rewrite,[status(thm)],[])).
% 4.74/5.02 tff(25910,plain,
% 4.74/5.02 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 4.74/5.02 inference(quant_inst,[status(thm)],[])).
% 4.74/5.02 tff(25911,plain,
% 4.74/5.02 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 4.74/5.02 inference(modus_ponens,[status(thm)],[25910, 25909])).
% 4.74/5.02 tff(25912,plain,
% 4.74/5.02 ($false),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[25911, 118, 24592, 25908, 25872])).
% 4.74/5.02 tff(25913,plain,((~(s(elem!1) = s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | (~b(z, s(s(s(z))))) | (s(s(z)) = elem!1) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | (z = elem!1) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 4.74/5.02 tff(25914,plain,
% 4.74/5.02 (~(s(elem!1) = s(s(z)))),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[25913, 12, 25870, 25439, 25336, 24761, 507, 47, 25744])).
% 4.74/5.02 tff(25915,plain,
% 4.74/5.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), 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(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), 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(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 4.74/5.02 inference(rewrite,[status(thm)],[])).
% 4.74/5.02 tff(25916,plain,
% 4.74/5.02 (((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(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))))))))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 4.74/5.02 inference(rewrite,[status(thm)],[])).
% 4.74/5.02 tff(25917,plain,
% 4.74/5.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(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))))))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), 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(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 4.74/5.02 inference(monotonicity,[status(thm)],[25916])).
% 4.74/5.02 tff(25918,plain,
% 4.74/5.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(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))))))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), 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(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 4.74/5.02 inference(transitivity,[status(thm)],[25917, 25915])).
% 4.74/5.02 tff(25919,plain,
% 4.74/5.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(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))))))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 4.74/5.02 inference(quant_inst,[status(thm)],[])).
% 4.74/5.02 tff(25920,plain,
% 4.74/5.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), 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(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 4.74/5.02 inference(modus_ponens,[status(thm)],[25919, 25918])).
% 4.74/5.02 tff(25921,plain,
% 4.74/5.02 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[25920, 178, 166, 24641, 25336, 1146])).
% 4.74/5.02 tff(25922,plain,
% 4.74/5.02 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[222, 25921])).
% 4.74/5.02 tff(25923,plain,
% 4.74/5.02 (b(elem!1, z)),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[498, 25445, 2809])).
% 4.74/5.02 tff(25924,plain,
% 4.74/5.02 (b(z, s(s(s(elem!1))))),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[19647, 3170, 461, 1, 3240])).
% 4.74/5.02 tff(25925,plain,
% 4.74/5.02 (~r(z, elem!1)),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[3151, 302, 18872, 19481, 19491, 3244, 47])).
% 4.74/5.02 tff(25926,plain,
% 4.74/5.02 (~(elem!1 = s(s(s(elem!1))))),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[17470, 106, 47, 19039, 19481, 461, 18872, 25925, 25924])).
% 4.74/5.02 tff(25927,plain,
% 4.74/5.02 (r(elem!1, s(s(s(elem!1))))),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[2054, 25926, 3240])).
% 4.74/5.02 tff(25928,plain,
% 4.74/5.02 (~(s(s(s(elem!1))) = elem!1)),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[2489, 25926])).
% 4.74/5.02 tff(25929,plain,
% 4.74/5.02 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[951, 25928])).
% 4.74/5.02 tff(25930,plain,
% 4.74/5.02 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[4343, 25929])).
% 4.74/5.02 tff(25931,plain,
% 4.74/5.02 (~(z = elem!1)),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[18974, 25930, 461, 19481, 25927, 1, 3170])).
% 4.74/5.02 tff(25932,plain,
% 4.74/5.02 (~(s(s(z)) = elem!1)),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[7053, 3261, 25925])).
% 4.74/5.02 tff(25933,plain,
% 4.74/5.02 (~r(elem!1, z)),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[493, 25932, 19481, 19509, 106, 47, 302])).
% 4.74/5.02 tff(25934,plain,
% 4.74/5.02 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[261, 106, 19481, 19039, 47])).
% 4.74/5.02 tff(25935,plain,
% 4.74/5.02 (b(z, s(s(s(s(s(s(s(z))))))))),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[271, 25934])).
% 4.74/5.02 tff(25936,plain,
% 4.74/5.02 (~(elem!1 = s(s(z)))),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[311, 25932])).
% 4.74/5.02 tff(25937,plain,
% 4.74/5.02 (r(elem!1, s(s(z)))),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[467, 25936, 461])).
% 4.74/5.02 tff(25938,plain,
% 4.74/5.02 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[3121, 25937, 18872, 25935, 25925, 25933, 25931, 106])).
% 4.74/5.02 tff(25939,plain,
% 4.74/5.02 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[259, 25938, 19039, 19481, 302])).
% 4.74/5.02 tff(25940,plain,
% 4.74/5.02 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[222, 25939])).
% 4.74/5.02 tff(25941,plain,
% 4.74/5.02 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[17305, 25940, 302, 19481, 19491, 18872])).
% 4.74/5.02 tff(25942,plain,
% 4.74/5.02 (~(s(elem!1) = s(s(z)))),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[19578, 3261, 25928, 18872, 19039, 25927, 461, 1, 3170, 19481, 106])).
% 4.74/5.02 tff(25943,plain,
% 4.74/5.02 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[2840, 25942])).
% 4.74/5.02 tff(25944,plain,
% 4.74/5.02 (~(elem!1 = z)),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[2808, 25931])).
% 4.74/5.02 tff(25945,plain,
% 4.74/5.02 (b(elem!1, z)),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[498, 25933, 25944])).
% 4.74/5.02 tff(25946,plain,
% 4.74/5.02 (b(z, elem!1)),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[585, 25931, 25925])).
% 4.74/5.02 tff(25947,plain,
% 4.74/5.02 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[9376, 11095, 104, 2043, 595, 3311, 9310, 818, 506, 4245])).
% 4.74/5.02 tff(25948,plain,
% 4.74/5.02 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[4173, 25947, 2857])).
% 4.74/5.02 tff(25949,plain,
% 4.74/5.02 (~r(s(s(s(s(z)))), elem!1)),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[8038, 25948, 818, 949, 506, 145])).
% 4.74/5.02 tff(25950,plain,
% 4.74/5.02 (b(s(s(s(s(z)))), elem!1)),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[3142, 25949, 323])).
% 4.74/5.02 tff(25951,plain,
% 4.74/5.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 4.74/5.02 inference(rewrite,[status(thm)],[])).
% 4.74/5.02 tff(25952,plain,
% 4.74/5.02 (((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 4.74/5.02 inference(rewrite,[status(thm)],[])).
% 4.74/5.02 tff(25953,plain,
% 4.74/5.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 4.74/5.02 inference(monotonicity,[status(thm)],[25952])).
% 4.74/5.02 tff(25954,plain,
% 4.74/5.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 4.74/5.02 inference(transitivity,[status(thm)],[25953, 25951])).
% 4.74/5.02 tff(25955,plain,
% 4.74/5.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 4.74/5.02 inference(quant_inst,[status(thm)],[])).
% 4.74/5.02 tff(25956,plain,
% 4.74/5.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 4.74/5.02 inference(modus_ponens,[status(thm)],[25955, 25954])).
% 4.74/5.02 tff(25957,plain,
% 4.74/5.02 ($false),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[25956, 178, 817, 25950, 166, 11095, 202])).
% 4.74/5.02 tff(25958,plain,((elem!1 = s(s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (s(s(s(s(z)))) = elem!1) | (~b(z, elem!1)) | (s(s(s(elem!1))) = elem!1) | (~b(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(elem!1))))) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.74/5.02 tff(25959,plain,
% 4.74/5.02 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[25958, 25938, 18872, 19481, 19491, 25946, 25928, 25945, 47, 25943, 19039, 25924, 25935, 25927, 25941])).
% 4.74/5.02 tff(25960,plain,
% 4.74/5.02 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.74/5.02 inference(monotonicity,[status(thm)],[25959])).
% 4.74/5.02 tff(25961,plain,
% 4.74/5.02 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 4.74/5.02 inference(symmetry,[status(thm)],[25959])).
% 4.74/5.02 tff(25962,plain,
% 4.74/5.02 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 4.74/5.02 inference(monotonicity,[status(thm)],[25961])).
% 4.74/5.02 tff(25963,plain,
% 4.74/5.02 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 4.74/5.02 inference(transitivity,[status(thm)],[25962, 10421])).
% 4.74/5.02 tff(25964,plain,
% 4.74/5.02 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(s(s(s(z))) = elem!1))),
% 4.74/5.02 inference(monotonicity,[status(thm)],[25963])).
% 4.74/5.02 tff(25965,plain,
% 4.74/5.02 (~(s(s(s(z))) = elem!1)),
% 4.74/5.02 inference(modus_ponens,[status(thm)],[1104, 25964])).
% 4.74/5.02 tff(25966,plain,
% 4.74/5.02 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.74/5.02 inference(monotonicity,[status(thm)],[25959])).
% 4.74/5.02 tff(25967,plain,
% 4.74/5.02 (b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(z))), elem!1)),
% 4.74/5.02 inference(symmetry,[status(thm)],[25966])).
% 4.74/5.02 tff(25968,plain,
% 4.74/5.02 ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(s(s(z))), elem!1))),
% 4.74/5.02 inference(monotonicity,[status(thm)],[25967])).
% 4.74/5.02 tff(25969,plain,
% 4.74/5.02 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.74/5.02 inference(monotonicity,[status(thm)],[25959])).
% 4.74/5.02 tff(25970,plain,
% 4.74/5.02 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(z)))), elem!1)),
% 4.74/5.02 inference(symmetry,[status(thm)],[25969])).
% 4.74/5.02 tff(25971,plain,
% 4.74/5.02 (r(s(s(s(s(z)))), elem!1)),
% 4.74/5.02 inference(modus_ponens,[status(thm)],[25940, 25970])).
% 4.74/5.02 tff(25972,plain,
% 4.74/5.02 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[8038, 25971, 25946, 25928, 25945, 47])).
% 4.74/5.02 tff(25973,plain,
% 4.74/5.02 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.74/5.02 inference(unit_resolution,[status(thm)],[4173, 25972, 25943])).
% 4.74/5.02 tff(25974,plain,
% 4.74/5.02 (r(elem!1, s(s(z))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.74/5.02 inference(monotonicity,[status(thm)],[25959])).
% 4.74/5.02 tff(25975,plain,
% 4.74/5.02 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.74/5.02 inference(modus_ponens,[status(thm)],[25937, 25974])).
% 4.74/5.02 tff(25976,plain,
% 4.74/5.02 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 4.74/5.02 inference(monotonicity,[status(thm)],[25959])).
% 4.74/5.02 tff(25977,plain,
% 4.74/5.02 (s(s(elem!1)) = s(s(s(s(s(s(s(s(s(z)))))))))),
% 4.74/5.02 inference(monotonicity,[status(thm)],[25976])).
% 4.74/5.02 tff(25978,plain,
% 4.74/5.02 (s(s(s(elem!1))) = s(s(s(s(s(s(s(s(s(s(z))))))))))),
% 4.74/5.02 inference(monotonicity,[status(thm)],[25977])).
% 4.74/5.02 tff(25979,plain,
% 4.74/5.02 (s(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(s(elem!1)))),
% 4.74/5.02 inference(symmetry,[status(thm)],[25978])).
% 4.74/5.02 tff(25980,plain,
% 4.74/5.02 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z))))))))))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.74/5.02 inference(monotonicity,[status(thm)],[25979])).
% 4.74/5.02 tff(25981,plain,
% 4.74/5.02 (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(s(s(s(s(s(s(s(z)))))))))))),
% 4.74/5.02 inference(symmetry,[status(thm)],[25980])).
% 4.74/5.02 tff(25982,plain,
% 4.74/5.02 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.74/5.02 inference(monotonicity,[status(thm)],[25959])).
% 4.74/5.02 tff(25983,plain,
% 4.74/5.02 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.74/5.02 inference(modus_ponens,[status(thm)],[25927, 25982])).
% 4.87/5.02 tff(25984,plain,
% 4.87/5.02 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 4.87/5.02 inference(modus_ponens,[status(thm)],[25983, 25981])).
% 4.87/5.02 tff(25985,plain,
% 4.87/5.02 (~r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))),
% 4.87/5.02 inference(unit_resolution,[status(thm)],[7939, 25984, 25975])).
% 4.87/5.02 tff(25986,plain,
% 4.87/5.02 (~b(s(s(z)), s(s(s(elem!1))))),
% 4.87/5.02 inference(unit_resolution,[status(thm)],[10512, 25973, 19481, 25959, 25985, 302])).
% 4.87/5.02 tff(25987,plain,
% 4.87/5.02 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 4.87/5.02 inference(unit_resolution,[status(thm)],[19014, 25986, 461, 302, 19481, 25924, 3244, 25973, 3240, 18872])).
% 4.87/5.02 tff(25988,plain,
% 4.87/5.02 (r(s(s(s(z))), s(s(s(s(z)))))),
% 4.87/5.02 inference(unit_resolution,[status(thm)],[4928, 25987, 4890])).
% 4.87/5.02 tff(25989,plain,
% 4.87/5.02 (~r(s(s(s(z))), z)),
% 4.87/5.02 inference(unit_resolution,[status(thm)],[4899, 118, 47, 25988])).
% 4.87/5.02 tff(25990,plain,
% 4.87/5.02 (b(s(s(s(z))), z)),
% 4.87/5.02 inference(unit_resolution,[status(thm)],[4903, 41, 77, 25989])).
% 4.87/5.02 tff(25991,plain,
% 4.87/5.02 (~r(z, s(s(s(z))))),
% 4.87/5.02 inference(unit_resolution,[status(thm)],[4910, 118, 47, 25988])).
% 4.87/5.02 tff(25992,plain,
% 4.87/5.02 (b(z, s(s(s(z))))),
% 4.87/5.02 inference(unit_resolution,[status(thm)],[4920, 25991])).
% 4.87/5.02 tff(25993,plain,
% 4.87/5.02 (b(elem!1, z) <=> b(s(s(s(s(s(s(s(z))))))), z)),
% 4.87/5.02 inference(monotonicity,[status(thm)],[25959])).
% 4.87/5.02 tff(25994,plain,
% 4.87/5.02 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.87/5.02 inference(modus_ponens,[status(thm)],[25945, 25993])).
% 4.87/5.02 tff(25995,plain,
% 4.87/5.02 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.02 inference(unit_resolution,[status(thm)],[1319, 178, 25935, 25994, 25992, 25990])).
% 4.87/5.02 tff(25996,plain,
% 4.87/5.02 (~b(s(s(s(z))), elem!1)),
% 4.87/5.02 inference(modus_ponens,[status(thm)],[25995, 25968])).
% 4.87/5.02 tff(25997,plain,
% 4.87/5.02 (r(s(s(s(z))), elem!1)),
% 4.87/5.02 inference(unit_resolution,[status(thm)],[4981, 25996, 25965])).
% 4.87/5.02 tff(25998,plain,
% 4.87/5.02 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.02 inference(modus_ponens,[status(thm)],[25997, 25960])).
% 4.87/5.02 tff(25999,plain,
% 4.87/5.02 ($false),
% 4.87/5.02 inference(unit_resolution,[status(thm)],[21406, 118, 25940, 25988, 25998])).
% 4.87/5.02 tff(26000,plain,((~r(z, s(s(z)))) | b(elem!1, s(s(z))) | b(elem!1, s(s(s(elem!1)))) | (~r(s(s(z)), z)) | b(z, s(s(s(s(z))))) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 4.87/5.02 tff(26001,plain,
% 4.87/5.02 (b(elem!1, s(s(s(elem!1))))),
% 4.87/5.02 inference(unit_resolution,[status(thm)],[26000, 461, 1, 25334, 25744, 3170])).
% 4.87/5.02 tff(26002,plain,
% 4.87/5.02 (~r(z, s(s(s(elem!1))))),
% 4.87/5.02 inference(unit_resolution,[status(thm)],[25455, 13192, 47, 25334])).
% 4.87/5.02 tff(26003,plain,
% 4.87/5.02 (b(z, s(s(s(elem!1))))),
% 4.87/5.02 inference(unit_resolution,[status(thm)],[2095, 26002])).
% 4.87/5.02 tff(26004,plain,
% 4.87/5.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 4.87/5.03 inference(rewrite,[status(thm)],[])).
% 4.87/5.03 tff(26005,plain,
% 4.87/5.03 (((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 4.87/5.03 inference(rewrite,[status(thm)],[])).
% 4.87/5.03 tff(26006,plain,
% 4.87/5.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 4.87/5.03 inference(monotonicity,[status(thm)],[26005])).
% 4.87/5.03 tff(26007,plain,
% 4.87/5.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 4.87/5.03 inference(transitivity,[status(thm)],[26006, 26004])).
% 4.87/5.03 tff(26008,plain,
% 4.87/5.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 4.87/5.03 inference(quant_inst,[status(thm)],[])).
% 4.87/5.03 tff(26009,plain,
% 4.87/5.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 4.87/5.03 inference(modus_ponens,[status(thm)],[26008, 26007])).
% 4.87/5.03 tff(26010,plain,
% 4.87/5.03 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[26009, 178, 25923, 26003, 26001, 24647])).
% 4.87/5.03 tff(26011,plain,
% 4.87/5.03 (~(s(s(s(elem!1))) = elem!1)),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[16438, 26001])).
% 4.87/5.03 tff(26012,plain,
% 4.87/5.03 (~b(s(s(s(elem!1))), elem!1)),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[12925, 25447, 25923, 26001, 26003])).
% 4.87/5.03 tff(26013,plain,
% 4.87/5.03 (r(s(s(s(elem!1))), elem!1)),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[570, 26012, 26011])).
% 4.87/5.03 tff(26014,plain,
% 4.87/5.03 (~(s(s(s(s(z)))) = elem!1)),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[4509, 461, 25336])).
% 4.87/5.03 tff(26015,plain,
% 4.87/5.03 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[3502, 26014])).
% 4.87/5.03 tff(26016,plain,
% 4.87/5.03 (~r(s(s(s(elem!1))), s(s(z)))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[4205, 26013, 13066])).
% 4.87/5.03 tff(26017,plain,
% 4.87/5.03 (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[3682, 2953, 556])).
% 4.87/5.03 tff(26018,plain,
% 4.87/5.03 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[3612, 41, 26017, 11632])).
% 4.87/5.03 tff(26019,plain,
% 4.87/5.03 (b(s(s(s(elem!1))), s(s(z)))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[4209, 41, 5810, 4181])).
% 4.87/5.03 tff(26020,plain,
% 4.87/5.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), 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))))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), 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))))))), s(s(s(elem!1))))))),
% 4.87/5.03 inference(rewrite,[status(thm)],[])).
% 4.87/5.03 tff(26021,plain,
% 4.87/5.03 (((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(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(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(elem!1))), 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(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), 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))))))), s(s(s(elem!1))))))),
% 4.87/5.03 inference(rewrite,[status(thm)],[])).
% 4.87/5.03 tff(26022,plain,
% 4.87/5.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(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(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), 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))))))), s(s(s(elem!1)))))))),
% 4.87/5.03 inference(monotonicity,[status(thm)],[26021])).
% 4.87/5.03 tff(26023,plain,
% 4.87/5.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(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(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), 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))))))), s(s(s(elem!1))))))),
% 4.87/5.03 inference(transitivity,[status(thm)],[26022, 26020])).
% 4.87/5.03 tff(26024,plain,
% 4.87/5.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(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(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 4.87/5.03 inference(quant_inst,[status(thm)],[])).
% 4.87/5.03 tff(26025,plain,
% 4.87/5.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 4.87/5.03 inference(modus_ponens,[status(thm)],[26024, 26023])).
% 4.87/5.03 tff(26026,plain,
% 4.87/5.03 ($false),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[26025, 178, 166, 26019, 1146, 26018, 18365])).
% 4.87/5.03 tff(26027,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | r(s(s(s(elem!1))), s(s(z))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.87/5.03 tff(26028,plain,
% 4.87/5.03 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[26027, 26016, 1146, 166, 26015, 26013])).
% 4.87/5.03 tff(26029,plain,
% 4.87/5.03 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[3444, 26028, 26010])).
% 4.87/5.03 tff(26030,plain,
% 4.87/5.03 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[703, 26029])).
% 4.87/5.03 tff(26031,plain,
% 4.87/5.03 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[16181, 26030])).
% 4.87/5.03 tff(26032,plain,
% 4.87/5.03 (~(s(s(s(s(z)))) = s(elem!1))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[2168, 26031])).
% 4.87/5.03 tff(26033,plain,
% 4.87/5.03 (~(s(s(elem!1)) = elem!1)),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[2510, 26032, 26030])).
% 4.87/5.03 tff(26034,plain,
% 4.87/5.03 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[348, 26033])).
% 4.87/5.03 tff(26035,plain,
% 4.87/5.03 (~(s(elem!1) = elem!1)),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[2150, 26011])).
% 4.87/5.03 tff(26036,plain,
% 4.87/5.03 (~r(s(elem!1), s(s(z)))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[17418, 25447, 25744, 13066, 26035, 25923])).
% 4.87/5.03 tff(26037,plain,
% 4.87/5.03 (b(s(elem!1), s(s(z)))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[421, 26036, 1056])).
% 4.87/5.03 tff(26038,plain,
% 4.87/5.03 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[14677, 26037, 25334, 24649, 166, 1146, 2311])).
% 4.87/5.03 tff(26039,plain,
% 4.87/5.03 (~b(s(elem!1), elem!1)),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[686, 26030, 26038])).
% 4.87/5.03 tff(26040,plain,
% 4.87/5.03 (r(s(elem!1), elem!1)),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[677, 26039, 26035])).
% 4.87/5.03 tff(26041,plain,
% 4.87/5.03 (~r(s(s(s(elem!1))), s(elem!1))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[1576, 26040, 26013])).
% 4.87/5.03 tff(26042,plain,
% 4.87/5.03 (b(s(s(s(elem!1))), s(elem!1))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[373, 26041, 26034])).
% 4.87/5.03 tff(26043,plain,
% 4.87/5.03 (~b(z, s(elem!1))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[2052, 26042, 26003, 26001, 25923])).
% 4.87/5.03 tff(26044,plain,
% 4.87/5.03 (r(z, s(elem!1))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[2351, 26043])).
% 4.87/5.03 tff(26045,plain,
% 4.87/5.03 (r(elem!1, s(s(s(s(z)))))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[24769, 26030, 24761])).
% 4.87/5.03 tff(26046,plain,
% 4.87/5.03 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[25883, 26045])).
% 4.87/5.03 tff(26047,plain,
% 4.87/5.03 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[722, 26046, 24649, 25923, 26038, 26028, 26014, 24647])).
% 4.87/5.03 tff(26048,plain,
% 4.87/5.03 (~r(s(elem!1), s(s(s(s(z)))))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[25119, 26047])).
% 4.87/5.03 tff(26049,plain,
% 4.87/5.03 (b(s(elem!1), s(s(s(s(z)))))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[1084, 26048, 26031])).
% 4.87/5.03 tff(26050,plain,
% 4.87/5.03 (~b(s(s(z)), s(elem!1))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[1079, 26049, 25336, 24641, 26037])).
% 4.87/5.03 tff(26051,plain,
% 4.87/5.03 (r(s(s(z)), s(elem!1))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[1067, 26050, 2311])).
% 4.87/5.03 tff(26052,plain,
% 4.87/5.03 ($false),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[2341, 26051, 26044, 25744])).
% 4.87/5.03 tff(26053,plain,(b(elem!1, s(s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(s(z))) | (z = elem!1) | (elem!1 = s(s(z))) | b(z, s(s(s(s(z))))) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 4.87/5.03 tff(26054,plain,
% 4.87/5.03 (b(elem!1, s(s(z)))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[26053, 1056, 166, 1146, 507, 312, 1, 3170])).
% 4.87/5.03 tff(26055,plain,
% 4.87/5.03 ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~(elem!1 = s(s(s(elem!1))))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(z))))))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[8311, 24592])).
% 4.87/5.03 tff(26056,plain,
% 4.87/5.03 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[26055, 13450, 47, 701])).
% 4.87/5.03 tff(26057,plain,
% 4.87/5.03 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[4173, 26056, 2857])).
% 4.87/5.03 tff(26058,plain,
% 4.87/5.03 (~(s(s(s(s(z)))) = elem!1)),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[338, 12574, 12])).
% 4.87/5.03 tff(26059,plain,
% 4.87/5.03 (~r(z, s(s(s(elem!1))))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[25455, 2857, 47, 25334])).
% 4.87/5.03 tff(26060,plain,
% 4.87/5.03 (b(z, s(s(s(elem!1))))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[2095, 26059])).
% 4.87/5.03 tff(26061,plain,
% 4.87/5.03 (b(z, elem!1)),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[17579, 13449, 26060])).
% 4.87/5.03 tff(26062,plain,
% 4.87/5.03 (~(elem!1 = s(s(s(s(z)))))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[1846, 26061, 1])).
% 4.87/5.03 tff(26063,plain,
% 4.87/5.03 (~r(elem!1, z)),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[493, 26062, 25336, 25744, 12, 47, 24641])).
% 4.87/5.03 tff(26064,plain,
% 4.87/5.03 (~r(s(s(z)), elem!1)),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[9195, 26063, 47, 24761, 26060, 26058, 13450, 25336, 194, 24641, 26057])).
% 4.87/5.03 tff(26065,plain,
% 4.87/5.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.87/5.03 inference(rewrite,[status(thm)],[])).
% 4.87/5.03 tff(26066,plain,
% 4.87/5.03 (((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.87/5.03 inference(rewrite,[status(thm)],[])).
% 4.87/5.03 tff(26067,plain,
% 4.87/5.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 4.87/5.03 inference(monotonicity,[status(thm)],[26066])).
% 4.87/5.03 tff(26068,plain,
% 4.87/5.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.87/5.03 inference(transitivity,[status(thm)],[26067, 26065])).
% 4.87/5.03 tff(26069,plain,
% 4.87/5.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)))),
% 4.87/5.03 inference(quant_inst,[status(thm)],[])).
% 4.87/5.03 tff(26070,plain,
% 4.87/5.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 4.87/5.03 inference(modus_ponens,[status(thm)],[26069, 26068])).
% 4.87/5.03 tff(26071,plain,
% 4.87/5.03 ((~b(z, elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[26070, 178, 812, 24649, 1146])).
% 4.87/5.03 tff(26072,plain,
% 4.87/5.03 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[26071, 26061])).
% 4.87/5.03 tff(26073,plain,
% 4.87/5.03 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[691, 26072, 701])).
% 4.87/5.03 tff(26074,plain,
% 4.87/5.03 (~b(s(s(z)), elem!1)),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[17305, 26073, 24641, 204, 25336, 26058])).
% 4.87/5.03 tff(26075,plain,
% 4.87/5.03 ($false),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[448, 26074, 26064, 12])).
% 4.87/5.03 tff(26076,plain,((~(s(elem!1) = elem!1)) | (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)))), z)) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.87/5.03 tff(26077,plain,
% 4.87/5.03 (~(s(elem!1) = elem!1)),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[26076, 701, 204, 3244, 12, 13192, 812, 1146, 1])).
% 4.87/5.03 tff(26078,plain,
% 4.87/5.03 (elem!1 = s(s(s(s(z))))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[814, 521, 24641, 25744, 812, 12, 47, 25336])).
% 4.87/5.03 tff(26079,plain,
% 4.87/5.03 (s(elem!1) = s(s(s(s(s(z)))))),
% 4.87/5.03 inference(monotonicity,[status(thm)],[26078])).
% 4.87/5.03 tff(26080,plain,
% 4.87/5.03 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 4.87/5.03 inference(monotonicity,[status(thm)],[26079])).
% 4.87/5.03 tff(26081,plain,
% 4.87/5.03 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(s(z)))))),
% 4.87/5.03 inference(monotonicity,[status(thm)],[26078])).
% 4.87/5.03 tff(26082,plain,
% 4.87/5.03 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.87/5.03 inference(monotonicity,[status(thm)],[26078])).
% 4.87/5.03 tff(26083,plain,
% 4.87/5.03 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), elem!1)),
% 4.87/5.03 inference(symmetry,[status(thm)],[26082])).
% 4.87/5.03 tff(26084,plain,
% 4.87/5.03 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 4.87/5.03 inference(monotonicity,[status(thm)],[26079])).
% 4.87/5.03 tff(26085,plain,
% 4.87/5.03 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 4.87/5.03 inference(monotonicity,[status(thm)],[26084])).
% 4.87/5.03 tff(26086,plain,
% 4.87/5.03 (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)))))),
% 4.87/5.03 inference(monotonicity,[status(thm)],[26085])).
% 4.87/5.03 tff(26087,plain,
% 4.87/5.03 (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)))))),
% 4.87/5.03 inference(symmetry,[status(thm)],[26086])).
% 4.87/5.03 tff(26088,plain,
% 4.87/5.03 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), elem!1)),
% 4.87/5.03 inference(transitivity,[status(thm)],[26087, 26083])).
% 4.87/5.03 tff(26089,plain,
% 4.87/5.03 (r(s(s(s(elem!1))), elem!1)),
% 4.87/5.03 inference(modus_ponens,[status(thm)],[24592, 26088])).
% 4.87/5.03 tff(26090,plain,
% 4.87/5.03 (~r(s(s(s(s(z)))), elem!1)),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[20490, 521, 47])).
% 4.87/5.03 tff(26091,plain,
% 4.87/5.03 (s(s(s(s(z)))) = elem!1),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[24866, 11716, 24641, 812, 25336, 26090])).
% 4.87/5.03 tff(26092,plain,
% 4.87/5.03 (~(s(s(elem!1)) = elem!1)),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[338, 26091, 12])).
% 4.87/5.03 tff(26093,plain,
% 4.87/5.03 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[348, 26092])).
% 4.87/5.03 tff(26094,plain,
% 4.87/5.03 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.87/5.03 inference(monotonicity,[status(thm)],[26078])).
% 4.87/5.03 tff(26095,plain,
% 4.87/5.03 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), elem!1)),
% 4.87/5.03 inference(symmetry,[status(thm)],[26094])).
% 4.87/5.03 tff(26096,plain,
% 4.87/5.03 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 4.87/5.03 inference(monotonicity,[status(thm)],[26085])).
% 4.87/5.03 tff(26097,plain,
% 4.87/5.03 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.87/5.03 inference(symmetry,[status(thm)],[26096])).
% 4.87/5.03 tff(26098,plain,
% 4.87/5.03 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), elem!1)),
% 4.87/5.03 inference(transitivity,[status(thm)],[26097, 26095])).
% 4.87/5.03 tff(26099,plain,
% 4.87/5.03 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) <=> (~b(s(s(s(elem!1))), elem!1))),
% 4.87/5.03 inference(monotonicity,[status(thm)],[26098])).
% 4.87/5.03 tff(26100,plain,
% 4.87/5.03 (~b(s(s(s(elem!1))), elem!1)),
% 4.87/5.03 inference(modus_ponens,[status(thm)],[24761, 26099])).
% 4.87/5.03 tff(26101,plain,
% 4.87/5.03 (b(s(elem!1), elem!1)),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[24899, 26100, 521, 26003, 26093, 26089, 725])).
% 4.87/5.03 tff(26102,plain,
% 4.87/5.03 (b(s(elem!1), s(s(s(s(z)))))),
% 4.87/5.03 inference(modus_ponens,[status(thm)],[26101, 26081])).
% 4.87/5.03 tff(26103,plain,
% 4.87/5.03 (~r(z, s(elem!1))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[25755, 26102, 24641, 25336, 1056, 25334, 25744])).
% 4.87/5.03 tff(26104,plain,
% 4.87/5.03 (b(z, s(elem!1))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[2351, 26103])).
% 4.87/5.03 tff(26105,plain,
% 4.87/5.03 (s(s(s(s(s(z))))) = s(elem!1)),
% 4.87/5.03 inference(symmetry,[status(thm)],[26079])).
% 4.87/5.03 tff(26106,plain,
% 4.87/5.03 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.87/5.03 inference(monotonicity,[status(thm)],[26105])).
% 4.87/5.03 tff(26107,plain,
% 4.87/5.03 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) <=> (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 4.87/5.03 inference(monotonicity,[status(thm)],[26106])).
% 4.87/5.03 tff(26108,plain,
% 4.87/5.03 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.03 inference(monotonicity,[status(thm)],[26079])).
% 4.87/5.03 tff(26109,plain,
% 4.87/5.03 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.87/5.03 inference(monotonicity,[status(thm)],[26105])).
% 4.87/5.03 tff(26110,plain,
% 4.87/5.03 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))),
% 4.87/5.03 inference(monotonicity,[status(thm)],[26085, 26079])).
% 4.87/5.03 tff(26111,plain,
% 4.87/5.03 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 4.87/5.03 inference(transitivity,[status(thm)],[26110, 4625])).
% 4.87/5.03 tff(26112,plain,
% 4.87/5.03 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.87/5.03 inference(transitivity,[status(thm)],[26111, 26109])).
% 4.87/5.03 tff(26113,plain,
% 4.87/5.03 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 4.87/5.03 inference(monotonicity,[status(thm)],[26112])).
% 4.87/5.03 tff(26114,plain,
% 4.87/5.03 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.87/5.03 inference(modus_ponens,[status(thm)],[26093, 26113])).
% 4.87/5.03 tff(26115,plain,
% 4.87/5.03 (~r(z, s(s(s(z))))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[23351, 194, 47, 25334])).
% 4.87/5.03 tff(26116,plain,
% 4.87/5.03 (b(z, s(s(s(z))))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[4920, 26115])).
% 4.87/5.03 tff(26117,plain,
% 4.87/5.03 (~r(s(s(s(z))), z)),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[25391, 194, 24641, 25336, 24655, 25334])).
% 4.87/5.03 tff(26118,plain,
% 4.87/5.03 (b(s(s(s(z))), z)),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[21073, 26117])).
% 4.87/5.03 tff(26119,plain,
% 4.87/5.03 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[23358, 26118, 24649, 24647, 26116])).
% 4.87/5.03 tff(26120,plain,
% 4.87/5.03 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 26119])).
% 4.87/5.03 tff(26121,plain,
% 4.87/5.03 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[23137, 178, 855, 853, 24649, 24647])).
% 4.87/5.03 tff(26122,plain,
% 4.87/5.03 (~r(s(elem!1), s(s(s(s(z)))))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[25119, 382])).
% 4.87/5.03 tff(26123,plain,
% 4.87/5.03 (elem!1 = s(s(s(s(z))))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[814, 521, 24607, 106, 812, 12, 145, 202])).
% 4.87/5.03 tff(26124,plain,
% 4.87/5.03 (s(elem!1) = s(s(s(s(s(z)))))),
% 4.87/5.03 inference(monotonicity,[status(thm)],[26123])).
% 4.87/5.03 tff(26125,plain,
% 4.87/5.03 (s(s(s(s(s(z))))) = s(elem!1)),
% 4.87/5.03 inference(symmetry,[status(thm)],[26124])).
% 4.87/5.03 tff(26126,plain,
% 4.87/5.03 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) <=> r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.87/5.03 inference(monotonicity,[status(thm)],[26125])).
% 4.87/5.04 tff(26127,plain,
% 4.87/5.04 (r(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 4.87/5.04 inference(symmetry,[status(thm)],[26126])).
% 4.87/5.04 tff(26128,plain,
% 4.87/5.04 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 4.87/5.04 inference(monotonicity,[status(thm)],[26124])).
% 4.87/5.04 tff(26129,plain,
% 4.87/5.04 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 4.87/5.04 inference(monotonicity,[status(thm)],[26128])).
% 4.87/5.04 tff(26130,plain,
% 4.87/5.04 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.87/5.04 inference(monotonicity,[status(thm)],[26129])).
% 4.87/5.04 tff(26131,plain,
% 4.87/5.04 (s(s(s(s(z)))) = elem!1),
% 4.87/5.04 inference(unit_resolution,[status(thm)],[24866, 530, 24607, 812, 202, 25564])).
% 4.87/5.04 tff(26132,plain,
% 4.87/5.04 (~(s(s(elem!1)) = elem!1)),
% 4.87/5.04 inference(unit_resolution,[status(thm)],[338, 26131, 12])).
% 4.87/5.04 tff(26133,plain,
% 4.87/5.04 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.87/5.04 inference(unit_resolution,[status(thm)],[348, 26132])).
% 4.87/5.04 tff(26134,plain,
% 4.87/5.04 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.87/5.04 inference(monotonicity,[status(thm)],[26129])).
% 4.87/5.04 tff(26135,plain,
% 4.87/5.04 (b(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 4.87/5.04 inference(symmetry,[status(thm)],[26134])).
% 4.87/5.04 tff(26136,plain,
% 4.87/5.04 ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 4.87/5.04 inference(monotonicity,[status(thm)],[26135])).
% 4.87/5.04 tff(26137,assumption,(~b(s(s(s(s(s(s(s(z))))))), s(elem!1))), introduced(assumption)).
% 4.87/5.04 tff(26138,plain,
% 4.87/5.04 (~b(s(s(s(elem!1))), s(elem!1))),
% 4.87/5.04 inference(modus_ponens,[status(thm)],[26137, 26136])).
% 4.87/5.04 tff(26139,plain,
% 4.87/5.04 (r(s(s(s(elem!1))), s(elem!1))),
% 4.87/5.04 inference(unit_resolution,[status(thm)],[373, 26138, 26133])).
% 4.87/5.04 tff(26140,plain,
% 4.87/5.04 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.87/5.04 inference(modus_ponens,[status(thm)],[26139, 26130])).
% 4.87/5.04 tff(26141,plain,
% 4.87/5.04 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 4.87/5.04 inference(modus_ponens,[status(thm)],[26140, 26127])).
% 4.87/5.04 tff(26142,plain,
% 4.87/5.04 (b(z, s(elem!1)) <=> b(z, s(s(s(s(s(z))))))),
% 4.87/5.04 inference(monotonicity,[status(thm)],[26124])).
% 4.87/5.04 tff(26143,plain,
% 4.87/5.04 (b(z, s(s(s(s(s(z))))))),
% 4.87/5.04 inference(modus_ponens,[status(thm)],[855, 26142])).
% 4.87/5.04 tff(26144,plain,
% 4.87/5.04 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 4.87/5.04 inference(monotonicity,[status(thm)],[26125])).
% 4.87/5.04 tff(26145,plain,
% 4.87/5.04 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 4.87/5.04 inference(symmetry,[status(thm)],[26144])).
% 4.87/5.04 tff(26146,plain,
% 4.87/5.04 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(s(s(z)))))),
% 4.87/5.04 inference(monotonicity,[status(thm)],[26123])).
% 4.87/5.04 tff(26147,plain,
% 4.87/5.04 ((s(elem!1) = elem!1) <=> (s(s(s(s(z)))) = s(elem!1))),
% 4.87/5.04 inference(transitivity,[status(thm)],[26146, 2163])).
% 4.87/5.04 tff(26148,plain,
% 4.87/5.04 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(s(s(z)))))),
% 4.87/5.04 inference(transitivity,[status(thm)],[26147, 2164])).
% 4.87/5.04 tff(26149,plain,
% 4.87/5.04 ((~(s(elem!1) = elem!1)) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 4.87/5.04 inference(monotonicity,[status(thm)],[26148])).
% 4.87/5.04 tff(26150,plain,
% 4.87/5.04 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.87/5.04 inference(modus_ponens,[status(thm)],[725, 26149])).
% 4.87/5.04 tff(26151,plain,
% 4.87/5.04 (b(s(elem!1), s(s(s(s(z)))))),
% 4.87/5.04 inference(unit_resolution,[status(thm)],[1084, 26150, 926])).
% 4.87/5.04 tff(26152,plain,
% 4.87/5.04 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 4.87/5.04 inference(modus_ponens,[status(thm)],[26151, 26145])).
% 4.87/5.04 tff(26153,plain,
% 4.87/5.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 4.87/5.04 inference(rewrite,[status(thm)],[])).
% 4.87/5.04 tff(26154,plain,
% 4.87/5.04 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 4.87/5.04 inference(rewrite,[status(thm)],[])).
% 4.87/5.04 tff(26155,plain,
% 4.87/5.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 4.87/5.04 inference(monotonicity,[status(thm)],[26154])).
% 4.87/5.04 tff(26156,plain,
% 4.87/5.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 4.87/5.04 inference(transitivity,[status(thm)],[26155, 26153])).
% 4.87/5.04 tff(26157,plain,
% 4.87/5.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))))),
% 4.87/5.04 inference(quant_inst,[status(thm)],[])).
% 4.87/5.04 tff(26158,plain,
% 4.87/5.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 4.87/5.04 inference(modus_ponens,[status(thm)],[26157, 26156])).
% 4.87/5.04 tff(26159,plain,
% 4.87/5.04 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 4.87/5.04 inference(unit_resolution,[status(thm)],[26158, 178, 26152, 26143, 24604, 3008])).
% 4.87/5.04 tff(26160,plain,
% 4.87/5.04 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 4.87/5.04 inference(unit_resolution,[status(thm)],[9830, 41, 11413, 26159])).
% 4.87/5.04 tff(26161,plain,
% 4.87/5.04 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 4.87/5.04 inference(rewrite,[status(thm)],[])).
% 4.87/5.04 tff(26162,plain,
% 4.87/5.04 (((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
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% 4.87/5.04 inference(transitivity,[status(thm)],[26163, 26161])).
% 4.87/5.04 tff(26165,plain,
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% 4.87/5.04 tff(26167,plain,
% 4.87/5.04 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 4.87/5.04 inference(unit_resolution,[status(thm)],[26166, 118, 16063, 26160])).
% 4.87/5.04 tff(26168,plain,
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% 4.87/5.04 inference(unit_resolution,[status(thm)],[26167, 26141])).
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% 4.87/5.04 inference(unit_resolution,[status(thm)],[1846, 26171, 1])).
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% 4.87/5.04 tff(26181,plain,
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% 4.87/5.04 tff(26193,plain,
% 4.87/5.04 ((~r(s(s(s(s(z)))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.87/5.04 inference(unit_resolution,[status(thm)],[5583, 24592])).
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% 4.87/5.04 tff(26234,plain,
% 4.87/5.04 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.87/5.04 inference(unit_resolution,[status(thm)],[16181, 26225])).
% 4.87/5.04 tff(26235,plain,
% 4.87/5.04 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.87/5.04 inference(monotonicity,[status(thm)],[26225])).
% 4.87/5.04 tff(26236,plain,
% 4.87/5.04 ((~(s(elem!1) = elem!1)) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 4.87/5.04 inference(monotonicity,[status(thm)],[26235])).
% 4.87/5.04 tff(26237,plain,
% 4.87/5.04 (~(elem!1 = s(s(s(elem!1))))),
% 4.87/5.04 inference(unit_resolution,[status(thm)],[2859, 26225, 13192])).
% 4.87/5.04 tff(26238,plain,
% 4.87/5.04 (~(s(s(s(elem!1))) = elem!1)),
% 4.87/5.04 inference(unit_resolution,[status(thm)],[2489, 26237])).
% 4.87/5.04 tff(26239,plain,
% 4.87/5.04 (~(s(elem!1) = elem!1)),
% 4.87/5.04 inference(unit_resolution,[status(thm)],[2150, 26238])).
% 4.87/5.04 tff(26240,plain,
% 4.87/5.04 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.87/5.04 inference(modus_ponens,[status(thm)],[26239, 26236])).
% 4.87/5.04 tff(26241,plain,
% 4.87/5.04 ((s(elem!1) = elem!1) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 4.87/5.04 inference(transitivity,[status(thm)],[26235, 655])).
% 4.87/5.04 tff(26242,plain,
% 4.87/5.04 ((~(s(elem!1) = elem!1)) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 4.87/5.04 inference(monotonicity,[status(thm)],[26241])).
% 4.87/5.04 tff(26243,plain,
% 4.87/5.04 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 4.87/5.04 inference(modus_ponens,[status(thm)],[26239, 26242])).
% 4.87/5.04 tff(26244,plain,
% 4.87/5.04 (r(elem!1, s(s(s(s(z)))))),
% 4.87/5.04 inference(unit_resolution,[status(thm)],[24769, 26225, 24761])).
% 4.87/5.04 tff(26245,plain,
% 4.87/5.04 (~r(z, elem!1)),
% 4.87/5.04 inference(unit_resolution,[status(thm)],[529, 26244, 47])).
% 4.87/5.04 tff(26246,plain,
% 4.87/5.04 (b(z, elem!1)),
% 4.87/5.04 inference(unit_resolution,[status(thm)],[585, 26245, 507])).
% 4.87/5.04 tff(26247,plain,
% 4.87/5.04 (~r(elem!1, z)),
% 4.87/5.04 inference(unit_resolution,[status(thm)],[9980, 26244, 3244])).
% 4.87/5.04 tff(26248,plain,
% 4.87/5.04 (b(elem!1, z)),
% 4.87/5.04 inference(unit_resolution,[status(thm)],[498, 26247, 2809])).
% 4.87/5.04 tff(26249,plain,
% 4.87/5.04 (~(elem!1 = s(elem!1))),
% 4.87/5.04 inference(unit_resolution,[status(thm)],[748, 26239])).
% 4.87/5.04 tff(26250,plain,
% 4.87/5.04 (~r(z, s(elem!1))),
% 4.87/5.04 inference(unit_resolution,[status(thm)],[25758, 26234, 1056, 25334, 25744, 47])).
% 4.87/5.04 tff(26251,plain,
% 4.87/5.04 (b(z, s(elem!1))),
% 4.87/5.04 inference(unit_resolution,[status(thm)],[2351, 26250])).
% 4.87/5.04 tff(26252,plain,
% 4.87/5.04 (~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z))))),
% 4.87/5.04 inference(unit_resolution,[status(thm)],[24777, 26225, 23437])).
% 4.87/5.04 tff(26253,plain,
% 4.87/5.04 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.87/5.04 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 25870])).
% 4.87/5.04 tff(26254,plain,
% 4.87/5.04 (r(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 4.87/5.04 inference(symmetry,[status(thm)],[19264])).
% 4.87/5.04 tff(26255,plain,
% 4.87/5.04 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))) <=> r(elem!1, s(elem!1))),
% 4.87/5.04 inference(transitivity,[status(thm)],[19261, 26254])).
% 4.87/5.04 tff(26256,plain,
% 4.87/5.04 ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) <=> (~r(elem!1, s(elem!1)))),
% 4.87/5.04 inference(monotonicity,[status(thm)],[26255])).
% 4.87/5.04 tff(26257,plain,
% 4.87/5.04 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 4.87/5.04 inference(monotonicity,[status(thm)],[2823])).
% 4.87/5.04 tff(26258,plain,
% 4.87/5.04 (~r(s(elem!1), s(s(s(s(z)))))),
% 4.87/5.04 inference(unit_resolution,[status(thm)],[26193, 853, 194, 4017, 855, 2286])).
% 4.87/5.04 tff(26259,plain,
% 4.87/5.04 (b(s(elem!1), s(s(s(s(z)))))),
% 4.87/5.04 inference(unit_resolution,[status(thm)],[1084, 26258, 16182])).
% 4.87/5.04 tff(26260,plain,
% 4.87/5.04 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 4.87/5.04 inference(modus_ponens,[status(thm)],[26259, 26257])).
% 4.87/5.04 tff(26261,plain,
% 4.87/5.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 4.87/5.04 inference(rewrite,[status(thm)],[])).
% 4.87/5.04 tff(26262,plain,
% 4.87/5.04 (((~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(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(s(z))))))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 4.87/5.04 inference(rewrite,[status(thm)],[])).
% 4.87/5.04 tff(26263,plain,
% 4.87/5.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))))),
% 4.87/5.04 inference(monotonicity,[status(thm)],[26262])).
% 4.87/5.04 tff(26264,plain,
% 4.87/5.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 4.87/5.04 inference(transitivity,[status(thm)],[26263, 26261])).
% 4.87/5.04 tff(26265,plain,
% 4.87/5.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))))),
% 4.87/5.04 inference(quant_inst,[status(thm)],[])).
% 4.87/5.04 tff(26266,plain,
% 4.87/5.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 4.87/5.04 inference(modus_ponens,[status(thm)],[26265, 26264])).
% 4.87/5.04 tff(26267,plain,
% 4.87/5.04 ((~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 4.87/5.04 inference(unit_resolution,[status(thm)],[26266, 178, 1126, 3008, 26260])).
% 4.87/5.04 tff(26268,plain,
% 4.87/5.04 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 4.87/5.04 inference(unit_resolution,[status(thm)],[26267, 21928])).
% 4.87/5.04 tff(26269,plain,
% 4.87/5.04 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 4.87/5.04 inference(unit_resolution,[status(thm)],[24832, 26268, 24825])).
% 4.87/5.04 tff(26270,plain,
% 4.87/5.04 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 4.87/5.04 inference(rewrite,[status(thm)],[])).
% 4.87/5.04 tff(26271,plain,
% 4.87/5.04 (((~r(s(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))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 4.87/5.04 inference(rewrite,[status(thm)],[])).
% 4.87/5.04 tff(26272,plain,
% 4.87/5.04 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))))),
% 4.87/5.04 inference(monotonicity,[status(thm)],[26271])).
% 4.87/5.04 tff(26273,plain,
% 4.87/5.04 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 4.87/5.05 inference(transitivity,[status(thm)],[26272, 26270])).
% 4.87/5.05 tff(26274,plain,
% 4.87/5.05 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 4.87/5.05 inference(quant_inst,[status(thm)],[])).
% 4.87/5.05 tff(26275,plain,
% 4.87/5.05 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 4.87/5.05 inference(modus_ponens,[status(thm)],[26274, 26273])).
% 4.87/5.05 tff(26276,plain,
% 4.87/5.05 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[26275, 118, 16063, 26269])).
% 4.87/5.05 tff(26277,plain,
% 4.87/5.05 (~r(elem!1, s(elem!1))),
% 4.87/5.05 inference(modus_ponens,[status(thm)],[26276, 26256])).
% 4.87/5.05 tff(26278,plain,
% 4.87/5.05 (~b(elem!1, s(elem!1))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[863, 853, 506, 818, 855])).
% 4.87/5.05 tff(26279,plain,
% 4.87/5.05 (r(elem!1, s(elem!1))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[756, 26278, 750])).
% 4.87/5.05 tff(26280,plain,
% 4.87/5.05 ($false),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[26279, 26277])).
% 4.87/5.05 tff(26281,plain,((~b(s(elem!1), z)) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(z, s(elem!1))) | (elem!1 = s(elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (s(elem!1) = s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.87/5.05 tff(26282,plain,
% 4.87/5.05 (~b(s(elem!1), z)),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[26281, 26225, 26253, 26252, 24655, 25439, 26251, 26249, 26248, 26246, 3244, 26243, 26240])).
% 4.87/5.05 tff(26283,plain,
% 4.87/5.05 (r(s(elem!1), z)),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[774, 26282])).
% 4.87/5.05 tff(26284,plain,
% 4.87/5.05 (~r(s(elem!1), s(s(s(s(z)))))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[916, 26283, 3244])).
% 4.87/5.05 tff(26285,plain,
% 4.87/5.05 (b(s(elem!1), s(s(s(s(z)))))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[1084, 26284, 26234])).
% 4.87/5.05 tff(26286,plain,
% 4.87/5.05 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 4.87/5.05 inference(modus_ponens,[status(thm)],[26285, 26233])).
% 4.87/5.05 tff(26287,plain,
% 4.87/5.05 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 4.87/5.05 inference(monotonicity,[status(thm)],[26228])).
% 4.87/5.05 tff(26288,plain,
% 4.87/5.05 (~r(s(elem!1), s(s(z)))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[8621, 26283, 25334])).
% 4.87/5.05 tff(26289,plain,
% 4.87/5.05 (b(s(elem!1), s(s(z)))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[421, 26288, 1056])).
% 4.87/5.05 tff(26290,plain,
% 4.87/5.05 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 4.87/5.05 inference(modus_ponens,[status(thm)],[26289, 26287])).
% 4.87/5.05 tff(26291,plain,
% 4.87/5.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 4.87/5.05 inference(rewrite,[status(thm)],[])).
% 4.87/5.05 tff(26292,plain,
% 4.87/5.05 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(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(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~b(s(s(z)), 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(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 4.87/5.05 inference(rewrite,[status(thm)],[])).
% 4.87/5.05 tff(26293,plain,
% 4.87/5.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(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(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))))),
% 4.87/5.05 inference(monotonicity,[status(thm)],[26292])).
% 4.87/5.05 tff(26294,plain,
% 4.87/5.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(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(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 4.87/5.05 inference(transitivity,[status(thm)],[26293, 26291])).
% 4.87/5.05 tff(26295,plain,
% 4.87/5.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(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(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 4.87/5.05 inference(quant_inst,[status(thm)],[])).
% 4.87/5.05 tff(26296,plain,
% 4.87/5.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))),
% 4.87/5.05 inference(modus_ponens,[status(thm)],[26295, 26294])).
% 4.87/5.05 tff(26297,plain,
% 4.87/5.05 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[26296, 178, 24641, 1146, 26290, 26286])).
% 4.87/5.05 tff(26298,plain,
% 4.87/5.05 (~b(elem!1, s(elem!1))),
% 4.87/5.05 inference(modus_ponens,[status(thm)],[26297, 26232])).
% 4.87/5.05 tff(26299,plain,
% 4.87/5.05 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.05 inference(monotonicity,[status(thm)],[26225])).
% 4.87/5.05 tff(26300,plain,
% 4.87/5.05 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(z)))), elem!1)),
% 4.87/5.05 inference(symmetry,[status(thm)],[26299])).
% 4.87/5.05 tff(26301,plain,
% 4.87/5.05 (r(s(s(s(s(z)))), elem!1)),
% 4.87/5.05 inference(modus_ponens,[status(thm)],[25922, 26300])).
% 4.87/5.05 tff(26302,plain,
% 4.87/5.05 (~(elem!1 = s(s(s(s(z)))))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[1846, 26246, 1])).
% 4.87/5.05 tff(26303,plain,
% 4.87/5.05 (~r(s(s(s(s(z)))), s(elem!1))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[10992, 1587, 3132])).
% 4.87/5.05 tff(26304,plain,
% 4.87/5.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 4.87/5.05 inference(rewrite,[status(thm)],[])).
% 4.87/5.05 tff(26305,plain,
% 4.87/5.05 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1)))) <=> ((~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 4.87/5.05 inference(rewrite,[status(thm)],[])).
% 4.87/5.05 tff(26306,plain,
% 4.87/5.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 4.87/5.05 inference(monotonicity,[status(thm)],[26305])).
% 4.87/5.05 tff(26307,plain,
% 4.87/5.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 4.87/5.05 inference(transitivity,[status(thm)],[26306, 26304])).
% 4.87/5.05 tff(26308,plain,
% 4.87/5.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 4.87/5.05 inference(quant_inst,[status(thm)],[])).
% 4.87/5.05 tff(26309,plain,
% 4.87/5.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 4.87/5.05 inference(modus_ponens,[status(thm)],[26308, 26307])).
% 4.87/5.05 tff(26310,plain,
% 4.87/5.05 (~b(s(elem!1), s(s(z)))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[26309, 178, 8640, 22724, 167, 202])).
% 4.87/5.05 tff(26311,plain,
% 4.87/5.05 (~(s(elem!1) = s(s(z)))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[617, 11992, 506, 1140, 507, 1145, 202, 469, 12, 145, 106])).
% 4.87/5.05 tff(26312,plain,
% 4.87/5.05 ($false),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[421, 26311, 26310, 927])).
% 4.87/5.05 tff(26313,plain,((~r(elem!1, s(s(s(s(z)))))) | r(s(elem!1), s(s(z))) | (~b(elem!1, z)) | (z = elem!1) | (~b(s(s(s(s(z)))), s(s(z)))) | (elem!1 = s(s(s(s(z))))) | (s(s(z)) = elem!1) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (s(elem!1) = s(s(s(s(z))))) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 4.87/5.05 tff(26314,plain,
% 4.87/5.05 (~b(s(s(s(s(z)))), s(elem!1))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[26313, 1587, 506, 507, 202, 469, 12, 145, 106, 470, 167, 1130, 1369, 927])).
% 4.87/5.05 tff(26315,plain,
% 4.87/5.05 ($false),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[2173, 26314, 26303, 2169])).
% 4.87/5.05 tff(26316,plain,((~r(elem!1, s(elem!1))) | (~b(elem!1, z)) | (z = elem!1) | (~b(s(s(s(s(z)))), s(s(z)))) | (elem!1 = s(s(s(s(z))))) | (s(s(z)) = elem!1) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (s(elem!1) = s(s(s(s(z))))) | r(s(elem!1), s(s(z))) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.87/5.05 tff(26317,plain,
% 4.87/5.05 ((~r(elem!1, s(elem!1))) | (~b(elem!1, z)) | (z = elem!1) | (~b(s(s(s(s(z)))), s(s(z)))) | (elem!1 = s(s(s(s(z))))) | (s(s(z)) = elem!1) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (s(elem!1) = s(s(s(s(z))))) | r(s(elem!1), s(s(z))) | (~r(s(s(s(s(z)))), elem!1))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[26316, 24592])).
% 4.87/5.05 tff(26318,plain,
% 4.87/5.05 (~r(elem!1, s(elem!1))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[26317, 26288, 25336, 25744, 507, 47, 12, 26302, 26248, 24641, 26301, 26234, 26244])).
% 4.87/5.05 tff(26319,plain,
% 4.87/5.05 (b(elem!1, s(elem!1))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[756, 26318, 26249])).
% 4.87/5.05 tff(26320,plain,
% 4.87/5.05 ($false),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[26319, 26298])).
% 4.87/5.05 tff(26321,plain,((s(elem!1) = s(s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (z = elem!1) | (s(s(z)) = elem!1) | b(z, s(s(s(s(z))))) | b(s(s(s(s(z)))), z) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.87/5.05 tff(26322,plain,
% 4.87/5.05 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[26321, 25914, 507, 12, 1, 3170, 166])).
% 4.87/5.05 tff(26323,plain,
% 4.87/5.05 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[3578, 26322])).
% 4.87/5.05 tff(26324,plain,
% 4.87/5.05 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[20457, 14548, 107])).
% 4.87/5.05 tff(26325,plain,
% 4.87/5.05 (~r(z, elem!1)),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[4862, 14548, 25334])).
% 4.87/5.05 tff(26326,plain,
% 4.87/5.05 (~r(elem!1, z)),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[8416, 14548, 25334])).
% 4.87/5.05 tff(26327,plain,
% 4.87/5.05 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[2820, 26326, 24649, 24647, 507, 26325])).
% 4.87/5.05 tff(26328,plain,
% 4.87/5.05 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[691, 26327, 26324])).
% 4.87/5.05 tff(26329,plain,
% 4.87/5.05 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[16181, 26328])).
% 4.87/5.05 tff(26330,plain,
% 4.87/5.05 (~(s(s(s(s(z)))) = s(elem!1))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[2168, 26329])).
% 4.87/5.05 tff(26331,plain,
% 4.87/5.05 (r(elem!1, s(s(s(s(z)))))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[24769, 26328, 24761])).
% 4.87/5.05 tff(26332,plain,
% 4.87/5.05 (~(elem!1 = s(elem!1))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[748, 26035])).
% 4.87/5.05 tff(26333,plain,
% 4.87/5.05 (~r(z, s(elem!1))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[25758, 26329, 25914, 25334, 25744, 47])).
% 4.87/5.05 tff(26334,plain,
% 4.87/5.05 (b(z, s(elem!1))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[2351, 26333])).
% 4.87/5.05 tff(26335,plain,
% 4.87/5.05 (b(z, elem!1)),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[585, 26325, 507])).
% 4.87/5.05 tff(26336,plain,
% 4.87/5.05 (b(elem!1, z)),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[498, 26326, 2809])).
% 4.87/5.05 tff(26337,plain,
% 4.87/5.05 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[2840, 25914])).
% 4.87/5.05 tff(26338,plain,
% 4.87/5.05 (~r(z, s(s(s(elem!1))))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[25455, 26337, 47, 25334])).
% 4.87/5.05 tff(26339,plain,
% 4.87/5.05 (b(z, s(s(s(elem!1))))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[2095, 26338])).
% 4.87/5.05 tff(26340,plain,
% 4.87/5.05 (~b(s(s(s(elem!1))), elem!1)),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[12925, 26335, 26339, 26001, 26336])).
% 4.87/5.05 tff(26341,plain,
% 4.87/5.05 (r(s(s(s(elem!1))), elem!1)),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[570, 26340, 26011])).
% 4.87/5.05 tff(26342,plain,
% 4.87/5.05 (~(s(s(elem!1)) = elem!1)),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[2510, 26330, 26328])).
% 4.87/5.05 tff(26343,plain,
% 4.87/5.05 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[348, 26342])).
% 4.87/5.05 tff(26344,plain,
% 4.87/5.05 (~b(s(s(s(elem!1))), s(elem!1))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[2052, 26334, 26339, 26001, 26336])).
% 4.87/5.05 tff(26345,plain,
% 4.87/5.05 (r(s(s(s(elem!1))), s(elem!1))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[373, 26344, 26343])).
% 4.87/5.05 tff(26346,plain,
% 4.87/5.05 (~r(s(elem!1), elem!1)),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[1576, 26345, 26341])).
% 4.87/5.05 tff(26347,plain,
% 4.87/5.05 (b(s(elem!1), elem!1)),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[677, 26346, 26035])).
% 4.87/5.05 tff(26348,plain,
% 4.87/5.05 (~b(elem!1, s(elem!1))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[1396, 26347, 26336, 26335, 26334])).
% 4.87/5.05 tff(26349,plain,
% 4.87/5.05 (r(elem!1, s(elem!1))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[756, 26348, 26332])).
% 4.87/5.05 tff(26350,plain,
% 4.87/5.05 (~r(s(s(s(s(z)))), s(elem!1))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[11326, 26349, 26331])).
% 4.87/5.05 tff(26351,plain,
% 4.87/5.05 (~r(s(elem!1), s(s(z)))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[17418, 26035, 25744, 14548, 26336, 26335])).
% 4.87/5.05 tff(26352,plain,
% 4.87/5.05 (~(elem!1 = s(s(s(s(z)))))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[325, 26014])).
% 4.87/5.05 tff(26353,plain,
% 4.87/5.05 ((~r(elem!1, s(s(s(s(z)))))) | r(s(elem!1), s(s(z))) | (~b(elem!1, z)) | (z = elem!1) | (~b(s(s(s(s(z)))), s(s(z)))) | (elem!1 = s(s(s(s(z))))) | (s(s(z)) = elem!1) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(z)), s(s(s(s(z)))))) | (s(elem!1) = s(s(s(s(z))))) | (~r(elem!1, s(elem!1)))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[26313, 24592])).
% 4.87/5.05 tff(26354,plain,
% 4.87/5.05 (~b(s(s(s(s(z)))), s(elem!1))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[26353, 26349, 25336, 25744, 507, 12, 47, 26352, 26336, 24641, 26331, 26329, 26351])).
% 4.87/5.05 tff(26355,plain,
% 4.87/5.05 ($false),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[2173, 26354, 26350, 26330])).
% 4.87/5.05 tff(26356,plain,(b(elem!1, s(s(z))) | (z = elem!1) | (s(s(z)) = elem!1) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | b(z, s(s(s(s(z))))) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 4.87/5.05 tff(26357,plain,
% 4.87/5.05 (b(elem!1, s(s(z)))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[26356, 12, 507, 26323, 1, 3170])).
% 4.87/5.05 tff(26358,plain,
% 4.87/5.05 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[25284, 26357, 26322])).
% 4.87/5.05 tff(26359,plain,
% 4.87/5.05 (~(elem!1 = s(s(s(s(z)))))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[1846, 3123, 1])).
% 4.87/5.05 tff(26360,plain,
% 4.87/5.05 (~r(elem!1, z)),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[493, 26359, 25336, 25744, 12, 47, 24641])).
% 4.87/5.05 tff(26361,plain,
% 4.87/5.05 (b(elem!1, z)),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[498, 26360, 2809])).
% 4.87/5.05 tff(26362,plain,
% 4.87/5.05 (~(s(s(s(s(z)))) = elem!1)),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[504, 26359])).
% 4.87/5.05 tff(26363,plain,
% 4.87/5.05 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[2820, 26360, 24649, 24647, 507, 2811])).
% 4.87/5.05 tff(26364,plain,
% 4.87/5.05 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[691, 26363, 701])).
% 4.87/5.05 tff(26365,plain,
% 4.87/5.05 (~r(elem!1, s(s(s(s(z)))))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[25883, 26364])).
% 4.87/5.05 tff(26366,plain,
% 4.87/5.05 (r(s(s(s(s(z)))), elem!1)),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[24866, 26365, 24641, 812, 25336, 26362])).
% 4.87/5.05 tff(26367,plain,
% 4.87/5.05 (b(elem!1, s(s(s(s(z)))))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[483, 26365, 26359])).
% 4.87/5.05 tff(26368,plain,
% 4.87/5.05 ($false),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[3457, 26367, 26366, 47, 24761, 26361, 3123])).
% 4.87/5.05 tff(26369,plain,(r(z, elem!1) | (~b(elem!1, s(s(z)))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (z = elem!1) | (s(s(z)) = elem!1) | b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.87/5.05 tff(26370,plain,
% 4.87/5.05 (r(z, elem!1)),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[26369, 26357, 26358, 507, 12, 1])).
% 4.87/5.05 tff(26371,plain,
% 4.87/5.05 (elem!1 = s(s(s(s(z))))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[814, 26370, 24641, 25744, 26357, 12, 47, 25336])).
% 4.87/5.05 tff(26372,plain,
% 4.87/5.05 (s(elem!1) = s(s(s(s(s(z)))))),
% 4.87/5.05 inference(monotonicity,[status(thm)],[26371])).
% 4.87/5.05 tff(26373,plain,
% 4.87/5.05 (s(s(s(s(s(z))))) = s(elem!1)),
% 4.87/5.05 inference(symmetry,[status(thm)],[26372])).
% 4.87/5.05 tff(26374,plain,
% 4.87/5.05 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.87/5.05 inference(monotonicity,[status(thm)],[26373])).
% 4.87/5.05 tff(26375,plain,
% 4.87/5.05 (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(s(z))))))),
% 4.87/5.05 inference(symmetry,[status(thm)],[26374])).
% 4.87/5.05 tff(26376,plain,
% 4.87/5.05 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(s(s(z)))))),
% 4.87/5.05 inference(monotonicity,[status(thm)],[26371])).
% 4.87/5.05 tff(26377,plain,
% 4.87/5.05 ((s(elem!1) = elem!1) <=> (s(s(s(s(z)))) = s(elem!1))),
% 4.87/5.05 inference(transitivity,[status(thm)],[26376, 2163])).
% 4.87/5.05 tff(26378,plain,
% 4.87/5.05 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(s(s(z)))))),
% 4.87/5.05 inference(transitivity,[status(thm)],[26377, 2164])).
% 4.87/5.05 tff(26379,plain,
% 4.87/5.05 ((~(s(elem!1) = elem!1)) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 4.87/5.05 inference(monotonicity,[status(thm)],[26378])).
% 4.87/5.05 tff(26380,plain,
% 4.87/5.05 (~r(s(s(s(s(z)))), elem!1)),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[20490, 26370, 47])).
% 4.87/5.05 tff(26381,plain,
% 4.87/5.05 (~r(elem!1, s(s(s(s(z)))))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[529, 26370, 47])).
% 4.87/5.05 tff(26382,plain,
% 4.87/5.05 (s(s(s(s(z)))) = elem!1),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[24866, 26381, 24641, 26357, 25336, 26380])).
% 4.87/5.05 tff(26383,plain,
% 4.87/5.05 (~(s(s(elem!1)) = elem!1)),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[338, 26382, 12])).
% 4.87/5.05 tff(26384,plain,
% 4.87/5.05 (~(s(elem!1) = elem!1)),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[672, 26383])).
% 4.87/5.05 tff(26385,plain,
% 4.87/5.05 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.87/5.05 inference(modus_ponens,[status(thm)],[26384, 26379])).
% 4.87/5.05 tff(26386,plain,
% 4.87/5.05 (~r(z, s(elem!1))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[25758, 26385, 25914, 25334, 25744, 47])).
% 4.87/5.05 tff(26387,plain,
% 4.87/5.05 (b(z, s(elem!1))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[2351, 26386])).
% 4.87/5.05 tff(26388,plain,
% 4.87/5.05 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.87/5.05 inference(monotonicity,[status(thm)],[26373])).
% 4.87/5.05 tff(26389,plain,
% 4.87/5.05 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 4.87/5.05 inference(monotonicity,[status(thm)],[26372])).
% 4.87/5.05 tff(26390,plain,
% 4.87/5.05 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 4.87/5.05 inference(monotonicity,[status(thm)],[26389])).
% 4.87/5.05 tff(26391,plain,
% 4.87/5.05 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))),
% 4.87/5.05 inference(monotonicity,[status(thm)],[26390, 26372])).
% 4.87/5.05 tff(26392,plain,
% 4.87/5.05 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 4.87/5.05 inference(transitivity,[status(thm)],[26391, 4625])).
% 4.87/5.05 tff(26393,plain,
% 4.87/5.05 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.87/5.05 inference(transitivity,[status(thm)],[26392, 26388])).
% 4.87/5.05 tff(26394,plain,
% 4.87/5.05 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 4.87/5.05 inference(monotonicity,[status(thm)],[26393])).
% 4.87/5.05 tff(26395,plain,
% 4.87/5.05 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[348, 26383])).
% 4.87/5.05 tff(26396,plain,
% 4.87/5.05 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.87/5.05 inference(modus_ponens,[status(thm)],[26395, 26394])).
% 4.87/5.05 tff(26397,plain,
% 4.87/5.05 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 4.87/5.05 inference(transitivity,[status(thm)],[26392, 26388, 655])).
% 4.87/5.05 tff(26398,plain,
% 4.87/5.05 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 4.87/5.05 inference(monotonicity,[status(thm)],[26397])).
% 4.87/5.05 tff(26399,plain,
% 4.87/5.05 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 4.87/5.05 inference(modus_ponens,[status(thm)],[26395, 26398])).
% 4.87/5.05 tff(26400,plain,
% 4.87/5.05 (~(elem!1 = s(elem!1))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[748, 26384])).
% 4.87/5.05 tff(26401,plain,
% 4.87/5.05 (~b(elem!1, z)),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[3172, 26371, 3170])).
% 4.87/5.05 tff(26402,plain,
% 4.87/5.05 (r(elem!1, z)),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[498, 26401, 2809])).
% 4.87/5.06 tff(26403,plain,
% 4.87/5.06 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 4.87/5.06 inference(monotonicity,[status(thm)],[26372])).
% 4.87/5.06 tff(26404,plain,
% 4.87/5.06 (b(s(elem!1), s(s(z)))),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[2373, 26371, 25744, 166, 26323, 12])).
% 4.87/5.06 tff(26405,plain,
% 4.87/5.06 (b(s(s(s(s(s(z))))), s(s(z)))),
% 4.87/5.06 inference(modus_ponens,[status(thm)],[26404, 26403])).
% 4.87/5.06 tff(26406,plain,
% 4.87/5.06 (~r(s(elem!1), z)),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[2715, 26405, 24641, 26371, 26402, 26400, 26385, 25336, 3244])).
% 4.87/5.06 tff(26407,plain,
% 4.87/5.06 (b(s(elem!1), z)),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[774, 26406])).
% 4.87/5.06 tff(26408,plain,
% 4.87/5.06 (~r(s(elem!1), s(s(s(s(z)))))),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[26193, 26407, 3244, 26399, 26387, 26396])).
% 4.87/5.06 tff(26409,plain,
% 4.87/5.06 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[26169, 26408, 25439, 26370, 26384, 26387, 26253, 12, 26357, 25336, 25744, 47])).
% 4.87/5.06 tff(26410,plain,
% 4.87/5.06 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 4.87/5.06 inference(modus_ponens,[status(thm)],[26409, 26375])).
% 4.87/5.06 tff(26411,plain,
% 4.87/5.06 (b(z, s(elem!1)) <=> b(z, s(s(s(s(s(z))))))),
% 4.87/5.06 inference(monotonicity,[status(thm)],[26372])).
% 4.87/5.06 tff(26412,plain,
% 4.87/5.06 (b(z, s(s(s(s(s(z))))))),
% 4.87/5.06 inference(modus_ponens,[status(thm)],[26387, 26411])).
% 4.87/5.06 tff(26413,plain,
% 4.87/5.06 (r(s(elem!1), z) <=> r(s(s(s(s(s(z))))), z)),
% 4.87/5.06 inference(monotonicity,[status(thm)],[26372])).
% 4.87/5.06 tff(26414,plain,
% 4.87/5.06 ((~r(s(elem!1), z)) <=> (~r(s(s(s(s(s(z))))), z))),
% 4.87/5.06 inference(monotonicity,[status(thm)],[26413])).
% 4.87/5.06 tff(26415,plain,
% 4.87/5.06 (~r(s(s(s(s(s(z))))), z)),
% 4.87/5.06 inference(modus_ponens,[status(thm)],[26406, 26414])).
% 4.87/5.06 tff(26416,plain,
% 4.87/5.06 (b(s(s(s(s(s(z))))), z)),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[410, 41, 242, 26415])).
% 4.87/5.06 tff(26417,plain,
% 4.87/5.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 4.87/5.06 inference(rewrite,[status(thm)],[])).
% 4.87/5.06 tff(26418,plain,
% 4.87/5.06 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 4.87/5.06 inference(rewrite,[status(thm)],[])).
% 4.87/5.06 tff(26419,plain,
% 4.87/5.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 4.87/5.06 inference(monotonicity,[status(thm)],[26418])).
% 4.87/5.06 tff(26420,plain,
% 4.87/5.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 4.87/5.06 inference(transitivity,[status(thm)],[26419, 26417])).
% 4.87/5.06 tff(26421,plain,
% 4.87/5.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 4.87/5.06 inference(quant_inst,[status(thm)],[])).
% 4.87/5.06 tff(26422,plain,
% 4.87/5.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 4.87/5.06 inference(modus_ponens,[status(thm)],[26421, 26420])).
% 4.87/5.06 tff(26423,plain,
% 4.87/5.06 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[26422, 178, 24649, 26416, 26412, 24647])).
% 4.87/5.06 tff(26424,plain,
% 4.87/5.06 ($false),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[26423, 26410])).
% 4.87/5.06 tff(26425,plain,((s(s(z)) = elem!1) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(z)))), z) | (z = elem!1) | b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.87/5.06 tff(26426,plain,
% 4.87/5.06 (s(s(z)) = elem!1),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[26425, 3170, 166, 507, 1])).
% 4.87/5.06 tff(26427,plain,
% 4.87/5.06 (s(s(s(z))) = s(elem!1)),
% 4.87/5.06 inference(monotonicity,[status(thm)],[26426])).
% 4.87/5.06 tff(26428,plain,
% 4.87/5.06 (s(s(s(s(z)))) = s(s(elem!1))),
% 4.87/5.06 inference(monotonicity,[status(thm)],[26427])).
% 4.87/5.06 tff(26429,plain,
% 4.87/5.06 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 4.87/5.06 inference(monotonicity,[status(thm)],[26428])).
% 4.87/5.06 tff(26430,plain,
% 4.87/5.06 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(elem!1))), elem!1)),
% 4.87/5.06 inference(monotonicity,[status(thm)],[26429, 26426])).
% 4.87/5.06 tff(26431,plain,
% 4.87/5.06 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 4.87/5.06 inference(symmetry,[status(thm)],[26430])).
% 4.87/5.06 tff(26432,plain,
% 4.87/5.06 (~b(elem!1, s(s(z)))),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[3223, 26426])).
% 4.87/5.06 tff(26433,plain,
% 4.87/5.06 (b(elem!1, s(s(s(elem!1))))),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[26000, 26432, 1, 25334, 25744, 3170])).
% 4.87/5.06 tff(26434,plain,
% 4.87/5.06 (~(s(s(s(elem!1))) = elem!1)),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[16438, 26433])).
% 4.87/5.06 tff(26435,plain,
% 4.87/5.06 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 4.87/5.06 inference(monotonicity,[status(thm)],[26427])).
% 4.87/5.06 tff(26436,plain,
% 4.87/5.06 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 4.87/5.06 inference(transitivity,[status(thm)],[26435, 3881])).
% 4.87/5.06 tff(26437,plain,
% 4.87/5.06 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 4.87/5.06 inference(monotonicity,[status(thm)],[26436])).
% 4.87/5.06 tff(26438,plain,
% 4.87/5.06 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[8244, 2387])).
% 4.87/5.06 tff(26439,plain,
% 4.87/5.06 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.87/5.06 inference(modus_ponens,[status(thm)],[26438, 26437])).
% 4.87/5.06 tff(26440,plain,
% 4.87/5.06 (s(s(elem!1)) = s(s(s(s(z))))),
% 4.87/5.06 inference(symmetry,[status(thm)],[26428])).
% 4.87/5.06 tff(26441,plain,
% 4.87/5.06 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 4.87/5.06 inference(monotonicity,[status(thm)],[26440])).
% 4.87/5.06 tff(26442,plain,
% 4.87/5.06 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), s(s(elem!1)))),
% 4.87/5.06 inference(symmetry,[status(thm)],[26441])).
% 4.87/5.06 tff(26443,plain,
% 4.87/5.06 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 4.87/5.06 inference(monotonicity,[status(thm)],[26427])).
% 4.87/5.06 tff(26444,plain,
% 4.87/5.06 (b(s(elem!1), s(s(s(s(z)))))),
% 4.87/5.06 inference(modus_ponens,[status(thm)],[24655, 26443])).
% 4.87/5.06 tff(26445,plain,
% 4.87/5.06 (b(s(elem!1), s(s(elem!1)))),
% 4.87/5.06 inference(modus_ponens,[status(thm)],[26444, 26442])).
% 4.87/5.06 tff(26446,plain,
% 4.87/5.06 ((s(elem!1) = s(s(z))) <=> (s(elem!1) = elem!1)),
% 4.87/5.06 inference(monotonicity,[status(thm)],[26426])).
% 4.87/5.06 tff(26447,plain,
% 4.87/5.06 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(z)))),
% 4.87/5.06 inference(symmetry,[status(thm)],[26446])).
% 4.87/5.06 tff(26448,plain,
% 4.87/5.06 ((~(s(elem!1) = elem!1)) <=> (~(s(elem!1) = s(s(z))))),
% 4.87/5.06 inference(monotonicity,[status(thm)],[26447])).
% 4.87/5.06 tff(26449,plain,
% 4.87/5.06 (~(s(elem!1) = elem!1)),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[2150, 26434])).
% 4.87/5.06 tff(26450,plain,
% 4.87/5.06 (~(s(elem!1) = s(s(z)))),
% 4.87/5.06 inference(modus_ponens,[status(thm)],[26449, 26448])).
% 4.87/5.06 tff(26451,plain,
% 4.87/5.06 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[2840, 26450])).
% 4.87/5.06 tff(26452,plain,
% 4.87/5.06 (~(s(s(s(s(z)))) = elem!1)),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[4509, 26432, 25336])).
% 4.87/5.06 tff(26453,plain,
% 4.87/5.06 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[3502, 26452])).
% 4.87/5.06 tff(26454,plain,
% 4.87/5.06 (b(s(s(z)), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 4.87/5.06 inference(monotonicity,[status(thm)],[26426])).
% 4.87/5.06 tff(26455,plain,
% 4.87/5.06 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 4.87/5.06 inference(symmetry,[status(thm)],[26454])).
% 4.87/5.06 tff(26456,plain,
% 4.87/5.06 (b(s(s(z)), s(s(s(elem!1))))),
% 4.87/5.06 inference(modus_ponens,[status(thm)],[26433, 26455])).
% 4.87/5.06 tff(26457,plain,
% 4.87/5.06 (~r(z, s(s(s(elem!1))))),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[10669, 26456, 47, 24641, 25336, 3244, 26451])).
% 4.87/5.06 tff(26458,plain,
% 4.87/5.06 (b(z, s(s(s(elem!1))))),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[2095, 26457])).
% 4.87/5.06 tff(26459,plain,
% 4.87/5.06 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[25326, 26458, 47, 26453])).
% 4.87/5.06 tff(26460,plain,
% 4.87/5.06 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[4173, 26459, 26451])).
% 4.87/5.06 tff(26461,plain,
% 4.87/5.06 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[10679, 26460, 26426])).
% 4.87/5.06 tff(26462,plain,
% 4.87/5.06 (b(z, s(s(s(z)))) <=> b(z, s(elem!1))),
% 4.87/5.06 inference(monotonicity,[status(thm)],[26427])).
% 4.87/5.06 tff(26463,plain,
% 4.87/5.06 (b(z, s(elem!1))),
% 4.87/5.06 inference(modus_ponens,[status(thm)],[25439, 26462])).
% 4.87/5.06 tff(26464,plain,
% 4.87/5.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 4.87/5.06 inference(rewrite,[status(thm)],[])).
% 4.87/5.06 tff(26465,plain,
% 4.87/5.06 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 4.87/5.06 inference(rewrite,[status(thm)],[])).
% 4.87/5.06 tff(26466,plain,
% 4.87/5.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 4.87/5.06 inference(monotonicity,[status(thm)],[26465])).
% 4.87/5.06 tff(26467,plain,
% 4.87/5.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 4.87/5.06 inference(transitivity,[status(thm)],[26466, 26464])).
% 4.87/5.06 tff(26468,plain,
% 4.87/5.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))))),
% 4.87/5.06 inference(quant_inst,[status(thm)],[])).
% 4.87/5.06 tff(26469,plain,
% 4.87/5.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 4.87/5.06 inference(modus_ponens,[status(thm)],[26468, 26467])).
% 4.87/5.06 tff(26470,plain,
% 4.87/5.06 (~b(s(s(s(elem!1))), s(elem!1))),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[26469, 178, 26463, 26458, 26461, 26445])).
% 4.87/5.06 tff(26471,plain,
% 4.87/5.06 (r(s(s(s(elem!1))), s(elem!1))),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[373, 26470, 26439])).
% 4.87/5.06 tff(26472,plain,
% 4.87/5.06 ((s(elem!1) = s(s(elem!1))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 4.87/5.06 inference(monotonicity,[status(thm)],[26440])).
% 4.87/5.06 tff(26473,plain,
% 4.87/5.06 ((s(elem!1) = s(s(elem!1))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 4.87/5.06 inference(transitivity,[status(thm)],[26472, 2163])).
% 4.87/5.06 tff(26474,plain,
% 4.87/5.06 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(elem!1) = s(s(elem!1)))),
% 4.87/5.06 inference(symmetry,[status(thm)],[26473])).
% 4.87/5.06 tff(26475,plain,
% 4.87/5.06 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(elem!1)) = s(elem!1))),
% 4.87/5.06 inference(transitivity,[status(thm)],[26474, 10922])).
% 4.87/5.06 tff(26476,plain,
% 4.87/5.06 ((~(s(s(s(s(z)))) = s(elem!1))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 4.87/5.06 inference(monotonicity,[status(thm)],[26475])).
% 4.87/5.06 tff(26477,plain,
% 4.87/5.06 (elem!1 = s(s(z))),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[3230, 26426])).
% 4.87/5.06 tff(26478,plain,
% 4.87/5.06 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[1353, 26452, 26477])).
% 4.87/5.06 tff(26479,plain,
% 4.87/5.06 (~(s(s(s(s(z)))) = s(elem!1))),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[2168, 26478])).
% 4.87/5.06 tff(26480,plain,
% 4.87/5.06 (~(s(s(elem!1)) = s(elem!1))),
% 4.87/5.06 inference(modus_ponens,[status(thm)],[26479, 26476])).
% 4.87/5.06 tff(26481,plain,
% 4.87/5.06 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[1649, 26439])).
% 4.87/5.06 tff(26482,plain,
% 4.87/5.06 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 4.87/5.06 inference(monotonicity,[status(thm)],[26428])).
% 4.87/5.06 tff(26483,plain,
% 4.87/5.06 (b(s(s(s(s(z)))), elem!1)),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[8526, 26426, 25336])).
% 4.87/5.06 tff(26484,plain,
% 4.87/5.06 (b(s(s(elem!1)), elem!1)),
% 4.87/5.06 inference(modus_ponens,[status(thm)],[26483, 26482])).
% 4.87/5.06 tff(26485,plain,
% 4.87/5.06 ((s(s(elem!1)) = s(s(z))) <=> (s(s(elem!1)) = elem!1)),
% 4.87/5.06 inference(monotonicity,[status(thm)],[26426])).
% 4.87/5.06 tff(26486,plain,
% 4.87/5.06 ((s(s(elem!1)) = s(s(z))) <=> (elem!1 = s(s(elem!1)))),
% 4.87/5.06 inference(transitivity,[status(thm)],[26485, 1542])).
% 4.87/5.06 tff(26487,plain,
% 4.87/5.06 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(elem!1 = s(s(elem!1))))),
% 4.87/5.06 inference(monotonicity,[status(thm)],[26486])).
% 4.87/5.06 tff(26488,plain,
% 4.87/5.06 (~(elem!1 = s(s(elem!1)))),
% 4.87/5.06 inference(modus_ponens,[status(thm)],[2387, 26487])).
% 4.87/5.06 tff(26489,plain,
% 4.87/5.06 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(s(elem!1)))),
% 4.87/5.06 inference(monotonicity,[status(thm)],[26428])).
% 4.87/5.06 tff(26490,plain,
% 4.87/5.06 ((~r(elem!1, s(s(s(s(z)))))) <=> (~r(elem!1, s(s(elem!1))))),
% 4.87/5.06 inference(monotonicity,[status(thm)],[26489])).
% 4.87/5.06 tff(26491,plain,
% 4.87/5.06 (r(z, elem!1)),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[7053, 26426, 25334])).
% 4.87/5.06 tff(26492,plain,
% 4.87/5.06 (~r(elem!1, s(s(s(s(z)))))),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[529, 26491, 47])).
% 4.87/5.06 tff(26493,plain,
% 4.87/5.06 (~r(elem!1, s(s(elem!1)))),
% 4.87/5.06 inference(modus_ponens,[status(thm)],[26492, 26490])).
% 4.87/5.06 tff(26494,plain,
% 4.87/5.06 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[5479, 26461, 26433, 26493, 26488, 26484])).
% 4.87/5.06 tff(26495,plain,
% 4.87/5.06 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[3375, 26494, 26481])).
% 4.87/5.06 tff(26496,plain,
% 4.87/5.06 (~r(s(s(elem!1)), s(elem!1))),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[15350, 26471, 26495])).
% 4.87/5.06 tff(26497,plain,
% 4.87/5.06 (b(s(s(elem!1)), s(elem!1))),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[1006, 26496, 26480])).
% 4.87/5.06 tff(26498,plain,
% 4.87/5.06 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(elem!1)))),
% 4.87/5.06 inference(monotonicity,[status(thm)],[26428])).
% 4.87/5.06 tff(26499,plain,
% 4.87/5.06 (b(elem!1, s(s(s(s(z)))))),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[17989, 26426, 24641])).
% 4.87/5.06 tff(26500,plain,
% 4.87/5.06 (b(elem!1, s(s(elem!1)))),
% 4.87/5.06 inference(modus_ponens,[status(thm)],[26499, 26498])).
% 4.87/5.06 tff(26501,plain,
% 4.87/5.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))))),
% 4.87/5.06 inference(rewrite,[status(thm)],[])).
% 4.87/5.06 tff(26502,plain,
% 4.87/5.06 (((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))))),
% 4.87/5.06 inference(rewrite,[status(thm)],[])).
% 4.87/5.06 tff(26503,plain,
% 4.87/5.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1))))))),
% 4.87/5.06 inference(monotonicity,[status(thm)],[26502])).
% 4.87/5.06 tff(26504,plain,
% 4.87/5.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))))),
% 4.87/5.06 inference(transitivity,[status(thm)],[26503, 26501])).
% 4.87/5.06 tff(26505,plain,
% 4.87/5.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 4.87/5.06 inference(quant_inst,[status(thm)],[])).
% 4.87/5.06 tff(26506,plain,
% 4.87/5.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1))))),
% 4.87/5.06 inference(modus_ponens,[status(thm)],[26505, 26504])).
% 4.87/5.06 tff(26507,plain,
% 4.87/5.06 ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1))),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[26506, 178, 26484, 26445, 26500])).
% 4.87/5.06 tff(26508,plain,
% 4.87/5.06 (~b(s(elem!1), elem!1)),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[26507, 26497])).
% 4.87/5.06 tff(26509,plain,
% 4.87/5.06 (r(s(elem!1), elem!1)),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[677, 26508, 26449])).
% 4.87/5.06 tff(26510,plain,
% 4.87/5.06 (~r(s(s(s(elem!1))), elem!1)),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[1576, 26509, 26471])).
% 4.87/5.06 tff(26511,plain,
% 4.87/5.06 (b(s(s(s(elem!1))), elem!1)),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[570, 26510, 26434])).
% 4.87/5.06 tff(26512,plain,
% 4.87/5.06 (b(s(s(s(s(s(z))))), s(s(z)))),
% 4.87/5.06 inference(modus_ponens,[status(thm)],[26511, 26431])).
% 4.87/5.06 tff(26513,plain,
% 4.87/5.06 (b(s(s(z)), s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(elem!1))))),
% 4.87/5.06 inference(monotonicity,[status(thm)],[26426, 26429])).
% 4.87/5.06 tff(26514,plain,
% 4.87/5.06 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(s(z))))))),
% 4.87/5.06 inference(symmetry,[status(thm)],[26513])).
% 4.87/5.06 tff(26515,plain,
% 4.87/5.06 (b(s(s(z)), s(s(s(s(s(z))))))),
% 4.87/5.06 inference(modus_ponens,[status(thm)],[26433, 26514])).
% 4.87/5.06 tff(26516,plain,
% 4.87/5.06 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 4.87/5.06 inference(monotonicity,[status(thm)],[26429, 26428])).
% 4.87/5.06 tff(26517,plain,
% 4.87/5.06 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 4.87/5.06 inference(symmetry,[status(thm)],[26516])).
% 4.87/5.06 tff(26518,plain,
% 4.87/5.06 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 4.87/5.06 inference(modus_ponens,[status(thm)],[26461, 26517])).
% 4.87/5.06 tff(26519,plain,
% 4.87/5.06 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[1853, 26518, 25336, 24641, 26515])).
% 4.87/5.06 tff(26520,plain,
% 4.87/5.06 ($false),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[26519, 26512])).
% 4.87/5.06 tff(26521,plain,(b(s(s(s(s(z)))), z) | b(z, s(s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.87/5.06 tff(26522,plain,
% 4.87/5.06 (b(s(s(s(s(z)))), z)),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[26521, 507, 166, 1])).
% 4.87/5.06 tff(26523,plain,
% 4.87/5.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(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(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(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(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 4.87/5.06 inference(rewrite,[status(thm)],[])).
% 4.87/5.06 tff(26524,plain,
% 4.87/5.06 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(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))))))))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 4.87/5.06 inference(rewrite,[status(thm)],[])).
% 4.87/5.06 tff(26525,plain,
% 4.87/5.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(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))))))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(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(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 4.87/5.06 inference(monotonicity,[status(thm)],[26524])).
% 4.87/5.06 tff(26526,plain,
% 4.87/5.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(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))))))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(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(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 4.87/5.06 inference(transitivity,[status(thm)],[26525, 26523])).
% 4.87/5.06 tff(26527,plain,
% 4.87/5.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(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))))))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 4.87/5.06 inference(quant_inst,[status(thm)],[])).
% 4.87/5.06 tff(26528,plain,
% 4.87/5.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(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(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 4.87/5.06 inference(modus_ponens,[status(thm)],[26527, 26526])).
% 4.87/5.06 tff(26529,plain,
% 4.87/5.06 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[26528, 178, 166, 26522, 24641, 24647])).
% 4.87/5.06 tff(26530,plain,
% 4.87/5.06 (~(s(s(s(s(z)))) = elem!1)),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[4509, 461, 25566])).
% 4.87/5.06 tff(26531,plain,
% 4.87/5.06 (~(elem!1 = s(s(s(s(z)))))),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[325, 26530])).
% 4.87/5.06 tff(26532,plain,
% 4.87/5.06 (~r(elem!1, z)),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[493, 12, 25566, 106, 26531, 145, 24607])).
% 4.87/5.06 tff(26533,plain,
% 4.87/5.06 (~r(z, elem!1)),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[4862, 1042, 3261])).
% 4.87/5.06 tff(26534,plain,
% 4.87/5.06 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[2820, 26533, 24623, 24625, 507, 26532])).
% 4.87/5.06 tff(26535,plain,
% 4.87/5.06 (b(elem!1, z)),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[498, 26532, 2809])).
% 4.87/5.06 tff(26536,plain,
% 4.87/5.06 (b(z, elem!1)),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[585, 26533, 507])).
% 4.87/5.06 tff(26537,plain,
% 4.87/5.06 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[3455, 178, 26536, 26535, 24623, 24625])).
% 4.87/5.06 tff(26538,plain,
% 4.87/5.06 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[691, 701, 4289])).
% 4.87/5.06 tff(26539,plain,
% 4.87/5.06 (~r(elem!1, s(s(s(s(z)))))),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[25883, 26538])).
% 4.87/5.06 tff(26540,plain,
% 4.87/5.06 (b(elem!1, s(s(s(s(z)))))),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[483, 26539, 3130])).
% 4.87/5.06 tff(26541,plain,
% 4.87/5.06 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[3444, 4245, 19657])).
% 4.87/5.07 tff(26542,plain,
% 4.87/5.07 (~r(s(s(s(s(z)))), elem!1)),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[25879, 26541])).
% 4.87/5.07 tff(26543,plain,
% 4.87/5.07 (b(s(s(s(s(z)))), elem!1)),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[3142, 26542, 323])).
% 4.87/5.07 tff(26544,plain,
% 4.87/5.07 ($false),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[16429, 26543, 26540, 168, 506, 818])).
% 4.87/5.07 tff(26545,plain,((elem!1 = s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (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(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.87/5.07 tff(26546,plain,
% 4.87/5.07 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[26545, 26535, 168, 26536, 26530, 26537, 26534])).
% 4.87/5.07 tff(26547,plain,
% 4.87/5.07 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.07 inference(monotonicity,[status(thm)],[26546])).
% 4.87/5.07 tff(26548,plain,
% 4.87/5.07 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(z)))), elem!1)),
% 4.87/5.07 inference(symmetry,[status(thm)],[26547])).
% 4.87/5.07 tff(26549,plain,
% 4.87/5.07 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(s(s(s(z)))), elem!1))),
% 4.87/5.07 inference(monotonicity,[status(thm)],[26548])).
% 4.87/5.07 tff(26550,plain,
% 4.87/5.07 (~b(s(s(s(s(z)))), elem!1)),
% 4.87/5.07 inference(modus_ponens,[status(thm)],[17174, 26549])).
% 4.87/5.07 tff(26551,plain,
% 4.87/5.07 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[16181, 26546])).
% 4.87/5.07 tff(26552,plain,
% 4.87/5.07 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[3455, 178, 818, 506, 3449, 3447])).
% 4.87/5.07 tff(26553,plain,
% 4.87/5.07 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[3444, 3443, 26552])).
% 4.87/5.07 tff(26554,plain,
% 4.87/5.07 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[703, 26553])).
% 4.87/5.07 tff(26555,plain,
% 4.87/5.07 (~(s(s(elem!1)) = elem!1)),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[2510, 26554, 2169])).
% 4.87/5.07 tff(26556,plain,
% 4.87/5.07 (~(s(elem!1) = elem!1)),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[672, 26555])).
% 4.87/5.07 tff(26557,plain,
% 4.87/5.07 (~(elem!1 = s(elem!1))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[748, 26556])).
% 4.87/5.07 tff(26558,plain,
% 4.87/5.07 (~r(s(elem!1), s(s(z)))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[17418, 26556, 450, 506, 818, 106])).
% 4.87/5.07 tff(26559,plain,
% 4.87/5.07 (~b(elem!1, s(s(s(s(z)))))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[3434, 26554, 3428])).
% 4.87/5.07 tff(26560,plain,
% 4.87/5.07 (r(elem!1, s(s(s(s(z)))))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[483, 26559, 469])).
% 4.87/5.07 tff(26561,plain,
% 4.87/5.07 (~r(elem!1, s(elem!1))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[26316, 26560, 507, 202, 469, 12, 145, 106, 506, 167, 3437, 1369, 26558, 3132])).
% 4.87/5.07 tff(26562,plain,
% 4.87/5.07 (b(elem!1, s(elem!1))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[756, 26561, 26557])).
% 4.87/5.07 tff(26563,plain,
% 4.87/5.07 (~r(s(elem!1), s(s(s(s(z)))))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[16793, 26562, 506, 818, 26556, 3132, 145])).
% 4.87/5.07 tff(26564,plain,
% 4.87/5.07 (b(s(elem!1), s(s(s(s(z)))))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[1084, 26563, 1369])).
% 4.87/5.07 tff(26565,plain,
% 4.87/5.07 (~(s(elem!1) = s(s(z)))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[617, 3443, 506, 3447, 507, 3449, 202, 469, 12, 145, 106])).
% 4.87/5.07 tff(26566,plain,
% 4.87/5.07 (b(s(elem!1), s(s(z)))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[421, 26558, 26565])).
% 4.87/5.07 tff(26567,plain,
% 4.87/5.07 (~b(s(s(s(s(z)))), s(elem!1))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[26309, 178, 26566, 26564, 167, 202])).
% 4.87/5.07 tff(26568,plain,
% 4.87/5.07 (~(s(s(z)) = s(elem!1))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[1058, 26565])).
% 4.87/5.07 tff(26569,plain,
% 4.87/5.07 (~b(s(s(z)), s(elem!1))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[1079, 26564, 202, 167, 26566])).
% 4.87/5.07 tff(26570,plain,
% 4.87/5.07 (r(s(s(z)), s(elem!1))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[1067, 26569, 26568])).
% 4.87/5.07 tff(26571,plain,
% 4.87/5.07 (~r(z, s(elem!1))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[2341, 26570, 106])).
% 4.87/5.07 tff(26572,plain,
% 4.87/5.07 (b(z, s(elem!1))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[2351, 26571])).
% 4.87/5.07 tff(26573,plain,
% 4.87/5.07 (~b(s(elem!1), elem!1)),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[1396, 26572, 506, 26562, 818])).
% 4.87/5.07 tff(26574,plain,
% 4.87/5.07 (r(s(elem!1), elem!1)),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[677, 26573, 26556])).
% 4.87/5.07 tff(26575,plain,
% 4.87/5.07 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 4.87/5.07 inference(rewrite,[status(thm)],[])).
% 4.87/5.07 tff(26576,plain,
% 4.87/5.07 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 4.87/5.07 inference(quant_inst,[status(thm)],[])).
% 4.87/5.07 tff(26577,plain,
% 4.87/5.07 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 4.87/5.07 inference(modus_ponens,[status(thm)],[26576, 26575])).
% 4.87/5.07 tff(26578,plain,
% 4.87/5.07 (~r(s(s(s(s(z)))), s(elem!1))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[26577, 118, 26574, 3132])).
% 4.87/5.07 tff(26579,plain,
% 4.87/5.07 ($false),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[2173, 26578, 26567, 2169])).
% 4.87/5.07 tff(26580,plain,(b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~r(s(s(z)), z)) | (s(elem!1) = s(s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (z = elem!1) | (elem!1 = s(s(s(s(z))))) | (s(s(z)) = elem!1) | (~r(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.87/5.07 tff(26581,plain,
% 4.87/5.07 (~r(s(s(s(s(z)))), elem!1)),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[26580, 26551, 145, 3428, 25566, 106, 1042, 26535, 24607, 507, 26531, 12, 26536])).
% 4.87/5.07 tff(26582,plain,
% 4.87/5.07 (b(s(s(s(s(z)))), elem!1)),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[3142, 26581, 26530])).
% 4.87/5.07 tff(26583,plain,
% 4.87/5.07 ($false),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[26582, 26550])).
% 4.87/5.07 tff(26584,plain,((s(s(z)) = elem!1) | b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(z)))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | (~r(s(s(z)), z)) | (z = elem!1) | (~b(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))) | b(elem!1, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.87/5.07 tff(26585,plain,
% 4.87/5.07 (s(s(z)) = elem!1),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[26584, 461, 145, 3428, 106, 507, 168, 3261, 17174])).
% 4.87/5.07 tff(26586,plain,
% 4.87/5.07 (s(s(s(z))) = s(elem!1)),
% 4.87/5.07 inference(monotonicity,[status(thm)],[26585])).
% 4.87/5.07 tff(26587,plain,
% 4.87/5.07 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 4.87/5.07 inference(monotonicity,[status(thm)],[26586])).
% 4.87/5.07 tff(26588,plain,
% 4.87/5.07 (b(s(elem!1), s(s(s(s(z)))))),
% 4.87/5.07 inference(modus_ponens,[status(thm)],[24604, 26587])).
% 4.87/5.07 tff(26589,plain,
% 4.87/5.07 (elem!1 = s(s(z))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[3230, 26585])).
% 4.87/5.07 tff(26590,plain,
% 4.87/5.07 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[1353, 26589, 26530])).
% 4.87/5.07 tff(26591,plain,
% 4.87/5.07 (~(s(s(s(s(z)))) = s(elem!1))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[2168, 26590])).
% 4.87/5.07 tff(26592,plain,
% 4.87/5.07 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 4.87/5.07 inference(monotonicity,[status(thm)],[26586])).
% 4.87/5.07 tff(26593,plain,
% 4.87/5.07 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 4.87/5.07 inference(transitivity,[status(thm)],[26592, 3881])).
% 4.87/5.07 tff(26594,plain,
% 4.87/5.07 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 4.87/5.07 inference(monotonicity,[status(thm)],[26593])).
% 4.87/5.07 tff(26595,plain,
% 4.87/5.07 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.87/5.07 inference(modus_ponens,[status(thm)],[26438, 26594])).
% 4.87/5.07 tff(26596,plain,
% 4.87/5.07 (s(s(s(s(z)))) = s(s(elem!1))),
% 4.87/5.07 inference(monotonicity,[status(thm)],[26586])).
% 4.87/5.07 tff(26597,plain,
% 4.87/5.07 (s(s(elem!1)) = s(s(s(s(z))))),
% 4.87/5.07 inference(symmetry,[status(thm)],[26596])).
% 4.87/5.07 tff(26598,plain,
% 4.87/5.07 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 4.87/5.07 inference(monotonicity,[status(thm)],[26597])).
% 4.87/5.07 tff(26599,plain,
% 4.87/5.07 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), s(s(elem!1)))),
% 4.87/5.07 inference(symmetry,[status(thm)],[26598])).
% 4.87/5.07 tff(26600,plain,
% 4.87/5.07 (b(s(elem!1), s(s(elem!1)))),
% 4.87/5.07 inference(modus_ponens,[status(thm)],[26588, 26599])).
% 4.87/5.07 tff(26601,plain,
% 4.87/5.07 ((s(elem!1) = s(s(z))) <=> (s(elem!1) = elem!1)),
% 4.87/5.07 inference(monotonicity,[status(thm)],[26585])).
% 4.87/5.07 tff(26602,plain,
% 4.87/5.07 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(z)))),
% 4.87/5.07 inference(symmetry,[status(thm)],[26601])).
% 4.87/5.07 tff(26603,plain,
% 4.87/5.07 ((elem!1 = s(s(s(z)))) <=> (elem!1 = s(elem!1))),
% 4.87/5.07 inference(monotonicity,[status(thm)],[26586])).
% 4.87/5.07 tff(26604,plain,
% 4.87/5.07 ((elem!1 = s(s(s(z)))) <=> (s(elem!1) = elem!1)),
% 4.87/5.07 inference(transitivity,[status(thm)],[26603, 3190])).
% 4.87/5.07 tff(26605,plain,
% 4.87/5.07 ((elem!1 = s(s(s(z)))) <=> (s(elem!1) = s(s(z)))),
% 4.87/5.07 inference(transitivity,[status(thm)],[26604, 26602])).
% 4.87/5.07 tff(26606,plain,
% 4.87/5.07 ((~(elem!1 = s(s(s(z))))) <=> (~(s(elem!1) = s(s(z))))),
% 4.87/5.07 inference(monotonicity,[status(thm)],[26605])).
% 4.87/5.07 tff(26607,plain,
% 4.87/5.07 ((s(s(z)) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 4.87/5.07 inference(monotonicity,[status(thm)],[26585])).
% 4.87/5.07 tff(26608,plain,
% 4.87/5.07 ((~(s(s(z)) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 4.87/5.07 inference(monotonicity,[status(thm)],[26607])).
% 4.87/5.07 tff(26609,plain,
% 4.87/5.07 (~(elem!1 = s(s(s(z))))),
% 4.87/5.07 inference(modus_ponens,[status(thm)],[3205, 26608])).
% 4.87/5.07 tff(26610,plain,
% 4.87/5.07 (~(s(elem!1) = s(s(z)))),
% 4.87/5.07 inference(modus_ponens,[status(thm)],[26609, 26606])).
% 4.87/5.07 tff(26611,plain,
% 4.87/5.07 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[2840, 26610])).
% 4.87/5.07 tff(26612,plain,
% 4.87/5.07 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[3502, 26530])).
% 4.87/5.07 tff(26613,plain,
% 4.87/5.07 (~r(z, s(s(s(elem!1))))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[25455, 26611, 145, 3261])).
% 4.87/5.07 tff(26614,plain,
% 4.87/5.07 (b(z, s(s(s(elem!1))))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[2095, 26613])).
% 4.87/5.07 tff(26615,plain,
% 4.87/5.07 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[25326, 26614, 145, 26612])).
% 4.87/5.07 tff(26616,plain,
% 4.87/5.07 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[4173, 26615, 26611])).
% 4.87/5.07 tff(26617,plain,
% 4.87/5.07 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[10679, 26616, 26585])).
% 4.87/5.07 tff(26618,plain,
% 4.87/5.07 (~r(z, s(elem!1))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[25755, 26588, 24607, 25566, 26610, 3261, 106])).
% 4.87/5.07 tff(26619,plain,
% 4.87/5.07 (b(z, s(elem!1))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[2351, 26618])).
% 4.87/5.07 tff(26620,plain,
% 4.87/5.07 (~b(s(s(s(elem!1))), s(elem!1))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[26469, 178, 26619, 26614, 26617, 26600])).
% 4.87/5.07 tff(26621,plain,
% 4.87/5.07 (r(s(s(s(elem!1))), s(elem!1))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[373, 26620, 26595])).
% 4.87/5.07 tff(26622,plain,
% 4.87/5.07 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[7917, 26611])).
% 4.87/5.07 tff(26623,plain,
% 4.87/5.07 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 4.87/5.07 inference(monotonicity,[status(thm)],[26586])).
% 4.87/5.07 tff(26624,plain,
% 4.87/5.07 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 4.87/5.07 inference(symmetry,[status(thm)],[26623])).
% 4.87/5.07 tff(26625,plain,
% 4.87/5.07 ((~b(s(elem!1), s(s(s(elem!1))))) <=> (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 4.87/5.07 inference(monotonicity,[status(thm)],[26624])).
% 4.87/5.07 tff(26626,plain,
% 4.87/5.07 (~b(s(elem!1), s(s(s(elem!1))))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[11702, 178, 26619, 26614, 26617, 26600])).
% 4.87/5.07 tff(26627,plain,
% 4.87/5.07 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 4.87/5.07 inference(modus_ponens,[status(thm)],[26626, 26625])).
% 4.87/5.07 tff(26628,plain,
% 4.87/5.07 (r(s(s(s(z))), s(s(s(elem!1))))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[9126, 26627, 26438])).
% 4.87/5.07 tff(26629,plain,
% 4.87/5.07 (~r(s(s(z)), s(s(s(elem!1))))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[8364, 26628, 24607, 25566, 24604])).
% 4.87/5.07 tff(26630,plain,
% 4.87/5.07 (b(s(s(z)), s(s(s(elem!1))))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[4223, 26629])).
% 4.87/5.07 tff(26631,plain,
% 4.87/5.07 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[10667, 26630, 24607, 25566, 26616])).
% 4.87/5.07 tff(26632,plain,
% 4.87/5.07 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[10664, 26631, 26622])).
% 4.87/5.07 tff(26633,plain,
% 4.87/5.07 (~r(s(s(s(s(z)))), s(elem!1))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[22679, 26632, 26621])).
% 4.87/5.07 tff(26634,plain,
% 4.87/5.07 (b(s(s(s(s(z)))), s(elem!1))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[2173, 26633, 26591])).
% 4.87/5.07 tff(26635,plain,
% 4.87/5.07 (b(elem!1, s(s(s(s(z)))))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[17989, 26585, 24607])).
% 4.87/5.07 tff(26636,plain,
% 4.87/5.07 (r(elem!1, z)),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[1345, 26585, 106])).
% 4.87/5.07 tff(26637,plain,
% 4.87/5.07 ((elem!1 = s(s(s(z)))) <=> (elem!1 = s(elem!1))),
% 4.87/5.07 inference(transitivity,[status(thm)],[26604, 3880])).
% 4.87/5.07 tff(26638,plain,
% 4.87/5.07 ((~(elem!1 = s(s(s(z))))) <=> (~(elem!1 = s(elem!1)))),
% 4.87/5.07 inference(monotonicity,[status(thm)],[26637])).
% 4.87/5.07 tff(26639,plain,
% 4.87/5.07 (~(elem!1 = s(elem!1))),
% 4.87/5.07 inference(modus_ponens,[status(thm)],[26609, 26638])).
% 4.87/5.07 tff(26640,plain,
% 4.87/5.07 (~r(elem!1, s(elem!1))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[15563, 26634, 168, 26636, 26588])).
% 4.87/5.07 tff(26641,plain,
% 4.87/5.07 (b(elem!1, s(elem!1))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[756, 26640, 26639])).
% 4.87/5.07 tff(26642,plain,
% 4.87/5.07 (~b(s(elem!1), z)),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[8659, 26641, 26636, 26530, 26635, 26634, 26588])).
% 4.87/5.07 tff(26643,plain,
% 4.87/5.07 (r(s(elem!1), z)),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[774, 26642])).
% 4.87/5.07 tff(26644,plain,
% 4.87/5.07 ((~(elem!1 = s(s(s(z))))) <=> (~(s(elem!1) = elem!1))),
% 4.87/5.07 inference(monotonicity,[status(thm)],[26604])).
% 4.87/5.07 tff(26645,plain,
% 4.87/5.07 (~(s(elem!1) = elem!1)),
% 4.87/5.07 inference(modus_ponens,[status(thm)],[26609, 26644])).
% 4.87/5.07 tff(26646,plain,
% 4.87/5.07 (b(s(s(z)), s(elem!1))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[1337, 26640, 26585, 26645])).
% 4.87/5.07 tff(26647,plain,
% 4.87/5.07 (~b(s(elem!1), s(s(z)))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[1079, 26646, 25566, 24607, 26588])).
% 4.87/5.07 tff(26648,plain,
% 4.87/5.07 (r(s(elem!1), s(s(z)))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[421, 26647, 26610])).
% 4.87/5.07 tff(26649,plain,
% 4.87/5.07 ($false),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[8621, 26648, 26643, 3261])).
% 4.87/5.07 tff(26650,plain,(b(elem!1, s(s(z))) | (~r(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | (z = elem!1) | b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.87/5.07 tff(26651,plain,
% 4.87/5.07 (b(elem!1, s(s(z)))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[26650, 26522, 25334, 47, 25744, 24761, 507, 26529])).
% 4.87/5.07 tff(26652,plain,
% 4.87/5.07 (~(s(s(z)) = elem!1)),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[3223, 26651])).
% 4.87/5.07 tff(26653,plain,
% 4.87/5.07 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[222, 26529])).
% 4.87/5.07 tff(26654,plain,
% 4.87/5.07 (elem!1 = s(s(s(s(z))))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[814, 521, 24607, 106, 812, 24289, 145, 25566])).
% 4.87/5.07 tff(26655,plain,
% 4.87/5.07 (~(s(elem!1) = s(s(z)))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[11438, 26654])).
% 4.87/5.07 tff(26656,plain,
% 4.87/5.07 (s(elem!1) = s(s(s(s(s(z)))))),
% 4.87/5.07 inference(monotonicity,[status(thm)],[26654])).
% 4.87/5.07 tff(26657,plain,
% 4.87/5.07 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 4.87/5.07 inference(monotonicity,[status(thm)],[26656])).
% 4.87/5.07 tff(26658,plain,
% 4.87/5.07 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(elem!1), s(s(z)))),
% 4.87/5.07 inference(symmetry,[status(thm)],[26657])).
% 4.87/5.07 tff(26659,plain,
% 4.87/5.07 ((~b(s(s(s(s(s(z))))), s(s(z)))) <=> (~b(s(elem!1), s(s(z))))),
% 4.87/5.07 inference(monotonicity,[status(thm)],[26658])).
% 4.87/5.07 tff(26660,plain,
% 4.87/5.07 (s(s(s(s(s(z))))) = s(elem!1)),
% 4.87/5.07 inference(symmetry,[status(thm)],[26656])).
% 4.87/5.07 tff(26661,plain,
% 4.87/5.07 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 4.87/5.07 inference(monotonicity,[status(thm)],[26660])).
% 4.87/5.07 tff(26662,plain,
% 4.87/5.07 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 4.87/5.07 inference(symmetry,[status(thm)],[26661])).
% 4.87/5.07 tff(26663,plain,
% 4.87/5.07 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(s(s(z)))))),
% 4.87/5.07 inference(monotonicity,[status(thm)],[26654])).
% 4.87/5.07 tff(26664,plain,
% 4.87/5.07 ((s(elem!1) = elem!1) <=> (s(s(s(s(z)))) = s(elem!1))),
% 4.87/5.07 inference(transitivity,[status(thm)],[26663, 2163])).
% 4.87/5.07 tff(26665,plain,
% 4.87/5.07 ((~(s(elem!1) = elem!1)) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 4.87/5.07 inference(monotonicity,[status(thm)],[26664])).
% 4.87/5.07 tff(26666,plain,
% 4.87/5.07 (~(s(s(elem!1)) = elem!1)),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[338, 25567, 24289])).
% 4.87/5.07 tff(26667,plain,
% 4.87/5.07 (~(s(elem!1) = elem!1)),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[672, 26666])).
% 4.87/5.07 tff(26668,plain,
% 4.87/5.07 (~(s(s(s(s(z)))) = s(elem!1))),
% 4.87/5.07 inference(modus_ponens,[status(thm)],[26667, 26665])).
% 4.87/5.07 tff(26669,plain,
% 4.87/5.07 (r(elem!1, s(elem!1)) <=> r(s(s(s(s(z)))), s(elem!1))),
% 4.87/5.07 inference(monotonicity,[status(thm)],[26654])).
% 4.87/5.07 tff(26670,plain,
% 4.87/5.07 ((~r(elem!1, s(elem!1))) <=> (~r(s(s(s(s(z)))), s(elem!1)))),
% 4.87/5.07 inference(monotonicity,[status(thm)],[26669])).
% 4.87/5.07 tff(26671,plain,
% 4.87/5.07 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.07 inference(monotonicity,[status(thm)],[26654])).
% 4.87/5.07 tff(26672,plain,
% 4.87/5.07 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.87/5.07 inference(symmetry,[status(thm)],[26671])).
% 4.87/5.07 tff(26673,plain,
% 4.87/5.07 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.87/5.07 inference(modus_ponens,[status(thm)],[204, 26672])).
% 4.87/5.07 tff(26674,plain,
% 4.87/5.07 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.87/5.07 inference(monotonicity,[status(thm)],[26654])).
% 4.87/5.07 tff(26675,plain,
% 4.87/5.07 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 4.87/5.07 inference(symmetry,[status(thm)],[26674])).
% 4.87/5.07 tff(26676,plain,
% 4.87/5.07 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 4.87/5.07 inference(monotonicity,[status(thm)],[26656])).
% 4.87/5.07 tff(26677,plain,
% 4.87/5.07 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 4.87/5.07 inference(monotonicity,[status(thm)],[26676])).
% 4.87/5.07 tff(26678,plain,
% 4.87/5.07 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.07 inference(monotonicity,[status(thm)],[26677])).
% 4.87/5.07 tff(26679,plain,
% 4.87/5.07 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.87/5.07 inference(symmetry,[status(thm)],[26678])).
% 4.87/5.07 tff(26680,plain,
% 4.87/5.07 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(elem!1))))),
% 4.87/5.07 inference(transitivity,[status(thm)],[26679, 26675])).
% 4.87/5.07 tff(26681,plain,
% 4.87/5.07 (r(elem!1, s(s(s(elem!1))))),
% 4.87/5.07 inference(modus_ponens,[status(thm)],[204, 26680])).
% 4.87/5.07 tff(26682,plain,
% 4.87/5.07 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[348, 26666])).
% 4.87/5.07 tff(26683,plain,
% 4.87/5.07 (b(z, s(elem!1)) <=> b(z, s(s(s(s(s(z))))))),
% 4.87/5.07 inference(monotonicity,[status(thm)],[26656])).
% 4.87/5.07 tff(26684,plain,
% 4.87/5.07 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(s(s(z)))))),
% 4.87/5.07 inference(transitivity,[status(thm)],[26664, 2164])).
% 4.87/5.07 tff(26685,plain,
% 4.87/5.07 ((~(s(elem!1) = elem!1)) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 4.87/5.07 inference(monotonicity,[status(thm)],[26684])).
% 4.87/5.07 tff(26686,plain,
% 4.87/5.07 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.87/5.07 inference(modus_ponens,[status(thm)],[26667, 26685])).
% 4.87/5.07 tff(26687,plain,
% 4.87/5.07 (~r(z, s(elem!1))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[25758, 26686, 26655, 3261, 106, 145])).
% 4.87/5.07 tff(26688,plain,
% 4.87/5.07 (b(z, s(elem!1))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[2351, 26687])).
% 4.87/5.07 tff(26689,plain,
% 4.87/5.07 (b(z, s(s(s(s(s(z))))))),
% 4.87/5.07 inference(modus_ponens,[status(thm)],[26688, 26683])).
% 4.87/5.07 tff(26690,plain,
% 4.87/5.07 (~r(s(s(s(elem!1))), s(elem!1))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[1591, 1587, 3311])).
% 4.87/5.07 tff(26691,plain,
% 4.87/5.07 (b(s(s(s(elem!1))), s(elem!1))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[373, 26690, 356])).
% 4.87/5.07 tff(26692,plain,
% 4.87/5.07 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.87/5.07 inference(modus_ponens,[status(thm)],[26691, 17016])).
% 4.87/5.07 tff(26693,plain,
% 4.87/5.07 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 4.87/5.07 inference(modus_ponens,[status(thm)],[26692, 17015])).
% 4.87/5.07 tff(26694,plain,
% 4.87/5.07 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[2935, 1587, 1265])).
% 4.87/5.07 tff(26695,plain,
% 4.87/5.07 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[395, 26694, 16941])).
% 4.87/5.07 tff(26696,plain,
% 4.87/5.07 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.07 inference(modus_ponens,[status(thm)],[26695, 376])).
% 4.87/5.07 tff(26697,plain,
% 4.87/5.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 4.87/5.07 inference(rewrite,[status(thm)],[])).
% 4.87/5.07 tff(26698,plain,
% 4.87/5.07 (((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))) <=> ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 4.87/5.07 inference(rewrite,[status(thm)],[])).
% 4.87/5.07 tff(26699,plain,
% 4.87/5.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 4.87/5.07 inference(monotonicity,[status(thm)],[26698])).
% 4.87/5.07 tff(26700,plain,
% 4.87/5.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 4.87/5.07 inference(transitivity,[status(thm)],[26699, 26697])).
% 4.87/5.07 tff(26701,plain,
% 4.87/5.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 4.87/5.07 inference(quant_inst,[status(thm)],[])).
% 4.87/5.07 tff(26702,plain,
% 4.87/5.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 4.87/5.07 inference(modus_ponens,[status(thm)],[26701, 26700])).
% 4.87/5.07 tff(26703,plain,
% 4.87/5.07 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[26702, 178, 595, 13560, 146, 26696])).
% 4.87/5.07 tff(26704,plain,
% 4.87/5.07 ($false),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[26703, 26693])).
% 4.87/5.07 tff(26705,plain,((~r(elem!1, s(elem!1))) | (~(elem!1 = s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.87/5.07 tff(26706,plain,
% 4.87/5.07 (~r(elem!1, s(elem!1))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[26705, 26654, 24623, 26689, 24625, 26682, 26681, 26673])).
% 4.87/5.07 tff(26707,plain,
% 4.87/5.07 (~r(s(s(s(s(z)))), s(elem!1))),
% 4.87/5.07 inference(modus_ponens,[status(thm)],[26706, 26670])).
% 4.87/5.07 tff(26708,plain,
% 4.87/5.07 (b(s(s(s(s(z)))), s(elem!1))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[2173, 26707, 26668])).
% 4.87/5.07 tff(26709,plain,
% 4.87/5.07 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 4.87/5.07 inference(modus_ponens,[status(thm)],[26708, 26662])).
% 4.87/5.07 tff(26710,plain,
% 4.87/5.07 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 4.87/5.07 inference(monotonicity,[status(thm)],[26660])).
% 4.87/5.07 tff(26711,plain,
% 4.87/5.07 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 4.87/5.07 inference(symmetry,[status(thm)],[26710])).
% 4.87/5.07 tff(26712,plain,
% 4.87/5.07 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(s(z)))))),
% 4.87/5.07 inference(monotonicity,[status(thm)],[26654])).
% 4.87/5.07 tff(26713,plain,
% 4.87/5.07 (b(s(elem!1), elem!1) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 4.87/5.07 inference(transitivity,[status(thm)],[26712, 26711])).
% 4.87/5.07 tff(26714,plain,
% 4.87/5.07 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.87/5.07 inference(monotonicity,[status(thm)],[26654])).
% 4.87/5.07 tff(26715,plain,
% 4.87/5.07 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), elem!1)),
% 4.87/5.07 inference(symmetry,[status(thm)],[26714])).
% 4.87/5.07 tff(26716,plain,
% 4.87/5.07 (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)))))),
% 4.87/5.07 inference(monotonicity,[status(thm)],[26677])).
% 4.87/5.07 tff(26717,plain,
% 4.87/5.07 (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)))))),
% 4.87/5.07 inference(symmetry,[status(thm)],[26716])).
% 4.87/5.07 tff(26718,plain,
% 4.87/5.07 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), elem!1)),
% 4.87/5.07 inference(transitivity,[status(thm)],[26717, 26715])).
% 4.87/5.07 tff(26719,plain,
% 4.87/5.07 (r(s(s(s(elem!1))), elem!1)),
% 4.87/5.07 inference(modus_ponens,[status(thm)],[24592, 26718])).
% 4.87/5.07 tff(26720,plain,
% 4.87/5.07 (b(z, s(s(s(elem!1))))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[17717, 26654, 24623])).
% 4.87/5.07 tff(26721,plain,
% 4.87/5.07 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.87/5.07 inference(monotonicity,[status(thm)],[26654])).
% 4.87/5.07 tff(26722,plain,
% 4.87/5.07 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), elem!1)),
% 4.87/5.07 inference(symmetry,[status(thm)],[26721])).
% 4.87/5.07 tff(26723,plain,
% 4.87/5.07 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 4.87/5.07 inference(monotonicity,[status(thm)],[26677])).
% 4.87/5.07 tff(26724,plain,
% 4.87/5.07 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.87/5.07 inference(symmetry,[status(thm)],[26723])).
% 4.87/5.07 tff(26725,plain,
% 4.87/5.07 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), elem!1)),
% 4.87/5.07 inference(transitivity,[status(thm)],[26724, 26722])).
% 4.87/5.07 tff(26726,plain,
% 4.87/5.07 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) <=> (~b(s(s(s(elem!1))), elem!1))),
% 4.87/5.07 inference(monotonicity,[status(thm)],[26725])).
% 4.87/5.07 tff(26727,plain,
% 4.87/5.07 (~b(s(s(s(elem!1))), elem!1)),
% 4.87/5.07 inference(modus_ponens,[status(thm)],[3428, 26726])).
% 4.87/5.07 tff(26728,plain,
% 4.87/5.07 (b(s(elem!1), elem!1)),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[24899, 26727, 521, 26720, 26682, 26719, 26667])).
% 4.87/5.07 tff(26729,plain,
% 4.87/5.07 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 4.87/5.07 inference(modus_ponens,[status(thm)],[26728, 26713])).
% 4.87/5.07 tff(26730,plain,
% 4.87/5.07 ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[2702, 178, 24607, 25566, 26729])).
% 4.87/5.07 tff(26731,plain,
% 4.87/5.07 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[26730, 26709])).
% 4.87/5.07 tff(26732,plain,
% 4.87/5.07 (~b(s(elem!1), s(s(z)))),
% 4.87/5.07 inference(modus_ponens,[status(thm)],[26731, 26659])).
% 4.87/5.08 tff(26733,plain,
% 4.87/5.08 (r(s(elem!1), s(s(z)))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[421, 26732, 26655])).
% 4.87/5.08 tff(26734,plain,
% 4.87/5.08 (~r(s(elem!1), z)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[2258, 26733, 106])).
% 4.87/5.08 tff(26735,plain,
% 4.87/5.08 (b(s(elem!1), z)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[774, 26734])).
% 4.87/5.08 tff(26736,plain,
% 4.87/5.08 (~(s(s(z)) = s(elem!1))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[1058, 26655])).
% 4.87/5.08 tff(26737,plain,
% 4.87/5.08 (b(s(s(z)), elem!1)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[448, 11800, 24289])).
% 4.87/5.08 tff(26738,plain,
% 4.87/5.08 (b(elem!1, z)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[12557, 26654, 168])).
% 4.87/5.08 tff(26739,plain,
% 4.87/5.08 (r(s(elem!1), elem!1)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[2481, 26735, 106, 26738, 26737, 26736, 26667, 26706])).
% 4.87/5.08 tff(26740,plain,
% 4.87/5.08 (~r(s(s(s(elem!1))), s(elem!1))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[1576, 26739, 26719])).
% 4.87/5.08 tff(26741,plain,
% 4.87/5.08 (b(s(s(s(elem!1))), s(elem!1))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[373, 26740, 26682])).
% 4.87/5.08 tff(26742,plain,
% 4.87/5.08 (~(s(elem!1) = s(s(s(elem!1))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[5395, 26682])).
% 4.87/5.08 tff(26743,plain,
% 4.87/5.08 (~r(s(elem!1), s(s(s(elem!1))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[2110, 26739, 26719])).
% 4.87/5.08 tff(26744,plain,
% 4.87/5.08 (b(s(elem!1), s(s(s(elem!1))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[5432, 26743, 26742])).
% 4.87/5.08 tff(26745,plain,
% 4.87/5.08 ($false),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[6736, 26744, 26741, 26720, 26688, 26735])).
% 4.87/5.08 tff(26746,plain,((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(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(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.87/5.08 tff(26747,plain,
% 4.87/5.08 (~r(z, elem!1)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[26746, 26653, 25334, 47, 24761, 25744, 26522, 26651])).
% 4.87/5.08 tff(26748,plain,
% 4.87/5.08 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[26369, 26747, 26651, 507, 26652, 1])).
% 4.87/5.08 tff(26749,plain,
% 4.87/5.08 (b(elem!1, s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26748])).
% 4.87/5.08 tff(26750,plain,
% 4.87/5.08 (b(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 4.87/5.08 inference(symmetry,[status(thm)],[26749])).
% 4.87/5.08 tff(26751,plain,
% 4.87/5.08 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26748])).
% 4.87/5.08 tff(26752,plain,
% 4.87/5.08 (s(s(s(s(s(s(s(s(z)))))))) = s(elem!1)),
% 4.87/5.08 inference(symmetry,[status(thm)],[26751])).
% 4.87/5.08 tff(26753,plain,
% 4.87/5.08 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26752])).
% 4.87/5.08 tff(26754,plain,
% 4.87/5.08 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))) <=> b(elem!1, s(elem!1))),
% 4.87/5.08 inference(transitivity,[status(thm)],[26753, 26750])).
% 4.87/5.08 tff(26755,plain,
% 4.87/5.08 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) <=> (~b(elem!1, s(elem!1)))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26754])).
% 4.87/5.08 tff(26756,plain,
% 4.87/5.08 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26751])).
% 4.87/5.08 tff(26757,plain,
% 4.87/5.08 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[16181, 26748])).
% 4.87/5.08 tff(26758,plain,
% 4.87/5.08 (~(s(s(s(s(z)))) = s(elem!1))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[2168, 26757])).
% 4.87/5.08 tff(26759,plain,
% 4.87/5.08 (~(s(s(elem!1)) = elem!1)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[2510, 26758, 26748])).
% 4.87/5.08 tff(26760,plain,
% 4.87/5.08 (~(s(elem!1) = elem!1)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[672, 26759])).
% 4.87/5.08 tff(26761,plain,
% 4.87/5.08 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26748])).
% 4.87/5.08 tff(26762,plain,
% 4.87/5.08 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(z)))), elem!1)),
% 4.87/5.08 inference(symmetry,[status(thm)],[26761])).
% 4.87/5.08 tff(26763,plain,
% 4.87/5.08 (r(s(s(s(s(z)))), elem!1)),
% 4.87/5.08 inference(modus_ponens,[status(thm)],[26653, 26762])).
% 4.87/5.08 tff(26764,plain,
% 4.87/5.08 (b(z, elem!1)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[585, 26747, 507])).
% 4.87/5.08 tff(26765,plain,
% 4.87/5.08 (~(elem!1 = s(s(s(s(z)))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[1846, 26764, 1])).
% 4.87/5.08 tff(26766,plain,
% 4.87/5.08 (~r(elem!1, z)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[493, 26765, 25336, 25744, 26652, 47, 24641])).
% 4.87/5.08 tff(26767,plain,
% 4.87/5.08 (b(elem!1, z)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[498, 26766, 2809])).
% 4.87/5.08 tff(26768,plain,
% 4.87/5.08 (~(elem!1 = s(elem!1))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[748, 26760])).
% 4.87/5.08 tff(26769,plain,
% 4.87/5.08 (r(elem!1, s(s(s(s(z)))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[24769, 26748, 24761])).
% 4.87/5.08 tff(26770,plain,
% 4.87/5.08 (~(s(elem!1) = s(s(z)))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[2832, 26748])).
% 4.87/5.08 tff(26771,plain,
% 4.87/5.08 (~r(z, s(elem!1))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[25758, 26757, 26770, 25334, 25744, 47])).
% 4.87/5.08 tff(26772,plain,
% 4.87/5.08 (b(z, s(elem!1))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[2351, 26771])).
% 4.87/5.08 tff(26773,plain,
% 4.87/5.08 (~(elem!1 = s(elem!1))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[748, 25677])).
% 4.87/5.08 tff(26774,plain,
% 4.87/5.08 (~b(elem!1, s(elem!1))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[863, 853, 818, 506, 855])).
% 4.87/5.08 tff(26775,plain,
% 4.87/5.08 (r(elem!1, s(elem!1))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[756, 26774, 26773])).
% 4.87/5.08 tff(26776,plain,
% 4.87/5.08 (~r(s(s(s(s(z)))), s(elem!1))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[11326, 26775, 470])).
% 4.87/5.08 tff(26777,plain,
% 4.87/5.08 (b(s(s(s(s(z)))), s(elem!1))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[2173, 26776, 16183])).
% 4.87/5.08 tff(26778,plain,
% 4.87/5.08 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.87/5.08 inference(modus_ponens,[status(thm)],[26777, 15449])).
% 4.87/5.08 tff(26779,plain,
% 4.87/5.08 (~r(s(elem!1), s(s(s(s(z)))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[14364, 26775, 470])).
% 4.87/5.08 tff(26780,plain,
% 4.87/5.08 (b(s(elem!1), s(s(s(s(z)))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[1084, 26779, 16182])).
% 4.87/5.08 tff(26781,plain,
% 4.87/5.08 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 4.87/5.08 inference(modus_ponens,[status(thm)],[26780, 26257])).
% 4.87/5.08 tff(26782,plain,
% 4.87/5.08 (b(s(s(s(s(s(s(s(s(z)))))))), z)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[24205, 853, 679])).
% 4.87/5.08 tff(26783,plain,
% 4.87/5.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 4.87/5.08 inference(rewrite,[status(thm)],[])).
% 4.87/5.08 tff(26784,plain,
% 4.87/5.08 (((~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 4.87/5.08 inference(rewrite,[status(thm)],[])).
% 4.87/5.08 tff(26785,plain,
% 4.87/5.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26784])).
% 4.87/5.08 tff(26786,plain,
% 4.87/5.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 4.87/5.08 inference(transitivity,[status(thm)],[26785, 26783])).
% 4.87/5.08 tff(26787,plain,
% 4.87/5.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 4.87/5.08 inference(quant_inst,[status(thm)],[])).
% 4.87/5.08 tff(26788,plain,
% 4.87/5.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))),
% 4.87/5.08 inference(modus_ponens,[status(thm)],[26787, 26786])).
% 4.87/5.08 tff(26789,plain,
% 4.87/5.08 ($false),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[26788, 178, 168, 26782, 26781, 26778, 21928])).
% 4.87/5.08 tff(26790,plain,((~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(elem!1))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 4.87/5.08 tff(26791,plain,
% 4.87/5.08 (~b(s(elem!1), z)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[26790, 26522, 26772, 26748, 26769, 26764, 26767])).
% 4.87/5.08 tff(26792,plain,
% 4.87/5.08 (r(s(elem!1), z)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[774, 26791])).
% 4.87/5.08 tff(26793,plain,
% 4.87/5.08 (~r(s(elem!1), s(s(z)))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[8621, 26792, 25334])).
% 4.87/5.08 tff(26794,plain,
% 4.87/5.08 (~r(elem!1, s(elem!1))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[26317, 26793, 25336, 25744, 507, 47, 26652, 26765, 26767, 24641, 26763, 26757, 26769])).
% 4.87/5.08 tff(26795,plain,
% 4.87/5.08 (b(elem!1, s(elem!1))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[756, 26794, 26768])).
% 4.87/5.08 tff(26796,plain,
% 4.87/5.08 (~r(s(elem!1), s(s(s(s(z)))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[16793, 26795, 47, 26764, 26767, 26763, 26760])).
% 4.87/5.08 tff(26797,plain,
% 4.87/5.08 (b(s(elem!1), s(s(s(s(z)))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[1084, 26796, 26757])).
% 4.87/5.08 tff(26798,plain,
% 4.87/5.08 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 4.87/5.08 inference(modus_ponens,[status(thm)],[26797, 26756])).
% 4.87/5.08 tff(26799,plain,
% 4.87/5.08 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26751])).
% 4.87/5.08 tff(26800,plain,
% 4.87/5.08 (b(s(elem!1), s(s(z)))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[421, 26793, 26770])).
% 4.87/5.08 tff(26801,plain,
% 4.87/5.08 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 4.87/5.08 inference(modus_ponens,[status(thm)],[26800, 26799])).
% 4.87/5.08 tff(26802,plain,
% 4.87/5.08 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[25284, 26748, 26651])).
% 4.87/5.08 tff(26803,plain,
% 4.87/5.08 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[26296, 178, 24641, 26802, 26801, 26798])).
% 4.87/5.08 tff(26804,plain,
% 4.87/5.08 (~b(elem!1, s(elem!1))),
% 4.87/5.08 inference(modus_ponens,[status(thm)],[26803, 26755])).
% 4.87/5.08 tff(26805,plain,
% 4.87/5.08 ($false),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[26795, 26804])).
% 4.87/5.08 tff(26806,plain,((z = elem!1) | b(z, s(s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.87/5.08 tff(26807,plain,
% 4.87/5.08 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[26806, 25869, 1])).
% 4.87/5.08 tff(26808,plain,
% 4.87/5.08 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[249, 26807])).
% 4.87/5.08 tff(26809,plain,
% 4.87/5.08 (~r(z, elem!1)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[580, 515, 25336, 25744, 12, 47, 25873])).
% 4.87/5.08 tff(26810,plain,
% 4.87/5.08 (~b(elem!1, s(s(z)))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[26369, 26809, 12393, 25869, 12, 1])).
% 4.87/5.08 tff(26811,plain,
% 4.87/5.08 (r(elem!1, s(s(z)))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[467, 26810, 312])).
% 4.87/5.08 tff(26812,plain,
% 4.87/5.08 (~r(elem!1, z)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[493, 25873, 25336, 25744, 12, 47, 24641])).
% 4.87/5.08 tff(26813,plain,
% 4.87/5.08 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[2820, 26812, 24649, 24647, 25869, 26809])).
% 4.87/5.08 tff(26814,plain,
% 4.87/5.08 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[691, 26813, 12393])).
% 4.87/5.08 tff(26815,plain,
% 4.87/5.08 ($false),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[3113, 26814, 26811, 26808])).
% 4.87/5.08 tff(26816,plain,((~(s(elem!1) = s(s(z)))) | (s(s(z)) = elem!1) | b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.87/5.08 tff(26817,plain,
% 4.87/5.08 (~(s(elem!1) = s(s(z)))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[26816, 12, 1])).
% 4.87/5.08 tff(26818,plain,
% 4.87/5.08 (~r(z, s(s(s(elem!1))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[25455, 2857, 145, 3261])).
% 4.87/5.08 tff(26819,plain,
% 4.87/5.08 (b(z, s(s(s(elem!1))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[2095, 26818])).
% 4.87/5.08 tff(26820,plain,
% 4.87/5.08 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[25326, 26612, 145, 26819])).
% 4.87/5.08 tff(26821,plain,
% 4.87/5.08 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[4173, 26820, 2857])).
% 4.87/5.08 tff(26822,plain,
% 4.87/5.08 (~r(elem!1, z)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[8416, 14548, 3261])).
% 4.87/5.08 tff(26823,plain,
% 4.87/5.08 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[2820, 14551, 24623, 24625, 507, 26822])).
% 4.87/5.08 tff(26824,plain,
% 4.87/5.08 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[3113, 14548, 287])).
% 4.87/5.08 tff(26825,plain,
% 4.87/5.08 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[691, 26824, 26823])).
% 4.87/5.08 tff(26826,plain,
% 4.87/5.08 (~b(s(s(z)), elem!1)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[3121, 14548, 24623, 106, 507, 286, 14551, 26822])).
% 4.87/5.08 tff(26827,plain,
% 4.87/5.08 (r(s(s(z)), elem!1)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[448, 26826, 12])).
% 4.87/5.08 tff(26828,plain,
% 4.87/5.08 (~(elem!1 = s(s(s(elem!1))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[2859, 26825, 2857])).
% 4.87/5.08 tff(26829,plain,
% 4.87/5.08 (b(z, elem!1)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[585, 14551, 507])).
% 4.87/5.08 tff(26830,plain,
% 4.87/5.08 (b(elem!1, z)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[498, 26822, 2809])).
% 4.87/5.08 tff(26831,plain,
% 4.87/5.08 (~b(elem!1, s(s(s(elem!1))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[25478, 26830, 145, 287, 14548, 26829, 3261, 26823])).
% 4.87/5.08 tff(26832,plain,
% 4.87/5.08 (r(elem!1, s(s(s(elem!1))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[2054, 26831, 26828])).
% 4.87/5.08 tff(26833,plain,
% 4.87/5.08 (~r(s(s(z)), s(s(s(elem!1))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[7973, 26832, 26827])).
% 4.87/5.08 tff(26834,plain,
% 4.87/5.08 (b(s(s(z)), s(s(s(elem!1))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[4223, 26833])).
% 4.87/5.08 tff(26835,plain,
% 4.87/5.08 (r(s(s(s(s(s(s(s(s(s(s(z)))))))))), s(s(z)))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[10512, 26834, 25566, 24607, 26825, 26821])).
% 4.87/5.08 tff(26836,plain,
% 4.87/5.08 (r(elem!1, s(s(z))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26825])).
% 4.87/5.08 tff(26837,plain,
% 4.87/5.08 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.87/5.08 inference(modus_ponens,[status(thm)],[14548, 26836])).
% 4.87/5.08 tff(26838,plain,
% 4.87/5.08 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26825])).
% 4.87/5.08 tff(26839,plain,
% 4.87/5.08 (s(s(elem!1)) = s(s(s(s(s(s(s(s(s(z)))))))))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26838])).
% 4.87/5.08 tff(26840,plain,
% 4.87/5.08 (s(s(s(elem!1))) = s(s(s(s(s(s(s(s(s(s(z))))))))))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26839])).
% 4.87/5.08 tff(26841,plain,
% 4.87/5.08 (s(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(s(elem!1)))),
% 4.87/5.08 inference(symmetry,[status(thm)],[26840])).
% 4.87/5.08 tff(26842,plain,
% 4.87/5.08 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z))))))))))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26841])).
% 4.87/5.08 tff(26843,plain,
% 4.87/5.08 (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(s(s(s(s(s(s(s(z)))))))))))),
% 4.87/5.08 inference(symmetry,[status(thm)],[26842])).
% 4.87/5.08 tff(26844,plain,
% 4.87/5.08 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26825])).
% 4.87/5.08 tff(26845,plain,
% 4.87/5.08 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.87/5.08 inference(modus_ponens,[status(thm)],[26832, 26844])).
% 4.87/5.08 tff(26846,plain,
% 4.87/5.08 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(s(s(z)))))))))))),
% 4.87/5.08 inference(modus_ponens,[status(thm)],[26845, 26843])).
% 4.87/5.08 tff(26847,plain,
% 4.87/5.08 ($false),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[7939, 26846, 26837, 26835])).
% 4.87/5.08 tff(26848,plain,(b(elem!1, s(s(z))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (s(s(z)) = elem!1) | (z = elem!1) | (~r(s(s(z)), z)) | b(s(s(z)), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.87/5.08 tff(26849,plain,
% 4.87/5.08 (b(elem!1, s(s(z)))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[26848, 13192, 47, 25334, 12, 25869, 25744, 26807])).
% 4.87/5.08 tff(26850,plain,
% 4.87/5.08 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[26369, 2811, 26849, 25869, 12, 1])).
% 4.87/5.08 tff(26851,plain,
% 4.87/5.08 (b(z, elem!1)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[585, 2811, 25869])).
% 4.87/5.08 tff(26852,plain,
% 4.87/5.08 (r(elem!1, s(s(s(s(z)))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[24769, 26850, 24761])).
% 4.87/5.08 tff(26853,plain,
% 4.87/5.08 (~r(z, s(elem!1))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[25758, 1056, 1369, 25334, 25744, 47])).
% 4.87/5.08 tff(26854,plain,
% 4.87/5.08 (b(z, s(elem!1))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[2351, 26853])).
% 4.87/5.08 tff(26855,plain,
% 4.87/5.08 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[2820, 25445, 24649, 24647, 25869, 25444])).
% 4.87/5.08 tff(26856,plain,
% 4.87/5.08 (~(elem!1 = z)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[2808, 25869])).
% 4.87/5.08 tff(26857,plain,
% 4.87/5.08 (b(elem!1, z)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[498, 25445, 26856])).
% 4.87/5.08 tff(26858,plain,
% 4.87/5.08 (b(z, elem!1)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[585, 25444, 25869])).
% 4.87/5.08 tff(26859,plain,
% 4.87/5.08 ($false),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[25478, 26858, 26857, 47, 26808, 13066, 26001, 25334, 26855])).
% 4.87/5.08 tff(26860,plain,(b(elem!1, s(s(z))) | b(z, s(s(s(s(z))))) | b(s(s(s(s(z)))), z) | (elem!1 = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.87/5.08 tff(26861,plain,
% 4.87/5.08 (b(elem!1, s(s(z)))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[26860, 3170, 1, 312])).
% 4.87/5.08 tff(26862,plain,
% 4.87/5.08 (elem!1 = s(s(s(s(z))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[493, 437, 25336, 25744, 12, 47, 24641])).
% 4.87/5.08 tff(26863,plain,
% 4.87/5.08 (s(elem!1) = s(s(s(s(s(z)))))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26862])).
% 4.87/5.08 tff(26864,plain,
% 4.87/5.08 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26863])).
% 4.87/5.08 tff(26865,plain,
% 4.87/5.08 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26864])).
% 4.87/5.08 tff(26866,plain,
% 4.87/5.08 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26863, 26865])).
% 4.87/5.08 tff(26867,plain,
% 4.87/5.08 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 4.87/5.08 inference(symmetry,[status(thm)],[26866])).
% 4.87/5.08 tff(26868,plain,
% 4.87/5.08 ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(elem!1), s(s(s(elem!1)))))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26867])).
% 4.87/5.08 tff(26869,plain,
% 4.87/5.08 (b(z, s(elem!1)) <=> b(z, s(s(s(s(s(z))))))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26863])).
% 4.87/5.08 tff(26870,plain,
% 4.87/5.08 (b(z, s(s(s(s(s(z))))))),
% 4.87/5.08 inference(modus_ponens,[status(thm)],[26854, 26869])).
% 4.87/5.08 tff(26871,plain,
% 4.87/5.08 (r(s(elem!1), z) <=> r(s(s(s(s(s(z))))), z)),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26863])).
% 4.87/5.08 tff(26872,plain,
% 4.87/5.08 ((~r(s(elem!1), z)) <=> (~r(s(s(s(s(s(z))))), z))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26871])).
% 4.87/5.08 tff(26873,plain,
% 4.87/5.08 (s(s(s(s(z)))) = elem!1),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[24866, 24693, 24641, 26861, 25336, 24695])).
% 4.87/5.08 tff(26874,plain,
% 4.87/5.08 (~(s(s(elem!1)) = elem!1)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[338, 26873, 12])).
% 4.87/5.08 tff(26875,plain,
% 4.87/5.08 (~(s(elem!1) = elem!1)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[672, 26874])).
% 4.87/5.08 tff(26876,plain,
% 4.87/5.08 (~(elem!1 = s(elem!1))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[748, 26875])).
% 4.87/5.08 tff(26877,plain,
% 4.87/5.08 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26863])).
% 4.87/5.08 tff(26878,plain,
% 4.87/5.08 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[24769, 24693, 24761])).
% 4.87/5.08 tff(26879,plain,
% 4.87/5.08 (r(z, elem!1)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[26369, 26878, 26861, 25869, 12, 1])).
% 4.87/5.08 tff(26880,plain,
% 4.87/5.08 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[26211, 26875, 12, 3170, 1056, 26861, 26879, 1, 25869, 26878])).
% 4.87/5.08 tff(26881,plain,
% 4.87/5.08 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[3578, 26880])).
% 4.87/5.08 tff(26882,plain,
% 4.87/5.08 (b(s(elem!1), s(s(z)))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[435, 26881, 25744, 26808, 26862, 12])).
% 4.87/5.08 tff(26883,plain,
% 4.87/5.08 (b(s(s(s(s(s(z))))), s(s(z)))),
% 4.87/5.08 inference(modus_ponens,[status(thm)],[26882, 26877])).
% 4.87/5.08 tff(26884,plain,
% 4.87/5.08 (~r(s(elem!1), z)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[2715, 26883, 24641, 26862, 437, 26876, 1369, 25336, 3244])).
% 4.87/5.08 tff(26885,plain,
% 4.87/5.08 (~r(s(s(s(s(s(z))))), z)),
% 4.87/5.08 inference(modus_ponens,[status(thm)],[26884, 26872])).
% 4.87/5.08 tff(26886,plain,
% 4.87/5.08 (b(s(s(s(s(s(z))))), z)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[410, 41, 242, 26885])).
% 4.87/5.08 tff(26887,plain,
% 4.87/5.08 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[25171, 178, 24649, 26886, 26870, 24647])).
% 4.87/5.08 tff(26888,plain,
% 4.87/5.08 (~b(s(elem!1), s(s(s(elem!1))))),
% 4.87/5.08 inference(modus_ponens,[status(thm)],[26887, 26868])).
% 4.87/5.08 tff(26889,plain,
% 4.87/5.08 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[348, 26874])).
% 4.87/5.08 tff(26890,plain,
% 4.87/5.08 (~(s(elem!1) = s(s(s(elem!1))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[5395, 26889])).
% 4.87/5.08 tff(26891,plain,
% 4.87/5.08 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26865])).
% 4.87/5.08 tff(26892,plain,
% 4.87/5.08 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 4.87/5.08 inference(symmetry,[status(thm)],[26891])).
% 4.87/5.08 tff(26893,plain,
% 4.87/5.08 ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(s(z)), s(s(s(elem!1)))))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26892])).
% 4.87/5.08 tff(26894,plain,
% 4.87/5.08 (~b(s(s(z)), s(s(s(elem!1))))),
% 4.87/5.08 inference(modus_ponens,[status(thm)],[26807, 26893])).
% 4.87/5.08 tff(26895,plain,
% 4.87/5.08 (~r(s(s(z)), elem!1)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[443, 437, 25744])).
% 4.87/5.08 tff(26896,plain,
% 4.87/5.08 (b(s(s(z)), elem!1)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[448, 26895, 12])).
% 4.87/5.08 tff(26897,plain,
% 4.87/5.08 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26862])).
% 4.87/5.08 tff(26898,plain,
% 4.87/5.08 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), elem!1)),
% 4.87/5.08 inference(symmetry,[status(thm)],[26897])).
% 4.87/5.08 tff(26899,plain,
% 4.87/5.08 (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)))))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26865])).
% 4.87/5.08 tff(26900,plain,
% 4.87/5.08 (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)))))),
% 4.87/5.08 inference(symmetry,[status(thm)],[26899])).
% 4.87/5.08 tff(26901,plain,
% 4.87/5.08 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), elem!1)),
% 4.87/5.08 inference(transitivity,[status(thm)],[26900, 26898])).
% 4.87/5.08 tff(26902,plain,
% 4.87/5.08 (r(s(s(s(elem!1))), elem!1)),
% 4.87/5.08 inference(modus_ponens,[status(thm)],[24592, 26901])).
% 4.87/5.08 tff(26903,plain,
% 4.87/5.08 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26862])).
% 4.87/5.08 tff(26904,plain,
% 4.87/5.08 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), elem!1)),
% 4.87/5.08 inference(symmetry,[status(thm)],[26903])).
% 4.87/5.08 tff(26905,plain,
% 4.87/5.08 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26865])).
% 4.87/5.08 tff(26906,plain,
% 4.87/5.08 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.87/5.08 inference(symmetry,[status(thm)],[26905])).
% 4.87/5.08 tff(26907,plain,
% 4.87/5.08 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), elem!1)),
% 4.87/5.08 inference(transitivity,[status(thm)],[26906, 26904])).
% 4.87/5.08 tff(26908,plain,
% 4.87/5.08 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) <=> (~b(s(s(s(elem!1))), elem!1))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26907])).
% 4.87/5.08 tff(26909,plain,
% 4.87/5.08 (~b(s(s(s(elem!1))), elem!1)),
% 4.87/5.08 inference(modus_ponens,[status(thm)],[24761, 26908])).
% 4.87/5.08 tff(26910,plain,
% 4.87/5.08 (b(s(elem!1), elem!1)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[24899, 26909, 26879, 26003, 26889, 26902, 26875])).
% 4.87/5.08 tff(26911,plain,
% 4.87/5.08 (~b(s(s(z)), s(elem!1))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[13708, 26910, 26896, 26882, 26861])).
% 4.87/5.08 tff(26912,plain,
% 4.87/5.08 (r(s(s(z)), s(elem!1))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[1067, 26911, 2311])).
% 4.87/5.08 tff(26913,plain,
% 4.87/5.08 (b(s(elem!1), s(s(s(elem!1))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[6127, 26912, 26894, 26890])).
% 4.87/5.08 tff(26914,plain,
% 4.87/5.08 ($false),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[26913, 26888])).
% 4.87/5.08 tff(26915,plain,((~r(elem!1, z)) | (s(elem!1) = s(s(s(s(z))))) | (s(s(z)) = elem!1) | b(s(s(s(s(z)))), z) | (s(elem!1) = s(s(z))) | b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.87/5.08 tff(26916,plain,
% 4.87/5.08 (~r(elem!1, z)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[26915, 3170, 12, 1369, 1056, 1])).
% 4.87/5.08 tff(26917,plain,
% 4.87/5.08 (b(elem!1, z)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[498, 26916, 26856])).
% 4.87/5.08 tff(26918,plain,
% 4.87/5.08 (~(elem!1 = s(s(s(s(z)))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[3172, 26917, 3170])).
% 4.87/5.08 tff(26919,plain,
% 4.87/5.08 (~r(z, elem!1)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[814, 26918, 24641, 25744, 26861, 12, 47, 25336])).
% 4.87/5.08 tff(26920,plain,
% 4.87/5.08 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[26369, 26919, 26861, 25869, 12, 1])).
% 4.87/5.08 tff(26921,plain,
% 4.87/5.08 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26920])).
% 4.87/5.08 tff(26922,plain,
% 4.87/5.08 (s(s(s(s(s(s(s(s(z)))))))) = s(elem!1)),
% 4.87/5.08 inference(symmetry,[status(thm)],[26921])).
% 4.87/5.08 tff(26923,plain,
% 4.87/5.08 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26922])).
% 4.87/5.08 tff(26924,plain,
% 4.87/5.08 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.08 inference(symmetry,[status(thm)],[26923])).
% 4.87/5.08 tff(26925,plain,
% 4.87/5.08 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26920])).
% 4.87/5.08 tff(26926,plain,
% 4.87/5.08 (~(s(s(elem!1)) = elem!1)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[2510, 26920, 2169])).
% 4.87/5.08 tff(26927,plain,
% 4.87/5.08 (~(s(elem!1) = elem!1)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[672, 26926])).
% 4.87/5.08 tff(26928,plain,
% 4.87/5.08 (b(z, elem!1)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[585, 26919, 25869])).
% 4.87/5.08 tff(26929,plain,
% 4.87/5.08 (~(elem!1 = s(elem!1))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[748, 26927])).
% 4.87/5.08 tff(26930,plain,
% 4.87/5.08 (r(elem!1, s(s(s(s(z)))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[24769, 26920, 24761])).
% 4.87/5.08 tff(26931,plain,
% 4.87/5.08 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z))))))))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26922])).
% 4.87/5.08 tff(26932,plain,
% 4.87/5.08 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) <=> (~b(s(s(s(s(z)))), s(elem!1)))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26931])).
% 4.87/5.08 tff(26933,plain,
% 4.87/5.08 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26921])).
% 4.87/5.08 tff(26934,plain,
% 4.87/5.08 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26920])).
% 4.87/5.08 tff(26935,plain,
% 4.87/5.08 ((~(s(elem!1) = elem!1)) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26934])).
% 4.87/5.08 tff(26936,plain,
% 4.87/5.08 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.87/5.08 inference(modus_ponens,[status(thm)],[26927, 26935])).
% 4.87/5.08 tff(26937,plain,
% 4.87/5.08 ((s(elem!1) = elem!1) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 4.87/5.08 inference(transitivity,[status(thm)],[26934, 655])).
% 4.87/5.08 tff(26938,plain,
% 4.87/5.08 ((~(s(elem!1) = elem!1)) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26937])).
% 4.87/5.08 tff(26939,plain,
% 4.87/5.08 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 4.87/5.08 inference(modus_ponens,[status(thm)],[26927, 26938])).
% 4.87/5.08 tff(26940,plain,
% 4.87/5.08 (~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[24777, 26920, 23437])).
% 4.87/5.08 tff(26941,plain,
% 4.87/5.08 (r(elem!1, s(s(s(z)))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26920])).
% 4.87/5.08 tff(26942,plain,
% 4.87/5.08 ((elem!1 = s(s(s(z)))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(z))))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26920])).
% 4.87/5.08 tff(26943,plain,
% 4.87/5.08 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 4.87/5.08 inference(symmetry,[status(thm)],[26942])).
% 4.87/5.08 tff(26944,plain,
% 4.87/5.08 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26943])).
% 4.87/5.08 tff(26945,plain,
% 4.87/5.08 (~(elem!1 = s(s(s(z))))),
% 4.87/5.08 inference(modus_ponens,[status(thm)],[1104, 26944])).
% 4.87/5.08 tff(26946,plain,
% 4.87/5.08 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26920])).
% 4.87/5.08 tff(26947,plain,
% 4.87/5.08 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 4.87/5.08 inference(symmetry,[status(thm)],[26946])).
% 4.87/5.08 tff(26948,plain,
% 4.87/5.08 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) <=> (~b(elem!1, s(s(s(z)))))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26947])).
% 4.87/5.08 tff(26949,plain,
% 4.87/5.08 (~b(elem!1, s(s(s(z))))),
% 4.87/5.08 inference(modus_ponens,[status(thm)],[25870, 26948])).
% 4.87/5.08 tff(26950,plain,
% 4.87/5.08 (r(elem!1, s(s(s(z))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[17275, 26949, 26945])).
% 4.87/5.08 tff(26951,plain,
% 4.87/5.08 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.87/5.08 inference(modus_ponens,[status(thm)],[26950, 26941])).
% 4.87/5.08 tff(26952,plain,
% 4.87/5.08 (~b(s(elem!1), z)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[26281, 26951, 25439, 26940, 24655, 26920, 26939, 26929, 26917, 26928, 3244, 26854, 26936])).
% 4.87/5.08 tff(26953,plain,
% 4.87/5.08 (r(s(elem!1), z)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[774, 26952])).
% 4.87/5.08 tff(26954,plain,
% 4.87/5.08 (~r(s(elem!1), s(s(s(s(z)))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[916, 26953, 3244])).
% 4.87/5.08 tff(26955,plain,
% 4.87/5.08 (b(s(elem!1), s(s(s(s(z)))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[1084, 26954, 1369])).
% 4.87/5.08 tff(26956,plain,
% 4.87/5.08 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 4.87/5.08 inference(modus_ponens,[status(thm)],[26955, 26933])).
% 4.87/5.08 tff(26957,plain,
% 4.87/5.08 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[26921])).
% 4.87/5.08 tff(26958,plain,
% 4.87/5.08 (~r(s(elem!1), s(s(z)))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[8621, 26953, 25334])).
% 4.87/5.08 tff(26959,plain,
% 4.87/5.08 (b(s(elem!1), s(s(z)))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[421, 26958, 1056])).
% 4.87/5.08 tff(26960,plain,
% 4.87/5.08 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 4.87/5.08 inference(modus_ponens,[status(thm)],[26959, 26957])).
% 4.87/5.08 tff(26961,plain,
% 4.87/5.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 4.87/5.09 inference(rewrite,[status(thm)],[])).
% 4.87/5.09 tff(26962,plain,
% 4.87/5.09 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 4.87/5.09 inference(rewrite,[status(thm)],[])).
% 4.87/5.09 tff(26963,plain,
% 4.87/5.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))))),
% 4.87/5.09 inference(monotonicity,[status(thm)],[26962])).
% 4.87/5.09 tff(26964,plain,
% 4.87/5.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 4.87/5.09 inference(transitivity,[status(thm)],[26963, 26961])).
% 4.87/5.09 tff(26965,plain,
% 4.87/5.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))))),
% 4.87/5.09 inference(quant_inst,[status(thm)],[])).
% 4.87/5.09 tff(26966,plain,
% 4.87/5.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))),
% 4.87/5.09 inference(modus_ponens,[status(thm)],[26965, 26964])).
% 4.87/5.09 tff(26967,plain,
% 4.87/5.09 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.87/5.09 inference(unit_resolution,[status(thm)],[26966, 178, 24641, 25336, 26960, 26956])).
% 4.87/5.09 tff(26968,plain,
% 4.87/5.09 (~b(s(s(s(s(z)))), s(elem!1))),
% 4.87/5.09 inference(modus_ponens,[status(thm)],[26967, 26932])).
% 4.87/5.09 tff(26969,plain,
% 4.87/5.09 (r(s(s(s(s(z)))), s(elem!1))),
% 4.87/5.09 inference(unit_resolution,[status(thm)],[2173, 26968, 2169])).
% 4.87/5.09 tff(26970,plain,
% 4.87/5.09 (~r(elem!1, s(elem!1))),
% 4.87/5.09 inference(unit_resolution,[status(thm)],[11326, 26969, 26930])).
% 4.87/5.09 tff(26971,plain,
% 4.87/5.09 (b(elem!1, s(elem!1))),
% 4.87/5.09 inference(unit_resolution,[status(thm)],[756, 26970, 26929])).
% 4.87/5.09 tff(26972,plain,
% 4.87/5.09 (~b(s(elem!1), elem!1)),
% 4.87/5.09 inference(unit_resolution,[status(thm)],[1396, 26971, 26928, 26917, 26854])).
% 4.87/5.09 tff(26973,plain,
% 4.87/5.09 (r(s(elem!1), elem!1)),
% 4.87/5.09 inference(unit_resolution,[status(thm)],[677, 26972, 26927])).
% 4.87/5.09 tff(26974,plain,
% 4.87/5.09 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.09 inference(modus_ponens,[status(thm)],[26973, 26925])).
% 4.87/5.09 tff(26975,plain,
% 4.87/5.09 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.09 inference(modus_ponens,[status(thm)],[26974, 26924])).
% 4.87/5.09 tff(26976,plain,
% 4.87/5.09 ((s(s(z)) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(s(z)) = s(elem!1))),
% 4.87/5.09 inference(monotonicity,[status(thm)],[26922])).
% 4.87/5.09 tff(26977,plain,
% 4.87/5.09 ((s(s(z)) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(elem!1) = s(s(z)))),
% 4.87/5.09 inference(transitivity,[status(thm)],[26976, 1358])).
% 4.87/5.09 tff(26978,plain,
% 4.87/5.09 ((s(elem!1) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(s(s(s(z)))))))))),
% 4.87/5.09 inference(symmetry,[status(thm)],[26977])).
% 4.87/5.09 tff(26979,plain,
% 4.87/5.09 ((~(s(elem!1) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(s(s(s(s(z))))))))))),
% 4.87/5.09 inference(monotonicity,[status(thm)],[26978])).
% 4.87/5.09 tff(26980,plain,
% 4.87/5.09 (~(s(s(z)) = s(s(s(s(s(s(s(s(z)))))))))),
% 4.87/5.09 inference(modus_ponens,[status(thm)],[1056, 26979])).
% 4.87/5.09 tff(26981,plain,
% 4.87/5.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 4.87/5.09 inference(rewrite,[status(thm)],[])).
% 4.87/5.09 tff(26982,plain,
% 4.87/5.09 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(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(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 4.87/5.09 inference(rewrite,[status(thm)],[])).
% 4.87/5.09 tff(26983,plain,
% 4.87/5.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(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(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))))),
% 4.87/5.09 inference(monotonicity,[status(thm)],[26982])).
% 4.87/5.09 tff(26984,plain,
% 4.87/5.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(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(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 4.87/5.09 inference(transitivity,[status(thm)],[26983, 26981])).
% 4.87/5.09 tff(26985,plain,
% 4.87/5.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(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(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))),
% 4.87/5.09 inference(quant_inst,[status(thm)],[])).
% 4.87/5.09 tff(26986,plain,
% 4.87/5.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))),
% 4.87/5.09 inference(modus_ponens,[status(thm)],[26985, 26984])).
% 4.87/5.09 tff(26987,plain,
% 4.87/5.09 (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 4.87/5.09 inference(unit_resolution,[status(thm)],[26986, 178, 24641, 25336, 26960, 26956])).
% 4.87/5.09 tff(26988,plain,
% 4.87/5.09 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(s(s(s(z))))))))) | b(s(s(z)), s(s(s(s(s(s(s(s(z))))))))) | r(s(s(z)), s(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(s(z))))))))) | b(s(s(z)), s(s(s(s(s(s(s(s(z))))))))) | r(s(s(z)), s(s(s(s(s(s(s(s(z))))))))))),
% 4.87/5.09 inference(rewrite,[status(thm)],[])).
% 4.87/5.09 tff(26989,plain,
% 4.87/5.09 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(s(s(s(z))))))))) | b(s(s(z)), s(s(s(s(s(s(s(s(z))))))))) | r(s(s(z)), s(s(s(s(s(s(s(s(z))))))))))),
% 4.87/5.09 inference(quant_inst,[status(thm)],[])).
% 4.87/5.09 tff(26990,plain,
% 4.87/5.09 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(s(s(s(z))))))))) | b(s(s(z)), s(s(s(s(s(s(s(s(z))))))))) | r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 4.87/5.09 inference(modus_ponens,[status(thm)],[26989, 26988])).
% 4.87/5.09 tff(26991,plain,
% 4.87/5.09 ((s(s(z)) = s(s(s(s(s(s(s(s(z))))))))) | r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 4.87/5.09 inference(unit_resolution,[status(thm)],[26990, 41, 26987])).
% 4.87/5.09 tff(26992,plain,
% 4.87/5.09 (r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 4.87/5.09 inference(unit_resolution,[status(thm)],[26991, 26980])).
% 4.87/5.09 tff(26993,plain,
% 4.87/5.09 ((~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))),
% 4.87/5.09 inference(unit_resolution,[status(thm)],[21956, 118, 26808])).
% 4.87/5.09 tff(26994,plain,
% 4.87/5.09 (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.09 inference(unit_resolution,[status(thm)],[26993, 26992])).
% 4.87/5.09 tff(26995,plain,
% 4.87/5.09 ($false),
% 4.87/5.09 inference(unit_resolution,[status(thm)],[26994, 26975])).
% 4.87/5.09 tff(26996,plain,(b(s(s(s(s(z)))), z) | (s(elem!1) = s(s(z))) | (s(elem!1) = s(s(s(s(z))))) | (s(s(z)) = elem!1) | b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.87/5.09 tff(26997,plain,
% 4.87/5.09 (b(s(s(s(s(z)))), z)),
% 4.87/5.09 inference(unit_resolution,[status(thm)],[26996, 1056, 1369, 12, 1])).
% 4.87/5.09 tff(26998,plain,
% 4.87/5.09 (~(elem!1 = s(s(s(s(z)))))),
% 4.87/5.09 inference(unit_resolution,[status(thm)],[1846, 26851, 1])).
% 4.87/5.09 tff(26999,plain,
% 4.87/5.09 (~r(elem!1, z)),
% 4.87/5.09 inference(unit_resolution,[status(thm)],[493, 26998, 25336, 25744, 12, 47, 24641])).
% 4.87/5.09 tff(27000,plain,
% 4.87/5.09 (b(elem!1, z)),
% 4.87/5.09 inference(unit_resolution,[status(thm)],[498, 26999, 26856])).
% 4.87/5.09 tff(27001,plain,
% 4.87/5.09 (~b(s(elem!1), z)),
% 4.87/5.09 inference(unit_resolution,[status(thm)],[26790, 27000, 26997, 26854, 26852, 26851, 26850])).
% 4.87/5.09 tff(27002,plain,
% 4.87/5.09 (r(s(elem!1), z)),
% 4.87/5.09 inference(unit_resolution,[status(thm)],[774, 27001])).
% 4.87/5.09 tff(27003,plain,
% 4.87/5.09 (~r(s(elem!1), s(s(z)))),
% 4.87/5.09 inference(unit_resolution,[status(thm)],[8621, 27002, 25334])).
% 4.87/5.09 tff(27004,plain,
% 4.87/5.09 (~(s(s(elem!1)) = elem!1)),
% 4.87/5.09 inference(unit_resolution,[status(thm)],[2510, 26850, 2169])).
% 4.87/5.09 tff(27005,plain,
% 4.87/5.09 (~(s(elem!1) = elem!1)),
% 4.87/5.09 inference(unit_resolution,[status(thm)],[672, 27004])).
% 4.87/5.09 tff(27006,plain,
% 4.87/5.09 (~(elem!1 = s(elem!1))),
% 4.87/5.09 inference(unit_resolution,[status(thm)],[748, 27005])).
% 4.87/5.09 tff(27007,plain,
% 4.87/5.09 (b(elem!1, s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.87/5.09 inference(monotonicity,[status(thm)],[26850])).
% 4.87/5.09 tff(27008,plain,
% 4.87/5.09 (b(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 4.87/5.09 inference(symmetry,[status(thm)],[27007])).
% 4.87/5.09 tff(27009,plain,
% 4.87/5.09 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 4.87/5.09 inference(monotonicity,[status(thm)],[26850])).
% 4.87/5.09 tff(27010,plain,
% 4.87/5.09 (s(s(s(s(s(s(s(s(z)))))))) = s(elem!1)),
% 4.87/5.09 inference(symmetry,[status(thm)],[27009])).
% 4.87/5.09 tff(27011,plain,
% 4.87/5.09 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.87/5.09 inference(monotonicity,[status(thm)],[27010])).
% 4.87/5.09 tff(27012,plain,
% 4.87/5.09 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))) <=> b(elem!1, s(elem!1))),
% 4.87/5.09 inference(transitivity,[status(thm)],[27011, 27008])).
% 4.87/5.09 tff(27013,plain,
% 4.87/5.09 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) <=> (~b(elem!1, s(elem!1)))),
% 4.87/5.09 inference(monotonicity,[status(thm)],[27012])).
% 4.87/5.09 tff(27014,plain,
% 4.87/5.09 (b(z, s(s(s(s(s(s(s(s(z))))))))) <=> b(z, s(elem!1))),
% 4.87/5.09 inference(monotonicity,[status(thm)],[27010])).
% 4.87/5.09 tff(27015,plain,
% 4.87/5.09 (b(z, s(elem!1)) <=> b(z, s(s(s(s(s(s(s(s(z)))))))))),
% 4.87/5.09 inference(symmetry,[status(thm)],[27014])).
% 4.87/5.09 tff(27016,plain,
% 4.87/5.09 (b(z, s(s(s(s(s(s(s(s(z)))))))))),
% 4.87/5.09 inference(modus_ponens,[status(thm)],[26854, 27015])).
% 4.87/5.09 tff(27017,plain,
% 4.87/5.09 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 4.87/5.09 inference(monotonicity,[status(thm)],[27009])).
% 4.87/5.09 tff(27018,plain,
% 4.87/5.09 (b(s(elem!1), s(s(z)))),
% 4.87/5.09 inference(unit_resolution,[status(thm)],[421, 27003, 1056])).
% 4.87/5.09 tff(27019,plain,
% 4.87/5.09 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 4.87/5.09 inference(modus_ponens,[status(thm)],[27018, 27017])).
% 4.87/5.09 tff(27020,plain,
% 4.87/5.09 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.87/5.09 inference(unit_resolution,[status(thm)],[25284, 26850, 26849])).
% 4.87/5.09 tff(27021,plain,
% 4.87/5.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 4.87/5.09 inference(rewrite,[status(thm)],[])).
% 4.87/5.09 tff(27022,plain,
% 4.87/5.09 (((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(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(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, 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(s(z)))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 4.87/5.09 inference(rewrite,[status(thm)],[])).
% 4.87/5.09 tff(27023,plain,
% 4.87/5.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(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(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))))),
% 4.87/5.09 inference(monotonicity,[status(thm)],[27022])).
% 4.87/5.09 tff(27024,plain,
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% 4.87/5.09 inference(transitivity,[status(thm)],[27023, 27021])).
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% 4.87/5.09 tff(27032,plain,
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% 4.87/5.09 tff(27033,plain,
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% 4.87/5.09 tff(27035,plain,
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% 4.87/5.09 tff(27037,plain,
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% 4.87/5.09 inference(symmetry,[status(thm)],[27037])).
% 4.87/5.09 tff(27039,plain,
% 4.87/5.09 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.87/5.09 inference(monotonicity,[status(thm)],[27038])).
% 4.87/5.09 tff(27040,plain,
% 4.87/5.09 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 4.87/5.09 inference(monotonicity,[status(thm)],[27037])).
% 4.87/5.09 tff(27041,plain,
% 4.87/5.09 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 4.87/5.09 inference(monotonicity,[status(thm)],[27040])).
% 4.87/5.09 tff(27042,plain,
% 4.87/5.09 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))),
% 4.87/5.09 inference(monotonicity,[status(thm)],[27041, 27037])).
% 4.87/5.09 tff(27043,plain,
% 4.87/5.09 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 4.87/5.09 inference(transitivity,[status(thm)],[27042, 4625])).
% 4.87/5.09 tff(27044,plain,
% 4.87/5.09 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.87/5.09 inference(transitivity,[status(thm)],[27043, 27039])).
% 4.87/5.09 tff(27045,plain,
% 4.87/5.09 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 4.87/5.09 inference(monotonicity,[status(thm)],[27044])).
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% 4.87/5.09 inference(unit_resolution,[status(thm)],[529, 27035, 47])).
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% 4.87/5.09 (s(s(s(s(z)))) = elem!1),
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% 4.87/5.09 tff(27049,plain,
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% 4.87/5.09 (~(s(s(s(elem!1))) = s(elem!1))),
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% 4.87/5.09 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.87/5.09 inference(modus_ponens,[status(thm)],[27050, 27045])).
% 4.87/5.09 tff(27052,plain,
% 4.87/5.09 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.09 inference(monotonicity,[status(thm)],[27037])).
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% 4.87/5.09 (b(s(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))))))))),
% 4.87/5.09 inference(symmetry,[status(thm)],[27052])).
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% 4.87/5.09 ((~b(s(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)))))))))),
% 4.87/5.09 inference(monotonicity,[status(thm)],[27053])).
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% 4.87/5.09 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
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% 4.87/5.09 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 4.87/5.09 inference(symmetry,[status(thm)],[27055])).
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% 4.87/5.09 (b(s(elem!1), elem!1) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
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% 4.87/5.09 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.87/5.09 inference(monotonicity,[status(thm)],[27036])).
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% 4.87/5.09 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), elem!1)),
% 4.87/5.09 inference(symmetry,[status(thm)],[27060])).
% 4.87/5.09 tff(27062,plain,
% 4.87/5.09 (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)))))),
% 4.87/5.09 inference(monotonicity,[status(thm)],[27041])).
% 4.87/5.09 tff(27063,plain,
% 4.87/5.09 (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)))))),
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% 4.87/5.09 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), elem!1)),
% 4.87/5.09 inference(transitivity,[status(thm)],[27063, 27061])).
% 4.87/5.09 tff(27065,plain,
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% 4.87/5.09 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.87/5.09 inference(monotonicity,[status(thm)],[27036])).
% 4.87/5.09 tff(27067,plain,
% 4.87/5.09 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), elem!1)),
% 4.87/5.09 inference(symmetry,[status(thm)],[27066])).
% 4.87/5.09 tff(27068,plain,
% 4.87/5.09 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 4.87/5.09 inference(monotonicity,[status(thm)],[27041])).
% 4.87/5.09 tff(27069,plain,
% 4.87/5.09 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.87/5.10 inference(symmetry,[status(thm)],[27068])).
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% 4.87/5.10 inference(monotonicity,[status(thm)],[27070])).
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% 4.87/5.10 inference(modus_ponens,[status(thm)],[24761, 27071])).
% 4.87/5.10 tff(27073,plain,
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% 4.87/5.10 tff(27074,plain,
% 4.87/5.10 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
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% 4.87/5.10 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
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% 4.87/5.10 tff(27076,plain,
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% 4.87/5.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 4.87/5.10 inference(rewrite,[status(thm)],[])).
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% 4.87/5.10 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 4.87/5.10 inference(rewrite,[status(thm)],[])).
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% 4.87/5.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 4.87/5.10 inference(monotonicity,[status(thm)],[27078])).
% 4.87/5.10 tff(27080,plain,
% 4.87/5.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 4.87/5.10 inference(transitivity,[status(thm)],[27079, 27077])).
% 4.87/5.10 tff(27081,plain,
% 4.87/5.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 4.87/5.10 inference(quant_inst,[status(thm)],[])).
% 4.87/5.10 tff(27082,plain,
% 4.87/5.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 4.87/5.10 inference(modus_ponens,[status(thm)],[27081, 27080])).
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% 4.87/5.10 ($false),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[27082, 178, 168, 251, 1664, 146, 14440])).
% 4.87/5.10 tff(27084,plain,((~b(s(s(s(s(s(z))))), s(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(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 4.87/5.10 tff(27085,plain,
% 4.87/5.10 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[27084, 26997, 27076, 27074, 24647])).
% 4.87/5.10 tff(27086,plain,
% 4.87/5.10 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.10 inference(modus_ponens,[status(thm)],[27085, 27054])).
% 4.87/5.10 tff(27087,plain,
% 4.87/5.10 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[395, 27086, 27051])).
% 4.87/5.10 tff(27088,plain,
% 4.87/5.10 (~r(s(elem!1), s(s(z)))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[390, 27087, 26808])).
% 4.87/5.10 tff(27089,plain,
% 4.87/5.10 (b(s(elem!1), s(s(s(s(z)))))),
% 4.87/5.10 inference(modus_ponens,[status(thm)],[27073, 27057])).
% 4.87/5.10 tff(27090,plain,
% 4.87/5.10 (~(s(elem!1) = s(s(s(elem!1))))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[5395, 27050])).
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% 4.87/5.10 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.10 inference(monotonicity,[status(thm)],[27041])).
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% 4.87/5.10 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 4.87/5.10 inference(symmetry,[status(thm)],[27091])).
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% 4.87/5.10 ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(s(z)), s(s(s(elem!1)))))),
% 4.87/5.10 inference(monotonicity,[status(thm)],[27092])).
% 4.87/5.10 tff(27094,plain,
% 4.87/5.10 (~b(s(s(z)), s(s(s(elem!1))))),
% 4.87/5.10 inference(modus_ponens,[status(thm)],[26807, 27093])).
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% 4.87/5.10 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.10 inference(monotonicity,[status(thm)],[27037, 27041])).
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% 4.87/5.10 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 4.87/5.10 inference(symmetry,[status(thm)],[27095])).
% 4.87/5.10 tff(27097,plain,
% 4.87/5.10 ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(elem!1), s(s(s(elem!1)))))),
% 4.87/5.10 inference(monotonicity,[status(thm)],[27096])).
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% 4.87/5.10 inference(modus_ponens,[status(thm)],[27085, 27097])).
% 4.87/5.10 tff(27099,plain,
% 4.87/5.10 (~r(s(s(z)), s(elem!1))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[6127, 27098, 27094, 27090])).
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% 4.87/5.10 tff(27101,plain,
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% 4.87/5.10 tff(27102,plain,
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% 4.87/5.10 tff(27103,plain,((s(elem!1) = s(s(z))) | (s(s(z)) = elem!1) | (s(elem!1) = s(s(s(s(z))))) | b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.87/5.10 tff(27104,plain,
% 4.87/5.10 (s(elem!1) = s(s(s(s(z))))),
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% 4.87/5.10 tff(27117,plain,
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% 4.87/5.10 ((~(elem!1 = s(s(s(z))))) <=> (~(elem!1 = s(elem!1)))),
% 4.87/5.10 inference(monotonicity,[status(thm)],[27163])).
% 4.87/5.10 tff(27165,plain,
% 4.87/5.10 (~(elem!1 = s(elem!1))),
% 4.87/5.10 inference(modus_ponens,[status(thm)],[27131, 27164])).
% 4.87/5.10 tff(27166,plain,
% 4.87/5.10 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 4.87/5.10 inference(monotonicity,[status(thm)],[27153])).
% 4.87/5.10 tff(27167,plain,
% 4.87/5.10 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 4.87/5.10 inference(symmetry,[status(thm)],[27166])).
% 4.87/5.10 tff(27168,plain,
% 4.87/5.10 (elem!1 = s(s(z))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[3230, 27117])).
% 4.87/5.10 tff(27169,plain,
% 4.87/5.10 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[1353, 27135, 27168])).
% 4.87/5.10 tff(27170,plain,
% 4.87/5.10 (~(s(s(s(s(z)))) = s(elem!1))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[2168, 27169])).
% 4.87/5.10 tff(27171,plain,
% 4.87/5.10 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[7917, 27133])).
% 4.87/5.10 tff(27172,plain,
% 4.87/5.10 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 4.87/5.10 inference(monotonicity,[status(thm)],[27118])).
% 4.87/5.10 tff(27173,plain,
% 4.87/5.10 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 4.87/5.10 inference(symmetry,[status(thm)],[27172])).
% 4.87/5.10 tff(27174,plain,
% 4.87/5.10 ((~b(s(elem!1), s(s(s(elem!1))))) <=> (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 4.87/5.10 inference(monotonicity,[status(thm)],[27173])).
% 4.87/5.10 tff(27175,plain,
% 4.87/5.10 (~b(s(elem!1), s(s(s(elem!1))))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[11702, 178, 27160, 27138, 27141, 27158])).
% 4.87/5.10 tff(27176,plain,
% 4.87/5.10 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 4.87/5.10 inference(modus_ponens,[status(thm)],[27175, 27174])).
% 4.87/5.10 tff(27177,plain,
% 4.87/5.10 (r(s(s(s(z))), s(s(s(elem!1))))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[9126, 27176, 27151])).
% 4.87/5.10 tff(27178,plain,
% 4.87/5.10 (~r(s(s(z)), s(s(s(elem!1))))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[8364, 27177, 24641, 25336, 24655])).
% 4.87/5.10 tff(27179,plain,
% 4.87/5.10 (b(s(s(z)), s(s(s(elem!1))))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[4223, 27178])).
% 4.87/5.10 tff(27180,plain,
% 4.87/5.10 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[10667, 27179, 24641, 25336, 27140])).
% 4.87/5.10 tff(27181,plain,
% 4.87/5.10 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[10664, 27180, 27171])).
% 4.87/5.10 tff(27182,plain,
% 4.87/5.10 (~r(s(s(s(s(z)))), s(elem!1))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[22679, 27181, 27162])).
% 4.87/5.10 tff(27183,plain,
% 4.87/5.10 (b(s(s(s(s(z)))), s(elem!1))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[2173, 27182, 27170])).
% 4.87/5.10 tff(27184,plain,
% 4.87/5.10 (b(s(s(elem!1)), s(elem!1))),
% 4.87/5.10 inference(modus_ponens,[status(thm)],[27183, 27167])).
% 4.87/5.10 tff(27185,plain,
% 4.87/5.10 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 4.87/5.10 inference(monotonicity,[status(thm)],[27119])).
% 4.87/5.10 tff(27186,plain,
% 4.87/5.10 (b(s(s(s(s(z)))), elem!1)),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[8526, 27117, 25336])).
% 4.87/5.10 tff(27187,plain,
% 4.87/5.10 (b(s(s(elem!1)), elem!1)),
% 4.87/5.10 inference(modus_ponens,[status(thm)],[27186, 27185])).
% 4.87/5.10 tff(27188,plain,
% 4.87/5.10 (~b(elem!1, s(elem!1))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[9150, 178, 27187, 27184, 27158, 27122])).
% 4.87/5.10 tff(27189,plain,
% 4.87/5.10 (r(elem!1, s(elem!1))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[756, 27188, 27165])).
% 4.87/5.10 tff(27190,plain,
% 4.87/5.10 (~r(elem!1, s(s(s(elem!1))))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[1591, 27189, 27162])).
% 4.87/5.10 tff(27191,plain,
% 4.87/5.10 (b(elem!1, s(s(s(elem!1))))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[2054, 27190, 27146])).
% 4.87/5.10 tff(27192,plain,
% 4.87/5.10 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 4.87/5.10 inference(monotonicity,[status(thm)],[27143])).
% 4.87/5.10 tff(27193,plain,
% 4.87/5.10 (~(s(s(s(elem!1))) = elem!1)),
% 4.87/5.10 inference(modus_ponens,[status(thm)],[1683, 27192])).
% 4.87/5.10 tff(27194,plain,
% 4.87/5.10 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 4.87/5.10 inference(transitivity,[status(thm)],[27148, 7104])).
% 4.87/5.10 tff(27195,plain,
% 4.87/5.10 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 4.87/5.10 inference(monotonicity,[status(thm)],[27194])).
% 4.87/5.10 tff(27196,plain,
% 4.87/5.10 (~(s(elem!1) = s(s(s(elem!1))))),
% 4.87/5.10 inference(modus_ponens,[status(thm)],[27151, 27195])).
% 4.87/5.10 tff(27197,plain,
% 4.87/5.10 (r(s(elem!1), s(s(s(elem!1))))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[5432, 27175, 27196])).
% 4.87/5.10 tff(27198,plain,
% 4.87/5.10 ((~(elem!1 = s(s(s(z))))) <=> (~(s(elem!1) = elem!1))),
% 4.87/5.10 inference(monotonicity,[status(thm)],[27126])).
% 4.87/5.10 tff(27199,plain,
% 4.87/5.10 (~(s(elem!1) = elem!1)),
% 4.87/5.10 inference(modus_ponens,[status(thm)],[27131, 27198])).
% 4.87/5.10 tff(27200,plain,
% 4.87/5.10 ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[26506, 178, 27187, 27158, 27122])).
% 4.87/5.10 tff(27201,plain,
% 4.87/5.10 (~b(s(elem!1), elem!1)),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[27200, 27184])).
% 4.87/5.10 tff(27202,plain,
% 4.87/5.10 (r(s(elem!1), elem!1)),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[677, 27201, 27199])).
% 4.87/5.10 tff(27203,plain,
% 4.87/5.10 (~r(s(s(s(elem!1))), elem!1)),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[2110, 27202, 27197])).
% 4.87/5.10 tff(27204,plain,
% 4.87/5.10 (b(s(s(s(elem!1))), elem!1)),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[570, 27203, 27193])).
% 4.87/5.10 tff(27205,plain,
% 4.87/5.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 4.87/5.10 inference(rewrite,[status(thm)],[])).
% 4.87/5.10 tff(27206,plain,
% 4.87/5.10 (((~b(s(s(elem!1)), 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(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 4.87/5.10 inference(rewrite,[status(thm)],[])).
% 4.87/5.10 tff(27207,plain,
% 4.87/5.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 4.87/5.10 inference(monotonicity,[status(thm)],[27206])).
% 4.87/5.10 tff(27208,plain,
% 4.87/5.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 4.87/5.10 inference(transitivity,[status(thm)],[27207, 27205])).
% 4.87/5.10 tff(27209,plain,
% 4.87/5.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))),
% 4.87/5.10 inference(quant_inst,[status(thm)],[])).
% 4.87/5.10 tff(27210,plain,
% 4.87/5.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 4.87/5.10 inference(modus_ponens,[status(thm)],[27209, 27208])).
% 4.87/5.10 tff(27211,plain,
% 4.87/5.10 ($false),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[27210, 178, 27204, 27187, 27191, 27141, 27122])).
% 4.87/5.10 tff(27212,plain,(b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.87/5.10 tff(27213,plain,
% 4.87/5.10 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[24140, 86])).
% 4.87/5.10 tff(27214,plain,
% 4.87/5.10 (~r(elem!1, s(s(s(s(z)))))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[3785, 1042, 103])).
% 4.87/5.10 tff(27215,plain,
% 4.87/5.10 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[24769, 27214, 27213])).
% 4.87/5.10 tff(27216,plain,
% 4.87/5.10 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[24626, 103])).
% 4.87/5.10 tff(27217,plain,
% 4.87/5.10 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[3578, 27216])).
% 4.87/5.10 tff(27218,plain,
% 4.87/5.10 (~r(z, s(s(z)))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[14873, 12, 86, 5618])).
% 4.87/5.10 tff(27219,plain,
% 4.87/5.10 (b(z, s(s(z)))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[143, 27218])).
% 4.87/5.10 tff(27220,plain,
% 4.87/5.10 ($false),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[3468, 118, 1130, 224, 147])).
% 4.87/5.10 tff(27221,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.87/5.10 tff(27222,plain,
% 4.87/5.10 ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[27221, 24592])).
% 4.87/5.10 tff(27223,plain,
% 4.87/5.10 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[27222, 10794])).
% 4.87/5.10 tff(27224,plain,
% 4.87/5.10 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[249, 27223])).
% 4.87/5.10 tff(27225,plain,
% 4.87/5.10 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[17204, 27219, 5619, 27224, 27217])).
% 4.87/5.10 tff(27226,plain,
% 4.87/5.10 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[271, 27225])).
% 4.87/5.10 tff(27227,plain,
% 4.87/5.10 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[22538, 27226, 27212, 5619, 103, 27219, 10794])).
% 4.87/5.10 tff(27228,plain,
% 4.87/5.10 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[20667, 27227])).
% 4.87/5.10 tff(27229,plain,
% 4.87/5.10 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[4057, 27219, 5619, 27224, 27217])).
% 4.87/5.10 tff(27230,plain,
% 4.87/5.10 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[133, 27229])).
% 4.87/5.10 tff(27231,plain,
% 4.87/5.10 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 4.87/5.10 inference(rewrite,[status(thm)],[])).
% 4.87/5.10 tff(27232,plain,
% 4.87/5.10 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 4.87/5.10 inference(rewrite,[status(thm)],[])).
% 4.87/5.10 tff(27233,plain,
% 4.87/5.10 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 4.87/5.10 inference(monotonicity,[status(thm)],[27232])).
% 4.87/5.10 tff(27234,plain,
% 4.87/5.10 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 4.87/5.10 inference(transitivity,[status(thm)],[27233, 27231])).
% 4.87/5.10 tff(27235,plain,
% 4.87/5.10 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 4.87/5.10 inference(quant_inst,[status(thm)],[])).
% 4.87/5.10 tff(27236,plain,
% 4.87/5.10 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 4.87/5.10 inference(modus_ponens,[status(thm)],[27235, 27234])).
% 4.87/5.10 tff(27237,plain,
% 4.87/5.10 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[27236, 118, 1130, 4891])).
% 4.87/5.10 tff(27238,plain,
% 4.87/5.10 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[5031, 41, 27237, 10712])).
% 4.87/5.10 tff(27239,plain,
% 4.87/5.10 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[27221, 147, 1130])).
% 4.87/5.10 tff(27240,plain,
% 4.87/5.10 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[249, 27239])).
% 4.87/5.10 tff(27241,plain,
% 4.87/5.10 ($false),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[21437, 178, 27240, 5089, 5073, 1146, 27238])).
% 4.87/5.10 tff(27242,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(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(s(z))))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.87/5.10 tff(27243,plain,
% 4.87/5.10 ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[27242, 24592])).
% 4.87/5.10 tff(27244,plain,
% 4.87/5.10 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[27243, 10794, 27217])).
% 4.87/5.10 tff(27245,plain,
% 4.87/5.10 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[10755, 27244])).
% 4.87/5.10 tff(27246,plain,
% 4.87/5.10 ($false),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[5581, 118, 1130, 194, 108])).
% 4.87/5.10 tff(27247,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 4.87/5.10 tff(27248,plain,
% 4.87/5.10 ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[27247, 24592])).
% 4.87/5.10 tff(27249,plain,
% 4.87/5.10 (~r(s(s(s(s(z)))), z)),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[27248, 27230])).
% 4.87/5.10 tff(27250,plain,
% 4.87/5.10 (b(s(s(s(s(z)))), z)),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[191, 27249])).
% 4.87/5.10 tff(27251,plain,
% 4.87/5.10 ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[7229, 178, 3461, 27212, 1126])).
% 4.87/5.10 tff(27252,plain,
% 4.87/5.10 (~b(s(s(z)), s(s(s(z))))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[27251, 1127])).
% 4.87/5.10 tff(27253,plain,
% 4.87/5.10 (r(s(s(z)), s(s(s(z))))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[5088, 27252])).
% 4.87/5.10 tff(27254,plain,
% 4.87/5.10 ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[21371, 178, 27212, 168, 1126])).
% 4.87/5.10 tff(27255,plain,
% 4.87/5.10 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[27254, 1127])).
% 4.87/5.10 tff(27256,plain,
% 4.87/5.10 (r(s(s(s(s(z)))), s(s(s(z))))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[11185, 27255])).
% 4.87/5.10 tff(27257,plain,
% 4.87/5.10 ($false),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[24478, 27256, 27253, 147])).
% 4.87/5.10 tff(27258,plain,((~b(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 4.87/5.10 tff(27259,plain,
% 4.87/5.10 (~b(s(s(s(z))), z)),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[27258, 27250, 10794, 27245, 5619])).
% 4.87/5.10 tff(27260,plain,
% 4.87/5.10 (r(s(s(s(z))), z)),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[21073, 27259])).
% 4.87/5.10 tff(27261,plain,
% 4.87/5.10 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[20758, 27260, 27230])).
% 4.87/5.10 tff(27262,plain,
% 4.87/5.10 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.87/5.10 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 27261])).
% 4.87/5.10 tff(27263,plain,
% 4.87/5.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), 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))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), 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))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.87/5.10 inference(rewrite,[status(thm)],[])).
% 4.87/5.10 tff(27264,plain,
% 4.87/5.11 (((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(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(s(z)))))) <=> ((~b(s(s(z)), 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))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.87/5.11 inference(rewrite,[status(thm)],[])).
% 4.87/5.11 tff(27265,plain,
% 4.87/5.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(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(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), 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))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z))))))),
% 4.87/5.11 inference(monotonicity,[status(thm)],[27264])).
% 4.87/5.11 tff(27266,plain,
% 4.87/5.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(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(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), 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))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))))),
% 4.87/5.11 inference(transitivity,[status(thm)],[27265, 27263])).
% 4.87/5.11 tff(27267,plain,
% 4.87/5.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(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(s(z))))))),
% 4.87/5.11 inference(quant_inst,[status(thm)],[])).
% 4.87/5.11 tff(27268,plain,
% 4.87/5.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), 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))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z))))),
% 4.87/5.11 inference(modus_ponens,[status(thm)],[27267, 27266])).
% 4.87/5.11 tff(27269,plain,
% 4.87/5.11 (~b(s(s(s(z))), s(s(z)))),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[27268, 178, 27224, 27217, 27228, 27262])).
% 4.87/5.11 tff(27270,plain,
% 4.87/5.11 (r(s(s(s(z))), s(s(z)))),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[4966, 27269])).
% 4.87/5.11 tff(27271,plain,
% 4.87/5.11 (~r(s(s(s(z))), elem!1)),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[24660, 118, 1042, 27270])).
% 4.87/5.11 tff(27272,plain,
% 4.87/5.11 (~r(s(s(s(s(z)))), elem!1)),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[10883, 1042, 103])).
% 4.87/5.11 tff(27273,plain,
% 4.87/5.11 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[4057, 273, 3461, 27224, 1146])).
% 4.87/5.11 tff(27274,plain,
% 4.87/5.11 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[133, 27273])).
% 4.87/5.11 tff(27275,plain,
% 4.87/5.11 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[27243, 10794, 1146])).
% 4.87/5.11 tff(27276,plain,
% 4.87/5.11 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[10755, 27275])).
% 4.87/5.11 tff(27277,plain,
% 4.87/5.11 (~r(s(s(s(s(z)))), z)),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[27248, 27274])).
% 4.87/5.11 tff(27278,plain,
% 4.87/5.11 (b(s(s(s(s(z)))), z)),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[191, 27277])).
% 4.87/5.11 tff(27279,plain,
% 4.87/5.11 (~b(s(s(s(z))), z)),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[27258, 27278, 10794, 27276, 3461])).
% 4.87/5.11 tff(27280,plain,
% 4.87/5.11 (r(s(s(s(z))), z)),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[21073, 27279])).
% 4.87/5.11 tff(27281,plain,
% 4.87/5.11 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[20758, 27280, 27274])).
% 4.87/5.11 tff(27282,plain,
% 4.87/5.11 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 27281])).
% 4.87/5.11 tff(27283,plain,
% 4.87/5.11 (elem!1 = s(s(s(s(z))))),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[22090, 2811, 3461, 273, 507, 27212, 27278, 12])).
% 4.87/5.11 tff(27284,plain,
% 4.87/5.11 (s(elem!1) = s(s(s(s(s(z)))))),
% 4.87/5.11 inference(monotonicity,[status(thm)],[27283])).
% 4.87/5.11 tff(27285,plain,
% 4.87/5.11 (s(s(s(s(s(z))))) = s(elem!1)),
% 4.87/5.11 inference(symmetry,[status(thm)],[27284])).
% 4.87/5.11 tff(27286,plain,
% 4.87/5.11 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 4.87/5.11 inference(monotonicity,[status(thm)],[27285])).
% 4.87/5.11 tff(27287,plain,
% 4.87/5.11 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 4.87/5.11 inference(symmetry,[status(thm)],[27286])).
% 4.87/5.11 tff(27288,plain,
% 4.87/5.11 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(s(z)))))),
% 4.87/5.11 inference(monotonicity,[status(thm)],[27283])).
% 4.87/5.11 tff(27289,plain,
% 4.87/5.11 (b(s(elem!1), elem!1) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 4.87/5.11 inference(transitivity,[status(thm)],[27288, 27287])).
% 4.87/5.11 tff(27290,plain,
% 4.87/5.11 (s(s(s(s(z)))) = elem!1),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[325, 27283])).
% 4.87/5.11 tff(27291,plain,
% 4.87/5.11 (~(s(s(elem!1)) = elem!1)),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[338, 27290, 12])).
% 4.87/5.11 tff(27292,plain,
% 4.87/5.11 (~(s(elem!1) = elem!1)),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[672, 27291])).
% 4.87/5.11 tff(27293,plain,
% 4.87/5.11 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[348, 27291])).
% 4.87/5.11 tff(27294,plain,
% 4.87/5.11 (~b(s(s(z)), elem!1)),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[17684, 27283, 105])).
% 4.87/5.11 tff(27295,plain,
% 4.87/5.11 (r(s(s(z)), elem!1)),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[448, 27294, 12])).
% 4.87/5.11 tff(27296,plain,
% 4.87/5.11 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.87/5.11 inference(monotonicity,[status(thm)],[27283])).
% 4.87/5.11 tff(27297,plain,
% 4.87/5.11 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), elem!1)),
% 4.87/5.11 inference(symmetry,[status(thm)],[27296])).
% 4.87/5.11 tff(27298,plain,
% 4.87/5.11 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 4.87/5.11 inference(monotonicity,[status(thm)],[27284])).
% 4.87/5.11 tff(27299,plain,
% 4.87/5.11 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 4.87/5.11 inference(monotonicity,[status(thm)],[27298])).
% 4.87/5.11 tff(27300,plain,
% 4.87/5.11 (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)))))),
% 4.87/5.11 inference(monotonicity,[status(thm)],[27299])).
% 4.87/5.11 tff(27301,plain,
% 4.87/5.11 (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)))))),
% 4.87/5.11 inference(symmetry,[status(thm)],[27300])).
% 4.87/5.11 tff(27302,plain,
% 4.87/5.11 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), elem!1)),
% 4.87/5.11 inference(transitivity,[status(thm)],[27301, 27297])).
% 4.87/5.11 tff(27303,plain,
% 4.87/5.11 (r(s(s(s(elem!1))), elem!1)),
% 4.87/5.11 inference(modus_ponens,[status(thm)],[24592, 27302])).
% 4.87/5.11 tff(27304,plain,
% 4.87/5.11 (~r(s(elem!1), elem!1)),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[12991, 27303, 10794, 27295, 27293])).
% 4.87/5.11 tff(27305,plain,
% 4.87/5.11 (b(s(elem!1), elem!1)),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[677, 27304, 27292])).
% 4.87/5.11 tff(27306,plain,
% 4.87/5.11 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 4.87/5.11 inference(modus_ponens,[status(thm)],[27305, 27289])).
% 4.87/5.11 tff(27307,plain,
% 4.87/5.11 (r(z, s(elem!1)) <=> r(z, s(s(s(s(s(z))))))),
% 4.87/5.11 inference(monotonicity,[status(thm)],[27284])).
% 4.87/5.11 tff(27308,plain,
% 4.87/5.11 (b(elem!1, z)),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[12557, 27283, 27278])).
% 4.87/5.11 tff(27309,plain,
% 4.87/5.11 (~(elem!1 = s(elem!1))),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[748, 27292])).
% 4.87/5.11 tff(27310,plain,
% 4.87/5.11 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(s(s(s(z))))))), z)),
% 4.87/5.11 inference(monotonicity,[status(thm)],[27299])).
% 4.87/5.11 tff(27311,plain,
% 4.87/5.11 (r(s(s(s(s(s(s(s(z))))))), z) <=> r(s(s(s(elem!1))), z)),
% 4.87/5.11 inference(symmetry,[status(thm)],[27310])).
% 4.87/5.11 tff(27312,plain,
% 4.87/5.11 (r(s(s(s(elem!1))), z)),
% 4.87/5.11 inference(modus_ponens,[status(thm)],[27274, 27311])).
% 4.87/5.11 tff(27313,plain,
% 4.87/5.11 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.11 inference(monotonicity,[status(thm)],[27284])).
% 4.87/5.11 tff(27314,plain,
% 4.87/5.11 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.87/5.11 inference(monotonicity,[status(thm)],[27285])).
% 4.87/5.11 tff(27315,plain,
% 4.87/5.11 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))),
% 4.87/5.11 inference(monotonicity,[status(thm)],[27299, 27284])).
% 4.87/5.11 tff(27316,plain,
% 4.87/5.11 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 4.87/5.11 inference(transitivity,[status(thm)],[27315, 4625])).
% 4.87/5.11 tff(27317,plain,
% 4.87/5.11 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.87/5.11 inference(transitivity,[status(thm)],[27316, 27314])).
% 4.87/5.11 tff(27318,plain,
% 4.87/5.11 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 4.87/5.11 inference(monotonicity,[status(thm)],[27317])).
% 4.87/5.11 tff(27319,plain,
% 4.87/5.11 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.87/5.11 inference(modus_ponens,[status(thm)],[27293, 27318])).
% 4.87/5.11 tff(27320,plain,
% 4.87/5.11 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[17204, 273, 3461, 27224, 1146])).
% 4.87/5.11 tff(27321,plain,
% 4.87/5.11 (~b(z, s(s(s(elem!1))))),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[11477, 27283, 27320])).
% 4.87/5.11 tff(27322,plain,
% 4.87/5.11 (r(z, s(s(s(elem!1))))),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[2095, 27321])).
% 4.87/5.11 tff(27323,plain,
% 4.87/5.11 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.87/5.11 inference(monotonicity,[status(thm)],[27283])).
% 4.87/5.11 tff(27324,plain,
% 4.87/5.11 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 4.87/5.11 inference(symmetry,[status(thm)],[27323])).
% 4.87/5.11 tff(27325,plain,
% 4.87/5.11 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.11 inference(monotonicity,[status(thm)],[27299])).
% 4.87/5.11 tff(27326,plain,
% 4.87/5.11 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.87/5.11 inference(symmetry,[status(thm)],[27325])).
% 4.87/5.11 tff(27327,plain,
% 4.87/5.11 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(elem!1))))),
% 4.87/5.11 inference(transitivity,[status(thm)],[27326, 27324])).
% 4.87/5.11 tff(27328,plain,
% 4.87/5.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), 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))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), 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))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))))),
% 4.87/5.11 inference(rewrite,[status(thm)],[])).
% 4.87/5.11 tff(27329,plain,
% 4.87/5.11 (((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(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(z)), 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))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))))),
% 4.87/5.11 inference(rewrite,[status(thm)],[])).
% 4.87/5.11 tff(27330,plain,
% 4.87/5.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), 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))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 4.87/5.11 inference(monotonicity,[status(thm)],[27329])).
% 4.87/5.11 tff(27331,plain,
% 4.87/5.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), 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))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))))),
% 4.87/5.11 inference(transitivity,[status(thm)],[27330, 27328])).
% 4.87/5.11 tff(27332,plain,
% 4.87/5.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 4.87/5.11 inference(quant_inst,[status(thm)],[])).
% 4.87/5.11 tff(27333,plain,
% 4.87/5.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z)))))),
% 4.87/5.11 inference(modus_ponens,[status(thm)],[27332, 27331])).
% 4.87/5.11 tff(27334,plain,
% 4.87/5.11 ($false),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[27333, 178, 166, 5090, 1146, 3002, 21855])).
% 4.87/5.11 tff(27335,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(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(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.87/5.11 tff(27336,plain,
% 4.87/5.11 (~b(s(s(z)), s(s(s(z))))),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[27335, 27282, 27224, 1146, 3002])).
% 4.87/5.11 tff(27337,plain,
% 4.87/5.11 (r(s(s(z)), s(s(s(z))))),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[5088, 27336])).
% 4.87/5.11 tff(27338,plain,
% 4.87/5.11 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[24478, 27337, 10794])).
% 4.87/5.11 tff(27339,plain,
% 4.87/5.11 (b(s(s(s(s(z)))), s(s(s(z))))),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[11185, 27338])).
% 4.87/5.11 tff(27340,plain,
% 4.87/5.11 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[24749, 178, 27276, 27339, 3002, 27282])).
% 4.87/5.11 tff(27341,plain,
% 4.87/5.11 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[222, 27340])).
% 4.87/5.11 tff(27342,plain,
% 4.87/5.11 (r(elem!1, s(s(s(elem!1))))),
% 4.87/5.11 inference(modus_ponens,[status(thm)],[27341, 27327])).
% 4.87/5.11 tff(27343,plain,
% 4.87/5.11 (~r(s(elem!1), s(s(s(elem!1))))),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[5423, 27342, 3123, 27322, 27292, 27308])).
% 4.87/5.11 tff(27344,plain,
% 4.87/5.11 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
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% 4.87/5.11 tff(27345,plain,
% 4.87/5.11 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[395, 27344, 27319])).
% 4.87/5.11 tff(27346,plain,
% 4.87/5.11 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.11 inference(modus_ponens,[status(thm)],[27345, 27313])).
% 4.87/5.11 tff(27347,plain,
% 4.87/5.11 (b(s(elem!1), z) <=> b(s(s(s(s(s(z))))), z)),
% 4.87/5.11 inference(monotonicity,[status(thm)],[320])).
% 4.87/5.11 tff(27348,plain,
% 4.87/5.11 (b(s(s(s(s(s(z))))), z) <=> b(s(elem!1), z)),
% 4.87/5.11 inference(symmetry,[status(thm)],[27347])).
% 4.87/5.11 tff(27349,plain,
% 4.87/5.11 ((~b(s(s(s(s(s(z))))), z)) <=> (~b(s(elem!1), z))),
% 4.87/5.11 inference(monotonicity,[status(thm)],[27348])).
% 4.87/5.11 tff(27350,plain,
% 4.87/5.11 ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[13363, 178, 3461, 1687, 1664])).
% 4.87/5.11 tff(27351,plain,
% 4.87/5.11 (~b(s(s(s(s(s(z))))), z)),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[27350, 1665])).
% 4.87/5.11 tff(27352,plain,
% 4.87/5.11 (~b(s(elem!1), z)),
% 4.87/5.11 inference(modus_ponens,[status(thm)],[27351, 27349])).
% 4.87/5.11 tff(27353,plain,
% 4.87/5.11 (r(s(elem!1), z)),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[774, 27352])).
% 4.87/5.11 tff(27354,plain,
% 4.87/5.11 (~r(s(s(s(elem!1))), s(elem!1))),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[1557, 27353, 1552])).
% 4.87/5.11 tff(27355,plain,
% 4.87/5.11 (b(s(s(s(elem!1))), s(elem!1))),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[373, 27354, 356])).
% 4.87/5.11 tff(27356,plain,
% 4.87/5.11 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.87/5.11 inference(modus_ponens,[status(thm)],[27355, 17016])).
% 4.87/5.11 tff(27357,plain,
% 4.87/5.11 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 4.87/5.11 inference(modus_ponens,[status(thm)],[27356, 17015])).
% 4.87/5.11 tff(27358,plain,
% 4.87/5.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), 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(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), 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(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 4.87/5.11 inference(rewrite,[status(thm)],[])).
% 4.87/5.11 tff(27359,plain,
% 4.87/5.11 (((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), 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))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), 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(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 4.87/5.11 inference(rewrite,[status(thm)],[])).
% 4.87/5.11 tff(27360,plain,
% 4.87/5.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), 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(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 4.87/5.11 inference(monotonicity,[status(thm)],[27359])).
% 4.87/5.11 tff(27361,plain,
% 4.87/5.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), 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(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 4.87/5.11 inference(transitivity,[status(thm)],[27360, 27358])).
% 4.87/5.11 tff(27362,plain,
% 4.87/5.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 4.87/5.11 inference(quant_inst,[status(thm)],[])).
% 4.87/5.11 tff(27363,plain,
% 4.87/5.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 4.87/5.11 inference(modus_ponens,[status(thm)],[27362, 27361])).
% 4.87/5.11 tff(27364,plain,
% 4.87/5.11 ($false),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[27363, 178, 166, 1665, 1146, 14440, 27357])).
% 4.87/5.11 tff(27365,plain,((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), 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(z))))), s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(s(s(s(z)))))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.87/5.11 tff(27366,plain,
% 4.87/5.11 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[27365, 27346, 3461, 27224, 1146, 27283, 27293, 27312, 27212, 27306])).
% 4.87/5.11 tff(27367,plain,
% 4.87/5.11 (~b(s(s(z)), s(elem!1))),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[2330, 27366, 27283])).
% 4.87/5.11 tff(27368,plain,
% 4.87/5.11 (r(s(s(z)), s(elem!1))),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[1067, 27367, 1060])).
% 4.87/5.11 tff(27369,plain,
% 4.87/5.11 (~r(elem!1, s(elem!1))),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[12646, 27368, 10794, 27283])).
% 4.87/5.11 tff(27370,plain,
% 4.87/5.11 (b(elem!1, s(elem!1))),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[756, 27369, 27309])).
% 4.87/5.11 tff(27371,plain,
% 4.87/5.11 (~b(z, s(elem!1))),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[1396, 27370, 3123, 27308, 27305])).
% 4.87/5.11 tff(27372,plain,
% 4.87/5.11 (r(z, s(elem!1))),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[2351, 27371])).
% 4.87/5.11 tff(27373,plain,
% 4.87/5.11 (r(z, s(s(s(s(s(z))))))),
% 4.87/5.11 inference(modus_ponens,[status(thm)],[27372, 27307])).
% 4.87/5.11 tff(27374,plain,
% 4.87/5.11 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 4.87/5.11 inference(monotonicity,[status(thm)],[27299, 27284])).
% 4.87/5.11 tff(27375,plain,
% 4.87/5.11 (~r(s(s(s(elem!1))), s(elem!1))),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[5447, 27372, 27322])).
% 4.87/5.11 tff(27376,plain,
% 4.87/5.11 (b(s(s(s(elem!1))), s(elem!1))),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[373, 27375, 27293])).
% 4.87/5.11 tff(27377,plain,
% 4.87/5.11 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 4.87/5.11 inference(modus_ponens,[status(thm)],[27376, 27374])).
% 4.87/5.11 tff(27378,assumption,(b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))), introduced(assumption)).
% 4.87/5.11 tff(27379,plain,
% 4.87/5.11 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[27243, 147, 1146])).
% 4.87/5.11 tff(27380,plain,
% 4.87/5.11 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[10755, 27379])).
% 4.87/5.11 tff(27381,assumption,(~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))), introduced(assumption)).
% 4.87/5.11 tff(27382,assumption,(b(s(s(s(z))), s(s(s(s(s(z))))))), introduced(assumption)).
% 4.87/5.11 tff(27383,plain,
% 4.87/5.11 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.87/5.11 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 27381])).
% 4.87/5.11 tff(27384,plain,
% 4.87/5.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 4.87/5.12 inference(rewrite,[status(thm)],[])).
% 4.87/5.12 tff(27385,plain,
% 4.87/5.12 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 4.87/5.12 inference(rewrite,[status(thm)],[])).
% 4.87/5.12 tff(27386,plain,
% 4.87/5.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 4.87/5.12 inference(monotonicity,[status(thm)],[27385])).
% 4.87/5.12 tff(27387,plain,
% 4.87/5.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 4.87/5.12 inference(transitivity,[status(thm)],[27386, 27384])).
% 4.87/5.12 tff(27388,plain,
% 4.87/5.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 4.87/5.12 inference(quant_inst,[status(thm)],[])).
% 4.87/5.12 tff(27389,plain,
% 4.87/5.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 4.87/5.12 inference(modus_ponens,[status(thm)],[27388, 27387])).
% 4.87/5.12 tff(27390,plain,
% 4.87/5.12 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[27389, 178, 1664, 1126])).
% 4.87/5.12 tff(27391,plain,
% 4.87/5.12 ($false),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[27390, 27383, 27382, 27378])).
% 4.87/5.12 tff(27392,plain,((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.87/5.12 tff(27393,plain,
% 4.87/5.12 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[27392, 27381, 1664, 27380, 27378])).
% 4.87/5.12 tff(27394,plain,
% 4.87/5.12 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[9830, 41, 11413, 27393])).
% 4.87/5.12 tff(27395,plain,
% 4.87/5.12 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[27222, 147])).
% 4.87/5.12 tff(27396,plain,
% 4.87/5.12 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[249, 27395])).
% 4.87/5.12 tff(27397,plain,
% 4.87/5.12 (~b(s(s(z)), s(s(s(z))))),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[27335, 27383, 27396, 1146, 3002])).
% 4.87/5.12 tff(27398,plain,
% 4.87/5.12 (r(s(s(z)), s(s(s(z))))),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[5088, 27397])).
% 4.87/5.12 tff(27399,plain,
% 4.87/5.12 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[24478, 27398, 147])).
% 4.87/5.12 tff(27400,plain,
% 4.87/5.12 (b(s(s(s(s(z)))), s(s(s(z))))),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[11185, 27399])).
% 4.87/5.12 tff(27401,plain,
% 4.87/5.12 ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[21371, 178, 27212, 168, 27380])).
% 4.87/5.12 tff(27402,plain,
% 4.87/5.12 (~b(s(s(s(z))), z)),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[27401, 27400])).
% 4.87/5.12 tff(27403,plain,
% 4.87/5.12 (r(s(s(s(z))), z)),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[21073, 27402])).
% 4.87/5.12 tff(27404,plain,
% 4.87/5.12 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 4.87/5.12 inference(rewrite,[status(thm)],[])).
% 4.87/5.12 tff(27405,plain,
% 4.87/5.12 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 4.87/5.12 inference(rewrite,[status(thm)],[])).
% 4.87/5.12 tff(27406,plain,
% 4.87/5.12 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 4.87/5.12 inference(monotonicity,[status(thm)],[27405])).
% 4.87/5.12 tff(27407,plain,
% 4.87/5.12 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 4.87/5.12 inference(transitivity,[status(thm)],[27406, 27404])).
% 4.87/5.12 tff(27408,plain,
% 4.87/5.12 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)))),
% 4.87/5.12 inference(quant_inst,[status(thm)],[])).
% 4.87/5.12 tff(27409,plain,
% 4.87/5.12 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 4.87/5.12 inference(modus_ponens,[status(thm)],[27408, 27407])).
% 4.87/5.12 tff(27410,plain,
% 4.87/5.12 ($false),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[27409, 118, 23856, 27403, 27394])).
% 4.87/5.12 tff(27411,plain,(r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 4.87/5.12 tff(27412,plain,
% 4.87/5.12 ($false),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[27411, 27377, 27373, 27278, 10794, 1146, 3002, 27281, 27306])).
% 4.87/5.12 tff(27413,plain,(r(z, elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (s(s(z)) = s(elem!1)) | (~b(s(s(z)), z)) | (s(s(z)) = elem!1) | b(s(s(z)), s(s(s(s(z))))) | (~b(z, s(s(z)))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.87/5.12 tff(27414,plain,
% 4.87/5.12 (r(z, elem!1)),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[27413, 2311, 3002, 1146, 3461, 12, 105, 273, 507])).
% 4.87/5.12 tff(27415,plain,
% 4.87/5.12 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[11027, 27414, 27274])).
% 4.87/5.12 tff(27416,plain,
% 4.87/5.12 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[3444, 27415, 4245])).
% 4.87/5.12 tff(27417,plain,
% 4.87/5.12 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[271, 27320])).
% 4.87/5.12 tff(27418,plain,
% 4.87/5.12 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[3818, 27414, 27417])).
% 4.87/5.12 tff(27419,plain,
% 4.87/5.12 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[691, 27418, 701])).
% 4.87/5.12 tff(27420,plain,
% 4.87/5.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)))),
% 4.87/5.12 inference(rewrite,[status(thm)],[])).
% 4.87/5.12 tff(27421,plain,
% 4.87/5.12 (((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)))),
% 4.87/5.12 inference(rewrite,[status(thm)],[])).
% 4.87/5.12 tff(27422,plain,
% 4.87/5.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1))))),
% 4.87/5.12 inference(monotonicity,[status(thm)],[27421])).
% 4.87/5.12 tff(27423,plain,
% 4.87/5.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)))),
% 4.87/5.12 inference(transitivity,[status(thm)],[27422, 27420])).
% 4.87/5.12 tff(27424,plain,
% 4.87/5.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 4.87/5.12 inference(quant_inst,[status(thm)],[])).
% 4.87/5.12 tff(27425,plain,
% 4.87/5.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1))),
% 4.87/5.12 inference(modus_ponens,[status(thm)],[27424, 27423])).
% 4.87/5.12 tff(27426,plain,
% 4.87/5.12 (~b(s(s(s(z))), elem!1)),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[27425, 178, 27419, 27416, 3002, 27282])).
% 4.87/5.12 tff(27427,plain,
% 4.87/5.12 (s(s(s(z))) = elem!1),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[4981, 27426, 22979])).
% 4.87/5.12 tff(27428,plain,
% 4.87/5.12 (~(elem!1 = s(s(s(elem!1))))),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[4830, 27427, 2387])).
% 4.87/5.12 tff(27429,plain,
% 4.87/5.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.87/5.12 inference(rewrite,[status(thm)],[])).
% 4.87/5.12 tff(27430,plain,
% 4.87/5.12 (((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.87/5.12 inference(rewrite,[status(thm)],[])).
% 4.87/5.12 tff(27431,plain,
% 4.87/5.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 4.87/5.12 inference(monotonicity,[status(thm)],[27430])).
% 4.87/5.12 tff(27432,plain,
% 4.87/5.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.87/5.12 inference(transitivity,[status(thm)],[27431, 27429])).
% 4.87/5.12 tff(27433,plain,
% 4.87/5.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 4.87/5.12 inference(quant_inst,[status(thm)],[])).
% 4.87/5.12 tff(27434,plain,
% 4.87/5.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 4.87/5.12 inference(modus_ponens,[status(thm)],[27433, 27432])).
% 4.87/5.12 tff(27435,plain,
% 4.87/5.12 (~b(s(s(z)), elem!1)),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[27434, 178, 27224, 27419, 1146, 27416])).
% 4.87/5.12 tff(27436,plain,
% 4.87/5.12 (r(s(s(z)), elem!1)),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[448, 27435, 12])).
% 4.87/5.12 tff(27437,plain,
% 4.87/5.12 (~b(elem!1, z)),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[24730, 27427, 27279])).
% 4.87/5.12 tff(27438,plain,
% 4.87/5.12 (r(elem!1, z)),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[498, 27437, 2809])).
% 4.87/5.12 tff(27439,plain,
% 4.87/5.12 (~r(elem!1, s(s(s(elem!1))))),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[10847, 27438, 3461, 273, 27436, 27414])).
% 4.87/5.12 tff(27440,plain,
% 4.87/5.12 (b(elem!1, s(s(s(elem!1))))),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[2054, 27439, 27428])).
% 4.87/5.12 tff(27441,plain,
% 4.87/5.12 (s(s(s(s(z)))) = s(elem!1)),
% 4.87/5.12 inference(monotonicity,[status(thm)],[27427])).
% 4.87/5.12 tff(27442,plain,
% 4.87/5.12 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(elem!1))),
% 4.87/5.12 inference(monotonicity,[status(thm)],[27441])).
% 4.87/5.12 tff(27443,plain,
% 4.87/5.12 (~(elem!1 = s(s(s(s(z)))))),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[12557, 27437, 27278])).
% 4.87/5.12 tff(27444,plain,
% 4.87/5.12 (b(elem!1, s(s(s(s(z)))))),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[483, 27443, 5721])).
% 4.87/5.12 tff(27445,plain,
% 4.87/5.12 (b(elem!1, s(elem!1))),
% 4.87/5.12 inference(modus_ponens,[status(thm)],[27444, 27442])).
% 4.87/5.12 tff(27446,plain,
% 4.87/5.12 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 4.87/5.12 inference(monotonicity,[status(thm)],[27441])).
% 4.87/5.12 tff(27447,plain,
% 4.87/5.12 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 4.87/5.12 inference(monotonicity,[status(thm)],[27446])).
% 4.87/5.12 tff(27448,plain,
% 4.87/5.12 (s(s(s(s(s(s(s(z))))))) = s(s(s(s(elem!1))))),
% 4.87/5.12 inference(monotonicity,[status(thm)],[27447])).
% 4.87/5.12 tff(27449,plain,
% 4.87/5.12 ((s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 4.87/5.12 inference(monotonicity,[status(thm)],[27448])).
% 4.87/5.12 tff(27450,plain,
% 4.87/5.12 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(elem!1)))))),
% 4.87/5.12 inference(monotonicity,[status(thm)],[27449])).
% 4.87/5.12 tff(27451,plain,
% 4.87/5.12 (~(s(s(s(s(z)))) = elem!1)),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[504, 27443])).
% 4.87/5.12 tff(27452,plain,
% 4.87/5.12 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[3502, 27451])).
% 4.87/5.12 tff(27453,plain,
% 4.87/5.12 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 4.87/5.12 inference(modus_ponens,[status(thm)],[27452, 27450])).
% 4.87/5.12 tff(27454,plain,
% 4.87/5.12 (~(s(s(s(elem!1))) = elem!1)),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[2489, 27428])).
% 4.87/5.12 tff(27455,plain,
% 4.87/5.12 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[951, 27454])).
% 4.87/5.12 tff(27456,plain,
% 4.87/5.12 (s(elem!1) = s(s(s(s(z))))),
% 4.87/5.12 inference(symmetry,[status(thm)],[27441])).
% 4.87/5.12 tff(27457,plain,
% 4.87/5.12 (b(s(elem!1), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 4.87/5.12 inference(monotonicity,[status(thm)],[27456])).
% 4.87/5.12 tff(27458,plain,
% 4.87/5.12 (b(s(s(s(s(z)))), elem!1) <=> b(s(elem!1), elem!1)),
% 4.87/5.12 inference(symmetry,[status(thm)],[27457])).
% 4.87/5.12 tff(27459,plain,
% 4.87/5.12 (b(s(s(s(s(z)))), elem!1)),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[3142, 27451, 5369])).
% 4.87/5.12 tff(27460,plain,
% 4.87/5.12 (b(s(elem!1), elem!1)),
% 4.87/5.12 inference(modus_ponens,[status(thm)],[27459, 27458])).
% 4.87/5.12 tff(27461,plain,
% 4.87/5.12 (~r(s(s(s(elem!1))), elem!1)),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[6388, 27436, 27414, 3461, 273])).
% 4.87/5.12 tff(27462,plain,
% 4.87/5.12 (b(s(s(s(elem!1))), elem!1)),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[570, 27454, 27461])).
% 4.87/5.12 tff(27463,plain,
% 4.87/5.12 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 4.87/5.12 inference(monotonicity,[status(thm)],[27441])).
% 4.87/5.12 tff(27464,plain,
% 4.87/5.12 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 4.87/5.12 inference(transitivity,[status(thm)],[27463, 7104])).
% 4.87/5.12 tff(27465,plain,
% 4.87/5.12 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 4.87/5.12 inference(monotonicity,[status(thm)],[27464])).
% 4.87/5.12 tff(27466,plain,
% 4.87/5.12 (~(s(elem!1) = s(s(s(elem!1))))),
% 4.87/5.12 inference(modus_ponens,[status(thm)],[13192, 27465])).
% 4.87/5.12 tff(27467,plain,
% 4.87/5.12 (s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(z)))))))),
% 4.87/5.12 inference(symmetry,[status(thm)],[27448])).
% 4.87/5.12 tff(27468,plain,
% 4.87/5.12 (b(elem!1, s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.87/5.12 inference(monotonicity,[status(thm)],[27467])).
% 4.87/5.12 tff(27469,plain,
% 4.87/5.12 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 4.87/5.12 inference(symmetry,[status(thm)],[27468])).
% 4.87/5.12 tff(27470,plain,
% 4.87/5.12 (b(elem!1, s(s(s(s(elem!1)))))),
% 4.87/5.12 inference(modus_ponens,[status(thm)],[27419, 27469])).
% 4.87/5.12 tff(27471,plain,
% 4.87/5.12 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.87/5.12 inference(monotonicity,[status(thm)],[27467])).
% 4.87/5.12 tff(27472,plain,
% 4.87/5.12 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 4.87/5.12 inference(symmetry,[status(thm)],[27471])).
% 4.87/5.12 tff(27473,plain,
% 4.87/5.12 (b(s(s(s(s(elem!1)))), elem!1)),
% 4.87/5.12 inference(modus_ponens,[status(thm)],[27416, 27472])).
% 4.87/5.12 tff(27474,plain,
% 4.87/5.12 ($false),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[24015, 27473, 27470, 27466, 27462, 27460, 27455, 27453, 27445, 27440])).
% 4.87/5.12 tff(27475,plain,((s(elem!1) = s(s(z))) | r(s(s(s(s(z)))), elem!1) | r(elem!1, s(s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | r(s(s(s(z))), elem!1) | (s(s(z)) = elem!1) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | b(s(s(z)), s(s(s(s(z))))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.87/5.12 tff(27476,plain,
% 4.87/5.12 (s(elem!1) = s(s(z))),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[27475, 27272, 27214, 5619, 27219, 27271, 12, 27228, 27217, 27215, 105, 507])).
% 4.87/5.12 tff(27477,plain,
% 4.87/5.12 (~(elem!1 = s(s(s(s(elem!1)))))),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[1422, 27476])).
% 4.87/5.12 tff(27478,plain,
% 4.87/5.12 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[1509, 27477])).
% 4.87/5.12 tff(27479,plain,
% 4.87/5.12 (~(elem!1 = s(s(elem!1)))),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[1539, 27478])).
% 4.87/5.12 tff(27480,plain,
% 4.87/5.12 (~(s(s(elem!1)) = elem!1)),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[1546, 27479])).
% 4.87/5.12 tff(27481,plain,
% 4.87/5.12 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 4.87/5.12 inference(monotonicity,[status(thm)],[27476])).
% 4.87/5.12 tff(27482,plain,
% 4.87/5.12 (elem!1 = s(z)),
% 4.87/5.12 inference(transitivity,[status(thm)],[517, 27481, 70])).
% 4.87/5.12 tff(27483,plain,
% 4.87/5.12 (s(s(elem!1)) = s(s(s(z)))),
% 4.87/5.12 inference(monotonicity,[status(thm)],[27476])).
% 4.87/5.12 tff(27484,plain,
% 4.87/5.12 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(z))), s(z))),
% 4.87/5.12 inference(monotonicity,[status(thm)],[27483, 27482])).
% 4.87/5.12 tff(27485,plain,
% 4.87/5.12 (r(s(s(s(z))), s(z)) <=> r(s(s(elem!1)), elem!1)),
% 4.87/5.12 inference(symmetry,[status(thm)],[27484])).
% 4.87/5.12 tff(27486,plain,
% 4.87/5.12 ((~r(s(s(s(z))), s(z))) <=> (~r(s(s(elem!1)), elem!1))),
% 4.87/5.12 inference(monotonicity,[status(thm)],[27485])).
% 4.87/5.12 tff(27487,plain,
% 4.87/5.12 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(z))),
% 4.87/5.12 inference(monotonicity,[status(thm)],[27482])).
% 4.87/5.12 tff(27488,plain,
% 4.87/5.12 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(s(s(z))), s(z)))),
% 4.87/5.12 inference(monotonicity,[status(thm)],[27487])).
% 4.87/5.12 tff(27489,plain,
% 4.87/5.12 (~r(s(s(s(z))), s(z))),
% 4.87/5.12 inference(modus_ponens,[status(thm)],[27271, 27488])).
% 4.87/5.12 tff(27490,plain,
% 4.87/5.12 (~r(s(s(elem!1)), elem!1)),
% 4.87/5.12 inference(modus_ponens,[status(thm)],[27489, 27486])).
% 4.87/5.12 tff(27491,plain,
% 4.87/5.12 (b(s(s(elem!1)), elem!1)),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[3362, 27490, 27480])).
% 4.87/5.12 tff(27492,plain,
% 4.87/5.12 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 4.87/5.12 inference(monotonicity,[status(thm)],[27483])).
% 4.87/5.12 tff(27493,plain,
% 4.87/5.12 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 4.87/5.12 inference(monotonicity,[status(thm)],[27492, 27483])).
% 4.87/5.12 tff(27494,plain,
% 4.87/5.12 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 4.87/5.12 inference(symmetry,[status(thm)],[27493])).
% 4.87/5.12 tff(27495,plain,
% 4.87/5.12 (~b(s(s(z)), s(s(s(z))))),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[27335, 27262, 27224, 27217, 27228])).
% 4.87/5.12 tff(27496,plain,
% 4.87/5.12 (r(s(s(z)), s(s(s(z))))),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[5088, 27495])).
% 4.87/5.12 tff(27497,plain,
% 4.87/5.12 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[24478, 27496, 10794])).
% 4.87/5.12 tff(27498,plain,
% 4.87/5.12 (b(s(s(s(s(z)))), s(s(s(z))))),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[11185, 27497])).
% 4.87/5.12 tff(27499,plain,
% 4.87/5.12 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 4.87/5.12 inference(modus_ponens,[status(thm)],[27498, 27494])).
% 4.87/5.12 tff(27500,plain,
% 4.87/5.12 (b(elem!1, s(s(s(elem!1)))) <=> b(s(z), s(s(s(s(z)))))),
% 4.87/5.12 inference(monotonicity,[status(thm)],[27482, 27492])).
% 4.87/5.12 tff(27501,plain,
% 4.87/5.12 (b(s(z), s(s(s(s(z))))) <=> b(elem!1, s(s(s(elem!1))))),
% 4.87/5.12 inference(symmetry,[status(thm)],[27500])).
% 4.87/5.12 tff(27502,plain,
% 4.87/5.12 (b(elem!1, s(s(s(s(z))))) <=> b(s(z), s(s(s(s(z)))))),
% 4.87/5.12 inference(monotonicity,[status(thm)],[27482])).
% 4.87/5.12 tff(27503,plain,
% 4.87/5.12 (~(elem!1 = s(s(s(s(z)))))),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[11438, 27476])).
% 4.87/5.12 tff(27504,plain,
% 4.87/5.12 (b(elem!1, s(s(s(s(z)))))),
% 4.87/5.12 inference(unit_resolution,[status(thm)],[483, 27503, 27214])).
% 4.87/5.12 tff(27505,plain,
% 4.87/5.12 (b(s(z), s(s(s(s(z)))))),
% 4.87/5.12 inference(modus_ponens,[status(thm)],[27504, 27502])).
% 4.87/5.12 tff(27506,plain,
% 4.87/5.12 (b(elem!1, s(s(s(elem!1))))),
% 4.87/5.12 inference(modus_ponens,[status(thm)],[27505, 27501])).
% 4.87/5.12 tff(27507,plain,
% 4.87/5.12 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(s(z))))),
% 4.87/5.12 inference(monotonicity,[status(thm)],[27482, 27483])).
% 4.87/5.12 tff(27508,plain,
% 4.97/5.12 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 4.97/5.12 inference(symmetry,[status(thm)],[27507])).
% 4.97/5.12 tff(27509,plain,
% 4.97/5.12 ((~r(s(z), s(s(s(z))))) <=> (~r(elem!1, s(s(elem!1))))),
% 4.97/5.12 inference(monotonicity,[status(thm)],[27508])).
% 4.97/5.12 tff(27510,plain,
% 4.97/5.12 (r(elem!1, s(s(s(z)))) <=> r(s(z), s(s(s(z))))),
% 4.97/5.12 inference(monotonicity,[status(thm)],[27482])).
% 4.97/5.12 tff(27511,plain,
% 4.97/5.12 ((~r(elem!1, s(s(s(z))))) <=> (~r(s(z), s(s(s(z)))))),
% 4.97/5.12 inference(monotonicity,[status(thm)],[27510])).
% 4.97/5.12 tff(27512,plain,
% 4.97/5.12 (~r(elem!1, s(s(s(z))))),
% 4.97/5.12 inference(unit_resolution,[status(thm)],[24684, 118, 1042, 27270])).
% 4.97/5.12 tff(27513,plain,
% 4.97/5.12 (~r(s(z), s(s(s(z))))),
% 4.97/5.12 inference(modus_ponens,[status(thm)],[27512, 27511])).
% 4.97/5.12 tff(27514,plain,
% 4.97/5.12 (~r(elem!1, s(s(elem!1)))),
% 4.97/5.12 inference(modus_ponens,[status(thm)],[27513, 27509])).
% 4.97/5.12 tff(27515,plain,
% 4.97/5.12 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 4.97/5.12 inference(monotonicity,[status(thm)],[27483])).
% 4.97/5.12 tff(27516,plain,
% 4.97/5.12 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.97/5.12 inference(symmetry,[status(thm)],[27515])).
% 4.97/5.12 tff(27517,plain,
% 4.97/5.12 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 4.97/5.12 inference(symmetry,[status(thm)],[27492])).
% 4.97/5.12 tff(27518,plain,
% 4.97/5.12 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 4.97/5.12 inference(monotonicity,[status(thm)],[27517])).
% 4.97/5.12 tff(27519,plain,
% 4.97/5.12 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.97/5.12 inference(transitivity,[status(thm)],[27518, 27516])).
% 4.97/5.12 tff(27520,plain,
% 4.97/5.12 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.97/5.12 inference(modus_ponens,[status(thm)],[27245, 27519])).
% 4.97/5.12 tff(27521,plain,
% 4.97/5.12 ($false),
% 4.97/5.12 inference(unit_resolution,[status(thm)],[5479, 27520, 27514, 27506, 27499, 27479, 27491])).
% 4.97/5.12 tff(27522,plain,((s(s(z)) = elem!1) | b(s(s(z)), s(s(s(s(z))))) | (z = elem!1) | b(elem!1, s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 4.97/5.12 tff(27523,plain,
% 4.97/5.12 (b(elem!1, s(s(z)))),
% 4.97/5.12 inference(unit_resolution,[status(thm)],[27522, 12, 507, 105, 86, 5618])).
% 4.97/5.13 tff(27524,plain,
% 4.97/5.13 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[17204, 273, 3461, 27224, 24628])).
% 4.97/5.13 tff(27525,plain,
% 4.97/5.13 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[271, 27524])).
% 4.97/5.13 tff(27526,plain,
% 4.97/5.13 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[27243, 10794, 24628])).
% 4.97/5.13 tff(27527,plain,
% 4.97/5.13 (b(s(s(s(z))), s(s(s(s(z)))))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[10755, 27526])).
% 4.97/5.13 tff(27528,plain,
% 4.97/5.13 (~r(z, s(s(z)))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[9569, 194, 193])).
% 4.97/5.13 tff(27529,plain,
% 4.97/5.13 (b(z, s(s(z)))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[143, 27528])).
% 4.97/5.13 tff(27530,plain,
% 4.97/5.13 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[27248, 194])).
% 4.97/5.13 tff(27531,plain,
% 4.97/5.13 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[133, 27530])).
% 4.97/5.13 tff(27532,plain,
% 4.97/5.13 ($false),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[4057, 27531, 27529, 3461, 166, 24628])).
% 4.97/5.13 tff(27533,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 4.97/5.13 tff(27534,plain,
% 4.97/5.13 (~r(s(s(s(s(z)))), z)),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[27533, 27224, 3461, 193])).
% 4.97/5.13 tff(27535,plain,
% 4.97/5.13 (b(s(s(s(s(z)))), z)),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[191, 27534])).
% 4.97/5.13 tff(27536,plain,
% 4.97/5.13 (~b(s(s(s(z))), z)),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[27258, 27535, 10794, 27527, 3461])).
% 4.97/5.13 tff(27537,plain,
% 4.97/5.13 (r(s(s(s(z))), z)),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[21073, 27536])).
% 4.97/5.13 tff(27538,plain,
% 4.97/5.13 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[21452, 273, 27224, 27537, 24628])).
% 4.97/5.13 tff(27539,plain,
% 4.97/5.13 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[20667, 27538])).
% 4.97/5.13 tff(27540,plain,
% 4.97/5.13 (r(z, elem!1)),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[27413, 2311, 12, 24628, 3461, 27539, 105, 273, 507])).
% 4.97/5.13 tff(27541,plain,
% 4.97/5.13 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[3818, 27540, 27525])).
% 4.97/5.13 tff(27542,plain,
% 4.97/5.13 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[4057, 273, 3461, 27224, 24628])).
% 4.97/5.13 tff(27543,plain,
% 4.97/5.13 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[133, 27542])).
% 4.97/5.13 tff(27544,plain,
% 4.97/5.13 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[11027, 27540, 27543])).
% 4.97/5.13 tff(27545,plain,
% 4.97/5.13 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[14184, 27544, 27224, 812, 24628, 27541])).
% 4.97/5.13 tff(27546,plain,
% 4.97/5.13 (~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z))))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[24777, 27545, 23437])).
% 4.97/5.13 tff(27547,plain,
% 4.97/5.13 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 4.97/5.13 inference(monotonicity,[status(thm)],[27545])).
% 4.97/5.13 tff(27548,plain,
% 4.97/5.13 (s(s(s(s(s(s(s(s(z)))))))) = s(elem!1)),
% 4.97/5.13 inference(symmetry,[status(thm)],[27547])).
% 4.97/5.13 tff(27549,plain,
% 4.97/5.13 (b(s(s(s(s(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))))))))),
% 4.97/5.13 inference(monotonicity,[status(thm)],[27548])).
% 4.97/5.13 tff(27550,plain,
% 4.97/5.13 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.13 inference(symmetry,[status(thm)],[27549])).
% 4.97/5.13 tff(27551,plain,
% 4.97/5.13 (~(elem!1 = s(s(s(elem!1))))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[2859, 27545, 13192])).
% 4.97/5.13 tff(27552,plain,
% 4.97/5.13 (~(s(s(s(elem!1))) = elem!1)),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[2489, 27551])).
% 4.97/5.13 tff(27553,plain,
% 4.97/5.13 (~(s(elem!1) = elem!1)),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[2150, 27552])).
% 4.97/5.13 tff(27554,plain,
% 4.97/5.13 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[16181, 27545])).
% 4.97/5.13 tff(27555,plain,
% 4.97/5.13 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[20758, 27543, 27537])).
% 4.97/5.13 tff(27556,plain,
% 4.97/5.13 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 27555])).
% 4.97/5.13 tff(27557,plain,
% 4.97/5.13 (~b(s(s(z)), s(s(s(z))))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[27335, 27556, 27224, 24628, 27539])).
% 4.97/5.13 tff(27558,plain,
% 4.97/5.13 (r(s(s(z)), s(s(s(z))))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[5088, 27557])).
% 4.97/5.13 tff(27559,plain,
% 4.97/5.13 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[24478, 27558, 10794])).
% 4.97/5.13 tff(27560,plain,
% 4.97/5.13 (b(s(s(s(s(z)))), s(s(s(z))))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[11185, 27559])).
% 4.97/5.13 tff(27561,plain,
% 4.97/5.13 (~b(z, s(s(s(z))))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[12104, 178, 27212, 27535, 27527, 27560])).
% 4.97/5.13 tff(27562,plain,
% 4.97/5.13 (r(z, s(s(s(z))))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[4920, 27561])).
% 4.97/5.13 tff(27563,plain,
% 4.97/5.13 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 4.97/5.13 inference(monotonicity,[status(thm)],[27548])).
% 4.97/5.13 tff(27564,plain,
% 4.97/5.13 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.97/5.13 inference(transitivity,[status(thm)],[27563, 377])).
% 4.97/5.13 tff(27565,plain,
% 4.97/5.13 ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z)))))))))),
% 4.97/5.13 inference(symmetry,[status(thm)],[27564])).
% 4.97/5.13 tff(27566,plain,
% 4.97/5.13 ((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z))))))))))),
% 4.97/5.13 inference(monotonicity,[status(thm)],[27565])).
% 4.97/5.13 tff(27567,plain,
% 4.97/5.13 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.97/5.13 inference(monotonicity,[status(thm)],[27545])).
% 4.97/5.13 tff(27568,plain,
% 4.97/5.13 ((~(s(elem!1) = elem!1)) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 4.97/5.13 inference(monotonicity,[status(thm)],[27567])).
% 4.97/5.13 tff(27569,plain,
% 4.97/5.13 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.97/5.13 inference(modus_ponens,[status(thm)],[27553, 27568])).
% 4.97/5.13 tff(27570,plain,
% 4.97/5.13 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z)))))))))),
% 4.97/5.13 inference(modus_ponens,[status(thm)],[27569, 27566])).
% 4.97/5.13 tff(27571,plain,
% 4.97/5.13 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))) <=> r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.97/5.13 inference(monotonicity,[status(thm)],[27548])).
% 4.97/5.13 tff(27572,plain,
% 4.97/5.13 (r(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.97/5.13 inference(symmetry,[status(thm)],[27571])).
% 4.97/5.13 tff(27573,plain,
% 4.97/5.13 (r(elem!1, s(elem!1)) <=> r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.97/5.13 inference(monotonicity,[status(thm)],[27545])).
% 4.97/5.13 tff(27574,plain,
% 4.97/5.13 (r(elem!1, s(elem!1)) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.97/5.13 inference(transitivity,[status(thm)],[27573, 27572])).
% 4.97/5.13 tff(27575,plain,
% 4.97/5.13 ((~r(elem!1, s(elem!1))) <=> (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))),
% 4.97/5.13 inference(monotonicity,[status(thm)],[27574])).
% 4.97/5.13 tff(27576,plain,
% 4.97/5.13 (r(elem!1, s(s(s(s(z)))))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[24769, 27545, 3428])).
% 4.97/5.13 tff(27577,plain,
% 4.97/5.13 (r(elem!1, z) <=> r(s(s(s(s(s(s(s(z))))))), z)),
% 4.97/5.13 inference(monotonicity,[status(thm)],[27545])).
% 4.97/5.13 tff(27578,plain,
% 4.97/5.13 (r(s(s(s(s(s(s(s(z))))))), z) <=> r(elem!1, z)),
% 4.97/5.13 inference(symmetry,[status(thm)],[27577])).
% 4.97/5.13 tff(27579,plain,
% 4.97/5.13 (r(elem!1, z)),
% 4.97/5.13 inference(modus_ponens,[status(thm)],[27543, 27578])).
% 4.97/5.13 tff(27580,plain,
% 4.97/5.13 (~r(s(s(s(s(z)))), s(elem!1))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[11326, 1587, 470])).
% 4.97/5.13 tff(27581,plain,
% 4.97/5.13 (b(s(s(s(s(z)))), s(elem!1))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[2173, 27580, 2169])).
% 4.97/5.13 tff(27582,plain,
% 4.97/5.13 (~r(s(elem!1), s(s(s(s(z)))))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[14364, 1587, 470])).
% 4.97/5.13 tff(27583,plain,
% 4.97/5.13 (b(s(elem!1), s(s(s(s(z)))))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[1084, 27582, 1369])).
% 4.97/5.13 tff(27584,plain,
% 4.97/5.13 ($false),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[15563, 27583, 27581, 168, 437, 1587])).
% 4.97/5.13 tff(27585,plain,((~r(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (s(elem!1) = s(s(s(s(z))))) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.97/5.13 tff(27586,plain,
% 4.97/5.13 (~r(elem!1, s(elem!1))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[27585, 27579, 27576, 27554, 27535])).
% 4.97/5.13 tff(27587,plain,
% 4.97/5.13 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.97/5.13 inference(modus_ponens,[status(thm)],[27586, 27575])).
% 4.97/5.13 tff(27588,plain,
% 4.97/5.13 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[16349, 41, 27587])).
% 4.97/5.13 tff(27589,plain,
% 4.97/5.13 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[27588, 27570])).
% 4.97/5.13 tff(27590,plain,
% 4.97/5.13 (r(z, s(s(s(s(s(s(s(s(z)))))))))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[24812, 2333, 679])).
% 4.97/5.13 tff(27591,plain,
% 4.97/5.13 (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[24823, 27590, 4952])).
% 4.97/5.13 tff(27592,plain,
% 4.97/5.13 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[24832, 27591, 24825])).
% 4.97/5.13 tff(27593,plain,
% 4.97/5.13 (~r(s(elem!1), elem!1)),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[7070, 2333, 521])).
% 4.97/5.13 tff(27594,plain,
% 4.97/5.13 (b(s(elem!1), elem!1)),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[677, 27593, 725])).
% 4.97/5.13 tff(27595,plain,
% 4.97/5.13 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[686, 27594, 679])).
% 4.97/5.13 tff(27596,plain,
% 4.97/5.13 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.13 inference(modus_ponens,[status(thm)],[27595, 11735])).
% 4.97/5.13 tff(27597,assumption,(b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))), introduced(assumption)).
% 4.97/5.13 tff(27598,plain,
% 4.97/5.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 4.97/5.13 inference(rewrite,[status(thm)],[])).
% 4.97/5.13 tff(27599,plain,
% 4.97/5.13 (((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(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))))) | (~b(s(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(s(s(s(s(z))))))))))) <=> ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 4.97/5.13 inference(rewrite,[status(thm)],[])).
% 4.97/5.13 tff(27600,plain,
% 4.97/5.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(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))))) | (~b(s(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(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))))),
% 4.97/5.13 inference(monotonicity,[status(thm)],[27599])).
% 4.97/5.13 tff(27601,plain,
% 4.97/5.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(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))))) | (~b(s(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(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 4.97/5.13 inference(transitivity,[status(thm)],[27600, 27598])).
% 4.97/5.13 tff(27602,plain,
% 4.97/5.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(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))))) | (~b(s(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(s(s(s(s(z)))))))))))),
% 4.97/5.13 inference(quant_inst,[status(thm)],[])).
% 4.97/5.13 tff(27603,plain,
% 4.97/5.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 4.97/5.13 inference(modus_ponens,[status(thm)],[27602, 27601])).
% 4.97/5.13 tff(27604,plain,
% 4.97/5.13 ($false),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[27603, 178, 3002, 21855, 27597, 27596, 27592])).
% 4.97/5.13 tff(27605,plain,((~r(z, s(elem!1))) | (~b(s(s(s(z))), s(s(s(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(s(s(s(s(z)))))))))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z)))) | (~r(z, s(s(s(z))))) | (s(elem!1) = elem!1) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.97/5.13 tff(27606,plain,
% 4.97/5.13 (~r(z, s(elem!1))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[27605, 27589, 27556, 27539, 27545, 27546, 27562, 27553, 27540])).
% 4.97/5.13 tff(27607,plain,
% 4.97/5.13 (b(z, s(elem!1))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[2351, 27606])).
% 4.97/5.13 tff(27608,plain,
% 4.97/5.13 (~b(s(elem!1), z)),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[22412, 27607, 27212, 273, 1056, 193, 27554, 27535])).
% 4.97/5.13 tff(27609,plain,
% 4.97/5.13 (r(s(elem!1), z)),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[774, 27608])).
% 4.97/5.13 tff(27610,plain,
% 4.97/5.13 (~r(s(elem!1), elem!1)),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[1284, 27609, 27540])).
% 4.97/5.13 tff(27611,plain,
% 4.97/5.13 (b(s(elem!1), elem!1)),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[677, 27610, 27553])).
% 4.97/5.13 tff(27612,plain,
% 4.97/5.13 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[686, 27611, 27545])).
% 4.97/5.13 tff(27613,plain,
% 4.97/5.13 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.13 inference(modus_ponens,[status(thm)],[27612, 27550])).
% 4.97/5.13 tff(27614,plain,
% 4.97/5.13 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[27603, 178, 27539, 27556, 27589, 27613])).
% 4.97/5.13 tff(27615,plain,
% 4.97/5.13 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[24832, 27614, 27546])).
% 4.97/5.13 tff(27616,plain,
% 4.97/5.13 (r(s(elem!1), s(s(z))) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 4.97/5.13 inference(monotonicity,[status(thm)],[27547])).
% 4.97/5.13 tff(27617,plain,
% 4.97/5.13 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 4.97/5.13 inference(monotonicity,[status(thm)],[27547])).
% 4.97/5.13 tff(27618,plain,
% 4.97/5.13 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(z))) <=> b(s(elem!1), s(s(z)))),
% 4.97/5.13 inference(symmetry,[status(thm)],[27617])).
% 4.97/5.13 tff(27619,plain,
% 4.97/5.13 ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) <=> (~b(s(elem!1), s(s(z))))),
% 4.97/5.13 inference(monotonicity,[status(thm)],[27618])).
% 4.97/5.13 tff(27620,plain,
% 4.97/5.13 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[13746, 178, 27224, 24628, 27589, 27613])).
% 4.97/5.13 tff(27621,plain,
% 4.97/5.13 (~b(s(elem!1), s(s(z)))),
% 4.97/5.13 inference(modus_ponens,[status(thm)],[27620, 27619])).
% 4.97/5.13 tff(27622,plain,
% 4.97/5.13 (r(s(elem!1), s(s(z)))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[421, 27621, 1056])).
% 4.97/5.13 tff(27623,plain,
% 4.97/5.13 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 4.97/5.13 inference(modus_ponens,[status(thm)],[27622, 27616])).
% 4.97/5.13 tff(27624,plain,
% 4.97/5.13 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 4.97/5.13 inference(rewrite,[status(thm)],[])).
% 4.97/5.13 tff(27625,plain,
% 4.97/5.13 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 4.97/5.13 inference(rewrite,[status(thm)],[])).
% 4.97/5.13 tff(27626,plain,
% 4.97/5.13 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))))),
% 4.97/5.13 inference(monotonicity,[status(thm)],[27625])).
% 4.97/5.13 tff(27627,plain,
% 4.97/5.13 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 4.97/5.13 inference(transitivity,[status(thm)],[27626, 27624])).
% 4.97/5.13 tff(27628,plain,
% 4.97/5.13 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))))),
% 4.97/5.13 inference(quant_inst,[status(thm)],[])).
% 4.97/5.13 tff(27629,plain,
% 4.97/5.13 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 4.97/5.13 inference(modus_ponens,[status(thm)],[27628, 27627])).
% 4.97/5.13 tff(27630,plain,
% 4.97/5.13 ($false),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[27629, 118, 27558, 27623, 27615])).
% 4.97/5.13 tff(27631,plain,((s(elem!1) = s(s(z))) | (~b(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (s(s(z)) = elem!1) | (~b(s(s(z)), z)) | b(s(s(z)), s(s(s(s(z))))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.97/5.13 tff(27632,plain,
% 4.97/5.13 (s(elem!1) = s(s(z))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[27631, 27219, 103, 27213, 27523, 12, 5619, 105, 507])).
% 4.97/5.13 tff(27633,plain,
% 4.97/5.13 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[2832, 27632])).
% 4.97/5.13 tff(27634,plain,
% 4.97/5.13 (~r(s(s(s(s(z)))), z)),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[27533, 27224, 5619, 103])).
% 4.97/5.13 tff(27635,plain,
% 4.97/5.13 (b(s(s(s(s(z)))), z)),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[191, 27634])).
% 4.97/5.13 tff(27636,plain,
% 4.97/5.13 (~(elem!1 = s(s(s(s(z)))))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[11438, 27632])).
% 4.97/5.13 tff(27637,plain,
% 4.97/5.13 (r(z, elem!1)),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[22090, 27636, 5619, 27635, 507, 27212, 27219, 12])).
% 4.97/5.13 tff(27638,plain,
% 4.97/5.13 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[11027, 27637, 27230])).
% 4.97/5.13 tff(27639,plain,
% 4.97/5.13 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[3818, 27637, 27226])).
% 4.97/5.13 tff(27640,plain,
% 4.97/5.13 ($false),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[14184, 27639, 27638, 27224, 27523, 27217, 27633])).
% 4.97/5.13 tff(27641,plain,((s(s(z)) = elem!1) | (z = elem!1) | b(s(s(z)), s(s(s(s(z))))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 4.97/5.13 tff(27642,plain,
% 4.97/5.13 (s(s(z)) = elem!1),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[27641, 507, 105, 86, 5618])).
% 4.97/5.13 tff(27643,plain,
% 4.97/5.13 (s(s(s(z))) = s(elem!1)),
% 4.97/5.13 inference(monotonicity,[status(thm)],[27642])).
% 4.97/5.13 tff(27644,plain,
% 4.97/5.13 (r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.13 inference(monotonicity,[status(thm)],[27643])).
% 4.97/5.13 tff(27645,plain,
% 4.97/5.13 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.13 inference(symmetry,[status(thm)],[27644])).
% 4.97/5.13 tff(27646,plain,
% 4.97/5.13 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[5361, 27642])).
% 4.97/5.13 tff(27647,plain,
% 4.97/5.13 (~b(s(s(s(z))), z)),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[27258, 27635, 10794, 27245, 5619])).
% 4.97/5.13 tff(27648,plain,
% 4.97/5.13 (elem!1 = s(s(z))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[3230, 27642])).
% 4.97/5.13 tff(27649,plain,
% 4.97/5.13 (~b(s(elem!1), z)),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[7042, 27648, 27647])).
% 4.97/5.13 tff(27650,plain,
% 4.97/5.13 (r(s(elem!1), z)),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[774, 27649])).
% 4.97/5.13 tff(27651,plain,
% 4.97/5.13 (r(s(s(elem!1)), s(s(z))) <=> r(s(s(elem!1)), elem!1)),
% 4.97/5.13 inference(monotonicity,[status(thm)],[27642])).
% 4.97/5.13 tff(27652,plain,
% 4.97/5.13 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(s(z)))),
% 4.97/5.13 inference(symmetry,[status(thm)],[27651])).
% 4.97/5.13 tff(27653,plain,
% 4.97/5.13 (s(s(s(s(z)))) = s(s(elem!1))),
% 4.97/5.13 inference(monotonicity,[status(thm)],[27643])).
% 4.97/5.13 tff(27654,plain,
% 4.97/5.13 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 4.97/5.13 inference(monotonicity,[status(thm)],[27653])).
% 4.97/5.13 tff(27655,plain,
% 4.97/5.13 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(elem!1)), s(s(z)))),
% 4.97/5.13 inference(transitivity,[status(thm)],[27654, 27652])).
% 4.97/5.13 tff(27656,plain,
% 4.97/5.13 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(z)))), elem!1)),
% 4.97/5.13 inference(monotonicity,[status(thm)],[27642])).
% 4.97/5.13 tff(27657,plain,
% 4.97/5.13 (r(s(s(s(s(z)))), elem!1)),
% 4.97/5.13 inference(modus_ponens,[status(thm)],[103, 27656])).
% 4.97/5.13 tff(27658,plain,
% 4.97/5.13 (r(s(s(elem!1)), s(s(z)))),
% 4.97/5.13 inference(modus_ponens,[status(thm)],[27657, 27655])).
% 4.97/5.13 tff(27659,plain,
% 4.97/5.13 (b(elem!1, z)),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[6641, 27648, 5618])).
% 4.97/5.13 tff(27660,plain,
% 4.97/5.13 (~(s(elem!1) = elem!1)),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[790, 27649, 27659])).
% 4.97/5.13 tff(27661,plain,
% 4.97/5.13 (s(s(elem!1)) = s(s(s(s(z))))),
% 4.97/5.13 inference(symmetry,[status(thm)],[27653])).
% 4.97/5.13 tff(27662,plain,
% 4.97/5.13 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 4.97/5.13 inference(monotonicity,[status(thm)],[27661])).
% 4.97/5.13 tff(27663,plain,
% 4.97/5.13 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), s(s(elem!1)))),
% 4.97/5.13 inference(symmetry,[status(thm)],[27662])).
% 4.97/5.13 tff(27664,plain,
% 4.97/5.13 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 4.97/5.13 inference(monotonicity,[status(thm)],[27643])).
% 4.97/5.13 tff(27665,plain,
% 4.97/5.13 (b(s(elem!1), s(s(s(s(z)))))),
% 4.97/5.13 inference(modus_ponens,[status(thm)],[27245, 27664])).
% 4.97/5.13 tff(27666,plain,
% 4.97/5.13 (b(s(elem!1), s(s(elem!1)))),
% 4.97/5.13 inference(modus_ponens,[status(thm)],[27665, 27663])).
% 4.97/5.13 tff(27667,plain,
% 4.97/5.13 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 4.97/5.13 inference(monotonicity,[status(thm)],[27653])).
% 4.97/5.13 tff(27668,plain,
% 4.97/5.13 ((~b(s(s(s(s(z)))), elem!1)) <=> (~b(s(s(elem!1)), elem!1))),
% 4.97/5.13 inference(monotonicity,[status(thm)],[27667])).
% 4.97/5.13 tff(27669,plain,
% 4.97/5.13 (~b(s(s(s(s(z)))), elem!1)),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[3774, 27642, 86])).
% 4.97/5.13 tff(27670,plain,
% 4.97/5.13 (~b(s(s(elem!1)), elem!1)),
% 4.97/5.13 inference(modus_ponens,[status(thm)],[27669, 27668])).
% 4.97/5.13 tff(27671,plain,
% 4.97/5.13 (b(s(s(s(s(z)))), z) <=> b(s(s(elem!1)), z)),
% 4.97/5.13 inference(monotonicity,[status(thm)],[27653])).
% 4.97/5.13 tff(27672,plain,
% 4.97/5.13 (b(s(s(elem!1)), z)),
% 4.97/5.13 inference(modus_ponens,[status(thm)],[27635, 27671])).
% 4.97/5.13 tff(27673,plain,
% 4.97/5.13 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 4.97/5.13 inference(monotonicity,[status(thm)],[27653])).
% 4.97/5.13 tff(27674,plain,
% 4.97/5.13 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 4.97/5.13 inference(transitivity,[status(thm)],[27673, 3400])).
% 4.97/5.13 tff(27675,plain,
% 4.97/5.13 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 4.97/5.13 inference(transitivity,[status(thm)],[27674, 12033])).
% 4.97/5.13 tff(27676,plain,
% 4.97/5.13 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 4.97/5.13 inference(monotonicity,[status(thm)],[27675])).
% 4.97/5.13 tff(27677,plain,
% 4.97/5.13 (~(s(s(z)) = s(elem!1))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[11742, 27650, 5618])).
% 4.97/5.13 tff(27678,plain,
% 4.97/5.13 (~(s(elem!1) = s(s(z)))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[1362, 27677])).
% 4.97/5.13 tff(27679,plain,
% 4.97/5.13 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[2840, 27678])).
% 4.97/5.13 tff(27680,plain,
% 4.97/5.13 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 4.97/5.13 inference(modus_ponens,[status(thm)],[27679, 27676])).
% 4.97/5.13 tff(27681,plain,
% 4.97/5.13 (r(elem!1, s(s(elem!1)))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[9352, 27642, 10794])).
% 4.97/5.13 tff(27682,plain,
% 4.97/5.13 (~r(z, s(s(z)))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[7053, 2811, 1324])).
% 4.97/5.13 tff(27683,plain,
% 4.97/5.13 (b(z, s(s(z)))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[143, 27682])).
% 4.97/5.13 tff(27684,plain,
% 4.97/5.13 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[4057, 27683, 3461, 166, 1146])).
% 4.97/5.13 tff(27685,plain,
% 4.97/5.13 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[133, 27684])).
% 4.97/5.13 tff(27686,plain,
% 4.97/5.13 ((s(s(z)) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(z)))))),
% 4.97/5.13 inference(monotonicity,[status(thm)],[1324])).
% 4.97/5.13 tff(27687,plain,
% 4.97/5.13 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 4.97/5.13 inference(transitivity,[status(thm)],[27686, 321])).
% 4.97/5.13 tff(27688,plain,
% 4.97/5.13 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 4.97/5.13 inference(monotonicity,[status(thm)],[27687])).
% 4.97/5.13 tff(27689,plain,
% 4.97/5.13 (~(s(s(s(s(z)))) = elem!1)),
% 4.97/5.13 inference(modus_ponens,[status(thm)],[159, 27688])).
% 4.97/5.13 tff(27690,plain,
% 4.97/5.13 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[3502, 27689])).
% 4.97/5.13 tff(27691,plain,
% 4.97/5.13 (~(s(elem!1) = s(s(s(elem!1))))),
% 4.97/5.13 inference(modus_ponens,[status(thm)],[26438, 11691])).
% 4.97/5.13 tff(27692,plain,
% 4.97/5.13 (~(s(s(elem!1)) = s(elem!1))),
% 4.97/5.13 inference(modus_ponens,[status(thm)],[8129, 10924])).
% 4.97/5.13 tff(27693,plain,
% 4.97/5.13 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 4.97/5.13 inference(modus_ponens,[status(thm)],[8112, 2561])).
% 4.97/5.13 tff(27694,plain,
% 4.97/5.13 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[14966, 118, 844, 27685])).
% 4.97/5.13 tff(27695,plain,
% 4.97/5.13 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[806, 41, 27694, 27693])).
% 4.97/5.13 tff(27696,plain,
% 4.97/5.13 (b(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.97/5.13 inference(monotonicity,[status(thm)],[1324])).
% 4.97/5.13 tff(27697,plain,
% 4.97/5.13 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.97/5.13 inference(modus_ponens,[status(thm)],[1146, 27696])).
% 4.97/5.13 tff(27698,plain,
% 4.97/5.13 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[15120, 118, 844, 27685])).
% 4.97/5.13 tff(27699,plain,
% 4.97/5.13 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.13 inference(unit_resolution,[status(thm)],[395, 27698, 8112])).
% 4.97/5.13 tff(27700,plain,
% 4.97/5.13 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.97/5.13 inference(monotonicity,[status(thm)],[1324])).
% 4.97/5.13 tff(27701,plain,
% 4.97/5.13 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.97/5.13 inference(modus_ponens,[status(thm)],[166, 27700])).
% 4.97/5.13 tff(27702,plain,
% 4.97/5.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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), s(s(s(s(s(s(s(z))))))))) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 4.97/5.14 inference(rewrite,[status(thm)],[])).
% 4.97/5.14 tff(27703,plain,
% 4.97/5.14 (((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(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))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 4.97/5.14 inference(rewrite,[status(thm)],[])).
% 4.97/5.14 tff(27704,plain,
% 4.97/5.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 4.97/5.14 inference(monotonicity,[status(thm)],[27703])).
% 4.97/5.14 tff(27705,plain,
% 4.97/5.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 4.97/5.14 inference(transitivity,[status(thm)],[27704, 27702])).
% 4.97/5.14 tff(27706,plain,
% 4.97/5.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 4.97/5.14 inference(quant_inst,[status(thm)],[])).
% 4.97/5.14 tff(27707,plain,
% 4.97/5.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 4.97/5.14 inference(modus_ponens,[status(thm)],[27706, 27705])).
% 4.97/5.14 tff(27708,plain,
% 4.97/5.14 (~b(s(elem!1), elem!1)),
% 4.97/5.14 inference(unit_resolution,[status(thm)],[27707, 178, 27701, 27699, 27697, 27695])).
% 4.97/5.14 tff(27709,plain,
% 4.97/5.14 (r(s(elem!1), elem!1)),
% 4.97/5.14 inference(unit_resolution,[status(thm)],[677, 27708, 725])).
% 4.97/5.14 tff(27710,plain,
% 4.97/5.14 (r(s(elem!1), s(s(z)))),
% 4.97/5.14 inference(unit_resolution,[status(thm)],[7028, 27709, 10916])).
% 4.97/5.14 tff(27711,plain,
% 4.97/5.14 (~r(s(s(elem!1)), s(elem!1))),
% 4.97/5.14 inference(unit_resolution,[status(thm)],[8846, 27710, 8838])).
% 4.97/5.14 tff(27712,plain,
% 4.97/5.14 (b(s(s(elem!1)), s(elem!1))),
% 4.97/5.14 inference(unit_resolution,[status(thm)],[1006, 27711, 27692])).
% 4.97/5.14 tff(27713,plain,
% 4.97/5.14 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.97/5.14 inference(modus_ponens,[status(thm)],[26438, 11668])).
% 4.97/5.14 tff(27714,plain,
% 4.97/5.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 4.97/5.14 inference(rewrite,[status(thm)],[])).
% 4.97/5.14 tff(27715,plain,
% 4.97/5.14 (((~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(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(elem!1, 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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 4.97/5.14 inference(rewrite,[status(thm)],[])).
% 4.97/5.14 tff(27716,plain,
% 4.97/5.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 4.97/5.14 inference(monotonicity,[status(thm)],[27715])).
% 4.97/5.14 tff(27717,plain,
% 4.97/5.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 4.97/5.14 inference(transitivity,[status(thm)],[27716, 27714])).
% 4.97/5.14 tff(27718,plain,
% 4.97/5.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 4.97/5.14 inference(quant_inst,[status(thm)],[])).
% 4.97/5.14 tff(27719,plain,
% 4.97/5.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 4.97/5.14 inference(modus_ponens,[status(thm)],[27718, 27717])).
% 4.97/5.14 tff(27720,plain,
% 4.97/5.14 (~b(elem!1, s(elem!1))),
% 4.97/5.14 inference(unit_resolution,[status(thm)],[27719, 178, 27701, 27699, 27697, 27695])).
% 4.97/5.14 tff(27721,plain,
% 4.97/5.14 (r(elem!1, s(elem!1))),
% 4.97/5.14 inference(unit_resolution,[status(thm)],[756, 27720, 749])).
% 4.97/5.14 tff(27722,plain,
% 4.97/5.14 (r(s(s(z)), s(elem!1))),
% 4.97/5.14 inference(unit_resolution,[status(thm)],[13127, 27721, 1324])).
% 4.97/5.14 tff(27723,plain,
% 4.97/5.14 (b(z, s(s(s(s(z))))) <=> b(z, s(s(elem!1)))),
% 4.97/5.14 inference(monotonicity,[status(thm)],[3506])).
% 4.97/5.14 tff(27724,plain,
% 4.97/5.14 (b(z, s(s(elem!1)))),
% 4.97/5.14 inference(modus_ponens,[status(thm)],[27212, 27723])).
% 4.97/5.14 tff(27725,plain,
% 4.97/5.14 (~b(z, s(elem!1))),
% 4.97/5.14 inference(unit_resolution,[status(thm)],[25075, 178, 6604, 27724, 27712, 5391])).
% 4.97/5.14 tff(27726,plain,
% 4.97/5.14 (r(z, s(elem!1))),
% 4.97/5.14 inference(unit_resolution,[status(thm)],[2351, 27725])).
% 4.97/5.14 tff(27727,plain,
% 4.97/5.14 (~r(s(s(s(elem!1))), s(elem!1))),
% 4.97/5.14 inference(unit_resolution,[status(thm)],[6297, 27726, 3461, 27683, 27722])).
% 4.97/5.14 tff(27728,plain,
% 4.97/5.14 (b(s(s(s(elem!1))), s(elem!1))),
% 4.97/5.14 inference(unit_resolution,[status(thm)],[373, 27727, 27713])).
% 4.97/5.14 tff(27729,plain,
% 4.97/5.14 (~r(s(elem!1), s(s(s(elem!1))))),
% 4.97/5.14 inference(unit_resolution,[status(thm)],[5423, 3311, 818, 557, 725, 506])).
% 4.97/5.14 tff(27730,plain,
% 4.97/5.14 (b(s(elem!1), s(s(s(elem!1))))),
% 4.97/5.14 inference(unit_resolution,[status(thm)],[5432, 27729, 5425])).
% 4.97/5.14 tff(27731,plain,
% 4.97/5.14 ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 4.97/5.14 inference(unit_resolution,[status(thm)],[9160, 178, 2044, 1013, 5391])).
% 4.97/5.14 tff(27732,plain,
% 4.97/5.14 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 4.97/5.14 inference(unit_resolution,[status(thm)],[27731, 27730])).
% 4.97/5.14 tff(27733,plain,
% 4.97/5.14 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 4.97/5.14 inference(unit_resolution,[status(thm)],[3409, 27732, 5222])).
% 4.97/5.14 tff(27734,plain,
% 4.97/5.14 ($false),
% 4.97/5.14 inference(unit_resolution,[status(thm)],[12160, 118, 3311, 27733, 5816])).
% 4.97/5.14 tff(27735,plain,((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (s(elem!1) = s(s(s(elem!1)))) | (~b(z, elem!1)) | (~r(z, s(s(s(elem!1))))) | (s(elem!1) = elem!1) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 4.97/5.14 tff(27736,plain,
% 4.97/5.14 (~r(elem!1, s(s(s(elem!1))))),
% 4.97/5.14 inference(unit_resolution,[status(thm)],[27735, 557, 5222, 2044, 1013, 5391, 5425, 818, 5816, 725, 506])).
% 4.97/5.14 tff(27737,plain,
% 4.97/5.14 (b(elem!1, s(s(s(elem!1))))),
% 4.97/5.14 inference(unit_resolution,[status(thm)],[2054, 27736, 1586])).
% 4.97/5.14 tff(27738,plain,
% 4.97/5.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(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(s(s(s(z))))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(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(s(s(s(z))))))), s(s(s(elem!1))))))),
% 4.97/5.14 inference(rewrite,[status(thm)],[])).
% 4.97/5.14 tff(27739,plain,
% 4.97/5.14 (((~b(s(s(s(elem!1))), 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(s(s(s(s(s(s(z))))))), s(s(s(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(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(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(s(s(s(z))))))), s(s(s(elem!1))))))),
% 4.97/5.14 inference(rewrite,[status(thm)],[])).
% 4.97/5.14 tff(27740,plain,
% 4.97/5.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(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(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(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(s(s(s(z))))))), s(s(s(elem!1)))))))),
% 4.97/5.14 inference(monotonicity,[status(thm)],[27739])).
% 4.97/5.14 tff(27741,plain,
% 4.97/5.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(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(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(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(s(s(s(z))))))), s(s(s(elem!1))))))),
% 4.97/5.14 inference(transitivity,[status(thm)],[27740, 27738])).
% 4.97/5.14 tff(27742,plain,
% 4.97/5.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(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(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 4.97/5.14 inference(quant_inst,[status(thm)],[])).
% 4.97/5.14 tff(27743,plain,
% 4.97/5.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 4.97/5.14 inference(modus_ponens,[status(thm)],[27742, 27741])).
% 4.97/5.14 tff(27744,plain,
% 4.97/5.14 ($false),
% 4.97/5.14 inference(unit_resolution,[status(thm)],[27743, 178, 2044, 27737, 869, 19278, 17855])).
% 4.97/5.14 tff(27745,plain,((~r(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (elem!1 = s(s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (s(elem!1) = s(s(s(elem!1)))) | (~b(z, elem!1)) | (~r(elem!1, s(s(elem!1)))) | (s(elem!1) = elem!1) | (~b(elem!1, z)) | (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 4.97/5.14 tff(27746,plain,
% 4.97/5.14 (~r(z, s(s(s(elem!1))))),
% 4.97/5.14 inference(unit_resolution,[status(thm)],[27745, 27728, 27701, 27695, 11627, 5222, 27712, 5391, 27691, 3123, 5816, 725, 506, 27690, 27685])).
% 4.97/5.14 tff(27747,plain,
% 4.97/5.14 (b(z, s(s(s(elem!1))))),
% 4.97/5.14 inference(unit_resolution,[status(thm)],[2095, 27746])).
% 4.97/5.14 tff(27748,plain,
% 4.97/5.14 (~(s(s(elem!1)) = elem!1)),
% 4.97/5.14 inference(modus_ponens,[status(thm)],[2387, 8801])).
% 4.97/5.14 tff(27749,plain,
% 4.97/5.14 (~r(elem!1, s(s(s(elem!1))))),
% 4.97/5.14 inference(unit_resolution,[status(thm)],[22317, 27747, 5816, 27724, 5222, 6604, 3358, 27748])).
% 4.97/5.14 tff(27750,plain,
% 4.97/5.14 (b(elem!1, s(s(s(elem!1))))),
% 4.97/5.14 inference(unit_resolution,[status(thm)],[2054, 27749, 11627])).
% 4.97/5.14 tff(27751,plain,
% 4.97/5.14 (~b(s(s(s(elem!1))), elem!1)),
% 4.97/5.14 inference(unit_resolution,[status(thm)],[12925, 27750, 506, 3123, 27747])).
% 4.97/5.14 tff(27752,plain,
% 4.97/5.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 4.97/5.14 inference(rewrite,[status(thm)],[])).
% 4.97/5.14 tff(27753,plain,
% 4.97/5.14 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(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(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 4.97/5.14 inference(rewrite,[status(thm)],[])).
% 4.97/5.14 tff(27754,plain,
% 4.97/5.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1))))))),
% 4.97/5.14 inference(monotonicity,[status(thm)],[27753])).
% 4.97/5.14 tff(27755,plain,
% 4.97/5.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 4.97/5.14 inference(transitivity,[status(thm)],[27754, 27752])).
% 4.97/5.14 tff(27756,plain,
% 4.97/5.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 4.97/5.14 inference(quant_inst,[status(thm)],[])).
% 4.97/5.14 tff(27757,plain,
% 4.97/5.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1))))),
% 4.97/5.14 inference(modus_ponens,[status(thm)],[27756, 27755])).
% 4.97/5.14 tff(27758,plain,
% 4.97/5.14 ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 4.97/5.14 inference(unit_resolution,[status(thm)],[27757, 178, 27728, 27724, 27712])).
% 4.97/5.14 tff(27759,plain,
% 4.97/5.14 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 4.97/5.14 inference(unit_resolution,[status(thm)],[27758, 27747])).
% 4.97/5.14 tff(27760,plain,
% 4.97/5.14 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 4.97/5.14 inference(unit_resolution,[status(thm)],[3409, 27759, 5222])).
% 4.97/5.14 tff(27761,plain,
% 4.97/5.14 (~r(s(s(s(elem!1))), elem!1)),
% 4.97/5.14 inference(unit_resolution,[status(thm)],[10206, 27760, 5816])).
% 4.97/5.14 tff(27762,plain,
% 4.97/5.14 ($false),
% 4.97/5.14 inference(unit_resolution,[status(thm)],[570, 27761, 27751, 18320])).
% 4.97/5.14 tff(27763,plain,(r(z, elem!1) | (~r(elem!1, s(s(elem!1)))) | (~b(elem!1, z)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(s(elem!1)), z)) | b(s(s(elem!1)), elem!1) | (~b(s(elem!1), s(s(elem!1)))) | (s(elem!1) = elem!1) | (~b(s(s(z)), z)) | (~(s(s(z)) = elem!1)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(elem!1), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.97/5.14 tff(27764,plain,
% 4.97/5.14 (r(z, elem!1)),
% 4.97/5.14 inference(unit_resolution,[status(thm)],[27763, 27681, 27659, 27680, 27672, 27670, 27666, 27660, 5619, 27642, 27658, 27650, 27224, 27217, 507])).
% 4.97/5.14 tff(27765,plain,
% 4.97/5.14 (r(z, s(s(z)))),
% 4.97/5.14 inference(unit_resolution,[status(thm)],[18165, 27764, 27642])).
% 4.97/5.14 tff(27766,plain,
% 4.97/5.14 (b(s(elem!1), s(s(z)))),
% 4.97/5.14 inference(unit_resolution,[status(thm)],[11747, 27765, 5618, 27650])).
% 4.97/5.14 tff(27767,plain,
% 4.97/5.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 4.97/5.14 inference(rewrite,[status(thm)],[])).
% 4.97/5.14 tff(27768,plain,
% 4.97/5.14 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 4.97/5.14 inference(rewrite,[status(thm)],[])).
% 4.97/5.14 tff(27769,plain,
% 4.97/5.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))))),
% 4.97/5.14 inference(monotonicity,[status(thm)],[27768])).
% 4.97/5.14 tff(27770,plain,
% 4.97/5.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 4.97/5.14 inference(transitivity,[status(thm)],[27769, 27767])).
% 4.97/5.14 tff(27771,plain,
% 4.97/5.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 4.97/5.14 inference(quant_inst,[status(thm)],[])).
% 4.97/5.14 tff(27772,plain,
% 4.97/5.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 4.97/5.14 inference(modus_ponens,[status(thm)],[27771, 27770])).
% 4.97/5.14 tff(27773,plain,
% 4.97/5.14 (~b(s(s(z)), s(s(z)))),
% 4.97/5.14 inference(unit_resolution,[status(thm)],[27772, 178, 5619, 27217])).
% 4.97/5.14 tff(27774,plain,
% 4.97/5.14 (~b(s(s(z)), elem!1)),
% 4.97/5.14 inference(unit_resolution,[status(thm)],[3238, 27648, 27773])).
% 4.97/5.14 tff(27775,plain,
% 4.97/5.14 (s(s(z)) = elem!1),
% 4.97/5.14 inference(unit_resolution,[status(thm)],[14873, 5618, 86, 3261])).
% 4.97/5.14 tff(27776,plain,
% 4.97/5.14 (s(s(s(z))) = s(elem!1)),
% 4.97/5.14 inference(monotonicity,[status(thm)],[27775])).
% 4.97/5.14 tff(27777,plain,
% 4.97/5.14 (s(s(s(s(z)))) = s(s(elem!1))),
% 4.97/5.14 inference(monotonicity,[status(thm)],[27776])).
% 4.97/5.14 tff(27778,plain,
% 4.97/5.14 (s(s(elem!1)) = s(s(s(s(z))))),
% 4.97/5.14 inference(symmetry,[status(thm)],[27777])).
% 4.97/5.15 tff(27779,plain,
% 4.97/5.15 (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(s(z)))))),
% 4.97/5.15 inference(monotonicity,[status(thm)],[27778])).
% 4.97/5.15 tff(27780,plain,
% 4.97/5.15 (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(elem!1)))),
% 4.97/5.15 inference(symmetry,[status(thm)],[27779])).
% 4.97/5.15 tff(27781,plain,
% 4.97/5.15 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.97/5.15 inference(modus_ponens,[status(thm)],[1130, 27780])).
% 4.97/5.15 tff(27782,plain,
% 4.97/5.15 ((s(s(z)) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(z)))))),
% 4.97/5.15 inference(monotonicity,[status(thm)],[27775])).
% 4.97/5.15 tff(27783,plain,
% 4.97/5.15 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 4.97/5.15 inference(transitivity,[status(thm)],[27782, 321])).
% 4.97/5.15 tff(27784,plain,
% 4.97/5.15 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 4.97/5.15 inference(monotonicity,[status(thm)],[27783])).
% 4.97/5.15 tff(27785,plain,
% 4.97/5.15 (~(s(s(s(s(z)))) = elem!1)),
% 4.97/5.15 inference(modus_ponens,[status(thm)],[159, 27784])).
% 4.97/5.15 tff(27786,plain,
% 4.97/5.15 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[3502, 27785])).
% 4.97/5.15 tff(27787,plain,
% 4.97/5.15 (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[8403, 27786])).
% 4.97/5.15 tff(27788,plain,
% 4.97/5.15 (elem!1 = s(s(z))),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[3230, 27775])).
% 4.97/5.15 tff(27789,plain,
% 4.97/5.15 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 4.97/5.15 inference(monotonicity,[status(thm)],[27775])).
% 4.97/5.15 tff(27790,plain,
% 4.97/5.15 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 4.97/5.15 inference(transitivity,[status(thm)],[27789, 1526])).
% 4.97/5.15 tff(27791,plain,
% 4.97/5.15 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 4.97/5.15 inference(transitivity,[status(thm)],[27790, 2486])).
% 4.97/5.15 tff(27792,plain,
% 4.97/5.15 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 4.97/5.15 inference(monotonicity,[status(thm)],[27791])).
% 4.97/5.15 tff(27793,plain,
% 4.97/5.15 (~(elem!1 = s(s(s(elem!1))))),
% 4.97/5.15 inference(modus_ponens,[status(thm)],[1683, 27792])).
% 4.97/5.15 tff(27794,plain,
% 4.97/5.15 (r(z, elem!1)),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[7053, 27775, 3261])).
% 4.97/5.15 tff(27795,plain,
% 4.97/5.15 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 4.97/5.15 inference(monotonicity,[status(thm)],[27790])).
% 4.97/5.15 tff(27796,plain,
% 4.97/5.15 (~(s(s(s(elem!1))) = elem!1)),
% 4.97/5.15 inference(modus_ponens,[status(thm)],[1683, 27795])).
% 4.97/5.15 tff(27797,plain,
% 4.97/5.15 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 4.97/5.15 inference(monotonicity,[status(thm)],[27775])).
% 4.97/5.15 tff(27798,plain,
% 4.97/5.15 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 4.97/5.15 inference(transitivity,[status(thm)],[27797, 3660])).
% 4.97/5.15 tff(27799,plain,
% 4.97/5.15 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = elem!1))),
% 4.97/5.15 inference(monotonicity,[status(thm)],[27798])).
% 4.97/5.15 tff(27800,plain,
% 4.97/5.15 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 4.97/5.15 inference(modus_ponens,[status(thm)],[244, 27799])).
% 4.97/5.15 tff(27801,plain,
% 4.97/5.15 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.97/5.15 inference(monotonicity,[status(thm)],[27775])).
% 4.97/5.15 tff(27802,plain,
% 4.97/5.15 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[3891, 103, 1130])).
% 4.97/5.15 tff(27803,plain,
% 4.97/5.15 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[3578, 27802])).
% 4.97/5.15 tff(27804,plain,
% 4.97/5.15 (~r(s(s(z)), z)),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[232, 224, 203])).
% 4.97/5.15 tff(27805,plain,
% 4.97/5.15 (b(s(s(z)), z)),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[3249, 27804])).
% 4.97/5.15 tff(27806,plain,
% 4.97/5.15 (~r(z, s(s(s(s(z)))))),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[4843, 1130, 203])).
% 4.97/5.15 tff(27807,plain,
% 4.97/5.15 (b(z, s(s(s(s(z)))))),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[46, 27806])).
% 4.97/5.15 tff(27808,plain,
% 4.97/5.15 (~r(s(s(z)), s(s(s(s(z)))))),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[27221, 224, 1130])).
% 4.97/5.15 tff(27809,plain,
% 4.97/5.15 (b(s(s(z)), s(s(s(s(z)))))),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[164, 27808])).
% 4.97/5.15 tff(27810,plain,
% 4.97/5.15 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[12409, 27809, 27807, 27805, 1146])).
% 4.97/5.15 tff(27811,plain,
% 4.97/5.15 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[133, 27810])).
% 4.97/5.15 tff(27812,plain,
% 4.97/5.15 (~r(z, s(s(z)))),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[4690, 224, 203])).
% 4.97/5.15 tff(27813,plain,
% 4.97/5.15 (b(z, s(s(z)))),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[143, 27812])).
% 4.97/5.15 tff(27814,plain,
% 4.97/5.15 (~b(s(s(s(s(z)))), z)),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[21653, 27809, 27805, 27813, 27807])).
% 4.97/5.15 tff(27815,plain,
% 4.97/5.15 (r(s(s(s(s(z)))), z)),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[191, 27814])).
% 4.97/5.15 tff(27816,plain,
% 4.97/5.15 ($false),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[5581, 118, 1130, 27815, 27811])).
% 4.97/5.15 tff(27817,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.97/5.15 tff(27818,plain,
% 4.97/5.15 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[27817, 27803, 1130, 203])).
% 4.97/5.15 tff(27819,plain,
% 4.97/5.15 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[249, 27818])).
% 4.97/5.15 tff(27820,plain,
% 4.97/5.15 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.97/5.15 inference(modus_ponens,[status(thm)],[27819, 27801])).
% 4.97/5.15 tff(27821,plain,
% 4.97/5.15 ((s(elem!1) = s(s(z))) <=> (s(elem!1) = elem!1)),
% 4.97/5.15 inference(monotonicity,[status(thm)],[27775])).
% 4.97/5.15 tff(27822,plain,
% 4.97/5.15 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(z)))),
% 4.97/5.15 inference(symmetry,[status(thm)],[27821])).
% 4.97/5.15 tff(27823,plain,
% 4.97/5.15 ((elem!1 = s(s(s(z)))) <=> (elem!1 = s(elem!1))),
% 4.97/5.15 inference(monotonicity,[status(thm)],[27776])).
% 4.97/5.15 tff(27824,plain,
% 4.97/5.15 ((elem!1 = s(s(s(z)))) <=> (s(elem!1) = elem!1)),
% 4.97/5.15 inference(transitivity,[status(thm)],[27823, 3190])).
% 4.97/5.15 tff(27825,plain,
% 4.97/5.15 ((elem!1 = s(s(s(z)))) <=> (s(elem!1) = s(s(z)))),
% 4.97/5.15 inference(transitivity,[status(thm)],[27824, 27822])).
% 4.97/5.15 tff(27826,plain,
% 4.97/5.15 ((~(elem!1 = s(s(s(z))))) <=> (~(s(elem!1) = s(s(z))))),
% 4.97/5.15 inference(monotonicity,[status(thm)],[27825])).
% 4.97/5.15 tff(27827,plain,
% 4.97/5.15 ((s(s(z)) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 4.97/5.15 inference(monotonicity,[status(thm)],[27775])).
% 4.97/5.15 tff(27828,plain,
% 4.97/5.15 ((~(s(s(z)) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 4.97/5.15 inference(monotonicity,[status(thm)],[27827])).
% 4.97/5.15 tff(27829,plain,
% 4.97/5.15 (~(elem!1 = s(s(s(z))))),
% 4.97/5.15 inference(modus_ponens,[status(thm)],[3205, 27828])).
% 4.97/5.15 tff(27830,plain,
% 4.97/5.15 (~(s(elem!1) = s(s(z)))),
% 4.97/5.15 inference(modus_ponens,[status(thm)],[27829, 27826])).
% 4.97/5.15 tff(27831,plain,
% 4.97/5.15 (b(s(s(z)), s(s(s(s(z)))))),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[14046, 126, 193, 3261, 3575, 5618, 1056])).
% 4.97/5.15 tff(27832,plain,
% 4.97/5.15 ($false),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[12409, 27831, 13774, 1687, 3461, 15269])).
% 4.97/5.15 tff(27833,plain,(r(s(s(s(s(s(s(s(z))))))), z) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | r(s(s(s(s(s(s(s(z))))))), s(s(z))) | r(s(s(z)), z) | (s(elem!1) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.97/5.15 tff(27834,plain,
% 4.97/5.15 (r(s(s(s(s(s(s(s(z))))))), z)),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[27833, 5618, 3461, 103, 3261, 27802, 27807, 27830])).
% 4.97/5.15 tff(27835,plain,
% 4.97/5.15 (~r(z, s(s(s(elem!1))))),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[17868, 27834, 27820, 27800, 27796, 27794, 27786, 27793])).
% 4.97/5.15 tff(27836,plain,
% 4.97/5.15 (b(z, s(s(s(elem!1))))),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[2095, 27835])).
% 4.97/5.15 tff(27837,plain,
% 4.97/5.15 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.97/5.15 inference(monotonicity,[status(thm)],[7077])).
% 4.97/5.15 tff(27838,plain,
% 4.97/5.15 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 4.97/5.15 inference(symmetry,[status(thm)],[27837])).
% 4.97/5.15 tff(27839,plain,
% 4.97/5.15 ((s(elem!1) = s(s(z))) <=> (s(s(s(z))) = s(s(z)))),
% 4.97/5.15 inference(monotonicity,[status(thm)],[5636])).
% 4.97/5.15 tff(27840,plain,
% 4.97/5.15 ((s(elem!1) = s(s(z))) <=> (s(s(z)) = s(s(s(z))))),
% 4.97/5.15 inference(transitivity,[status(thm)],[27839, 3003])).
% 4.97/5.15 tff(27841,plain,
% 4.97/5.15 ((s(s(z)) = s(s(s(z)))) <=> (s(elem!1) = s(s(z)))),
% 4.97/5.15 inference(symmetry,[status(thm)],[27840])).
% 4.97/5.15 tff(27842,plain,
% 4.97/5.15 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(z))))),
% 4.97/5.15 inference(monotonicity,[status(thm)],[27841])).
% 4.97/5.15 tff(27843,plain,
% 4.97/5.15 (~(s(elem!1) = s(s(z)))),
% 4.97/5.15 inference(modus_ponens,[status(thm)],[3205, 27842])).
% 4.97/5.15 tff(27844,plain,
% 4.97/5.15 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[2840, 27843])).
% 4.97/5.15 tff(27845,plain,
% 4.97/5.15 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(s(z))))), z)),
% 4.97/5.15 inference(monotonicity,[status(thm)],[7074])).
% 4.97/5.15 tff(27846,plain,
% 4.97/5.15 (r(s(s(s(s(s(z))))), z) <=> r(s(s(s(elem!1))), z)),
% 4.97/5.15 inference(symmetry,[status(thm)],[27845])).
% 4.97/5.15 tff(27847,plain,
% 4.97/5.15 ((~r(s(s(s(s(s(z))))), z)) <=> (~r(s(s(s(elem!1))), z))),
% 4.97/5.15 inference(monotonicity,[status(thm)],[27846])).
% 4.97/5.15 tff(27848,plain,
% 4.97/5.15 (~r(s(s(s(s(s(z))))), z)),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[15071, 118, 203, 23855])).
% 4.97/5.15 tff(27849,plain,
% 4.97/5.15 (~r(s(s(s(elem!1))), z)),
% 4.97/5.15 inference(modus_ponens,[status(thm)],[27848, 27847])).
% 4.97/5.15 tff(27850,plain,
% 4.97/5.15 (b(s(s(s(elem!1))), z)),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[1565, 27849])).
% 4.97/5.15 tff(27851,plain,
% 4.97/5.15 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[22234, 27850, 27807, 168, 2043])).
% 4.97/5.15 tff(27852,plain,
% 4.97/5.15 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[4173, 27851, 27844])).
% 4.97/5.15 tff(27853,plain,
% 4.97/5.15 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 4.97/5.15 inference(modus_ponens,[status(thm)],[27852, 27838])).
% 4.97/5.15 tff(27854,plain,
% 4.97/5.15 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 4.97/5.15 inference(rewrite,[status(thm)],[])).
% 4.97/5.15 tff(27855,plain,
% 4.97/5.15 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 4.97/5.15 inference(rewrite,[status(thm)],[])).
% 4.97/5.15 tff(27856,plain,
% 4.97/5.15 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 4.97/5.15 inference(monotonicity,[status(thm)],[27855])).
% 4.97/5.15 tff(27857,plain,
% 4.97/5.15 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 4.97/5.15 inference(transitivity,[status(thm)],[27856, 27854])).
% 4.97/5.15 tff(27858,plain,
% 4.97/5.15 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 4.97/5.15 inference(quant_inst,[status(thm)],[])).
% 4.97/5.15 tff(27859,plain,
% 4.97/5.15 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 4.97/5.15 inference(modus_ponens,[status(thm)],[27858, 27857])).
% 4.97/5.15 tff(27860,plain,
% 4.97/5.15 ($false),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[27859, 118, 1130, 27853, 23855])).
% 4.97/5.15 tff(27861,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~(elem!1 = s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.97/5.15 tff(27862,plain,
% 4.97/5.15 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[27861, 27836, 1130, 14646, 27788, 203])).
% 4.97/5.15 tff(27863,plain,
% 4.97/5.15 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 4.97/5.15 inference(monotonicity,[status(thm)],[3506])).
% 4.97/5.15 tff(27864,plain,
% 4.97/5.15 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.15 inference(monotonicity,[status(thm)],[27863])).
% 4.97/5.15 tff(27865,plain,
% 4.97/5.15 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.15 inference(symmetry,[status(thm)],[27864])).
% 4.97/5.15 tff(27866,plain,
% 4.97/5.15 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.15 inference(modus_ponens,[status(thm)],[3615, 27865])).
% 4.97/5.15 tff(27867,plain,
% 4.97/5.15 ($false),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[18755, 27866])).
% 4.97/5.15 tff(27868,plain,((~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) | (~(s(s(z)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.97/5.15 tff(27869,plain,
% 4.97/5.15 (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[27868, 27862, 27775])).
% 4.97/5.15 tff(27870,plain,
% 4.97/5.15 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[3612, 41, 27869, 27787])).
% 4.97/5.15 tff(27871,plain,
% 4.97/5.15 (b(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.97/5.15 inference(monotonicity,[status(thm)],[27775])).
% 4.97/5.15 tff(27872,plain,
% 4.97/5.15 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.97/5.15 inference(modus_ponens,[status(thm)],[27803, 27871])).
% 4.97/5.15 tff(27873,plain,
% 4.97/5.15 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 4.97/5.15 inference(monotonicity,[status(thm)],[27776])).
% 4.97/5.15 tff(27874,plain,
% 4.97/5.15 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 4.97/5.15 inference(transitivity,[status(thm)],[27873, 3881])).
% 4.97/5.15 tff(27875,plain,
% 4.97/5.15 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 4.97/5.15 inference(monotonicity,[status(thm)],[27874])).
% 4.97/5.15 tff(27876,plain,
% 4.97/5.15 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.97/5.15 inference(modus_ponens,[status(thm)],[8686, 27875])).
% 4.97/5.15 tff(27877,plain,
% 4.97/5.15 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[1649, 27876])).
% 4.97/5.15 tff(27878,plain,
% 4.97/5.15 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 4.97/5.15 inference(monotonicity,[status(thm)],[27777])).
% 4.97/5.15 tff(27879,plain,
% 4.97/5.15 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(z)))), elem!1)),
% 4.97/5.15 inference(monotonicity,[status(thm)],[27775])).
% 4.97/5.15 tff(27880,plain,
% 4.97/5.15 (r(s(s(s(s(z)))), elem!1)),
% 4.97/5.15 inference(modus_ponens,[status(thm)],[103, 27879])).
% 4.97/5.15 tff(27881,plain,
% 4.97/5.15 (r(s(s(elem!1)), elem!1)),
% 4.97/5.15 inference(modus_ponens,[status(thm)],[27880, 27878])).
% 4.97/5.15 tff(27882,plain,
% 4.97/5.15 (~r(s(s(s(elem!1))), elem!1)),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[23717, 27881, 27794, 27877])).
% 4.97/5.15 tff(27883,plain,
% 4.97/5.15 (b(s(s(s(elem!1))), elem!1)),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[570, 27882, 27796])).
% 4.97/5.15 tff(27884,plain,
% 4.97/5.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 4.97/5.15 inference(rewrite,[status(thm)],[])).
% 4.97/5.15 tff(27885,plain,
% 4.97/5.15 (((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(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))), 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(s(s(s(s(z))))))), 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(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 4.97/5.15 inference(rewrite,[status(thm)],[])).
% 4.97/5.15 tff(27886,plain,
% 4.97/5.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(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))), 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(s(s(s(s(z))))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))))),
% 4.97/5.15 inference(monotonicity,[status(thm)],[27885])).
% 4.97/5.15 tff(27887,plain,
% 4.97/5.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(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))), 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(s(s(s(s(z))))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 4.97/5.15 inference(transitivity,[status(thm)],[27886, 27884])).
% 4.97/5.15 tff(27888,plain,
% 4.97/5.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(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))), 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(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 4.97/5.15 inference(quant_inst,[status(thm)],[])).
% 4.97/5.15 tff(27889,plain,
% 4.97/5.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 4.97/5.15 inference(modus_ponens,[status(thm)],[27888, 27887])).
% 4.97/5.15 tff(27890,plain,
% 4.97/5.15 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[27889, 178, 27883, 27820, 27872, 27870])).
% 4.97/5.15 tff(27891,plain,
% 4.97/5.15 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[5118, 27890, 27786])).
% 4.97/5.15 tff(27892,plain,
% 4.97/5.15 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[3404, 27877])).
% 4.97/5.15 tff(27893,plain,
% 4.97/5.15 (b(s(s(s(s(z)))), z) <=> b(s(s(elem!1)), z)),
% 4.97/5.15 inference(monotonicity,[status(thm)],[27777])).
% 4.97/5.15 tff(27894,plain,
% 4.97/5.15 (b(s(s(elem!1)), z)),
% 4.97/5.15 inference(modus_ponens,[status(thm)],[14646, 27893])).
% 4.97/5.15 tff(27895,plain,
% 4.97/5.15 (b(z, s(s(s(s(z))))) <=> b(z, s(s(elem!1)))),
% 4.97/5.15 inference(monotonicity,[status(thm)],[27777])).
% 4.97/5.15 tff(27896,plain,
% 4.97/5.15 (b(z, s(s(elem!1)))),
% 4.97/5.15 inference(modus_ponens,[status(thm)],[27807, 27895])).
% 4.97/5.15 tff(27897,plain,
% 4.97/5.15 ((s(s(elem!1)) = s(s(z))) <=> (s(s(elem!1)) = elem!1)),
% 4.97/5.15 inference(monotonicity,[status(thm)],[27775])).
% 4.97/5.15 tff(27898,plain,
% 4.97/5.15 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(elem!1)) = elem!1))),
% 4.97/5.15 inference(monotonicity,[status(thm)],[27897])).
% 4.97/5.15 tff(27899,plain,
% 4.97/5.15 (~(s(s(elem!1)) = elem!1)),
% 4.97/5.15 inference(modus_ponens,[status(thm)],[2484, 27898])).
% 4.97/5.15 tff(27900,plain,
% 4.97/5.15 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 4.97/5.15 inference(monotonicity,[status(thm)],[27777])).
% 4.97/5.15 tff(27901,plain,
% 4.97/5.15 ((~b(s(s(s(s(z)))), elem!1)) <=> (~b(s(s(elem!1)), elem!1))),
% 4.97/5.15 inference(monotonicity,[status(thm)],[27900])).
% 4.97/5.15 tff(27902,plain,
% 4.97/5.15 (~b(s(s(s(s(z)))), elem!1)),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[3774, 27775, 86])).
% 4.97/5.15 tff(27903,plain,
% 4.97/5.15 (~b(s(s(elem!1)), elem!1)),
% 4.97/5.15 inference(modus_ponens,[status(thm)],[27902, 27901])).
% 4.97/5.15 tff(27904,plain,
% 4.97/5.15 ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[25419, 178, 27883, 27820, 27872])).
% 4.97/5.15 tff(27905,plain,
% 4.97/5.15 (~b(elem!1, s(s(s(elem!1))))),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[27904, 27870])).
% 4.97/5.15 tff(27906,plain,
% 4.97/5.15 (r(elem!1, s(s(s(elem!1))))),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[2054, 27905, 27793])).
% 4.97/5.15 tff(27907,plain,
% 4.97/5.15 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[3377, 27906, 27903, 27899])).
% 4.97/5.15 tff(27908,plain,
% 4.97/5.15 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[18614, 27907, 27896, 27836, 27894])).
% 4.97/5.15 tff(27909,plain,
% 4.97/5.15 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[3409, 27908, 27892])).
% 4.97/5.15 tff(27910,plain,
% 4.97/5.15 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(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(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(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(s(s(elem!1))))))),
% 4.97/5.15 inference(rewrite,[status(thm)],[])).
% 4.97/5.15 tff(27911,plain,
% 4.97/5.15 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(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(s(s(elem!1))))))),
% 4.97/5.15 inference(quant_inst,[status(thm)],[])).
% 4.97/5.15 tff(27912,plain,
% 4.97/5.15 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 4.97/5.15 inference(modus_ponens,[status(thm)],[27911, 27910])).
% 4.97/5.15 tff(27913,plain,
% 4.97/5.15 ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[27912, 118, 27909])).
% 4.97/5.15 tff(27914,plain,
% 4.97/5.15 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[27913, 27891])).
% 4.97/5.15 tff(27915,plain,
% 4.97/5.15 ($false),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[27914, 27781])).
% 4.97/5.15 tff(27916,plain,(r(s(s(z)), z) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~r(z, s(s(z)))) | (s(s(elem!1)) = s(s(z))) | b(s(s(s(s(z)))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 4.97/5.15 tff(27917,plain,
% 4.97/5.15 (r(s(s(z)), z)),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[27916, 3340, 4236, 3461, 3261, 1130, 86])).
% 4.97/5.15 tff(27918,plain,
% 4.97/5.15 (~r(z, s(s(s(s(z)))))),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[4843, 1130, 4236])).
% 4.97/5.15 tff(27919,plain,
% 4.97/5.15 (b(z, s(s(s(s(z)))))),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[46, 27918])).
% 4.97/5.15 tff(27920,plain,
% 4.97/5.15 (~r(elem!1, z)),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[443, 4256, 106])).
% 4.97/5.15 tff(27921,plain,
% 4.97/5.15 (b(elem!1, z)),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[498, 27920, 290])).
% 4.97/5.15 tff(27922,plain,
% 4.97/5.15 (~r(z, elem!1)),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[541, 4256, 106])).
% 4.97/5.15 tff(27923,plain,
% 4.97/5.15 (b(z, elem!1)),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[585, 27922, 318])).
% 4.97/5.15 tff(27924,plain,
% 4.97/5.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 4.97/5.15 inference(rewrite,[status(thm)],[])).
% 4.97/5.15 tff(27925,plain,
% 4.97/5.15 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 4.97/5.15 inference(rewrite,[status(thm)],[])).
% 4.97/5.15 tff(27926,plain,
% 4.97/5.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z))))))))),
% 4.97/5.15 inference(monotonicity,[status(thm)],[27925])).
% 4.97/5.15 tff(27927,plain,
% 4.97/5.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 4.97/5.15 inference(transitivity,[status(thm)],[27926, 27924])).
% 4.97/5.15 tff(27928,plain,
% 4.97/5.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 4.97/5.15 inference(quant_inst,[status(thm)],[])).
% 4.97/5.15 tff(27929,plain,
% 4.97/5.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z))))))),
% 4.97/5.15 inference(modus_ponens,[status(thm)],[27928, 27927])).
% 4.97/5.15 tff(27930,plain,
% 4.97/5.15 (~b(s(s(s(s(z)))), elem!1)),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[27929, 178, 27923, 27921, 27919, 11753])).
% 4.97/5.15 tff(27931,plain,
% 4.97/5.15 (s(s(s(s(z)))) = elem!1),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[3142, 27930, 8765])).
% 4.97/5.15 tff(27932,plain,
% 4.97/5.15 (elem!1 = s(s(s(s(z))))),
% 4.97/5.15 inference(unit_resolution,[status(thm)],[504, 27931])).
% 4.97/5.15 tff(27933,plain,
% 4.97/5.15 (s(s(s(s(s(z))))) = s(elem!1)),
% 4.97/5.15 inference(monotonicity,[status(thm)],[27931])).
% 4.97/5.15 tff(27934,plain,
% 4.97/5.15 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 4.97/5.15 inference(monotonicity,[status(thm)],[27933])).
% 4.97/5.15 tff(27935,plain,
% 4.97/5.15 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 4.97/5.15 inference(monotonicity,[status(thm)],[27934])).
% 4.97/5.15 tff(27936,plain,
% 4.97/5.15 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 4.97/5.15 inference(symmetry,[status(thm)],[27935])).
% 4.97/5.15 tff(27937,plain,
% 4.97/5.15 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 4.97/5.15 inference(monotonicity,[status(thm)],[27936])).
% 4.97/5.15 tff(27938,plain,
% 4.97/5.15 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.97/5.15 inference(transitivity,[status(thm)],[27937, 377])).
% 4.97/5.15 tff(27939,plain,
% 4.97/5.15 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 4.97/5.15 inference(monotonicity,[status(thm)],[27938])).
% 4.97/5.15 tff(27940,plain,
% 4.97/5.16 (~(s(s(elem!1)) = elem!1)),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[338, 27931, 12])).
% 4.97/5.16 tff(27941,plain,
% 4.97/5.16 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[348, 27940])).
% 4.97/5.16 tff(27942,plain,
% 4.97/5.16 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.97/5.16 inference(modus_ponens,[status(thm)],[27941, 27939])).
% 4.97/5.16 tff(27943,plain,
% 4.97/5.16 (~(s(elem!1) = s(s(z)))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[11438, 27932])).
% 4.97/5.16 tff(27944,plain,
% 4.97/5.16 (~(s(elem!1) = elem!1)),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[672, 27940])).
% 4.97/5.16 tff(27945,plain,
% 4.97/5.16 (r(s(s(s(s(z)))), s(s(z))) <=> r(elem!1, s(s(z)))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[27931])).
% 4.97/5.16 tff(27946,plain,
% 4.97/5.16 (r(elem!1, s(s(z)))),
% 4.97/5.16 inference(modus_ponens,[status(thm)],[193, 27945])).
% 4.97/5.16 tff(27947,plain,
% 4.97/5.16 (~r(s(elem!1), s(s(z)))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[17418, 27946, 106, 27921, 27923, 27944])).
% 4.97/5.16 tff(27948,plain,
% 4.97/5.16 (b(s(elem!1), s(s(z)))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[421, 27947, 27943])).
% 4.97/5.16 tff(27949,plain,
% 4.97/5.16 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.97/5.16 inference(monotonicity,[status(thm)],[27931])).
% 4.97/5.16 tff(27950,plain,
% 4.97/5.16 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.97/5.16 inference(modus_ponens,[status(thm)],[1130, 27949])).
% 4.97/5.16 tff(27951,plain,
% 4.97/5.16 (~(s(s(z)) = s(elem!1))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[1058, 27943])).
% 4.97/5.16 tff(27952,plain,
% 4.97/5.16 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(z)), elem!1)),
% 4.97/5.16 inference(monotonicity,[status(thm)],[27931])).
% 4.97/5.16 tff(27953,plain,
% 4.97/5.16 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(s(s(z)))))),
% 4.97/5.16 inference(symmetry,[status(thm)],[27952])).
% 4.97/5.16 tff(27954,plain,
% 4.97/5.16 (r(s(s(z)), s(s(s(s(z)))))),
% 4.97/5.16 inference(modus_ponens,[status(thm)],[4256, 27953])).
% 4.97/5.16 tff(27955,plain,
% 4.97/5.16 (~(elem!1 = s(elem!1))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[748, 27944])).
% 4.97/5.16 tff(27956,plain,
% 4.97/5.16 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 4.97/5.16 inference(monotonicity,[status(thm)],[27935])).
% 4.97/5.16 tff(27957,plain,
% 4.97/5.16 (r(s(s(s(elem!1))), elem!1)),
% 4.97/5.16 inference(modus_ponens,[status(thm)],[27950, 27956])).
% 4.97/5.16 tff(27958,plain,
% 4.97/5.16 (~r(s(elem!1), elem!1)),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[12991, 27954, 4256, 27941, 27957])).
% 4.97/5.16 tff(27959,plain,
% 4.97/5.16 (b(s(elem!1), elem!1)),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[677, 27958, 27944])).
% 4.97/5.16 tff(27960,plain,
% 4.97/5.16 ($false),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[1396, 12627, 18730, 506, 818, 683])).
% 4.97/5.16 tff(27961,plain,((~r(s(s(z)), s(elem!1))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (elem!1 = s(elem!1)) | (~r(z, s(s(z)))) | (~(elem!1 = s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.97/5.16 tff(27962,plain,
% 4.97/5.16 (~r(s(s(z)), s(elem!1))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[27961, 27959, 27923, 27921, 27955, 3261, 27932, 27954])).
% 4.97/5.16 tff(27963,plain,
% 4.97/5.16 (b(s(s(z)), s(elem!1))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[1067, 27962, 27951])).
% 4.97/5.16 tff(27964,plain,
% 4.97/5.16 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[2979, 27963, 4256, 27950, 27948])).
% 4.97/5.16 tff(27965,plain,
% 4.97/5.16 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[395, 27964, 27942])).
% 4.97/5.16 tff(27966,plain,
% 4.97/5.16 (r(s(elem!1), s(s(s(elem!1))))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[14608, 27965, 27932])).
% 4.97/5.16 tff(27967,plain,
% 4.97/5.16 (~b(z, s(s(s(elem!1))))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[11477, 27932, 4235])).
% 4.97/5.16 tff(27968,plain,
% 4.97/5.16 (r(z, s(s(s(elem!1))))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[2095, 27967])).
% 4.97/5.16 tff(27969,plain,
% 4.97/5.16 ((s(s(s(s(z)))) = s(elem!1)) <=> (elem!1 = s(elem!1))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[27931])).
% 4.97/5.16 tff(27970,plain,
% 4.97/5.16 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(elem!1) = elem!1)),
% 4.97/5.16 inference(transitivity,[status(thm)],[27969, 3190])).
% 4.97/5.16 tff(27971,plain,
% 4.97/5.16 ((s(elem!1) = elem!1) <=> (s(s(s(s(z)))) = s(elem!1))),
% 4.97/5.16 inference(symmetry,[status(thm)],[27970])).
% 4.97/5.16 tff(27972,plain,
% 4.97/5.16 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(s(s(z)))))),
% 4.97/5.16 inference(transitivity,[status(thm)],[27971, 2164])).
% 4.97/5.16 tff(27973,plain,
% 4.97/5.16 ((~(s(elem!1) = elem!1)) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[27972])).
% 4.97/5.16 tff(27974,plain,
% 4.97/5.16 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.97/5.16 inference(modus_ponens,[status(thm)],[27944, 27973])).
% 4.97/5.16 tff(27975,plain,
% 4.97/5.16 (~r(s(elem!1), s(s(s(s(z)))))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[5568, 27965, 1130])).
% 4.97/5.16 tff(27976,plain,
% 4.97/5.16 (b(s(elem!1), s(s(s(s(z)))))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[1084, 27975, 27974])).
% 4.97/5.16 tff(27977,plain,
% 4.97/5.16 (~b(s(elem!1), z)),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[13803, 27976, 27919, 3261, 3461, 11753, 27951, 27948])).
% 4.97/5.16 tff(27978,plain,
% 4.97/5.16 (r(s(elem!1), z)),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[774, 27977])).
% 4.97/5.16 tff(27979,plain,
% 4.97/5.16 ($false),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[11560, 118, 27978, 27968, 27966])).
% 4.97/5.16 tff(27980,plain,((s(s(z)) = elem!1) | (~r(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | b(z, s(s(s(s(s(s(s(z)))))))) | (elem!1 = z) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 4.97/5.16 tff(27981,plain,
% 4.97/5.16 (s(s(z)) = elem!1),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[27980, 27917, 3461, 1130, 3261, 103, 4235, 290, 3241])).
% 4.97/5.16 tff(27982,plain,
% 4.97/5.16 ((s(s(z)) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(z)))))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[27981])).
% 4.97/5.16 tff(27983,plain,
% 4.97/5.16 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 4.97/5.16 inference(transitivity,[status(thm)],[27982, 321])).
% 4.97/5.16 tff(27984,plain,
% 4.97/5.16 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[27983])).
% 4.97/5.16 tff(27985,plain,
% 4.97/5.16 (~(s(s(s(s(z)))) = elem!1)),
% 4.97/5.16 inference(modus_ponens,[status(thm)],[159, 27984])).
% 4.97/5.16 tff(27986,plain,
% 4.97/5.16 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[3502, 27985])).
% 4.97/5.16 tff(27987,plain,
% 4.97/5.16 (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[8403, 27986])).
% 4.97/5.16 tff(27988,plain,
% 4.97/5.16 (s(s(s(z))) = s(elem!1)),
% 4.97/5.16 inference(monotonicity,[status(thm)],[27981])).
% 4.97/5.16 tff(27989,plain,
% 4.97/5.16 (s(s(s(s(z)))) = s(s(elem!1))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[27988])).
% 4.97/5.16 tff(27990,plain,
% 4.97/5.16 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[27989])).
% 4.97/5.16 tff(27991,plain,
% 4.97/5.16 (r(z, s(s(s(s(s(z)))))) <=> r(z, s(s(s(elem!1))))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[27990])).
% 4.97/5.16 tff(27992,plain,
% 4.97/5.16 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(s(z))))))),
% 4.97/5.16 inference(symmetry,[status(thm)],[27991])).
% 4.97/5.16 tff(27993,plain,
% 4.97/5.16 (~b(elem!1, s(s(z)))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[3223, 27981])).
% 4.97/5.16 tff(27994,plain,
% 4.97/5.16 (~(elem!1 = s(s(s(s(z)))))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[11477, 2043, 4235])).
% 4.97/5.16 tff(27995,plain,
% 4.97/5.16 (r(s(s(z)), elem!1)),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[448, 23423, 3241])).
% 4.97/5.16 tff(27996,plain,
% 4.97/5.16 (~r(z, elem!1)),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[541, 27995, 106])).
% 4.97/5.16 tff(27997,plain,
% 4.97/5.16 (b(z, elem!1)),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[585, 27996, 318])).
% 4.97/5.16 tff(27998,plain,
% 4.97/5.16 (~r(s(s(s(s(z)))), elem!1)),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[3329, 27995, 193])).
% 4.97/5.16 tff(27999,plain,
% 4.97/5.16 (b(s(s(s(s(z)))), elem!1)),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[3142, 27998, 551])).
% 4.97/5.16 tff(28000,plain,
% 4.97/5.16 (~(elem!1 = s(s(z)))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[311, 23423])).
% 4.97/5.16 tff(28001,plain,
% 4.97/5.16 (r(elem!1, s(s(z)))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[467, 28000, 461])).
% 4.97/5.16 tff(28002,plain,
% 4.97/5.16 (~r(elem!1, s(s(s(s(z)))))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[3785, 28001, 193])).
% 4.97/5.16 tff(28003,plain,
% 4.97/5.16 (b(elem!1, s(s(s(s(z)))))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[483, 28002, 469])).
% 4.97/5.16 tff(28004,plain,
% 4.97/5.16 ($false),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[7020, 28003, 27999, 1687, 5284, 27997])).
% 4.97/5.16 tff(28005,plain,(r(elem!1, z) | (~b(z, s(s(s(s(z)))))) | (elem!1 = s(s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), z)) | b(elem!1, s(s(z))) | b(s(s(z)), elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 4.97/5.16 tff(28006,plain,
% 4.97/5.16 (r(elem!1, z)),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[28005, 27994, 27919, 103, 106, 461, 3241, 290])).
% 4.97/5.16 tff(28007,plain,
% 4.97/5.16 (~r(elem!1, s(s(z)))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[8416, 28006, 3261])).
% 4.97/5.16 tff(28008,plain,
% 4.97/5.16 (elem!1 = s(s(z))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[467, 28007, 461])).
% 4.97/5.16 tff(28009,plain,
% 4.97/5.16 (s(elem!1) = s(s(s(z)))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[28008])).
% 4.97/5.16 tff(28010,plain,
% 4.97/5.16 (s(s(elem!1)) = s(s(s(s(z))))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[28009])).
% 4.97/5.16 tff(28011,plain,
% 4.97/5.16 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[28010])).
% 4.97/5.16 tff(28012,plain,
% 4.97/5.16 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(s(s(z))))))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[28011])).
% 4.97/5.16 tff(28013,plain,
% 4.97/5.16 (b(z, s(s(s(s(s(z))))))),
% 4.97/5.16 inference(modus_ponens,[status(thm)],[2043, 28012])).
% 4.97/5.16 tff(28014,plain,
% 4.97/5.16 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(s(z))))), z)),
% 4.97/5.16 inference(monotonicity,[status(thm)],[28011])).
% 4.97/5.16 tff(28015,plain,
% 4.97/5.16 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = s(s(z)))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[28008])).
% 4.97/5.16 tff(28016,plain,
% 4.97/5.16 ((s(s(s(elem!1))) = elem!1) <=> (s(s(z)) = s(s(s(elem!1))))),
% 4.97/5.16 inference(transitivity,[status(thm)],[28015, 7921])).
% 4.97/5.16 tff(28017,plain,
% 4.97/5.16 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 4.97/5.16 inference(symmetry,[status(thm)],[28016])).
% 4.97/5.16 tff(28018,plain,
% 4.97/5.16 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 4.97/5.16 inference(transitivity,[status(thm)],[28017, 2486])).
% 4.97/5.16 tff(28019,plain,
% 4.97/5.16 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[28018])).
% 4.97/5.16 tff(28020,plain,
% 4.97/5.16 (~(elem!1 = s(s(s(elem!1))))),
% 4.97/5.16 inference(modus_ponens,[status(thm)],[1683, 28019])).
% 4.97/5.16 tff(28021,plain,
% 4.97/5.16 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[28008])).
% 4.97/5.16 tff(28022,plain,
% 4.97/5.16 (b(s(s(z)), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 4.97/5.16 inference(symmetry,[status(thm)],[28021])).
% 4.97/5.16 tff(28023,plain,
% 4.97/5.16 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 4.97/5.16 inference(symmetry,[status(thm)],[28011])).
% 4.97/5.16 tff(28024,plain,
% 4.97/5.16 (b(s(s(z)), s(s(s(s(s(z)))))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[28023])).
% 4.97/5.16 tff(28025,plain,
% 4.97/5.16 (b(s(s(z)), s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(elem!1))))),
% 4.97/5.16 inference(transitivity,[status(thm)],[28024, 28022])).
% 4.97/5.16 tff(28026,plain,
% 4.97/5.16 ((~b(s(s(z)), s(s(s(s(s(z))))))) <=> (~b(elem!1, s(s(s(elem!1)))))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[28025])).
% 4.97/5.16 tff(28027,plain,
% 4.97/5.16 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[28023])).
% 4.97/5.16 tff(28028,plain,
% 4.97/5.16 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 4.97/5.16 inference(symmetry,[status(thm)],[28027])).
% 4.97/5.16 tff(28029,plain,
% 4.97/5.16 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(z)))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[28008])).
% 4.97/5.16 tff(28030,plain,
% 4.97/5.16 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 4.97/5.16 inference(transitivity,[status(thm)],[28029, 28028])).
% 4.97/5.16 tff(28031,plain,
% 4.97/5.16 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[28017])).
% 4.97/5.16 tff(28032,plain,
% 4.97/5.16 (~(s(s(s(elem!1))) = elem!1)),
% 4.97/5.16 inference(modus_ponens,[status(thm)],[1683, 28031])).
% 4.97/5.16 tff(28033,plain,
% 4.97/5.16 (s(s(s(z))) = s(elem!1)),
% 4.97/5.16 inference(symmetry,[status(thm)],[28009])).
% 4.97/5.16 tff(28034,plain,
% 4.97/5.16 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[28033])).
% 4.97/5.16 tff(28035,plain,
% 4.97/5.16 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 4.97/5.16 inference(transitivity,[status(thm)],[28034, 3881])).
% 4.97/5.16 tff(28036,plain,
% 4.97/5.16 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[28035])).
% 4.97/5.16 tff(28037,plain,
% 4.97/5.16 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.97/5.16 inference(modus_ponens,[status(thm)],[11613, 28036])).
% 4.97/5.16 tff(28038,plain,
% 4.97/5.16 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[1649, 28037])).
% 4.97/5.16 tff(28039,plain,
% 4.97/5.16 (~r(s(s(z)), elem!1)),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[443, 28006, 106])).
% 4.97/5.16 tff(28040,plain,
% 4.97/5.16 (s(s(z)) = elem!1),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[448, 28039, 3241])).
% 4.97/5.16 tff(28041,plain,
% 4.97/5.16 (r(z, elem!1)),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[7053, 28040, 3261])).
% 4.97/5.16 tff(28042,plain,
% 4.97/5.16 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(s(z)))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[28008])).
% 4.97/5.16 tff(28043,plain,
% 4.97/5.16 (r(s(s(elem!1)), s(s(z))) <=> r(s(s(elem!1)), elem!1)),
% 4.97/5.16 inference(symmetry,[status(thm)],[28042])).
% 4.97/5.16 tff(28044,plain,
% 4.97/5.16 (r(s(s(elem!1)), s(s(z))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[28010])).
% 4.97/5.16 tff(28045,plain,
% 4.97/5.16 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(elem!1)), s(s(z)))),
% 4.97/5.16 inference(symmetry,[status(thm)],[28044])).
% 4.97/5.16 tff(28046,plain,
% 4.97/5.16 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(elem!1)), elem!1)),
% 4.97/5.16 inference(transitivity,[status(thm)],[28045, 28043])).
% 4.97/5.16 tff(28047,plain,
% 4.97/5.16 (r(s(s(elem!1)), elem!1)),
% 4.97/5.16 inference(modus_ponens,[status(thm)],[103, 28046])).
% 4.97/5.16 tff(28048,plain,
% 4.97/5.16 (~r(s(s(s(elem!1))), elem!1)),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[23717, 28047, 28041, 28038])).
% 4.97/5.16 tff(28049,plain,
% 4.97/5.16 (b(s(s(s(elem!1))), elem!1)),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[570, 28048, 28032])).
% 4.97/5.16 tff(28050,plain,
% 4.97/5.16 (b(s(s(s(s(s(z))))), s(s(z)))),
% 4.97/5.16 inference(modus_ponens,[status(thm)],[28049, 28030])).
% 4.97/5.16 tff(28051,plain,
% 4.97/5.16 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[27817, 27803, 1130, 4236])).
% 4.97/5.16 tff(28052,plain,
% 4.97/5.16 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[249, 28051])).
% 4.97/5.16 tff(28053,plain,
% 4.97/5.16 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[27861, 28008, 1130, 14646, 2043, 4236])).
% 4.97/5.16 tff(28054,plain,
% 4.97/5.16 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[28023])).
% 4.97/5.16 tff(28055,plain,
% 4.97/5.16 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 4.97/5.16 inference(transitivity,[status(thm)],[28054, 3539])).
% 4.97/5.16 tff(28056,plain,
% 4.97/5.16 ((s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 4.97/5.16 inference(symmetry,[status(thm)],[28055])).
% 4.97/5.16 tff(28057,plain,
% 4.97/5.16 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))) <=> (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[28056])).
% 4.97/5.16 tff(28058,plain,
% 4.97/5.16 (~(s(s(s(s(z)))) = elem!1)),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[504, 27994])).
% 4.97/5.16 tff(28059,plain,
% 4.97/5.16 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[3502, 28058])).
% 4.97/5.16 tff(28060,plain,
% 4.97/5.16 (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 4.97/5.16 inference(modus_ponens,[status(thm)],[28059, 28057])).
% 4.97/5.16 tff(28061,plain,
% 4.97/5.16 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[18760, 41, 28060, 28053])).
% 4.97/5.16 tff(28062,plain,
% 4.97/5.16 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[14448, 28061, 27803, 28052, 28050])).
% 4.97/5.16 tff(28063,plain,
% 4.97/5.16 (~b(elem!1, s(s(s(elem!1))))),
% 4.97/5.16 inference(modus_ponens,[status(thm)],[28062, 28026])).
% 4.97/5.16 tff(28064,plain,
% 4.97/5.16 (r(elem!1, s(s(s(elem!1))))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[2054, 28063, 28020])).
% 4.97/5.16 tff(28065,plain,
% 4.97/5.16 (~r(s(s(s(elem!1))), z)),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[6071, 28064, 28006])).
% 4.97/5.16 tff(28066,plain,
% 4.97/5.16 (b(s(s(s(elem!1))), z)),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[1565, 28065])).
% 4.97/5.16 tff(28067,plain,
% 4.97/5.16 (b(s(s(s(s(s(z))))), z)),
% 4.97/5.16 inference(modus_ponens,[status(thm)],[28066, 28014])).
% 4.97/5.16 tff(28068,plain,
% 4.97/5.16 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[28023])).
% 4.97/5.16 tff(28069,plain,
% 4.97/5.16 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 4.97/5.16 inference(symmetry,[status(thm)],[28068])).
% 4.97/5.16 tff(28070,plain,
% 4.97/5.16 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[8811, 28064, 86, 3340, 28040])).
% 4.97/5.16 tff(28071,plain,
% 4.97/5.16 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 4.97/5.16 inference(modus_ponens,[status(thm)],[28070, 28069])).
% 4.97/5.16 tff(28072,plain,
% 4.97/5.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 4.97/5.16 inference(rewrite,[status(thm)],[])).
% 4.97/5.16 tff(28073,plain,
% 4.97/5.16 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 4.97/5.16 inference(rewrite,[status(thm)],[])).
% 4.97/5.16 tff(28074,plain,
% 4.97/5.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z))))))))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[28073])).
% 4.97/5.16 tff(28075,plain,
% 4.97/5.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 4.97/5.16 inference(transitivity,[status(thm)],[28074, 28072])).
% 4.97/5.16 tff(28076,plain,
% 4.97/5.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))),
% 4.97/5.16 inference(quant_inst,[status(thm)],[])).
% 4.97/5.16 tff(28077,plain,
% 4.97/5.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z))))))),
% 4.97/5.16 inference(modus_ponens,[status(thm)],[28076, 28075])).
% 4.97/5.16 tff(28078,plain,
% 4.97/5.16 ($false),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[28077, 178, 27919, 14646, 28071, 28067, 28013])).
% 4.97/5.16 tff(28079,plain,((~b(z, s(s(s(elem!1))))) | b(s(s(s(s(z)))), s(s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | b(s(s(z)), elem!1) | b(elem!1, s(s(z))) | (~r(s(s(z)), z)) | (elem!1 = z) | b(z, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 4.97/5.16 tff(28080,plain,
% 4.97/5.16 (~b(z, s(s(s(elem!1))))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[28079, 27993, 1130, 3261, 3241, 86, 290, 27917, 4235])).
% 4.97/5.16 tff(28081,plain,
% 4.97/5.16 (r(z, s(s(s(elem!1))))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[2095, 28080])).
% 4.97/5.16 tff(28082,plain,
% 4.97/5.16 (r(z, s(s(s(s(s(z))))))),
% 4.97/5.16 inference(modus_ponens,[status(thm)],[28081, 27992])).
% 4.97/5.16 tff(28083,plain,
% 4.97/5.16 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[23864, 28082, 4236])).
% 4.97/5.16 tff(28084,plain,
% 4.97/5.16 (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[27868, 28083, 27981])).
% 4.97/5.16 tff(28085,plain,
% 4.97/5.16 (b(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.97/5.16 inference(monotonicity,[status(thm)],[27981])).
% 4.97/5.16 tff(28086,plain,
% 4.97/5.16 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.97/5.16 inference(modus_ponens,[status(thm)],[27803, 28085])).
% 4.97/5.16 tff(28087,plain,
% 4.97/5.16 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[27981])).
% 4.97/5.16 tff(28088,plain,
% 4.97/5.16 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.97/5.16 inference(modus_ponens,[status(thm)],[28052, 28087])).
% 4.97/5.16 tff(28089,plain,
% 4.97/5.16 (~(elem!1 = s(s(s(elem!1))))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[4868, 28080, 3261, 27993, 318])).
% 4.97/5.16 tff(28090,plain,
% 4.97/5.16 (r(z, elem!1)),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[7053, 27981, 3261])).
% 4.97/5.16 tff(28091,plain,
% 4.97/5.16 (~r(elem!1, s(s(s(elem!1))))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[3319, 28081, 28090])).
% 4.97/5.16 tff(28092,plain,
% 4.97/5.16 (b(elem!1, s(s(s(elem!1))))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[2054, 28091, 28089])).
% 4.97/5.16 tff(28093,plain,
% 4.97/5.16 (~(s(s(s(elem!1))) = elem!1)),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[2489, 28089])).
% 4.97/5.16 tff(28094,plain,
% 4.97/5.16 (~r(s(s(s(elem!1))), elem!1)),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[565, 28081, 28090])).
% 4.97/5.16 tff(28095,plain,
% 4.97/5.16 (b(s(s(s(elem!1))), elem!1)),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[570, 28094, 28093])).
% 4.97/5.16 tff(28096,plain,
% 4.97/5.16 (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[25419, 178, 28095, 28092, 28088, 28086])).
% 4.97/5.16 tff(28097,plain,
% 4.97/5.16 ($false),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[3612, 41, 28096, 28084, 27987])).
% 4.97/5.16 tff(28098,plain,((elem!1 = z) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | b(s(s(z)), elem!1) | b(s(s(s(s(z)))), s(s(z))) | b(z, s(s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 4.97/5.16 tff(28099,plain,
% 4.97/5.16 ((elem!1 = z) | (~r(z, s(s(z)))) | b(s(s(z)), elem!1) | b(s(s(s(s(z)))), s(s(z))) | b(z, s(s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[28098, 24592])).
% 4.97/5.16 tff(28100,plain,
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% 4.97/5.16 inference(unit_resolution,[status(thm)],[24075, 28105, 28104])).
% 4.97/5.16 tff(28107,plain,
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% 4.97/5.16 inference(unit_resolution,[status(thm)],[28106, 28103])).
% 4.97/5.16 tff(28108,plain,((z = elem!1) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(z)), z) | b(s(s(z)), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 4.97/5.16 tff(28109,plain,
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% 4.97/5.16 inference(unit_resolution,[status(thm)],[28108, 105, 5618, 86])).
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% 4.97/5.16 inference(monotonicity,[status(thm)],[28109])).
% 4.97/5.16 tff(28111,plain,
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% 4.97/5.16 inference(monotonicity,[status(thm)],[28110])).
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% 4.97/5.16 tff(28113,plain,
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% 4.97/5.16 inference(unit_resolution,[status(thm)],[317, 28109])).
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% 4.97/5.16 inference(unit_resolution,[status(thm)],[20730, 28109, 27635])).
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% 4.97/5.16 inference(unit_resolution,[status(thm)],[3774, 28114, 86])).
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% 4.97/5.16 inference(unit_resolution,[status(thm)],[14873, 28115, 86, 5618])).
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% 4.97/5.16 inference(unit_resolution,[status(thm)],[143, 28116])).
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% 4.97/5.16 inference(unit_resolution,[status(thm)],[3276, 28117, 28113])).
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% 4.97/5.16 inference(modus_ponens,[status(thm)],[28118, 28112])).
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% 4.97/5.16 inference(symmetry,[status(thm)],[28111])).
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% 4.97/5.16 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(z)))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[28120])).
% 4.97/5.16 tff(28122,plain,
% 4.97/5.16 (b(s(elem!1), s(s(z))) <=> b(s(elem!1), s(s(elem!1)))),
% 4.97/5.16 inference(symmetry,[status(thm)],[28121])).
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% 4.97/5.16 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[4057, 28117, 5619, 27224, 27217])).
% 4.97/5.16 tff(28124,plain,
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% 4.97/5.16 inference(unit_resolution,[status(thm)],[133, 28123])).
% 4.97/5.16 tff(28125,plain,
% 4.97/5.16 (r(z, elem!1) <=> r(elem!1, elem!1)),
% 4.97/5.16 inference(monotonicity,[status(thm)],[28109])).
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% 4.97/5.16 (r(elem!1, elem!1) <=> r(z, elem!1)),
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% 4.97/5.16 inference(monotonicity,[status(thm)],[28126])).
% 4.97/5.16 tff(28128,plain,
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% 4.97/5.16 inference(bind,[status(th)],[])).
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% 4.97/5.16 (![X: $i] : (~r(X, X)) <=> ![X: $i] : (~r(X, X))),
% 4.97/5.16 inference(quant_intro,[status(thm)],[28128])).
% 4.97/5.16 tff(28130,plain,
% 4.97/5.16 (![X: $i] : (~r(X, X)) <=> ![X: $i] : (~r(X, X))),
% 4.97/5.16 inference(rewrite,[status(thm)],[])).
% 4.97/5.16 tff(28131,axiom,(![X: $i] : (~r(X, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ri')).
% 4.97/5.16 tff(28132,plain,
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% 4.97/5.16 inference(modus_ponens,[status(thm)],[28131, 28130])).
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% 4.97/5.16 inference(skolemize,[status(sab)],[28132])).
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% 4.97/5.16 inference(modus_ponens,[status(thm)],[28133, 28129])).
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% 4.97/5.16 inference(quant_inst,[status(thm)],[])).
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% 4.97/5.16 inference(unit_resolution,[status(thm)],[28135, 28134])).
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% 4.97/5.16 inference(modus_ponens,[status(thm)],[28136, 28127])).
% 4.97/5.16 tff(28138,plain,
% 4.97/5.16 (~b(elem!1, z)),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[6991, 28109])).
% 4.97/5.16 tff(28139,plain,
% 4.97/5.16 (~(elem!1 = s(s(s(s(z)))))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[12557, 28138, 27635])).
% 4.97/5.16 tff(28140,plain,
% 4.97/5.16 (~(s(elem!1) = s(s(s(s(z)))))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[25360, 28109])).
% 4.97/5.16 tff(28141,plain,
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% 4.97/5.16 inference(monotonicity,[status(thm)],[28111])).
% 4.97/5.16 tff(28142,plain,
% 4.97/5.16 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[28141])).
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% 4.97/5.16 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 4.97/5.16 inference(symmetry,[status(thm)],[28142])).
% 4.97/5.16 tff(28144,plain,
% 4.97/5.16 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[28143])).
% 4.97/5.16 tff(28145,plain,
% 4.97/5.16 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.97/5.16 inference(transitivity,[status(thm)],[28144, 3289])).
% 4.97/5.16 tff(28146,plain,
% 4.97/5.16 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 4.97/5.16 inference(symmetry,[status(thm)],[28145])).
% 4.97/5.16 tff(28147,plain,
% 4.97/5.16 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(elem!1)))))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[28146])).
% 4.97/5.16 tff(28148,plain,
% 4.97/5.16 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[28141])).
% 4.97/5.16 tff(28149,plain,
% 4.97/5.16 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.97/5.16 inference(transitivity,[status(thm)],[28148, 3289])).
% 4.97/5.16 tff(28150,plain,
% 4.97/5.16 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(z))))))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[28149])).
% 4.97/5.16 tff(28151,plain,
% 4.97/5.16 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 4.97/5.16 inference(modus_ponens,[status(thm)],[4938, 28150])).
% 4.97/5.16 tff(28152,plain,
% 4.97/5.16 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 4.97/5.16 inference(modus_ponens,[status(thm)],[28151, 28147])).
% 4.97/5.16 tff(28153,plain,
% 4.97/5.16 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(s(s(s(elem!1)))), s(s(z)))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[28120])).
% 4.97/5.16 tff(28154,plain,
% 4.97/5.16 (r(s(s(s(s(elem!1)))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 4.97/5.16 inference(symmetry,[status(thm)],[28153])).
% 4.97/5.16 tff(28155,plain,
% 4.97/5.16 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(s(z)))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[28142])).
% 4.97/5.16 tff(28156,plain,
% 4.97/5.16 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 4.97/5.16 inference(modus_ponens,[status(thm)],[103, 28155])).
% 4.97/5.16 tff(28157,plain,
% 4.97/5.16 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 4.97/5.16 inference(modus_ponens,[status(thm)],[28156, 28154])).
% 4.97/5.16 tff(28158,plain,
% 4.97/5.16 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[28111])).
% 4.97/5.16 tff(28159,plain,
% 4.97/5.16 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 4.97/5.16 inference(transitivity,[status(thm)],[28158, 12033])).
% 4.97/5.16 tff(28160,plain,
% 4.97/5.16 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[28159])).
% 4.97/5.16 tff(28161,plain,
% 4.97/5.16 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 4.97/5.16 inference(modus_ponens,[status(thm)],[1683, 28160])).
% 4.97/5.16 tff(28162,plain,
% 4.97/5.16 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[28111])).
% 4.97/5.16 tff(28163,plain,
% 4.97/5.16 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.16 inference(modus_ponens,[status(thm)],[27224, 28162])).
% 4.97/5.16 tff(28164,plain,
% 4.97/5.16 (b(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[28111])).
% 4.97/5.16 tff(28165,plain,
% 4.97/5.16 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.97/5.16 inference(modus_ponens,[status(thm)],[27217, 28164])).
% 4.97/5.16 tff(28166,plain,
% 4.97/5.16 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[20823, 28113, 27244])).
% 4.97/5.16 tff(28167,plain,
% 4.97/5.16 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[5320, 24592])).
% 4.97/5.16 tff(28168,plain,
% 4.97/5.16 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[28167, 28166])).
% 4.97/5.16 tff(28169,plain,
% 4.97/5.16 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[28141])).
% 4.97/5.16 tff(28170,plain,
% 4.97/5.16 ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) <=> (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 4.97/5.16 inference(monotonicity,[status(thm)],[28169])).
% 4.97/5.16 tff(28171,plain,
% 4.97/5.16 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[20758, 28124, 28104])).
% 4.97/5.16 tff(28172,plain,
% 4.97/5.16 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.97/5.16 inference(modus_ponens,[status(thm)],[28171, 28170])).
% 4.97/5.16 tff(28173,plain,
% 4.97/5.16 (b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[5118, 28172, 28168])).
% 4.97/5.16 tff(28174,plain,
% 4.97/5.16 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[21452, 28117, 27224, 28104, 27217])).
% 4.97/5.16 tff(28175,plain,
% 4.97/5.16 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.16 inference(unit_resolution,[status(thm)],[20667, 28174])).
% 4.97/5.16 tff(28176,plain,
% 4.97/5.16 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.17 inference(unit_resolution,[status(thm)],[20942, 28175, 28113])).
% 4.97/5.17 tff(28177,plain,
% 4.97/5.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(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(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(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(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 4.97/5.17 inference(rewrite,[status(thm)],[])).
% 4.97/5.17 tff(28178,plain,
% 4.97/5.17 (((~b(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(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), 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(s(s(s(s(z))))))), 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(elem!1)), s(s(s(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(elem!1))))))),
% 4.97/5.17 inference(rewrite,[status(thm)],[])).
% 4.97/5.17 tff(28179,plain,
% 4.97/5.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(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(s(s(s(s(z))))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(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(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))))),
% 4.97/5.17 inference(monotonicity,[status(thm)],[28178])).
% 4.97/5.17 tff(28180,plain,
% 4.97/5.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(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(s(s(s(s(z))))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(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(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 4.97/5.17 inference(transitivity,[status(thm)],[28179, 28177])).
% 4.97/5.17 tff(28181,plain,
% 4.97/5.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(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(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 4.97/5.17 inference(quant_inst,[status(thm)],[])).
% 4.97/5.17 tff(28182,plain,
% 4.97/5.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(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(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 4.97/5.17 inference(modus_ponens,[status(thm)],[28181, 28180])).
% 4.97/5.17 tff(28183,plain,
% 4.97/5.17 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 4.97/5.17 inference(unit_resolution,[status(thm)],[28182, 178, 28176, 28173, 28165, 28163])).
% 4.97/5.17 tff(28184,plain,
% 4.97/5.17 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 4.97/5.17 inference(unit_resolution,[status(thm)],[3409, 28183, 28161])).
% 4.97/5.17 tff(28185,plain,
% 4.97/5.17 ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 4.97/5.17 inference(unit_resolution,[status(thm)],[12173, 118, 28184])).
% 4.97/5.17 tff(28186,plain,
% 4.97/5.17 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 4.97/5.17 inference(unit_resolution,[status(thm)],[28185, 28157])).
% 4.97/5.17 tff(28187,plain,
% 4.97/5.17 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 4.97/5.17 inference(unit_resolution,[status(thm)],[1988, 28186, 28152])).
% 4.97/5.17 tff(28188,plain,
% 4.97/5.17 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.97/5.17 inference(monotonicity,[status(thm)],[28143])).
% 4.97/5.17 tff(28189,plain,
% 4.97/5.17 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 4.97/5.17 inference(symmetry,[status(thm)],[28188])).
% 4.97/5.17 tff(28190,plain,
% 4.97/5.17 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.97/5.17 inference(monotonicity,[status(thm)],[28141])).
% 4.97/5.17 tff(28191,plain,
% 4.97/5.17 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 4.97/5.17 inference(modus_ponens,[status(thm)],[27245, 28190])).
% 4.97/5.17 tff(28192,plain,
% 4.97/5.17 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 4.97/5.17 inference(modus_ponens,[status(thm)],[28191, 28189])).
% 4.97/5.17 tff(28193,plain,
% 4.97/5.17 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 4.97/5.17 inference(monotonicity,[status(thm)],[28142])).
% 4.97/5.17 tff(28194,plain,
% 4.97/5.17 (b(s(s(s(s(elem!1)))), elem!1)),
% 4.97/5.17 inference(modus_ponens,[status(thm)],[28114, 28193])).
% 4.97/5.17 tff(28195,plain,
% 4.97/5.17 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 4.97/5.17 inference(monotonicity,[status(thm)],[28142])).
% 4.97/5.17 tff(28196,plain,
% 4.97/5.17 (b(z, s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 4.97/5.17 inference(monotonicity,[status(thm)],[28109])).
% 4.97/5.17 tff(28197,plain,
% 4.97/5.17 (b(elem!1, s(s(s(s(z)))))),
% 4.97/5.17 inference(modus_ponens,[status(thm)],[27212, 28196])).
% 4.97/5.17 tff(28198,plain,
% 4.97/5.17 (b(elem!1, s(s(s(s(elem!1)))))),
% 4.97/5.17 inference(modus_ponens,[status(thm)],[28197, 28195])).
% 4.97/5.17 tff(28199,plain,
% 4.97/5.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 4.97/5.17 inference(rewrite,[status(thm)],[])).
% 4.97/5.17 tff(28200,plain,
% 4.97/5.17 (((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 4.97/5.17 inference(rewrite,[status(thm)],[])).
% 4.97/5.17 tff(28201,plain,
% 4.97/5.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 4.97/5.17 inference(monotonicity,[status(thm)],[28200])).
% 4.97/5.17 tff(28202,plain,
% 4.97/5.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 4.97/5.17 inference(transitivity,[status(thm)],[28201, 28199])).
% 4.97/5.17 tff(28203,plain,
% 4.97/5.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 4.97/5.17 inference(quant_inst,[status(thm)],[])).
% 4.97/5.17 tff(28204,plain,
% 4.97/5.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 4.97/5.17 inference(modus_ponens,[status(thm)],[28203, 28202])).
% 4.97/5.17 tff(28205,plain,
% 4.97/5.17 (~b(elem!1, s(s(s(elem!1))))),
% 4.97/5.17 inference(unit_resolution,[status(thm)],[28204, 178, 28198, 28194, 28192, 28187])).
% 4.97/5.17 tff(28206,plain,
% 4.97/5.17 (b(s(s(s(s(z)))), elem!1)),
% 4.97/5.17 inference(unit_resolution,[status(thm)],[22079, 2811, 469, 3461, 1687, 273, 193, 168, 12])).
% 4.97/5.17 tff(28207,plain,
% 4.97/5.17 (s(s(s(elem!1))) = s(s(s(z)))),
% 4.97/5.17 inference(symmetry,[status(thm)],[16])).
% 4.97/5.17 tff(28208,plain,
% 4.97/5.17 (r(s(s(s(s(s(s(s(z))))))), z) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.97/5.17 inference(monotonicity,[status(thm)],[13])).
% 4.97/5.17 tff(28209,plain,
% 4.97/5.17 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.97/5.17 inference(modus_ponens,[status(thm)],[108, 28208])).
% 4.97/5.17 tff(28210,plain,
% 4.97/5.17 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 4.97/5.17 inference(monotonicity,[status(thm)],[15, 17])).
% 4.97/5.17 tff(28211,plain,
% 4.97/5.17 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 4.97/5.17 inference(modus_ponens,[status(thm)],[147, 28210])).
% 4.97/5.17 tff(28212,plain,
% 4.97/5.17 ((~(s(s(s(s(z)))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(elem!1))))))),
% 4.97/5.17 inference(monotonicity,[status(thm)],[25353])).
% 4.97/5.17 tff(28213,plain,
% 4.97/5.17 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 4.97/5.17 inference(modus_ponens,[status(thm)],[2169, 28212])).
% 4.97/5.17 tff(28214,plain,
% 4.97/5.17 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 4.97/5.17 inference(unit_resolution,[status(thm)],[4343, 28213])).
% 4.97/5.17 tff(28215,plain,
% 4.97/5.17 ((s(elem!1) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 4.97/5.17 inference(symmetry,[status(thm)],[25351])).
% 4.97/5.17 tff(28216,plain,
% 4.97/5.17 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 4.97/5.17 inference(transitivity,[status(thm)],[25353, 28215])).
% 4.97/5.17 tff(28217,plain,
% 4.97/5.17 ((~(s(s(s(s(z)))) = s(elem!1))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 4.97/5.17 inference(monotonicity,[status(thm)],[28216])).
% 4.97/5.17 tff(28218,plain,
% 4.97/5.17 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 4.97/5.17 inference(modus_ponens,[status(thm)],[2169, 28217])).
% 4.97/5.17 tff(28219,plain,
% 4.97/5.17 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(s(z)))),
% 4.97/5.17 inference(monotonicity,[status(thm)],[17])).
% 4.97/5.17 tff(28220,plain,
% 4.97/5.17 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 4.97/5.17 inference(modus_ponens,[status(thm)],[193, 28219])).
% 4.97/5.17 tff(28221,plain,
% 4.97/5.17 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 4.97/5.17 inference(modus_ponens,[status(thm)],[28220, 12141])).
% 4.97/5.17 tff(28222,plain,
% 4.97/5.17 ((~b(s(elem!1), s(s(z)))) <=> (~b(s(elem!1), s(s(elem!1))))),
% 4.97/5.17 inference(monotonicity,[status(thm)],[25826])).
% 4.97/5.17 tff(28223,plain,
% 4.97/5.17 (~b(s(elem!1), s(s(elem!1)))),
% 4.97/5.17 inference(modus_ponens,[status(thm)],[305, 28222])).
% 4.97/5.17 tff(28224,plain,
% 4.97/5.17 (r(s(elem!1), s(s(elem!1)))),
% 4.97/5.17 inference(unit_resolution,[status(thm)],[1028, 28223, 13483])).
% 4.97/5.17 tff(28225,plain,
% 4.97/5.17 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 4.97/5.17 inference(rewrite,[status(thm)],[])).
% 4.97/5.17 tff(28226,plain,
% 4.97/5.17 (((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 4.97/5.17 inference(rewrite,[status(thm)],[])).
% 4.97/5.17 tff(28227,plain,
% 4.97/5.17 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 4.97/5.17 inference(monotonicity,[status(thm)],[28226])).
% 4.97/5.17 tff(28228,plain,
% 4.97/5.17 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 4.97/5.17 inference(transitivity,[status(thm)],[28227, 28225])).
% 4.97/5.17 tff(28229,plain,
% 4.97/5.17 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 4.97/5.17 inference(quant_inst,[status(thm)],[])).
% 4.97/5.17 tff(28230,plain,
% 4.97/5.17 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 4.97/5.17 inference(modus_ponens,[status(thm)],[28229, 28228])).
% 4.97/5.17 tff(28231,plain,
% 4.97/5.17 ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 4.97/5.17 inference(unit_resolution,[status(thm)],[28230, 118, 28224])).
% 4.97/5.17 tff(28232,plain,
% 4.97/5.17 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 4.97/5.17 inference(unit_resolution,[status(thm)],[28231, 28221])).
% 4.97/5.17 tff(28233,plain,
% 4.97/5.17 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1)) | r(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1)) | r(s(s(s(s(elem!1)))), s(elem!1)))),
% 4.97/5.17 inference(rewrite,[status(thm)],[])).
% 4.97/5.17 tff(28234,plain,
% 4.97/5.17 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1)) | r(s(s(s(s(elem!1)))), s(elem!1)))),
% 4.97/5.17 inference(quant_inst,[status(thm)],[])).
% 4.97/5.17 tff(28235,plain,
% 4.97/5.17 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1)) | r(s(s(s(s(elem!1)))), s(elem!1))),
% 4.97/5.17 inference(modus_ponens,[status(thm)],[28234, 28233])).
% 4.97/5.17 tff(28236,plain,
% 4.97/5.17 ((s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1)) | r(s(s(s(s(elem!1)))), s(elem!1))),
% 4.97/5.17 inference(unit_resolution,[status(thm)],[28235, 41])).
% 4.97/5.17 tff(28237,plain,
% 4.97/5.17 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 4.97/5.17 inference(unit_resolution,[status(thm)],[28236, 28232, 28218])).
% 4.97/5.17 tff(28238,plain,
% 4.97/5.17 (r(s(elem!1), s(s(z)))),
% 4.97/5.17 inference(modus_ponens,[status(thm)],[28224, 13473])).
% 4.97/5.17 tff(28239,plain,
% 4.97/5.17 (~r(s(elem!1), s(s(s(s(z)))))),
% 4.97/5.17 inference(unit_resolution,[status(thm)],[3949, 28238, 193])).
% 4.97/5.17 tff(28240,plain,
% 4.97/5.17 (b(s(elem!1), s(s(s(s(z)))))),
% 4.97/5.17 inference(unit_resolution,[status(thm)],[1084, 28239, 1369])).
% 4.97/5.17 tff(28241,plain,
% 4.97/5.17 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 4.97/5.17 inference(modus_ponens,[status(thm)],[28240, 25350])).
% 4.97/5.17 tff(28242,plain,
% 4.97/5.17 (b(elem!1, s(s(z)))),
% 4.97/5.17 inference(unit_resolution,[status(thm)],[3276, 5198, 273])).
% 4.97/5.17 tff(28243,plain,
% 4.97/5.17 (b(s(s(z)), s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 4.97/5.17 inference(monotonicity,[status(thm)],[15])).
% 4.97/5.17 tff(28244,plain,
% 4.97/5.17 ((~b(s(s(z)), s(s(z)))) <=> (~b(s(s(elem!1)), s(s(z))))),
% 4.97/5.17 inference(monotonicity,[status(thm)],[28243])).
% 4.97/5.17 tff(28245,plain,
% 4.97/5.17 (~b(s(s(elem!1)), s(s(z)))),
% 4.97/5.17 inference(modus_ponens,[status(thm)],[20177, 28244])).
% 4.97/5.17 tff(28246,plain,
% 4.97/5.17 (~(s(elem!1) = s(s(s(elem!1))))),
% 4.97/5.17 inference(unit_resolution,[status(thm)],[20889, 28245, 28242])).
% 4.97/5.17 tff(28247,plain,
% 4.97/5.17 (r(elem!1, s(s(s(elem!1))))),
% 4.97/5.17 inference(unit_resolution,[status(thm)],[2054, 12149, 3240])).
% 4.97/5.17 tff(28248,plain,
% 4.97/5.17 (b(s(s(s(s(elem!1)))), elem!1)),
% 4.97/5.17 inference(modus_ponens,[status(thm)],[3771, 5174])).
% 4.97/5.17 tff(28249,plain,
% 4.97/5.17 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 4.97/5.17 inference(monotonicity,[status(thm)],[17])).
% 4.97/5.17 tff(28250,plain,
% 4.97/5.17 (b(z, s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 4.97/5.17 inference(monotonicity,[status(thm)],[13])).
% 4.97/5.17 tff(28251,plain,
% 4.97/5.17 (b(elem!1, s(s(s(s(z)))))),
% 4.97/5.17 inference(modus_ponens,[status(thm)],[1687, 28250])).
% 4.97/5.17 tff(28252,plain,
% 4.97/5.17 (b(elem!1, s(s(s(s(elem!1)))))),
% 4.97/5.17 inference(modus_ponens,[status(thm)],[28251, 28249])).
% 4.97/5.17 tff(28253,plain,
% 4.97/5.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 4.97/5.17 inference(rewrite,[status(thm)],[])).
% 4.97/5.17 tff(28254,plain,
% 4.97/5.17 (((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 4.97/5.17 inference(rewrite,[status(thm)],[])).
% 4.97/5.17 tff(28255,plain,
% 4.97/5.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 4.97/5.17 inference(monotonicity,[status(thm)],[28254])).
% 4.97/5.17 tff(28256,plain,
% 4.97/5.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 4.97/5.17 inference(transitivity,[status(thm)],[28255, 28253])).
% 4.97/5.17 tff(28257,plain,
% 4.97/5.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 4.97/5.17 inference(quant_inst,[status(thm)],[])).
% 4.97/5.17 tff(28258,plain,
% 4.97/5.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 4.97/5.17 inference(modus_ponens,[status(thm)],[28257, 28256])).
% 4.97/5.17 tff(28259,plain,
% 4.97/5.17 ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), elem!1))),
% 4.97/5.17 inference(unit_resolution,[status(thm)],[28258, 178, 28252, 28248, 28241])).
% 4.97/5.17 tff(28260,plain,
% 4.97/5.17 (~b(s(elem!1), elem!1)),
% 4.97/5.17 inference(unit_resolution,[status(thm)],[28259, 28237])).
% 4.97/5.17 tff(28261,plain,
% 4.97/5.17 (r(s(elem!1), elem!1)),
% 4.97/5.17 inference(unit_resolution,[status(thm)],[677, 28260, 25767])).
% 4.97/5.17 tff(28262,plain,
% 4.97/5.17 (~r(s(elem!1), s(s(s(elem!1))))),
% 4.97/5.17 inference(unit_resolution,[status(thm)],[9138, 28261, 28247])).
% 4.97/5.17 tff(28263,plain,
% 4.97/5.17 (b(s(elem!1), s(s(s(elem!1))))),
% 4.97/5.17 inference(unit_resolution,[status(thm)],[5432, 28262, 28246])).
% 4.97/5.17 tff(28264,plain,
% 4.97/5.17 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.97/5.17 inference(unit_resolution,[status(thm)],[348, 13482])).
% 4.97/5.17 tff(28265,plain,
% 4.97/5.17 ((s(elem!1) = z) <=> (elem!1 = s(elem!1))),
% 4.97/5.17 inference(transitivity,[status(thm)],[25765, 3880])).
% 4.97/5.17 tff(28266,plain,
% 4.97/5.17 ((~(s(elem!1) = z)) <=> (~(elem!1 = s(elem!1)))),
% 4.97/5.17 inference(monotonicity,[status(thm)],[28265])).
% 4.97/5.17 tff(28267,plain,
% 4.97/5.17 (~(elem!1 = s(elem!1))),
% 4.97/5.17 inference(modus_ponens,[status(thm)],[769, 28266])).
% 4.97/5.17 tff(28268,plain,
% 4.97/5.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 4.97/5.17 inference(rewrite,[status(thm)],[])).
% 4.97/5.17 tff(28269,plain,
% 4.97/5.17 (((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 4.97/5.17 inference(rewrite,[status(thm)],[])).
% 4.97/5.17 tff(28270,plain,
% 4.97/5.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 4.97/5.18 inference(monotonicity,[status(thm)],[28269])).
% 4.97/5.18 tff(28271,plain,
% 4.97/5.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 4.97/5.18 inference(transitivity,[status(thm)],[28270, 28268])).
% 4.97/5.18 tff(28272,plain,
% 4.97/5.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 4.97/5.18 inference(quant_inst,[status(thm)],[])).
% 4.97/5.18 tff(28273,plain,
% 4.97/5.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 4.97/5.18 inference(modus_ponens,[status(thm)],[28272, 28271])).
% 4.97/5.18 tff(28274,plain,
% 4.97/5.18 (~b(elem!1, s(elem!1))),
% 4.97/5.18 inference(unit_resolution,[status(thm)],[28273, 178, 28252, 28248, 28241, 28237])).
% 4.97/5.18 tff(28275,plain,
% 4.97/5.18 (r(elem!1, s(elem!1))),
% 4.97/5.18 inference(unit_resolution,[status(thm)],[756, 28274, 28267])).
% 4.97/5.18 tff(28276,plain,
% 4.97/5.18 (~r(s(s(s(elem!1))), s(elem!1))),
% 4.97/5.18 inference(unit_resolution,[status(thm)],[1591, 28275, 28247])).
% 4.97/5.18 tff(28277,plain,
% 4.97/5.18 (b(s(s(s(elem!1))), s(elem!1))),
% 4.97/5.18 inference(unit_resolution,[status(thm)],[373, 28276, 28264])).
% 4.97/5.18 tff(28278,plain,
% 4.97/5.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 4.97/5.18 inference(rewrite,[status(thm)],[])).
% 4.97/5.18 tff(28279,plain,
% 4.97/5.18 (((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 4.97/5.18 inference(rewrite,[status(thm)],[])).
% 4.97/5.18 tff(28280,plain,
% 4.97/5.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 4.97/5.18 inference(monotonicity,[status(thm)],[28279])).
% 4.97/5.18 tff(28281,plain,
% 4.97/5.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 4.97/5.18 inference(transitivity,[status(thm)],[28280, 28278])).
% 4.97/5.18 tff(28282,plain,
% 4.97/5.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 4.97/5.18 inference(quant_inst,[status(thm)],[])).
% 4.97/5.18 tff(28283,plain,
% 4.97/5.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 4.97/5.18 inference(modus_ponens,[status(thm)],[28282, 28281])).
% 4.97/5.18 tff(28284,plain,
% 4.97/5.18 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 4.97/5.18 inference(unit_resolution,[status(thm)],[28283, 178, 28277, 28263, 28241, 28237])).
% 4.97/5.18 tff(28285,plain,
% 4.97/5.18 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 4.97/5.18 inference(unit_resolution,[status(thm)],[1750, 28284, 28214])).
% 4.97/5.18 tff(28286,plain,
% 4.97/5.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 4.97/5.18 inference(rewrite,[status(thm)],[])).
% 4.97/5.18 tff(28287,plain,
% 4.97/5.18 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 4.97/5.18 inference(rewrite,[status(thm)],[])).
% 4.97/5.18 tff(28288,plain,
% 4.97/5.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 4.97/5.18 inference(monotonicity,[status(thm)],[28287])).
% 4.97/5.18 tff(28289,plain,
% 4.97/5.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 4.97/5.18 inference(transitivity,[status(thm)],[28288, 28286])).
% 4.97/5.18 tff(28290,plain,
% 4.97/5.18 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 4.97/5.18 inference(quant_inst,[status(thm)],[])).
% 4.97/5.18 tff(28291,plain,
% 4.97/5.18 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 4.97/5.18 inference(modus_ponens,[status(thm)],[28290, 28289])).
% 4.97/5.18 tff(28292,plain,
% 4.97/5.18 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 4.97/5.18 inference(unit_resolution,[status(thm)],[28291, 118, 28285, 28211])).
% 4.97/5.18 tff(28293,plain,
% 4.97/5.18 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 4.97/5.18 inference(unit_resolution,[status(thm)],[3375, 28292, 25342])).
% 4.97/5.18 tff(28294,plain,
% 4.97/5.18 (b(elem!1, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 4.97/5.18 inference(monotonicity,[status(thm)],[15])).
% 4.97/5.18 tff(28295,plain,
% 4.97/5.18 (b(elem!1, s(s(elem!1)))),
% 4.97/5.18 inference(modus_ponens,[status(thm)],[28242, 28294])).
% 4.97/5.18 tff(28296,plain,
% 4.97/5.18 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 4.97/5.18 inference(unit_resolution,[status(thm)],[12318, 28285, 28211])).
% 4.97/5.18 tff(28297,plain,
% 4.97/5.18 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 4.97/5.18 inference(unit_resolution,[status(thm)],[3409, 28296, 25409])).
% 4.97/5.18 tff(28298,plain,
% 4.97/5.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 4.97/5.18 inference(rewrite,[status(thm)],[])).
% 4.97/5.18 tff(28299,plain,
% 4.97/5.18 (((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 4.97/5.18 inference(rewrite,[status(thm)],[])).
% 4.97/5.18 tff(28300,plain,
% 4.97/5.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 4.97/5.18 inference(monotonicity,[status(thm)],[28299])).
% 4.97/5.18 tff(28301,plain,
% 4.97/5.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 4.97/5.18 inference(transitivity,[status(thm)],[28300, 28298])).
% 4.97/5.18 tff(28302,plain,
% 4.97/5.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 4.97/5.18 inference(quant_inst,[status(thm)],[])).
% 4.97/5.18 tff(28303,plain,
% 4.97/5.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 4.97/5.18 inference(modus_ponens,[status(thm)],[28302, 28301])).
% 4.97/5.18 tff(28304,plain,
% 4.97/5.18 ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 4.97/5.18 inference(unit_resolution,[status(thm)],[28303, 178, 25406, 28297, 28295])).
% 4.97/5.18 tff(28305,plain,
% 4.97/5.18 (~b(s(s(s(elem!1))), elem!1)),
% 4.97/5.18 inference(unit_resolution,[status(thm)],[28304, 28293])).
% 4.97/5.18 tff(28306,plain,
% 4.97/5.18 (r(s(s(s(elem!1))), elem!1)),
% 4.97/5.18 inference(unit_resolution,[status(thm)],[570, 28305, 25357])).
% 4.97/5.18 tff(28307,plain,
% 4.97/5.18 (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.18 inference(unit_resolution,[status(thm)],[3680, 118, 28306, 28209])).
% 4.97/5.18 tff(28308,plain,
% 4.97/5.18 ((s(s(s(s(s(s(s(z))))))) = s(z)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 4.97/5.18 inference(monotonicity,[status(thm)],[14])).
% 4.97/5.18 tff(28309,plain,
% 4.97/5.18 ((s(s(s(s(s(s(s(z))))))) = s(z)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.97/5.18 inference(transitivity,[status(thm)],[28308, 377])).
% 4.97/5.18 tff(28310,plain,
% 4.97/5.18 ((s(s(s(s(s(s(s(z))))))) = s(z)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 4.97/5.18 inference(transitivity,[status(thm)],[28309, 655])).
% 4.97/5.18 tff(28311,plain,
% 4.97/5.18 ((~(s(s(s(s(s(s(s(z))))))) = s(z))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 4.97/5.18 inference(monotonicity,[status(thm)],[28310])).
% 4.97/5.18 tff(28312,plain,
% 4.97/5.18 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 4.97/5.18 inference(modus_ponens,[status(thm)],[612, 28311])).
% 4.97/5.18 tff(28313,plain,
% 4.97/5.18 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.97/5.18 inference(unit_resolution,[status(thm)],[14053, 118, 28261, 28209])).
% 4.97/5.18 tff(28314,plain,
% 4.97/5.18 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 4.97/5.18 inference(unit_resolution,[status(thm)],[806, 41, 28313, 28312])).
% 4.97/5.18 tff(28315,plain,
% 4.97/5.18 ((~(s(s(s(s(s(s(s(z))))))) = s(z))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 4.97/5.18 inference(monotonicity,[status(thm)],[28309])).
% 4.97/5.18 tff(28316,plain,
% 4.97/5.18 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.97/5.18 inference(modus_ponens,[status(thm)],[612, 28315])).
% 4.97/5.18 tff(28317,plain,
% 4.97/5.18 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.18 inference(unit_resolution,[status(thm)],[8168, 118, 28261, 28209])).
% 4.97/5.18 tff(28318,plain,
% 4.97/5.18 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.18 inference(unit_resolution,[status(thm)],[395, 28317, 28316])).
% 4.97/5.18 tff(28319,plain,
% 4.97/5.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(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))))),
% 4.97/5.18 inference(rewrite,[status(thm)],[])).
% 4.97/5.18 tff(28320,plain,
% 4.97/5.18 (((~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(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(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(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))))),
% 4.97/5.18 inference(rewrite,[status(thm)],[])).
% 4.97/5.18 tff(28321,plain,
% 4.97/5.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(elem!1))), s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(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)))))),
% 4.97/5.18 inference(monotonicity,[status(thm)],[28320])).
% 4.97/5.18 tff(28322,plain,
% 4.97/5.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(elem!1))), s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(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))))),
% 4.97/5.18 inference(transitivity,[status(thm)],[28321, 28319])).
% 4.97/5.18 tff(28323,plain,
% 4.97/5.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 4.97/5.18 inference(quant_inst,[status(thm)],[])).
% 4.97/5.18 tff(28324,plain,
% 4.97/5.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 4.97/5.18 inference(modus_ponens,[status(thm)],[28323, 28322])).
% 4.97/5.18 tff(28325,plain,
% 4.97/5.18 (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.18 inference(unit_resolution,[status(thm)],[28324, 178, 28277, 28263, 28318, 28314])).
% 4.97/5.18 tff(28326,plain,
% 4.97/5.18 ((s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))) | r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.18 inference(unit_resolution,[status(thm)],[3612, 41, 28325])).
% 4.97/5.18 tff(28327,plain,
% 4.97/5.18 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 4.97/5.18 inference(unit_resolution,[status(thm)],[28326, 28307])).
% 4.97/5.18 tff(28328,plain,
% 4.97/5.18 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 4.97/5.18 inference(symmetry,[status(thm)],[28327])).
% 4.97/5.18 tff(28329,plain,
% 4.97/5.18 (s(s(s(s(s(s(s(z))))))) = s(s(s(z)))),
% 4.97/5.18 inference(transitivity,[status(thm)],[28328, 28207])).
% 4.97/5.18 tff(28330,plain,
% 4.97/5.18 ($false),
% 4.97/5.18 inference(unit_resolution,[status(thm)],[1104, 28329])).
% 4.97/5.18 tff(28331,plain,((~(z = elem!1)) | (s(elem!1) = s(s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | b(elem!1, s(s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | b(s(elem!1), s(s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 4.97/5.18 tff(28332,plain,
% 4.97/5.18 (~(z = elem!1)),
% 4.97/5.18 inference(unit_resolution,[status(thm)],[28331, 28206, 193, 3240, 147, 1369, 305, 108, 1687, 273, 3461])).
% 4.97/5.18 tff(28333,plain,
% 4.97/5.18 (b(z, elem!1)),
% 4.97/5.18 inference(unit_resolution,[status(thm)],[585, 28332, 2811])).
% 4.97/5.18 tff(28334,plain,
% 4.97/5.18 (~b(elem!1, s(s(s(s(z)))))),
% 4.97/5.18 inference(unit_resolution,[status(thm)],[21920, 28333, 28206, 1687, 168])).
% 4.97/5.18 tff(28335,plain,
% 4.97/5.18 (r(elem!1, s(s(s(s(z)))))),
% 4.97/5.18 inference(unit_resolution,[status(thm)],[483, 28334, 469])).
% 4.97/5.18 tff(28336,plain,
% 4.97/5.18 (~r(elem!1, s(s(z)))),
% 4.97/5.18 inference(unit_resolution,[status(thm)],[3785, 28335, 193])).
% 4.97/5.18 tff(28337,plain,
% 4.97/5.18 (b(elem!1, s(s(z)))),
% 4.97/5.18 inference(unit_resolution,[status(thm)],[467, 28336, 312])).
% 4.97/5.18 tff(28338,plain,
% 4.97/5.18 (~r(s(s(z)), elem!1)),
% 4.97/5.18 inference(unit_resolution,[status(thm)],[8763, 28335, 147])).
% 4.97/5.18 tff(28339,plain,
% 4.97/5.18 (b(s(s(z)), elem!1)),
% 4.97/5.18 inference(unit_resolution,[status(thm)],[448, 28338, 12])).
% 4.97/5.18 tff(28340,plain,
% 4.97/5.18 ($false),
% 4.97/5.18 inference(unit_resolution,[status(thm)],[10893, 28339, 28337, 3461, 273, 28333])).
% 4.97/5.18 tff(28341,plain,(r(z, elem!1) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (s(s(z)) = elem!1) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (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(elem!1)))) | (s(elem!1) = s(s(s(s(z))))) | b(s(elem!1), s(s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 4.97/5.18 tff(28342,plain,
% 4.97/5.18 (b(s(elem!1), s(s(z)))),
% 4.97/5.18 inference(unit_resolution,[status(thm)],[28341, 28205, 27212, 5619, 28115, 103, 27635, 28140, 10794, 28117, 28139, 28137, 28124])).
% 4.97/5.18 tff(28343,plain,
% 4.97/5.18 (b(s(elem!1), s(s(elem!1)))),
% 4.97/5.18 inference(modus_ponens,[status(thm)],[28342, 28122])).
% 4.97/5.18 tff(28344,plain,
% 4.97/5.18 (b(s(s(elem!1)), elem!1)),
% 4.97/5.18 inference(unit_resolution,[status(thm)],[5878, 28109, 5619])).
% 4.97/5.18 tff(28345,plain,
% 4.97/5.18 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.97/5.18 inference(monotonicity,[status(thm)],[28143])).
% 4.97/5.18 tff(28346,plain,
% 4.97/5.18 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.97/5.18 inference(modus_ponens,[status(thm)],[28187, 28345])).
% 4.97/5.18 tff(28347,plain,
% 4.97/5.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 4.97/5.18 inference(rewrite,[status(thm)],[])).
% 4.97/5.18 tff(28348,plain,
% 4.97/5.18 (((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 4.97/5.18 inference(rewrite,[status(thm)],[])).
% 4.97/5.18 tff(28349,plain,
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% 4.97/5.18 inference(monotonicity,[status(thm)],[28348])).
% 4.97/5.18 tff(28350,plain,
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% 4.97/5.18 inference(transitivity,[status(thm)],[28349, 28347])).
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% 4.97/5.18 inference(quant_inst,[status(thm)],[])).
% 4.97/5.18 tff(28352,plain,
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% 4.97/5.18 inference(modus_ponens,[status(thm)],[28351, 28350])).
% 4.97/5.18 tff(28353,plain,
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% 4.97/5.18 inference(unit_resolution,[status(thm)],[28352, 178, 2043, 1687, 168, 3828, 3831])).
% 4.97/5.18 tff(28354,plain,((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 4.97/5.18 tff(28355,plain,
% 4.97/5.18 (~b(z, s(s(s(elem!1))))),
% 4.97/5.18 inference(unit_resolution,[status(thm)],[28354, 28346, 27212, 27635, 28191])).
% 4.97/5.18 tff(28356,plain,
% 4.97/5.18 (r(z, s(s(s(elem!1))))),
% 4.97/5.18 inference(unit_resolution,[status(thm)],[2095, 28355])).
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% 4.97/5.18 (r(z, s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.97/5.18 inference(monotonicity,[status(thm)],[28109])).
% 4.97/5.18 tff(28358,plain,
% 4.97/5.18 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 4.97/5.18 inference(unit_resolution,[status(thm)],[17204, 28117, 5619, 27224, 27217])).
% 4.97/5.18 tff(28359,plain,
% 4.97/5.18 (r(z, s(s(s(s(s(s(s(z))))))))),
% 4.97/5.18 inference(unit_resolution,[status(thm)],[271, 28358])).
% 4.97/5.18 tff(28360,plain,
% 4.97/5.18 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 4.97/5.18 inference(modus_ponens,[status(thm)],[28359, 28357])).
% 4.97/5.18 tff(28361,plain,
% 4.97/5.18 ((s(elem!1) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 4.97/5.18 inference(monotonicity,[status(thm)],[28141])).
% 4.97/5.18 tff(28362,plain,
% 4.97/5.18 ((s(elem!1) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 4.97/5.18 inference(transitivity,[status(thm)],[28361, 3881])).
% 4.97/5.18 tff(28363,plain,
% 4.97/5.18 ((~(s(elem!1) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
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% 4.97/5.18 tff(28365,plain,
% 4.97/5.18 (~(s(s(s(elem!1))) = s(elem!1))),
% 4.97/5.18 inference(modus_ponens,[status(thm)],[28364, 28363])).
% 4.97/5.18 tff(28366,plain,
% 4.97/5.18 ((s(s(s(s(s(s(s(z))))))) = s(z)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 4.97/5.18 inference(monotonicity,[status(thm)],[28110])).
% 4.97/5.18 tff(28367,plain,
% 4.97/5.18 ((s(s(s(s(s(s(s(z))))))) = s(z)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.97/5.18 inference(transitivity,[status(thm)],[28366, 377])).
% 4.97/5.18 tff(28368,plain,
% 4.97/5.18 ((~(s(s(s(s(s(s(s(z))))))) = s(z))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 4.97/5.18 inference(monotonicity,[status(thm)],[28367])).
% 4.97/5.18 tff(28369,plain,
% 4.97/5.19 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 4.97/5.19 inference(modus_ponens,[status(thm)],[612, 28368])).
% 4.97/5.19 tff(28370,plain,
% 4.97/5.19 (~r(s(s(s(elem!1))), s(elem!1))),
% 4.97/5.19 inference(unit_resolution,[status(thm)],[5447, 2333, 557])).
% 4.97/5.19 tff(28371,plain,
% 4.97/5.19 (b(s(s(s(elem!1))), s(elem!1))),
% 4.97/5.19 inference(unit_resolution,[status(thm)],[373, 28370, 356])).
% 4.97/5.19 tff(28372,plain,
% 4.97/5.19 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.19 inference(unit_resolution,[status(thm)],[395, 23950, 2286])).
% 4.97/5.19 tff(28373,plain,
% 4.97/5.19 ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 4.97/5.19 inference(unit_resolution,[status(thm)],[8182, 178, 5391, 3830, 3504])).
% 4.97/5.19 tff(28374,plain,
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% 4.97/5.19 inference(unit_resolution,[status(thm)],[28373, 28372, 28371])).
% 4.97/5.19 tff(28375,plain,((~r(z, s(elem!1))) | (~b(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(s(elem!1)))) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(elem!1))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 4.97/5.19 tff(28376,plain,
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% 4.97/5.19 tff(28379,plain,
% 4.97/5.19 ((s(elem!1) = z) <=> (s(elem!1) = elem!1)),
% 4.97/5.19 inference(monotonicity,[status(thm)],[28109])).
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% 4.97/5.19 ((~(s(elem!1) = z)) <=> (~(s(elem!1) = elem!1))),
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% 4.97/5.19 inference(unit_resolution,[status(thm)],[14170, 28342, 27217, 27224, 28113, 28124])).
% 4.97/5.19 tff(28383,plain,
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% 4.97/5.19 tff(28384,plain,
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% 4.97/5.19 inference(modus_ponens,[status(thm)],[1426, 28384])).
% 4.97/5.19 tff(28386,plain,
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% 4.97/5.19 tff(28387,plain,((~r(s(elem!1), elem!1)) | r(s(elem!1), z) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 4.97/5.19 tff(28388,plain,
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% 4.97/5.19 tff(28392,plain,
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% 4.97/5.19 tff(28400,plain,
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% 4.97/5.19 tff(28401,plain,
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% 4.97/5.19 tff(28409,plain,
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% 4.97/5.19 inference(modus_ponens,[status(thm)],[28409, 28406])).
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% 4.97/5.19 inference(unit_resolution,[status(thm)],[2386, 28412])).
% 4.97/5.19 tff(28414,plain,
% 4.97/5.19 (r(s(s(z)), z) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~r(z, s(s(z)))) | (s(s(elem!1)) = s(s(z))) | b(s(s(s(s(z)))), s(s(z)))),
% 4.97/5.19 inference(unit_resolution,[status(thm)],[27916, 24592])).
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% 4.97/5.19 inference(unit_resolution,[status(thm)],[28471, 3461, 202])).
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% 4.97/5.19 inference(monotonicity,[status(thm)],[25768])).
% 4.97/5.19 tff(28528,plain,
% 4.97/5.19 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.19 inference(symmetry,[status(thm)],[28527])).
% 4.97/5.19 tff(28529,plain,
% 4.97/5.19 ((~b(s(s(s(s(elem!1)))), s(elem!1))) <=> (~b(s(s(s(s(z)))), s(elem!1)))),
% 4.97/5.19 inference(monotonicity,[status(thm)],[25828])).
% 4.97/5.19 tff(28530,plain,
% 4.97/5.19 ((s(s(s(s(s(s(s(z))))))) = z) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 4.97/5.19 inference(transitivity,[status(thm)],[28511, 3660])).
% 4.97/5.19 tff(28531,plain,
% 4.97/5.19 ((~(s(s(s(s(s(s(s(z))))))) = z)) <=> (~(s(s(s(s(s(s(s(z))))))) = elem!1))),
% 4.97/5.19 inference(monotonicity,[status(thm)],[28530])).
% 4.97/5.19 tff(28532,plain,
% 4.97/5.19 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 4.97/5.19 inference(modus_ponens,[status(thm)],[128, 28531])).
% 4.97/5.19 tff(28533,plain,
% 4.97/5.19 ((~b(s(s(s(s(s(s(s(z))))))), z)) <=> (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 4.97/5.19 inference(monotonicity,[status(thm)],[25410])).
% 4.97/5.19 tff(28534,plain,
% 4.97/5.19 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.97/5.19 inference(modus_ponens,[status(thm)],[125, 28533])).
% 4.97/5.19 tff(28535,plain,
% 4.97/5.19 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.97/5.19 inference(unit_resolution,[status(thm)],[3444, 28534, 28532])).
% 4.97/5.19 tff(28536,plain,
% 4.97/5.19 (~r(s(s(s(s(z)))), z)),
% 4.97/5.19 inference(unit_resolution,[status(thm)],[199, 193, 28500])).
% 4.97/5.19 tff(28537,plain,
% 4.97/5.19 (b(s(s(s(s(z)))), z)),
% 4.97/5.19 inference(unit_resolution,[status(thm)],[191, 28536])).
% 4.97/5.19 tff(28538,plain,
% 4.97/5.19 (~b(s(elem!1), s(s(z)))),
% 4.97/5.19 inference(unit_resolution,[status(thm)],[14170, 844, 1146, 166, 928, 108])).
% 4.97/5.19 tff(28539,plain,
% 4.97/5.19 (~r(s(elem!1), s(s(z)))),
% 4.97/5.19 inference(unit_resolution,[status(thm)],[2258, 844, 28500])).
% 4.97/5.19 tff(28540,plain,
% 4.97/5.19 ($false),
% 4.97/5.19 inference(unit_resolution,[status(thm)],[421, 28539, 28538, 1056])).
% 4.97/5.19 tff(28541,plain,((~r(s(elem!1), z)) | (s(elem!1) = s(s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = z)) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 4.97/5.19 tff(28542,plain,
% 4.97/5.19 (~r(s(elem!1), z)),
% 4.97/5.19 inference(unit_resolution,[status(thm)],[28541, 24392, 24628, 166, 5198, 1056])).
% 4.97/5.19 tff(28543,plain,
% 4.97/5.19 (b(s(elem!1), z)),
% 4.97/5.19 inference(unit_resolution,[status(thm)],[774, 28542])).
% 4.97/5.19 tff(28544,plain,
% 4.97/5.19 (~b(z, s(elem!1))),
% 4.97/5.19 inference(unit_resolution,[status(thm)],[22412, 28543, 27212, 273, 1056, 193, 25361, 28537])).
% 4.97/5.19 tff(28545,plain,
% 4.97/5.19 (r(z, s(elem!1))),
% 4.97/5.19 inference(unit_resolution,[status(thm)],[2351, 28544])).
% 4.97/5.19 tff(28546,plain,
% 4.97/5.19 (~r(s(s(z)), s(elem!1))),
% 4.97/5.19 inference(unit_resolution,[status(thm)],[2341, 28545, 28500])).
% 4.97/5.19 tff(28547,plain,
% 4.97/5.19 (b(s(s(z)), s(elem!1))),
% 4.97/5.19 inference(unit_resolution,[status(thm)],[1067, 28546, 2311])).
% 4.97/5.19 tff(28548,plain,
% 4.97/5.19 (r(s(s(z)), elem!1)),
% 4.97/5.19 inference(modus_ponens,[status(thm)],[28500, 25131])).
% 4.97/5.19 tff(28549,plain,
% 4.97/5.19 (r(elem!1, s(elem!1))),
% 4.97/5.19 inference(unit_resolution,[status(thm)],[6201, 28545, 5198])).
% 4.97/5.19 tff(28550,plain,
% 4.97/5.19 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.19 inference(unit_resolution,[status(thm)],[2935, 28549, 1265])).
% 4.97/5.19 tff(28551,plain,
% 4.97/5.19 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.19 inference(unit_resolution,[status(thm)],[395, 28550, 28316])).
% 4.97/5.19 tff(28552,plain,
% 4.97/5.19 (~b(s(elem!1), s(s(z)))),
% 4.97/5.19 inference(unit_resolution,[status(thm)],[2979, 28551, 28548, 28547, 28535])).
% 4.97/5.19 tff(28553,plain,
% 4.97/5.19 (r(s(elem!1), s(s(z)))),
% 4.97/5.19 inference(unit_resolution,[status(thm)],[421, 28552, 1056])).
% 4.97/5.19 tff(28554,plain,
% 4.97/5.19 (~r(s(elem!1), s(s(s(s(z)))))),
% 4.97/5.19 inference(unit_resolution,[status(thm)],[3949, 28553, 193])).
% 4.97/5.19 tff(28555,plain,
% 4.97/5.19 (b(s(elem!1), s(s(s(s(z)))))),
% 4.97/5.19 inference(unit_resolution,[status(thm)],[1084, 28554, 25361])).
% 4.97/5.19 tff(28556,plain,
% 4.97/5.19 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 4.97/5.19 inference(modus_ponens,[status(thm)],[28555, 25350])).
% 4.97/5.19 tff(28557,plain,
% 4.97/5.19 (b(s(s(s(s(z)))), elem!1)),
% 4.97/5.19 inference(unit_resolution,[status(thm)],[20730, 13, 28537])).
% 4.97/5.19 tff(28558,plain,
% 4.97/5.19 (b(s(s(s(s(elem!1)))), elem!1)),
% 4.97/5.19 inference(modus_ponens,[status(thm)],[28557, 5174])).
% 4.97/5.19 tff(28559,plain,
% 4.97/5.19 (~r(s(elem!1), elem!1)),
% 4.97/5.19 inference(unit_resolution,[status(thm)],[28387, 28542, 13])).
% 4.97/5.19 tff(28560,plain,
% 4.97/5.19 (b(s(elem!1), elem!1)),
% 4.97/5.19 inference(unit_resolution,[status(thm)],[677, 28559, 25767])).
% 4.97/5.19 tff(28561,plain,
% 4.97/5.19 (b(elem!1, s(s(s(s(z)))))),
% 4.97/5.19 inference(modus_ponens,[status(thm)],[27212, 28250])).
% 4.97/5.19 tff(28562,plain,
% 4.97/5.19 (b(elem!1, s(s(s(s(elem!1)))))),
% 4.97/5.19 inference(modus_ponens,[status(thm)],[28561, 28249])).
% 4.97/5.19 tff(28563,plain,
% 4.97/5.19 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 4.97/5.19 inference(unit_resolution,[status(thm)],[28258, 178, 28562, 28560, 28558, 28556])).
% 4.97/5.19 tff(28564,plain,
% 4.97/5.19 (~b(s(s(s(s(z)))), s(elem!1))),
% 4.97/5.19 inference(modus_ponens,[status(thm)],[28563, 28529])).
% 4.97/5.19 tff(28565,plain,
% 4.97/5.19 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 4.97/5.19 inference(modus_ponens,[status(thm)],[3831, 25789])).
% 4.97/5.19 tff(28566,plain,
% 4.97/5.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 4.97/5.19 inference(rewrite,[status(thm)],[])).
% 4.97/5.19 tff(28567,plain,
% 4.97/5.19 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 4.97/5.19 inference(rewrite,[status(thm)],[])).
% 4.97/5.19 tff(28568,plain,
% 4.97/5.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 4.97/5.19 inference(monotonicity,[status(thm)],[28567])).
% 4.97/5.19 tff(28569,plain,
% 4.97/5.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 4.97/5.19 inference(transitivity,[status(thm)],[28568, 28566])).
% 4.97/5.19 tff(28570,plain,
% 4.97/5.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 4.97/5.19 inference(quant_inst,[status(thm)],[])).
% 4.97/5.19 tff(28571,plain,
% 4.97/5.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 4.97/5.19 inference(modus_ponens,[status(thm)],[28570, 28569])).
% 4.97/5.19 tff(28572,plain,
% 4.97/5.19 (~b(s(s(s(elem!1))), s(elem!1))),
% 4.97/5.19 inference(unit_resolution,[status(thm)],[28571, 178, 28560, 28558, 28565, 28556])).
% 4.97/5.19 tff(28573,plain,
% 4.97/5.19 (r(s(s(s(elem!1))), s(elem!1))),
% 4.97/5.19 inference(unit_resolution,[status(thm)],[373, 28572, 356])).
% 4.97/5.19 tff(28574,plain,
% 4.97/5.19 (~r(z, s(s(s(elem!1))))),
% 4.97/5.19 inference(unit_resolution,[status(thm)],[5447, 28573, 28545])).
% 4.97/5.19 tff(28575,plain,
% 4.97/5.19 (b(z, s(s(s(elem!1))))),
% 4.97/5.19 inference(unit_resolution,[status(thm)],[2095, 28574])).
% 4.97/5.19 tff(28576,plain,
% 4.97/5.19 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.97/5.19 inference(unit_resolution,[status(thm)],[28354, 28575, 27212, 28537, 3831])).
% 4.97/5.19 tff(28577,plain,
% 4.97/5.19 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 4.97/5.19 inference(unit_resolution,[status(thm)],[10664, 28576, 25833])).
% 4.97/5.19 tff(28578,plain,
% 4.97/5.19 (~r(s(s(s(s(z)))), s(elem!1))),
% 4.97/5.19 inference(unit_resolution,[status(thm)],[22679, 28577, 28573])).
% 4.97/5.19 tff(28579,plain,
% 4.97/5.19 (b(s(s(s(s(z)))), s(elem!1))),
% 4.97/5.19 inference(unit_resolution,[status(thm)],[2173, 28578, 25830])).
% 4.97/5.19 tff(28580,plain,
% 4.97/5.19 ($false),
% 4.97/5.19 inference(unit_resolution,[status(thm)],[28579, 28564])).
% 4.97/5.19 tff(28581,plain,(b(s(s(s(s(s(s(s(z))))))), z) | (~(z = elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))) | (s(elem!1) = s(s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 4.97/5.19 tff(28582,plain,
% 4.97/5.19 (b(s(s(s(s(s(s(s(z))))))), z)),
% 4.97/5.19 inference(unit_resolution,[status(thm)],[28581, 1056, 3831, 356, 193, 13, 1265, 273, 166])).
% 4.97/5.19 tff(28583,plain,
% 4.97/5.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), 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))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), 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))))))), z)))),
% 4.97/5.19 inference(rewrite,[status(thm)],[])).
% 4.97/5.19 tff(28584,plain,
% 4.97/5.19 (((~b(z, 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(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), 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))))))), z)))),
% 4.97/5.19 inference(rewrite,[status(thm)],[])).
% 4.97/5.19 tff(28585,plain,
% 4.97/5.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), 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))))))), z))))),
% 4.97/5.19 inference(monotonicity,[status(thm)],[28584])).
% 4.97/5.19 tff(28586,plain,
% 4.97/5.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), 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))))))), z)))),
% 4.97/5.19 inference(transitivity,[status(thm)],[28585, 28583])).
% 4.97/5.19 tff(28587,plain,
% 4.97/5.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 4.97/5.20 inference(quant_inst,[status(thm)],[])).
% 4.97/5.20 tff(28588,plain,
% 4.97/5.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), 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))))))), z))),
% 4.97/5.20 inference(modus_ponens,[status(thm)],[28587, 28586])).
% 4.97/5.20 tff(28589,plain,
% 4.97/5.20 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 4.97/5.20 inference(unit_resolution,[status(thm)],[28588, 178, 273, 28537, 24628])).
% 4.97/5.20 tff(28590,plain,
% 4.97/5.20 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.20 inference(unit_resolution,[status(thm)],[28589, 28582])).
% 4.97/5.20 tff(28591,plain,
% 4.97/5.20 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.20 inference(unit_resolution,[status(thm)],[222, 28590])).
% 4.97/5.20 tff(28592,plain,
% 4.97/5.20 (r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.20 inference(modus_ponens,[status(thm)],[28591, 28528])).
% 4.97/5.20 tff(28593,plain,
% 4.97/5.20 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 4.97/5.20 inference(monotonicity,[status(thm)],[13])).
% 4.97/5.20 tff(28594,plain,
% 4.97/5.20 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), z)),
% 4.97/5.20 inference(symmetry,[status(thm)],[28593])).
% 4.97/5.20 tff(28595,plain,
% 4.97/5.20 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 4.97/5.20 inference(monotonicity,[status(thm)],[15])).
% 4.97/5.20 tff(28596,plain,
% 4.97/5.20 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), z)),
% 4.97/5.20 inference(transitivity,[status(thm)],[28595, 28594])).
% 4.97/5.20 tff(28597,plain,
% 4.97/5.20 (r(s(s(elem!1)), z)),
% 4.97/5.20 inference(modus_ponens,[status(thm)],[28548, 28596])).
% 4.97/5.20 tff(28598,plain,
% 4.97/5.20 (b(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.97/5.20 inference(monotonicity,[status(thm)],[15])).
% 4.97/5.20 tff(28599,plain,
% 4.97/5.20 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 4.97/5.20 inference(modus_ponens,[status(thm)],[24628, 28598])).
% 4.97/5.20 tff(28600,plain,
% 4.97/5.20 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 4.97/5.20 inference(modus_ponens,[status(thm)],[28582, 25410])).
% 4.97/5.20 tff(28601,plain,
% 4.97/5.20 (~r(s(elem!1), z)),
% 4.97/5.20 inference(unit_resolution,[status(thm)],[2258, 363, 28500])).
% 4.97/5.20 tff(28602,plain,
% 4.97/5.20 (b(s(elem!1), z)),
% 4.97/5.20 inference(unit_resolution,[status(thm)],[774, 28601])).
% 4.97/5.20 tff(28603,plain,
% 4.97/5.20 (~b(z, s(elem!1))),
% 4.97/5.20 inference(unit_resolution,[status(thm)],[22412, 28602, 27212, 273, 1056, 193, 1369, 28537])).
% 4.97/5.20 tff(28604,plain,
% 4.97/5.20 (r(z, s(elem!1))),
% 4.97/5.20 inference(unit_resolution,[status(thm)],[2351, 28603])).
% 4.97/5.20 tff(28605,plain,
% 4.97/5.20 (r(elem!1, s(elem!1))),
% 4.97/5.20 inference(unit_resolution,[status(thm)],[6201, 28604, 928])).
% 4.97/5.20 tff(28606,plain,
% 4.97/5.20 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.20 inference(unit_resolution,[status(thm)],[2935, 28605, 1265])).
% 4.97/5.20 tff(28607,plain,
% 4.97/5.20 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 4.97/5.20 inference(unit_resolution,[status(thm)],[395, 28606, 2286])).
% 4.97/5.20 tff(28608,plain,
% 4.97/5.20 (~r(s(elem!1), elem!1)),
% 4.97/5.20 inference(unit_resolution,[status(thm)],[2249, 363, 438])).
% 5.04/5.20 tff(28609,plain,
% 5.04/5.20 (b(s(elem!1), elem!1)),
% 5.04/5.20 inference(unit_resolution,[status(thm)],[677, 28608, 725])).
% 5.04/5.20 tff(28610,plain,
% 5.04/5.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(elem!1), s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 5.04/5.20 inference(rewrite,[status(thm)],[])).
% 5.04/5.20 tff(28611,plain,
% 5.04/5.20 (((~b(elem!1, 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(s(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)))))))))) <=> ((~b(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(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 5.04/5.20 inference(rewrite,[status(thm)],[])).
% 5.04/5.20 tff(28612,plain,
% 5.04/5.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, 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(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 5.04/5.20 inference(monotonicity,[status(thm)],[28611])).
% 5.04/5.20 tff(28613,plain,
% 5.04/5.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, 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(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 5.04/5.20 inference(transitivity,[status(thm)],[28612, 28610])).
% 5.04/5.20 tff(28614,plain,
% 5.04/5.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, 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(s(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))))))))))),
% 5.04/5.20 inference(quant_inst,[status(thm)],[])).
% 5.04/5.20 tff(28615,plain,
% 5.04/5.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 5.04/5.20 inference(modus_ponens,[status(thm)],[28614, 28613])).
% 5.04/5.20 tff(28616,plain,
% 5.04/5.20 ($false),
% 5.04/5.20 inference(unit_resolution,[status(thm)],[28615, 178, 28609, 28607, 6572, 3664, 3504])).
% 5.04/5.20 tff(28617,plain,((~r(s(elem!1), s(s(z)))) | (~b(elem!1, s(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(elem!1)))) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = z)) | (~b(z, s(s(z)))) | (s(elem!1) = s(s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (s(elem!1) = s(s(s(s(z))))) | (s(elem!1) = elem!1) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.20 tff(28618,plain,
% 5.04/5.20 (~r(s(elem!1), s(s(z)))),
% 5.04/5.20 inference(unit_resolution,[status(thm)],[28617, 28600, 28295, 28599, 28316, 1265, 5198, 273, 1056, 193, 25361, 25767, 28548])).
% 5.04/5.20 tff(28619,plain,
% 5.04/5.20 (b(s(elem!1), s(s(z)))),
% 5.04/5.20 inference(unit_resolution,[status(thm)],[421, 28618, 1056])).
% 5.04/5.20 tff(28620,plain,
% 5.04/5.20 (b(s(elem!1), s(s(elem!1)))),
% 5.04/5.20 inference(modus_ponens,[status(thm)],[28619, 25826])).
% 5.04/5.20 tff(28621,plain,
% 5.04/5.20 (~r(s(elem!1), elem!1)),
% 5.04/5.20 inference(unit_resolution,[status(thm)],[28387, 767, 13])).
% 5.04/5.20 tff(28622,plain,
% 5.04/5.20 (b(s(elem!1), elem!1)),
% 5.04/5.20 inference(unit_resolution,[status(thm)],[677, 28621, 25767])).
% 5.04/5.20 tff(28623,plain,
% 5.04/5.20 (~b(z, s(elem!1))),
% 5.04/5.20 inference(unit_resolution,[status(thm)],[22412, 10020, 27212, 273, 1056, 193, 25361, 28537])).
% 5.04/5.20 tff(28624,plain,
% 5.04/5.20 (r(z, s(elem!1))),
% 5.04/5.20 inference(unit_resolution,[status(thm)],[2351, 28623])).
% 5.04/5.20 tff(28625,plain,
% 5.04/5.20 (~r(s(s(z)), s(elem!1))),
% 5.04/5.20 inference(unit_resolution,[status(thm)],[2341, 28624, 28500])).
% 5.04/5.20 tff(28626,plain,
% 5.04/5.20 (b(s(s(elem!1)), s(elem!1))),
% 5.04/5.20 inference(unit_resolution,[status(thm)],[14326, 28625, 13, 1056])).
% 5.04/5.20 tff(28627,plain,
% 5.04/5.20 (r(elem!1, s(elem!1))),
% 5.04/5.20 inference(unit_resolution,[status(thm)],[6201, 28624, 5198])).
% 5.04/5.20 tff(28628,plain,
% 5.04/5.20 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.20 inference(unit_resolution,[status(thm)],[2935, 28627, 1265])).
% 5.04/5.20 tff(28629,plain,
% 5.04/5.20 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.20 inference(unit_resolution,[status(thm)],[395, 28628, 28316])).
% 5.04/5.20 tff(28630,plain,
% 5.04/5.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(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(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(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(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(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(elem!1)))))),
% 5.04/5.20 inference(rewrite,[status(thm)],[])).
% 5.04/5.20 tff(28631,plain,
% 5.04/5.20 (((~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(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(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(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(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(elem!1)))))),
% 5.04/5.20 inference(rewrite,[status(thm)],[])).
% 5.04/5.20 tff(28632,plain,
% 5.04/5.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(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(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(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(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(elem!1))))))),
% 5.04/5.20 inference(monotonicity,[status(thm)],[28631])).
% 5.04/5.20 tff(28633,plain,
% 5.04/5.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(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(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(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(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(elem!1)))))),
% 5.04/5.20 inference(transitivity,[status(thm)],[28632, 28630])).
% 5.04/5.20 tff(28634,plain,
% 5.04/5.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(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(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 5.04/5.20 inference(quant_inst,[status(thm)],[])).
% 5.04/5.20 tff(28635,plain,
% 5.04/5.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 5.04/5.20 inference(modus_ponens,[status(thm)],[28634, 28633])).
% 5.04/5.20 tff(28636,plain,
% 5.04/5.20 ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 5.04/5.20 inference(unit_resolution,[status(thm)],[28635, 178, 5391, 28295, 28599, 18309])).
% 5.04/5.20 tff(28637,plain,
% 5.04/5.20 ($false),
% 5.04/5.20 inference(unit_resolution,[status(thm)],[28636, 28629, 28626, 28622])).
% 5.04/5.20 tff(28638,plain,(r(s(elem!1), z) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~(z = elem!1)) | (s(elem!1) = s(s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.20 tff(28639,plain,
% 5.04/5.20 (r(s(elem!1), z)),
% 5.04/5.20 inference(unit_resolution,[status(thm)],[28638, 28620, 28509, 13, 1056, 1265, 273, 193])).
% 5.04/5.20 tff(28640,plain,
% 5.04/5.20 (~r(s(s(elem!1)), s(elem!1))),
% 5.04/5.20 inference(unit_resolution,[status(thm)],[997, 28639, 28597])).
% 5.04/5.20 tff(28641,plain,
% 5.04/5.20 (b(s(s(elem!1)), s(elem!1))),
% 5.04/5.20 inference(unit_resolution,[status(thm)],[1006, 28640, 28523])).
% 5.04/5.20 tff(28642,plain,
% 5.04/5.20 ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 5.04/5.20 inference(unit_resolution,[status(thm)],[10953, 178, 28620, 28599, 28509])).
% 5.04/5.20 tff(28643,plain,
% 5.04/5.20 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.20 inference(unit_resolution,[status(thm)],[28642, 28641])).
% 5.04/5.20 tff(28644,plain,
% 5.04/5.20 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.20 inference(unit_resolution,[status(thm)],[395, 28643, 28316])).
% 5.04/5.20 tff(28645,plain,
% 5.04/5.20 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(elem!1))),
% 5.04/5.20 inference(monotonicity,[status(thm)],[25768])).
% 5.04/5.20 tff(28646,plain,
% 5.04/5.20 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 5.04/5.20 inference(symmetry,[status(thm)],[28645])).
% 5.04/5.20 tff(28647,plain,
% 5.04/5.20 (~r(elem!1, s(elem!1))),
% 5.04/5.20 inference(unit_resolution,[status(thm)],[2935, 28644, 1265])).
% 5.04/5.20 tff(28648,plain,
% 5.04/5.20 (~r(z, s(elem!1))),
% 5.04/5.20 inference(unit_resolution,[status(thm)],[6201, 28647, 5198])).
% 5.04/5.20 tff(28649,plain,
% 5.04/5.20 (b(z, s(elem!1))),
% 5.04/5.20 inference(unit_resolution,[status(thm)],[2351, 28648])).
% 5.04/5.20 tff(28650,plain,
% 5.04/5.20 (~b(s(s(s(s(z)))), s(elem!1))),
% 5.04/5.20 inference(unit_resolution,[status(thm)],[10985, 28649, 273, 28537, 28619])).
% 5.04/5.20 tff(28651,plain,
% 5.04/5.20 (r(s(s(s(s(z)))), s(elem!1))),
% 5.04/5.20 inference(unit_resolution,[status(thm)],[2173, 28650, 25830])).
% 5.04/5.20 tff(28652,plain,
% 5.04/5.20 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 5.04/5.20 inference(modus_ponens,[status(thm)],[28651, 28646])).
% 5.04/5.20 tff(28653,plain,
% 5.04/5.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 5.04/5.20 inference(rewrite,[status(thm)],[])).
% 5.04/5.20 tff(28654,plain,
% 5.04/5.20 (((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 5.04/5.20 inference(rewrite,[status(thm)],[])).
% 5.04/5.20 tff(28655,plain,
% 5.04/5.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))))),
% 5.04/5.20 inference(monotonicity,[status(thm)],[28654])).
% 5.04/5.20 tff(28656,plain,
% 5.04/5.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 5.04/5.20 inference(transitivity,[status(thm)],[28655, 28653])).
% 5.04/5.20 tff(28657,plain,
% 5.04/5.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 5.04/5.20 inference(quant_inst,[status(thm)],[])).
% 5.04/5.20 tff(28658,plain,
% 5.04/5.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))),
% 5.04/5.20 inference(modus_ponens,[status(thm)],[28657, 28656])).
% 5.04/5.20 tff(28659,plain,
% 5.04/5.20 ($false),
% 5.04/5.20 inference(unit_resolution,[status(thm)],[28658, 118, 28652, 28644, 28592])).
% 5.04/5.20 tff(28660,plain,((s(elem!1) = s(s(z))) | (~(z = elem!1)) | (~b(z, s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.20 tff(28661,plain,
% 5.04/5.20 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.20 inference(unit_resolution,[status(thm)],[28660, 28526, 273, 13, 103, 28518, 28517, 166])).
% 5.04/5.20 tff(28662,plain,
% 5.04/5.20 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.20 inference(unit_resolution,[status(thm)],[691, 28661, 28513])).
% 5.04/5.20 tff(28663,plain,
% 5.04/5.20 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), z)),
% 5.04/5.20 inference(symmetry,[status(thm)],[28208])).
% 5.04/5.20 tff(28664,plain,
% 5.04/5.20 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.04/5.20 inference(unit_resolution,[status(thm)],[14184, 28661, 166, 28513, 27217, 28242])).
% 5.04/5.20 tff(28665,plain,
% 5.04/5.20 (r(s(s(s(s(s(s(s(z))))))), z)),
% 5.04/5.20 inference(modus_ponens,[status(thm)],[28664, 28663])).
% 5.04/5.20 tff(28666,plain,
% 5.04/5.20 (~r(s(elem!1), z)),
% 5.04/5.20 inference(unit_resolution,[status(thm)],[28541, 28665, 27217, 166, 5198, 28526])).
% 5.04/5.20 tff(28667,plain,
% 5.04/5.20 (~r(s(elem!1), elem!1)),
% 5.04/5.20 inference(unit_resolution,[status(thm)],[28387, 28666, 13])).
% 5.04/5.20 tff(28668,plain,
% 5.04/5.20 (b(s(elem!1), elem!1)),
% 5.04/5.20 inference(unit_resolution,[status(thm)],[677, 28667, 25767])).
% 5.04/5.20 tff(28669,plain,
% 5.04/5.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 5.04/5.20 inference(rewrite,[status(thm)],[])).
% 5.04/5.20 tff(28670,plain,
% 5.04/5.20 (((~b(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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 5.04/5.20 inference(rewrite,[status(thm)],[])).
% 5.04/5.20 tff(28671,plain,
% 5.04/5.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 5.04/5.20 inference(monotonicity,[status(thm)],[28670])).
% 5.04/5.20 tff(28672,plain,
% 5.04/5.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 5.04/5.20 inference(transitivity,[status(thm)],[28671, 28669])).
% 5.04/5.20 tff(28673,plain,
% 5.04/5.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 5.04/5.20 inference(quant_inst,[status(thm)],[])).
% 5.04/5.20 tff(28674,plain,
% 5.04/5.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 5.04/5.20 inference(modus_ponens,[status(thm)],[28673, 28672])).
% 5.04/5.20 tff(28675,plain,
% 5.04/5.20 ($false),
% 5.04/5.20 inference(unit_resolution,[status(thm)],[28674, 178, 683, 5391, 869, 6572, 18309])).
% 5.04/5.20 tff(28676,plain,((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.20 tff(28677,plain,
% 5.04/5.20 (~b(s(elem!1), s(s(elem!1)))),
% 5.04/5.20 inference(unit_resolution,[status(thm)],[28676, 28668, 28662, 28295, 28509])).
% 5.04/5.20 tff(28678,plain,
% 5.04/5.20 (r(s(elem!1), s(s(elem!1)))),
% 5.04/5.20 inference(unit_resolution,[status(thm)],[1028, 28677, 13483])).
% 5.04/5.20 tff(28679,plain,
% 5.04/5.20 (r(s(elem!1), s(s(z)))),
% 5.04/5.20 inference(modus_ponens,[status(thm)],[28678, 13473])).
% 5.04/5.20 tff(28680,plain,
% 5.04/5.20 (~r(s(elem!1), s(s(s(s(z)))))),
% 5.04/5.20 inference(unit_resolution,[status(thm)],[3949, 28679, 103])).
% 5.04/5.20 tff(28681,plain,
% 5.04/5.20 (b(s(elem!1), s(s(s(s(z)))))),
% 5.04/5.20 inference(unit_resolution,[status(thm)],[1084, 28680, 25361])).
% 5.04/5.20 tff(28682,plain,
% 5.04/5.20 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 5.04/5.20 inference(modus_ponens,[status(thm)],[28681, 25350])).
% 5.04/5.20 tff(28683,plain,
% 5.04/5.20 (b(s(s(s(s(elem!1)))), elem!1)),
% 5.04/5.20 inference(modus_ponens,[status(thm)],[28514, 5174])).
% 5.04/5.20 tff(28684,plain,
% 5.04/5.20 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 5.04/5.20 inference(unit_resolution,[status(thm)],[28258, 178, 28562, 28668, 28683, 28682])).
% 5.04/5.20 tff(28685,plain,
% 5.04/5.20 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 5.04/5.20 inference(modus_ponens,[status(thm)],[103, 28219])).
% 5.04/5.20 tff(28686,plain,
% 5.04/5.21 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 5.04/5.21 inference(modus_ponens,[status(thm)],[28685, 12141])).
% 5.04/5.21 tff(28687,plain,
% 5.04/5.21 ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[28230, 118, 28678])).
% 5.04/5.21 tff(28688,plain,
% 5.04/5.21 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[28687, 28686])).
% 5.04/5.21 tff(28689,plain,
% 5.04/5.21 ($false),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[28236, 28688, 28684, 28507])).
% 5.04/5.21 tff(28690,plain,((~(z = elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.21 tff(28691,plain,
% 5.04/5.21 (~(z = elem!1)),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[28690, 27224, 273, 27245, 86])).
% 5.04/5.21 tff(28692,plain,
% 5.04/5.21 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[21520, 4236, 27245, 28506, 27212])).
% 5.04/5.21 tff(28693,plain,
% 5.04/5.21 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[20667, 28692])).
% 5.04/5.21 tff(28694,plain,
% 5.04/5.21 (r(s(s(z)), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 5.04/5.21 inference(monotonicity,[status(thm)],[1324])).
% 5.04/5.21 tff(28695,plain,
% 5.04/5.21 (r(elem!1, s(s(s(z)))) <=> r(s(s(z)), s(s(s(z))))),
% 5.04/5.21 inference(symmetry,[status(thm)],[28694])).
% 5.04/5.21 tff(28696,plain,
% 5.04/5.21 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(elem!1))),
% 5.04/5.21 inference(monotonicity,[status(thm)],[3505])).
% 5.04/5.21 tff(28697,plain,
% 5.04/5.21 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(z))))),
% 5.04/5.21 inference(symmetry,[status(thm)],[28696])).
% 5.04/5.21 tff(28698,plain,
% 5.04/5.21 (r(elem!1, s(elem!1)) <=> r(s(s(z)), s(s(s(z))))),
% 5.04/5.21 inference(transitivity,[status(thm)],[28697, 28695])).
% 5.04/5.21 tff(28699,plain,
% 5.04/5.21 ((~r(elem!1, s(elem!1))) <=> (~r(s(s(z)), s(s(s(z)))))),
% 5.04/5.21 inference(monotonicity,[status(thm)],[28698])).
% 5.04/5.21 tff(28700,plain,
% 5.04/5.21 (~b(elem!1, z)),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[23817, 10916, 23814])).
% 5.04/5.21 tff(28701,plain,
% 5.04/5.21 (~(elem!1 = s(s(s(s(z)))))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[12557, 28700, 28506])).
% 5.04/5.21 tff(28702,plain,
% 5.04/5.21 (~(s(s(s(s(z)))) = elem!1)),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[504, 28701])).
% 5.04/5.21 tff(28703,plain,
% 5.04/5.21 (~(s(elem!1) = s(s(s(s(z)))))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[1353, 28702, 10916])).
% 5.04/5.21 tff(28704,plain,
% 5.04/5.21 (r(elem!1, z)),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[1345, 1324, 28500])).
% 5.04/5.21 tff(28705,plain,
% 5.04/5.21 (r(elem!1, s(s(s(s(z)))))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[483, 28701, 24376])).
% 5.04/5.21 tff(28706,plain,
% 5.04/5.21 (~r(elem!1, s(elem!1))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[27585, 28705, 28704, 28703, 28506])).
% 5.04/5.21 tff(28707,plain,
% 5.04/5.21 (~r(s(s(z)), s(s(s(z))))),
% 5.04/5.21 inference(modus_ponens,[status(thm)],[28706, 28699])).
% 5.04/5.21 tff(28708,plain,
% 5.04/5.21 (b(s(s(z)), s(s(s(z))))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[5088, 28707])).
% 5.04/5.21 tff(28709,plain,
% 5.04/5.21 (~b(s(s(s(z))), s(s(z)))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[21439, 28708, 27224, 27217, 3002])).
% 5.04/5.21 tff(28710,plain,
% 5.04/5.21 (r(s(s(s(z))), s(s(z)))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[4966, 28709])).
% 5.04/5.21 tff(28711,plain,
% 5.04/5.21 (~r(s(s(s(z))), z)),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[24599, 28710, 28500])).
% 5.04/5.21 tff(28712,plain,
% 5.04/5.21 (b(s(s(s(z))), z)),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[21073, 28711])).
% 5.04/5.21 tff(28713,plain,
% 5.04/5.21 ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[21371, 178, 27212, 28506, 27245])).
% 5.04/5.21 tff(28714,plain,
% 5.04/5.21 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[28713, 28712])).
% 5.04/5.21 tff(28715,plain,
% 5.04/5.21 (r(s(s(s(s(z)))), s(s(s(z))))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[11185, 28714])).
% 5.04/5.21 tff(28716,plain,
% 5.04/5.21 (r(s(s(elem!1)), s(elem!1))),
% 5.04/5.21 inference(modus_ponens,[status(thm)],[28715, 8581])).
% 5.04/5.21 tff(28717,plain,
% 5.04/5.21 (r(s(s(s(s(z)))), elem!1)),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[3142, 28702, 8804])).
% 5.04/5.21 tff(28718,plain,
% 5.04/5.21 (r(s(s(elem!1)), elem!1)),
% 5.04/5.21 inference(modus_ponens,[status(thm)],[28717, 10919])).
% 5.04/5.21 tff(28719,plain,
% 5.04/5.21 (r(s(elem!1), elem!1)),
% 5.04/5.21 inference(modus_ponens,[status(thm)],[28710, 8116])).
% 5.04/5.21 tff(28720,plain,
% 5.04/5.21 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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))))),
% 5.04/5.21 inference(rewrite,[status(thm)],[])).
% 5.04/5.21 tff(28721,plain,
% 5.04/5.21 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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))))),
% 5.04/5.21 inference(quant_inst,[status(thm)],[])).
% 5.04/5.21 tff(28722,plain,
% 5.04/5.21 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))),
% 5.04/5.21 inference(modus_ponens,[status(thm)],[28721, 28720])).
% 5.04/5.21 tff(28723,plain,
% 5.04/5.21 ($false),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[28722, 118, 28719, 28718, 28716])).
% 5.04/5.21 tff(28724,plain,((~(s(s(z)) = elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | b(s(s(z)), z) | b(s(s(z)), s(s(s(s(z))))) | b(s(s(s(s(z)))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.21 tff(28725,plain,
% 5.04/5.21 (~(s(s(z)) = elem!1)),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[28724, 28693, 23814, 105, 86])).
% 5.04/5.21 tff(28726,plain,
% 5.04/5.21 (r(elem!1, z)),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[498, 5723, 2809])).
% 5.04/5.21 tff(28727,plain,
% 5.04/5.21 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[10809, 28726, 4236])).
% 5.04/5.21 tff(28728,plain,
% 5.04/5.21 (~r(elem!1, s(s(z)))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[458, 28726, 28500])).
% 5.04/5.21 tff(28729,plain,
% 5.04/5.21 (b(elem!1, s(s(z)))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[467, 28728, 312])).
% 5.04/5.21 tff(28730,plain,
% 5.04/5.21 (~r(s(s(z)), elem!1)),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[443, 28726, 28500])).
% 5.04/5.21 tff(28731,plain,
% 5.04/5.21 (b(s(s(z)), elem!1)),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[448, 28730, 12])).
% 5.04/5.21 tff(28732,plain,
% 5.04/5.21 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[11859, 28731, 24628, 27396, 28729])).
% 5.04/5.21 tff(28733,plain,
% 5.04/5.21 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[691, 28732, 28727])).
% 5.04/5.21 tff(28734,plain,
% 5.04/5.21 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 5.04/5.21 inference(monotonicity,[status(thm)],[28733])).
% 5.04/5.21 tff(28735,plain,
% 5.04/5.21 (r(s(s(z)), s(elem!1)) <=> r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 5.04/5.21 inference(monotonicity,[status(thm)],[28734])).
% 5.04/5.21 tff(28736,plain,
% 5.04/5.21 (r(s(s(z)), s(s(s(s(s(s(s(s(z))))))))) <=> r(s(s(z)), s(elem!1))),
% 5.04/5.21 inference(symmetry,[status(thm)],[28735])).
% 5.04/5.21 tff(28737,plain,
% 5.04/5.21 ((~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) <=> (~r(s(s(z)), s(elem!1)))),
% 5.04/5.21 inference(monotonicity,[status(thm)],[28736])).
% 5.04/5.21 tff(28738,plain,
% 5.04/5.21 (~(s(elem!1) = s(s(s(s(z)))))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[16181, 28733])).
% 5.04/5.21 tff(28739,plain,
% 5.04/5.21 (~(s(s(s(s(z)))) = s(elem!1))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[2168, 28738])).
% 5.04/5.21 tff(28740,plain,
% 5.04/5.21 (r(elem!1, s(s(s(s(z)))))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[24769, 28733, 3428])).
% 5.04/5.21 tff(28741,plain,
% 5.04/5.21 (~r(elem!1, s(elem!1))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[27585, 28740, 28726, 28738, 28537])).
% 5.04/5.21 tff(28742,plain,
% 5.04/5.21 (~(elem!1 = s(s(s(s(z)))))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[12557, 5723, 28537])).
% 5.04/5.21 tff(28743,plain,
% 5.04/5.21 (~(s(s(elem!1)) = elem!1)),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[2510, 28739, 28733])).
% 5.04/5.21 tff(28744,plain,
% 5.04/5.21 (~(s(elem!1) = elem!1)),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[672, 28743])).
% 5.04/5.21 tff(28745,plain,
% 5.04/5.21 (r(s(elem!1), elem!1)),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[677, 725, 2141])).
% 5.04/5.21 tff(28746,plain,
% 5.04/5.21 (~r(s(elem!1), z)),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[13694, 28745, 437])).
% 5.04/5.21 tff(28747,plain,
% 5.04/5.21 (~(s(elem!1) = s(s(z)))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[906, 28746, 106])).
% 5.04/5.21 tff(28748,plain,
% 5.04/5.21 (b(s(elem!1), z)),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[774, 28746])).
% 5.04/5.21 tff(28749,plain,
% 5.04/5.21 (~(s(s(z)) = s(elem!1))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[1058, 28747])).
% 5.04/5.21 tff(28750,plain,
% 5.04/5.21 (~r(z, s(elem!1))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[2341, 1329, 106])).
% 5.04/5.21 tff(28751,plain,
% 5.04/5.21 (b(z, s(elem!1))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[2351, 28750])).
% 5.04/5.21 tff(28752,plain,
% 5.04/5.21 (~b(z, s(s(s(s(z)))))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[22412, 28751, 273, 853, 1056, 193, 1369, 168])).
% 5.04/5.21 tff(28753,plain,
% 5.04/5.21 (r(z, s(s(s(s(z)))))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[46, 28752])).
% 5.04/5.21 tff(28754,plain,
% 5.04/5.21 (~r(elem!1, s(s(s(s(z)))))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[478, 28753, 437])).
% 5.04/5.21 tff(28755,plain,
% 5.04/5.21 (b(elem!1, s(s(s(s(z)))))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[483, 28754, 469])).
% 5.04/5.21 tff(28756,plain,
% 5.04/5.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 5.04/5.21 inference(rewrite,[status(thm)],[])).
% 5.04/5.21 tff(28757,plain,
% 5.04/5.21 (((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 5.04/5.21 inference(rewrite,[status(thm)],[])).
% 5.04/5.21 tff(28758,plain,
% 5.04/5.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 5.04/5.21 inference(monotonicity,[status(thm)],[28757])).
% 5.04/5.21 tff(28759,plain,
% 5.04/5.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 5.04/5.21 inference(transitivity,[status(thm)],[28758, 28756])).
% 5.04/5.21 tff(28760,plain,
% 5.04/5.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))))),
% 5.04/5.21 inference(quant_inst,[status(thm)],[])).
% 5.04/5.21 tff(28761,plain,
% 5.04/5.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 5.04/5.21 inference(modus_ponens,[status(thm)],[28760, 28759])).
% 5.04/5.21 tff(28762,plain,
% 5.04/5.21 ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[28761, 178, 854, 853, 168])).
% 5.04/5.21 tff(28763,plain,
% 5.04/5.21 (~b(s(s(s(s(z)))), s(elem!1))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[28762, 28755])).
% 5.04/5.21 tff(28764,plain,
% 5.04/5.21 (r(s(s(s(s(z)))), s(elem!1))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[2173, 28763, 2169])).
% 5.04/5.21 tff(28765,plain,
% 5.04/5.21 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 5.04/5.21 inference(rewrite,[status(thm)],[])).
% 5.04/5.21 tff(28766,plain,
% 5.04/5.21 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 5.04/5.21 inference(quant_inst,[status(thm)],[])).
% 5.04/5.21 tff(28767,plain,
% 5.04/5.21 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 5.04/5.21 inference(modus_ponens,[status(thm)],[28766, 28765])).
% 5.04/5.21 tff(28768,plain,
% 5.04/5.21 ($false),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[28767, 118, 1329, 28764, 193])).
% 5.04/5.21 tff(28769,plain,((~r(s(s(z)), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (elem!1 = s(s(s(s(z))))) | (~r(elem!1, z)) | (~b(z, s(s(z)))) | (s(elem!1) = s(s(z))) | (s(elem!1) = s(s(s(s(z))))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.21 tff(28770,plain,
% 5.04/5.21 (~r(s(s(z)), s(elem!1))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[28769, 757, 193, 28748, 168, 469, 437, 273, 28747, 1369, 106])).
% 5.04/5.21 tff(28771,plain,
% 5.04/5.21 (b(s(s(z)), s(elem!1))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[1067, 28770, 28749])).
% 5.04/5.21 tff(28772,plain,
% 5.04/5.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 5.04/5.21 inference(rewrite,[status(thm)],[])).
% 5.04/5.21 tff(28773,plain,
% 5.04/5.21 (((~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1))) <=> ((~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 5.04/5.21 inference(rewrite,[status(thm)],[])).
% 5.04/5.21 tff(28774,plain,
% 5.04/5.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z))))))),
% 5.04/5.21 inference(monotonicity,[status(thm)],[28773])).
% 5.04/5.21 tff(28775,plain,
% 5.04/5.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 5.04/5.21 inference(transitivity,[status(thm)],[28774, 28772])).
% 5.04/5.21 tff(28776,plain,
% 5.04/5.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)))),
% 5.04/5.21 inference(quant_inst,[status(thm)],[])).
% 5.04/5.21 tff(28777,plain,
% 5.04/5.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z))))),
% 5.04/5.21 inference(modus_ponens,[status(thm)],[28776, 28775])).
% 5.04/5.21 tff(28778,plain,
% 5.04/5.21 (~b(z, elem!1)),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[28777, 178, 757, 273, 812, 28771])).
% 5.04/5.21 tff(28779,plain,
% 5.04/5.21 (r(z, elem!1)),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[585, 28778, 507])).
% 5.04/5.21 tff(28780,plain,
% 5.04/5.21 (~r(z, s(elem!1))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[7070, 28779, 28745])).
% 5.04/5.21 tff(28781,plain,
% 5.04/5.21 (b(z, s(elem!1))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[2351, 28780])).
% 5.04/5.21 tff(28782,plain,
% 5.04/5.21 (~b(z, s(s(s(s(z)))))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[22412, 28781, 273, 28748, 28747, 193, 1369, 168])).
% 5.04/5.21 tff(28783,plain,
% 5.04/5.21 (r(z, s(s(s(s(z)))))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[46, 28782])).
% 5.04/5.21 tff(28784,plain,
% 5.04/5.21 (~r(s(s(z)), s(s(s(s(z)))))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[155, 28783, 106])).
% 5.04/5.21 tff(28785,plain,
% 5.04/5.21 (b(s(s(z)), s(s(s(s(z)))))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[164, 28784])).
% 5.04/5.21 tff(28786,plain,
% 5.04/5.21 (~b(s(elem!1), s(s(z)))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[2776, 28781, 273, 28771, 28748])).
% 5.04/5.21 tff(28787,plain,
% 5.04/5.21 (r(s(elem!1), s(s(z)))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[421, 28786, 28747])).
% 5.04/5.21 tff(28788,plain,
% 5.04/5.21 (~r(s(elem!1), s(s(s(s(z)))))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[3949, 28787, 193])).
% 5.04/5.21 tff(28789,plain,
% 5.04/5.21 (b(s(elem!1), s(s(s(s(z)))))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[1084, 28788, 1369])).
% 5.04/5.21 tff(28790,plain,
% 5.04/5.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 5.04/5.21 inference(rewrite,[status(thm)],[])).
% 5.04/5.21 tff(28791,plain,
% 5.04/5.21 (((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(s(z))))) <=> ((~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 5.04/5.21 inference(rewrite,[status(thm)],[])).
% 5.04/5.21 tff(28792,plain,
% 5.04/5.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 5.04/5.21 inference(monotonicity,[status(thm)],[28791])).
% 5.04/5.21 tff(28793,plain,
% 5.04/5.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 5.04/5.21 inference(transitivity,[status(thm)],[28792, 28790])).
% 5.04/5.21 tff(28794,plain,
% 5.04/5.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(s(z)))))),
% 5.04/5.21 inference(quant_inst,[status(thm)],[])).
% 5.04/5.21 tff(28795,plain,
% 5.04/5.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 5.04/5.21 inference(modus_ponens,[status(thm)],[28794, 28793])).
% 5.04/5.21 tff(28796,plain,
% 5.04/5.21 ($false),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[28795, 178, 28781, 273, 28771, 28789, 28785])).
% 5.04/5.21 tff(28797,plain,((s(elem!1) = elem!1) | (~b(z, s(s(z)))) | (s(elem!1) = s(s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (z = elem!1) | (~b(elem!1, s(s(z)))) | (elem!1 = s(s(s(s(z))))) | (~r(elem!1, z)) | r(elem!1, s(elem!1)) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 5.04/5.21 tff(28798,plain,
% 5.04/5.21 (b(s(elem!1), elem!1)),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[28797, 28744, 28500, 273, 193, 28537, 507, 28742, 28729, 28726, 28738, 28741])).
% 5.04/5.21 tff(28799,plain,
% 5.04/5.21 (~(elem!1 = s(elem!1))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[748, 28744])).
% 5.04/5.21 tff(28800,plain,
% 5.04/5.21 (~(s(elem!1) = s(s(z)))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[2832, 28733])).
% 5.04/5.21 tff(28801,plain,
% 5.04/5.21 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[2840, 28800])).
% 5.04/5.21 tff(28802,plain,
% 5.04/5.21 (~(elem!1 = s(s(s(elem!1))))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[2859, 28801, 28733])).
% 5.04/5.21 tff(28803,plain,
% 5.04/5.21 (~r(elem!1, s(s(s(elem!1))))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[23784, 2043, 2857, 470, 1687, 168, 437])).
% 5.04/5.21 tff(28804,plain,
% 5.04/5.21 (b(elem!1, s(s(s(elem!1))))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[2054, 28803, 1586])).
% 5.04/5.21 tff(28805,plain,
% 5.04/5.21 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[22224, 28804, 812, 817, 6403, 147, 470])).
% 5.04/5.21 tff(28806,plain,
% 5.04/5.21 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[3825, 41, 2857, 28805])).
% 5.04/5.21 tff(28807,plain,
% 5.04/5.21 (~b(s(s(s(elem!1))), z)),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[22234, 2043, 1687, 168, 28806])).
% 5.04/5.21 tff(28808,plain,
% 5.04/5.21 (r(s(s(s(elem!1))), z)),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[1565, 28807])).
% 5.04/5.21 tff(28809,plain,
% 5.04/5.21 (~r(s(s(s(elem!1))), s(s(z)))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[22820, 118, 28808, 106])).
% 5.04/5.21 tff(28810,plain,
% 5.04/5.21 (b(s(s(s(elem!1))), s(s(z)))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[4209, 41, 28809, 4181])).
% 5.04/5.21 tff(28811,plain,
% 5.04/5.21 (~r(s(s(s(elem!1))), elem!1)),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[22252, 118, 437, 28808])).
% 5.04/5.21 tff(28812,plain,
% 5.04/5.21 (b(s(s(s(elem!1))), elem!1)),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[570, 28811, 6403])).
% 5.04/5.21 tff(28813,plain,
% 5.04/5.21 ($false),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[22222, 178, 28812, 817, 812, 28804, 28810])).
% 5.04/5.21 tff(28814,plain,((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.21 tff(28815,plain,
% 5.04/5.21 (~b(z, s(s(s(elem!1))))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[28814, 28802, 28500, 147, 28726, 27212, 28537, 28729, 28731, 28801, 28740])).
% 5.04/5.21 tff(28816,plain,
% 5.04/5.21 (r(z, s(s(s(elem!1))))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[2095, 28815])).
% 5.04/5.21 tff(28817,plain,
% 5.04/5.21 (~(s(s(s(elem!1))) = s(elem!1))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[348, 28743])).
% 5.04/5.21 tff(28818,plain,
% 5.04/5.21 (~(s(s(s(elem!1))) = elem!1)),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[2489, 28802])).
% 5.04/5.21 tff(28819,plain,
% 5.04/5.21 (~b(z, elem!1)),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[23466, 28731, 193, 24628, 27396, 312, 28727, 28500, 2809, 28742, 4235])).
% 5.04/5.21 tff(28820,plain,
% 5.04/5.21 (r(z, elem!1)),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[585, 28819, 507])).
% 5.04/5.21 tff(28821,plain,
% 5.04/5.21 (~r(s(s(s(elem!1))), elem!1)),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[565, 28816, 28820])).
% 5.04/5.21 tff(28822,plain,
% 5.04/5.21 (b(s(s(s(elem!1))), elem!1)),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[570, 28821, 28818])).
% 5.04/5.21 tff(28823,plain,
% 5.04/5.21 (~r(z, s(elem!1))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[16948, 28822, 28726, 28817, 28816, 28799, 28798])).
% 5.04/5.21 tff(28824,plain,
% 5.04/5.21 (b(z, s(elem!1))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[2351, 28823])).
% 5.04/5.21 tff(28825,plain,
% 5.04/5.21 (~b(s(elem!1), z)),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[22412, 28824, 27212, 273, 28800, 193, 28738, 28537])).
% 5.04/5.21 tff(28826,plain,
% 5.04/5.21 (r(s(elem!1), z)),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[774, 28825])).
% 5.04/5.21 tff(28827,plain,
% 5.04/5.21 (~r(s(elem!1), s(s(z)))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[2258, 28826, 28500])).
% 5.04/5.21 tff(28828,plain,
% 5.04/5.21 (b(s(elem!1), s(s(z)))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[421, 28827, 28800])).
% 5.04/5.21 tff(28829,plain,
% 5.04/5.21 (~b(s(s(s(s(z)))), s(elem!1))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[10985, 28828, 273, 28537, 28824])).
% 5.04/5.21 tff(28830,plain,
% 5.04/5.21 (r(s(s(s(s(z)))), s(elem!1))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[2173, 28829, 28739])).
% 5.04/5.21 tff(28831,plain,
% 5.04/5.21 (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[16335, 28830, 147, 28733])).
% 5.04/5.21 tff(28832,plain,
% 5.04/5.21 (~r(s(s(z)), s(elem!1))),
% 5.04/5.21 inference(modus_ponens,[status(thm)],[28831, 28737])).
% 5.04/5.21 tff(28833,plain,
% 5.04/5.21 (~b(s(s(z)), s(elem!1))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[13708, 28828, 28731, 28798, 28729])).
% 5.04/5.21 tff(28834,plain,
% 5.04/5.21 (r(s(s(z)), s(elem!1))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[2879, 28833, 28828])).
% 5.04/5.21 tff(28835,plain,
% 5.04/5.21 ($false),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[28834, 28832])).
% 5.04/5.21 tff(28836,plain,(b(elem!1, z) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (z = elem!1) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | b(z, s(s(s(s(s(s(s(z)))))))) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 5.04/5.21 tff(28837,plain,
% 5.04/5.21 (b(elem!1, z)),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[28836, 12, 273, 103, 507, 3428, 4235, 10794])).
% 5.04/5.21 tff(28838,plain,
% 5.04/5.21 (b(s(s(s(s(s(s(s(z))))))), z) <=> b(elem!1, z)),
% 5.04/5.21 inference(symmetry,[status(thm)],[4356])).
% 5.04/5.21 tff(28839,plain,
% 5.04/5.21 ((~b(s(s(s(s(s(s(s(z))))))), z)) <=> (~b(elem!1, z))),
% 5.04/5.21 inference(monotonicity,[status(thm)],[28838])).
% 5.04/5.21 tff(28840,plain,
% 5.04/5.21 (~b(elem!1, z)),
% 5.04/5.21 inference(modus_ponens,[status(thm)],[125, 28839])).
% 5.04/5.21 tff(28841,plain,
% 5.04/5.21 ($false),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[506, 28840])).
% 5.04/5.21 tff(28842,plain,((~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | b(s(s(s(s(s(s(s(z))))))), z)), inference(lemma,lemma(discharge,[]))).
% 5.04/5.21 tff(28843,plain,
% 5.04/5.21 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[28842, 28837, 125])).
% 5.04/5.21 tff(28844,plain,
% 5.04/5.21 (~r(elem!1, s(s(s(s(z)))))),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[3785, 450, 103])).
% 5.04/5.21 tff(28845,plain,
% 5.04/5.21 (~r(s(s(s(s(z)))), elem!1)),
% 5.04/5.21 inference(unit_resolution,[status(thm)],[10883, 450, 103])).
% 5.04/5.21 tff(28846,plain,
% 5.04/5.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 5.04/5.22 inference(rewrite,[status(thm)],[])).
% 5.04/5.22 tff(28847,plain,
% 5.04/5.22 (((~b(z, s(s(s(s(z)))))) | (~b(z, 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(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 5.04/5.22 inference(rewrite,[status(thm)],[])).
% 5.04/5.22 tff(28848,plain,
% 5.04/5.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z))))))))),
% 5.04/5.22 inference(monotonicity,[status(thm)],[28847])).
% 5.04/5.22 tff(28849,plain,
% 5.04/5.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 5.04/5.22 inference(transitivity,[status(thm)],[28848, 28846])).
% 5.04/5.22 tff(28850,plain,
% 5.04/5.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 5.04/5.22 inference(quant_inst,[status(thm)],[])).
% 5.04/5.22 tff(28851,plain,
% 5.04/5.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z))))))),
% 5.04/5.22 inference(modus_ponens,[status(thm)],[28850, 28849])).
% 5.04/5.22 tff(28852,plain,
% 5.04/5.22 ($false),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[28851, 178, 506, 8546, 27212, 168, 8545])).
% 5.04/5.22 tff(28853,plain,((elem!1 = s(s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | r(s(s(s(s(z)))), elem!1) | r(elem!1, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.22 tff(28854,plain,
% 5.04/5.22 (elem!1 = s(s(s(s(z))))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[28853, 28845, 28506, 506, 28844])).
% 5.04/5.22 tff(28855,plain,
% 5.04/5.22 (s(elem!1) = s(s(s(s(s(z)))))),
% 5.04/5.22 inference(monotonicity,[status(thm)],[28854])).
% 5.04/5.22 tff(28856,plain,
% 5.04/5.22 (r(s(elem!1), z) <=> r(s(s(s(s(s(z))))), z)),
% 5.04/5.22 inference(monotonicity,[status(thm)],[28855])).
% 5.04/5.22 tff(28857,plain,
% 5.04/5.22 (r(s(s(s(s(s(z))))), z) <=> r(s(elem!1), z)),
% 5.04/5.22 inference(symmetry,[status(thm)],[28856])).
% 5.04/5.22 tff(28858,plain,
% 5.04/5.22 ((~r(s(s(s(s(s(z))))), z)) <=> (~r(s(elem!1), z))),
% 5.04/5.22 inference(monotonicity,[status(thm)],[28857])).
% 5.04/5.22 tff(28859,plain,
% 5.04/5.22 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 5.04/5.22 inference(monotonicity,[status(thm)],[28855])).
% 5.04/5.22 tff(28860,plain,
% 5.04/5.22 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 5.04/5.22 inference(monotonicity,[status(thm)],[28859])).
% 5.04/5.22 tff(28861,plain,
% 5.04/5.22 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))),
% 5.04/5.22 inference(monotonicity,[status(thm)],[28860, 28855])).
% 5.04/5.22 tff(28862,plain,
% 5.04/5.22 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 5.04/5.22 inference(transitivity,[status(thm)],[28861, 4625])).
% 5.04/5.22 tff(28863,plain,
% 5.04/5.22 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))))),
% 5.04/5.22 inference(monotonicity,[status(thm)],[28862])).
% 5.04/5.22 tff(28864,plain,
% 5.04/5.22 (s(s(s(s(z)))) = elem!1),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[325, 28854])).
% 5.04/5.22 tff(28865,plain,
% 5.04/5.22 (~(s(s(elem!1)) = elem!1)),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[338, 28864, 12])).
% 5.04/5.22 tff(28866,plain,
% 5.04/5.22 (~(s(s(s(elem!1))) = s(elem!1))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[348, 28865])).
% 5.04/5.22 tff(28867,plain,
% 5.04/5.22 (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 5.04/5.22 inference(modus_ponens,[status(thm)],[28866, 28863])).
% 5.04/5.22 tff(28868,plain,
% 5.04/5.22 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 5.04/5.22 inference(monotonicity,[status(thm)],[28855])).
% 5.04/5.22 tff(28869,plain,
% 5.04/5.22 (~(s(elem!1) = s(s(z)))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[11438, 28854])).
% 5.04/5.22 tff(28870,plain,
% 5.04/5.22 (~(s(elem!1) = elem!1)),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[672, 28865])).
% 5.04/5.22 tff(28871,plain,
% 5.04/5.22 (~b(s(s(z)), elem!1)),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[17684, 28854, 105])).
% 5.04/5.22 tff(28872,plain,
% 5.04/5.22 (r(s(s(z)), elem!1)),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[448, 28871, 12])).
% 5.04/5.22 tff(28873,plain,
% 5.04/5.22 (~r(z, elem!1)),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[541, 28872, 28500])).
% 5.04/5.22 tff(28874,plain,
% 5.04/5.22 (b(z, elem!1)),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[585, 28873, 507])).
% 5.04/5.22 tff(28875,plain,
% 5.04/5.22 (~r(s(elem!1), s(s(z)))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[17418, 28874, 28500, 450, 506, 28870])).
% 5.04/5.22 tff(28876,plain,
% 5.04/5.22 (b(s(elem!1), s(s(z)))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[421, 28875, 28869])).
% 5.04/5.22 tff(28877,plain,
% 5.04/5.22 (b(s(s(s(s(s(z))))), s(s(z)))),
% 5.04/5.22 inference(modus_ponens,[status(thm)],[28876, 28868])).
% 5.04/5.22 tff(28878,plain,
% 5.04/5.22 (~(s(s(z)) = s(elem!1))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[1058, 28869])).
% 5.04/5.22 tff(28879,plain,
% 5.04/5.22 (~(elem!1 = s(elem!1))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[748, 28870])).
% 5.04/5.22 tff(28880,plain,
% 5.04/5.22 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 5.04/5.22 inference(monotonicity,[status(thm)],[28854])).
% 5.04/5.22 tff(28881,plain,
% 5.04/5.22 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), elem!1)),
% 5.04/5.22 inference(symmetry,[status(thm)],[28880])).
% 5.04/5.22 tff(28882,plain,
% 5.04/5.22 (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)))))),
% 5.04/5.22 inference(monotonicity,[status(thm)],[28860])).
% 5.04/5.22 tff(28883,plain,
% 5.04/5.22 (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)))))),
% 5.04/5.22 inference(symmetry,[status(thm)],[28882])).
% 5.04/5.22 tff(28884,plain,
% 5.04/5.22 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), elem!1)),
% 5.04/5.22 inference(transitivity,[status(thm)],[28883, 28881])).
% 5.04/5.22 tff(28885,plain,
% 5.04/5.22 (r(s(s(s(elem!1))), elem!1)),
% 5.04/5.22 inference(modus_ponens,[status(thm)],[24592, 28884])).
% 5.04/5.22 tff(28886,plain,
% 5.04/5.22 (~r(s(elem!1), elem!1)),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[12991, 28885, 10794, 28872, 28866])).
% 5.04/5.22 tff(28887,plain,
% 5.04/5.22 (b(s(elem!1), elem!1)),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[677, 28886, 28870])).
% 5.04/5.22 tff(28888,plain,
% 5.04/5.22 (r(z, s(elem!1)) <=> r(z, s(s(s(s(s(z))))))),
% 5.04/5.22 inference(monotonicity,[status(thm)],[320])).
% 5.04/5.22 tff(28889,plain,
% 5.04/5.22 (r(z, s(s(s(s(s(z))))))),
% 5.04/5.22 inference(modus_ponens,[status(thm)],[2333, 28888])).
% 5.04/5.22 tff(28890,plain,
% 5.04/5.22 (~r(s(s(z)), s(elem!1))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[2341, 2333, 28500])).
% 5.04/5.22 tff(28891,plain,
% 5.04/5.22 (b(s(s(z)), s(elem!1))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[1067, 28890, 17020])).
% 5.04/5.22 tff(28892,plain,
% 5.04/5.22 (b(s(s(z)), s(s(s(s(s(z))))))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[2330, 28891, 319])).
% 5.04/5.22 tff(28893,plain,
% 5.04/5.22 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[14448, 28892, 166, 1146, 1851])).
% 5.04/5.22 tff(28894,plain,
% 5.04/5.22 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[18762, 28893, 18756])).
% 5.04/5.22 tff(28895,plain,
% 5.04/5.22 (~r(z, s(s(s(s(s(z))))))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[23864, 28894, 203])).
% 5.04/5.22 tff(28896,plain,
% 5.04/5.22 ($false),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[28895, 28889])).
% 5.04/5.22 tff(28897,plain,((~r(z, s(elem!1))) | (~(elem!1 = s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), 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(z))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.22 tff(28898,plain,
% 5.04/5.22 (~r(z, s(elem!1))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[28897, 28854, 203, 28867, 27224, 27217, 28877])).
% 5.04/5.22 tff(28899,plain,
% 5.04/5.22 (b(z, s(elem!1))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[2351, 28898])).
% 5.04/5.22 tff(28900,plain,
% 5.04/5.22 (~b(elem!1, s(elem!1))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[1396, 28899, 28874, 506, 28887])).
% 5.04/5.22 tff(28901,plain,
% 5.04/5.22 (r(elem!1, s(elem!1))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[756, 28900, 28879])).
% 5.04/5.22 tff(28902,plain,
% 5.04/5.22 (~r(s(s(z)), s(elem!1))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[12646, 28901, 10794, 28854])).
% 5.04/5.22 tff(28903,plain,
% 5.04/5.22 (b(s(s(z)), s(elem!1))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[1067, 28902, 28878])).
% 5.04/5.22 tff(28904,plain,
% 5.04/5.22 (b(s(s(z)), s(s(s(s(s(z))))))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[2330, 28903, 28854])).
% 5.04/5.22 tff(28905,plain,
% 5.04/5.22 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[14448, 28904, 27224, 27217, 28877])).
% 5.04/5.22 tff(28906,plain,
% 5.04/5.22 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[18762, 28905, 28867])).
% 5.04/5.22 tff(28907,plain,
% 5.04/5.22 (~r(s(s(s(s(s(z))))), z)),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[15071, 118, 203, 28906])).
% 5.04/5.22 tff(28908,plain,
% 5.04/5.22 (~r(s(elem!1), z)),
% 5.04/5.22 inference(modus_ponens,[status(thm)],[28907, 28858])).
% 5.04/5.22 tff(28909,plain,
% 5.04/5.22 (~(s(elem!1) = s(s(s(s(z)))))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[12552, 28876, 86])).
% 5.04/5.22 tff(28910,plain,
% 5.04/5.22 (~b(s(elem!1), z)),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[22412, 28899, 27212, 273, 28869, 103, 28909, 28506])).
% 5.04/5.22 tff(28911,plain,
% 5.04/5.22 (r(s(elem!1), z)),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[774, 28910])).
% 5.04/5.22 tff(28912,plain,
% 5.04/5.22 ($false),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[28911, 28908])).
% 5.04/5.22 tff(28913,plain,((~r(elem!1, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | b(s(s(s(s(z)))), s(s(z))) | (z = elem!1) | (s(s(z)) = elem!1) | b(s(s(z)), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.22 tff(28914,plain,
% 5.04/5.22 (~r(elem!1, s(s(z)))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[28913, 28837, 273, 4236, 86, 507, 12, 105])).
% 5.04/5.22 tff(28915,plain,
% 5.04/5.22 (b(elem!1, s(s(z)))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[467, 28914, 312])).
% 5.04/5.22 tff(28916,plain,
% 5.04/5.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 5.04/5.22 inference(rewrite,[status(thm)],[])).
% 5.04/5.22 tff(28917,plain,
% 5.04/5.22 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 5.04/5.22 inference(rewrite,[status(thm)],[])).
% 5.04/5.22 tff(28918,plain,
% 5.04/5.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))))),
% 5.04/5.22 inference(monotonicity,[status(thm)],[28917])).
% 5.04/5.22 tff(28919,plain,
% 5.04/5.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 5.04/5.22 inference(transitivity,[status(thm)],[28918, 28916])).
% 5.04/5.22 tff(28920,plain,
% 5.04/5.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 5.04/5.22 inference(quant_inst,[status(thm)],[])).
% 5.04/5.22 tff(28921,plain,
% 5.04/5.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))),
% 5.04/5.22 inference(modus_ponens,[status(thm)],[28920, 28919])).
% 5.04/5.22 tff(28922,plain,
% 5.04/5.22 (~b(s(s(s(s(z)))), elem!1)),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[28921, 178, 506, 273, 812, 28537])).
% 5.04/5.22 tff(28923,plain,
% 5.04/5.22 (r(s(s(s(s(z)))), elem!1)),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[3142, 551, 28922])).
% 5.04/5.22 tff(28924,plain,
% 5.04/5.22 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[25879, 28923])).
% 5.04/5.22 tff(28925,plain,
% 5.04/5.22 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[14184, 28924, 166, 812, 24628, 701])).
% 5.04/5.22 tff(28926,plain,
% 5.04/5.22 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[3891, 193, 1130])).
% 5.04/5.22 tff(28927,plain,
% 5.04/5.22 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[3578, 28926])).
% 5.04/5.22 tff(28928,plain,
% 5.04/5.22 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[27817, 28927, 1130, 4236])).
% 5.04/5.22 tff(28929,plain,
% 5.04/5.22 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[249, 28928])).
% 5.04/5.22 tff(28930,plain,
% 5.04/5.22 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[4243, 2863, 4235])).
% 5.04/5.22 tff(28931,plain,
% 5.04/5.22 (~b(elem!1, s(s(s(s(z)))))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[7020, 22102, 27919, 2795, 2863])).
% 5.04/5.22 tff(28932,plain,
% 5.04/5.22 (r(elem!1, s(s(s(s(z)))))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[483, 28931, 469])).
% 5.04/5.22 tff(28933,plain,
% 5.04/5.22 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[18983, 28932, 1130])).
% 5.04/5.22 tff(28934,plain,
% 5.04/5.22 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[14184, 28933, 812, 28930, 28929, 28927])).
% 5.04/5.22 tff(28935,plain,
% 5.04/5.22 ($false),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[11991, 118, 1130, 28932, 28934])).
% 5.04/5.22 tff(28936,plain,((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (elem!1 = s(s(s(s(z))))) | b(z, s(s(s(s(s(s(s(z)))))))) | (elem!1 = z) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.22 tff(28937,plain,
% 5.04/5.22 ((~r(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (elem!1 = s(s(s(s(z))))) | b(z, s(s(s(s(s(s(s(z)))))))) | (elem!1 = z) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z))))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[28936, 24592])).
% 5.04/5.22 tff(28938,plain,
% 5.04/5.22 (~r(s(s(z)), elem!1)),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[28937, 469, 28500, 2809, 4235, 812, 193])).
% 5.04/5.22 tff(28939,plain,
% 5.04/5.22 (b(s(s(z)), elem!1)),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[448, 28938, 12])).
% 5.04/5.22 tff(28940,plain,
% 5.04/5.22 (~b(z, elem!1)),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[826, 28939, 273, 506, 812])).
% 5.04/5.22 tff(28941,plain,
% 5.04/5.22 (r(z, elem!1)),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[585, 28940, 507])).
% 5.04/5.22 tff(28942,plain,
% 5.04/5.22 ($false),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[3818, 28941, 28925, 4236])).
% 5.04/5.22 tff(28943,plain,((elem!1 = s(s(s(s(z))))) | (z = elem!1) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z)))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (s(s(z)) = elem!1) | b(z, s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.22 tff(28944,plain,
% 5.04/5.22 (elem!1 = s(s(s(s(z))))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[28943, 28915, 27224, 507, 28843, 273, 28837, 12, 4235, 103])).
% 5.04/5.22 tff(28945,plain,
% 5.04/5.22 (b(elem!1, s(s(z))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 5.04/5.22 inference(monotonicity,[status(thm)],[28944])).
% 5.04/5.22 tff(28946,plain,
% 5.04/5.22 (b(s(s(s(s(z)))), s(s(z))) <=> b(elem!1, s(s(z)))),
% 5.04/5.22 inference(symmetry,[status(thm)],[28945])).
% 5.04/5.22 tff(28947,plain,
% 5.04/5.22 ((~b(s(s(s(s(z)))), s(s(z)))) <=> (~b(elem!1, s(s(z))))),
% 5.04/5.22 inference(monotonicity,[status(thm)],[28946])).
% 5.04/5.22 tff(28948,plain,
% 5.04/5.22 (~b(elem!1, s(s(z)))),
% 5.04/5.22 inference(modus_ponens,[status(thm)],[86, 28947])).
% 5.04/5.22 tff(28949,plain,
% 5.04/5.22 ($false),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[28915, 28948])).
% 5.04/5.22 tff(28950,plain,((s(s(z)) = elem!1) | b(s(s(s(s(z)))), s(s(z))) | (z = elem!1) | (~b(z, s(s(z)))) | b(z, s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(s(s(s(z))))))), z) | b(s(s(z)), s(s(s(s(z))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.22 tff(28951,plain,
% 5.04/5.22 (b(s(s(s(s(s(s(s(z))))))), z)),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[28950, 28725, 507, 273, 4235, 86, 105, 3428])).
% 5.04/5.22 tff(28952,plain,
% 5.04/5.22 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[28588, 178, 273, 28506, 27217])).
% 5.04/5.22 tff(28953,plain,
% 5.04/5.22 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[28952, 28951])).
% 5.04/5.22 tff(28954,plain,
% 5.04/5.22 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[222, 28953])).
% 5.04/5.22 tff(28955,plain,
% 5.04/5.22 (~(elem!1 = s(s(z)))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[311, 28725])).
% 5.04/5.22 tff(28956,plain,
% 5.04/5.22 (b(elem!1, z)),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[28836, 28725, 273, 103, 507, 3428, 4235, 10794])).
% 5.04/5.22 tff(28957,plain,
% 5.04/5.22 (~r(elem!1, s(s(z)))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[28913, 28956, 273, 4236, 86, 507, 28725, 105])).
% 5.04/5.22 tff(28958,plain,
% 5.04/5.22 (b(elem!1, s(s(z)))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[467, 28957, 28955])).
% 5.04/5.22 tff(28959,plain,
% 5.04/5.22 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[28943, 469, 166, 507, 812, 273, 506, 12, 4235, 193])).
% 5.04/5.22 tff(28960,plain,
% 5.04/5.22 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 5.04/5.22 inference(monotonicity,[status(thm)],[28959])).
% 5.04/5.22 tff(28961,plain,
% 5.04/5.22 (s(s(s(s(s(s(s(s(z)))))))) = s(elem!1)),
% 5.04/5.22 inference(symmetry,[status(thm)],[28960])).
% 5.04/5.22 tff(28962,plain,
% 5.04/5.22 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z))))))))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 5.04/5.22 inference(monotonicity,[status(thm)],[28961])).
% 5.04/5.22 tff(28963,plain,
% 5.04/5.22 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))),
% 5.04/5.22 inference(symmetry,[status(thm)],[28962])).
% 5.04/5.22 tff(28964,plain,
% 5.04/5.22 (~(s(elem!1) = s(s(s(s(z)))))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[16181, 28959])).
% 5.04/5.22 tff(28965,plain,
% 5.04/5.22 (~(s(s(s(s(z)))) = s(elem!1))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[2168, 28964])).
% 5.04/5.22 tff(28966,plain,
% 5.04/5.22 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.22 inference(monotonicity,[status(thm)],[28959])).
% 5.04/5.22 tff(28967,plain,
% 5.04/5.22 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(z)))), elem!1)),
% 5.04/5.22 inference(symmetry,[status(thm)],[28966])).
% 5.04/5.22 tff(28968,plain,
% 5.04/5.22 (r(s(s(s(s(z)))), elem!1)),
% 5.04/5.22 inference(modus_ponens,[status(thm)],[204, 28967])).
% 5.04/5.22 tff(28969,plain,
% 5.04/5.22 (~b(z, elem!1)),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[4243, 28959, 4235])).
% 5.04/5.22 tff(28970,plain,
% 5.04/5.22 (r(z, elem!1)),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[585, 28969, 507])).
% 5.04/5.22 tff(28971,plain,
% 5.04/5.22 (~b(s(elem!1), z)),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[22412, 855, 27212, 273, 10483, 193, 16182, 28537])).
% 5.04/5.22 tff(28972,plain,
% 5.04/5.22 (b(s(elem!1), elem!1)),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[19342, 28971, 521, 506])).
% 5.04/5.22 tff(28973,plain,
% 5.04/5.22 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[686, 28972, 679])).
% 5.04/5.22 tff(28974,plain,
% 5.04/5.22 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.22 inference(modus_ponens,[status(thm)],[28973, 11735])).
% 5.04/5.22 tff(28975,plain,
% 5.04/5.22 (r(s(elem!1), z)),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[774, 28971])).
% 5.04/5.22 tff(28976,plain,
% 5.04/5.22 (~r(s(elem!1), s(s(z)))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[2258, 28975, 28500])).
% 5.04/5.22 tff(28977,plain,
% 5.04/5.22 (b(s(elem!1), s(s(z)))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[421, 28976, 10483])).
% 5.04/5.22 tff(28978,plain,
% 5.04/5.22 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 5.04/5.22 inference(modus_ponens,[status(thm)],[28977, 11737])).
% 5.04/5.22 tff(28979,plain,
% 5.04/5.22 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[13746, 178, 166, 24628, 28978, 28974])).
% 5.04/5.22 tff(28980,plain,
% 5.04/5.22 (~b(elem!1, s(elem!1))),
% 5.04/5.22 inference(modus_ponens,[status(thm)],[28979, 11733])).
% 5.04/5.22 tff(28981,plain,
% 5.04/5.22 (~b(s(s(s(s(z)))), s(elem!1))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[10985, 28977, 273, 28537, 855])).
% 5.04/5.22 tff(28982,plain,
% 5.04/5.22 (r(s(s(s(s(z)))), s(elem!1))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[2173, 28981, 16183])).
% 5.04/5.22 tff(28983,plain,
% 5.04/5.22 (~r(elem!1, s(elem!1))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[10992, 28982, 3132])).
% 5.04/5.22 tff(28984,plain,
% 5.04/5.22 (b(elem!1, s(elem!1))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[756, 28983, 26773])).
% 5.04/5.22 tff(28985,plain,
% 5.04/5.22 ($false),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[28984, 28980])).
% 5.04/5.22 tff(28986,plain,((~b(z, s(elem!1))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(z)))) | (~r(z, elem!1)) | (~b(elem!1, z)) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.22 tff(28987,plain,
% 5.04/5.22 (~b(z, s(elem!1))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[28986, 28959, 166, 28968, 273, 28970, 506, 193])).
% 5.04/5.22 tff(28988,plain,
% 5.04/5.22 (r(z, s(elem!1))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[2351, 28987])).
% 5.04/5.22 tff(28989,plain,
% 5.04/5.22 (~r(s(elem!1), elem!1)),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[7070, 28988, 28970])).
% 5.04/5.22 tff(28990,plain,
% 5.04/5.22 (~(s(s(elem!1)) = elem!1)),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[2510, 28965, 28959])).
% 5.04/5.22 tff(28991,plain,
% 5.04/5.22 (~(s(elem!1) = elem!1)),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[672, 28990])).
% 5.04/5.22 tff(28992,plain,
% 5.04/5.22 (~(s(elem!1) = s(s(z)))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[2832, 28959])).
% 5.04/5.22 tff(28993,plain,
% 5.04/5.22 (~(s(s(z)) = s(elem!1))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[1058, 28992])).
% 5.04/5.22 tff(28994,plain,
% 5.04/5.22 (b(s(elem!1), elem!1)),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[677, 28989, 28991])).
% 5.04/5.22 tff(28995,plain,
% 5.04/5.22 (~r(s(s(z)), s(elem!1))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[2341, 28988, 28500])).
% 5.04/5.22 tff(28996,plain,
% 5.04/5.22 (b(s(s(z)), s(elem!1))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[1067, 28995, 28993])).
% 5.04/5.22 tff(28997,plain,
% 5.04/5.22 (~b(s(elem!1), s(s(z)))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[13708, 28996, 28939, 28994, 812])).
% 5.04/5.22 tff(28998,plain,
% 5.04/5.22 (r(s(elem!1), s(s(z)))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[421, 28997, 28992])).
% 5.04/5.22 tff(28999,plain,
% 5.04/5.22 (~r(s(elem!1), z)),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[2258, 28998, 28500])).
% 5.04/5.22 tff(29000,plain,
% 5.04/5.22 (b(s(elem!1), z)),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[774, 28999])).
% 5.04/5.22 tff(29001,plain,
% 5.04/5.22 (r(elem!1, s(elem!1))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[2481, 29000, 28500, 506, 28939, 28993, 28991, 28989])).
% 5.04/5.22 tff(29002,plain,
% 5.04/5.22 (~r(s(s(s(s(z)))), s(elem!1))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[10992, 29001, 28968])).
% 5.04/5.22 tff(29003,plain,
% 5.04/5.22 (b(s(s(s(s(z)))), s(elem!1))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[2173, 29002, 28965])).
% 5.04/5.22 tff(29004,plain,
% 5.04/5.22 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))),
% 5.04/5.22 inference(modus_ponens,[status(thm)],[29003, 28963])).
% 5.04/5.22 tff(29005,plain,
% 5.04/5.22 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 5.04/5.22 inference(monotonicity,[status(thm)],[28960])).
% 5.04/5.22 tff(29006,plain,
% 5.04/5.22 (~r(s(elem!1), s(s(s(s(z)))))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[3949, 28998, 193])).
% 5.04/5.22 tff(29007,plain,
% 5.04/5.22 (b(s(elem!1), s(s(s(s(z)))))),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[1084, 29006, 28964])).
% 5.04/5.22 tff(29008,plain,
% 5.04/5.22 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 5.04/5.22 inference(modus_ponens,[status(thm)],[29007, 29005])).
% 5.04/5.22 tff(29009,plain,
% 5.04/5.22 (b(s(s(s(s(s(s(s(s(z)))))))), z)),
% 5.04/5.22 inference(unit_resolution,[status(thm)],[24205, 29000, 28959])).
% 5.04/5.22 tff(29010,plain,
% 5.04/5.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 5.04/5.22 inference(rewrite,[status(thm)],[])).
% 5.04/5.22 tff(29011,plain,
% 5.04/5.22 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 5.04/5.22 inference(rewrite,[status(thm)],[])).
% 5.04/5.22 tff(29012,plain,
% 5.04/5.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))))),
% 5.04/5.22 inference(monotonicity,[status(thm)],[29011])).
% 5.04/5.22 tff(29013,plain,
% 5.04/5.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 5.04/5.22 inference(transitivity,[status(thm)],[29012, 29010])).
% 5.04/5.22 tff(29014,plain,
% 5.04/5.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))))),
% 5.04/5.23 inference(quant_inst,[status(thm)],[])).
% 5.04/5.23 tff(29015,plain,
% 5.04/5.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))),
% 5.04/5.23 inference(modus_ponens,[status(thm)],[29014, 29013])).
% 5.04/5.23 tff(29016,plain,
% 5.04/5.23 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[29015, 178, 27212, 28537, 29009, 29008])).
% 5.04/5.23 tff(29017,plain,
% 5.04/5.23 ($false),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[29016, 29004])).
% 5.04/5.23 tff(29018,plain,((elem!1 = s(s(s(s(z))))) | (~b(elem!1, z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (z = elem!1) | b(z, s(s(s(s(s(s(s(z)))))))) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 5.04/5.23 tff(29019,plain,
% 5.04/5.23 (elem!1 = s(s(s(s(z))))),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[29018, 28956, 103, 28958, 27224, 273, 28954, 507, 4235, 28725])).
% 5.04/5.23 tff(29020,plain,
% 5.04/5.23 (b(elem!1, s(s(z))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 5.04/5.23 inference(monotonicity,[status(thm)],[29019])).
% 5.04/5.23 tff(29021,plain,
% 5.04/5.23 (b(s(s(s(s(z)))), s(s(z))) <=> b(elem!1, s(s(z)))),
% 5.04/5.23 inference(symmetry,[status(thm)],[29020])).
% 5.04/5.23 tff(29022,plain,
% 5.04/5.23 ((~b(s(s(s(s(z)))), s(s(z)))) <=> (~b(elem!1, s(s(z))))),
% 5.04/5.23 inference(monotonicity,[status(thm)],[29021])).
% 5.04/5.23 tff(29023,plain,
% 5.04/5.23 (~b(elem!1, s(s(z)))),
% 5.04/5.23 inference(modus_ponens,[status(thm)],[86, 29022])).
% 5.04/5.23 tff(29024,plain,
% 5.04/5.23 ($false),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[28958, 29023])).
% 5.04/5.23 tff(29025,plain,(b(z, s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(z)))), s(s(z))) | (~b(z, s(s(z)))) | (z = elem!1) | b(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(z)), z)), inference(lemma,lemma(discharge,[]))).
% 5.04/5.23 tff(29026,plain,
% 5.04/5.23 (b(z, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[29025, 507, 273, 86, 105, 3428, 23814])).
% 5.04/5.23 tff(29027,plain,
% 5.04/5.23 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[1154, 29026, 273, 27224, 27217])).
% 5.04/5.23 tff(29028,plain,
% 5.04/5.23 (r(s(s(s(s(s(s(s(z))))))), z)),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[133, 29027])).
% 5.04/5.23 tff(29029,plain,
% 5.04/5.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 5.04/5.23 inference(rewrite,[status(thm)],[])).
% 5.04/5.23 tff(29030,plain,
% 5.04/5.23 (((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 5.04/5.23 inference(rewrite,[status(thm)],[])).
% 5.04/5.23 tff(29031,plain,
% 5.04/5.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 5.04/5.23 inference(monotonicity,[status(thm)],[29030])).
% 5.04/5.23 tff(29032,plain,
% 5.04/5.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 5.04/5.23 inference(transitivity,[status(thm)],[29031, 29029])).
% 5.04/5.23 tff(29033,plain,
% 5.04/5.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)))),
% 5.04/5.23 inference(quant_inst,[status(thm)],[])).
% 5.04/5.23 tff(29034,plain,
% 5.04/5.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 5.04/5.23 inference(modus_ponens,[status(thm)],[29033, 29032])).
% 5.04/5.23 tff(29035,plain,
% 5.04/5.23 ($false),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[29034, 178, 273, 168, 251, 595, 1146])).
% 5.04/5.23 tff(29036,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.23 tff(29037,plain,
% 5.04/5.23 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[29036, 29026, 28506, 273, 27217])).
% 5.04/5.23 tff(29038,plain,
% 5.04/5.23 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[222, 29037])).
% 5.04/5.23 tff(29039,plain,
% 5.04/5.23 (~r(s(s(s(z))), z)),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[24075, 8216, 108])).
% 5.04/5.23 tff(29040,plain,
% 5.04/5.23 (~b(s(s(s(z))), z)),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[21413, 8216, 27212, 204, 168])).
% 5.04/5.23 tff(29041,plain,
% 5.04/5.23 ($false),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[21073, 29040, 29039])).
% 5.04/5.23 tff(29042,plain,((~r(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))))))))) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.23 tff(29043,plain,
% 5.04/5.23 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[29042, 29038, 28506, 29028])).
% 5.04/5.23 tff(29044,plain,
% 5.04/5.23 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[20667, 29043])).
% 5.04/5.23 tff(29045,plain,
% 5.04/5.23 (~(s(s(z)) = elem!1)),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[28724, 29044, 23814, 105, 86])).
% 5.04/5.23 tff(29046,plain,
% 5.04/5.23 (~(elem!1 = s(s(z)))),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[311, 29045])).
% 5.04/5.23 tff(29047,plain,
% 5.04/5.23 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[1154, 595, 273, 166, 24628])).
% 5.04/5.23 tff(29048,plain,
% 5.04/5.23 (r(s(s(s(s(s(s(s(z))))))), z)),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[133, 29047])).
% 5.04/5.23 tff(29049,plain,
% 5.04/5.23 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[11134, 118, 437, 29048])).
% 5.04/5.23 tff(29050,plain,
% 5.04/5.23 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[11809, 118, 437, 29048])).
% 5.04/5.23 tff(29051,plain,
% 5.04/5.23 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[14184, 812, 166, 29050, 24628, 29049])).
% 5.04/5.23 tff(29052,plain,
% 5.04/5.23 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 5.04/5.23 inference(monotonicity,[status(thm)],[29051])).
% 5.04/5.23 tff(29053,plain,
% 5.04/5.23 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 5.04/5.23 inference(monotonicity,[status(thm)],[29052])).
% 5.04/5.23 tff(29054,plain,
% 5.04/5.23 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(z))) <=> b(s(elem!1), s(s(z)))),
% 5.04/5.23 inference(symmetry,[status(thm)],[29053])).
% 5.04/5.23 tff(29055,plain,
% 5.04/5.23 ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) <=> (~b(s(elem!1), s(s(z))))),
% 5.04/5.23 inference(monotonicity,[status(thm)],[29054])).
% 5.04/5.23 tff(29056,plain,
% 5.04/5.23 (s(s(s(s(s(s(s(s(z)))))))) = s(elem!1)),
% 5.04/5.23 inference(symmetry,[status(thm)],[29052])).
% 5.04/5.23 tff(29057,plain,
% 5.04/5.23 (b(s(s(s(s(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))))))))),
% 5.04/5.23 inference(monotonicity,[status(thm)],[29056])).
% 5.04/5.23 tff(29058,plain,
% 5.04/5.23 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.23 inference(symmetry,[status(thm)],[29057])).
% 5.04/5.23 tff(29059,plain,
% 5.04/5.23 (~(s(elem!1) = s(s(s(s(z)))))),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[16181, 29051])).
% 5.04/5.23 tff(29060,plain,
% 5.04/5.23 (r(elem!1, s(s(s(s(z)))))),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[24769, 29051, 3428])).
% 5.04/5.23 tff(29061,plain,
% 5.04/5.23 (~r(elem!1, s(elem!1))),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[27585, 29060, 437, 29059, 28537])).
% 5.04/5.23 tff(29062,plain,
% 5.04/5.23 (~(s(s(s(s(z)))) = s(elem!1))),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[2168, 29059])).
% 5.04/5.23 tff(29063,plain,
% 5.04/5.23 (~(s(s(elem!1)) = elem!1)),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[2510, 29062, 29051])).
% 5.04/5.23 tff(29064,plain,
% 5.04/5.23 (~(s(elem!1) = elem!1)),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[672, 29063])).
% 5.04/5.23 tff(29065,plain,
% 5.04/5.23 (b(s(elem!1), elem!1)),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[28797, 29064, 28500, 273, 193, 28537, 507, 437, 469, 812, 29059, 29061])).
% 5.04/5.23 tff(29066,plain,
% 5.04/5.23 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[686, 29065, 29051])).
% 5.04/5.23 tff(29067,plain,
% 5.04/5.23 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.23 inference(modus_ponens,[status(thm)],[29066, 29058])).
% 5.04/5.23 tff(29068,plain,
% 5.04/5.23 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 5.04/5.23 inference(monotonicity,[status(thm)],[29056])).
% 5.04/5.23 tff(29069,plain,
% 5.04/5.23 (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(s(s(s(s(z)))))))))),
% 5.04/5.23 inference(symmetry,[status(thm)],[29068])).
% 5.04/5.23 tff(29070,plain,
% 5.04/5.23 (b(elem!1, s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 5.04/5.23 inference(monotonicity,[status(thm)],[29051])).
% 5.04/5.23 tff(29071,plain,
% 5.04/5.23 (~(elem!1 = s(elem!1))),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[748, 29064])).
% 5.04/5.23 tff(29072,plain,
% 5.04/5.23 (b(elem!1, s(elem!1))),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[756, 29071, 29061])).
% 5.04/5.23 tff(29073,plain,
% 5.04/5.23 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 5.04/5.23 inference(modus_ponens,[status(thm)],[29072, 29070])).
% 5.04/5.23 tff(29074,plain,
% 5.04/5.23 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 5.04/5.23 inference(modus_ponens,[status(thm)],[29073, 29069])).
% 5.04/5.23 tff(29075,plain,
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% 5.04/5.23 inference(modus_ponens,[status(thm)],[29075, 29055])).
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% 5.04/5.23 inference(unit_resolution,[status(thm)],[2832, 29051])).
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% 5.04/5.23 inference(unit_resolution,[status(thm)],[774, 29081])).
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% 5.04/5.23 inference(unit_resolution,[status(thm)],[2258, 29082, 28500])).
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% 5.04/5.23 inference(unit_resolution,[status(thm)],[29084, 29076])).
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% 5.04/5.23 tff(29087,plain,
% 5.04/5.23 (~b(elem!1, s(s(z)))),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[29086, 28726, 166, 595, 193, 507, 273, 28742, 3428])).
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% 5.04/5.23 inference(unit_resolution,[status(thm)],[28853, 23457, 23459, 28537, 506, 469])).
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% 5.04/5.23 inference(unit_resolution,[status(thm)],[29093, 469, 506, 193])).
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% 5.04/5.23 inference(unit_resolution,[status(thm)],[467, 29094, 312])).
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% 5.04/5.23 inference(unit_resolution,[status(thm)],[826, 818, 273, 506, 812])).
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% 5.04/5.23 inference(unit_resolution,[status(thm)],[448, 29096, 12])).
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% 5.04/5.23 inference(unit_resolution,[status(thm)],[12519, 178, 506, 27212, 168])).
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% 5.04/5.23 inference(unit_resolution,[status(thm)],[29098, 818])).
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% 5.04/5.23 inference(unit_resolution,[status(thm)],[483, 29099, 469])).
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% 5.04/5.23 inference(unit_resolution,[status(thm)],[8763, 29100, 29097, 147])).
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% 5.04/5.23 tff(29103,plain,
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% 5.04/5.23 inference(unit_resolution,[status(thm)],[585, 29103, 507])).
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% 5.04/5.23 inference(unit_resolution,[status(thm)],[11027, 29104, 108])).
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% 5.04/5.23 inference(unit_resolution,[status(thm)],[448, 29107, 12])).
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% 5.04/5.23 inference(unit_resolution,[status(thm)],[3559, 17175, 193])).
% 5.04/5.23 tff(29110,plain,
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% 5.04/5.23 inference(unit_resolution,[status(thm)],[11848, 178, 817, 812, 1146])).
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% 5.04/5.23 inference(unit_resolution,[status(thm)],[29111, 29110])).
% 5.04/5.23 tff(29113,plain,
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% 5.04/5.23 inference(unit_resolution,[status(thm)],[3444, 29112, 605])).
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% 5.04/5.23 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(z)))), elem!1)),
% 5.04/5.23 inference(monotonicity,[status(thm)],[29113])).
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% 5.04/5.23 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.23 inference(symmetry,[status(thm)],[29114])).
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% 5.04/5.23 inference(modus_ponens,[status(thm)],[3771, 29115])).
% 5.04/5.23 tff(29117,plain,
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% 5.04/5.23 inference(unit_resolution,[status(thm)],[17174, 29116])).
% 5.04/5.23 tff(29118,plain,(b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), elem!1)) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.23 tff(29119,plain,
% 5.04/5.23 (~b(s(s(s(s(z)))), elem!1)),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[29118, 29105, 193, 17174, 29095, 24628, 29108])).
% 5.04/5.23 tff(29120,plain,
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% 5.04/5.23 inference(unit_resolution,[status(thm)],[3142, 29119, 551])).
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% 5.04/5.23 inference(unit_resolution,[status(thm)],[17301, 118, 29120, 29106, 17175])).
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% 5.04/5.23 tff(29123,plain,
% 5.04/5.23 (elem!1 = s(s(s(s(z))))),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[29122, 29091, 103, 29037, 29045, 29028, 507, 10794, 29090, 273])).
% 5.04/5.23 tff(29124,plain,
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% 5.04/5.23 inference(unit_resolution,[status(thm)],[325, 29123])).
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% 5.04/5.23 inference(unit_resolution,[status(thm)],[338, 29124, 29045])).
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% 5.04/5.23 inference(unit_resolution,[status(thm)],[672, 29125])).
% 5.04/5.23 tff(29127,plain,
% 5.04/5.23 (~(s(s(s(elem!1))) = s(elem!1))),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[348, 29125])).
% 5.04/5.23 tff(29128,plain,
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% 5.04/5.23 inference(unit_resolution,[status(thm)],[17684, 29123, 105])).
% 5.04/5.23 tff(29129,plain,
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% 5.04/5.23 inference(unit_resolution,[status(thm)],[448, 29128, 29045])).
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% 5.04/5.23 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 5.04/5.23 inference(monotonicity,[status(thm)],[29123])).
% 5.04/5.23 tff(29131,plain,
% 5.04/5.23 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), elem!1)),
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% 5.04/5.23 inference(monotonicity,[status(thm)],[29123])).
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% 5.04/5.23 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
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% 5.04/5.23 (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)))))),
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% 5.04/5.23 inference(modus_ponens,[status(thm)],[24592, 29137])).
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% 5.04/5.23 inference(unit_resolution,[status(thm)],[541, 29129, 28500])).
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% 5.04/5.23 inference(unit_resolution,[status(thm)],[18706, 178, 273, 27224, 29026, 29155])).
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% 5.04/5.23 tff(29166,plain,
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% 5.04/5.23 tff(29167,plain,
% 5.04/5.23 (~r(elem!1, s(elem!1))),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[12646, 29163, 10794, 29123])).
% 5.04/5.23 tff(29168,plain,
% 5.04/5.23 (b(elem!1, s(elem!1))),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[756, 29167, 29166])).
% 5.04/5.23 tff(29169,plain,
% 5.04/5.23 ($false),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[1396, 29168, 29165, 29090, 29142, 29140])).
% 5.04/5.23 tff(29170,plain,((z = elem!1) | (~b(z, s(s(z)))) | b(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(z)), z) | b(s(s(s(s(z)))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.23 tff(29171,plain,
% 5.04/5.23 (b(s(s(z)), z)),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[29170, 28691, 105, 3428, 273, 86])).
% 5.04/5.23 tff(29172,plain,
% 5.04/5.23 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[4057, 29171, 273, 27224, 27217])).
% 5.04/5.23 tff(29173,plain,
% 5.04/5.23 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[17204, 29171, 273, 27224, 27217])).
% 5.04/5.23 tff(29174,plain,
% 5.04/5.23 (s(s(z)) = elem!1),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[28950, 29173, 28691, 273, 29172, 86, 105, 3428])).
% 5.04/5.23 tff(29175,plain,
% 5.04/5.23 (s(s(s(z))) = s(elem!1)),
% 5.04/5.23 inference(monotonicity,[status(thm)],[29174])).
% 5.04/5.23 tff(29176,plain,
% 5.04/5.23 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(elem!1))),
% 5.04/5.23 inference(monotonicity,[status(thm)],[29175])).
% 5.04/5.23 tff(29177,plain,
% 5.04/5.23 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(z))))),
% 5.04/5.23 inference(symmetry,[status(thm)],[29176])).
% 5.04/5.23 tff(29178,plain,
% 5.04/5.23 ((~r(elem!1, s(elem!1))) <=> (~r(elem!1, s(s(s(z)))))),
% 5.04/5.23 inference(monotonicity,[status(thm)],[29177])).
% 5.04/5.23 tff(29179,plain,
% 5.04/5.23 (r(elem!1, z)),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[1345, 29174, 28500])).
% 5.04/5.23 tff(29180,plain,
% 5.04/5.23 (~b(s(s(s(z))), z)),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[27258, 29171, 28506, 10794, 27245])).
% 5.04/5.23 tff(29181,plain,
% 5.04/5.23 (elem!1 = s(s(z))),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[3230, 29174])).
% 5.04/5.23 tff(29182,plain,
% 5.04/5.23 (~b(s(elem!1), z)),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[7042, 29181, 29180])).
% 5.04/5.23 tff(29183,plain,
% 5.04/5.23 (r(s(elem!1), z)),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[774, 29182])).
% 5.04/5.23 tff(29184,plain,
% 5.04/5.23 (~r(elem!1, s(elem!1))),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[2711, 29183, 29179])).
% 5.04/5.23 tff(29185,plain,
% 5.04/5.23 (~r(elem!1, s(s(s(z))))),
% 5.04/5.23 inference(modus_ponens,[status(thm)],[29184, 29178])).
% 5.04/5.23 tff(29186,plain,
% 5.04/5.23 (r(s(s(z)), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 5.04/5.23 inference(monotonicity,[status(thm)],[29174])).
% 5.04/5.23 tff(29187,plain,
% 5.04/5.23 (r(z, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[271, 29173])).
% 5.04/5.23 tff(29188,plain,
% 5.04/5.23 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[21520, 29187, 27245, 28506, 27212])).
% 5.04/5.23 tff(29189,plain,
% 5.04/5.23 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[20667, 29188])).
% 5.04/5.23 tff(29190,plain,
% 5.04/5.23 (r(s(s(s(z))), z)),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[21073, 29180])).
% 5.04/5.23 tff(29191,plain,
% 5.04/5.23 (~r(s(s(s(z))), s(s(z)))),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[24599, 29190, 28500])).
% 5.04/5.23 tff(29192,plain,
% 5.04/5.23 (b(s(s(s(z))), s(s(z)))),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[4966, 29191])).
% 5.04/5.23 tff(29193,plain,
% 5.04/5.23 (~b(s(s(z)), s(s(s(z))))),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[21439, 29192, 27224, 27217, 29189])).
% 5.04/5.23 tff(29194,plain,
% 5.04/5.23 (r(s(s(z)), s(s(s(z))))),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[5088, 29193])).
% 5.04/5.23 tff(29195,plain,
% 5.04/5.23 (r(elem!1, s(s(s(z))))),
% 5.04/5.23 inference(modus_ponens,[status(thm)],[29194, 29186])).
% 5.04/5.23 tff(29196,plain,
% 5.04/5.23 ($false),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[29195, 29185])).
% 5.04/5.23 tff(29197,plain,(b(s(s(z)), s(s(s(s(z))))) | (~b(z, s(s(z)))) | b(s(s(s(s(z)))), s(s(z))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.23 tff(29198,plain,
% 5.04/5.23 (b(s(s(z)), s(s(s(s(z)))))),
% 5.04/5.23 inference(unit_resolution,[status(thm)],[29197, 86, 273, 3428])).
% 5.04/5.23 tff(29199,plain,
% 5.04/5.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), 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))))))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), 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))))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 5.04/5.23 inference(rewrite,[status(thm)],[])).
% 5.04/5.23 tff(29200,plain,
% 5.04/5.23 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), 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))))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 5.04/5.24 inference(rewrite,[status(thm)],[])).
% 5.04/5.24 tff(29201,plain,
% 5.04/5.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), 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))))))), z)) | (~b(z, s(s(s(s(z))))))))),
% 5.04/5.24 inference(monotonicity,[status(thm)],[29200])).
% 5.04/5.24 tff(29202,plain,
% 5.04/5.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), 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))))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 5.04/5.24 inference(transitivity,[status(thm)],[29201, 29199])).
% 5.04/5.24 tff(29203,plain,
% 5.04/5.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 5.04/5.24 inference(quant_inst,[status(thm)],[])).
% 5.04/5.24 tff(29204,plain,
% 5.04/5.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z))))))),
% 5.04/5.24 inference(modus_ponens,[status(thm)],[29203, 29202])).
% 5.04/5.24 tff(29205,plain,
% 5.04/5.24 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[29204, 178, 273, 27212, 29198, 27217])).
% 5.04/5.24 tff(29206,plain,
% 5.04/5.24 (r(s(s(s(s(s(s(s(z))))))), z)),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[133, 29205])).
% 5.04/5.24 tff(29207,plain,
% 5.04/5.24 ($false),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[9606, 178, 853, 273, 1070, 27212, 167])).
% 5.04/5.24 tff(29208,plain,((~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.24 tff(29209,plain,
% 5.04/5.24 (~b(s(elem!1), s(s(z)))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[29208, 853, 273, 167])).
% 5.04/5.24 tff(29210,plain,
% 5.04/5.24 (r(s(elem!1), s(s(z)))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[421, 29209, 1056])).
% 5.04/5.24 tff(29211,plain,
% 5.04/5.24 (~r(s(elem!1), s(s(s(s(z)))))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[3949, 29210, 193])).
% 5.04/5.24 tff(29212,plain,
% 5.04/5.24 (b(s(elem!1), s(s(s(s(z)))))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[1084, 1369, 29211])).
% 5.04/5.24 tff(29213,plain,
% 5.04/5.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 5.04/5.24 inference(rewrite,[status(thm)],[])).
% 5.04/5.24 tff(29214,plain,
% 5.04/5.24 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 5.04/5.24 inference(rewrite,[status(thm)],[])).
% 5.04/5.24 tff(29215,plain,
% 5.04/5.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 5.04/5.24 inference(monotonicity,[status(thm)],[29214])).
% 5.04/5.24 tff(29216,plain,
% 5.04/5.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 5.04/5.24 inference(transitivity,[status(thm)],[29215, 29213])).
% 5.04/5.24 tff(29217,plain,
% 5.04/5.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))))),
% 5.04/5.24 inference(quant_inst,[status(thm)],[])).
% 5.04/5.24 tff(29218,plain,
% 5.04/5.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 5.04/5.24 inference(modus_ponens,[status(thm)],[29217, 29216])).
% 5.04/5.24 tff(29219,plain,
% 5.04/5.24 ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[29218, 178, 853, 28537, 167])).
% 5.04/5.24 tff(29220,plain,
% 5.04/5.24 (~b(s(s(z)), s(elem!1))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[29219, 29212])).
% 5.04/5.24 tff(29221,plain,
% 5.04/5.24 (~b(z, s(elem!1))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[22412, 1369, 27212, 273, 1056, 193, 853, 28537])).
% 5.04/5.24 tff(29222,plain,
% 5.04/5.24 (r(z, s(elem!1))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[2351, 29221])).
% 5.04/5.24 tff(29223,plain,
% 5.04/5.24 (~r(s(s(z)), s(elem!1))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[2341, 29222, 28500])).
% 5.04/5.24 tff(29224,plain,
% 5.04/5.24 ($false),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[1067, 29223, 29220, 2311])).
% 5.04/5.24 tff(29225,plain,((s(elem!1) = s(s(s(s(z))))) | (~b(s(elem!1), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (s(elem!1) = s(s(z))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.24 tff(29226,plain,
% 5.04/5.24 (s(elem!1) = s(s(s(s(z))))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[29225, 10020, 167, 273, 1056, 193])).
% 5.04/5.24 tff(29227,plain,
% 5.04/5.24 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 5.04/5.24 inference(monotonicity,[status(thm)],[29226])).
% 5.04/5.24 tff(29228,plain,
% 5.04/5.24 (elem!1 = s(s(s(z)))),
% 5.04/5.24 inference(transitivity,[status(thm)],[517, 29227, 11])).
% 5.04/5.24 tff(29229,plain,
% 5.04/5.24 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 5.04/5.24 inference(monotonicity,[status(thm)],[29228])).
% 5.04/5.24 tff(29230,plain,
% 5.04/5.24 ((~b(elem!1, s(s(s(s(z)))))) <=> (~b(s(s(s(z))), s(s(s(s(z))))))),
% 5.04/5.24 inference(monotonicity,[status(thm)],[29229])).
% 5.04/5.24 tff(29231,plain,
% 5.04/5.24 (~b(s(s(z)), z)),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[21653, 167, 27212, 273, 28537])).
% 5.04/5.24 tff(29232,plain,
% 5.04/5.24 (b(elem!1, s(s(z)))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[467, 312, 28728])).
% 5.04/5.24 tff(29233,plain,
% 5.04/5.24 ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[27817, 24592])).
% 5.04/5.24 tff(29234,plain,
% 5.04/5.24 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[29233, 224, 24628])).
% 5.04/5.24 tff(29235,plain,
% 5.04/5.24 (b(z, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[271, 29234])).
% 5.04/5.24 tff(29236,plain,
% 5.04/5.24 ($false),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[29036, 14122, 29235, 28537, 273, 24628])).
% 5.04/5.24 tff(29237,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.24 tff(29238,plain,
% 5.04/5.24 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[29237, 193, 273])).
% 5.04/5.24 tff(29239,plain,
% 5.04/5.24 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[249, 29238])).
% 5.04/5.24 tff(29240,plain,
% 5.04/5.24 (b(s(s(z)), elem!1)),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[448, 12, 28730])).
% 5.04/5.24 tff(29241,plain,
% 5.04/5.24 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[11859, 29240, 24628, 29239, 29232])).
% 5.04/5.24 tff(29242,plain,
% 5.04/5.24 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[29089, 312, 29239, 507, 193, 5723, 273, 3428])).
% 5.04/5.24 tff(29243,plain,
% 5.04/5.24 (r(z, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[271, 29242])).
% 5.04/5.24 tff(29244,plain,
% 5.04/5.24 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[10809, 29243, 28726])).
% 5.04/5.24 tff(29245,plain,
% 5.04/5.24 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[691, 29244, 29241])).
% 5.04/5.24 tff(29246,plain,
% 5.04/5.24 (~(s(elem!1) = s(s(s(s(z)))))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[16181, 29245])).
% 5.04/5.24 tff(29247,plain,
% 5.04/5.24 (r(elem!1, s(s(s(s(z)))))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[24769, 29245, 3428])).
% 5.04/5.24 tff(29248,plain,
% 5.04/5.24 (~r(elem!1, s(elem!1))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[27585, 29247, 28726, 29246, 28537])).
% 5.04/5.24 tff(29249,plain,
% 5.04/5.24 (~(elem!1 = s(s(s(elem!1))))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[2859, 29245, 13192])).
% 5.04/5.24 tff(29250,plain,
% 5.04/5.24 (~(s(s(s(elem!1))) = elem!1)),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[2489, 29249])).
% 5.04/5.24 tff(29251,plain,
% 5.04/5.24 (~(s(elem!1) = elem!1)),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[2150, 29250])).
% 5.04/5.24 tff(29252,plain,
% 5.04/5.24 (~b(z, s(elem!1))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[22412, 29246, 27212, 273, 1056, 193, 10020, 28537])).
% 5.04/5.24 tff(29253,plain,
% 5.04/5.24 (r(z, s(elem!1))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[2351, 29252])).
% 5.04/5.24 tff(29254,plain,
% 5.04/5.24 (~(elem!1 = s(elem!1))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[12026, 5723, 10020])).
% 5.04/5.24 tff(29255,plain,
% 5.04/5.24 (b(elem!1, s(elem!1))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[756, 29248, 29254])).
% 5.04/5.24 tff(29256,plain,
% 5.04/5.24 (~(s(elem!1) = s(s(z)))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[906, 106, 767])).
% 5.04/5.24 tff(29257,plain,
% 5.04/5.24 (~(s(s(z)) = s(elem!1))),
% 5.04/5.24 inference(modus_ponens,[status(thm)],[29256, 12966])).
% 5.04/5.24 tff(29258,plain,
% 5.04/5.24 (~r(elem!1, s(s(z)))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[458, 106, 437])).
% 5.04/5.24 tff(29259,plain,
% 5.04/5.24 (b(elem!1, s(s(z)))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[465, 41, 462, 29258])).
% 5.04/5.24 tff(29260,plain,
% 5.04/5.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))))),
% 5.04/5.24 inference(rewrite,[status(thm)],[])).
% 5.04/5.24 tff(29261,plain,
% 5.04/5.24 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(s(z))))) <=> ((~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))))),
% 5.04/5.24 inference(rewrite,[status(thm)],[])).
% 5.04/5.24 tff(29262,plain,
% 5.04/5.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z))))))),
% 5.04/5.24 inference(monotonicity,[status(thm)],[29261])).
% 5.04/5.24 tff(29263,plain,
% 5.04/5.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))))),
% 5.04/5.24 inference(transitivity,[status(thm)],[29262, 29260])).
% 5.04/5.24 tff(29264,plain,
% 5.04/5.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(s(z)))))),
% 5.04/5.24 inference(quant_inst,[status(thm)],[])).
% 5.04/5.24 tff(29265,plain,
% 5.04/5.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z))))),
% 5.04/5.24 inference(modus_ponens,[status(thm)],[29264, 29263])).
% 5.04/5.24 tff(29266,plain,
% 5.04/5.24 ((~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(s(z))))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[29265, 178, 683, 817, 854])).
% 5.04/5.24 tff(29267,plain,
% 5.04/5.24 (~b(s(s(z)), s(elem!1))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[29266, 29259])).
% 5.04/5.24 tff(29268,plain,
% 5.04/5.24 ((s(s(z)) = s(elem!1)) | r(s(s(z)), s(elem!1))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[1065, 41, 29267])).
% 5.04/5.24 tff(29269,plain,
% 5.04/5.24 (r(s(s(z)), s(elem!1))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[29268, 29257])).
% 5.04/5.24 tff(29270,plain,
% 5.04/5.24 ($false),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[2339, 118, 2333, 106, 29269])).
% 5.04/5.24 tff(29271,plain,((~r(s(s(z)), z)) | (~r(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(elem!1))) | (elem!1 = s(s(z))) | (~r(elem!1, z)) | r(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 5.04/5.24 tff(29272,plain,
% 5.04/5.24 (~b(s(elem!1), elem!1)),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[29271, 29255, 28500, 767, 28726, 312, 29240, 29253])).
% 5.04/5.24 tff(29273,plain,
% 5.04/5.24 ($false),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[28797, 29272, 29251, 28500, 273, 193, 28537, 507, 28726, 28742, 29232, 29246, 29248])).
% 5.04/5.24 tff(29274,plain,((s(s(z)) = elem!1) | (~b(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (z = elem!1) | r(s(elem!1), z) | (s(elem!1) = s(s(z))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 5.04/5.24 tff(29275,plain,
% 5.04/5.24 (s(s(z)) = elem!1),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[29274, 5723, 193, 507, 767, 1056, 3428, 273])).
% 5.04/5.24 tff(29276,plain,
% 5.04/5.24 (s(s(s(z))) = s(elem!1)),
% 5.04/5.24 inference(monotonicity,[status(thm)],[29275])).
% 5.04/5.24 tff(29277,plain,
% 5.04/5.24 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 5.04/5.24 inference(monotonicity,[status(thm)],[29276])).
% 5.04/5.24 tff(29278,plain,
% 5.04/5.24 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 5.04/5.24 inference(symmetry,[status(thm)],[29277])).
% 5.04/5.24 tff(29279,plain,
% 5.04/5.24 ((~b(s(elem!1), s(s(s(s(z)))))) <=> (~b(s(s(s(z))), s(s(s(s(z))))))),
% 5.04/5.24 inference(monotonicity,[status(thm)],[29278])).
% 5.04/5.24 tff(29280,plain,
% 5.04/5.24 (~(s(s(s(s(z)))) = elem!1)),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[504, 28742])).
% 5.04/5.24 tff(29281,plain,
% 5.04/5.24 (elem!1 = s(s(z))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[3230, 29275])).
% 5.04/5.24 tff(29282,plain,
% 5.04/5.24 (~(s(elem!1) = s(s(s(s(z)))))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[1353, 29281, 29280])).
% 5.04/5.24 tff(29283,plain,
% 5.04/5.24 (~b(z, s(elem!1))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[22412, 29282, 27212, 273, 1056, 193, 10020, 28537])).
% 5.04/5.24 tff(29284,plain,
% 5.04/5.24 (r(z, s(elem!1))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[2351, 29283])).
% 5.04/5.24 tff(29285,plain,
% 5.04/5.24 (~r(s(s(z)), s(elem!1))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[2341, 29284, 28500])).
% 5.04/5.24 tff(29286,plain,
% 5.04/5.24 (b(s(s(z)), s(elem!1))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[1067, 29285, 2311])).
% 5.04/5.24 tff(29287,plain,
% 5.04/5.24 ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[29218, 178, 10020, 28537, 167])).
% 5.04/5.24 tff(29288,plain,
% 5.04/5.24 (~b(s(elem!1), s(s(s(s(z)))))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[29287, 29286])).
% 5.04/5.24 tff(29289,plain,
% 5.04/5.24 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 5.04/5.24 inference(modus_ponens,[status(thm)],[29288, 29279])).
% 5.04/5.24 tff(29290,plain,
% 5.04/5.24 (b(s(s(s(z))), z)),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[7042, 29281, 10020])).
% 5.04/5.24 tff(29291,plain,
% 5.04/5.24 (~b(s(s(s(z))), s(s(z)))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[21357, 29290, 27212, 273, 167])).
% 5.04/5.24 tff(29292,plain,
% 5.04/5.24 (r(s(s(s(z))), s(s(z)))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[4966, 29291])).
% 5.04/5.24 tff(29293,plain,
% 5.04/5.24 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[20838, 29292, 193])).
% 5.04/5.24 tff(29294,plain,
% 5.04/5.24 (b(s(s(s(z))), s(s(s(s(z)))))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[10755, 29293])).
% 5.04/5.24 tff(29295,plain,
% 5.04/5.24 ($false),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[29294, 29289])).
% 5.04/5.24 tff(29296,plain,(b(elem!1, z) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (s(elem!1) = s(s(z))) | (z = elem!1) | r(s(elem!1), z) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.24 tff(29297,plain,
% 5.04/5.24 (b(elem!1, z)),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[29296, 767, 193, 273, 1056, 507, 167, 3428])).
% 5.04/5.24 tff(29298,plain,
% 5.04/5.24 (~(elem!1 = s(s(z)))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[23817, 29297, 29231])).
% 5.04/5.24 tff(29299,plain,
% 5.04/5.24 (~(s(s(z)) = elem!1)),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[3230, 29298])).
% 5.04/5.24 tff(29300,plain,
% 5.04/5.24 (~b(s(elem!1), s(s(z)))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[29208, 10020, 273, 167])).
% 5.04/5.24 tff(29301,plain,
% 5.04/5.24 (r(s(elem!1), s(s(z)))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[421, 29300, 1056])).
% 5.04/5.24 tff(29302,plain,
% 5.04/5.24 (~(elem!1 = s(s(s(elem!1))))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[2498, 29226, 2387])).
% 5.04/5.24 tff(29303,plain,
% 5.04/5.24 (~(s(s(s(elem!1))) = elem!1)),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[2489, 29302])).
% 5.04/5.24 tff(29304,plain,
% 5.04/5.24 (~(s(elem!1) = elem!1)),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[2150, 29303])).
% 5.04/5.24 tff(29305,plain,
% 5.04/5.24 (~b(z, elem!1)),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[2558, 29304, 273, 29297, 10020, 29299, 29301])).
% 5.04/5.24 tff(29306,plain,
% 5.04/5.24 (r(z, elem!1)),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[585, 29305, 507])).
% 5.04/5.24 tff(29307,plain,
% 5.04/5.24 (~r(s(s(z)), elem!1)),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[541, 29306, 28500])).
% 5.04/5.24 tff(29308,plain,
% 5.04/5.24 (b(s(s(z)), elem!1)),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[448, 29307, 29299])).
% 5.04/5.24 tff(29309,plain,
% 5.04/5.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 5.04/5.24 inference(rewrite,[status(thm)],[])).
% 5.04/5.24 tff(29310,plain,
% 5.04/5.24 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~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(z)), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 5.04/5.24 inference(rewrite,[status(thm)],[])).
% 5.04/5.24 tff(29311,plain,
% 5.04/5.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~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(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 5.04/5.24 inference(monotonicity,[status(thm)],[29310])).
% 5.04/5.24 tff(29312,plain,
% 5.04/5.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~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(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 5.04/5.24 inference(transitivity,[status(thm)],[29311, 29309])).
% 5.04/5.24 tff(29313,plain,
% 5.04/5.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~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(z)), elem!1)))),
% 5.04/5.24 inference(quant_inst,[status(thm)],[])).
% 5.04/5.24 tff(29314,plain,
% 5.04/5.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 5.04/5.24 inference(modus_ponens,[status(thm)],[29313, 29312])).
% 5.04/5.24 tff(29315,plain,
% 5.04/5.24 ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(z))))))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[29314, 178, 29297, 28537, 167])).
% 5.04/5.24 tff(29316,plain,
% 5.04/5.24 (~b(elem!1, s(s(s(s(z)))))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[29315, 29308])).
% 5.04/5.24 tff(29317,plain,
% 5.04/5.24 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 5.04/5.24 inference(modus_ponens,[status(thm)],[29316, 29230])).
% 5.04/5.24 tff(29318,plain,
% 5.04/5.24 (r(s(s(s(z))), s(s(s(s(z)))))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[10755, 29317])).
% 5.04/5.24 tff(29319,plain,
% 5.04/5.24 (b(elem!1, z) <=> b(s(s(s(z))), z)),
% 5.04/5.24 inference(monotonicity,[status(thm)],[29228])).
% 5.04/5.24 tff(29320,plain,
% 5.04/5.24 (b(s(s(s(z))), z)),
% 5.04/5.24 inference(modus_ponens,[status(thm)],[29297, 29319])).
% 5.04/5.24 tff(29321,plain,
% 5.04/5.24 (~b(s(s(s(z))), s(s(z)))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[21357, 29320, 27212, 273, 167])).
% 5.04/5.24 tff(29322,plain,
% 5.04/5.24 (r(s(s(s(z))), s(s(z)))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[4966, 29321])).
% 5.04/5.24 tff(29323,plain,
% 5.04/5.24 ($false),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[20838, 29322, 29318, 193])).
% 5.04/5.24 tff(29324,plain,(r(s(elem!1), z) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (z = elem!1) | (s(elem!1) = s(s(z))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.24 tff(29325,plain,
% 5.04/5.24 (r(s(elem!1), z)),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[29324, 1056, 273, 29198, 507, 103, 3428])).
% 5.04/5.24 tff(29326,plain,
% 5.04/5.24 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[14966, 118, 29325, 29206])).
% 5.04/5.24 tff(29327,plain,
% 5.04/5.24 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[29237, 103, 273])).
% 5.04/5.24 tff(29328,plain,
% 5.04/5.24 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[249, 29327])).
% 5.04/5.24 tff(29329,plain,
% 5.04/5.24 (~r(s(elem!1), s(s(z)))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[2258, 29325, 28500])).
% 5.04/5.24 tff(29330,plain,
% 5.04/5.24 (b(s(elem!1), s(s(z)))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[421, 29329, 1056])).
% 5.04/5.24 tff(29331,plain,
% 5.04/5.24 (~r(s(s(z)), s(elem!1))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[1052, 118, 29325, 28500])).
% 5.04/5.24 tff(29332,plain,
% 5.04/5.24 (b(s(s(z)), s(elem!1))),
% 5.04/5.24 inference(unit_resolution,[status(thm)],[1067, 29331, 2311])).
% 5.04/5.24 tff(29333,plain,
% 5.04/5.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), 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))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), 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))))))), s(elem!1))))),
% 5.04/5.24 inference(rewrite,[status(thm)],[])).
% 5.04/5.24 tff(29334,plain,
% 5.04/5.24 (((~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), 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(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), 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))))))), s(elem!1))))),
% 5.04/5.24 inference(rewrite,[status(thm)],[])).
% 5.04/5.24 tff(29335,plain,
% 5.04/5.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), 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(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), 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))))))), s(elem!1)))))),
% 5.04/5.24 inference(monotonicity,[status(thm)],[29334])).
% 5.04/5.24 tff(29336,plain,
% 5.04/5.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), 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(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), 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))))))), s(elem!1))))),
% 5.04/5.25 inference(transitivity,[status(thm)],[29335, 29333])).
% 5.04/5.25 tff(29337,plain,
% 5.04/5.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), 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(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 5.04/5.25 inference(quant_inst,[status(thm)],[])).
% 5.04/5.25 tff(29338,plain,
% 5.04/5.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), 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))))))), s(elem!1)))),
% 5.04/5.25 inference(modus_ponens,[status(thm)],[29337, 29336])).
% 5.04/5.25 tff(29339,plain,
% 5.04/5.25 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[29338, 178, 29332, 29330, 29328, 27217])).
% 5.04/5.25 tff(29340,plain,
% 5.04/5.25 ((s(s(s(s(s(s(s(z))))))) = s(elem!1)) | r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[806, 41, 29339])).
% 5.04/5.25 tff(29341,plain,
% 5.04/5.25 (s(s(s(s(s(s(s(z))))))) = s(elem!1)),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[29340, 29326])).
% 5.04/5.25 tff(29342,plain,
% 5.04/5.25 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(elem!1))),
% 5.04/5.25 inference(monotonicity,[status(thm)],[29341])).
% 5.04/5.25 tff(29343,plain,
% 5.04/5.25 (s(s(s(s(s(s(z)))))) = elem!1),
% 5.04/5.25 inference(transitivity,[status(thm)],[609, 29342, 304])).
% 5.04/5.25 tff(29344,plain,
% 5.04/5.25 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(z)))) = elem!1)),
% 5.04/5.25 inference(monotonicity,[status(thm)],[29343])).
% 5.04/5.25 tff(29345,plain,
% 5.04/5.25 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (elem!1 = s(s(s(s(z)))))),
% 5.04/5.25 inference(transitivity,[status(thm)],[29344, 501])).
% 5.04/5.25 tff(29346,plain,
% 5.04/5.25 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))) <=> (~(elem!1 = s(s(s(s(z))))))),
% 5.04/5.25 inference(monotonicity,[status(thm)],[29345])).
% 5.04/5.25 tff(29347,plain,
% 5.04/5.25 (~(elem!1 = s(s(s(s(z)))))),
% 5.04/5.25 inference(modus_ponens,[status(thm)],[3698, 29346])).
% 5.04/5.25 tff(29348,plain,
% 5.04/5.25 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 5.04/5.25 inference(monotonicity,[status(thm)],[29341])).
% 5.04/5.25 tff(29349,plain,
% 5.04/5.25 (r(s(elem!1), s(s(s(s(z)))))),
% 5.04/5.25 inference(modus_ponens,[status(thm)],[24592, 29348])).
% 5.04/5.25 tff(29350,plain,
% 5.04/5.25 (~(s(elem!1) = s(s(s(s(z)))))),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[12552, 29330, 86])).
% 5.04/5.25 tff(29351,plain,
% 5.04/5.25 (~(s(s(s(s(z)))) = s(elem!1))),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[2168, 29350])).
% 5.04/5.25 tff(29352,plain,
% 5.04/5.25 (~(elem!1 = s(s(s(elem!1))))),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[4015, 29341, 29351])).
% 5.04/5.25 tff(29353,plain,
% 5.04/5.25 (~(s(s(s(elem!1))) = elem!1)),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[2489, 29352])).
% 5.04/5.25 tff(29354,plain,
% 5.04/5.25 (~(s(elem!1) = elem!1)),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[2150, 29353])).
% 5.04/5.25 tff(29355,plain,
% 5.04/5.25 (~(elem!1 = s(elem!1))),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[748, 29354])).
% 5.04/5.25 tff(29356,plain,
% 5.04/5.25 (b(z, s(s(s(s(s(s(s(z)))))))) <=> b(z, s(elem!1))),
% 5.04/5.25 inference(monotonicity,[status(thm)],[29341])).
% 5.04/5.25 tff(29357,plain,
% 5.04/5.25 (b(s(s(z)), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 5.04/5.25 inference(monotonicity,[status(thm)],[1324])).
% 5.04/5.25 tff(29358,plain,
% 5.04/5.25 (b(elem!1, s(s(s(z)))) <=> b(s(s(z)), s(s(s(z))))),
% 5.04/5.25 inference(symmetry,[status(thm)],[29357])).
% 5.04/5.25 tff(29359,plain,
% 5.04/5.25 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(elem!1))),
% 5.04/5.25 inference(monotonicity,[status(thm)],[3505])).
% 5.04/5.25 tff(29360,plain,
% 5.04/5.25 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(z))))),
% 5.04/5.25 inference(symmetry,[status(thm)],[29359])).
% 5.04/5.25 tff(29361,plain,
% 5.04/5.25 (b(elem!1, s(elem!1)) <=> b(s(s(z)), s(s(s(z))))),
% 5.04/5.25 inference(transitivity,[status(thm)],[29360, 29358])).
% 5.04/5.25 tff(29362,plain,
% 5.04/5.25 (b(s(s(z)), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 5.04/5.25 inference(monotonicity,[status(thm)],[1324])).
% 5.04/5.25 tff(29363,plain,
% 5.04/5.25 (b(elem!1, s(elem!1))),
% 5.04/5.25 inference(modus_ponens,[status(thm)],[1071, 29362])).
% 5.04/5.25 tff(29364,plain,
% 5.04/5.25 (b(s(s(z)), s(s(s(z))))),
% 5.04/5.25 inference(modus_ponens,[status(thm)],[29363, 29361])).
% 5.04/5.25 tff(29365,plain,
% 5.04/5.25 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(z)))),
% 5.04/5.25 inference(symmetry,[status(thm)],[8530])).
% 5.04/5.25 tff(29366,plain,
% 5.04/5.25 (b(s(elem!1), elem!1) <=> b(s(s(s(z))), elem!1)),
% 5.04/5.25 inference(symmetry,[status(thm)],[8529])).
% 5.04/5.25 tff(29367,plain,
% 5.04/5.25 (b(s(elem!1), elem!1) <=> b(s(s(s(z))), s(s(z)))),
% 5.04/5.25 inference(transitivity,[status(thm)],[29366, 29365])).
% 5.04/5.25 tff(29368,plain,
% 5.04/5.25 (b(s(elem!1), s(s(z))) <=> b(s(elem!1), elem!1)),
% 5.04/5.25 inference(monotonicity,[status(thm)],[1324])).
% 5.04/5.25 tff(29369,plain,
% 5.04/5.25 (b(s(elem!1), elem!1)),
% 5.04/5.25 inference(modus_ponens,[status(thm)],[1070, 29368])).
% 5.04/5.25 tff(29370,plain,
% 5.04/5.25 (b(s(s(s(z))), s(s(z)))),
% 5.04/5.25 inference(modus_ponens,[status(thm)],[29369, 29367])).
% 5.04/5.25 tff(29371,plain,
% 5.04/5.25 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[21439, 29370, 166, 1146, 29364])).
% 5.04/5.25 tff(29372,plain,
% 5.04/5.25 (r(s(s(s(z))), z) <=> r(s(elem!1), z)),
% 5.04/5.25 inference(monotonicity,[status(thm)],[3505])).
% 5.04/5.25 tff(29373,plain,
% 5.04/5.25 (r(s(elem!1), z) <=> r(s(s(s(z))), z)),
% 5.04/5.25 inference(symmetry,[status(thm)],[29372])).
% 5.04/5.25 tff(29374,plain,
% 5.04/5.25 (r(s(s(s(z))), z)),
% 5.04/5.25 inference(modus_ponens,[status(thm)],[844, 29373])).
% 5.04/5.25 tff(29375,plain,
% 5.04/5.25 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[21452, 29374, 273, 166, 1146])).
% 5.04/5.25 tff(29376,plain,
% 5.04/5.25 ($false),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[20667, 29375, 29371])).
% 5.04/5.25 tff(29377,plain,((~(s(s(z)) = elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.25 tff(29378,plain,
% 5.04/5.25 (~(s(s(z)) = elem!1)),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[29377, 29325, 29328, 27217, 273, 29330, 29332])).
% 5.04/5.25 tff(29379,plain,
% 5.04/5.25 ((elem!1 = s(s(s(s(s(s(s(z)))))))) <=> (elem!1 = s(elem!1))),
% 5.04/5.25 inference(monotonicity,[status(thm)],[29341])).
% 5.04/5.25 tff(29380,plain,
% 5.04/5.25 ((elem!1 = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = elem!1)),
% 5.04/5.25 inference(transitivity,[status(thm)],[29379, 3190])).
% 5.04/5.25 tff(29381,plain,
% 5.04/5.25 ((s(elem!1) = elem!1) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 5.04/5.25 inference(symmetry,[status(thm)],[29380])).
% 5.04/5.25 tff(29382,plain,
% 5.04/5.25 ((~(s(elem!1) = elem!1)) <=> (~(elem!1 = s(s(s(s(s(s(s(z)))))))))),
% 5.04/5.25 inference(monotonicity,[status(thm)],[29381])).
% 5.04/5.25 tff(29383,plain,
% 5.04/5.25 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 5.04/5.25 inference(modus_ponens,[status(thm)],[29354, 29382])).
% 5.04/5.25 tff(29384,plain,
% 5.04/5.25 (~(s(s(z)) = elem!1)),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[29377, 844, 29239, 24628, 273, 1070, 1071])).
% 5.04/5.25 tff(29385,plain,
% 5.04/5.25 (~b(s(elem!1), elem!1)),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[13708, 29240, 1070, 1071, 29232])).
% 5.04/5.25 tff(29386,plain,
% 5.04/5.25 (s(elem!1) = elem!1),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[28797, 29385, 28500, 273, 193, 28537, 507, 28726, 28742, 29232, 1369, 744])).
% 5.04/5.25 tff(29387,plain,
% 5.04/5.25 (s(s(elem!1)) = elem!1),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[672, 29386])).
% 5.04/5.25 tff(29388,plain,
% 5.04/5.25 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[11859, 29232, 24628, 29239, 29240])).
% 5.04/5.25 tff(29389,plain,
% 5.04/5.25 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[691, 29244, 29388])).
% 5.04/5.25 tff(29390,plain,
% 5.04/5.25 ($false),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[2510, 29389, 29387, 2169])).
% 5.04/5.25 tff(29391,plain,((s(s(z)) = elem!1) | (~b(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (z = elem!1) | (s(elem!1) = s(s(s(s(z))))) | r(elem!1, s(elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(elem!1))) | b(elem!1, z) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.25 tff(29392,plain,
% 5.04/5.25 (r(elem!1, s(elem!1))),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[29391, 5723, 193, 507, 1369, 273, 1070, 1071, 29384, 3428])).
% 5.04/5.25 tff(29393,plain,
% 5.04/5.25 ($false),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[2711, 29392, 28726, 844])).
% 5.04/5.25 tff(29394,plain,(b(elem!1, z) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (z = elem!1) | (s(elem!1) = s(s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(elem!1))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.25 tff(29395,plain,
% 5.04/5.25 (b(elem!1, z)),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[29394, 29325, 103, 507, 29350, 273, 29330, 29332, 3428])).
% 5.04/5.25 tff(29396,plain,
% 5.04/5.25 (~(elem!1 = s(s(z)))),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[311, 29378])).
% 5.04/5.25 tff(29397,plain,
% 5.04/5.25 (~r(elem!1, s(s(z)))),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[29093, 29395, 29347, 103])).
% 5.04/5.25 tff(29398,plain,
% 5.04/5.25 (b(elem!1, s(s(z)))),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[467, 29397, 29396])).
% 5.04/5.25 tff(29399,plain,
% 5.04/5.25 (b(z, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[28943, 29398, 29328, 507, 29395, 273, 29383, 29378, 29347, 103])).
% 5.04/5.25 tff(29400,plain,
% 5.04/5.25 (b(z, s(elem!1))),
% 5.04/5.25 inference(modus_ponens,[status(thm)],[29399, 29356])).
% 5.04/5.25 tff(29401,plain,
% 5.04/5.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, z)))),
% 5.04/5.25 inference(rewrite,[status(thm)],[])).
% 5.04/5.25 tff(29402,plain,
% 5.04/5.25 (((~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, z))) <=> ((~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, z)))),
% 5.04/5.25 inference(rewrite,[status(thm)],[])).
% 5.04/5.25 tff(29403,plain,
% 5.04/5.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, z))))),
% 5.04/5.25 inference(monotonicity,[status(thm)],[29402])).
% 5.04/5.25 tff(29404,plain,
% 5.04/5.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, z)))),
% 5.04/5.25 inference(transitivity,[status(thm)],[29403, 29401])).
% 5.04/5.25 tff(29405,plain,
% 5.04/5.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, z)))),
% 5.04/5.25 inference(quant_inst,[status(thm)],[])).
% 5.04/5.25 tff(29406,plain,
% 5.04/5.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, z))),
% 5.04/5.25 inference(modus_ponens,[status(thm)],[29405, 29404])).
% 5.04/5.25 tff(29407,plain,
% 5.04/5.25 ($false),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[29406, 178, 506, 855, 854, 273, 1070])).
% 5.04/5.25 tff(29408,plain,((~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.25 tff(29409,plain,
% 5.04/5.25 (~b(elem!1, s(elem!1))),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[29408, 29395, 29400, 273, 29330])).
% 5.04/5.25 tff(29410,plain,
% 5.04/5.25 (r(elem!1, s(elem!1))),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[756, 29409, 29355])).
% 5.04/5.25 tff(29411,plain,
% 5.04/5.25 (~r(elem!1, s(s(s(s(z)))))),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[14364, 29410, 29349])).
% 5.04/5.25 tff(29412,plain,
% 5.04/5.25 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 5.04/5.25 inference(monotonicity,[status(thm)],[29344])).
% 5.04/5.25 tff(29413,plain,
% 5.04/5.25 (~(s(s(s(s(z)))) = elem!1)),
% 5.04/5.25 inference(modus_ponens,[status(thm)],[3698, 29412])).
% 5.04/5.25 tff(29414,plain,
% 5.04/5.25 (~b(s(s(z)), elem!1)),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[29314, 178, 506, 168, 1301, 167])).
% 5.04/5.25 tff(29415,plain,
% 5.04/5.25 (r(s(s(z)), elem!1)),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[448, 29414, 12])).
% 5.04/5.25 tff(29416,plain,
% 5.04/5.25 (~r(z, elem!1)),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[541, 29415, 106])).
% 5.04/5.25 tff(29417,plain,
% 5.04/5.25 (b(z, elem!1)),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[585, 29416, 507])).
% 5.04/5.25 tff(29418,plain,
% 5.04/5.25 (~b(s(s(s(s(z)))), elem!1)),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[16429, 29417, 168, 506, 1301])).
% 5.04/5.25 tff(29419,plain,
% 5.04/5.25 (r(s(s(s(s(z)))), elem!1)),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[3142, 29418, 323])).
% 5.04/5.25 tff(29420,plain,
% 5.04/5.25 (~r(s(s(s(s(z)))), s(elem!1))),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[10992, 29419, 1587])).
% 5.04/5.25 tff(29421,plain,
% 5.04/5.25 (b(s(s(s(s(z)))), s(elem!1))),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[2173, 29420, 2508])).
% 5.04/5.25 tff(29422,plain,
% 5.04/5.25 (~r(s(elem!1), elem!1)),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[7010, 29419, 908])).
% 5.04/5.25 tff(29423,plain,
% 5.04/5.25 (b(s(elem!1), elem!1)),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[677, 29422, 725])).
% 5.04/5.25 tff(29424,plain,
% 5.04/5.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 5.04/5.25 inference(rewrite,[status(thm)],[])).
% 5.04/5.25 tff(29425,plain,
% 5.04/5.25 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 5.04/5.25 inference(rewrite,[status(thm)],[])).
% 5.04/5.25 tff(29426,plain,
% 5.04/5.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 5.04/5.25 inference(monotonicity,[status(thm)],[29425])).
% 5.04/5.25 tff(29427,plain,
% 5.04/5.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 5.04/5.25 inference(transitivity,[status(thm)],[29426, 29424])).
% 5.04/5.25 tff(29428,plain,
% 5.04/5.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)))),
% 5.04/5.25 inference(quant_inst,[status(thm)],[])).
% 5.04/5.25 tff(29429,plain,
% 5.04/5.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 5.04/5.25 inference(modus_ponens,[status(thm)],[29428, 29427])).
% 5.04/5.25 tff(29430,plain,
% 5.04/5.25 (~b(z, s(elem!1))),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[29429, 178, 29417, 29423, 168, 29421])).
% 5.04/5.25 tff(29431,plain,
% 5.04/5.25 (r(z, s(elem!1))),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[2351, 29430])).
% 5.04/5.25 tff(29432,plain,
% 5.04/5.25 (~r(z, s(s(s(s(z)))))),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[2766, 29431, 908])).
% 5.04/5.25 tff(29433,plain,
% 5.04/5.25 (b(z, s(s(s(s(z)))))),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[46, 29432])).
% 5.04/5.25 tff(29434,plain,
% 5.04/5.25 ($false),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[12519, 178, 29417, 506, 29433, 168, 1301])).
% 5.04/5.25 tff(29435,plain,((~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (s(elem!1) = elem!1) | (s(s(s(s(z)))) = s(elem!1)) | (~r(elem!1, s(elem!1))) | (s(s(s(s(z)))) = elem!1) | (z = elem!1) | (~r(s(s(z)), z)) | (s(s(z)) = elem!1) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.25 tff(29436,plain,
% 5.04/5.25 (~b(elem!1, s(s(s(s(z)))))),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[29435, 29410, 28500, 28506, 29349, 29354, 29413, 29351, 507, 29395, 29378, 29198])).
% 5.04/5.25 tff(29437,plain,
% 5.04/5.25 ($false),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[483, 29436, 29411, 29347])).
% 5.04/5.25 tff(29438,plain,((s(elem!1) = s(s(z))) | (z = elem!1) | (~b(z, 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(z)))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.25 tff(29439,plain,
% 5.04/5.25 (s(elem!1) = s(s(z))),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[29438, 507, 273, 3428, 86])).
% 5.04/5.25 tff(29440,plain,
% 5.04/5.25 (s(s(elem!1)) = s(s(s(z)))),
% 5.04/5.25 inference(monotonicity,[status(thm)],[29439])).
% 5.04/5.25 tff(29441,plain,
% 5.04/5.25 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 5.04/5.25 inference(monotonicity,[status(thm)],[29440])).
% 5.04/5.25 tff(29442,plain,
% 5.04/5.25 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(s(z)))) = elem!1)),
% 5.04/5.25 inference(monotonicity,[status(thm)],[29441])).
% 5.04/5.25 tff(29443,plain,
% 5.04/5.25 ((s(s(s(s(z)))) = elem!1) <=> (s(s(s(elem!1))) = elem!1)),
% 5.04/5.25 inference(symmetry,[status(thm)],[29442])).
% 5.04/5.25 tff(29444,plain,
% 5.04/5.25 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 5.04/5.25 inference(monotonicity,[status(thm)],[29443])).
% 5.04/5.25 tff(29445,plain,
% 5.04/5.25 (~(elem!1 = s(s(s(s(z)))))),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[11438, 29439])).
% 5.04/5.25 tff(29446,plain,
% 5.04/5.25 (~(s(s(s(s(z)))) = elem!1)),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[504, 29445])).
% 5.04/5.25 tff(29447,plain,
% 5.04/5.25 (~(s(s(s(elem!1))) = elem!1)),
% 5.04/5.25 inference(modus_ponens,[status(thm)],[29446, 29444])).
% 5.04/5.25 tff(29448,plain,
% 5.04/5.25 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.25 inference(monotonicity,[status(thm)],[29441])).
% 5.04/5.25 tff(29449,plain,
% 5.04/5.25 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.25 inference(symmetry,[status(thm)],[29448])).
% 5.04/5.25 tff(29450,plain,
% 5.04/5.25 ((s(elem!1) = elem!1) <=> (s(s(z)) = elem!1)),
% 5.04/5.25 inference(monotonicity,[status(thm)],[29439])).
% 5.04/5.25 tff(29451,plain,
% 5.04/5.25 ((~(s(elem!1) = elem!1)) <=> (~(s(s(z)) = elem!1))),
% 5.04/5.25 inference(monotonicity,[status(thm)],[29450])).
% 5.04/5.25 tff(29452,plain,
% 5.04/5.25 (~(elem!1 = s(s(s(s(elem!1)))))),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[1422, 29439])).
% 5.04/5.25 tff(29453,plain,
% 5.04/5.25 (~(s(s(s(elem!1))) = s(elem!1))),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[1509, 29452])).
% 5.04/5.25 tff(29454,plain,
% 5.04/5.25 (~(elem!1 = s(s(elem!1)))),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[1539, 29453])).
% 5.04/5.25 tff(29455,plain,
% 5.04/5.25 (~(s(s(elem!1)) = elem!1)),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[1546, 29454])).
% 5.04/5.25 tff(29456,plain,
% 5.04/5.25 (~(s(elem!1) = elem!1)),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[672, 29455])).
% 5.04/5.25 tff(29457,plain,
% 5.04/5.25 (~(s(s(z)) = elem!1)),
% 5.04/5.25 inference(modus_ponens,[status(thm)],[29456, 29451])).
% 5.04/5.25 tff(29458,plain,
% 5.04/5.25 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[2832, 29439])).
% 5.04/5.25 tff(29459,plain,
% 5.04/5.25 ((s(elem!1) = elem!1) <=> (elem!1 = s(s(z)))),
% 5.04/5.25 inference(transitivity,[status(thm)],[29450, 1666])).
% 5.04/5.25 tff(29460,plain,
% 5.04/5.25 ((~(s(elem!1) = elem!1)) <=> (~(elem!1 = s(s(z))))),
% 5.04/5.25 inference(monotonicity,[status(thm)],[29459])).
% 5.04/5.25 tff(29461,plain,
% 5.04/5.25 (~(elem!1 = s(s(z)))),
% 5.04/5.25 inference(modus_ponens,[status(thm)],[29456, 29460])).
% 5.04/5.25 tff(29462,plain,
% 5.04/5.25 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[29089, 5723, 29239, 507, 193, 462, 273, 3428])).
% 5.04/5.25 tff(29463,plain,
% 5.04/5.25 (r(z, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[271, 29462])).
% 5.04/5.25 tff(29464,plain,
% 5.04/5.25 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[10809, 29463, 28726])).
% 5.04/5.25 tff(29465,plain,
% 5.04/5.25 (b(elem!1, s(s(z)))),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[467, 28728, 462])).
% 5.04/5.25 tff(29466,plain,
% 5.04/5.25 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[11859, 28731, 24628, 29239, 29465])).
% 5.04/5.25 tff(29467,plain,
% 5.04/5.25 ($false),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[691, 29466, 29464, 701])).
% 5.04/5.25 tff(29468,plain,(b(elem!1, z) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (s(s(z)) = elem!1) | (elem!1 = s(s(z))) | (z = elem!1) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.25 tff(29469,plain,
% 5.04/5.25 (b(elem!1, z)),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[29468, 29458, 29457, 29461, 507, 103, 273, 3428])).
% 5.04/5.25 tff(29470,plain,
% 5.04/5.25 (~r(elem!1, s(s(z)))),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[29093, 29469, 29445, 103])).
% 5.04/5.25 tff(29471,plain,
% 5.04/5.25 (b(elem!1, s(s(z)))),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[467, 29470, 29461])).
% 5.04/5.25 tff(29472,plain,
% 5.04/5.25 (b(z, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[28943, 29471, 29328, 507, 29469, 273, 29458, 29457, 29445, 103])).
% 5.04/5.25 tff(29473,plain,
% 5.04/5.25 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[29036, 29472, 28506, 273, 27217])).
% 5.04/5.25 tff(29474,plain,
% 5.04/5.25 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[222, 29473])).
% 5.04/5.25 tff(29475,plain,
% 5.04/5.25 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.25 inference(modus_ponens,[status(thm)],[29474, 29449])).
% 5.04/5.25 tff(29476,plain,
% 5.04/5.25 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.04/5.25 inference(unit_resolution,[status(thm)],[3444, 605, 4245])).
% 5.04/5.25 tff(29477,plain,
% 5.04/5.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(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(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(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(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 5.04/5.25 inference(rewrite,[status(thm)],[])).
% 5.04/5.25 tff(29478,plain,
% 5.04/5.25 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~b(elem!1, s(s(z)))) | (~b(s(s(s(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(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 5.04/5.25 inference(rewrite,[status(thm)],[])).
% 5.04/5.25 tff(29479,plain,
% 5.04/5.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(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(s(s(s(s(s(s(s(z))))))), s(s(z))))))),
% 5.04/5.25 inference(monotonicity,[status(thm)],[29478])).
% 5.04/5.25 tff(29480,plain,
% 5.04/5.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(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(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 5.04/5.26 inference(transitivity,[status(thm)],[29479, 29477])).
% 5.04/5.26 tff(29481,plain,
% 5.04/5.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 5.04/5.26 inference(quant_inst,[status(thm)],[])).
% 5.04/5.26 tff(29482,plain,
% 5.04/5.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 5.04/5.26 inference(modus_ponens,[status(thm)],[29481, 29480])).
% 5.04/5.26 tff(29483,plain,
% 5.04/5.26 ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[29482, 178])).
% 5.04/5.26 tff(29484,plain,
% 5.04/5.26 (~b(elem!1, s(s(s(s(z)))))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[29483, 29476, 167, 812, 1146])).
% 5.04/5.26 tff(29485,plain,
% 5.04/5.26 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[14184, 605, 166, 701, 1146, 812])).
% 5.04/5.26 tff(29486,plain,
% 5.04/5.26 (~r(elem!1, s(s(s(s(z)))))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[25883, 29485])).
% 5.04/5.26 tff(29487,plain,
% 5.04/5.26 ($false),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[483, 29486, 29484, 469])).
% 5.04/5.26 tff(29488,plain,(r(s(s(s(s(s(s(s(z))))))), elem!1) | (elem!1 = s(s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.26 tff(29489,plain,
% 5.04/5.26 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[29488, 29445, 29198, 29471, 27217, 29328, 29458])).
% 5.04/5.26 tff(29490,plain,
% 5.04/5.26 (~r(s(s(s(elem!1))), elem!1)),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[3682, 29489, 29475])).
% 5.04/5.26 tff(29491,plain,
% 5.04/5.26 (b(s(s(s(elem!1))), elem!1)),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[570, 29490, 29447])).
% 5.04/5.26 tff(29492,plain,
% 5.04/5.26 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(s(z)))))),
% 5.04/5.26 inference(monotonicity,[status(thm)],[29441])).
% 5.04/5.26 tff(29493,plain,
% 5.04/5.26 (b(z, s(s(s(s(z))))) <=> b(z, s(s(s(elem!1))))),
% 5.04/5.26 inference(symmetry,[status(thm)],[29492])).
% 5.04/5.26 tff(29494,plain,
% 5.04/5.26 (b(z, s(s(s(elem!1))))),
% 5.04/5.26 inference(modus_ponens,[status(thm)],[27212, 29493])).
% 5.04/5.26 tff(29495,plain,
% 5.04/5.26 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[1154, 29472, 273, 29328, 27217])).
% 5.04/5.26 tff(29496,plain,
% 5.04/5.26 (r(s(s(s(s(s(s(s(z))))))), z)),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[133, 29495])).
% 5.04/5.26 tff(29497,plain,
% 5.04/5.26 (~r(z, elem!1)),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[11027, 29489, 29496])).
% 5.04/5.26 tff(29498,plain,
% 5.04/5.26 (b(z, elem!1)),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[585, 29497, 507])).
% 5.04/5.26 tff(29499,plain,
% 5.04/5.26 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(s(s(elem!1))))),
% 5.04/5.26 inference(transitivity,[status(thm)],[29443, 2486])).
% 5.04/5.26 tff(29500,plain,
% 5.04/5.26 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 5.04/5.26 inference(monotonicity,[status(thm)],[29499])).
% 5.04/5.26 tff(29501,plain,
% 5.04/5.26 (~(elem!1 = s(s(s(elem!1))))),
% 5.04/5.26 inference(modus_ponens,[status(thm)],[29446, 29500])).
% 5.04/5.26 tff(29502,plain,
% 5.04/5.26 (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(s(z)))))),
% 5.04/5.26 inference(monotonicity,[status(thm)],[29441])).
% 5.04/5.26 tff(29503,plain,
% 5.04/5.26 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 5.04/5.26 inference(symmetry,[status(thm)],[29502])).
% 5.04/5.26 tff(29504,plain,
% 5.04/5.26 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 5.04/5.26 inference(modus_ponens,[status(thm)],[24592, 29503])).
% 5.04/5.26 tff(29505,plain,
% 5.04/5.26 (~r(elem!1, s(s(s(elem!1))))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[8969, 29489, 29504])).
% 5.04/5.26 tff(29506,plain,
% 5.04/5.26 (b(elem!1, s(s(s(elem!1))))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[2054, 29505, 29501])).
% 5.04/5.26 tff(29507,plain,
% 5.04/5.26 ($false),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[12925, 29506, 29498, 29494, 29469, 29491])).
% 5.04/5.26 tff(29508,plain,((z = elem!1) | (~b(z, 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(z)))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.26 tff(29509,plain,
% 5.04/5.26 (z = elem!1),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[29508, 86, 3428, 273])).
% 5.04/5.26 tff(29510,plain,
% 5.04/5.26 (~b(elem!1, z)),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[6991, 29509])).
% 5.04/5.26 tff(29511,plain,
% 5.04/5.26 (~(elem!1 = s(s(s(s(z)))))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[12557, 29510, 28506])).
% 5.04/5.26 tff(29512,plain,
% 5.04/5.26 (elem!1 = z),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[317, 29509])).
% 5.04/5.26 tff(29513,plain,
% 5.04/5.26 (b(elem!1, s(s(z)))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[3276, 29512, 273])).
% 5.04/5.26 tff(29514,plain,
% 5.04/5.26 ((s(s(s(s(s(s(s(z))))))) = z) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 5.04/5.26 inference(monotonicity,[status(thm)],[29509])).
% 5.04/5.26 tff(29515,plain,
% 5.04/5.26 ((s(s(s(s(s(s(s(z))))))) = z) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 5.04/5.26 inference(transitivity,[status(thm)],[29514, 836])).
% 5.04/5.26 tff(29516,plain,
% 5.04/5.26 ((~(s(s(s(s(s(s(s(z))))))) = z)) <=> (~(elem!1 = s(s(s(s(s(s(s(z)))))))))),
% 5.04/5.26 inference(monotonicity,[status(thm)],[29515])).
% 5.04/5.26 tff(29517,plain,
% 5.04/5.26 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 5.04/5.26 inference(modus_ponens,[status(thm)],[128, 29516])).
% 5.04/5.26 tff(29518,plain,
% 5.04/5.26 (r(s(s(s(s(s(s(s(z))))))), z) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.04/5.26 inference(monotonicity,[status(thm)],[29509])).
% 5.04/5.26 tff(29519,plain,
% 5.04/5.26 ((~r(s(s(s(s(s(s(s(z))))))), z)) <=> (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 5.04/5.26 inference(monotonicity,[status(thm)],[29518])).
% 5.04/5.26 tff(29520,plain,
% 5.04/5.26 (~(s(elem!1) = s(s(z)))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[28525, 29509])).
% 5.04/5.26 tff(29521,plain,
% 5.04/5.26 (~(s(elem!1) = s(s(s(s(z)))))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[25360, 29509])).
% 5.04/5.26 tff(29522,plain,
% 5.04/5.26 (~b(s(elem!1), z)),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[29225, 29521, 29198, 273, 29520, 103])).
% 5.04/5.26 tff(29523,plain,
% 5.04/5.26 (r(s(elem!1), z)),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[774, 29522])).
% 5.04/5.26 tff(29524,plain,
% 5.04/5.26 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[28541, 29523, 27217, 29328, 29512, 29520])).
% 5.04/5.26 tff(29525,plain,
% 5.04/5.26 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.04/5.26 inference(modus_ponens,[status(thm)],[29524, 29519])).
% 5.04/5.26 tff(29526,plain,
% 5.04/5.26 ($false),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[29488, 29525, 29517, 29198, 29513, 27217, 29328, 29511])).
% 5.04/5.26 tff(29527,plain,(b(s(s(s(s(z)))), s(s(z))) | (~b(z, s(s(z)))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.26 tff(29528,plain,
% 5.04/5.26 (b(s(s(s(s(z)))), s(s(z)))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[29527, 144, 28504])).
% 5.04/5.26 tff(29529,plain,
% 5.04/5.26 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[27248, 3244])).
% 5.04/5.26 tff(29530,plain,
% 5.04/5.26 (b(s(s(s(s(s(s(s(z))))))), z)),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[133, 29529])).
% 5.04/5.26 tff(29531,plain,
% 5.04/5.26 (~r(s(s(z)), s(s(s(s(z)))))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[21308, 3244, 28500])).
% 5.04/5.26 tff(29532,plain,
% 5.04/5.26 (b(s(s(z)), s(s(s(s(z)))))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[164, 29531])).
% 5.04/5.26 tff(29533,plain,
% 5.04/5.26 ($false),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[29204, 178, 273, 27212, 167, 146, 1146])).
% 5.04/5.26 tff(29534,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.26 tff(29535,plain,
% 5.04/5.26 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[29534, 29532, 144, 29530])).
% 5.04/5.26 tff(29536,plain,
% 5.04/5.26 (~r(elem!1, s(s(z)))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[458, 437, 28500])).
% 5.04/5.26 tff(29537,plain,
% 5.04/5.26 (b(elem!1, s(s(z)))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[467, 312, 29536])).
% 5.04/5.26 tff(29538,plain,
% 5.04/5.26 (~r(s(s(z)), elem!1)),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[443, 437, 28500])).
% 5.04/5.26 tff(29539,plain,
% 5.04/5.26 (b(s(s(z)), elem!1)),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[448, 12, 29538])).
% 5.04/5.26 tff(29540,plain,
% 5.04/5.26 (elem!1 = s(s(s(s(z))))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[13518, 29539, 194, 437, 29537, 202])).
% 5.04/5.26 tff(29541,plain,
% 5.04/5.26 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(s(s(z)))))),
% 5.04/5.26 inference(monotonicity,[status(thm)],[29540])).
% 5.04/5.26 tff(29542,plain,
% 5.04/5.26 ((s(elem!1) = elem!1) <=> (s(s(s(s(z)))) = s(elem!1))),
% 5.04/5.26 inference(transitivity,[status(thm)],[29541, 2163])).
% 5.04/5.26 tff(29543,plain,
% 5.04/5.26 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(elem!1) = elem!1)),
% 5.04/5.26 inference(symmetry,[status(thm)],[29542])).
% 5.04/5.26 tff(29544,plain,
% 5.04/5.26 (~(s(elem!1) = s(s(z)))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[11438, 29540])).
% 5.04/5.26 tff(29545,plain,
% 5.04/5.26 (~(s(s(z)) = s(elem!1))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[1058, 29544])).
% 5.04/5.26 tff(29546,plain,
% 5.04/5.26 (~r(s(s(z)), s(s(s(s(z)))))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[21308, 194, 28500])).
% 5.04/5.26 tff(29547,plain,
% 5.04/5.26 (b(s(s(z)), s(s(s(s(z)))))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[164, 29546])).
% 5.04/5.26 tff(29548,plain,
% 5.04/5.26 (b(s(elem!1), s(s(z)))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[435, 29540, 28500, 107, 224, 12])).
% 5.04/5.26 tff(29549,plain,
% 5.04/5.26 (~b(s(elem!1), s(s(s(s(z)))))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[2756, 29548, 273, 29547, 202, 28500, 29540, 29545])).
% 5.04/5.26 tff(29550,plain,
% 5.04/5.26 (~b(s(elem!1), z)),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[29208, 29548, 273, 29547])).
% 5.04/5.26 tff(29551,plain,
% 5.04/5.26 (r(s(elem!1), z)),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[774, 29550])).
% 5.04/5.26 tff(29552,plain,
% 5.04/5.26 (~r(s(elem!1), s(s(s(s(z)))))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[916, 29551, 194])).
% 5.04/5.26 tff(29553,plain,
% 5.04/5.26 (s(elem!1) = s(s(s(s(z))))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[1084, 29552, 29549])).
% 5.04/5.26 tff(29554,plain,
% 5.04/5.26 (s(s(s(s(z)))) = s(elem!1)),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[13963, 29553])).
% 5.04/5.26 tff(29555,plain,
% 5.04/5.26 (s(elem!1) = elem!1),
% 5.04/5.26 inference(modus_ponens,[status(thm)],[29554, 29543])).
% 5.04/5.26 tff(29556,plain,
% 5.04/5.26 (s(s(s(s(z)))) = elem!1),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[24866, 29537, 202, 29547, 24288, 14934])).
% 5.04/5.26 tff(29557,plain,
% 5.04/5.26 (~(s(s(elem!1)) = elem!1)),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[338, 29556, 12])).
% 5.04/5.26 tff(29558,plain,
% 5.04/5.26 (~(s(elem!1) = elem!1)),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[672, 29557])).
% 5.04/5.26 tff(29559,plain,
% 5.04/5.26 ($false),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[29558, 29555])).
% 5.04/5.26 tff(29560,plain,((s(s(z)) = elem!1) | (~r(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.26 tff(29561,plain,
% 5.04/5.26 (s(s(z)) = elem!1),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[29560, 437, 144, 29528, 107, 224, 194])).
% 5.04/5.26 tff(29562,plain,
% 5.04/5.26 (s(s(s(z))) = s(elem!1)),
% 5.04/5.26 inference(monotonicity,[status(thm)],[29561])).
% 5.04/5.26 tff(29563,plain,
% 5.04/5.26 ((elem!1 = s(s(s(z)))) <=> (elem!1 = s(elem!1))),
% 5.04/5.26 inference(monotonicity,[status(thm)],[29562])).
% 5.04/5.26 tff(29564,plain,
% 5.04/5.26 ((elem!1 = s(s(s(z)))) <=> (s(elem!1) = elem!1)),
% 5.04/5.26 inference(transitivity,[status(thm)],[29563, 3190])).
% 5.04/5.26 tff(29565,plain,
% 5.04/5.26 ((~(elem!1 = s(s(s(z))))) <=> (~(s(elem!1) = elem!1))),
% 5.04/5.26 inference(monotonicity,[status(thm)],[29564])).
% 5.04/5.26 tff(29566,plain,
% 5.04/5.26 ((s(s(z)) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 5.04/5.26 inference(monotonicity,[status(thm)],[29561])).
% 5.04/5.26 tff(29567,plain,
% 5.04/5.26 ((~(s(s(z)) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 5.04/5.26 inference(monotonicity,[status(thm)],[29566])).
% 5.04/5.26 tff(29568,plain,
% 5.04/5.26 (~(elem!1 = s(s(s(z))))),
% 5.04/5.26 inference(modus_ponens,[status(thm)],[3205, 29567])).
% 5.04/5.26 tff(29569,plain,
% 5.04/5.26 (~(s(elem!1) = elem!1)),
% 5.04/5.26 inference(modus_ponens,[status(thm)],[29568, 29565])).
% 5.04/5.26 tff(29570,plain,
% 5.04/5.26 (r(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.04/5.26 inference(monotonicity,[status(thm)],[29561])).
% 5.04/5.26 tff(29571,plain,
% 5.04/5.26 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.04/5.26 inference(modus_ponens,[status(thm)],[107, 29570])).
% 5.04/5.26 tff(29572,plain,
% 5.04/5.26 (~r(z, elem!1)),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[18165, 29561, 48])).
% 5.04/5.26 tff(29573,plain,
% 5.04/5.26 (b(z, elem!1)),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[585, 29572, 507])).
% 5.04/5.26 tff(29574,plain,
% 5.04/5.26 (b(elem!1, s(s(s(s(z)))))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[17989, 1324, 29547])).
% 5.04/5.26 tff(29575,plain,
% 5.04/5.26 (b(elem!1, s(s(elem!1)))),
% 5.04/5.26 inference(modus_ponens,[status(thm)],[29574, 9141])).
% 5.04/5.26 tff(29576,plain,
% 5.04/5.26 (b(s(s(s(z))), z)),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[7042, 853, 10916])).
% 5.04/5.26 tff(29577,plain,
% 5.04/5.26 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[232, 224, 28500])).
% 5.04/5.26 tff(29578,plain,
% 5.04/5.26 (b(z, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[271, 29577])).
% 5.04/5.26 tff(29579,plain,
% 5.04/5.26 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 5.04/5.26 inference(monotonicity,[status(thm)],[3505])).
% 5.04/5.26 tff(29580,plain,
% 5.04/5.26 (b(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.04/5.26 inference(symmetry,[status(thm)],[29579])).
% 5.04/5.26 tff(29581,plain,
% 5.04/5.26 (~b(s(elem!1), s(s(z)))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[29208, 853, 273, 29547])).
% 5.04/5.26 tff(29582,plain,
% 5.04/5.26 (r(s(elem!1), s(s(z)))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[421, 29581, 10976])).
% 5.04/5.26 tff(29583,plain,
% 5.04/5.26 (r(s(elem!1), elem!1)),
% 5.04/5.26 inference(modus_ponens,[status(thm)],[29582, 8497])).
% 5.04/5.26 tff(29584,plain,
% 5.04/5.26 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[14053, 118, 29583, 2953])).
% 5.04/5.26 tff(29585,plain,
% 5.04/5.26 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[806, 41, 29584, 27693])).
% 5.04/5.26 tff(29586,plain,
% 5.04/5.26 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.04/5.26 inference(modus_ponens,[status(thm)],[29585, 29580])).
% 5.04/5.26 tff(29587,plain,
% 5.04/5.26 (~b(z, s(s(s(z))))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[23358, 29586, 29578, 27531, 29576])).
% 5.04/5.26 tff(29588,plain,
% 5.04/5.26 (r(z, s(s(s(z))))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[4920, 29587])).
% 5.04/5.26 tff(29589,plain,
% 5.04/5.26 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[4961, 29588, 194])).
% 5.04/5.26 tff(29590,plain,
% 5.04/5.26 (b(s(s(s(s(z)))), s(s(s(z))))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[11185, 29589])).
% 5.04/5.26 tff(29591,plain,
% 5.04/5.26 (b(s(s(elem!1)), s(elem!1))),
% 5.04/5.26 inference(modus_ponens,[status(thm)],[29590, 9112])).
% 5.04/5.26 tff(29592,plain,
% 5.04/5.26 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[390, 29582, 224])).
% 5.04/5.26 tff(29593,plain,
% 5.04/5.26 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[395, 29592, 8112])).
% 5.04/5.26 tff(29594,plain,
% 5.04/5.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~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(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~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(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 5.04/5.26 inference(rewrite,[status(thm)],[])).
% 5.04/5.26 tff(29595,plain,
% 5.04/5.26 (((~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(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z))) <=> ((~b(z, s(elem!1))) | (~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(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 5.04/5.26 inference(rewrite,[status(thm)],[])).
% 5.04/5.26 tff(29596,plain,
% 5.04/5.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(z, s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~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(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 5.04/5.26 inference(monotonicity,[status(thm)],[29595])).
% 5.04/5.26 tff(29597,plain,
% 5.04/5.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(z, s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~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(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 5.04/5.26 inference(transitivity,[status(thm)],[29596, 29594])).
% 5.04/5.26 tff(29598,plain,
% 5.04/5.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 5.04/5.26 inference(quant_inst,[status(thm)],[])).
% 5.04/5.26 tff(29599,plain,
% 5.04/5.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~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(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 5.04/5.26 inference(modus_ponens,[status(thm)],[29598, 29597])).
% 5.04/5.26 tff(29600,plain,
% 5.04/5.26 (~b(z, s(elem!1))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[29599, 178, 29593, 29578, 27531, 29585])).
% 5.04/5.26 tff(29601,plain,
% 5.04/5.26 (r(z, s(elem!1))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[2351, 29600])).
% 5.04/5.26 tff(29602,plain,
% 5.04/5.26 (~r(elem!1, s(elem!1))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[12189, 29601, 437])).
% 5.04/5.26 tff(29603,plain,
% 5.04/5.26 (b(elem!1, s(elem!1))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[756, 29602, 10913])).
% 5.04/5.26 tff(29604,plain,
% 5.04/5.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 5.04/5.26 inference(rewrite,[status(thm)],[])).
% 5.04/5.26 tff(29605,plain,
% 5.04/5.26 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 5.04/5.26 inference(rewrite,[status(thm)],[])).
% 5.04/5.26 tff(29606,plain,
% 5.04/5.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1))))))),
% 5.04/5.26 inference(monotonicity,[status(thm)],[29605])).
% 5.04/5.26 tff(29607,plain,
% 5.04/5.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 5.04/5.26 inference(transitivity,[status(thm)],[29606, 29604])).
% 5.04/5.26 tff(29608,plain,
% 5.04/5.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)))),
% 5.04/5.26 inference(quant_inst,[status(thm)],[])).
% 5.04/5.26 tff(29609,plain,
% 5.04/5.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1))))),
% 5.04/5.26 inference(modus_ponens,[status(thm)],[29608, 29607])).
% 5.04/5.26 tff(29610,plain,
% 5.04/5.26 ($false),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[29609, 178, 818, 29603, 27724, 29591, 29575])).
% 5.04/5.26 tff(29611,plain,((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~(s(s(z)) = elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.26 tff(29612,plain,
% 5.04/5.26 (~b(s(elem!1), z)),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[29611, 29573, 29561, 194, 437, 29571, 224, 144])).
% 5.04/5.26 tff(29613,plain,
% 5.04/5.26 (r(s(elem!1), z)),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[774, 29612])).
% 5.04/5.26 tff(29614,plain,
% 5.04/5.26 (~r(elem!1, s(elem!1))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[2711, 29613, 437])).
% 5.04/5.26 tff(29615,plain,
% 5.04/5.26 (b(s(s(z)), s(elem!1))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[1337, 29614, 29561, 29569])).
% 5.04/5.26 tff(29616,plain,
% 5.04/5.26 ((s(elem!1) = s(s(z))) <=> (s(elem!1) = elem!1)),
% 5.04/5.26 inference(monotonicity,[status(thm)],[29561])).
% 5.04/5.26 tff(29617,plain,
% 5.04/5.26 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(z)))),
% 5.04/5.26 inference(symmetry,[status(thm)],[29616])).
% 5.04/5.26 tff(29618,plain,
% 5.04/5.26 ((elem!1 = s(s(s(z)))) <=> (s(elem!1) = s(s(z)))),
% 5.04/5.26 inference(transitivity,[status(thm)],[29564, 29617])).
% 5.04/5.26 tff(29619,plain,
% 5.04/5.26 ((~(elem!1 = s(s(s(z))))) <=> (~(s(elem!1) = s(s(z))))),
% 5.04/5.26 inference(monotonicity,[status(thm)],[29618])).
% 5.04/5.26 tff(29620,plain,
% 5.04/5.26 (~(s(elem!1) = s(s(z)))),
% 5.04/5.26 inference(modus_ponens,[status(thm)],[29568, 29619])).
% 5.04/5.26 tff(29621,plain,
% 5.04/5.26 (~r(s(elem!1), s(s(z)))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[2258, 29613, 28500])).
% 5.04/5.26 tff(29622,plain,
% 5.04/5.26 (b(s(elem!1), s(s(z)))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[421, 29621, 29620])).
% 5.04/5.26 tff(29623,plain,
% 5.04/5.26 (elem!1 = s(s(z))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[3230, 29561])).
% 5.04/5.26 tff(29624,plain,
% 5.04/5.26 (~b(elem!1, s(s(z)))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[3223, 29561])).
% 5.04/5.26 tff(29625,plain,
% 5.04/5.26 (~(s(s(s(s(z)))) = elem!1)),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[4509, 29624, 29528])).
% 5.04/5.26 tff(29626,plain,
% 5.04/5.26 (~(s(elem!1) = s(s(s(s(z)))))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[1353, 29625, 29623])).
% 5.04/5.26 tff(29627,plain,
% 5.04/5.26 (~r(s(elem!1), s(s(s(s(z)))))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[916, 29613, 194])).
% 5.04/5.26 tff(29628,plain,
% 5.04/5.26 (b(s(elem!1), s(s(s(s(z)))))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[1084, 29627, 29626])).
% 5.04/5.26 tff(29629,plain,
% 5.04/5.26 ($false),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[1079, 29628, 29622, 29528, 29547, 29615])).
% 5.04/5.26 tff(29630,plain,((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (z = elem!1) | r(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.26 tff(29631,plain,
% 5.04/5.26 (~r(elem!1, z)),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[29630, 287, 3244, 15765, 507, 48])).
% 5.04/5.26 tff(29632,plain,
% 5.04/5.26 (~(s(s(z)) = elem!1)),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[1345, 29631, 28500])).
% 5.04/5.26 tff(29633,plain,
% 5.04/5.26 (~(elem!1 = s(s(z)))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[311, 29632])).
% 5.04/5.26 tff(29634,plain,
% 5.04/5.26 (b(elem!1, z)),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[498, 29631, 2809])).
% 5.04/5.26 tff(29635,plain,
% 5.04/5.26 (~(elem!1 = s(s(s(s(z)))))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[3172, 29634, 3170])).
% 5.04/5.26 tff(29636,plain,
% 5.04/5.26 (~(s(s(s(s(z)))) = elem!1)),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[504, 29635])).
% 5.04/5.26 tff(29637,plain,
% 5.04/5.26 (~r(s(s(z)), elem!1)),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[541, 521, 28500])).
% 5.04/5.26 tff(29638,plain,
% 5.04/5.26 (b(s(s(z)), elem!1)),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[448, 29637, 12])).
% 5.04/5.26 tff(29639,plain,
% 5.04/5.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, 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, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, 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, s(s(s(s(z)))))))),
% 5.04/5.26 inference(rewrite,[status(thm)],[])).
% 5.04/5.26 tff(29640,plain,
% 5.04/5.26 (((~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(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z))))) <=> ((~b(z, 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, s(s(s(s(z)))))))),
% 5.04/5.26 inference(rewrite,[status(thm)],[])).
% 5.04/5.26 tff(29641,plain,
% 5.04/5.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, 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, s(s(s(s(z))))))))),
% 5.04/5.26 inference(monotonicity,[status(thm)],[29640])).
% 5.04/5.26 tff(29642,plain,
% 5.04/5.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, 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, s(s(s(s(z)))))))),
% 5.04/5.26 inference(transitivity,[status(thm)],[29641, 29639])).
% 5.04/5.26 tff(29643,plain,
% 5.04/5.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))))),
% 5.04/5.26 inference(quant_inst,[status(thm)],[])).
% 5.04/5.26 tff(29644,plain,
% 5.04/5.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z))))))),
% 5.04/5.26 inference(modus_ponens,[status(thm)],[29643, 29642])).
% 5.04/5.26 tff(29645,plain,
% 5.04/5.26 ($false),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[29644, 178, 29638, 273, 3143, 27212, 29547])).
% 5.04/5.26 tff(29646,plain,((~r(z, elem!1)) | (~b(z, s(s(z)))) | (s(s(s(s(z)))) = elem!1) | (s(s(z)) = elem!1) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.26 tff(29647,plain,
% 5.04/5.26 (~r(z, elem!1)),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[29646, 29636, 144, 29632, 3244])).
% 5.04/5.26 tff(29648,plain,
% 5.04/5.26 (~b(s(s(z)), elem!1)),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[3126, 29647, 28500, 144, 507, 286, 29634, 29633, 29631])).
% 5.04/5.26 tff(29649,plain,
% 5.04/5.26 (r(s(s(z)), elem!1)),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[448, 29648, 29632])).
% 5.04/5.26 tff(29650,plain,
% 5.04/5.26 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[11351, 29649, 287])).
% 5.04/5.26 tff(29651,plain,
% 5.04/5.26 (b(z, elem!1)),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[585, 29647, 507])).
% 5.04/5.26 tff(29652,plain,
% 5.04/5.26 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[232, 287, 28500])).
% 5.04/5.26 tff(29653,plain,
% 5.04/5.26 (b(z, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[271, 29652])).
% 5.04/5.26 tff(29654,plain,
% 5.04/5.26 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[2803, 29649, 287])).
% 5.04/5.26 tff(29655,plain,
% 5.04/5.26 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[18193, 29654, 29634, 29653, 29651, 29650])).
% 5.04/5.26 tff(29656,plain,
% 5.04/5.26 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 5.04/5.26 inference(monotonicity,[status(thm)],[29655])).
% 5.04/5.26 tff(29657,plain,
% 5.04/5.26 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 5.04/5.26 inference(monotonicity,[status(thm)],[29656])).
% 5.04/5.26 tff(29658,plain,
% 5.04/5.26 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 5.04/5.26 inference(symmetry,[status(thm)],[29657])).
% 5.04/5.26 tff(29659,plain,
% 5.04/5.26 ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) <=> (~b(s(elem!1), s(s(s(s(z))))))),
% 5.04/5.26 inference(monotonicity,[status(thm)],[29658])).
% 5.04/5.26 tff(29660,plain,
% 5.04/5.26 (~(s(elem!1) = s(s(s(s(z)))))),
% 5.04/5.26 inference(unit_resolution,[status(thm)],[16181, 29655])).
% 5.04/5.27 tff(29661,plain,
% 5.04/5.27 (~(s(s(s(s(z)))) = s(elem!1))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[2168, 29660])).
% 5.04/5.27 tff(29662,plain,
% 5.04/5.27 (~(s(s(elem!1)) = elem!1)),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[2510, 29661, 29655])).
% 5.04/5.27 tff(29663,plain,
% 5.04/5.27 (~(s(elem!1) = elem!1)),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[672, 29662])).
% 5.04/5.27 tff(29664,plain,
% 5.04/5.27 (~(s(elem!1) = s(s(z)))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[2832, 29655])).
% 5.04/5.27 tff(29665,plain,
% 5.04/5.27 (~(s(s(z)) = s(elem!1))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[1058, 29664])).
% 5.04/5.27 tff(29666,plain,
% 5.04/5.27 (~b(elem!1, s(s(z)))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[25284, 29655, 3576])).
% 5.04/5.27 tff(29667,plain,
% 5.04/5.27 (r(elem!1, s(s(z)))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[467, 29666, 29633])).
% 5.04/5.27 tff(29668,plain,
% 5.04/5.27 (~r(s(elem!1), s(s(z)))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[17418, 29663, 28500, 29651, 29634, 29667])).
% 5.04/5.27 tff(29669,plain,
% 5.04/5.27 (b(s(elem!1), s(s(z)))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[421, 29668, 29664])).
% 5.04/5.27 tff(29670,plain,
% 5.04/5.27 (~b(s(elem!1), z)),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[29208, 29669, 144, 29532])).
% 5.04/5.27 tff(29671,plain,
% 5.04/5.27 (r(s(elem!1), z)),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[774, 29670])).
% 5.04/5.27 tff(29672,plain,
% 5.04/5.27 (~r(s(elem!1), s(s(s(s(z)))))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[916, 29671, 3244])).
% 5.04/5.27 tff(29673,plain,
% 5.04/5.27 (b(s(elem!1), s(s(s(s(z)))))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[1084, 29672, 29660])).
% 5.04/5.27 tff(29674,plain,
% 5.04/5.27 (~b(s(s(z)), s(elem!1))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[1079, 29673, 29528, 29532, 29669])).
% 5.04/5.27 tff(29675,plain,
% 5.04/5.27 (r(s(s(z)), s(elem!1))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[1067, 29674, 29665])).
% 5.04/5.27 tff(29676,plain,
% 5.04/5.27 (~r(z, s(elem!1))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[2341, 29675, 28500])).
% 5.04/5.27 tff(29677,plain,
% 5.04/5.27 (b(z, s(elem!1))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[2351, 29676])).
% 5.04/5.27 tff(29678,plain,
% 5.04/5.27 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[24804, 29677, 29532, 15765, 29634, 29651, 29649, 29663, 144, 29655])).
% 5.04/5.27 tff(29679,plain,
% 5.04/5.27 (~b(s(elem!1), s(s(s(s(z)))))),
% 5.04/5.27 inference(modus_ponens,[status(thm)],[29678, 29659])).
% 5.04/5.27 tff(29680,plain,
% 5.04/5.27 ($false),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[29673, 29679])).
% 5.04/5.27 tff(29681,plain,(b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(s(s(s(z))))))), s(s(z))) | (z = elem!1) | b(s(s(s(s(z)))), z) | r(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.27 tff(29682,plain,
% 5.04/5.27 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[29681, 3576, 507, 3170, 48])).
% 5.04/5.27 tff(29683,plain,
% 5.04/5.27 (b(elem!1, s(s(z)))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[467, 29536, 312])).
% 5.04/5.27 tff(29684,plain,
% 5.04/5.27 (s(s(s(s(z)))) = elem!1),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[24866, 29683, 202, 29547, 24288, 14934])).
% 5.04/5.27 tff(29685,plain,
% 5.04/5.27 (b(s(s(z)), elem!1)),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[448, 29538, 12])).
% 5.04/5.27 tff(29686,plain,
% 5.04/5.27 (elem!1 = s(s(s(s(z))))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[13518, 29685, 194, 437, 29683, 202])).
% 5.04/5.27 tff(29687,plain,
% 5.04/5.27 (b(s(elem!1), s(s(z)))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[2373, 29686, 28500, 107, 166, 12])).
% 5.04/5.27 tff(29688,plain,
% 5.04/5.27 (~b(s(elem!1), s(s(s(s(z)))))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[2756, 29686, 273, 29547, 202, 28500, 29687, 1060])).
% 5.04/5.27 tff(29689,plain,
% 5.04/5.27 (~b(s(elem!1), z)),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[29208, 29687, 273, 29547])).
% 5.04/5.27 tff(29690,plain,
% 5.04/5.27 (r(s(elem!1), z)),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[774, 29689])).
% 5.04/5.27 tff(29691,plain,
% 5.04/5.27 (~r(s(elem!1), s(s(s(s(z)))))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[916, 29690, 194])).
% 5.04/5.27 tff(29692,plain,
% 5.04/5.27 (s(elem!1) = s(s(s(s(z))))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[1084, 29691, 29688])).
% 5.04/5.27 tff(29693,plain,
% 5.04/5.27 (s(elem!1) = elem!1),
% 5.04/5.27 inference(transitivity,[status(thm)],[29692, 29684])).
% 5.04/5.27 tff(29694,plain,
% 5.04/5.27 (~(s(s(elem!1)) = elem!1)),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[338, 29684, 12])).
% 5.04/5.27 tff(29695,plain,
% 5.04/5.27 (~(s(elem!1) = elem!1)),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[672, 29694])).
% 5.04/5.27 tff(29696,plain,
% 5.04/5.27 ($false),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[29695, 29693])).
% 5.04/5.27 tff(29697,plain,((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (s(s(z)) = s(elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 5.04/5.27 tff(29698,plain,
% 5.04/5.27 (~r(elem!1, z)),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[29697, 2311, 273, 202, 3244, 107, 166, 12])).
% 5.04/5.27 tff(29699,plain,
% 5.04/5.27 (b(elem!1, z)),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[498, 29698, 2809])).
% 5.04/5.27 tff(29700,plain,
% 5.04/5.27 (~(elem!1 = s(s(s(s(z)))))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[3172, 29699, 3170])).
% 5.04/5.27 tff(29701,plain,
% 5.04/5.27 (~(s(s(s(s(z)))) = elem!1)),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[504, 29700])).
% 5.04/5.27 tff(29702,plain,
% 5.04/5.27 (~r(z, elem!1)),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[29646, 29701, 273, 12, 3244])).
% 5.04/5.27 tff(29703,plain,
% 5.04/5.27 (b(z, elem!1)),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[585, 29702, 507])).
% 5.04/5.27 tff(29704,plain,
% 5.04/5.27 (r(s(elem!1), s(s(z)))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[421, 29581, 1056])).
% 5.04/5.27 tff(29705,plain,
% 5.04/5.27 (s(elem!1) = elem!1),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[2558, 29704, 273, 506, 818, 12, 853])).
% 5.04/5.27 tff(29706,plain,
% 5.04/5.27 (s(s(s(elem!1))) = elem!1),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[2150, 29705])).
% 5.04/5.27 tff(29707,plain,
% 5.04/5.27 (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)),
% 5.04/5.27 inference(monotonicity,[status(thm)],[29706])).
% 5.04/5.27 tff(29708,plain,
% 5.04/5.27 (s(s(elem!1)) = elem!1),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[672, 29705])).
% 5.04/5.27 tff(29709,plain,
% 5.04/5.27 (elem!1 = s(s(elem!1))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[1546, 29708])).
% 5.04/5.27 tff(29710,plain,
% 5.04/5.27 (s(s(s(elem!1))) = s(elem!1)),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[1539, 29709])).
% 5.04/5.27 tff(29711,plain,
% 5.04/5.27 (r(s(s(s(elem!1))), s(s(z)))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[19306, 29710, 29704])).
% 5.04/5.27 tff(29712,plain,
% 5.04/5.27 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[10401, 29711, 107])).
% 5.04/5.27 tff(29713,plain,
% 5.04/5.27 (b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[5118, 29712, 9310])).
% 5.04/5.27 tff(29714,plain,
% 5.04/5.27 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.04/5.27 inference(modus_ponens,[status(thm)],[29713, 29707])).
% 5.04/5.27 tff(29715,plain,
% 5.04/5.27 (b(s(elem!1), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 5.04/5.27 inference(monotonicity,[status(thm)],[29705])).
% 5.04/5.27 tff(29716,plain,
% 5.04/5.27 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[666, 29708, 323])).
% 5.04/5.27 tff(29717,plain,
% 5.04/5.27 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[4019, 29716])).
% 5.04/5.27 tff(29718,plain,
% 5.04/5.27 (b(z, s(elem!1)) <=> b(z, elem!1)),
% 5.04/5.27 inference(monotonicity,[status(thm)],[29705])).
% 5.04/5.27 tff(29719,plain,
% 5.04/5.27 (b(z, elem!1) <=> b(z, s(elem!1))),
% 5.04/5.27 inference(symmetry,[status(thm)],[29718])).
% 5.04/5.27 tff(29720,plain,
% 5.04/5.27 (b(z, s(elem!1))),
% 5.04/5.27 inference(modus_ponens,[status(thm)],[818, 29719])).
% 5.04/5.27 tff(29721,plain,
% 5.04/5.27 (~r(s(elem!1), s(s(s(s(z)))))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[26193, 29720, 194, 29716, 853, 29717])).
% 5.04/5.27 tff(29722,plain,
% 5.04/5.27 (b(s(elem!1), s(s(s(s(z)))))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[1084, 29721, 1369])).
% 5.04/5.27 tff(29723,plain,
% 5.04/5.27 (b(elem!1, s(s(s(s(z)))))),
% 5.04/5.27 inference(modus_ponens,[status(thm)],[29722, 29715])).
% 5.04/5.27 tff(29724,plain,
% 5.04/5.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 5.04/5.27 inference(rewrite,[status(thm)],[])).
% 5.04/5.27 tff(29725,plain,
% 5.04/5.27 (((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, 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)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 5.04/5.27 inference(rewrite,[status(thm)],[])).
% 5.04/5.27 tff(29726,plain,
% 5.04/5.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z))))))))),
% 5.04/5.27 inference(monotonicity,[status(thm)],[29725])).
% 5.04/5.27 tff(29727,plain,
% 5.04/5.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 5.04/5.27 inference(transitivity,[status(thm)],[29726, 29724])).
% 5.04/5.27 tff(29728,plain,
% 5.04/5.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 5.04/5.27 inference(quant_inst,[status(thm)],[])).
% 5.04/5.27 tff(29729,plain,
% 5.04/5.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(z))))))),
% 5.04/5.27 inference(modus_ponens,[status(thm)],[29728, 29727])).
% 5.04/5.27 tff(29730,plain,
% 5.04/5.27 ($false),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[29729, 178, 818, 27212, 29723, 27531, 29714])).
% 5.04/5.27 tff(29731,plain,((~b(s(elem!1), z)) | (~b(z, elem!1)) | (s(elem!1) = s(s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (s(s(s(s(z)))) = elem!1) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (s(s(z)) = elem!1) | (s(elem!1) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.27 tff(29732,plain,
% 5.04/5.27 (~b(s(elem!1), z)),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[29731, 1369, 818, 194, 107, 323, 273, 506, 12, 1056])).
% 5.04/5.27 tff(29733,plain,
% 5.04/5.27 (r(s(elem!1), z)),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[774, 29732])).
% 5.04/5.27 tff(29734,plain,
% 5.04/5.27 (~r(s(elem!1), s(s(s(s(z)))))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[916, 29733, 194])).
% 5.04/5.27 tff(29735,plain,
% 5.04/5.27 (b(s(elem!1), s(s(s(s(z)))))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[1084, 29734, 1369])).
% 5.04/5.27 tff(29736,plain,
% 5.04/5.27 (~r(s(elem!1), s(s(z)))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[2258, 29733, 28500])).
% 5.04/5.27 tff(29737,plain,
% 5.04/5.27 (b(s(elem!1), s(s(z)))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[421, 29736, 1056])).
% 5.04/5.27 tff(29738,plain,
% 5.04/5.27 (~b(s(s(z)), s(elem!1))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[1079, 29737, 202, 29547, 29735])).
% 5.04/5.27 tff(29739,plain,
% 5.04/5.27 (r(s(s(z)), s(elem!1))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[1067, 29738, 2311])).
% 5.04/5.27 tff(29740,plain,
% 5.04/5.27 (~r(z, s(elem!1))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[2341, 29739, 28500])).
% 5.04/5.27 tff(29741,plain,
% 5.04/5.27 (b(z, s(elem!1))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[2351, 29740])).
% 5.04/5.27 tff(29742,plain,
% 5.04/5.27 ($false),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[14207, 178, 29741, 29737, 27212, 29735, 202])).
% 5.04/5.27 tff(29743,plain,((s(elem!1) = s(s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (s(elem!1) = s(s(z))) | (~r(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (s(s(s(s(z)))) = elem!1) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 5.04/5.27 tff(29744,plain,
% 5.04/5.27 (s(elem!1) = s(s(s(s(z))))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[29743, 1056, 202, 3244, 29703, 107, 29701, 273, 29699, 12])).
% 5.04/5.27 tff(29745,plain,
% 5.04/5.27 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 5.04/5.27 inference(monotonicity,[status(thm)],[29744])).
% 5.04/5.27 tff(29746,plain,
% 5.04/5.27 (elem!1 = s(s(s(z)))),
% 5.04/5.27 inference(transitivity,[status(thm)],[517, 29745, 11])).
% 5.04/5.27 tff(29747,plain,
% 5.04/5.27 (b(elem!1, z) <=> b(s(s(s(z))), z)),
% 5.04/5.27 inference(monotonicity,[status(thm)],[29746])).
% 5.04/5.27 tff(29748,plain,
% 5.04/5.27 (b(s(s(s(z))), z)),
% 5.04/5.27 inference(modus_ponens,[status(thm)],[29699, 29747])).
% 5.04/5.27 tff(29749,plain,
% 5.04/5.27 (~b(s(s(s(z))), s(s(z)))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[21357, 29748, 27212, 273, 29532])).
% 5.04/5.27 tff(29750,plain,
% 5.04/5.27 (r(s(s(s(z))), s(s(z)))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[4966, 29749])).
% 5.04/5.27 tff(29751,plain,
% 5.04/5.27 (b(z, s(s(s(z))))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[1238, 29744, 29703])).
% 5.04/5.27 tff(29752,plain,
% 5.04/5.27 ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[3024, 3205])).
% 5.04/5.27 tff(29753,plain,
% 5.04/5.27 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[29752, 29748, 273, 166, 29751, 29530, 107])).
% 5.04/5.27 tff(29754,plain,
% 5.04/5.27 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[20667, 29753])).
% 5.04/5.27 tff(29755,plain,
% 5.04/5.27 ($false),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[8218, 29754, 29750, 107])).
% 5.04/5.27 tff(29756,plain,((s(elem!1) = s(s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (s(s(z)) = elem!1) | (z = elem!1) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 5.04/5.27 tff(29757,plain,
% 5.04/5.27 (s(elem!1) = s(s(z))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[29756, 12, 273, 166, 202, 107, 507, 3170])).
% 5.04/5.27 tff(29758,plain,
% 5.04/5.27 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 5.04/5.27 inference(monotonicity,[status(thm)],[29757])).
% 5.04/5.27 tff(29759,plain,
% 5.04/5.27 (elem!1 = s(z)),
% 5.04/5.27 inference(transitivity,[status(thm)],[517, 29758, 70])).
% 5.04/5.27 tff(29760,plain,
% 5.04/5.27 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(s(z), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.27 inference(monotonicity,[status(thm)],[29759])).
% 5.04/5.27 tff(29761,plain,
% 5.04/5.27 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[2832, 29757])).
% 5.04/5.27 tff(29762,plain,
% 5.04/5.27 (~(elem!1 = s(s(s(s(z)))))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[11438, 29757])).
% 5.04/5.27 tff(29763,plain,
% 5.04/5.27 (b(z, s(elem!1)) <=> b(z, s(s(z)))),
% 5.04/5.27 inference(monotonicity,[status(thm)],[29757])).
% 5.04/5.27 tff(29764,plain,
% 5.04/5.27 (b(z, s(s(z))) <=> b(z, s(elem!1))),
% 5.04/5.27 inference(symmetry,[status(thm)],[29763])).
% 5.04/5.27 tff(29765,plain,
% 5.04/5.27 (b(z, s(elem!1))),
% 5.04/5.27 inference(modus_ponens,[status(thm)],[273, 29764])).
% 5.04/5.27 tff(29766,plain,
% 5.04/5.27 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(z)))),
% 5.04/5.27 inference(monotonicity,[status(thm)],[29757])).
% 5.04/5.27 tff(29767,plain,
% 5.04/5.27 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 5.04/5.27 inference(symmetry,[status(thm)],[29766])).
% 5.04/5.27 tff(29768,plain,
% 5.04/5.27 (b(s(s(s(s(z)))), s(elem!1))),
% 5.04/5.27 inference(modus_ponens,[status(thm)],[202, 29767])).
% 5.04/5.27 tff(29769,plain,
% 5.04/5.27 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 5.04/5.27 inference(monotonicity,[status(thm)],[29757])).
% 5.04/5.27 tff(29770,plain,
% 5.04/5.27 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 5.04/5.27 inference(symmetry,[status(thm)],[29769])).
% 5.04/5.27 tff(29771,plain,
% 5.04/5.27 (b(s(elem!1), s(s(s(s(z)))))),
% 5.04/5.27 inference(modus_ponens,[status(thm)],[29532, 29770])).
% 5.04/5.27 tff(29772,plain,
% 5.04/5.27 (r(s(elem!1), z)),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[906, 29757, 28500])).
% 5.04/5.27 tff(29773,plain,
% 5.04/5.27 (~b(s(s(z)), s(elem!1))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[28795, 178, 855, 273, 1069, 167])).
% 5.04/5.27 tff(29774,plain,
% 5.04/5.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 5.04/5.27 inference(rewrite,[status(thm)],[])).
% 5.04/5.27 tff(29775,plain,
% 5.04/5.27 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 5.04/5.27 inference(rewrite,[status(thm)],[])).
% 5.04/5.27 tff(29776,plain,
% 5.04/5.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 5.04/5.27 inference(monotonicity,[status(thm)],[29775])).
% 5.04/5.27 tff(29777,plain,
% 5.04/5.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 5.04/5.27 inference(transitivity,[status(thm)],[29776, 29774])).
% 5.04/5.27 tff(29778,plain,
% 5.04/5.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))))),
% 5.04/5.27 inference(quant_inst,[status(thm)],[])).
% 5.04/5.27 tff(29779,plain,
% 5.04/5.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 5.04/5.27 inference(modus_ponens,[status(thm)],[29778, 29777])).
% 5.04/5.27 tff(29780,plain,
% 5.04/5.27 (~b(s(elem!1), s(s(z)))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[29779, 178, 855, 273, 1069, 167])).
% 5.04/5.27 tff(29781,plain,
% 5.04/5.27 (s(elem!1) = s(s(z))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[421, 29780, 927])).
% 5.04/5.27 tff(29782,plain,
% 5.04/5.27 (~(elem!1 = s(s(s(s(elem!1)))))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[1422, 29781])).
% 5.04/5.27 tff(29783,plain,
% 5.04/5.27 (~(s(s(s(elem!1))) = s(elem!1))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[1509, 29782])).
% 5.04/5.27 tff(29784,plain,
% 5.04/5.27 (~(elem!1 = s(s(elem!1)))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[1539, 29783])).
% 5.04/5.27 tff(29785,plain,
% 5.04/5.27 (~(s(s(elem!1)) = elem!1)),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[1546, 29784])).
% 5.04/5.27 tff(29786,plain,
% 5.04/5.27 (~(s(elem!1) = elem!1)),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[672, 29785])).
% 5.04/5.27 tff(29787,plain,
% 5.04/5.27 (~(s(s(z)) = elem!1)),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[1337, 29786, 744, 29773])).
% 5.04/5.27 tff(29788,plain,
% 5.04/5.27 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 5.04/5.27 inference(monotonicity,[status(thm)],[29781])).
% 5.04/5.27 tff(29789,plain,
% 5.04/5.27 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 5.04/5.27 inference(symmetry,[status(thm)],[29788])).
% 5.04/5.27 tff(29790,plain,
% 5.04/5.27 (s(z) = elem!1),
% 5.04/5.27 inference(transitivity,[status(thm)],[71, 29789, 304])).
% 5.04/5.27 tff(29791,plain,
% 5.04/5.27 ((s(z) = z) <=> (elem!1 = z)),
% 5.04/5.27 inference(monotonicity,[status(thm)],[29790])).
% 5.04/5.27 tff(29792,plain,
% 5.04/5.27 ((s(z) = z) <=> (z = elem!1)),
% 5.04/5.27 inference(transitivity,[status(thm)],[29791, 313])).
% 5.04/5.27 tff(29793,plain,
% 5.04/5.27 ((s(z) = z) <=> (elem!1 = z)),
% 5.04/5.27 inference(transitivity,[status(thm)],[29792, 314])).
% 5.04/5.27 tff(29794,plain,
% 5.04/5.27 ((~(s(z) = z)) <=> (~(elem!1 = z))),
% 5.04/5.27 inference(monotonicity,[status(thm)],[29793])).
% 5.04/5.27 tff(29795,plain,
% 5.04/5.27 (~(elem!1 = z)),
% 5.04/5.27 inference(modus_ponens,[status(thm)],[1476, 29794])).
% 5.04/5.27 tff(29796,plain,
% 5.04/5.27 (r(elem!1, z)),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[498, 29795, 5723])).
% 5.04/5.27 tff(29797,plain,
% 5.04/5.27 (~r(s(s(z)), elem!1)),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[443, 29796, 106])).
% 5.04/5.27 tff(29798,plain,
% 5.04/5.27 (~r(elem!1, s(s(z)))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[1047, 29781, 744])).
% 5.04/5.27 tff(29799,plain,
% 5.04/5.27 (~(elem!1 = s(s(z)))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[311, 29787])).
% 5.04/5.27 tff(29800,plain,
% 5.04/5.27 (b(elem!1, s(s(z)))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[467, 29799, 29798])).
% 5.04/5.27 tff(29801,plain,
% 5.04/5.27 (~b(s(s(z)), elem!1)),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[13518, 29796, 194, 307, 469, 29800])).
% 5.04/5.27 tff(29802,plain,
% 5.04/5.27 ($false),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[448, 29801, 29797, 29787])).
% 5.04/5.27 tff(29803,plain,((~b(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (elem!1 = s(s(s(s(z))))) | (~r(s(s(z)), z)) | b(elem!1, z) | r(elem!1, s(elem!1)) | r(s(elem!1), s(s(z))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.27 tff(29804,plain,
% 5.04/5.27 (r(elem!1, s(elem!1))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[29803, 5723, 28500, 273, 194, 855, 469, 28539, 1069, 29547])).
% 5.04/5.27 tff(29805,plain,
% 5.04/5.27 ($false),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[2711, 29804, 10801, 844])).
% 5.04/5.27 tff(29806,plain,(b(elem!1, z) | (~r(s(elem!1), z)) | (~b(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~b(z, s(elem!1))) | (elem!1 = s(s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 5.04/5.27 tff(29807,plain,
% 5.04/5.27 (b(elem!1, z)),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[29806, 29772, 273, 3244, 29765, 29762, 29771, 2809])).
% 5.04/5.27 tff(29808,plain,
% 5.04/5.27 (~b(elem!1, s(s(s(s(z)))))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[12658, 29807, 27212, 29768, 29765])).
% 5.04/5.27 tff(29809,plain,
% 5.04/5.27 (r(elem!1, s(s(s(s(z)))))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[483, 29808, 29762])).
% 5.04/5.27 tff(29810,plain,
% 5.04/5.27 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[25883, 29809])).
% 5.04/5.27 tff(29811,plain,
% 5.04/5.27 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[691, 29810, 29761])).
% 5.04/5.27 tff(29812,plain,
% 5.04/5.27 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.27 inference(modus_ponens,[status(thm)],[29811, 29760])).
% 5.04/5.27 tff(29813,plain,
% 5.04/5.27 (b(z, elem!1) <=> b(z, s(z))),
% 5.04/5.27 inference(monotonicity,[status(thm)],[29759])).
% 5.04/5.27 tff(29814,plain,
% 5.04/5.27 (~(s(s(s(s(z)))) = elem!1)),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[504, 29762])).
% 5.04/5.27 tff(29815,plain,
% 5.04/5.27 (~r(z, elem!1)),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[29646, 29814, 273, 12, 3244])).
% 5.04/5.27 tff(29816,plain,
% 5.04/5.27 (b(z, elem!1)),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[585, 29815, 507])).
% 5.04/5.28 tff(29817,plain,
% 5.04/5.28 (b(z, s(z))),
% 5.04/5.28 inference(modus_ponens,[status(thm)],[29816, 29813])).
% 5.04/5.28 tff(29818,plain,
% 5.04/5.28 (~(s(z) = s(s(z)))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[2610, 29757, 12])).
% 5.04/5.28 tff(29819,plain,
% 5.04/5.28 (b(s(z), z)),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[593, 29807, 29757])).
% 5.04/5.28 tff(29820,plain,
% 5.04/5.28 (~r(s(z), s(s(z)))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[2651, 29819, 29530, 107, 29757, 29817])).
% 5.04/5.28 tff(29821,plain,
% 5.04/5.28 (b(s(z), s(s(z)))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[2657, 29820, 29818])).
% 5.04/5.28 tff(29822,plain,
% 5.04/5.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 5.04/5.28 inference(rewrite,[status(thm)],[])).
% 5.04/5.28 tff(29823,plain,
% 5.04/5.28 (((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z)))) <=> ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 5.04/5.28 inference(rewrite,[status(thm)],[])).
% 5.04/5.28 tff(29824,plain,
% 5.04/5.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 5.04/5.28 inference(monotonicity,[status(thm)],[29823])).
% 5.04/5.28 tff(29825,plain,
% 5.04/5.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 5.04/5.28 inference(transitivity,[status(thm)],[29824, 29822])).
% 5.04/5.28 tff(29826,plain,
% 5.04/5.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))),
% 5.04/5.28 inference(quant_inst,[status(thm)],[])).
% 5.04/5.28 tff(29827,plain,
% 5.04/5.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 5.04/5.28 inference(modus_ponens,[status(thm)],[29826, 29825])).
% 5.04/5.28 tff(29828,plain,
% 5.04/5.28 ($false),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[29827, 178, 273, 29821, 166, 29817, 29812])).
% 5.04/5.28 tff(29829,plain,((s(s(z)) = elem!1) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (z = elem!1) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 5.04/5.28 tff(29830,plain,
% 5.04/5.28 (s(s(z)) = elem!1),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[29829, 29682, 144, 15765, 29528, 507, 3170])).
% 5.04/5.28 tff(29831,plain,
% 5.04/5.28 (s(s(s(z))) = s(elem!1)),
% 5.04/5.28 inference(monotonicity,[status(thm)],[29830])).
% 5.04/5.28 tff(29832,plain,
% 5.04/5.28 ((elem!1 = s(s(s(z)))) <=> (elem!1 = s(elem!1))),
% 5.04/5.28 inference(monotonicity,[status(thm)],[29831])).
% 5.04/5.28 tff(29833,plain,
% 5.04/5.28 ((elem!1 = s(s(s(z)))) <=> (s(elem!1) = elem!1)),
% 5.04/5.28 inference(transitivity,[status(thm)],[29832, 3190])).
% 5.04/5.28 tff(29834,plain,
% 5.04/5.28 ((~(elem!1 = s(s(s(z))))) <=> (~(s(elem!1) = elem!1))),
% 5.04/5.28 inference(monotonicity,[status(thm)],[29833])).
% 5.04/5.28 tff(29835,plain,
% 5.04/5.28 ((s(s(z)) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 5.04/5.28 inference(monotonicity,[status(thm)],[29830])).
% 5.04/5.28 tff(29836,plain,
% 5.04/5.28 ((~(s(s(z)) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 5.04/5.28 inference(monotonicity,[status(thm)],[29835])).
% 5.04/5.28 tff(29837,plain,
% 5.04/5.28 (~(elem!1 = s(s(s(z))))),
% 5.04/5.28 inference(modus_ponens,[status(thm)],[3205, 29836])).
% 5.04/5.28 tff(29838,plain,
% 5.04/5.28 (~(s(elem!1) = elem!1)),
% 5.04/5.28 inference(modus_ponens,[status(thm)],[29837, 29834])).
% 5.04/5.28 tff(29839,plain,
% 5.04/5.28 (r(elem!1, z)),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[1345, 29830, 28500])).
% 5.04/5.28 tff(29840,plain,
% 5.04/5.28 (s(s(s(s(z)))) = s(s(elem!1))),
% 5.04/5.28 inference(monotonicity,[status(thm)],[29831])).
% 5.04/5.28 tff(29841,plain,
% 5.04/5.28 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 5.04/5.28 inference(monotonicity,[status(thm)],[29840])).
% 5.04/5.28 tff(29842,plain,
% 5.04/5.28 (b(s(s(s(s(z)))), elem!1)),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[8526, 29830, 29528])).
% 5.04/5.28 tff(29843,plain,
% 5.04/5.28 (b(s(s(elem!1)), elem!1)),
% 5.04/5.28 inference(modus_ponens,[status(thm)],[29842, 29841])).
% 5.04/5.28 tff(29844,plain,
% 5.04/5.28 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[8168, 118, 29583, 8113])).
% 5.04/5.28 tff(29845,plain,
% 5.04/5.28 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[395, 29844, 8112])).
% 5.04/5.28 tff(29846,plain,
% 5.04/5.28 (~b(s(s(s(z))), s(s(z)))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[21357, 29576, 27212, 273, 29547])).
% 5.04/5.28 tff(29847,plain,
% 5.04/5.28 (r(s(s(s(z))), s(s(z)))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[4966, 29846])).
% 5.04/5.28 tff(29848,plain,
% 5.04/5.28 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[8218, 29847, 107])).
% 5.04/5.28 tff(29849,plain,
% 5.04/5.28 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[20667, 29848])).
% 5.04/5.28 tff(29850,plain,
% 5.04/5.28 (~b(z, s(s(s(z))))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[29752, 29849, 273, 166, 29576, 27531, 107])).
% 5.04/5.28 tff(29851,plain,
% 5.04/5.28 (r(z, s(s(s(z))))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[4920, 29850])).
% 5.04/5.28 tff(29852,plain,
% 5.04/5.28 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[4961, 29851, 194])).
% 5.04/5.28 tff(29853,plain,
% 5.04/5.28 (b(s(s(s(s(z)))), s(s(s(z))))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[11185, 29852])).
% 5.04/5.28 tff(29854,plain,
% 5.04/5.28 (b(s(s(elem!1)), s(elem!1))),
% 5.04/5.28 inference(modus_ponens,[status(thm)],[29853, 9112])).
% 5.04/5.28 tff(29855,plain,
% 5.04/5.28 (r(z, s(s(s(z)))) <=> r(z, s(elem!1))),
% 5.04/5.28 inference(monotonicity,[status(thm)],[3505])).
% 5.04/5.28 tff(29856,plain,
% 5.04/5.28 (r(z, s(elem!1))),
% 5.04/5.28 inference(modus_ponens,[status(thm)],[29851, 29855])).
% 5.04/5.28 tff(29857,plain,
% 5.04/5.28 (~r(elem!1, s(elem!1))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[12189, 29856, 28704])).
% 5.04/5.28 tff(29858,plain,
% 5.04/5.28 (b(elem!1, s(elem!1))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[756, 29857, 10913])).
% 5.04/5.28 tff(29859,plain,
% 5.04/5.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 5.04/5.28 inference(rewrite,[status(thm)],[])).
% 5.04/5.28 tff(29860,plain,
% 5.04/5.28 (((~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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 5.04/5.28 inference(rewrite,[status(thm)],[])).
% 5.04/5.28 tff(29861,plain,
% 5.04/5.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 5.04/5.28 inference(monotonicity,[status(thm)],[29860])).
% 5.04/5.28 tff(29862,plain,
% 5.04/5.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 5.04/5.28 inference(transitivity,[status(thm)],[29861, 29859])).
% 5.04/5.28 tff(29863,plain,
% 5.04/5.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 5.04/5.28 inference(quant_inst,[status(thm)],[])).
% 5.04/5.28 tff(29864,plain,
% 5.04/5.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 5.04/5.28 inference(modus_ponens,[status(thm)],[29863, 29862])).
% 5.04/5.28 tff(29865,plain,
% 5.04/5.28 ($false),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[29864, 178, 29858, 5434, 29854, 27701, 29845])).
% 5.04/5.28 tff(29866,plain,((~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)) | (~(s(s(z)) = elem!1)) | (~r(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.28 tff(29867,plain,
% 5.04/5.28 (~b(s(elem!1), z)),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[29866, 29843, 29830, 3244, 144, 29682, 15765])).
% 5.04/5.28 tff(29868,plain,
% 5.04/5.28 (r(s(elem!1), z)),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[774, 29867])).
% 5.04/5.28 tff(29869,plain,
% 5.04/5.28 (~r(elem!1, s(elem!1))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[2711, 29868, 29839])).
% 5.04/5.28 tff(29870,plain,
% 5.04/5.28 (b(s(s(z)), s(elem!1))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[1337, 29869, 29830, 29838])).
% 5.04/5.28 tff(29871,plain,
% 5.04/5.28 ((s(elem!1) = s(s(z))) <=> (s(elem!1) = elem!1)),
% 5.04/5.28 inference(monotonicity,[status(thm)],[29830])).
% 5.04/5.28 tff(29872,plain,
% 5.04/5.28 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(z)))),
% 5.04/5.28 inference(symmetry,[status(thm)],[29871])).
% 5.04/5.28 tff(29873,plain,
% 5.04/5.28 ((elem!1 = s(s(s(z)))) <=> (s(elem!1) = s(s(z)))),
% 5.04/5.28 inference(transitivity,[status(thm)],[29833, 29872])).
% 5.04/5.28 tff(29874,plain,
% 5.04/5.28 ((~(elem!1 = s(s(s(z))))) <=> (~(s(elem!1) = s(s(z))))),
% 5.04/5.28 inference(monotonicity,[status(thm)],[29873])).
% 5.04/5.28 tff(29875,plain,
% 5.04/5.28 (~(s(elem!1) = s(s(z)))),
% 5.04/5.28 inference(modus_ponens,[status(thm)],[29837, 29874])).
% 5.04/5.28 tff(29876,plain,
% 5.04/5.28 (~r(s(elem!1), s(s(z)))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[2258, 29868, 28500])).
% 5.04/5.28 tff(29877,plain,
% 5.04/5.28 (b(s(elem!1), s(s(z)))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[421, 29876, 29875])).
% 5.04/5.28 tff(29878,plain,
% 5.04/5.28 (elem!1 = s(s(z))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[3230, 29830])).
% 5.04/5.28 tff(29879,plain,
% 5.04/5.28 (~b(elem!1, s(s(z)))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[3223, 29830])).
% 5.04/5.28 tff(29880,plain,
% 5.04/5.28 (~(s(s(s(s(z)))) = elem!1)),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[4509, 29879, 29528])).
% 5.04/5.28 tff(29881,plain,
% 5.04/5.28 (~(s(elem!1) = s(s(s(s(z)))))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[1353, 29880, 29878])).
% 5.04/5.28 tff(29882,plain,
% 5.04/5.28 (~r(s(elem!1), s(s(s(s(z)))))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[916, 29868, 3244])).
% 5.04/5.28 tff(29883,plain,
% 5.04/5.28 (b(s(elem!1), s(s(s(s(z)))))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[1084, 29882, 29881])).
% 5.04/5.28 tff(29884,plain,
% 5.04/5.28 ($false),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[1079, 29883, 29877, 29528, 29532, 29870])).
% 5.04/5.28 tff(29885,plain,(b(s(s(s(s(s(s(s(z))))))), s(s(z))) | (z = elem!1) | b(s(s(s(s(z)))), z) | r(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.28 tff(29886,plain,
% 5.04/5.28 (z = elem!1),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[29885, 29535, 3170, 48])).
% 5.04/5.28 tff(29887,plain,
% 5.04/5.28 (s(z) = s(elem!1)),
% 5.04/5.28 inference(monotonicity,[status(thm)],[29886])).
% 5.04/5.28 tff(29888,plain,
% 5.04/5.28 ((s(s(s(s(s(s(s(z))))))) = s(z)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 5.04/5.28 inference(monotonicity,[status(thm)],[29887])).
% 5.04/5.28 tff(29889,plain,
% 5.04/5.28 ((s(s(s(s(s(s(s(z))))))) = s(z)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 5.04/5.28 inference(transitivity,[status(thm)],[29888, 377])).
% 5.04/5.28 tff(29890,plain,
% 5.04/5.28 ((s(s(s(s(s(s(s(z))))))) = s(z)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 5.04/5.28 inference(transitivity,[status(thm)],[29889, 655])).
% 5.04/5.28 tff(29891,plain,
% 5.04/5.28 ((~(s(s(s(s(s(s(s(z))))))) = s(z))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 5.04/5.28 inference(monotonicity,[status(thm)],[29890])).
% 5.04/5.28 tff(29892,plain,
% 5.04/5.28 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 5.04/5.28 inference(modus_ponens,[status(thm)],[612, 29891])).
% 5.04/5.28 tff(29893,plain,
% 5.04/5.28 (s(s(z)) = s(s(elem!1))),
% 5.04/5.28 inference(monotonicity,[status(thm)],[29887])).
% 5.04/5.28 tff(29894,plain,
% 5.04/5.28 (s(s(elem!1)) = s(s(z))),
% 5.04/5.28 inference(symmetry,[status(thm)],[29893])).
% 5.04/5.28 tff(29895,plain,
% 5.04/5.28 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 5.04/5.28 inference(monotonicity,[status(thm)],[29894])).
% 5.04/5.28 tff(29896,plain,
% 5.04/5.28 (r(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 5.04/5.28 inference(symmetry,[status(thm)],[29895])).
% 5.04/5.28 tff(29897,plain,
% 5.04/5.28 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[3578, 29535])).
% 5.04/5.28 tff(29898,plain,
% 5.04/5.28 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 5.04/5.28 inference(modus_ponens,[status(thm)],[29897, 29896])).
% 5.04/5.28 tff(29899,plain,
% 5.04/5.28 (s(s(z)) = s(s(elem!1))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[25813, 29894])).
% 5.04/5.28 tff(29900,plain,
% 5.04/5.28 (~(s(elem!1) = s(s(z)))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[28525, 29886])).
% 5.04/5.28 tff(29901,plain,
% 5.04/5.28 (b(s(elem!1), z) <=> b(s(elem!1), elem!1)),
% 5.04/5.28 inference(monotonicity,[status(thm)],[29886])).
% 5.04/5.28 tff(29902,plain,
% 5.04/5.28 (b(s(elem!1), elem!1) <=> b(s(elem!1), z)),
% 5.04/5.28 inference(symmetry,[status(thm)],[29901])).
% 5.04/5.28 tff(29903,plain,
% 5.04/5.28 ((s(elem!1) = z) <=> (s(elem!1) = elem!1)),
% 5.04/5.28 inference(monotonicity,[status(thm)],[29886])).
% 5.04/5.28 tff(29904,plain,
% 5.04/5.28 ((~(s(elem!1) = z)) <=> (~(s(elem!1) = elem!1))),
% 5.04/5.28 inference(monotonicity,[status(thm)],[29903])).
% 5.04/5.28 tff(29905,plain,
% 5.04/5.28 (~(s(elem!1) = elem!1)),
% 5.04/5.28 inference(modus_ponens,[status(thm)],[769, 29904])).
% 5.04/5.28 tff(29906,plain,
% 5.04/5.28 (elem!1 = z),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[317, 29886])).
% 5.04/5.28 tff(29907,plain,
% 5.04/5.28 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(z)))), elem!1)),
% 5.04/5.28 inference(monotonicity,[status(thm)],[29886])).
% 5.04/5.28 tff(29908,plain,
% 5.04/5.28 (r(s(s(s(s(z)))), elem!1)),
% 5.04/5.28 inference(modus_ponens,[status(thm)],[3244, 29907])).
% 5.04/5.28 tff(29909,plain,
% 5.04/5.28 (~r(s(elem!1), elem!1)),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[22633, 29908, 28500, 29528, 29532, 29906])).
% 5.04/5.28 tff(29910,plain,
% 5.04/5.28 (b(s(elem!1), elem!1)),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[677, 29909, 29905])).
% 5.04/5.28 tff(29911,plain,
% 5.04/5.28 (b(s(elem!1), z)),
% 5.04/5.28 inference(modus_ponens,[status(thm)],[29910, 29902])).
% 5.04/5.28 tff(29912,plain,
% 5.04/5.28 (~b(s(elem!1), s(s(z)))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[29208, 29911, 144, 29532])).
% 5.04/5.28 tff(29913,plain,
% 5.04/5.28 (r(s(elem!1), s(s(z)))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[421, 29912, 29900])).
% 5.04/5.28 tff(29914,plain,
% 5.04/5.28 (r(s(elem!1), s(s(elem!1)))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[25861, 29913, 29899])).
% 5.04/5.28 tff(29915,plain,
% 5.04/5.28 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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(s(elem!1)))))),
% 5.04/5.28 inference(rewrite,[status(thm)],[])).
% 5.04/5.28 tff(29916,plain,
% 5.04/5.28 (((~r(s(elem!1), s(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(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(s(elem!1)))))),
% 5.04/5.28 inference(rewrite,[status(thm)],[])).
% 5.04/5.28 tff(29917,plain,
% 5.04/5.28 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(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(elem!1))))))),
% 5.04/5.28 inference(monotonicity,[status(thm)],[29916])).
% 5.04/5.28 tff(29918,plain,
% 5.04/5.28 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(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(elem!1)))))),
% 5.04/5.28 inference(transitivity,[status(thm)],[29917, 29915])).
% 5.04/5.28 tff(29919,plain,
% 5.04/5.28 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 5.04/5.28 inference(quant_inst,[status(thm)],[])).
% 5.04/5.28 tff(29920,plain,
% 5.04/5.28 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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(s(elem!1))))),
% 5.04/5.28 inference(modus_ponens,[status(thm)],[29919, 29918])).
% 5.04/5.28 tff(29921,plain,
% 5.04/5.28 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[29920, 118, 29914, 29898])).
% 5.04/5.28 tff(29922,plain,
% 5.04/5.28 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[806, 41, 29921, 29892])).
% 5.04/5.28 tff(29923,plain,
% 5.04/5.28 (b(s(s(s(s(s(s(s(z))))))), z) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.04/5.28 inference(monotonicity,[status(thm)],[29886])).
% 5.04/5.28 tff(29924,plain,
% 5.04/5.28 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.04/5.28 inference(modus_ponens,[status(thm)],[29530, 29923])).
% 5.04/5.28 tff(29925,plain,
% 5.04/5.28 ((~(s(s(s(s(s(s(s(z))))))) = s(z))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 5.04/5.28 inference(monotonicity,[status(thm)],[29889])).
% 5.04/5.28 tff(29926,plain,
% 5.04/5.28 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 5.04/5.28 inference(modus_ponens,[status(thm)],[612, 29925])).
% 5.04/5.28 tff(29927,plain,
% 5.04/5.28 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 5.04/5.28 inference(rewrite,[status(thm)],[])).
% 5.04/5.28 tff(29928,plain,
% 5.04/5.28 (((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 5.04/5.28 inference(rewrite,[status(thm)],[])).
% 5.04/5.28 tff(29929,plain,
% 5.04/5.28 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 5.04/5.28 inference(monotonicity,[status(thm)],[29928])).
% 5.04/5.28 tff(29930,plain,
% 5.04/5.28 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 5.04/5.28 inference(transitivity,[status(thm)],[29929, 29927])).
% 5.04/5.28 tff(29931,plain,
% 5.04/5.28 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 5.04/5.28 inference(quant_inst,[status(thm)],[])).
% 5.04/5.28 tff(29932,plain,
% 5.04/5.28 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 5.04/5.28 inference(modus_ponens,[status(thm)],[29931, 29930])).
% 5.04/5.28 tff(29933,plain,
% 5.04/5.28 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[29932, 118, 29914, 29898])).
% 5.04/5.28 tff(29934,plain,
% 5.04/5.28 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[395, 29933, 29926])).
% 5.04/5.28 tff(29935,plain,
% 5.04/5.28 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.28 inference(monotonicity,[status(thm)],[29893])).
% 5.04/5.28 tff(29936,plain,
% 5.04/5.28 (r(s(s(z)), z) <=> r(s(s(z)), elem!1)),
% 5.04/5.28 inference(monotonicity,[status(thm)],[29886])).
% 5.04/5.28 tff(29937,plain,
% 5.04/5.28 (r(s(s(z)), elem!1)),
% 5.04/5.28 inference(modus_ponens,[status(thm)],[28500, 29936])).
% 5.04/5.28 tff(29938,plain,
% 5.04/5.28 (b(elem!1, s(s(z)))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[3276, 29906, 144])).
% 5.04/5.28 tff(29939,plain,
% 5.04/5.28 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[25284, 29938, 29535])).
% 5.04/5.28 tff(29940,plain,
% 5.04/5.28 ($false),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[27707, 178, 683, 869, 727, 3664, 19278])).
% 5.04/5.28 tff(29941,plain,((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.28 tff(29942,plain,
% 5.04/5.28 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[29941, 29910, 29934, 29924, 29922])).
% 5.04/5.28 tff(29943,plain,
% 5.04/5.28 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[691, 29942, 29939])).
% 5.04/5.28 tff(29944,plain,
% 5.04/5.28 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[2803, 29943, 29937])).
% 5.04/5.28 tff(29945,plain,
% 5.04/5.28 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[249, 29944])).
% 5.04/5.28 tff(29946,plain,
% 5.04/5.28 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.28 inference(modus_ponens,[status(thm)],[29945, 29935])).
% 5.04/5.28 tff(29947,plain,
% 5.04/5.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(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))))))))) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(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))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 5.04/5.28 inference(rewrite,[status(thm)],[])).
% 5.04/5.28 tff(29948,plain,
% 5.04/5.28 (((~b(s(s(s(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(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(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(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))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 5.04/5.28 inference(rewrite,[status(thm)],[])).
% 5.04/5.28 tff(29949,plain,
% 5.04/5.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(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(elem!1), s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(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))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 5.04/5.28 inference(monotonicity,[status(thm)],[29948])).
% 5.04/5.28 tff(29950,plain,
% 5.04/5.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(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(elem!1), s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(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))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 5.04/5.28 inference(transitivity,[status(thm)],[29949, 29947])).
% 5.04/5.28 tff(29951,plain,
% 5.04/5.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(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(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 5.04/5.28 inference(quant_inst,[status(thm)],[])).
% 5.04/5.28 tff(29952,plain,
% 5.04/5.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(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))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 5.04/5.28 inference(modus_ponens,[status(thm)],[29951, 29950])).
% 5.04/5.28 tff(29953,plain,
% 5.04/5.28 (~b(s(s(elem!1)), s(elem!1))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[29952, 178, 29910, 29934, 29924, 29946])).
% 5.04/5.28 tff(29954,plain,
% 5.04/5.29 (r(s(s(z)), s(elem!1))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[14326, 29953, 29886, 29900])).
% 5.04/5.29 tff(29955,plain,
% 5.04/5.29 (~r(z, s(elem!1))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[2341, 29954, 28500])).
% 5.04/5.29 tff(29956,plain,
% 5.04/5.29 (b(z, s(elem!1))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[2351, 29955])).
% 5.04/5.29 tff(29957,plain,
% 5.04/5.29 (b(elem!1, s(elem!1))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[12054, 29956, 29906])).
% 5.04/5.29 tff(29958,plain,
% 5.04/5.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 5.04/5.29 inference(rewrite,[status(thm)],[])).
% 5.04/5.29 tff(29959,plain,
% 5.04/5.29 (((~b(elem!1, s(elem!1))) | (~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(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)))))))))) <=> ((~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(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 5.04/5.29 inference(rewrite,[status(thm)],[])).
% 5.04/5.29 tff(29960,plain,
% 5.04/5.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~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(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 5.04/5.29 inference(monotonicity,[status(thm)],[29959])).
% 5.04/5.29 tff(29961,plain,
% 5.04/5.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~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(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 5.04/5.29 inference(transitivity,[status(thm)],[29960, 29958])).
% 5.04/5.29 tff(29962,plain,
% 5.04/5.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~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(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))))))))))),
% 5.04/5.29 inference(quant_inst,[status(thm)],[])).
% 5.04/5.29 tff(29963,plain,
% 5.04/5.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 5.04/5.29 inference(modus_ponens,[status(thm)],[29962, 29961])).
% 5.04/5.29 tff(29964,plain,
% 5.04/5.29 ($false),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[29963, 178, 29910, 29957, 29934, 29924, 29922])).
% 5.04/5.29 tff(29965,plain,(b(s(s(s(s(z)))), z) | r(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.29 tff(29966,plain,
% 5.04/5.29 (b(s(s(s(s(z)))), z)),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[29965, 48])).
% 5.04/5.29 tff(29967,plain,
% 5.04/5.29 (~b(s(s(s(z))), z)),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[25128, 28449, 273, 202, 168])).
% 5.04/5.29 tff(29968,plain,
% 5.04/5.29 (r(s(s(s(z))), z)),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[21073, 29967])).
% 5.04/5.29 tff(29969,plain,
% 5.04/5.29 (~r(s(s(s(z))), s(s(z)))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[24599, 29968, 28500])).
% 5.04/5.29 tff(29970,plain,
% 5.04/5.29 (b(s(s(s(z))), s(s(z)))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[4966, 29969])).
% 5.04/5.29 tff(29971,plain,
% 5.04/5.29 ($false),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[17189, 178, 273, 166, 168, 202, 595])).
% 5.04/5.29 tff(29972,plain,((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.29 tff(29973,plain,
% 5.04/5.29 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[29972, 27396, 273, 202, 168])).
% 5.04/5.29 tff(29974,plain,
% 5.04/5.29 (r(z, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[271, 29973])).
% 5.04/5.29 tff(29975,plain,
% 5.04/5.29 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[21520, 28449, 29974, 168, 27212])).
% 5.04/5.29 tff(29976,plain,
% 5.04/5.29 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[20667, 29975])).
% 5.04/5.29 tff(29977,plain,
% 5.04/5.29 (~b(s(s(z)), s(s(s(z))))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[21439, 29970, 27396, 28447, 29976])).
% 5.04/5.29 tff(29978,plain,
% 5.04/5.29 (r(s(s(z)), s(s(s(z))))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[5088, 29977])).
% 5.04/5.29 tff(29979,plain,
% 5.04/5.29 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[24478, 29978, 147])).
% 5.04/5.29 tff(29980,plain,
% 5.04/5.29 (b(s(s(s(s(z)))), s(s(s(z))))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[11185, 29979])).
% 5.04/5.29 tff(29981,plain,
% 5.04/5.29 (~b(z, s(s(s(z))))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[24318, 29980, 27212, 202, 29970])).
% 5.04/5.29 tff(29982,plain,
% 5.04/5.29 (r(z, s(s(s(z))))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[4920, 29981])).
% 5.04/5.29 tff(29983,plain,
% 5.04/5.29 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 5.04/5.29 inference(rewrite,[status(thm)],[])).
% 5.04/5.29 tff(29984,plain,
% 5.04/5.29 (((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 5.04/5.29 inference(rewrite,[status(thm)],[])).
% 5.04/5.29 tff(29985,plain,
% 5.04/5.29 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z)))))))),
% 5.04/5.29 inference(monotonicity,[status(thm)],[29984])).
% 5.04/5.29 tff(29986,plain,
% 5.04/5.29 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 5.04/5.29 inference(transitivity,[status(thm)],[29985, 29983])).
% 5.04/5.29 tff(29987,plain,
% 5.04/5.29 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 5.04/5.29 inference(quant_inst,[status(thm)],[])).
% 5.04/5.29 tff(29988,plain,
% 5.04/5.29 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z)))))),
% 5.04/5.29 inference(modus_ponens,[status(thm)],[29987, 29986])).
% 5.04/5.29 tff(29989,plain,
% 5.04/5.29 ($false),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[29988, 118, 28500, 29978, 29982])).
% 5.04/5.29 tff(29990,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.29 tff(29991,plain,
% 5.04/5.29 (~r(s(s(z)), s(s(s(s(z)))))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[29990, 29528, 144, 29966])).
% 5.04/5.29 tff(29992,plain,
% 5.04/5.29 (b(s(s(z)), s(s(s(s(z)))))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[164, 29991])).
% 5.04/5.29 tff(29993,plain,
% 5.04/5.29 ($false),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[1736, 178, 144, 27212, 29966, 29992, 29528])).
% 5.04/5.29 tff(29994,plain,(r(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.29 tff(29995,plain,
% 5.04/5.29 (~r(s(elem!1), z)),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[2258, 23076, 28500])).
% 5.04/5.29 tff(29996,plain,
% 5.04/5.29 (b(s(elem!1), z)),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[774, 29995])).
% 5.04/5.29 tff(29997,plain,
% 5.04/5.29 (s(elem!1) = s(s(s(s(z))))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[11775, 29996, 27212, 29994, 28503, 23076, 147])).
% 5.04/5.29 tff(29998,plain,
% 5.04/5.29 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 5.04/5.29 inference(monotonicity,[status(thm)],[29997])).
% 5.04/5.29 tff(29999,plain,
% 5.04/5.29 (elem!1 = s(s(s(z)))),
% 5.04/5.29 inference(transitivity,[status(thm)],[517, 29998, 11])).
% 5.04/5.29 tff(30000,plain,
% 5.04/5.29 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.04/5.29 inference(monotonicity,[status(thm)],[29999])).
% 5.04/5.29 tff(30001,plain,
% 5.04/5.29 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[11783, 29996, 27212, 29994, 147, 28503, 305])).
% 5.04/5.29 tff(30002,plain,
% 5.04/5.29 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[703, 30001])).
% 5.04/5.29 tff(30003,plain,
% 5.04/5.29 ((s(elem!1) = elem!1) <=> (s(s(s(s(z)))) = elem!1)),
% 5.04/5.29 inference(monotonicity,[status(thm)],[29997])).
% 5.04/5.29 tff(30004,plain,
% 5.04/5.29 ((s(elem!1) = elem!1) <=> (elem!1 = s(s(s(s(z)))))),
% 5.04/5.29 inference(transitivity,[status(thm)],[30003, 501])).
% 5.04/5.29 tff(30005,plain,
% 5.04/5.29 ((~(s(elem!1) = elem!1)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 5.04/5.29 inference(monotonicity,[status(thm)],[30004])).
% 5.04/5.29 tff(30006,plain,
% 5.04/5.29 (~(s(s(s(elem!1))) = s(elem!1))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[13886, 29997])).
% 5.04/5.29 tff(30007,plain,
% 5.04/5.29 (~(elem!1 = s(s(elem!1)))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[1539, 30006])).
% 5.04/5.29 tff(30008,plain,
% 5.04/5.29 (~(s(s(elem!1)) = elem!1)),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[1546, 30007])).
% 5.04/5.29 tff(30009,plain,
% 5.04/5.29 (~(s(elem!1) = elem!1)),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[672, 30008])).
% 5.04/5.29 tff(30010,plain,
% 5.04/5.29 (~(elem!1 = s(s(s(s(z)))))),
% 5.04/5.29 inference(modus_ponens,[status(thm)],[30009, 30005])).
% 5.04/5.29 tff(30011,plain,
% 5.04/5.29 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 5.04/5.29 inference(symmetry,[status(thm)],[29998])).
% 5.04/5.29 tff(30012,plain,
% 5.04/5.29 (s(s(s(z))) = elem!1),
% 5.04/5.29 inference(transitivity,[status(thm)],[61, 30011, 304])).
% 5.04/5.29 tff(30013,plain,
% 5.04/5.29 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 5.04/5.29 inference(monotonicity,[status(thm)],[30012])).
% 5.04/5.29 tff(30014,plain,
% 5.04/5.29 ((~r(s(s(s(z))), s(s(s(s(z)))))) <=> (~r(elem!1, s(s(s(s(z))))))),
% 5.04/5.29 inference(monotonicity,[status(thm)],[30013])).
% 5.04/5.29 tff(30015,plain,
% 5.04/5.29 (~r(elem!1, s(s(s(s(z)))))),
% 5.04/5.29 inference(modus_ponens,[status(thm)],[28448, 30014])).
% 5.04/5.29 tff(30016,plain,
% 5.04/5.29 (~(z = elem!1)),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[25360, 29997])).
% 5.04/5.29 tff(30017,plain,
% 5.04/5.29 (~(elem!1 = z)),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[2808, 30016])).
% 5.04/5.29 tff(30018,plain,
% 5.04/5.29 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 5.04/5.29 inference(monotonicity,[status(thm)],[29999])).
% 5.04/5.29 tff(30019,plain,
% 5.04/5.29 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 5.04/5.29 inference(symmetry,[status(thm)],[30018])).
% 5.04/5.29 tff(30020,plain,
% 5.04/5.29 (b(elem!1, s(s(s(s(z)))))),
% 5.04/5.29 inference(modus_ponens,[status(thm)],[28449, 30019])).
% 5.04/5.29 tff(30021,plain,
% 5.04/5.29 (b(s(s(z)), elem!1)),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[23429, 30010, 27212, 28500, 29994, 147, 12, 30017])).
% 5.04/5.29 tff(30022,plain,
% 5.04/5.29 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.29 inference(monotonicity,[status(thm)],[1119])).
% 5.04/5.29 tff(30023,plain,
% 5.04/5.29 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.29 inference(symmetry,[status(thm)],[30022])).
% 5.04/5.29 tff(30024,plain,
% 5.04/5.29 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.29 inference(monotonicity,[status(thm)],[1119, 1120])).
% 5.04/5.29 tff(30025,plain,
% 5.04/5.29 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.29 inference(transitivity,[status(thm)],[30024, 30023])).
% 5.04/5.29 tff(30026,plain,
% 5.04/5.29 (~(z = elem!1)),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[25360, 1117])).
% 5.04/5.29 tff(30027,plain,
% 5.04/5.29 (~(s(s(elem!1)) = s(s(z)))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[2386, 30026])).
% 5.04/5.29 tff(30028,plain,
% 5.04/5.29 (~(elem!1 = s(s(s(elem!1))))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[2498, 30027, 1117])).
% 5.04/5.29 tff(30029,plain,
% 5.04/5.29 (b(elem!1, s(s(z)))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[467, 29536, 462])).
% 5.04/5.29 tff(30030,plain,
% 5.04/5.29 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.29 inference(monotonicity,[status(thm)],[1218])).
% 5.04/5.29 tff(30031,plain,
% 5.04/5.29 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[11859, 30029, 1146, 166, 817])).
% 5.04/5.29 tff(30032,plain,
% 5.04/5.29 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[691, 30031, 701])).
% 5.04/5.29 tff(30033,plain,
% 5.04/5.29 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.29 inference(modus_ponens,[status(thm)],[30032, 30030])).
% 5.04/5.29 tff(30034,plain,
% 5.04/5.29 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[11831, 30029, 29994, 701, 437, 817])).
% 5.04/5.29 tff(30035,plain,
% 5.04/5.29 (b(s(s(s(s(s(s(s(z))))))), z)),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[133, 30034])).
% 5.04/5.29 tff(30036,plain,
% 5.04/5.29 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[10809, 30032, 437])).
% 5.04/5.29 tff(30037,plain,
% 5.04/5.29 (b(z, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[271, 30036])).
% 5.04/5.29 tff(30038,plain,
% 5.04/5.29 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[13303, 178, 27212, 168, 30037, 30035])).
% 5.04/5.29 tff(30039,plain,
% 5.04/5.29 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[222, 30038])).
% 5.04/5.29 tff(30040,plain,
% 5.04/5.29 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[5042, 118, 30039, 30033])).
% 5.04/5.29 tff(30041,plain,
% 5.04/5.29 (~r(s(s(s(s(z)))), elem!1)),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[7220, 30040, 1117])).
% 5.04/5.29 tff(30042,plain,
% 5.04/5.29 (b(s(s(s(s(z)))), elem!1)),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[3142, 30041, 15757])).
% 5.04/5.29 tff(30043,plain,
% 5.04/5.29 (~b(z, elem!1)),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[21920, 30042, 27212, 168, 1301])).
% 5.04/5.29 tff(30044,plain,
% 5.04/5.29 (r(z, elem!1)),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[585, 30043, 30026])).
% 5.04/5.29 tff(30045,plain,
% 5.04/5.29 (~r(s(s(z)), s(s(s(elem!1))))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[4808, 557, 3261])).
% 5.04/5.29 tff(30046,plain,
% 5.04/5.29 (b(s(s(z)), s(s(s(elem!1))))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[4223, 30045])).
% 5.04/5.29 tff(30047,plain,
% 5.04/5.29 (~r(elem!1, s(s(s(elem!1))))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[3421, 557, 437])).
% 5.04/5.29 tff(30048,plain,
% 5.04/5.29 (b(elem!1, s(s(s(elem!1))))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[2054, 30047, 1586])).
% 5.04/5.29 tff(30049,plain,
% 5.04/5.29 (~r(s(s(s(elem!1))), elem!1)),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[565, 557, 521])).
% 5.04/5.29 tff(30050,plain,
% 5.04/5.29 (b(s(s(s(elem!1))), elem!1)),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[570, 30049, 6403])).
% 5.04/5.29 tff(30051,plain,
% 5.04/5.29 ($false),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[15603, 178, 30050, 817, 812, 30048, 30046])).
% 5.04/5.29 tff(30052,plain,((~r(z, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (elem!1 = s(s(s(elem!1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.29 tff(30053,plain,
% 5.04/5.29 (~r(z, s(s(s(elem!1))))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[30052, 30044, 29994, 437, 30029, 30028, 817])).
% 5.04/5.29 tff(30054,plain,
% 5.04/5.29 (b(z, s(s(s(elem!1))))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[2095, 30053])).
% 5.04/5.29 tff(30055,plain,
% 5.04/5.29 (~r(s(s(s(s(elem!1)))), z)),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[22651, 30034, 1117])).
% 5.04/5.29 tff(30056,plain,
% 5.04/5.29 (b(s(s(s(s(elem!1)))), z)),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[1716, 30055])).
% 5.04/5.29 tff(30057,plain,
% 5.04/5.29 (b(z, s(s(s(s(elem!1))))) <=> b(z, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.29 inference(monotonicity,[status(thm)],[1120])).
% 5.04/5.29 tff(30058,plain,
% 5.04/5.29 (b(z, s(s(s(s(s(s(s(z)))))))) <=> b(z, s(s(s(s(elem!1)))))),
% 5.04/5.29 inference(symmetry,[status(thm)],[30057])).
% 5.04/5.29 tff(30059,plain,
% 5.04/5.29 (b(z, s(s(s(s(elem!1)))))),
% 5.04/5.29 inference(modus_ponens,[status(thm)],[30037, 30058])).
% 5.04/5.29 tff(30060,plain,
% 5.04/5.29 (~(s(s(s(elem!1))) = elem!1)),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[2489, 30028])).
% 5.04/5.29 tff(30061,plain,
% 5.04/5.29 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[29118, 30042, 193, 817, 30029, 1146, 30038])).
% 5.04/5.29 tff(30062,plain,
% 5.04/5.29 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 5.04/5.29 inference(monotonicity,[status(thm)],[1120])).
% 5.04/5.29 tff(30063,plain,
% 5.04/5.29 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 5.04/5.29 inference(transitivity,[status(thm)],[30062, 3540])).
% 5.04/5.29 tff(30064,plain,
% 5.04/5.29 ((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))))),
% 5.04/5.29 inference(monotonicity,[status(thm)],[30063])).
% 5.04/5.29 tff(30065,plain,
% 5.04/5.29 (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 5.04/5.29 inference(modus_ponens,[status(thm)],[15769, 30064])).
% 5.04/5.29 tff(30066,plain,
% 5.04/5.29 (~r(s(s(s(elem!1))), elem!1)),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[20516, 30054, 30037, 30065, 30061, 30044])).
% 5.04/5.29 tff(30067,plain,
% 5.04/5.29 (b(s(s(s(elem!1))), elem!1)),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[570, 30066, 30060])).
% 5.04/5.29 tff(30068,plain,
% 5.04/5.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 5.04/5.29 inference(rewrite,[status(thm)],[])).
% 5.04/5.29 tff(30069,plain,
% 5.04/5.29 (((~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(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 5.04/5.29 inference(rewrite,[status(thm)],[])).
% 5.04/5.29 tff(30070,plain,
% 5.04/5.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 5.04/5.29 inference(monotonicity,[status(thm)],[30069])).
% 5.04/5.29 tff(30071,plain,
% 5.04/5.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 5.04/5.29 inference(transitivity,[status(thm)],[30070, 30068])).
% 5.04/5.29 tff(30072,plain,
% 5.04/5.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))))),
% 5.04/5.29 inference(quant_inst,[status(thm)],[])).
% 5.04/5.29 tff(30073,plain,
% 5.04/5.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 5.04/5.29 inference(modus_ponens,[status(thm)],[30072, 30071])).
% 5.04/5.29 tff(30074,plain,
% 5.04/5.29 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[30073, 178, 2043, 1597, 3771, 1687])).
% 5.04/5.29 tff(30075,plain,
% 5.04/5.29 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[3825, 41, 2857, 30074])).
% 5.04/5.29 tff(30076,plain,
% 5.04/5.29 (~b(s(s(s(elem!1))), s(s(z)))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[22222, 178, 1597, 817, 812, 2042])).
% 5.04/5.29 tff(30077,plain,
% 5.04/5.29 (r(s(s(s(elem!1))), s(s(z)))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[4209, 41, 30076, 4181])).
% 5.04/5.29 tff(30078,plain,
% 5.04/5.29 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 5.04/5.29 inference(rewrite,[status(thm)],[])).
% 5.04/5.29 tff(30079,plain,
% 5.04/5.29 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 5.04/5.29 inference(rewrite,[status(thm)],[])).
% 5.04/5.29 tff(30080,plain,
% 5.04/5.29 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 5.04/5.29 inference(monotonicity,[status(thm)],[30079])).
% 5.04/5.29 tff(30081,plain,
% 5.04/5.29 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 5.04/5.29 inference(transitivity,[status(thm)],[30080, 30078])).
% 5.04/5.29 tff(30082,plain,
% 5.04/5.29 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 5.04/5.29 inference(quant_inst,[status(thm)],[])).
% 5.04/5.29 tff(30083,plain,
% 5.04/5.29 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 5.04/5.29 inference(modus_ponens,[status(thm)],[30082, 30081])).
% 5.04/5.29 tff(30084,plain,
% 5.04/5.29 ($false),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[30083, 118, 30077, 193, 30075])).
% 5.04/5.29 tff(30085,plain,((~b(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.29 tff(30086,plain,
% 5.04/5.29 (~b(elem!1, s(s(s(elem!1))))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[30085, 30067, 27212, 193, 817, 30042, 2857, 30029, 30054])).
% 5.04/5.29 tff(30087,plain,
% 5.04/5.29 (r(elem!1, s(s(s(elem!1))))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[2054, 30086, 30028])).
% 5.04/5.29 tff(30088,plain,
% 5.04/5.29 (~r(s(s(s(elem!1))), z)),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[6071, 30087, 437])).
% 5.04/5.29 tff(30089,plain,
% 5.04/5.29 (b(s(s(s(elem!1))), z)),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[1565, 30088])).
% 5.04/5.29 tff(30090,plain,
% 5.04/5.29 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[12328, 30089, 30059, 30056, 30054])).
% 5.04/5.29 tff(30091,plain,
% 5.04/5.29 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[1750, 30090, 15770])).
% 5.04/5.29 tff(30092,plain,
% 5.04/5.29 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.29 inference(modus_ponens,[status(thm)],[30091, 30025])).
% 5.04/5.29 tff(30093,plain,
% 5.04/5.29 (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[3623, 30087, 30032])).
% 5.04/5.29 tff(30094,plain,
% 5.04/5.29 ($false),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[30093, 30092])).
% 5.04/5.29 tff(30095,plain,((~r(elem!1, z)) | (~(s(elem!1) = s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.29 tff(30096,plain,
% 5.04/5.29 (~r(elem!1, z)),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[30095, 29997, 193, 30021, 13192, 28447, 28503, 30020, 30001, 27396, 312])).
% 5.04/5.29 tff(30097,plain,
% 5.04/5.29 (b(elem!1, z)),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[498, 30096, 30017])).
% 5.04/5.29 tff(30098,plain,
% 5.04/5.29 (r(s(s(s(s(z)))), elem!1)),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[28853, 30097, 28503, 30015, 30010])).
% 5.04/5.29 tff(30099,plain,
% 5.04/5.29 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[25879, 30098])).
% 5.04/5.29 tff(30100,plain,
% 5.04/5.29 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[3444, 30099, 30002])).
% 5.04/5.29 tff(30101,plain,
% 5.04/5.29 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.04/5.29 inference(modus_ponens,[status(thm)],[30100, 30000])).
% 5.04/5.29 tff(30102,plain,
% 5.04/5.29 (r(z, elem!1) <=> r(z, s(s(s(z))))),
% 5.04/5.29 inference(monotonicity,[status(thm)],[29999])).
% 5.04/5.29 tff(30103,plain,
% 5.04/5.29 (~r(z, s(elem!1))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[11762, 23076, 29994])).
% 5.04/5.29 tff(30104,plain,
% 5.04/5.29 (b(z, s(elem!1))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[2351, 30103])).
% 5.04/5.29 tff(30105,plain,
% 5.04/5.29 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(s(z)))))),
% 5.04/5.29 inference(monotonicity,[status(thm)],[29997])).
% 5.04/5.29 tff(30106,plain,
% 5.04/5.29 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(elem!1))),
% 5.04/5.29 inference(symmetry,[status(thm)],[30105])).
% 5.04/5.29 tff(30107,plain,
% 5.04/5.29 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(elem!1, s(elem!1))),
% 5.04/5.29 inference(transitivity,[status(thm)],[30019, 30106])).
% 5.04/5.29 tff(30108,plain,
% 5.04/5.29 (b(elem!1, s(elem!1))),
% 5.04/5.29 inference(modus_ponens,[status(thm)],[28449, 30107])).
% 5.04/5.29 tff(30109,plain,
% 5.04/5.29 (~b(z, elem!1)),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[863, 30097, 29996, 30108, 30104])).
% 5.04/5.29 tff(30110,plain,
% 5.04/5.29 (r(z, elem!1)),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[585, 30109, 30016])).
% 5.04/5.29 tff(30111,plain,
% 5.04/5.29 (r(z, s(s(s(z))))),
% 5.04/5.29 inference(modus_ponens,[status(thm)],[30110, 30102])).
% 5.04/5.29 tff(30112,plain,
% 5.04/5.29 (~r(s(s(s(z))), s(s(z)))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[24302, 30111, 29994])).
% 5.04/5.29 tff(30113,plain,
% 5.04/5.29 (b(s(s(s(z))), s(s(z)))),
% 5.04/5.29 inference(unit_resolution,[status(thm)],[4966, 30112])).
% 5.04/5.29 tff(30114,plain,
% 5.04/5.29 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(z))))),
% 5.04/5.29 inference(monotonicity,[status(thm)],[29999])).
% 5.04/5.29 tff(30115,plain,
% 5.04/5.29 (b(s(s(z)), s(s(s(z))))),
% 5.04/5.29 inference(modus_ponens,[status(thm)],[30021, 30114])).
% 5.04/5.29 tff(30116,plain,
% 5.04/5.29 ($false),
% 5.04/5.30 inference(unit_resolution,[status(thm)],[15371, 178, 27396, 30115, 30113, 28447, 30101])).
% 5.04/5.30 tff(30117,plain,(b(s(elem!1), s(s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (s(s(z)) = elem!1) | (s(elem!1) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.30 tff(30118,plain,
% 5.04/5.30 (b(s(elem!1), s(s(z)))),
% 5.04/5.30 inference(unit_resolution,[status(thm)],[30117, 103, 10794, 12, 1056])).
% 5.04/5.30 tff(30119,plain,
% 5.04/5.30 (~(s(elem!1) = s(s(s(s(z)))))),
% 5.04/5.30 inference(unit_resolution,[status(thm)],[12552, 30118, 86])).
% 5.04/5.30 tff(30120,plain,
% 5.04/5.30 (~(s(s(s(s(z)))) = s(elem!1))),
% 5.04/5.30 inference(unit_resolution,[status(thm)],[2168, 30119])).
% 5.04/5.30 tff(30121,plain,
% 5.04/5.30 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 5.04/5.30 inference(unit_resolution,[status(thm)],[11839, 118, 24592, 10794])).
% 5.04/5.30 tff(30122,plain,
% 5.04/5.30 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 5.04/5.30 inference(unit_resolution,[status(thm)],[3578, 30121])).
% 5.04/5.30 tff(30123,plain,
% 5.04/5.30 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 5.04/5.30 inference(unit_resolution,[status(thm)],[27243, 30122, 10794])).
% 5.04/5.30 tff(30124,plain,
% 5.04/5.30 (b(s(s(s(z))), s(s(s(s(z)))))),
% 5.04/5.30 inference(unit_resolution,[status(thm)],[10755, 30123])).
% 5.04/5.30 tff(30125,plain,
% 5.04/5.30 (~r(s(s(s(s(z)))), z)),
% 5.04/5.30 inference(unit_resolution,[status(thm)],[21308, 10794, 28500])).
% 5.04/5.30 tff(30126,plain,
% 5.04/5.30 (b(s(s(s(s(z)))), z)),
% 5.04/5.30 inference(unit_resolution,[status(thm)],[191, 30125])).
% 5.04/5.30 tff(30127,plain,
% 5.04/5.30 (~r(s(s(s(z))), z)),
% 5.04/5.30 inference(unit_resolution,[status(thm)],[24599, 1125, 28500])).
% 5.04/5.30 tff(30128,plain,
% 5.04/5.30 (b(s(s(s(z))), z)),
% 5.04/5.30 inference(unit_resolution,[status(thm)],[21073, 30127])).
% 5.04/5.30 tff(30129,plain,
% 5.04/5.30 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 5.04/5.30 inference(unit_resolution,[status(thm)],[27254, 30128])).
% 5.04/5.30 tff(30130,plain,
% 5.04/5.30 (r(s(s(s(s(z)))), s(s(s(z))))),
% 5.04/5.30 inference(unit_resolution,[status(thm)],[11185, 30129])).
% 5.04/5.30 tff(30131,plain,
% 5.04/5.30 ($false),
% 5.04/5.30 inference(unit_resolution,[status(thm)],[8696, 118, 193, 30130, 1125])).
% 5.04/5.30 tff(30132,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.30 tff(30133,plain,
% 5.04/5.30 (~r(s(s(s(z))), s(s(z)))),
% 5.04/5.30 inference(unit_resolution,[status(thm)],[30132, 103, 30126, 30124])).
% 5.04/5.30 tff(30134,plain,
% 5.04/5.30 (b(s(s(s(z))), s(s(z)))),
% 5.04/5.30 inference(unit_resolution,[status(thm)],[4966, 30133])).
% 5.04/5.30 tff(30135,plain,
% 5.04/5.30 ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 5.04/5.30 inference(unit_resolution,[status(thm)],[21371, 178, 27212, 28503, 28449])).
% 5.04/5.30 tff(30136,plain,
% 5.04/5.30 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 5.04/5.30 inference(unit_resolution,[status(thm)],[30135, 1127])).
% 5.04/5.30 tff(30137,plain,
% 5.04/5.30 (r(s(s(s(s(z)))), s(s(s(z))))),
% 5.04/5.30 inference(unit_resolution,[status(thm)],[11185, 30136])).
% 5.04/5.30 tff(30138,plain,
% 5.04/5.30 (~r(s(s(z)), s(s(s(z))))),
% 5.04/5.30 inference(unit_resolution,[status(thm)],[24478, 30137, 147])).
% 5.04/5.30 tff(30139,plain,
% 5.04/5.30 (b(s(s(z)), s(s(s(z))))),
% 5.04/5.30 inference(unit_resolution,[status(thm)],[5088, 30138])).
% 5.04/5.30 tff(30140,plain,
% 5.04/5.30 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.30 inference(unit_resolution,[status(thm)],[21439, 30139, 27396, 28447, 4932])).
% 5.04/5.30 tff(30141,plain,
% 5.04/5.30 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.30 inference(unit_resolution,[status(thm)],[20667, 30140])).
% 5.04/5.30 tff(30142,plain,
% 5.04/5.30 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.30 inference(unit_resolution,[status(thm)],[21520, 30141, 28449, 28503, 27212])).
% 5.04/5.30 tff(30143,plain,
% 5.04/5.30 (b(z, s(s(s(s(s(s(s(z))))))))),
% 5.04/5.30 inference(unit_resolution,[status(thm)],[271, 30142])).
% 5.04/5.30 tff(30144,plain,
% 5.04/5.30 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.30 inference(unit_resolution,[status(thm)],[21413, 1127, 27212, 204, 28503])).
% 5.04/5.30 tff(30145,plain,
% 5.04/5.30 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.30 inference(unit_resolution,[status(thm)],[20667, 30144])).
% 5.04/5.30 tff(30146,plain,
% 5.04/5.30 (~b(s(s(z)), s(s(s(z))))),
% 5.04/5.30 inference(unit_resolution,[status(thm)],[21439, 30145, 27396, 28447, 4932])).
% 5.04/5.30 tff(30147,plain,
% 5.04/5.30 ($false),
% 5.04/5.30 inference(unit_resolution,[status(thm)],[5088, 30146, 30138])).
% 5.04/5.30 tff(30148,plain,((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.30 tff(30149,plain,
% 5.04/5.30 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.30 inference(unit_resolution,[status(thm)],[30148, 1127, 147, 4932])).
% 5.04/5.30 tff(30150,plain,
% 5.04/5.30 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 5.04/5.30 inference(unit_resolution,[status(thm)],[222, 30149])).
% 5.04/5.30 tff(30151,plain,
% 5.04/5.30 ($false),
% 5.04/5.30 inference(unit_resolution,[status(thm)],[24156, 178, 27212, 30150, 30143, 28449, 1127])).
% 5.04/5.30 tff(30152,plain,((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 5.04/5.30 tff(30153,plain,
% 5.04/5.30 (~b(s(s(s(z))), z)),
% 5.04/5.30 inference(unit_resolution,[status(thm)],[30152, 30134, 10794])).
% 5.04/5.30 tff(30154,plain,
% 5.04/5.30 (r(s(s(s(z))), z)),
% 5.04/5.30 inference(unit_resolution,[status(thm)],[21073, 30153])).
% 5.04/5.30 tff(30155,plain,
% 5.04/5.30 (~r(s(s(z)), s(s(s(z))))),
% 5.04/5.30 inference(unit_resolution,[status(thm)],[21465, 118, 28500, 30154])).
% 5.04/5.30 tff(30156,plain,
% 5.04/5.30 (b(s(s(z)), s(s(s(z))))),
% 5.04/5.30 inference(unit_resolution,[status(thm)],[5088, 30155])).
% 5.04/5.30 tff(30157,plain,
% 5.04/5.30 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[21439, 30156, 27224, 30122, 30134])).
% 5.14/5.30 tff(30158,plain,
% 5.14/5.30 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[20667, 30157])).
% 5.14/5.30 tff(30159,plain,
% 5.14/5.30 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[21520, 30158, 30124, 30126, 27212])).
% 5.14/5.30 tff(30160,plain,
% 5.14/5.30 (b(z, s(s(s(s(s(s(s(z))))))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[271, 30159])).
% 5.14/5.30 tff(30161,plain,
% 5.14/5.30 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[14677, 30160, 29994, 27224, 30122, 30118, 2311])).
% 5.14/5.30 tff(30162,plain,
% 5.14/5.30 (~(s(s(s(elem!1))) = s(elem!1))),
% 5.14/5.30 inference(modus_ponens,[status(thm)],[23528, 25816])).
% 5.14/5.30 tff(30163,plain,
% 5.14/5.30 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[395, 28316, 643])).
% 5.14/5.30 tff(30164,plain,
% 5.14/5.30 (~r(s(elem!1), s(s(s(s(z)))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[25119, 30163])).
% 5.14/5.30 tff(30165,plain,
% 5.14/5.30 (b(s(elem!1), s(s(s(s(z)))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[1084, 30164, 1369])).
% 5.14/5.30 tff(30166,plain,
% 5.14/5.30 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 5.14/5.30 inference(modus_ponens,[status(thm)],[30165, 25350])).
% 5.14/5.30 tff(30167,plain,
% 5.14/5.30 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[20823, 5198, 28448])).
% 5.14/5.30 tff(30168,plain,
% 5.14/5.30 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[4173, 30167, 2857])).
% 5.14/5.30 tff(30169,plain,
% 5.14/5.30 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 5.14/5.30 inference(modus_ponens,[status(thm)],[30168, 25789])).
% 5.14/5.30 tff(30170,plain,
% 5.14/5.30 (b(s(s(s(s(z)))), elem!1)),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[20730, 13, 28503])).
% 5.14/5.30 tff(30171,plain,
% 5.14/5.30 (b(s(s(s(s(elem!1)))), elem!1)),
% 5.14/5.30 inference(modus_ponens,[status(thm)],[30170, 5174])).
% 5.14/5.30 tff(30172,plain,
% 5.14/5.30 (r(s(s(s(z))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 5.14/5.30 inference(monotonicity,[status(thm)],[16])).
% 5.14/5.30 tff(30173,plain,
% 5.14/5.30 (r(s(s(s(z))), z) <=> r(s(s(s(z))), elem!1)),
% 5.14/5.30 inference(monotonicity,[status(thm)],[13])).
% 5.14/5.30 tff(30174,plain,
% 5.14/5.30 (r(s(s(s(z))), elem!1)),
% 5.14/5.30 inference(modus_ponens,[status(thm)],[16062, 30173])).
% 5.14/5.30 tff(30175,plain,
% 5.14/5.30 (r(s(s(s(elem!1))), elem!1)),
% 5.14/5.30 inference(modus_ponens,[status(thm)],[30174, 30172])).
% 5.14/5.30 tff(30176,plain,
% 5.14/5.30 (~r(s(elem!1), elem!1)),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[12991, 30175, 147, 28548, 30162])).
% 5.14/5.30 tff(30177,plain,
% 5.14/5.30 (b(s(elem!1), elem!1)),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[677, 30176, 25767])).
% 5.14/5.30 tff(30178,plain,
% 5.14/5.30 (~b(s(s(s(elem!1))), s(elem!1))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[28571, 178, 30177, 30171, 30169, 30166])).
% 5.14/5.30 tff(30179,plain,
% 5.14/5.30 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[21219, 5198, 8216])).
% 5.14/5.30 tff(30180,plain,
% 5.14/5.30 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~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))))))))))),
% 5.14/5.30 inference(rewrite,[status(thm)],[])).
% 5.14/5.30 tff(30181,plain,
% 5.14/5.30 (((~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(s(s(elem!1))), s(elem!1)))) <=> ((~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(s(s(s(s(s(s(z))))))))))),
% 5.14/5.30 inference(rewrite,[status(thm)],[])).
% 5.14/5.30 tff(30182,plain,
% 5.14/5.30 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))))),
% 5.14/5.30 inference(monotonicity,[status(thm)],[30181])).
% 5.14/5.30 tff(30183,plain,
% 5.14/5.30 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 5.14/5.30 inference(transitivity,[status(thm)],[30182, 30180])).
% 5.14/5.30 tff(30184,plain,
% 5.14/5.30 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(s(s(elem!1))), s(elem!1))))),
% 5.14/5.30 inference(quant_inst,[status(thm)],[])).
% 5.14/5.30 tff(30185,plain,
% 5.14/5.30 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 5.14/5.30 inference(modus_ponens,[status(thm)],[30184, 30183])).
% 5.14/5.30 tff(30186,plain,
% 5.14/5.30 (~r(s(s(s(elem!1))), s(elem!1))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[30185, 118, 30163, 30179])).
% 5.14/5.30 tff(30187,plain,
% 5.14/5.30 ($false),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[373, 30186, 30178, 30162])).
% 5.14/5.30 tff(30188,plain,((~(z = elem!1)) | (s(elem!1) = s(s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | b(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(s(s(z)))) | (~r(s(s(s(z))), z)) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.30 tff(30189,plain,
% 5.14/5.30 (~(z = elem!1)),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[30188, 30119, 10794, 30161, 23437, 30154, 13192, 30158])).
% 5.14/5.30 tff(30190,plain,
% 5.14/5.30 (~(elem!1 = z)),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[2808, 30189])).
% 5.14/5.30 tff(30191,plain,
% 5.14/5.30 (~r(elem!1, s(s(s(s(z)))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[5670, 450, 10794])).
% 5.14/5.30 tff(30192,plain,
% 5.14/5.30 (~r(elem!1, z)),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[8416, 450, 29994])).
% 5.14/5.30 tff(30193,plain,
% 5.14/5.30 (b(elem!1, z)),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[498, 30192, 2809])).
% 5.14/5.30 tff(30194,plain,
% 5.14/5.30 (elem!1 = s(s(s(s(z))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[28853, 28845, 30126, 30193, 30191])).
% 5.14/5.30 tff(30195,plain,
% 5.14/5.30 (s(elem!1) = s(s(s(s(s(z)))))),
% 5.14/5.30 inference(monotonicity,[status(thm)],[30194])).
% 5.14/5.30 tff(30196,plain,
% 5.14/5.30 (b(s(elem!1), z) <=> b(s(s(s(s(s(z))))), z)),
% 5.14/5.30 inference(monotonicity,[status(thm)],[30195])).
% 5.14/5.30 tff(30197,plain,
% 5.14/5.30 (elem!1 = s(s(s(s(z))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[29093, 30193, 103, 450])).
% 5.14/5.30 tff(30198,plain,
% 5.14/5.30 (s(elem!1) = s(s(s(s(s(z)))))),
% 5.14/5.30 inference(monotonicity,[status(thm)],[30197])).
% 5.14/5.30 tff(30199,plain,
% 5.14/5.30 (r(s(elem!1), z) <=> r(s(s(s(s(s(z))))), z)),
% 5.14/5.30 inference(monotonicity,[status(thm)],[30198])).
% 5.14/5.30 tff(30200,plain,
% 5.14/5.30 (r(s(s(s(s(s(z))))), z)),
% 5.14/5.30 inference(modus_ponens,[status(thm)],[12569, 30199])).
% 5.14/5.30 tff(30201,plain,
% 5.14/5.30 (~(s(elem!1) = elem!1)),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[790, 30193, 766])).
% 5.14/5.30 tff(30202,plain,
% 5.14/5.30 (~(elem!1 = s(elem!1))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[748, 30201])).
% 5.14/5.30 tff(30203,plain,
% 5.14/5.30 (~r(z, elem!1)),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[4862, 450, 29994])).
% 5.14/5.30 tff(30204,plain,
% 5.14/5.30 (b(z, elem!1)),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[585, 30203, 507])).
% 5.14/5.30 tff(30205,plain,
% 5.14/5.30 (s(s(s(s(z)))) = elem!1),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[325, 30197])).
% 5.14/5.30 tff(30206,plain,
% 5.14/5.30 (~(s(s(elem!1)) = elem!1)),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[338, 30205, 12])).
% 5.14/5.30 tff(30207,plain,
% 5.14/5.30 (~(s(s(s(elem!1))) = s(elem!1))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[348, 30206])).
% 5.14/5.30 tff(30208,plain,
% 5.14/5.30 (~b(s(s(z)), elem!1)),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[17684, 30197, 105])).
% 5.14/5.30 tff(30209,plain,
% 5.14/5.30 (r(s(s(z)), elem!1)),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[448, 30208, 12])).
% 5.14/5.30 tff(30210,plain,
% 5.14/5.30 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 5.14/5.30 inference(monotonicity,[status(thm)],[30197])).
% 5.14/5.30 tff(30211,plain,
% 5.14/5.30 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), elem!1)),
% 5.14/5.30 inference(symmetry,[status(thm)],[30210])).
% 5.14/5.30 tff(30212,plain,
% 5.14/5.30 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 5.14/5.30 inference(monotonicity,[status(thm)],[30198])).
% 5.14/5.30 tff(30213,plain,
% 5.14/5.30 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 5.14/5.30 inference(monotonicity,[status(thm)],[30212])).
% 5.14/5.30 tff(30214,plain,
% 5.14/5.30 (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)))))),
% 5.14/5.30 inference(monotonicity,[status(thm)],[30213])).
% 5.14/5.30 tff(30215,plain,
% 5.14/5.30 (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)))))),
% 5.14/5.30 inference(symmetry,[status(thm)],[30214])).
% 5.14/5.30 tff(30216,plain,
% 5.14/5.30 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), elem!1)),
% 5.14/5.30 inference(transitivity,[status(thm)],[30215, 30211])).
% 5.14/5.30 tff(30217,plain,
% 5.14/5.30 (r(s(s(s(elem!1))), elem!1)),
% 5.14/5.30 inference(modus_ponens,[status(thm)],[24592, 30216])).
% 5.14/5.30 tff(30218,plain,
% 5.14/5.30 (~r(s(elem!1), elem!1)),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[12991, 30217, 10794, 30209, 30207])).
% 5.14/5.30 tff(30219,plain,
% 5.14/5.30 (b(s(elem!1), elem!1)),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[677, 30218, 30201])).
% 5.14/5.30 tff(30220,plain,
% 5.14/5.30 (~r(s(s(z)), s(elem!1))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[27961, 30219, 29994, 30193, 30204, 30197, 30202, 10794])).
% 5.14/5.30 tff(30221,plain,
% 5.14/5.30 (b(s(s(z)), s(elem!1))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[1067, 30220, 1060])).
% 5.14/5.30 tff(30222,plain,
% 5.14/5.30 (b(s(s(z)), s(s(s(s(s(z))))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[2330, 30221, 30197])).
% 5.14/5.30 tff(30223,plain,
% 5.14/5.30 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 5.14/5.30 inference(monotonicity,[status(thm)],[30198])).
% 5.14/5.30 tff(30224,plain,
% 5.14/5.30 (b(s(s(s(s(s(z))))), s(s(z)))),
% 5.14/5.30 inference(modus_ponens,[status(thm)],[1070, 30223])).
% 5.14/5.30 tff(30225,assumption,(r(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 5.14/5.30 tff(30226,plain,
% 5.14/5.30 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[21884, 118, 30225, 16062])).
% 5.14/5.30 tff(30227,plain,
% 5.14/5.30 (~r(s(s(z)), s(s(s(z))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[21465, 118, 28500, 16062])).
% 5.14/5.30 tff(30228,plain,
% 5.14/5.30 (b(s(s(z)), s(s(s(z))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[5088, 30227])).
% 5.14/5.30 tff(30229,plain,
% 5.14/5.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 5.14/5.30 inference(rewrite,[status(thm)],[])).
% 5.14/5.30 tff(30230,plain,
% 5.14/5.30 (((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 5.14/5.30 inference(rewrite,[status(thm)],[])).
% 5.14/5.30 tff(30231,plain,
% 5.14/5.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 5.14/5.30 inference(monotonicity,[status(thm)],[30230])).
% 5.14/5.30 tff(30232,plain,
% 5.14/5.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 5.14/5.30 inference(transitivity,[status(thm)],[30231, 30229])).
% 5.14/5.30 tff(30233,plain,
% 5.14/5.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))))),
% 5.14/5.30 inference(quant_inst,[status(thm)],[])).
% 5.14/5.30 tff(30234,plain,
% 5.14/5.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 5.14/5.30 inference(modus_ponens,[status(thm)],[30233, 30232])).
% 5.14/5.30 tff(30235,plain,
% 5.14/5.30 ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[30234, 178, 1851, 1665, 4932])).
% 5.14/5.30 tff(30236,plain,
% 5.14/5.30 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[30235, 30228])).
% 5.14/5.30 tff(30237,plain,
% 5.14/5.30 ($false),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[9830, 41, 11413, 30236, 30226])).
% 5.14/5.30 tff(30238,plain,((~r(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.30 tff(30239,plain,
% 5.14/5.30 (~r(s(s(s(z))), z)),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[30238, 30224, 30222, 30134, 30200])).
% 5.14/5.30 tff(30240,plain,
% 5.14/5.30 (b(s(s(s(z))), z)),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[21073, 30239])).
% 5.14/5.30 tff(30241,plain,
% 5.14/5.30 ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[21371, 178, 27212, 30126, 30124])).
% 5.14/5.30 tff(30242,plain,
% 5.14/5.30 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[30241, 30240])).
% 5.14/5.30 tff(30243,plain,
% 5.14/5.30 (r(s(s(s(s(z)))), s(s(s(z))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[11185, 30242])).
% 5.14/5.30 tff(30244,plain,
% 5.14/5.30 (~r(s(s(z)), s(s(s(z))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[24478, 30243, 10794])).
% 5.14/5.30 tff(30245,plain,
% 5.14/5.30 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(s(s(s(z))))))), z)),
% 5.14/5.30 inference(monotonicity,[status(thm)],[30213])).
% 5.14/5.30 tff(30246,plain,
% 5.14/5.30 (~r(s(elem!1), s(s(z)))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[2258, 12569, 28500])).
% 5.14/5.30 tff(30247,plain,
% 5.14/5.30 (~r(s(s(s(elem!1))), z)),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[12937, 30221, 29994, 10794, 12569, 30246, 30193, 30204, 30209, 30205, 30219, 30207])).
% 5.14/5.30 tff(30248,plain,
% 5.14/5.30 (b(s(s(s(elem!1))), z)),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[1565, 30247])).
% 5.14/5.30 tff(30249,plain,
% 5.14/5.30 (b(s(s(s(s(s(s(s(z))))))), z)),
% 5.14/5.30 inference(modus_ponens,[status(thm)],[30248, 30245])).
% 5.14/5.30 tff(30250,plain,
% 5.14/5.30 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[24574, 30126, 10794])).
% 5.14/5.30 tff(30251,plain,
% 5.14/5.30 (r(z, s(s(z)))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[143, 28501])).
% 5.14/5.30 tff(30252,plain,
% 5.14/5.30 (r(s(s(z)), z)),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[3249, 23814])).
% 5.14/5.30 tff(30253,plain,
% 5.14/5.30 (~r(z, s(s(s(s(z)))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[4843, 3437, 4236])).
% 5.14/5.30 tff(30254,plain,
% 5.14/5.30 (b(z, s(s(s(s(z)))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[46, 30253])).
% 5.14/5.30 tff(30255,plain,
% 5.14/5.30 (~b(z, s(s(s(elem!1))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[28079, 461, 3437, 3261, 3241, 86, 30252, 290, 4235])).
% 5.14/5.30 tff(30256,plain,
% 5.14/5.30 (r(z, s(s(s(elem!1))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[2095, 30255])).
% 5.14/5.30 tff(30257,plain,
% 5.14/5.30 (r(elem!1, z)),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[498, 290, 5723])).
% 5.14/5.30 tff(30258,plain,
% 5.14/5.30 (~r(elem!1, s(s(s(elem!1))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[3421, 30257, 557])).
% 5.14/5.30 tff(30259,plain,
% 5.14/5.30 (~(elem!1 = s(s(z)))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[6641, 5618, 5723])).
% 5.14/5.30 tff(30260,plain,
% 5.14/5.30 (r(elem!1, s(s(z)))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[467, 30259, 461])).
% 5.14/5.30 tff(30261,plain,
% 5.14/5.30 (~r(elem!1, s(s(s(s(z)))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[3785, 30260, 193])).
% 5.14/5.30 tff(30262,plain,
% 5.14/5.30 (~r(s(s(s(s(z)))), elem!1)),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[10883, 30260, 193])).
% 5.14/5.30 tff(30263,plain,
% 5.14/5.30 (~r(z, s(s(z)))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[11793, 5618, 5723, 290, 461])).
% 5.14/5.30 tff(30264,plain,
% 5.14/5.30 (b(z, s(s(z)))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[143, 30263])).
% 5.14/5.30 tff(30265,plain,
% 5.14/5.30 (~(s(s(z)) = elem!1)),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[6206, 5618, 30257])).
% 5.14/5.30 tff(30266,plain,
% 5.14/5.30 (r(s(s(z)), elem!1)),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[448, 30265, 3241])).
% 5.14/5.30 tff(30267,plain,
% 5.14/5.30 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[3891, 193, 3437])).
% 5.14/5.30 tff(30268,plain,
% 5.14/5.30 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[3578, 30267])).
% 5.14/5.30 tff(30269,plain,
% 5.14/5.30 (r(s(s(z)), s(s(s(s(z)))))),
% 5.14/5.30 inference(modus_ponens,[status(thm)],[438, 13351])).
% 5.14/5.30 tff(30270,plain,
% 5.14/5.30 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[3468, 118, 1130, 30269])).
% 5.14/5.30 tff(30271,plain,
% 5.14/5.30 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[249, 30270])).
% 5.14/5.30 tff(30272,plain,
% 5.14/5.30 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[4057, 30271, 1146, 3461, 273])).
% 5.14/5.30 tff(30273,plain,
% 5.14/5.30 (r(s(s(s(s(s(s(s(z))))))), z)),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[133, 30272])).
% 5.14/5.30 tff(30274,plain,
% 5.14/5.30 (~b(s(s(s(s(z)))), z)),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[12557, 319, 5723])).
% 5.14/5.30 tff(30275,plain,
% 5.14/5.30 (r(s(s(s(s(z)))), z)),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[191, 30274])).
% 5.14/5.30 tff(30276,plain,
% 5.14/5.30 ($false),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[5581, 118, 1130, 30275, 30273])).
% 5.14/5.30 tff(30277,plain,((~(elem!1 = s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(s(s(z)), elem!1)) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 5.14/5.30 tff(30278,plain,
% 5.14/5.30 (~(elem!1 = s(s(s(s(z)))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[30277, 5619, 30268, 3437, 30264, 30266, 5723])).
% 5.14/5.30 tff(30279,plain,
% 5.14/5.30 (~r(z, s(s(s(s(z)))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[4843, 3437, 203])).
% 5.14/5.30 tff(30280,plain,
% 5.14/5.30 (b(z, s(s(s(s(z)))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[46, 30279])).
% 5.14/5.30 tff(30281,plain,
% 5.14/5.30 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[10809, 30257, 203])).
% 5.14/5.30 tff(30282,plain,
% 5.14/5.30 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[24769, 30261, 3428])).
% 5.14/5.30 tff(30283,plain,
% 5.14/5.30 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[691, 30282, 30281])).
% 5.14/5.30 tff(30284,plain,
% 5.14/5.30 (~r(s(s(z)), s(s(s(s(z)))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[27221, 224, 3437])).
% 5.14/5.30 tff(30285,plain,
% 5.14/5.30 (b(s(s(z)), s(s(s(s(z)))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[164, 30284])).
% 5.14/5.30 tff(30286,plain,
% 5.14/5.30 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[12409, 30285, 1687, 3461, 30268])).
% 5.14/5.30 tff(30287,plain,
% 5.14/5.30 (r(s(s(s(s(s(s(s(z))))))), z)),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[133, 30286])).
% 5.14/5.30 tff(30288,plain,
% 5.14/5.30 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[5130, 30287, 557])).
% 5.14/5.30 tff(30289,plain,
% 5.14/5.30 (b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[5118, 30288, 3521])).
% 5.14/5.30 tff(30290,plain,
% 5.14/5.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))))),
% 5.14/5.30 inference(rewrite,[status(thm)],[])).
% 5.14/5.30 tff(30291,plain,
% 5.14/5.30 (((~b(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))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))))),
% 5.14/5.30 inference(rewrite,[status(thm)],[])).
% 5.14/5.30 tff(30292,plain,
% 5.14/5.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z))))))))),
% 5.14/5.30 inference(monotonicity,[status(thm)],[30291])).
% 5.14/5.30 tff(30293,plain,
% 5.14/5.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))))),
% 5.14/5.30 inference(transitivity,[status(thm)],[30292, 30290])).
% 5.14/5.30 tff(30294,plain,
% 5.14/5.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)))),
% 5.14/5.31 inference(quant_inst,[status(thm)],[])).
% 5.14/5.31 tff(30295,plain,
% 5.14/5.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z))))))),
% 5.14/5.31 inference(modus_ponens,[status(thm)],[30294, 30293])).
% 5.14/5.31 tff(30296,plain,
% 5.14/5.31 (~b(z, elem!1)),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[30295, 178, 1687, 869, 1301, 14122])).
% 5.14/5.31 tff(30297,plain,
% 5.14/5.31 (r(z, elem!1)),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[585, 30296, 507])).
% 5.14/5.31 tff(30298,plain,
% 5.14/5.31 (~r(s(s(s(elem!1))), elem!1)),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[565, 30297, 557])).
% 5.14/5.31 tff(30299,plain,
% 5.14/5.31 (b(s(s(s(elem!1))), elem!1)),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[570, 30298, 949])).
% 5.14/5.31 tff(30300,plain,
% 5.14/5.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 5.14/5.31 inference(rewrite,[status(thm)],[])).
% 5.14/5.31 tff(30301,plain,
% 5.14/5.31 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), 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(s(z)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 5.14/5.31 inference(rewrite,[status(thm)],[])).
% 5.14/5.31 tff(30302,plain,
% 5.14/5.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), 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(s(z)))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 5.14/5.31 inference(monotonicity,[status(thm)],[30301])).
% 5.14/5.31 tff(30303,plain,
% 5.14/5.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), 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(s(z)))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 5.14/5.31 inference(transitivity,[status(thm)],[30302, 30300])).
% 5.14/5.31 tff(30304,plain,
% 5.14/5.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), 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(s(z)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 5.14/5.31 inference(quant_inst,[status(thm)],[])).
% 5.14/5.31 tff(30305,plain,
% 5.14/5.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 5.14/5.31 inference(modus_ponens,[status(thm)],[30304, 30303])).
% 5.14/5.31 tff(30306,plain,
% 5.14/5.31 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[30305, 178, 30299, 2042, 3771, 1301])).
% 5.14/5.31 tff(30307,plain,
% 5.14/5.31 (~b(s(s(s(s(z)))), z)),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[21653, 30285, 3461, 273, 1687])).
% 5.14/5.31 tff(30308,plain,
% 5.14/5.31 (r(s(s(s(s(z)))), z)),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[191, 30307])).
% 5.14/5.31 tff(30309,plain,
% 5.14/5.31 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[3287, 30308, 557])).
% 5.14/5.31 tff(30310,plain,
% 5.14/5.31 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[10664, 30309, 30306])).
% 5.14/5.31 tff(30311,plain,
% 5.14/5.31 ($false),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[18958, 30310, 30289, 3428])).
% 5.14/5.31 tff(30312,plain,((~r(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))))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (s(s(s(elem!1))) = elem!1) | (z = elem!1) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.31 tff(30313,plain,
% 5.14/5.31 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[30312, 4254, 3428, 557, 3461, 273, 1687, 2042, 8546, 8545, 949, 507, 869, 193])).
% 5.14/5.31 tff(30314,plain,
% 5.14/5.31 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[249, 30313])).
% 5.14/5.31 tff(30315,plain,
% 5.14/5.31 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[4057, 30314, 30268, 3461, 273])).
% 5.14/5.31 tff(30316,plain,
% 5.14/5.31 (r(s(s(s(s(s(s(s(z))))))), z)),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[133, 30315])).
% 5.14/5.31 tff(30317,plain,
% 5.14/5.31 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[24769, 5721, 3428])).
% 5.14/5.31 tff(30318,plain,
% 5.14/5.31 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[703, 30317])).
% 5.14/5.31 tff(30319,plain,
% 5.14/5.31 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[5130, 30316, 557])).
% 5.14/5.31 tff(30320,plain,
% 5.14/5.31 (b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[5118, 30319, 4254])).
% 5.14/5.31 tff(30321,plain,
% 5.14/5.31 (~r(z, elem!1)),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[17866, 30320, 869, 2042, 30318, 949, 30316, 557])).
% 5.14/5.31 tff(30322,plain,
% 5.14/5.31 (b(z, elem!1)),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[585, 30321, 507])).
% 5.14/5.31 tff(30323,plain,
% 5.14/5.31 (~b(s(s(s(s(z)))), z)),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[21920, 30322, 1687, 8545, 8546])).
% 5.14/5.31 tff(30324,plain,
% 5.14/5.31 (r(s(s(s(s(z)))), z)),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[191, 30323])).
% 5.14/5.31 tff(30325,plain,
% 5.14/5.31 ($false),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[5581, 118, 3437, 30324, 30316])).
% 5.14/5.31 tff(30326,plain,((elem!1 = s(s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (z = elem!1) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | r(s(s(s(s(z)))), elem!1) | r(elem!1, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.31 tff(30327,plain,
% 5.14/5.31 ($false),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[30326, 6401, 6403, 507, 869, 1687, 469, 557, 3461, 273, 3428, 193, 5369, 5721])).
% 5.14/5.31 tff(30328,plain,((elem!1 = s(s(s(elem!1)))) | (z = elem!1) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))) | (elem!1 = s(s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | r(s(s(s(s(z)))), elem!1) | r(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.31 tff(30329,plain,
% 5.14/5.31 (elem!1 = s(s(s(elem!1)))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[30328, 30283, 318, 30280, 30278, 557, 5619, 30264, 3428, 193, 30262, 30261, 30258])).
% 5.14/5.31 tff(30330,plain,
% 5.14/5.31 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 5.14/5.31 inference(monotonicity,[status(thm)],[30329])).
% 5.14/5.31 tff(30331,plain,
% 5.14/5.31 (b(elem!1, s(s(s(s(z)))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[483, 30278, 30261])).
% 5.14/5.31 tff(30332,plain,
% 5.14/5.31 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 5.14/5.31 inference(modus_ponens,[status(thm)],[30331, 30330])).
% 5.14/5.31 tff(30333,plain,
% 5.14/5.31 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 5.14/5.31 inference(monotonicity,[status(thm)],[30329])).
% 5.14/5.31 tff(30334,plain,
% 5.14/5.31 (~(s(s(s(s(z)))) = elem!1)),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[504, 30278])).
% 5.14/5.31 tff(30335,plain,
% 5.14/5.31 (b(s(s(s(s(z)))), elem!1)),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[3142, 30334, 30262])).
% 5.14/5.31 tff(30336,plain,
% 5.14/5.31 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 5.14/5.31 inference(modus_ponens,[status(thm)],[30335, 30333])).
% 5.14/5.31 tff(30337,plain,
% 5.14/5.31 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.31 inference(monotonicity,[status(thm)],[30329])).
% 5.14/5.31 tff(30338,plain,
% 5.14/5.31 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.31 inference(modus_ponens,[status(thm)],[30283, 30337])).
% 5.14/5.31 tff(30339,plain,
% 5.14/5.31 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[3502, 30334])).
% 5.14/5.31 tff(30340,plain,
% 5.14/5.31 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[3839, 14122, 3830, 3828, 3831])).
% 5.14/5.31 tff(30341,plain,
% 5.14/5.31 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[5118, 30340, 3521])).
% 5.14/5.31 tff(30342,plain,
% 5.14/5.31 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[12409, 27809, 1687, 3461, 28927])).
% 5.14/5.31 tff(30343,plain,
% 5.14/5.31 (r(s(s(s(s(s(s(s(z))))))), z)),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[133, 30342])).
% 5.14/5.31 tff(30344,plain,
% 5.14/5.31 ($false),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[5130, 30343, 30341, 557])).
% 5.14/5.31 tff(30345,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(elem!1))))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(s(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)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.31 tff(30346,plain,
% 5.14/5.31 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[30345, 30339, 557, 30280, 5619, 30338, 30336, 30332, 3437, 193])).
% 5.14/5.31 tff(30347,plain,
% 5.14/5.31 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[249, 30346])).
% 5.14/5.31 tff(30348,plain,
% 5.14/5.31 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[4057, 30347, 30268, 5619, 30264])).
% 5.14/5.31 tff(30349,plain,
% 5.14/5.31 (r(s(s(s(s(s(s(s(z))))))), z)),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[133, 30348])).
% 5.14/5.31 tff(30350,plain,
% 5.14/5.31 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[5130, 30349, 557])).
% 5.14/5.31 tff(30351,plain,
% 5.14/5.31 (b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[5118, 30350, 30339])).
% 5.14/5.31 tff(30352,plain,
% 5.14/5.31 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[3839, 30351, 30338, 30336, 30332])).
% 5.14/5.31 tff(30353,plain,
% 5.14/5.31 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[222, 30352])).
% 5.14/5.31 tff(30354,plain,
% 5.14/5.31 (r(elem!1, s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 5.14/5.31 inference(monotonicity,[status(thm)],[30329])).
% 5.14/5.31 tff(30355,plain,
% 5.14/5.31 (r(s(s(s(elem!1))), s(s(z)))),
% 5.14/5.31 inference(modus_ponens,[status(thm)],[30260, 30354])).
% 5.14/5.31 tff(30356,plain,
% 5.14/5.31 (~b(s(s(z)), s(s(s(s(z)))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[21653, 168, 3461, 273, 27807])).
% 5.14/5.31 tff(30357,plain,
% 5.14/5.31 (r(s(s(z)), s(s(s(s(z)))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[164, 30356])).
% 5.14/5.31 tff(30358,plain,
% 5.14/5.31 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[27221, 30357, 1130])).
% 5.14/5.31 tff(30359,plain,
% 5.14/5.31 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[249, 30358])).
% 5.14/5.31 tff(30360,plain,
% 5.14/5.31 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[4057, 30359, 28927, 3461, 273])).
% 5.14/5.31 tff(30361,plain,
% 5.14/5.31 (r(s(s(s(s(s(s(s(z))))))), z)),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[133, 30360])).
% 5.14/5.31 tff(30362,plain,
% 5.14/5.31 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[5130, 30361, 557])).
% 5.14/5.31 tff(30363,plain,
% 5.14/5.31 (b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[5118, 30362, 3521])).
% 5.14/5.31 tff(30364,plain,
% 5.14/5.31 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[3839, 30363, 3830, 3828, 3831])).
% 5.14/5.31 tff(30365,plain,
% 5.14/5.31 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[222, 30364])).
% 5.14/5.31 tff(30366,plain,
% 5.14/5.31 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[27242, 30357, 28927, 1130])).
% 5.14/5.31 tff(30367,plain,
% 5.14/5.31 (b(s(s(s(z))), s(s(s(s(z)))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[10755, 30366])).
% 5.14/5.31 tff(30368,plain,
% 5.14/5.31 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[21375, 168, 27807, 30367, 30365, 203])).
% 5.14/5.31 tff(30369,plain,
% 5.14/5.31 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[5031, 41, 30368, 10712])).
% 5.14/5.31 tff(30370,plain,
% 5.14/5.31 (~r(s(s(s(z))), s(s(z)))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[8701, 30367, 3859, 3828, 3831, 193, 8246])).
% 5.14/5.31 tff(30371,plain,
% 5.14/5.31 (b(s(s(s(z))), s(s(z)))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[4966, 30370])).
% 5.14/5.31 tff(30372,plain,
% 5.14/5.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 5.14/5.31 inference(rewrite,[status(thm)],[])).
% 5.14/5.31 tff(30373,plain,
% 5.14/5.31 (((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(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(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), 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(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 5.14/5.31 inference(rewrite,[status(thm)],[])).
% 5.14/5.31 tff(30374,plain,
% 5.14/5.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(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(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 5.14/5.31 inference(monotonicity,[status(thm)],[30373])).
% 5.14/5.31 tff(30375,plain,
% 5.14/5.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(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(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 5.14/5.31 inference(transitivity,[status(thm)],[30374, 30372])).
% 5.14/5.31 tff(30376,plain,
% 5.14/5.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(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(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 5.14/5.31 inference(quant_inst,[status(thm)],[])).
% 5.14/5.31 tff(30377,plain,
% 5.14/5.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 5.14/5.31 inference(modus_ponens,[status(thm)],[30376, 30375])).
% 5.14/5.31 tff(30378,plain,
% 5.14/5.31 ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[30377, 178, 30371, 28927, 3830])).
% 5.14/5.31 tff(30379,plain,
% 5.14/5.31 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[30378, 30369])).
% 5.14/5.31 tff(30380,plain,
% 5.14/5.31 (~b(elem!1, s(s(s(z))))),
% 5.14/5.31 inference(modus_ponens,[status(thm)],[30379, 17243])).
% 5.14/5.31 tff(30381,plain,
% 5.14/5.31 (r(elem!1, s(s(s(z))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[17275, 30380, 17241])).
% 5.14/5.31 tff(30382,plain,
% 5.14/5.31 (r(s(s(s(elem!1))), s(s(s(z))))),
% 5.14/5.31 inference(modus_ponens,[status(thm)],[30381, 17237])).
% 5.14/5.31 tff(30383,plain,
% 5.14/5.31 ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z)))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[21437, 178, 30359, 30371, 28927])).
% 5.14/5.31 tff(30384,plain,
% 5.14/5.31 (~b(s(s(z)), s(s(s(z))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[30383, 30369])).
% 5.14/5.31 tff(30385,plain,
% 5.14/5.31 (r(s(s(z)), s(s(s(z))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[5088, 30384])).
% 5.14/5.31 tff(30386,plain,
% 5.14/5.31 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 5.14/5.31 inference(rewrite,[status(thm)],[])).
% 5.14/5.31 tff(30387,plain,
% 5.14/5.31 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z))))) <=> ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 5.14/5.31 inference(rewrite,[status(thm)],[])).
% 5.14/5.31 tff(30388,plain,
% 5.14/5.31 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 5.14/5.31 inference(monotonicity,[status(thm)],[30387])).
% 5.14/5.31 tff(30389,plain,
% 5.14/5.31 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 5.14/5.31 inference(transitivity,[status(thm)],[30388, 30386])).
% 5.14/5.31 tff(30390,plain,
% 5.14/5.31 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 5.14/5.31 inference(quant_inst,[status(thm)],[])).
% 5.14/5.31 tff(30391,plain,
% 5.14/5.31 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 5.14/5.31 inference(modus_ponens,[status(thm)],[30390, 30389])).
% 5.14/5.31 tff(30392,plain,
% 5.14/5.31 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[30391, 118, 3859, 30385])).
% 5.14/5.31 tff(30393,plain,
% 5.14/5.31 ($false),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[30392, 30382])).
% 5.14/5.31 tff(30394,plain,((~b(s(s(s(s(z)))), z)) | (~(elem!1 = s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(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)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(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)))) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.31 tff(30395,plain,
% 5.14/5.31 (~b(s(s(s(s(z)))), z)),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[30394, 30329, 30355, 30338, 203, 30336, 30332, 193, 11613, 3437, 30339, 557, 5619, 30264])).
% 5.14/5.31 tff(30396,plain,
% 5.14/5.31 (r(s(s(s(s(z)))), z)),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[191, 30395])).
% 5.14/5.31 tff(30397,plain,
% 5.14/5.31 ($false),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[21331, 118, 30396, 30353, 203])).
% 5.14/5.31 tff(30398,plain,(r(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(z)))), s(s(z)))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | b(elem!1, z) | b(s(s(z)), elem!1) | b(elem!1, s(s(z))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 5.14/5.31 tff(30399,plain,
% 5.14/5.31 (r(s(s(z)), z)),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[30398, 290, 557, 193, 3428, 5723, 3241, 461, 203])).
% 5.14/5.31 tff(30400,plain,
% 5.14/5.31 (~r(elem!1, s(s(z)))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[458, 30399, 30257])).
% 5.14/5.31 tff(30401,plain,
% 5.14/5.31 (elem!1 = s(s(z))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[467, 30400, 461])).
% 5.14/5.31 tff(30402,plain,
% 5.14/5.31 (s(elem!1) = s(s(s(z)))),
% 5.14/5.31 inference(monotonicity,[status(thm)],[30401])).
% 5.14/5.31 tff(30403,plain,
% 5.14/5.31 (s(s(elem!1)) = s(s(s(s(z))))),
% 5.14/5.31 inference(monotonicity,[status(thm)],[30402])).
% 5.14/5.31 tff(30404,plain,
% 5.14/5.31 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 5.14/5.31 inference(monotonicity,[status(thm)],[30403])).
% 5.14/5.31 tff(30405,plain,
% 5.14/5.31 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 5.14/5.31 inference(symmetry,[status(thm)],[30404])).
% 5.14/5.31 tff(30406,plain,
% 5.14/5.31 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 5.14/5.31 inference(monotonicity,[status(thm)],[30405])).
% 5.14/5.31 tff(30407,plain,
% 5.14/5.31 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 5.14/5.31 inference(symmetry,[status(thm)],[30406])).
% 5.14/5.31 tff(30408,plain,
% 5.14/5.31 ((s(elem!1) = s(s(z))) <=> (s(s(s(z))) = s(s(z)))),
% 5.14/5.31 inference(monotonicity,[status(thm)],[30402])).
% 5.14/5.31 tff(30409,plain,
% 5.14/5.31 ((s(elem!1) = s(s(z))) <=> (s(s(z)) = s(s(s(z))))),
% 5.14/5.31 inference(transitivity,[status(thm)],[30408, 3003])).
% 5.14/5.31 tff(30410,plain,
% 5.14/5.31 ((s(s(z)) = s(s(s(z)))) <=> (s(elem!1) = s(s(z)))),
% 5.14/5.31 inference(symmetry,[status(thm)],[30409])).
% 5.14/5.31 tff(30411,plain,
% 5.14/5.31 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(z))))),
% 5.14/5.31 inference(monotonicity,[status(thm)],[30410])).
% 5.14/5.31 tff(30412,plain,
% 5.14/5.31 (~(s(elem!1) = s(s(z)))),
% 5.14/5.31 inference(modus_ponens,[status(thm)],[3205, 30411])).
% 5.14/5.31 tff(30413,plain,
% 5.14/5.31 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[2840, 30412])).
% 5.14/5.31 tff(30414,plain,
% 5.14/5.31 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[7917, 30413])).
% 5.14/5.31 tff(30415,plain,
% 5.14/5.31 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 5.14/5.31 inference(monotonicity,[status(thm)],[30405])).
% 5.14/5.31 tff(30416,plain,
% 5.14/5.31 ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) <=> (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 5.14/5.31 inference(monotonicity,[status(thm)],[30415])).
% 5.14/5.31 tff(30417,plain,
% 5.14/5.31 (r(s(s(s(s(s(z))))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 5.14/5.31 inference(monotonicity,[status(thm)],[30405])).
% 5.14/5.31 tff(30418,plain,
% 5.14/5.31 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(s(s(z))))), s(s(z)))),
% 5.14/5.31 inference(symmetry,[status(thm)],[30417])).
% 5.14/5.31 tff(30419,plain,
% 5.14/5.31 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(z)))),
% 5.14/5.31 inference(monotonicity,[status(thm)],[30401])).
% 5.14/5.31 tff(30420,plain,
% 5.14/5.31 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(z))))), s(s(z)))),
% 5.14/5.31 inference(transitivity,[status(thm)],[30419, 30418])).
% 5.14/5.31 tff(30421,plain,
% 5.14/5.31 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = s(s(z)))),
% 5.14/5.31 inference(monotonicity,[status(thm)],[30401])).
% 5.14/5.31 tff(30422,plain,
% 5.14/5.31 ((s(s(s(elem!1))) = elem!1) <=> (s(s(z)) = s(s(s(elem!1))))),
% 5.14/5.31 inference(transitivity,[status(thm)],[30421, 7921])).
% 5.14/5.31 tff(30423,plain,
% 5.14/5.31 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 5.14/5.31 inference(symmetry,[status(thm)],[30422])).
% 5.14/5.31 tff(30424,plain,
% 5.14/5.31 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 5.14/5.31 inference(monotonicity,[status(thm)],[30423])).
% 5.14/5.31 tff(30425,plain,
% 5.14/5.31 (~(s(s(s(elem!1))) = elem!1)),
% 5.14/5.31 inference(modus_ponens,[status(thm)],[1683, 30424])).
% 5.14/5.31 tff(30426,plain,
% 5.14/5.31 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(z)))),
% 5.14/5.31 inference(monotonicity,[status(thm)],[30401])).
% 5.14/5.31 tff(30427,plain,
% 5.14/5.31 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(elem!1))), elem!1)),
% 5.14/5.31 inference(symmetry,[status(thm)],[30426])).
% 5.14/5.31 tff(30428,plain,
% 5.14/5.31 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 5.14/5.31 inference(monotonicity,[status(thm)],[30405])).
% 5.14/5.31 tff(30429,plain,
% 5.14/5.31 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(elem!1))), elem!1)),
% 5.14/5.31 inference(transitivity,[status(thm)],[30428, 30427])).
% 5.14/5.31 tff(30430,plain,
% 5.14/5.31 ((~b(s(s(s(s(s(z))))), s(s(z)))) <=> (~b(s(s(s(elem!1))), elem!1))),
% 5.14/5.31 inference(monotonicity,[status(thm)],[30429])).
% 5.14/5.31 tff(30431,plain,
% 5.14/5.31 (b(s(s(z)), s(s(s(s(s(z)))))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 5.14/5.31 inference(monotonicity,[status(thm)],[30405])).
% 5.14/5.31 tff(30432,plain,
% 5.14/5.31 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(s(z))))))),
% 5.14/5.31 inference(symmetry,[status(thm)],[30431])).
% 5.14/5.31 tff(30433,plain,
% 5.14/5.31 (~r(s(s(z)), s(s(s(elem!1))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[1831, 30399, 557])).
% 5.14/5.31 tff(30434,plain,
% 5.14/5.31 (b(s(s(z)), s(s(s(elem!1))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[4223, 30433])).
% 5.14/5.31 tff(30435,plain,
% 5.14/5.31 (b(s(s(z)), s(s(s(s(s(z))))))),
% 5.14/5.31 inference(modus_ponens,[status(thm)],[30434, 30432])).
% 5.14/5.31 tff(30436,plain,
% 5.14/5.31 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[232, 30399, 203])).
% 5.14/5.31 tff(30437,plain,
% 5.14/5.31 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[249, 30436])).
% 5.14/5.31 tff(30438,plain,
% 5.14/5.31 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(s(z))))))),
% 5.14/5.31 inference(monotonicity,[status(thm)],[30404])).
% 5.14/5.31 tff(30439,plain,
% 5.14/5.31 (r(z, s(s(s(s(s(z))))))),
% 5.14/5.31 inference(modus_ponens,[status(thm)],[557, 30438])).
% 5.14/5.31 tff(30440,plain,
% 5.14/5.31 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[23864, 30439, 203])).
% 5.14/5.31 tff(30441,plain,
% 5.14/5.31 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 5.14/5.31 inference(monotonicity,[status(thm)],[30405])).
% 5.14/5.31 tff(30442,plain,
% 5.14/5.31 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 5.14/5.32 inference(transitivity,[status(thm)],[30441, 3539])).
% 5.14/5.32 tff(30443,plain,
% 5.14/5.32 ((s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 5.14/5.32 inference(symmetry,[status(thm)],[30442])).
% 5.14/5.32 tff(30444,plain,
% 5.14/5.32 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))) <=> (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))))),
% 5.14/5.32 inference(monotonicity,[status(thm)],[30443])).
% 5.14/5.32 tff(30445,plain,
% 5.14/5.32 (~r(s(s(s(s(z)))), z)),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[199, 30399, 193])).
% 5.14/5.32 tff(30446,plain,
% 5.14/5.32 (b(s(s(s(s(z)))), z)),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[191, 30445])).
% 5.14/5.32 tff(30447,plain,
% 5.14/5.32 (~(elem!1 = s(s(s(s(z)))))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[12557, 30446, 5723])).
% 5.14/5.32 tff(30448,plain,
% 5.14/5.32 (~(s(s(s(s(z)))) = elem!1)),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[504, 30447])).
% 5.14/5.32 tff(30449,plain,
% 5.14/5.32 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[3502, 30448])).
% 5.14/5.32 tff(30450,plain,
% 5.14/5.32 (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 5.14/5.32 inference(modus_ponens,[status(thm)],[30449, 30444])).
% 5.14/5.32 tff(30451,plain,
% 5.14/5.32 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[18760, 41, 30450, 30440])).
% 5.14/5.32 tff(30452,plain,
% 5.14/5.32 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[14448, 30451, 30268, 30437, 30435])).
% 5.14/5.32 tff(30453,plain,
% 5.14/5.32 (~b(s(s(s(elem!1))), elem!1)),
% 5.14/5.32 inference(modus_ponens,[status(thm)],[30452, 30430])).
% 5.14/5.32 tff(30454,plain,
% 5.14/5.32 (r(s(s(s(elem!1))), elem!1)),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[570, 30453, 30425])).
% 5.14/5.32 tff(30455,plain,
% 5.14/5.32 (r(s(s(s(s(s(z))))), s(s(z)))),
% 5.14/5.32 inference(modus_ponens,[status(thm)],[30454, 30420])).
% 5.14/5.32 tff(30456,plain,
% 5.14/5.32 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[15635, 118, 193, 30455])).
% 5.14/5.32 tff(30457,plain,
% 5.14/5.32 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 5.14/5.32 inference(modus_ponens,[status(thm)],[30456, 30416])).
% 5.14/5.32 tff(30458,plain,
% 5.14/5.32 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[10664, 30457, 30414])).
% 5.14/5.32 tff(30459,plain,
% 5.14/5.32 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 5.14/5.32 inference(modus_ponens,[status(thm)],[30458, 30407])).
% 5.14/5.32 tff(30460,plain,
% 5.14/5.32 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 5.14/5.32 inference(monotonicity,[status(thm)],[30405])).
% 5.14/5.32 tff(30461,plain,
% 5.14/5.32 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 5.14/5.32 inference(symmetry,[status(thm)],[30460])).
% 5.14/5.32 tff(30462,plain,
% 5.14/5.32 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 5.14/5.32 inference(monotonicity,[status(thm)],[30403])).
% 5.14/5.32 tff(30463,plain,
% 5.14/5.32 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 5.14/5.32 inference(transitivity,[status(thm)],[30462, 30461])).
% 5.14/5.32 tff(30464,plain,
% 5.14/5.32 (s(s(s(z))) = s(elem!1)),
% 5.14/5.32 inference(symmetry,[status(thm)],[30402])).
% 5.14/5.32 tff(30465,plain,
% 5.14/5.32 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 5.14/5.32 inference(monotonicity,[status(thm)],[30464])).
% 5.14/5.32 tff(30466,plain,
% 5.14/5.32 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 5.14/5.32 inference(transitivity,[status(thm)],[30465, 3881])).
% 5.14/5.32 tff(30467,plain,
% 5.14/5.32 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 5.14/5.32 inference(monotonicity,[status(thm)],[30466])).
% 5.14/5.32 tff(30468,plain,
% 5.14/5.32 (~(s(s(s(elem!1))) = s(elem!1))),
% 5.14/5.32 inference(modus_ponens,[status(thm)],[11613, 30467])).
% 5.14/5.32 tff(30469,plain,
% 5.14/5.32 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[1649, 30468])).
% 5.14/5.32 tff(30470,plain,
% 5.14/5.32 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[3404, 30469])).
% 5.14/5.32 tff(30471,plain,
% 5.14/5.32 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(s(z)))),
% 5.14/5.32 inference(monotonicity,[status(thm)],[30401])).
% 5.14/5.32 tff(30472,plain,
% 5.14/5.32 (r(s(s(elem!1)), s(s(z))) <=> r(s(s(elem!1)), elem!1)),
% 5.14/5.32 inference(symmetry,[status(thm)],[30471])).
% 5.14/5.32 tff(30473,plain,
% 5.14/5.32 (r(s(s(elem!1)), s(s(z))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 5.14/5.32 inference(monotonicity,[status(thm)],[30403])).
% 5.14/5.32 tff(30474,plain,
% 5.14/5.32 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(elem!1)), s(s(z)))),
% 5.14/5.32 inference(symmetry,[status(thm)],[30473])).
% 5.14/5.32 tff(30475,plain,
% 5.14/5.32 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(elem!1)), elem!1)),
% 5.14/5.32 inference(transitivity,[status(thm)],[30474, 30472])).
% 5.14/5.32 tff(30476,plain,
% 5.14/5.32 (r(s(s(elem!1)), elem!1)),
% 5.14/5.32 inference(modus_ponens,[status(thm)],[193, 30475])).
% 5.14/5.32 tff(30477,plain,
% 5.14/5.32 ($false),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[23705, 118, 556, 3365, 5227])).
% 5.14/5.32 tff(30478,plain,((~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))))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.32 tff(30479,plain,
% 5.14/5.32 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[30478, 30454, 30476])).
% 5.14/5.32 tff(30480,plain,
% 5.14/5.32 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[3409, 30479, 30470])).
% 5.14/5.32 tff(30481,plain,
% 5.14/5.32 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 5.14/5.32 inference(modus_ponens,[status(thm)],[30480, 30463])).
% 5.14/5.32 tff(30482,plain,
% 5.14/5.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 5.14/5.32 inference(rewrite,[status(thm)],[])).
% 5.14/5.32 tff(30483,plain,
% 5.14/5.32 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 5.14/5.32 inference(rewrite,[status(thm)],[])).
% 5.14/5.32 tff(30484,plain,
% 5.14/5.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z))))))))),
% 5.14/5.32 inference(monotonicity,[status(thm)],[30483])).
% 5.14/5.32 tff(30485,plain,
% 5.14/5.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 5.14/5.32 inference(transitivity,[status(thm)],[30484, 30482])).
% 5.14/5.32 tff(30486,plain,
% 5.14/5.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 5.14/5.32 inference(quant_inst,[status(thm)],[])).
% 5.14/5.32 tff(30487,plain,
% 5.14/5.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z))))))),
% 5.14/5.32 inference(modus_ponens,[status(thm)],[30486, 30485])).
% 5.14/5.32 tff(30488,plain,
% 5.14/5.32 ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[30487, 178, 30280, 30446, 30481])).
% 5.14/5.32 tff(30489,plain,
% 5.14/5.32 (~b(s(s(s(s(s(z))))), z)),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[30488, 30459])).
% 5.14/5.32 tff(30490,plain,
% 5.14/5.32 (r(s(s(s(s(s(z))))), z)),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[410, 41, 242, 30489])).
% 5.14/5.32 tff(30491,plain,
% 5.14/5.32 ($false),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[414, 118, 30399, 30455, 30490])).
% 5.14/5.32 tff(30492,plain,((elem!1 = z) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(elem!1))))) | b(elem!1, z) | b(elem!1, s(s(z))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 5.14/5.32 tff(30493,plain,
% 5.14/5.32 (b(elem!1, z)),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[30492, 30256, 4236, 290, 103, 461, 3428, 3241])).
% 5.14/5.32 tff(30494,plain,
% 5.14/5.32 (~(elem!1 = s(s(z)))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[23817, 30493, 23814])).
% 5.14/5.32 tff(30495,plain,
% 5.14/5.32 (r(elem!1, s(s(z)))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[467, 30494, 461])).
% 5.14/5.32 tff(30496,plain,
% 5.14/5.32 (~r(elem!1, z)),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[8416, 30495, 3261])).
% 5.14/5.32 tff(30497,plain,
% 5.14/5.32 (elem!1 = s(s(s(s(z))))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[28005, 30496, 30254, 103, 30252, 461, 3241, 290])).
% 5.14/5.32 tff(30498,plain,
% 5.14/5.32 (s(elem!1) = s(s(s(s(s(z)))))),
% 5.14/5.32 inference(monotonicity,[status(thm)],[30497])).
% 5.14/5.32 tff(30499,plain,
% 5.14/5.32 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 5.14/5.32 inference(monotonicity,[status(thm)],[30498])).
% 5.14/5.32 tff(30500,plain,
% 5.14/5.32 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 5.14/5.32 inference(monotonicity,[status(thm)],[30499])).
% 5.14/5.32 tff(30501,plain,
% 5.14/5.32 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))),
% 5.14/5.32 inference(monotonicity,[status(thm)],[30500, 30498])).
% 5.14/5.32 tff(30502,plain,
% 5.14/5.32 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 5.14/5.32 inference(transitivity,[status(thm)],[30501, 4625])).
% 5.14/5.32 tff(30503,plain,
% 5.14/5.32 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))))),
% 5.14/5.32 inference(monotonicity,[status(thm)],[30502])).
% 5.14/5.32 tff(30504,plain,
% 5.14/5.32 (~(s(s(z)) = elem!1)),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[1345, 30496, 30252])).
% 5.14/5.32 tff(30505,plain,
% 5.14/5.32 (s(s(s(s(z)))) = elem!1),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[325, 30497])).
% 5.14/5.32 tff(30506,plain,
% 5.14/5.32 (~(s(s(elem!1)) = elem!1)),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[338, 30505, 30504])).
% 5.14/5.32 tff(30507,plain,
% 5.14/5.32 (~(s(s(s(elem!1))) = s(elem!1))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[348, 30506])).
% 5.14/5.32 tff(30508,plain,
% 5.14/5.32 (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 5.14/5.32 inference(modus_ponens,[status(thm)],[30507, 30503])).
% 5.14/5.32 tff(30509,plain,
% 5.14/5.32 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 5.14/5.32 inference(monotonicity,[status(thm)],[30498])).
% 5.14/5.32 tff(30510,plain,
% 5.14/5.32 (~(s(elem!1) = s(s(z)))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[11438, 30497])).
% 5.14/5.32 tff(30511,plain,
% 5.14/5.32 (~(elem!1 = s(s(s(elem!1))))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[4868, 30255, 3261, 461, 318])).
% 5.14/5.32 tff(30512,plain,
% 5.14/5.32 (~(s(s(s(elem!1))) = elem!1)),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[2489, 30511])).
% 5.14/5.32 tff(30513,plain,
% 5.14/5.32 (~(s(elem!1) = elem!1)),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[2150, 30512])).
% 5.14/5.32 tff(30514,plain,
% 5.14/5.32 (~r(z, elem!1)),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[4862, 30495, 3261])).
% 5.14/5.32 tff(30515,plain,
% 5.14/5.32 (b(z, elem!1)),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[585, 30514, 318])).
% 5.14/5.32 tff(30516,plain,
% 5.14/5.32 (~r(s(elem!1), s(s(z)))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[17418, 30515, 30252, 30493, 30513, 30495])).
% 5.14/5.32 tff(30517,plain,
% 5.14/5.32 (b(s(elem!1), s(s(z)))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[421, 30516, 30510])).
% 5.14/5.32 tff(30518,plain,
% 5.14/5.32 (b(s(s(s(s(s(z))))), s(s(z)))),
% 5.14/5.32 inference(modus_ponens,[status(thm)],[30517, 30509])).
% 5.14/5.32 tff(30519,plain,
% 5.14/5.32 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[3891, 103, 3437])).
% 5.14/5.32 tff(30520,plain,
% 5.14/5.32 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[3578, 30519])).
% 5.14/5.32 tff(30521,plain,
% 5.14/5.32 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[27817, 30520, 3437, 4236])).
% 5.14/5.32 tff(30522,plain,
% 5.14/5.32 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[249, 30521])).
% 5.14/5.32 tff(30523,plain,
% 5.14/5.32 (~(s(s(z)) = s(elem!1))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[1058, 30510])).
% 5.14/5.32 tff(30524,plain,
% 5.14/5.32 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(s(s(z)))))),
% 5.14/5.32 inference(monotonicity,[status(thm)],[30497])).
% 5.14/5.32 tff(30525,plain,
% 5.14/5.32 (r(s(s(z)), elem!1)),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[448, 30504, 3241])).
% 5.14/5.32 tff(30526,plain,
% 5.14/5.32 (r(s(s(z)), s(s(s(s(z)))))),
% 5.14/5.32 inference(modus_ponens,[status(thm)],[30525, 30524])).
% 5.14/5.32 tff(30527,plain,
% 5.14/5.32 (~(elem!1 = s(elem!1))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[748, 30513])).
% 5.14/5.32 tff(30528,plain,
% 5.14/5.32 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 5.14/5.32 inference(monotonicity,[status(thm)],[30497])).
% 5.14/5.32 tff(30529,plain,
% 5.14/5.32 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), elem!1)),
% 5.14/5.32 inference(symmetry,[status(thm)],[30528])).
% 5.14/5.32 tff(30530,plain,
% 5.14/5.32 (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)))))),
% 5.14/5.32 inference(monotonicity,[status(thm)],[30500])).
% 5.14/5.32 tff(30531,plain,
% 5.14/5.32 (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)))))),
% 5.14/5.32 inference(symmetry,[status(thm)],[30530])).
% 5.14/5.32 tff(30532,plain,
% 5.14/5.32 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), elem!1)),
% 5.14/5.32 inference(transitivity,[status(thm)],[30531, 30529])).
% 5.14/5.32 tff(30533,plain,
% 5.14/5.32 (r(s(s(s(elem!1))), elem!1)),
% 5.14/5.32 inference(modus_ponens,[status(thm)],[3437, 30532])).
% 5.14/5.32 tff(30534,plain,
% 5.14/5.32 (~r(s(elem!1), elem!1)),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[12991, 30533, 30525, 30507, 30526])).
% 5.14/5.32 tff(30535,plain,
% 5.14/5.32 (b(s(elem!1), elem!1)),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[677, 30534, 30513])).
% 5.14/5.32 tff(30536,plain,
% 5.14/5.32 (~r(s(s(z)), s(elem!1))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[27961, 30493, 30515, 30535, 30527, 3261, 30497, 30526])).
% 5.14/5.32 tff(30537,plain,
% 5.14/5.32 (b(s(s(z)), s(elem!1))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[1067, 30536, 30523])).
% 5.14/5.32 tff(30538,plain,
% 5.14/5.32 (b(s(s(z)), s(s(s(s(s(z))))))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[2330, 30537, 30497])).
% 5.14/5.32 tff(30539,plain,
% 5.14/5.32 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[14448, 30538, 30520, 30522, 30518])).
% 5.14/5.32 tff(30540,plain,
% 5.14/5.32 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[18762, 30539, 30508])).
% 5.14/5.32 tff(30541,plain,
% 5.14/5.32 (~r(z, s(s(s(s(s(z))))))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[23864, 30540, 4236])).
% 5.14/5.32 tff(30542,plain,
% 5.14/5.32 (b(z, s(s(s(s(s(z))))))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[1490, 41, 30541, 9676])).
% 5.14/5.32 tff(30543,plain,
% 5.14/5.32 (~r(s(s(s(s(s(z))))), z)),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[15071, 118, 4236, 30540])).
% 5.14/5.32 tff(30544,plain,
% 5.14/5.32 (b(s(s(s(s(s(z))))), z)),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[410, 41, 242, 30543])).
% 5.14/5.32 tff(30545,plain,
% 5.14/5.32 (s(s(s(s(s(z))))) = s(elem!1)),
% 5.14/5.32 inference(symmetry,[status(thm)],[30498])).
% 5.14/5.32 tff(30546,plain,
% 5.14/5.32 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 5.14/5.32 inference(monotonicity,[status(thm)],[30545])).
% 5.14/5.32 tff(30547,plain,
% 5.14/5.32 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 5.14/5.32 inference(symmetry,[status(thm)],[30546])).
% 5.14/5.32 tff(30548,plain,
% 5.14/5.32 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(s(z)))))),
% 5.14/5.32 inference(monotonicity,[status(thm)],[30497])).
% 5.14/5.32 tff(30549,plain,
% 5.14/5.32 (b(s(elem!1), elem!1) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 5.14/5.32 inference(transitivity,[status(thm)],[30548, 30547])).
% 5.14/5.32 tff(30550,plain,
% 5.14/5.32 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 5.14/5.32 inference(modus_ponens,[status(thm)],[30535, 30549])).
% 5.14/5.32 tff(30551,plain,
% 5.14/5.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 5.14/5.32 inference(rewrite,[status(thm)],[])).
% 5.14/5.32 tff(30552,plain,
% 5.14/5.32 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 5.14/5.32 inference(rewrite,[status(thm)],[])).
% 5.14/5.32 tff(30553,plain,
% 5.14/5.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z))))))))),
% 5.14/5.32 inference(monotonicity,[status(thm)],[30552])).
% 5.14/5.32 tff(30554,plain,
% 5.14/5.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 5.14/5.32 inference(transitivity,[status(thm)],[30553, 30551])).
% 5.14/5.32 tff(30555,plain,
% 5.14/5.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))))),
% 5.14/5.32 inference(quant_inst,[status(thm)],[])).
% 5.14/5.32 tff(30556,plain,
% 5.14/5.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z))))))),
% 5.14/5.32 inference(modus_ponens,[status(thm)],[30555, 30554])).
% 5.14/5.32 tff(30557,plain,
% 5.14/5.32 ($false),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[30556, 178, 30254, 14646, 30550, 30544, 30542])).
% 5.14/5.32 tff(30558,plain,(b(elem!1, s(s(z))) | (~r(z, s(s(z)))) | b(s(s(z)), elem!1) | (elem!1 = z) | b(s(s(z)), z) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | b(s(s(s(s(z)))), s(s(z))) | b(z, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.32 tff(30559,plain,
% 5.14/5.32 (b(elem!1, s(s(z)))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[30558, 290, 3241, 3261, 23814, 3428, 86, 4235])).
% 5.14/5.32 tff(30560,plain,
% 5.14/5.32 (~(s(s(z)) = elem!1)),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[3223, 30559])).
% 5.14/5.32 tff(30561,plain,
% 5.14/5.32 (r(s(s(z)), elem!1)),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[448, 30560, 3241])).
% 5.14/5.32 tff(30562,plain,
% 5.14/5.32 (elem!1 = s(s(s(s(z))))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[28936, 30561, 30559, 3437, 4235, 290, 30252, 103])).
% 5.14/5.32 tff(30563,plain,
% 5.14/5.32 (b(elem!1, s(s(z))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 5.14/5.32 inference(monotonicity,[status(thm)],[30562])).
% 5.14/5.32 tff(30564,plain,
% 5.14/5.32 (b(s(s(s(s(z)))), s(s(z))) <=> b(elem!1, s(s(z)))),
% 5.14/5.32 inference(symmetry,[status(thm)],[30563])).
% 5.14/5.32 tff(30565,plain,
% 5.14/5.32 ((~b(s(s(s(s(z)))), s(s(z)))) <=> (~b(elem!1, s(s(z))))),
% 5.14/5.32 inference(monotonicity,[status(thm)],[30564])).
% 5.14/5.32 tff(30566,plain,
% 5.14/5.32 (~b(elem!1, s(s(z)))),
% 5.14/5.32 inference(modus_ponens,[status(thm)],[86, 30565])).
% 5.14/5.32 tff(30567,plain,
% 5.14/5.32 ($false),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[30559, 30566])).
% 5.14/5.32 tff(30568,plain,((elem!1 = z) | b(s(s(s(s(z)))), s(s(z))) | b(z, s(s(s(s(s(s(s(z)))))))) | b(s(s(z)), elem!1) | (~r(z, s(s(z)))) | b(s(s(z)), z) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.32 tff(30569,plain,
% 5.14/5.32 (elem!1 = z),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[30568, 23814, 4235, 3241, 30251, 86, 3428])).
% 5.14/5.32 tff(30570,plain,
% 5.14/5.32 (s(elem!1) = s(z)),
% 5.14/5.32 inference(monotonicity,[status(thm)],[30569])).
% 5.14/5.32 tff(30571,plain,
% 5.14/5.32 (s(s(elem!1)) = s(s(z))),
% 5.14/5.32 inference(monotonicity,[status(thm)],[30570])).
% 5.14/5.32 tff(30572,plain,
% 5.14/5.32 (s(s(s(elem!1))) = s(s(s(z)))),
% 5.14/5.32 inference(monotonicity,[status(thm)],[30571])).
% 5.14/5.32 tff(30573,plain,
% 5.14/5.32 (r(s(s(s(elem!1))), z) <=> r(s(s(s(z))), z)),
% 5.14/5.32 inference(monotonicity,[status(thm)],[30572])).
% 5.14/5.32 tff(30574,plain,
% 5.14/5.32 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), z)),
% 5.14/5.32 inference(monotonicity,[status(thm)],[30569])).
% 5.14/5.32 tff(30575,plain,
% 5.14/5.32 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(z))), z)),
% 5.14/5.32 inference(transitivity,[status(thm)],[30574, 30573])).
% 5.14/5.32 tff(30576,plain,
% 5.14/5.32 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = z)),
% 5.14/5.32 inference(monotonicity,[status(thm)],[30569])).
% 5.14/5.32 tff(30577,plain,
% 5.14/5.32 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 5.14/5.32 inference(symmetry,[status(thm)],[30576])).
% 5.14/5.32 tff(30578,plain,
% 5.14/5.32 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 5.14/5.32 inference(monotonicity,[status(thm)],[30577])).
% 5.14/5.32 tff(30579,plain,
% 5.14/5.32 (~(s(s(s(elem!1))) = elem!1)),
% 5.14/5.32 inference(modus_ponens,[status(thm)],[940, 30578])).
% 5.14/5.32 tff(30580,plain,
% 5.14/5.32 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(z))))),
% 5.14/5.32 inference(monotonicity,[status(thm)],[30572])).
% 5.14/5.32 tff(30581,plain,
% 5.14/5.32 (b(elem!1, s(s(z))) <=> b(z, s(s(z)))),
% 5.14/5.32 inference(monotonicity,[status(thm)],[30569])).
% 5.14/5.32 tff(30582,plain,
% 5.14/5.32 (b(z, s(s(z))) <=> b(elem!1, s(s(z)))),
% 5.14/5.32 inference(symmetry,[status(thm)],[30581])).
% 5.14/5.32 tff(30583,plain,
% 5.14/5.32 ((~b(z, s(s(z)))) <=> (~b(elem!1, s(s(z))))),
% 5.14/5.32 inference(monotonicity,[status(thm)],[30582])).
% 5.14/5.32 tff(30584,plain,
% 5.14/5.32 (~b(elem!1, s(s(z)))),
% 5.14/5.32 inference(modus_ponens,[status(thm)],[28501, 30583])).
% 5.14/5.32 tff(30585,plain,
% 5.14/5.32 (r(elem!1, s(s(s(elem!1))))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[4850, 928, 557])).
% 5.14/5.32 tff(30586,plain,
% 5.14/5.32 (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[3623, 20650, 30585])).
% 5.14/5.32 tff(30587,plain,
% 5.14/5.32 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[21219, 30586, 928])).
% 5.14/5.32 tff(30588,plain,
% 5.14/5.32 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[5031, 41, 30587, 10712])).
% 5.14/5.32 tff(30589,plain,
% 5.14/5.32 (~b(z, s(s(z)))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[3276, 928, 461])).
% 5.14/5.32 tff(30590,plain,
% 5.14/5.32 (r(z, s(s(z)))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[143, 30589])).
% 5.14/5.32 tff(30591,plain,
% 5.14/5.32 (~r(s(s(z)), s(s(s(elem!1))))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[4808, 30590, 557])).
% 5.14/5.32 tff(30592,plain,
% 5.14/5.32 (b(s(s(z)), s(s(s(elem!1))))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[4223, 30591])).
% 5.14/5.32 tff(30593,plain,
% 5.14/5.32 (b(s(s(z)), s(s(s(z))))),
% 5.14/5.32 inference(modus_ponens,[status(thm)],[30592, 5240])).
% 5.14/5.32 tff(30594,plain,
% 5.14/5.32 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[4690, 30590, 203])).
% 5.14/5.32 tff(30595,plain,
% 5.14/5.32 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[249, 30594])).
% 5.14/5.32 tff(30596,plain,
% 5.14/5.32 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[27335, 30595, 30593, 1146, 30588])).
% 5.14/5.32 tff(30597,plain,
% 5.14/5.32 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 30596])).
% 5.14/5.32 tff(30598,plain,
% 5.14/5.32 (r(z, s(s(s(z))))),
% 5.14/5.32 inference(modus_ponens,[status(thm)],[557, 10722])).
% 5.14/5.32 tff(30599,plain,
% 5.14/5.32 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 5.14/5.32 inference(rewrite,[status(thm)],[])).
% 5.14/5.32 tff(30600,plain,
% 5.14/5.32 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 5.14/5.32 inference(rewrite,[status(thm)],[])).
% 5.14/5.32 tff(30601,plain,
% 5.14/5.32 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(z)))))))),
% 5.14/5.32 inference(monotonicity,[status(thm)],[30600])).
% 5.14/5.32 tff(30602,plain,
% 5.14/5.32 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 5.14/5.32 inference(transitivity,[status(thm)],[30601, 30599])).
% 5.14/5.32 tff(30603,plain,
% 5.14/5.32 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 5.14/5.32 inference(quant_inst,[status(thm)],[])).
% 5.14/5.32 tff(30604,plain,
% 5.14/5.32 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(z, s(s(s(z)))))),
% 5.14/5.32 inference(modus_ponens,[status(thm)],[30603, 30602])).
% 5.14/5.32 tff(30605,plain,
% 5.14/5.32 ($false),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[30604, 118, 203, 30598, 30597])).
% 5.14/5.32 tff(30606,plain,((~(elem!1 = z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | b(elem!1, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.32 tff(30607,plain,
% 5.14/5.32 (~r(z, s(s(s(elem!1))))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[30606, 30584, 30520, 4236, 30569])).
% 5.14/5.32 tff(30608,plain,
% 5.14/5.32 (b(z, s(s(s(elem!1))))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[2095, 30607])).
% 5.14/5.32 tff(30609,plain,
% 5.14/5.32 (b(z, s(s(s(z))))),
% 5.14/5.32 inference(modus_ponens,[status(thm)],[30608, 30580])).
% 5.14/5.32 tff(30610,plain,
% 5.14/5.32 (~r(s(s(s(s(z)))), z)),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[9569, 30251, 103])).
% 5.14/5.32 tff(30611,plain,
% 5.14/5.32 (b(s(s(s(s(z)))), z)),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[191, 30610])).
% 5.14/5.32 tff(30612,plain,
% 5.14/5.32 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 5.14/5.32 inference(monotonicity,[status(thm)],[30572])).
% 5.14/5.32 tff(30613,plain,
% 5.14/5.32 (r(s(s(s(s(elem!1)))), s(s(z))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 5.14/5.32 inference(monotonicity,[status(thm)],[30612])).
% 5.14/5.32 tff(30614,plain,
% 5.14/5.32 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(s(z)))),
% 5.14/5.32 inference(symmetry,[status(thm)],[30613])).
% 5.14/5.32 tff(30615,plain,
% 5.14/5.32 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 5.14/5.32 inference(modus_ponens,[status(thm)],[103, 30614])).
% 5.14/5.32 tff(30616,plain,
% 5.14/5.32 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 5.14/5.32 inference(monotonicity,[status(thm)],[5207])).
% 5.14/5.32 tff(30617,plain,
% 5.14/5.32 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), z)),
% 5.14/5.32 inference(transitivity,[status(thm)],[10092, 22639])).
% 5.14/5.32 tff(30618,plain,
% 5.14/5.32 (b(s(s(s(z))), z)),
% 5.14/5.32 inference(modus_ponens,[status(thm)],[1597, 30617])).
% 5.14/5.32 tff(30619,plain,
% 5.14/5.32 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[21518, 178, 1687, 168, 3008, 30618])).
% 5.14/5.32 tff(30620,plain,
% 5.14/5.32 (r(s(s(s(z))), s(s(s(s(z)))))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[10755, 30619])).
% 5.14/5.32 tff(30621,plain,
% 5.14/5.32 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[27236, 118, 1130, 30620])).
% 5.14/5.32 tff(30622,plain,
% 5.14/5.32 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[5031, 41, 30621, 10712])).
% 5.14/5.32 tff(30623,plain,
% 5.14/5.32 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(s(elem!1))))),
% 5.14/5.32 inference(monotonicity,[status(thm)],[930])).
% 5.14/5.32 tff(30624,plain,
% 5.14/5.32 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 5.14/5.32 inference(symmetry,[status(thm)],[30623])).
% 5.14/5.32 tff(30625,plain,
% 5.14/5.32 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 5.14/5.32 inference(transitivity,[status(thm)],[30624, 12033])).
% 5.14/5.32 tff(30626,plain,
% 5.14/5.32 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 5.14/5.32 inference(monotonicity,[status(thm)],[30625])).
% 5.14/5.32 tff(30627,plain,
% 5.14/5.32 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 5.14/5.32 inference(modus_ponens,[status(thm)],[1683, 30626])).
% 5.14/5.32 tff(30628,plain,
% 5.14/5.32 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[12177, 1597, 12064, 20932, 12138, 3636, 3261])).
% 5.14/5.32 tff(30629,plain,
% 5.14/5.32 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[3409, 30628, 30627])).
% 5.14/5.32 tff(30630,plain,
% 5.14/5.32 (b(s(s(s(z))), s(s(z)))),
% 5.14/5.32 inference(modus_ponens,[status(thm)],[30629, 5221])).
% 5.14/5.32 tff(30631,plain,
% 5.14/5.32 ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z)))))),
% 5.14/5.32 inference(unit_resolution,[status(thm)],[21437, 178, 166, 30630, 1146])).
% 5.14/5.33 tff(30632,plain,
% 5.14/5.33 (~b(s(s(z)), s(s(s(z))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[30631, 30622])).
% 5.14/5.33 tff(30633,plain,
% 5.14/5.33 (r(s(s(z)), s(s(s(z))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[5088, 30632])).
% 5.14/5.33 tff(30634,plain,
% 5.14/5.33 (r(s(s(z)), s(s(s(elem!1))))),
% 5.14/5.33 inference(modus_ponens,[status(thm)],[30633, 30616])).
% 5.14/5.33 tff(30635,plain,
% 5.14/5.33 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[23651, 178, 1687, 168, 3008, 30618])).
% 5.14/5.33 tff(30636,plain,
% 5.14/5.33 (r(s(s(s(s(z)))), s(s(s(z))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[11185, 30635])).
% 5.14/5.33 tff(30637,plain,
% 5.14/5.33 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 5.14/5.33 inference(modus_ponens,[status(thm)],[30636, 20745])).
% 5.14/5.33 tff(30638,plain,
% 5.14/5.33 (~r(s(s(z)), s(s(s(elem!1))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[3644, 30637, 3636])).
% 5.14/5.33 tff(30639,plain,
% 5.14/5.33 ($false),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[30638, 30634])).
% 5.14/5.33 tff(30640,plain,((~b(s(s(s(elem!1))), elem!1)) | (~(elem!1 = z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.33 tff(30641,plain,
% 5.14/5.33 (~b(s(s(s(elem!1))), elem!1)),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[30640, 30569, 30522, 30520, 30615, 3437, 30254, 30611, 30609, 30251])).
% 5.14/5.33 tff(30642,plain,
% 5.14/5.33 (r(s(s(s(elem!1))), elem!1)),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[570, 30641, 30579])).
% 5.14/5.33 tff(30643,plain,
% 5.14/5.33 (r(s(s(s(z))), z)),
% 5.14/5.33 inference(modus_ponens,[status(thm)],[30642, 30575])).
% 5.14/5.33 tff(30644,plain,
% 5.14/5.33 (~r(s(s(z)), s(s(s(z))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[21465, 118, 30252, 30643])).
% 5.14/5.33 tff(30645,plain,
% 5.14/5.33 (b(s(s(z)), s(s(s(z))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[5088, 30644])).
% 5.14/5.33 tff(30646,plain,
% 5.14/5.33 (s(s(s(z))) = s(s(s(elem!1)))),
% 5.14/5.33 inference(symmetry,[status(thm)],[30572])).
% 5.14/5.33 tff(30647,plain,
% 5.14/5.33 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 5.14/5.33 inference(monotonicity,[status(thm)],[30646])).
% 5.14/5.33 tff(30648,plain,
% 5.14/5.33 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(z))), s(s(z)))),
% 5.14/5.33 inference(symmetry,[status(thm)],[30647])).
% 5.14/5.33 tff(30649,plain,
% 5.14/5.33 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 5.14/5.33 inference(monotonicity,[status(thm)],[30571])).
% 5.14/5.33 tff(30650,plain,
% 5.14/5.33 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(z)))),
% 5.14/5.33 inference(transitivity,[status(thm)],[30649, 30648])).
% 5.14/5.33 tff(30651,plain,
% 5.14/5.33 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(s(elem!1))))),
% 5.14/5.33 inference(monotonicity,[status(thm)],[30571])).
% 5.14/5.33 tff(30652,plain,
% 5.14/5.33 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 5.14/5.33 inference(symmetry,[status(thm)],[30651])).
% 5.14/5.33 tff(30653,plain,
% 5.14/5.33 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 5.14/5.33 inference(transitivity,[status(thm)],[30652, 12033])).
% 5.14/5.33 tff(30654,plain,
% 5.14/5.33 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 5.14/5.33 inference(monotonicity,[status(thm)],[30653])).
% 5.14/5.33 tff(30655,plain,
% 5.14/5.33 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 5.14/5.33 inference(modus_ponens,[status(thm)],[1683, 30654])).
% 5.14/5.33 tff(30656,plain,
% 5.14/5.33 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), z)),
% 5.14/5.33 inference(monotonicity,[status(thm)],[30569])).
% 5.14/5.33 tff(30657,plain,
% 5.14/5.33 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 5.14/5.33 inference(symmetry,[status(thm)],[30656])).
% 5.14/5.33 tff(30658,plain,
% 5.14/5.33 (r(s(s(elem!1)), z) <=> r(s(s(z)), z)),
% 5.14/5.33 inference(monotonicity,[status(thm)],[30571])).
% 5.14/5.33 tff(30659,plain,
% 5.14/5.33 (r(s(s(z)), z) <=> r(s(s(elem!1)), z)),
% 5.14/5.33 inference(symmetry,[status(thm)],[30658])).
% 5.14/5.33 tff(30660,plain,
% 5.14/5.33 (r(s(s(z)), z) <=> r(s(s(elem!1)), elem!1)),
% 5.14/5.33 inference(transitivity,[status(thm)],[30659, 30657])).
% 5.14/5.33 tff(30661,plain,
% 5.14/5.33 (r(s(s(elem!1)), elem!1)),
% 5.14/5.33 inference(modus_ponens,[status(thm)],[30252, 30660])).
% 5.14/5.33 tff(30662,plain,
% 5.14/5.33 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[30478, 30642, 30661])).
% 5.14/5.33 tff(30663,plain,
% 5.14/5.33 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[3409, 30662, 30655])).
% 5.14/5.33 tff(30664,plain,
% 5.14/5.33 (b(s(s(s(z))), s(s(z)))),
% 5.14/5.33 inference(modus_ponens,[status(thm)],[30663, 30650])).
% 5.14/5.33 tff(30665,plain,
% 5.14/5.33 ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(z)))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[21437, 178, 30522, 30664, 30520])).
% 5.14/5.33 tff(30666,plain,
% 5.14/5.33 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[30665, 30645])).
% 5.14/5.33 tff(30667,plain,
% 5.14/5.33 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[5031, 41, 30666, 10712])).
% 5.14/5.33 tff(30668,plain,
% 5.14/5.33 ($false),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[11272, 118, 4236, 30643, 30667])).
% 5.14/5.33 tff(30669,plain,(b(s(s(z)), z) | b(z, s(s(z))) | b(z, s(s(s(s(s(s(s(z)))))))) | b(s(s(z)), elem!1) | b(s(s(s(s(z)))), s(s(z))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.33 tff(30670,plain,
% 5.14/5.33 (b(s(s(z)), z)),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[30669, 28501, 4235, 3241, 86, 3428])).
% 5.14/5.33 tff(30671,plain,
% 5.14/5.33 (elem!1 = z),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[28098, 30251, 3437, 3241, 86, 4235, 30670])).
% 5.14/5.33 tff(30672,plain,
% 5.14/5.33 (b(s(s(z)), elem!1) <=> b(s(s(z)), z)),
% 5.14/5.33 inference(monotonicity,[status(thm)],[30671])).
% 5.14/5.33 tff(30673,plain,
% 5.14/5.33 (b(s(s(z)), z) <=> b(s(s(z)), elem!1)),
% 5.14/5.33 inference(symmetry,[status(thm)],[30672])).
% 5.14/5.33 tff(30674,plain,
% 5.14/5.33 (b(s(s(z)), elem!1)),
% 5.14/5.33 inference(modus_ponens,[status(thm)],[30670, 30673])).
% 5.14/5.33 tff(30675,plain,
% 5.14/5.33 ($false),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[3241, 30674])).
% 5.14/5.33 tff(30676,plain,(b(z, s(s(z))) | b(s(s(z)), elem!1) | b(s(s(s(s(z)))), s(s(z))) | b(z, s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.33 tff(30677,plain,
% 5.14/5.33 (b(z, s(s(s(s(s(s(s(z))))))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[30676, 30208, 28501, 30250, 86])).
% 5.14/5.33 tff(30678,plain,
% 5.14/5.33 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[13303, 178, 27212, 30126, 30677, 30249])).
% 5.14/5.33 tff(30679,plain,
% 5.14/5.33 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[222, 30678])).
% 5.14/5.33 tff(30680,plain,
% 5.14/5.33 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[21413, 30240, 27212, 30679, 30126])).
% 5.14/5.33 tff(30681,plain,
% 5.14/5.33 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[20667, 30680])).
% 5.14/5.33 tff(30682,plain,
% 5.14/5.33 (~b(s(s(z)), s(s(s(z))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[21439, 30681, 27224, 30122, 30134])).
% 5.14/5.33 tff(30683,plain,
% 5.14/5.33 ($false),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[5088, 30682, 30244])).
% 5.14/5.33 tff(30684,plain,((~r(elem!1, s(s(z)))) | (s(s(z)) = s(elem!1)) | (~b(s(elem!1), s(s(z)))) | (s(s(z)) = elem!1) | b(z, s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | b(s(s(z)), s(s(s(s(z))))) | b(s(elem!1), z) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 5.14/5.33 tff(30685,plain,
% 5.14/5.33 (~r(elem!1, s(s(z)))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[30684, 766, 1070, 12, 28501, 86, 105, 1060, 507])).
% 5.14/5.33 tff(30686,plain,
% 5.14/5.33 (b(elem!1, s(s(z)))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[467, 30685, 312])).
% 5.14/5.33 tff(30687,plain,
% 5.14/5.33 (~(s(elem!1) = s(s(s(s(z)))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[12552, 1070, 86])).
% 5.14/5.33 tff(30688,plain,
% 5.14/5.33 (~r(s(s(z)), s(elem!1))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[1052, 118, 12569, 28500])).
% 5.14/5.33 tff(30689,plain,
% 5.14/5.33 (b(s(s(z)), s(elem!1))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[1067, 30688, 1060])).
% 5.14/5.33 tff(30690,plain,
% 5.14/5.33 (b(s(s(z)), elem!1)),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[23429, 469, 27212, 28500, 29994, 147, 12, 2809])).
% 5.14/5.33 tff(30691,plain,
% 5.14/5.33 (~r(s(s(s(z))), s(s(z)))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[30132, 193, 28503, 28449])).
% 5.14/5.33 tff(30692,plain,
% 5.14/5.33 (b(s(s(s(z))), s(s(z)))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[4966, 30691])).
% 5.14/5.33 tff(30693,plain,
% 5.14/5.33 (~r(elem!1, s(elem!1))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[2711, 10801, 844])).
% 5.14/5.33 tff(30694,plain,
% 5.14/5.33 (~(elem!1 = s(s(s(s(z)))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[12557, 5723, 28503])).
% 5.14/5.33 tff(30695,plain,
% 5.14/5.33 (b(s(s(z)), elem!1)),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[23429, 30694, 27212, 28500, 29994, 147, 12, 290])).
% 5.14/5.33 tff(30696,plain,
% 5.14/5.33 ($false),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[24965, 178, 726, 817, 757, 812, 1070])).
% 5.14/5.33 tff(30697,plain,((s(elem!1) = elem!1) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | r(elem!1, s(elem!1)) | r(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 5.14/5.33 tff(30698,plain,
% 5.14/5.33 (s(elem!1) = elem!1),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[30697, 30695, 812, 1070, 30693, 13695])).
% 5.14/5.33 tff(30699,plain,
% 5.14/5.33 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))),
% 5.14/5.33 inference(rewrite,[status(thm)],[])).
% 5.14/5.33 tff(30700,plain,
% 5.14/5.33 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))),
% 5.14/5.33 inference(quant_inst,[status(thm)],[])).
% 5.14/5.33 tff(30701,plain,
% 5.14/5.33 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1))),
% 5.14/5.33 inference(modus_ponens,[status(thm)],[30700, 30699])).
% 5.14/5.33 tff(30702,plain,
% 5.14/5.33 (~r(s(s(s(z))), elem!1)),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[30701, 118, 437, 16062])).
% 5.14/5.33 tff(30703,plain,
% 5.14/5.33 (b(s(s(s(z))), s(elem!1))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[23093, 30702, 2484, 668])).
% 5.14/5.33 tff(30704,plain,
% 5.14/5.33 (b(s(s(s(z))), elem!1)),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[4981, 30702, 23088])).
% 5.14/5.33 tff(30705,plain,
% 5.14/5.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 5.14/5.33 inference(rewrite,[status(thm)],[])).
% 5.14/5.33 tff(30706,plain,
% 5.14/5.33 (((~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 5.14/5.33 inference(rewrite,[status(thm)],[])).
% 5.14/5.33 tff(30707,plain,
% 5.14/5.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1)))))),
% 5.14/5.33 inference(monotonicity,[status(thm)],[30706])).
% 5.14/5.33 tff(30708,plain,
% 5.14/5.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 5.14/5.33 inference(transitivity,[status(thm)],[30707, 30705])).
% 5.14/5.33 tff(30709,plain,
% 5.14/5.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 5.14/5.33 inference(quant_inst,[status(thm)],[])).
% 5.14/5.33 tff(30710,plain,
% 5.14/5.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1)))),
% 5.14/5.33 inference(modus_ponens,[status(thm)],[30709, 30708])).
% 5.14/5.33 tff(30711,plain,
% 5.14/5.33 ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1)))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[30710, 178, 812, 1071, 1070, 4932])).
% 5.14/5.33 tff(30712,plain,
% 5.14/5.33 ($false),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[30711, 30228, 30704, 30703])).
% 5.14/5.33 tff(30713,plain,((~r(s(s(s(z))), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (s(s(elem!1)) = s(s(z))) | (~(s(elem!1) = elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.33 tff(30714,plain,
% 5.14/5.33 (~r(s(s(s(z))), z)),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[30713, 30698, 1071, 1070, 4932, 2484, 812, 10801])).
% 5.14/5.33 tff(30715,plain,
% 5.14/5.33 (b(s(s(s(z))), z)),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[21073, 30714])).
% 5.14/5.33 tff(30716,plain,
% 5.14/5.33 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[30135, 30715])).
% 5.14/5.33 tff(30717,plain,
% 5.14/5.33 (r(s(s(s(s(z)))), s(s(s(z))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[11185, 30716])).
% 5.14/5.33 tff(30718,plain,
% 5.14/5.33 (~r(s(s(z)), s(s(s(z))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[24478, 30717, 147])).
% 5.14/5.33 tff(30719,plain,
% 5.14/5.33 (s(s(elem!1)) = elem!1),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[672, 30698])).
% 5.14/5.33 tff(30720,plain,
% 5.14/5.33 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[2510, 30719, 2508])).
% 5.14/5.33 tff(30721,plain,
% 5.14/5.33 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[11831, 30720, 29994, 10801, 812, 30695])).
% 5.14/5.33 tff(30722,plain,
% 5.14/5.33 (b(s(s(s(s(s(s(s(z))))))), z)),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[133, 30721])).
% 5.14/5.33 tff(30723,plain,
% 5.14/5.33 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[11859, 30695, 28447, 27396, 812])).
% 5.14/5.33 tff(30724,plain,
% 5.14/5.33 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[691, 30720, 30723])).
% 5.14/5.33 tff(30725,plain,
% 5.14/5.33 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[10809, 30724, 10801])).
% 5.14/5.33 tff(30726,plain,
% 5.14/5.33 (b(z, s(s(s(s(s(s(s(z))))))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[271, 30725])).
% 5.14/5.33 tff(30727,plain,
% 5.14/5.33 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[13303, 178, 27212, 28503, 30726, 30722])).
% 5.14/5.33 tff(30728,plain,
% 5.14/5.33 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[222, 30727])).
% 5.14/5.33 tff(30729,plain,
% 5.14/5.33 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[21413, 30715, 27212, 30728, 28503])).
% 5.14/5.33 tff(30730,plain,
% 5.14/5.33 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[20667, 30729])).
% 5.14/5.33 tff(30731,plain,
% 5.14/5.33 (~b(s(s(z)), s(s(s(z))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[21439, 30730, 27396, 28447, 4932])).
% 5.14/5.33 tff(30732,plain,
% 5.14/5.33 ($false),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[5088, 30731, 30718])).
% 5.14/5.33 tff(30733,plain,(b(elem!1, z) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (s(s(elem!1)) = s(s(z))) | (~b(elem!1, s(s(z)))) | (s(s(s(s(z)))) = s(elem!1)) | (~r(s(elem!1), z)) | (s(s(z)) = elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 5.14/5.33 tff(30734,plain,
% 5.14/5.33 (b(elem!1, z)),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[30733, 1071, 147, 30692, 1070, 2387, 812, 2169, 12569, 12, 2809])).
% 5.14/5.33 tff(30735,plain,
% 5.14/5.33 (~b(s(elem!1), elem!1)),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[13708, 30690, 1071, 1070, 812])).
% 5.14/5.33 tff(30736,plain,
% 5.14/5.33 (~r(z, elem!1)),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[19342, 30735, 766, 30734])).
% 5.14/5.33 tff(30737,plain,
% 5.14/5.33 (b(z, elem!1)),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[585, 30736, 507])).
% 5.14/5.33 tff(30738,plain,
% 5.14/5.33 ((~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z))))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[12519, 178, 30734, 27212, 28503])).
% 5.14/5.33 tff(30739,plain,
% 5.14/5.33 (~b(elem!1, s(s(s(s(z)))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[30738, 30737])).
% 5.14/5.33 tff(30740,plain,
% 5.14/5.33 (r(elem!1, s(s(s(s(z)))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[483, 30739, 469])).
% 5.14/5.33 tff(30741,plain,
% 5.14/5.33 ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[12005, 24592])).
% 5.14/5.33 tff(30742,plain,
% 5.14/5.33 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[30741, 30740, 147, 30690, 812])).
% 5.14/5.33 tff(30743,plain,
% 5.14/5.33 (~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[24777, 30742, 23437])).
% 5.14/5.33 tff(30744,plain,
% 5.14/5.33 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 5.14/5.33 inference(monotonicity,[status(thm)],[30742])).
% 5.14/5.33 tff(30745,plain,
% 5.14/5.33 (s(s(s(s(s(s(s(s(z)))))))) = s(elem!1)),
% 5.14/5.33 inference(symmetry,[status(thm)],[30744])).
% 5.14/5.33 tff(30746,plain,
% 5.14/5.33 (b(s(s(z)), s(s(s(s(s(s(s(s(z))))))))) <=> b(s(s(z)), s(elem!1))),
% 5.14/5.33 inference(monotonicity,[status(thm)],[30745])).
% 5.14/5.33 tff(30747,plain,
% 5.14/5.33 (b(s(s(z)), s(elem!1)) <=> b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 5.14/5.33 inference(symmetry,[status(thm)],[30746])).
% 5.14/5.33 tff(30748,plain,
% 5.14/5.33 (b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 5.14/5.33 inference(modus_ponens,[status(thm)],[1071, 30747])).
% 5.14/5.33 tff(30749,plain,
% 5.14/5.33 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 5.14/5.33 inference(monotonicity,[status(thm)],[30744])).
% 5.14/5.33 tff(30750,plain,
% 5.14/5.33 (~(s(elem!1) = elem!1)),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[790, 30734, 766])).
% 5.14/5.33 tff(30751,plain,
% 5.14/5.33 (~(elem!1 = s(elem!1))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[748, 30750])).
% 5.14/5.33 tff(30752,plain,
% 5.14/5.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))))),
% 5.14/5.33 inference(rewrite,[status(thm)],[])).
% 5.14/5.33 tff(30753,plain,
% 5.14/5.33 (((~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), elem!1))) <=> ((~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))))),
% 5.14/5.33 inference(rewrite,[status(thm)],[])).
% 5.14/5.33 tff(30754,plain,
% 5.14/5.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z))))))),
% 5.14/5.33 inference(monotonicity,[status(thm)],[30753])).
% 5.14/5.33 tff(30755,plain,
% 5.14/5.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))))),
% 5.14/5.33 inference(transitivity,[status(thm)],[30754, 30752])).
% 5.14/5.33 tff(30756,plain,
% 5.14/5.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), elem!1)))),
% 5.14/5.33 inference(quant_inst,[status(thm)],[])).
% 5.14/5.33 tff(30757,plain,
% 5.14/5.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z))))),
% 5.14/5.33 inference(modus_ponens,[status(thm)],[30756, 30755])).
% 5.14/5.33 tff(30758,plain,
% 5.14/5.33 ((~b(elem!1, s(elem!1))) | (~b(s(s(z)), elem!1))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[30757, 178, 812, 1071, 1070])).
% 5.14/5.33 tff(30759,plain,
% 5.14/5.33 (~b(elem!1, s(elem!1))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[30758, 30690])).
% 5.14/5.33 tff(30760,plain,
% 5.14/5.33 (r(elem!1, s(elem!1))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[756, 30759, 30751])).
% 5.14/5.33 tff(30761,plain,
% 5.14/5.33 (~r(s(elem!1), s(s(s(s(z)))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[14364, 30740, 30760])).
% 5.14/5.33 tff(30762,plain,
% 5.14/5.33 (b(s(elem!1), s(s(s(s(z)))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[1084, 30761, 1369])).
% 5.14/5.33 tff(30763,plain,
% 5.14/5.33 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 5.14/5.33 inference(modus_ponens,[status(thm)],[30762, 30749])).
% 5.14/5.33 tff(30764,plain,
% 5.14/5.33 (b(s(s(s(s(s(s(s(z))))))), z)),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[28842, 30742, 30734])).
% 5.14/5.33 tff(30765,plain,
% 5.14/5.33 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[25883, 30740])).
% 5.14/5.33 tff(30766,plain,
% 5.14/5.33 (b(z, s(s(s(s(s(s(s(z))))))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[23466, 30765, 193, 28447, 27396, 30690, 30737, 28500, 2809, 469, 312])).
% 5.14/5.33 tff(30767,plain,
% 5.14/5.33 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[13303, 178, 27212, 28503, 30766, 30764])).
% 5.14/5.33 tff(30768,plain,
% 5.14/5.33 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[222, 30767])).
% 5.14/5.33 tff(30769,plain,
% 5.14/5.33 (~b(s(s(s(z))), z)),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[30148, 30768, 147, 30692])).
% 5.14/5.33 tff(30770,plain,
% 5.14/5.33 (r(s(s(s(z))), z)),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[21073, 30769])).
% 5.14/5.33 tff(30771,plain,
% 5.14/5.33 (~r(s(s(z)), s(s(s(z))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[21465, 118, 28500, 30770])).
% 5.14/5.33 tff(30772,plain,
% 5.14/5.33 (b(s(s(z)), s(s(s(z))))),
% 5.14/5.33 inference(unit_resolution,[status(thm)],[5088, 30771])).
% 5.14/5.33 tff(30773,plain,
% 5.14/5.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 5.14/5.33 inference(rewrite,[status(thm)],[])).
% 5.14/5.33 tff(30774,plain,
% 5.14/5.33 (((~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(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 5.14/5.33 inference(rewrite,[status(thm)],[])).
% 5.14/5.33 tff(30775,plain,
% 5.14/5.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))))),
% 5.14/5.33 inference(monotonicity,[status(thm)],[30774])).
% 5.14/5.33 tff(30776,plain,
% 5.14/5.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 5.14/5.34 inference(transitivity,[status(thm)],[30775, 30773])).
% 5.14/5.34 tff(30777,plain,
% 5.14/5.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))),
% 5.14/5.34 inference(quant_inst,[status(thm)],[])).
% 5.14/5.34 tff(30778,plain,
% 5.14/5.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 5.14/5.34 inference(modus_ponens,[status(thm)],[30777, 30776])).
% 5.14/5.34 tff(30779,plain,
% 5.14/5.34 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[30778, 178, 28449, 30772, 30763, 30748])).
% 5.14/5.34 tff(30780,plain,
% 5.14/5.34 (r(s(s(s(s(s(s(s(s(z)))))))), z) <=> r(s(elem!1), z)),
% 5.14/5.34 inference(monotonicity,[status(thm)],[30745])).
% 5.14/5.34 tff(30781,plain,
% 5.14/5.34 (r(s(elem!1), z) <=> r(s(s(s(s(s(s(s(s(z)))))))), z)),
% 5.14/5.34 inference(symmetry,[status(thm)],[30780])).
% 5.14/5.34 tff(30782,plain,
% 5.14/5.34 (r(s(s(s(s(s(s(s(s(z)))))))), z)),
% 5.14/5.34 inference(modus_ponens,[status(thm)],[12569, 30781])).
% 5.14/5.34 tff(30783,plain,
% 5.14/5.34 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 5.14/5.34 inference(rewrite,[status(thm)],[])).
% 5.14/5.34 tff(30784,plain,
% 5.14/5.34 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 5.14/5.34 inference(quant_inst,[status(thm)],[])).
% 5.14/5.34 tff(30785,plain,
% 5.14/5.34 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 5.14/5.34 inference(modus_ponens,[status(thm)],[30784, 30783])).
% 5.14/5.34 tff(30786,plain,
% 5.14/5.34 ((~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[30785, 118, 30770])).
% 5.14/5.34 tff(30787,plain,
% 5.14/5.34 (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[30786, 30782])).
% 5.14/5.34 tff(30788,plain,
% 5.14/5.34 ($false),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[24832, 30787, 30779, 30743])).
% 5.14/5.34 tff(30789,plain,((elem!1 = s(s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))) | (s(elem!1) = s(s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (z = elem!1) | b(s(elem!1), z) | (~b(s(elem!1), s(s(z)))) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 5.14/5.34 tff(30790,plain,
% 5.14/5.34 (elem!1 = s(s(s(s(z))))),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[30789, 30689, 10794, 30687, 103, 30686, 507, 766, 1070, 12])).
% 5.14/5.34 tff(30791,plain,
% 5.14/5.34 (b(elem!1, s(s(z))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 5.14/5.34 inference(monotonicity,[status(thm)],[30790])).
% 5.14/5.34 tff(30792,plain,
% 5.14/5.34 (b(s(s(s(s(z)))), s(s(z))) <=> b(elem!1, s(s(z)))),
% 5.14/5.34 inference(symmetry,[status(thm)],[30791])).
% 5.14/5.34 tff(30793,plain,
% 5.14/5.34 ((~b(s(s(s(s(z)))), s(s(z)))) <=> (~b(elem!1, s(s(z))))),
% 5.14/5.34 inference(monotonicity,[status(thm)],[30792])).
% 5.14/5.34 tff(30794,plain,
% 5.14/5.34 (~b(elem!1, s(s(z)))),
% 5.14/5.34 inference(modus_ponens,[status(thm)],[86, 30793])).
% 5.14/5.34 tff(30795,plain,
% 5.14/5.34 ($false),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[30686, 30794])).
% 5.14/5.34 tff(30796,plain,(b(s(elem!1), z) | b(s(s(s(s(z)))), s(s(z))) | (z = elem!1) | (~b(s(elem!1), s(s(z)))) | (s(s(z)) = elem!1) | (s(s(z)) = s(elem!1)) | b(z, s(s(z))) | b(s(s(z)), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.34 tff(30797,plain,
% 5.14/5.34 (b(s(elem!1), z)),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[30796, 507, 86, 1070, 12, 1060, 28501, 105])).
% 5.14/5.34 tff(30798,plain,
% 5.14/5.34 (b(s(s(s(s(s(z))))), z)),
% 5.14/5.34 inference(modus_ponens,[status(thm)],[30797, 30196])).
% 5.14/5.34 tff(30799,plain,
% 5.14/5.34 (s(s(s(s(s(z))))) = s(elem!1)),
% 5.14/5.34 inference(symmetry,[status(thm)],[30195])).
% 5.14/5.34 tff(30800,plain,
% 5.14/5.34 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 5.14/5.34 inference(monotonicity,[status(thm)],[30799])).
% 5.14/5.34 tff(30801,plain,
% 5.14/5.34 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 5.14/5.34 inference(symmetry,[status(thm)],[30800])).
% 5.14/5.34 tff(30802,plain,
% 5.14/5.34 (~b(s(s(z)), elem!1)),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[17684, 30194, 105])).
% 5.14/5.34 tff(30803,plain,
% 5.14/5.34 (b(z, s(s(s(s(s(s(s(z))))))))),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[30676, 30802, 28501, 30250, 86])).
% 5.14/5.34 tff(30804,plain,
% 5.14/5.34 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[14677, 30803, 29994, 27224, 30122, 1070, 1060])).
% 5.14/5.34 tff(30805,plain,
% 5.14/5.34 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 5.14/5.34 inference(monotonicity,[status(thm)],[30799])).
% 5.14/5.34 tff(30806,plain,
% 5.14/5.34 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 5.14/5.34 inference(monotonicity,[status(thm)],[30195])).
% 5.14/5.34 tff(30807,plain,
% 5.14/5.34 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 5.14/5.34 inference(monotonicity,[status(thm)],[30806])).
% 5.14/5.34 tff(30808,plain,
% 5.14/5.34 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))),
% 5.14/5.34 inference(monotonicity,[status(thm)],[30807, 30195])).
% 5.14/5.34 tff(30809,plain,
% 5.14/5.34 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 5.14/5.34 inference(transitivity,[status(thm)],[30808, 4625])).
% 5.14/5.34 tff(30810,plain,
% 5.14/5.34 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 5.14/5.34 inference(transitivity,[status(thm)],[30809, 30805])).
% 5.14/5.34 tff(30811,plain,
% 5.14/5.34 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 5.14/5.34 inference(monotonicity,[status(thm)],[30810])).
% 5.14/5.34 tff(30812,plain,
% 5.14/5.34 (s(s(s(s(z)))) = elem!1),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[325, 30194])).
% 5.14/5.34 tff(30813,plain,
% 5.14/5.34 (~(s(s(elem!1)) = elem!1)),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[338, 30812, 12])).
% 5.14/5.34 tff(30814,plain,
% 5.14/5.34 (~(s(s(s(elem!1))) = s(elem!1))),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[348, 30813])).
% 5.14/5.34 tff(30815,plain,
% 5.14/5.34 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 5.14/5.34 inference(modus_ponens,[status(thm)],[30814, 30811])).
% 5.14/5.34 tff(30816,plain,
% 5.14/5.34 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[395, 30815, 30804])).
% 5.14/5.34 tff(30817,plain,
% 5.14/5.34 (~r(s(elem!1), s(s(s(s(z)))))),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[25119, 30816])).
% 5.14/5.34 tff(30818,plain,
% 5.14/5.34 (b(s(elem!1), s(s(s(s(z)))))),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[1084, 30817, 30687])).
% 5.14/5.34 tff(30819,plain,
% 5.14/5.34 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 5.14/5.34 inference(modus_ponens,[status(thm)],[30818, 30801])).
% 5.14/5.34 tff(30820,plain,
% 5.14/5.34 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.34 inference(monotonicity,[status(thm)],[30194])).
% 5.14/5.34 tff(30821,plain,
% 5.14/5.34 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[24769, 30191, 30250])).
% 5.14/5.34 tff(30822,plain,
% 5.14/5.34 (~(s(elem!1) = elem!1)),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[672, 30813])).
% 5.14/5.34 tff(30823,plain,
% 5.14/5.34 (~(elem!1 = s(elem!1))),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[748, 30822])).
% 5.14/5.34 tff(30824,plain,
% 5.14/5.34 (r(s(s(z)), elem!1)),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[448, 30802, 12])).
% 5.14/5.34 tff(30825,plain,
% 5.14/5.34 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 5.14/5.34 inference(monotonicity,[status(thm)],[30194])).
% 5.14/5.34 tff(30826,plain,
% 5.14/5.34 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), elem!1)),
% 5.14/5.34 inference(symmetry,[status(thm)],[30825])).
% 5.14/5.34 tff(30827,plain,
% 5.14/5.34 (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)))))),
% 5.14/5.34 inference(monotonicity,[status(thm)],[30807])).
% 5.14/5.34 tff(30828,plain,
% 5.14/5.34 (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)))))),
% 5.14/5.34 inference(symmetry,[status(thm)],[30827])).
% 5.14/5.34 tff(30829,plain,
% 5.14/5.34 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), elem!1)),
% 5.14/5.34 inference(transitivity,[status(thm)],[30828, 30826])).
% 5.14/5.34 tff(30830,plain,
% 5.14/5.34 (r(s(s(s(elem!1))), elem!1)),
% 5.14/5.34 inference(modus_ponens,[status(thm)],[24592, 30829])).
% 5.14/5.34 tff(30831,plain,
% 5.14/5.34 (~r(s(elem!1), elem!1)),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[12991, 30830, 10794, 30824, 30814])).
% 5.14/5.34 tff(30832,plain,
% 5.14/5.34 (b(s(elem!1), elem!1)),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[677, 30831, 30822])).
% 5.14/5.34 tff(30833,plain,
% 5.14/5.34 (~b(elem!1, s(elem!1))),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[2429, 30832, 30797, 30204, 30193])).
% 5.14/5.34 tff(30834,plain,
% 5.14/5.34 (r(elem!1, s(elem!1))),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[756, 30833, 30823])).
% 5.14/5.34 tff(30835,plain,
% 5.14/5.34 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[2935, 30834, 30816])).
% 5.14/5.34 tff(30836,plain,
% 5.14/5.34 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[691, 30835, 30821])).
% 5.14/5.34 tff(30837,plain,
% 5.14/5.34 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.34 inference(modus_ponens,[status(thm)],[30836, 30820])).
% 5.14/5.34 tff(30838,plain,
% 5.14/5.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, 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(z))))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, 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(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 5.14/5.34 inference(rewrite,[status(thm)],[])).
% 5.14/5.34 tff(30839,plain,
% 5.14/5.34 (((~b(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))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 5.14/5.34 inference(rewrite,[status(thm)],[])).
% 5.14/5.34 tff(30840,plain,
% 5.14/5.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, 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(z))))), z)) | (~b(z, s(s(s(s(z))))))))),
% 5.14/5.34 inference(monotonicity,[status(thm)],[30839])).
% 5.14/5.34 tff(30841,plain,
% 5.14/5.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, 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(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 5.14/5.34 inference(transitivity,[status(thm)],[30840, 30838])).
% 5.14/5.34 tff(30842,plain,
% 5.14/5.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 5.14/5.34 inference(quant_inst,[status(thm)],[])).
% 5.14/5.34 tff(30843,plain,
% 5.14/5.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z))))))),
% 5.14/5.34 inference(modus_ponens,[status(thm)],[30842, 30841])).
% 5.14/5.34 tff(30844,plain,
% 5.14/5.34 ($false),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[30843, 178, 27212, 30837, 30803, 30819, 30798])).
% 5.14/5.34 tff(30845,plain,((~r(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (s(s(z)) = s(elem!1)) | (s(s(z)) = elem!1) | b(z, s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | b(s(s(z)), s(s(s(s(z))))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 5.14/5.34 tff(30846,plain,
% 5.14/5.34 (~r(elem!1, s(s(z)))),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[30845, 30189, 2311, 12, 28501, 86, 105, 30118])).
% 5.14/5.34 tff(30847,plain,
% 5.14/5.34 (b(elem!1, s(s(z)))),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[467, 30846, 312])).
% 5.14/5.34 tff(30848,plain,
% 5.14/5.34 (b(elem!1, s(s(z))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 5.14/5.34 inference(monotonicity,[status(thm)],[319])).
% 5.14/5.34 tff(30849,plain,
% 5.14/5.34 (b(s(s(s(s(z)))), s(s(z))) <=> b(elem!1, s(s(z)))),
% 5.14/5.34 inference(symmetry,[status(thm)],[30848])).
% 5.14/5.34 tff(30850,plain,
% 5.14/5.34 ((~b(s(s(s(s(z)))), s(s(z)))) <=> (~b(elem!1, s(s(z))))),
% 5.14/5.34 inference(monotonicity,[status(thm)],[30849])).
% 5.14/5.34 tff(30851,plain,
% 5.14/5.34 (~b(elem!1, s(s(z)))),
% 5.14/5.34 inference(modus_ponens,[status(thm)],[86, 30850])).
% 5.14/5.34 tff(30852,plain,
% 5.14/5.34 ($false),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[812, 30851])).
% 5.14/5.34 tff(30853,plain,((~(elem!1 = s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | b(s(s(s(s(z)))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.34 tff(30854,plain,
% 5.14/5.34 (~(elem!1 = s(s(s(s(z)))))),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[30853, 30847, 86])).
% 5.14/5.34 tff(30855,plain,
% 5.14/5.34 ($false),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[2508, 23052])).
% 5.14/5.34 tff(30856,plain,((~(s(s(s(z))) = elem!1)) | (s(s(s(s(z)))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.34 tff(30857,plain,
% 5.14/5.34 (~(s(s(s(z))) = elem!1)),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[30856, 30120])).
% 5.14/5.34 tff(30858,plain,
% 5.14/5.34 (b(s(s(z)), elem!1)),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[23429, 30854, 27212, 28500, 29994, 10794, 12, 30190])).
% 5.14/5.34 tff(30859,plain,
% 5.14/5.34 (b(s(s(s(z))), elem!1)),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[4981, 30702, 4970])).
% 5.14/5.34 tff(30860,plain,
% 5.14/5.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)))),
% 5.14/5.34 inference(rewrite,[status(thm)],[])).
% 5.14/5.34 tff(30861,plain,
% 5.14/5.34 (((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)))),
% 5.14/5.34 inference(rewrite,[status(thm)],[])).
% 5.14/5.34 tff(30862,plain,
% 5.14/5.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1))))),
% 5.14/5.34 inference(monotonicity,[status(thm)],[30861])).
% 5.14/5.34 tff(30863,plain,
% 5.14/5.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)))),
% 5.14/5.34 inference(transitivity,[status(thm)],[30862, 30860])).
% 5.14/5.34 tff(30864,plain,
% 5.14/5.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 5.14/5.34 inference(quant_inst,[status(thm)],[])).
% 5.14/5.34 tff(30865,plain,
% 5.14/5.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1))),
% 5.14/5.34 inference(modus_ponens,[status(thm)],[30864, 30863])).
% 5.14/5.34 tff(30866,plain,
% 5.14/5.34 ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[30865, 178, 817, 812, 4932])).
% 5.14/5.34 tff(30867,plain,
% 5.14/5.34 ($false),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[30866, 30228, 30859])).
% 5.14/5.34 tff(30868,plain,((~r(s(s(s(z))), z)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (s(s(s(z))) = elem!1) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.34 tff(30869,plain,
% 5.14/5.34 (~r(elem!1, z)),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[30868, 30858, 30154, 30134, 30857, 30847])).
% 5.14/5.34 tff(30870,plain,
% 5.14/5.34 (b(elem!1, z)),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[498, 30869, 30190])).
% 5.14/5.34 tff(30871,plain,
% 5.14/5.34 (b(s(s(z)), elem!1)),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[23429, 469, 27212, 28500, 29994, 147, 12, 290])).
% 5.14/5.34 tff(30872,plain,
% 5.14/5.34 (~r(elem!1, s(s(s(s(z)))))),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[30741, 701, 147, 817, 812])).
% 5.14/5.34 tff(30873,plain,
% 5.14/5.34 (b(elem!1, s(s(s(s(z)))))),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[483, 30872, 469])).
% 5.14/5.34 tff(30874,plain,
% 5.14/5.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))),
% 5.14/5.34 inference(rewrite,[status(thm)],[])).
% 5.14/5.34 tff(30875,plain,
% 5.14/5.34 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~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(z))), elem!1))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))),
% 5.14/5.34 inference(rewrite,[status(thm)],[])).
% 5.14/5.34 tff(30876,plain,
% 5.14/5.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~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(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1))))),
% 5.14/5.34 inference(monotonicity,[status(thm)],[30875])).
% 5.14/5.34 tff(30877,plain,
% 5.14/5.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~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(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))),
% 5.14/5.34 inference(transitivity,[status(thm)],[30876, 30874])).
% 5.14/5.34 tff(30878,plain,
% 5.14/5.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~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(z))), elem!1)))),
% 5.14/5.34 inference(quant_inst,[status(thm)],[])).
% 5.14/5.34 tff(30879,plain,
% 5.14/5.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1))),
% 5.14/5.34 inference(modus_ponens,[status(thm)],[30878, 30877])).
% 5.14/5.34 tff(30880,plain,
% 5.14/5.34 ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1))),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[30879, 178, 506, 28503, 28449])).
% 5.14/5.34 tff(30881,plain,
% 5.14/5.34 (~b(s(s(s(z))), elem!1)),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[30880, 30873])).
% 5.14/5.34 tff(30882,plain,
% 5.14/5.34 (r(s(s(s(z))), elem!1)),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[4981, 30881, 4970])).
% 5.14/5.34 tff(30883,plain,
% 5.14/5.34 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[11859, 817, 28447, 27396, 812])).
% 5.14/5.34 tff(30884,plain,
% 5.14/5.34 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[691, 701, 30883])).
% 5.14/5.34 tff(30885,plain,
% 5.14/5.34 ($false),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[22949, 118, 30884, 30882, 8216])).
% 5.14/5.34 tff(30886,plain,((elem!1 = s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (s(s(s(z))) = elem!1) | (~b(elem!1, z)) | (elem!1 = s(s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.34 tff(30887,plain,
% 5.14/5.34 ($false),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[30886, 30871, 469, 4970, 506, 8216, 147, 701, 812])).
% 5.14/5.34 tff(30888,plain,((elem!1 = s(s(s(s(z))))) | (s(s(s(z))) = elem!1) | (~b(elem!1, z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(z)))) | (s(s(z)) = elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 5.14/5.34 tff(30889,plain,
% 5.14/5.34 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[30888, 30870, 30857, 30158, 10794, 30854, 30847, 12, 30190])).
% 5.14/5.34 tff(30890,plain,
% 5.14/5.34 (~(s(s(elem!1)) = elem!1)),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[2510, 30889, 30120])).
% 5.14/5.34 tff(30891,plain,
% 5.14/5.34 (b(s(elem!1), z)),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[30796, 30189, 86, 30118, 12, 2311, 28501, 105])).
% 5.14/5.34 tff(30892,plain,
% 5.14/5.34 (~b(s(elem!1), elem!1)),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[686, 679, 643])).
% 5.14/5.34 tff(30893,plain,
% 5.14/5.34 (r(s(elem!1), elem!1)),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[677, 30892, 725])).
% 5.14/5.34 tff(30894,plain,
% 5.14/5.34 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.34 inference(modus_ponens,[status(thm)],[30893, 21925])).
% 5.14/5.34 tff(30895,plain,
% 5.14/5.34 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.34 inference(modus_ponens,[status(thm)],[30894, 21924])).
% 5.14/5.34 tff(30896,plain,
% 5.14/5.34 (b(s(elem!1), s(s(s(z)))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 5.14/5.34 inference(monotonicity,[status(thm)],[2823])).
% 5.14/5.34 tff(30897,plain,
% 5.14/5.34 ((~b(s(elem!1), s(s(s(z))))) <=> (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 5.14/5.34 inference(monotonicity,[status(thm)],[30896])).
% 5.14/5.34 tff(30898,plain,
% 5.14/5.34 (r(elem!1, s(s(s(s(z)))))),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[24769, 679, 3428])).
% 5.14/5.34 tff(30899,plain,
% 5.14/5.34 (b(z, elem!1)),
% 5.14/5.34 inference(modus_ponens,[status(thm)],[595, 4239])).
% 5.14/5.34 tff(30900,plain,
% 5.14/5.34 (~b(z, s(elem!1))),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[26790, 30899, 168, 853, 506, 30898, 679])).
% 5.14/5.34 tff(30901,plain,
% 5.14/5.34 (r(z, s(elem!1))),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[2351, 30900])).
% 5.14/5.34 tff(30902,plain,
% 5.14/5.34 (~r(s(s(z)), s(elem!1))),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[2341, 30901, 28500])).
% 5.14/5.34 tff(30903,plain,
% 5.14/5.34 (b(s(s(z)), s(elem!1))),
% 5.14/5.34 inference(unit_resolution,[status(thm)],[1067, 30902, 1060])).
% 5.14/5.34 tff(30904,plain,
% 5.14/5.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))))),
% 5.14/5.34 inference(rewrite,[status(thm)],[])).
% 5.14/5.34 tff(30905,plain,
% 5.14/5.34 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))))),
% 5.14/5.35 inference(rewrite,[status(thm)],[])).
% 5.14/5.35 tff(30906,plain,
% 5.14/5.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(s(z)))))))),
% 5.14/5.35 inference(monotonicity,[status(thm)],[30905])).
% 5.14/5.35 tff(30907,plain,
% 5.14/5.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))))),
% 5.14/5.35 inference(transitivity,[status(thm)],[30906, 30904])).
% 5.14/5.35 tff(30908,plain,
% 5.14/5.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))))),
% 5.14/5.35 inference(quant_inst,[status(thm)],[])).
% 5.14/5.35 tff(30909,plain,
% 5.14/5.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(s(z)))))),
% 5.14/5.35 inference(modus_ponens,[status(thm)],[30908, 30907])).
% 5.14/5.35 tff(30910,plain,
% 5.14/5.35 ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(s(z)))))),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[30909, 178, 1070, 5090, 4932])).
% 5.14/5.35 tff(30911,plain,
% 5.14/5.35 (~b(s(elem!1), s(s(s(z))))),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[30910, 30903])).
% 5.14/5.35 tff(30912,plain,
% 5.14/5.35 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 5.14/5.35 inference(modus_ponens,[status(thm)],[30911, 30897])).
% 5.14/5.35 tff(30913,plain,
% 5.14/5.35 (~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z))))),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[24777, 679, 23528])).
% 5.14/5.35 tff(30914,plain,
% 5.14/5.35 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[24830, 41, 30913, 30912])).
% 5.14/5.35 tff(30915,plain,
% 5.14/5.35 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 5.14/5.35 inference(rewrite,[status(thm)],[])).
% 5.14/5.35 tff(30916,plain,
% 5.14/5.35 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 5.14/5.35 inference(quant_inst,[status(thm)],[])).
% 5.14/5.35 tff(30917,plain,
% 5.14/5.35 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 5.14/5.35 inference(modus_ponens,[status(thm)],[30916, 30915])).
% 5.14/5.35 tff(30918,plain,
% 5.14/5.35 ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[30917, 118, 8216])).
% 5.14/5.35 tff(30919,plain,
% 5.14/5.35 ($false),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[30918, 30914, 30895])).
% 5.14/5.35 tff(30920,plain,((~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (s(s(z)) = s(elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = elem!1) | b(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(s(s(z)))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.35 tff(30921,plain,
% 5.14/5.35 (s(elem!1) = elem!1),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[30920, 30889, 30118, 30156, 30134, 2311, 30126, 30891, 30158, 30160, 30870, 30161, 23437, 30250])).
% 5.14/5.35 tff(30922,plain,
% 5.14/5.35 ($false),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[672, 30921, 30890])).
% 5.14/5.35 tff(30923,plain,(b(s(s(s(s(z)))), s(s(z))) | (s(s(z)) = elem!1) | b(z, s(s(z))) | b(s(s(z)), s(s(s(s(z))))) | (s(elem!1) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.35 tff(30924,plain,
% 5.14/5.35 (b(s(s(s(s(z)))), s(s(z)))),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[30923, 1056, 28501, 105, 12])).
% 5.14/5.35 tff(30925,plain,
% 5.14/5.35 (~r(elem!1, z)),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[8416, 13066, 29994])).
% 5.14/5.35 tff(30926,plain,
% 5.14/5.35 (s(elem!1) = s(s(s(s(z))))),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[11775, 28602, 27212, 29994, 28503, 363, 147])).
% 5.14/5.35 tff(30927,plain,
% 5.14/5.35 (~(z = elem!1)),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[25360, 30926])).
% 5.14/5.35 tff(30928,plain,
% 5.14/5.35 (b(z, elem!1)),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[585, 30927, 30203])).
% 5.14/5.35 tff(30929,plain,
% 5.14/5.35 (~(elem!1 = z)),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[2808, 30927])).
% 5.14/5.35 tff(30930,plain,
% 5.14/5.35 (b(elem!1, z)),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[498, 30929, 30192])).
% 5.14/5.35 tff(30931,plain,
% 5.14/5.35 (~(s(s(s(elem!1))) = s(elem!1))),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[13886, 30926])).
% 5.14/5.35 tff(30932,plain,
% 5.14/5.35 (~(elem!1 = s(s(elem!1)))),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[1539, 30931])).
% 5.14/5.35 tff(30933,plain,
% 5.14/5.35 (~(s(s(elem!1)) = elem!1)),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[1546, 30932])).
% 5.14/5.35 tff(30934,plain,
% 5.14/5.35 (~(s(elem!1) = elem!1)),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[672, 30933])).
% 5.14/5.35 tff(30935,plain,
% 5.14/5.35 ($false),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[17418, 30934, 30930, 28500, 450, 363, 30928])).
% 5.14/5.35 tff(30936,plain,((~r(s(elem!1), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.35 tff(30937,plain,
% 5.14/5.35 (~r(s(elem!1), s(s(z)))),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[30936, 13066, 147])).
% 5.14/5.35 tff(30938,plain,
% 5.14/5.35 (b(s(elem!1), s(s(z)))),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[421, 30937, 1056])).
% 5.14/5.35 tff(30939,plain,
% 5.14/5.35 (r(s(s(z)), elem!1)),
% 5.14/5.35 inference(modus_ponens,[status(thm)],[28500, 10720])).
% 5.14/5.35 tff(30940,plain,
% 5.14/5.35 (r(z, s(s(elem!1)))),
% 5.14/5.35 inference(modus_ponens,[status(thm)],[29994, 5224])).
% 5.14/5.35 tff(30941,plain,
% 5.14/5.35 (b(z, s(s(s(s(elem!1)))))),
% 5.14/5.35 inference(modus_ponens,[status(thm)],[27212, 12136])).
% 5.14/5.35 tff(30942,plain,
% 5.14/5.35 (b(s(s(s(s(elem!1)))), z)),
% 5.14/5.35 inference(modus_ponens,[status(thm)],[28503, 12302])).
% 5.14/5.35 tff(30943,plain,
% 5.14/5.35 (r(elem!1, s(s(elem!1)))),
% 5.14/5.35 inference(modus_ponens,[status(thm)],[29994, 12031])).
% 5.14/5.35 tff(30944,plain,
% 5.14/5.35 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[12331, 30943, 928, 12299, 24470, 30942, 30941, 30940])).
% 5.14/5.35 tff(30945,plain,
% 5.14/5.35 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[3409, 30944, 30627])).
% 5.14/5.35 tff(30946,plain,
% 5.14/5.35 (b(s(s(s(z))), s(s(z)))),
% 5.14/5.35 inference(modus_ponens,[status(thm)],[30945, 5221])).
% 5.14/5.35 tff(30947,plain,
% 5.14/5.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 5.14/5.35 inference(rewrite,[status(thm)],[])).
% 5.14/5.35 tff(30948,plain,
% 5.14/5.35 (((~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(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(z, s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 5.14/5.35 inference(rewrite,[status(thm)],[])).
% 5.14/5.35 tff(30949,plain,
% 5.14/5.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))))),
% 5.14/5.35 inference(monotonicity,[status(thm)],[30948])).
% 5.14/5.35 tff(30950,plain,
% 5.14/5.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 5.14/5.35 inference(transitivity,[status(thm)],[30949, 30947])).
% 5.14/5.35 tff(30951,plain,
% 5.14/5.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 5.14/5.35 inference(quant_inst,[status(thm)],[])).
% 5.14/5.35 tff(30952,plain,
% 5.14/5.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 5.14/5.35 inference(modus_ponens,[status(thm)],[30951, 30950])).
% 5.14/5.35 tff(30953,plain,
% 5.14/5.35 (~b(z, s(s(s(z))))),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[30952, 178, 27212, 202, 28449, 30946])).
% 5.14/5.35 tff(30954,plain,
% 5.14/5.35 (r(z, s(s(s(z))))),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[4920, 30953])).
% 5.14/5.35 tff(30955,plain,
% 5.14/5.35 (r(elem!1, s(s(s(elem!1))))),
% 5.14/5.35 inference(modus_ponens,[status(thm)],[30954, 10724])).
% 5.14/5.35 tff(30956,plain,
% 5.14/5.35 (~r(s(s(z)), s(s(s(elem!1))))),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[7973, 30955, 30939])).
% 5.14/5.35 tff(30957,plain,
% 5.14/5.35 (b(s(s(z)), s(s(s(elem!1))))),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[4223, 30956])).
% 5.14/5.35 tff(30958,plain,
% 5.14/5.35 (b(s(s(z)), s(s(s(z))))),
% 5.14/5.35 inference(modus_ponens,[status(thm)],[30957, 5240])).
% 5.14/5.35 tff(30959,plain,
% 5.14/5.35 (~b(s(s(s(z))), z)),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[30152, 30946, 147])).
% 5.14/5.35 tff(30960,plain,
% 5.14/5.35 (r(s(s(s(z))), z)),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[21073, 30959])).
% 5.14/5.35 tff(30961,plain,
% 5.14/5.35 (~(s(elem!1) = s(s(s(s(z)))))),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[25360, 12064])).
% 5.14/5.35 tff(30962,plain,
% 5.14/5.35 (r(z, s(s(s(elem!1))))),
% 5.14/5.35 inference(modus_ponens,[status(thm)],[30954, 10723])).
% 5.14/5.35 tff(30963,plain,
% 5.14/5.35 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[30606, 30962, 461, 28447, 928])).
% 5.14/5.35 tff(30964,plain,
% 5.14/5.35 (b(z, s(s(s(s(s(s(s(z))))))))),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[271, 30963])).
% 5.14/5.35 tff(30965,plain,
% 5.14/5.35 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[14677, 30964, 29994, 27396, 28447, 1070, 1060])).
% 5.14/5.35 tff(30966,plain,
% 5.14/5.35 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[30188, 30965, 147, 12064, 23528, 30961, 2857, 30960])).
% 5.14/5.35 tff(30967,plain,
% 5.14/5.35 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[20667, 30966])).
% 5.14/5.35 tff(30968,plain,
% 5.14/5.35 (~b(s(s(z)), s(s(s(z))))),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[21439, 30967, 27396, 28447, 30946])).
% 5.14/5.35 tff(30969,plain,
% 5.14/5.35 ($false),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[30968, 30958])).
% 5.14/5.35 tff(30970,plain,((~(elem!1 = z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (s(elem!1) = s(s(s(z)))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~b(s(elem!1), s(s(z)))) | (s(s(z)) = s(elem!1)) | b(elem!1, s(s(z))) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.35 tff(30971,plain,
% 5.14/5.35 (~(elem!1 = z)),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[30970, 30938, 23528, 13192, 147, 2311, 461, 202])).
% 5.14/5.35 tff(30972,plain,
% 5.14/5.35 (b(elem!1, z)),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[498, 30971, 30925])).
% 5.14/5.35 tff(30973,plain,
% 5.14/5.35 (~r(z, elem!1)),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[4862, 13066, 29994])).
% 5.14/5.35 tff(30974,plain,
% 5.14/5.35 (~(z = elem!1)),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[317, 30971])).
% 5.14/5.35 tff(30975,plain,
% 5.14/5.35 (b(z, elem!1)),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[585, 30974, 30973])).
% 5.14/5.35 tff(30976,plain,
% 5.14/5.35 ($false),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[12519, 178, 30975, 30972, 27212, 28503, 13068])).
% 5.14/5.35 tff(30977,plain,(b(elem!1, s(s(z))) | (s(elem!1) = s(s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (s(elem!1) = s(s(z))) | (elem!1 = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.35 tff(30978,plain,
% 5.14/5.35 (b(elem!1, s(s(z)))),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[30977, 30924, 10794, 23437, 1056, 312])).
% 5.14/5.35 tff(30979,plain,
% 5.14/5.35 (b(z, s(s(z))) <=> b(elem!1, s(s(z)))),
% 5.14/5.35 inference(monotonicity,[status(thm)],[13])).
% 5.14/5.35 tff(30980,plain,
% 5.14/5.35 (b(elem!1, s(s(z))) <=> b(z, s(s(z)))),
% 5.14/5.35 inference(symmetry,[status(thm)],[30979])).
% 5.14/5.35 tff(30981,plain,
% 5.14/5.35 (b(z, s(s(z)))),
% 5.14/5.35 inference(modus_ponens,[status(thm)],[812, 30980])).
% 5.14/5.35 tff(30982,plain,
% 5.14/5.35 ($false),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[28501, 30981])).
% 5.14/5.35 tff(30983,plain,((~(z = elem!1)) | b(z, s(s(z))) | (~b(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.35 tff(30984,plain,
% 5.14/5.35 (~(z = elem!1)),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[30983, 30978, 28501])).
% 5.14/5.35 tff(30985,plain,
% 5.14/5.35 (~(elem!1 = z)),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[2808, 30984])).
% 5.14/5.35 tff(30986,plain,
% 5.14/5.35 (r(s(elem!1), s(s(z))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 5.14/5.35 inference(monotonicity,[status(thm)],[29997])).
% 5.14/5.35 tff(30987,plain,
% 5.14/5.35 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 5.14/5.35 inference(symmetry,[status(thm)],[30986])).
% 5.14/5.35 tff(30988,plain,
% 5.14/5.35 ((~r(s(s(s(s(z)))), s(s(z)))) <=> (~r(s(elem!1), s(s(z))))),
% 5.14/5.35 inference(monotonicity,[status(thm)],[30987])).
% 5.14/5.35 tff(30989,plain,
% 5.14/5.35 (~r(s(s(s(s(z)))), s(s(z)))),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[30117, 305, 147, 12, 1056])).
% 5.14/5.35 tff(30990,plain,
% 5.14/5.35 (~r(s(elem!1), s(s(z)))),
% 5.14/5.35 inference(modus_ponens,[status(thm)],[30989, 30988])).
% 5.14/5.35 tff(30991,plain,
% 5.14/5.35 ($false),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[23076, 30990])).
% 5.14/5.35 tff(30992,plain,(b(s(elem!1), s(s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (s(s(z)) = elem!1) | (s(elem!1) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.35 tff(30993,plain,
% 5.14/5.35 (b(s(elem!1), s(s(z)))),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[30992, 1056, 12, 10794])).
% 5.14/5.35 tff(30994,plain,
% 5.14/5.35 (b(s(s(z)), elem!1)),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[23429, 2809, 27212, 28500, 29994, 147, 12, 30694])).
% 5.14/5.35 tff(30995,plain,
% 5.14/5.35 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[11848, 178, 817, 812, 27396, 28447])).
% 5.14/5.35 tff(30996,plain,
% 5.14/5.35 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[3444, 4245, 30995])).
% 5.14/5.35 tff(30997,plain,
% 5.14/5.35 (~r(s(s(s(s(z)))), elem!1)),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[25879, 30996])).
% 5.14/5.35 tff(30998,plain,
% 5.14/5.35 (b(s(s(s(s(z)))), elem!1)),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[3142, 30997, 551])).
% 5.14/5.35 tff(30999,plain,
% 5.14/5.35 ($false),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[11936, 178, 817, 812, 30998, 30873, 202])).
% 5.14/5.35 tff(31000,plain,((elem!1 = s(s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (elem!1 = s(s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.35 tff(31001,plain,
% 5.14/5.35 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[31000, 30994, 812, 202, 30694, 147])).
% 5.14/5.35 tff(31002,plain,
% 5.14/5.35 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 5.14/5.35 inference(monotonicity,[status(thm)],[31001])).
% 5.14/5.35 tff(31003,plain,
% 5.14/5.35 (s(s(s(s(s(s(s(s(z)))))))) = s(elem!1)),
% 5.14/5.35 inference(symmetry,[status(thm)],[31002])).
% 5.14/5.35 tff(31004,plain,
% 5.14/5.35 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z))))))))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 5.14/5.35 inference(monotonicity,[status(thm)],[31003])).
% 5.14/5.35 tff(31005,plain,
% 5.14/5.35 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))),
% 5.14/5.35 inference(symmetry,[status(thm)],[31004])).
% 5.14/5.35 tff(31006,plain,
% 5.14/5.35 (~(s(elem!1) = s(s(s(s(z)))))),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[16181, 31001])).
% 5.14/5.35 tff(31007,plain,
% 5.14/5.35 (~(s(s(s(s(z)))) = s(elem!1))),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[2168, 31006])).
% 5.14/5.35 tff(31008,plain,
% 5.14/5.35 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z))))))))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 5.14/5.35 inference(monotonicity,[status(thm)],[31003])).
% 5.14/5.35 tff(31009,plain,
% 5.14/5.35 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) <=> (~b(s(s(s(s(z)))), s(elem!1)))),
% 5.14/5.35 inference(monotonicity,[status(thm)],[31008])).
% 5.14/5.35 tff(31010,plain,
% 5.14/5.35 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 5.14/5.35 inference(monotonicity,[status(thm)],[31002])).
% 5.14/5.35 tff(31011,plain,
% 5.14/5.35 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.35 inference(monotonicity,[status(thm)],[31001])).
% 5.14/5.35 tff(31012,plain,
% 5.14/5.35 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[24574, 28503, 147])).
% 5.14/5.35 tff(31013,plain,
% 5.14/5.35 (r(elem!1, s(s(s(s(z)))))),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[24769, 31001, 31012])).
% 5.14/5.35 tff(31014,plain,
% 5.14/5.35 (~r(elem!1, s(elem!1))),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[27585, 31013, 12567, 31006, 28503])).
% 5.14/5.35 tff(31015,plain,
% 5.14/5.35 (~(elem!1 = s(s(s(elem!1))))),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[2859, 31001, 2857])).
% 5.14/5.35 tff(31016,plain,
% 5.14/5.35 (~(s(s(s(elem!1))) = elem!1)),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[2489, 31015])).
% 5.14/5.35 tff(31017,plain,
% 5.14/5.35 (~(s(elem!1) = elem!1)),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[2150, 31016])).
% 5.14/5.35 tff(31018,plain,
% 5.14/5.35 (r(s(elem!1), elem!1)),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[30697, 31017, 812, 1070, 31014, 30994])).
% 5.14/5.35 tff(31019,plain,
% 5.14/5.35 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.35 inference(modus_ponens,[status(thm)],[31018, 31011])).
% 5.14/5.35 tff(31020,plain,
% 5.14/5.35 (~r(s(elem!1), s(s(s(s(z)))))),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[25119, 31019])).
% 5.14/5.35 tff(31021,plain,
% 5.14/5.35 (b(s(elem!1), s(s(s(s(z)))))),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[1084, 31020, 31006])).
% 5.14/5.35 tff(31022,plain,
% 5.14/5.35 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 5.14/5.35 inference(modus_ponens,[status(thm)],[31021, 31010])).
% 5.14/5.35 tff(31023,plain,
% 5.14/5.35 (~r(s(elem!1), z)),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[13694, 31018, 12567])).
% 5.14/5.35 tff(31024,plain,
% 5.14/5.35 (b(s(elem!1), z)),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[774, 31023])).
% 5.14/5.35 tff(31025,plain,
% 5.14/5.35 (b(s(s(s(s(s(s(s(s(z)))))))), z)),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[24205, 31024, 31001])).
% 5.14/5.35 tff(31026,plain,
% 5.14/5.35 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[29015, 178, 27212, 28503, 31025, 31022])).
% 5.14/5.35 tff(31027,plain,
% 5.14/5.35 (~b(s(s(s(s(z)))), s(elem!1))),
% 5.14/5.35 inference(modus_ponens,[status(thm)],[31026, 31009])).
% 5.14/5.35 tff(31028,plain,
% 5.14/5.35 (r(s(s(s(s(z)))), s(elem!1))),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[2173, 31027, 31007])).
% 5.14/5.35 tff(31029,plain,
% 5.14/5.35 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))),
% 5.14/5.35 inference(modus_ponens,[status(thm)],[31028, 31005])).
% 5.14/5.35 tff(31030,plain,
% 5.14/5.35 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.35 inference(monotonicity,[status(thm)],[31003])).
% 5.14/5.35 tff(31031,plain,
% 5.14/5.35 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.35 inference(symmetry,[status(thm)],[31030])).
% 5.14/5.35 tff(31032,plain,
% 5.14/5.35 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.35 inference(modus_ponens,[status(thm)],[31019, 31031])).
% 5.14/5.35 tff(31033,plain,
% 5.14/5.35 (~b(z, s(s(s(elem!1))))),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[28814, 31013, 28500, 147, 12567, 27212, 28503, 31015, 30994, 2857, 812])).
% 5.14/5.35 tff(31034,plain,
% 5.14/5.35 (r(z, s(s(s(elem!1))))),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[2095, 31033])).
% 5.14/5.35 tff(31035,plain,
% 5.14/5.35 (~r(z, elem!1)),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[30052, 31034, 29994, 12567, 812, 31015, 30994])).
% 5.14/5.35 tff(31036,plain,
% 5.14/5.35 (b(z, elem!1)),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[585, 31035, 507])).
% 5.14/5.35 tff(31037,plain,
% 5.14/5.35 (b(z, s(s(s(s(s(s(s(z))))))))),
% 5.14/5.35 inference(unit_resolution,[status(thm)],[4243, 31036, 31001])).
% 5.14/5.35 tff(31038,plain,
% 5.14/5.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 5.14/5.35 inference(rewrite,[status(thm)],[])).
% 5.14/5.35 tff(31039,plain,
% 5.14/5.35 (((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, 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(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 5.14/5.35 inference(rewrite,[status(thm)],[])).
% 5.14/5.35 tff(31040,plain,
% 5.14/5.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))))),
% 5.14/5.35 inference(monotonicity,[status(thm)],[31039])).
% 5.14/5.35 tff(31041,plain,
% 5.14/5.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 5.14/5.35 inference(transitivity,[status(thm)],[31040, 31038])).
% 5.14/5.35 tff(31042,plain,
% 5.14/5.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))))),
% 5.14/5.35 inference(quant_inst,[status(thm)],[])).
% 5.14/5.35 tff(31043,plain,
% 5.14/5.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))),
% 5.14/5.36 inference(modus_ponens,[status(thm)],[31042, 31041])).
% 5.14/5.36 tff(31044,plain,
% 5.14/5.36 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[31043, 178, 27212, 202, 31037, 28447])).
% 5.14/5.36 tff(31045,plain,
% 5.14/5.36 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[222, 31044])).
% 5.14/5.36 tff(31046,plain,
% 5.14/5.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 5.14/5.36 inference(rewrite,[status(thm)],[])).
% 5.14/5.36 tff(31047,plain,
% 5.14/5.36 (((~r(s(s(s(s(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))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(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(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 5.14/5.36 inference(rewrite,[status(thm)],[])).
% 5.14/5.36 tff(31048,plain,
% 5.14/5.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))))),
% 5.14/5.36 inference(monotonicity,[status(thm)],[31047])).
% 5.14/5.36 tff(31049,plain,
% 5.14/5.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 5.14/5.36 inference(transitivity,[status(thm)],[31048, 31046])).
% 5.14/5.36 tff(31050,plain,
% 5.14/5.36 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))))),
% 5.14/5.36 inference(quant_inst,[status(thm)],[])).
% 5.14/5.36 tff(31051,plain,
% 5.14/5.36 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))),
% 5.14/5.36 inference(modus_ponens,[status(thm)],[31050, 31049])).
% 5.14/5.36 tff(31052,plain,
% 5.14/5.36 ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[31051, 118, 31045])).
% 5.14/5.36 tff(31053,plain,
% 5.14/5.36 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[31052, 31032])).
% 5.14/5.36 tff(31054,plain,
% 5.14/5.36 ($false),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[31053, 31029])).
% 5.14/5.36 tff(31055,plain,((z = elem!1) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (s(s(z)) = elem!1) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 5.14/5.36 tff(31056,plain,
% 5.14/5.36 (b(elem!1, z)),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[31055, 30984, 30978, 30993, 10794, 13192, 12, 30924])).
% 5.14/5.36 tff(31057,plain,
% 5.14/5.36 (b(elem!1, s(s(z)))),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[30977, 202, 147, 23437, 1056, 312])).
% 5.14/5.36 tff(31058,plain,
% 5.14/5.36 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[31000, 30871, 31057, 202, 469, 147])).
% 5.14/5.36 tff(31059,plain,
% 5.14/5.36 (r(elem!1, s(s(s(z)))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.14/5.36 inference(monotonicity,[status(thm)],[679])).
% 5.14/5.36 tff(31060,plain,
% 5.14/5.36 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 5.14/5.36 inference(monotonicity,[status(thm)],[16594])).
% 5.14/5.36 tff(31061,plain,
% 5.14/5.36 (~(elem!1 = s(s(s(z))))),
% 5.14/5.36 inference(modus_ponens,[status(thm)],[1104, 31060])).
% 5.14/5.36 tff(31062,plain,
% 5.14/5.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, 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(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, 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(elem!1, s(s(s(z))))))),
% 5.14/5.36 inference(rewrite,[status(thm)],[])).
% 5.14/5.36 tff(31063,plain,
% 5.14/5.36 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(elem!1, 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(elem!1, s(s(s(z))))))),
% 5.14/5.36 inference(rewrite,[status(thm)],[])).
% 5.14/5.36 tff(31064,plain,
% 5.14/5.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, 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(elem!1, s(s(s(z)))))))),
% 5.14/5.36 inference(monotonicity,[status(thm)],[31063])).
% 5.14/5.36 tff(31065,plain,
% 5.14/5.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, 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(elem!1, s(s(s(z))))))),
% 5.14/5.36 inference(transitivity,[status(thm)],[31064, 31062])).
% 5.14/5.36 tff(31066,plain,
% 5.14/5.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 5.14/5.36 inference(quant_inst,[status(thm)],[])).
% 5.14/5.36 tff(31067,plain,
% 5.14/5.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))),
% 5.14/5.36 inference(modus_ponens,[status(thm)],[31066, 31065])).
% 5.14/5.36 tff(31068,plain,
% 5.14/5.36 ((~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[31067, 178, 506, 27212, 1126])).
% 5.14/5.36 tff(31069,plain,
% 5.14/5.36 (~b(elem!1, s(s(s(z))))),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[31068, 1127])).
% 5.14/5.36 tff(31070,plain,
% 5.14/5.36 (r(elem!1, s(s(s(z))))),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[17275, 31069, 31061])).
% 5.14/5.36 tff(31071,plain,
% 5.14/5.36 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.14/5.36 inference(modus_ponens,[status(thm)],[31070, 31059])).
% 5.14/5.36 tff(31072,plain,
% 5.14/5.36 ($false),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[25911, 118, 24592, 27256, 31071])).
% 5.14/5.36 tff(31073,plain,((~b(s(s(s(z))), z)) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.36 tff(31074,plain,
% 5.14/5.36 (~b(s(s(s(z))), z)),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[31073, 31058, 506, 28449, 28503])).
% 5.14/5.36 tff(31075,plain,
% 5.14/5.36 (r(s(s(s(z))), z)),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[21073, 31074])).
% 5.14/5.36 tff(31076,plain,
% 5.14/5.36 (~r(s(s(s(z))), s(s(z)))),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[24599, 31075, 28500])).
% 5.14/5.36 tff(31077,plain,
% 5.14/5.36 (b(s(s(s(z))), s(s(z)))),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[4966, 31076])).
% 5.14/5.36 tff(31078,plain,
% 5.14/5.36 (b(s(elem!1), s(s(z)))),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[30992, 1056, 12, 147])).
% 5.14/5.36 tff(31079,plain,
% 5.14/5.36 (r(elem!1, s(s(s(s(z)))))),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[24769, 31058, 31012])).
% 5.14/5.36 tff(31080,plain,
% 5.14/5.36 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[25883, 31079])).
% 5.14/5.36 tff(31081,plain,
% 5.14/5.36 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.36 inference(monotonicity,[status(thm)],[679])).
% 5.14/5.36 tff(31082,plain,
% 5.14/5.36 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.14/5.36 inference(symmetry,[status(thm)],[31081])).
% 5.14/5.36 tff(31083,plain,
% 5.14/5.36 ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(z))))))))) <=> (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 5.14/5.36 inference(monotonicity,[status(thm)],[31082])).
% 5.14/5.36 tff(31084,plain,
% 5.14/5.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 5.14/5.36 inference(rewrite,[status(thm)],[])).
% 5.14/5.36 tff(31085,plain,
% 5.14/5.36 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 5.14/5.36 inference(rewrite,[status(thm)],[])).
% 5.14/5.36 tff(31086,plain,
% 5.14/5.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 5.14/5.36 inference(monotonicity,[status(thm)],[31085])).
% 5.14/5.36 tff(31087,plain,
% 5.14/5.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 5.14/5.36 inference(transitivity,[status(thm)],[31086, 31084])).
% 5.14/5.36 tff(31088,plain,
% 5.14/5.36 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(z))))))))))),
% 5.14/5.36 inference(quant_inst,[status(thm)],[])).
% 5.14/5.36 tff(31089,plain,
% 5.14/5.36 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 5.14/5.36 inference(modus_ponens,[status(thm)],[31088, 31087])).
% 5.14/5.36 tff(31090,plain,
% 5.14/5.36 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[31089, 118, 24592])).
% 5.14/5.36 tff(31091,plain,
% 5.14/5.36 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.14/5.36 inference(modus_ponens,[status(thm)],[31090, 31083])).
% 5.14/5.36 tff(31092,plain,
% 5.14/5.36 (b(s(s(s(s(s(s(s(z))))))), z)),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[28842, 679, 506])).
% 5.14/5.36 tff(31093,plain,
% 5.14/5.36 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[14677, 595, 29994, 166, 1146, 1070, 2311])).
% 5.14/5.36 tff(31094,plain,
% 5.14/5.36 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[722, 31093, 31092, 31091, 506, 595, 323, 644])).
% 5.14/5.36 tff(31095,plain,
% 5.14/5.36 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.36 inference(modus_ponens,[status(thm)],[31094, 21924])).
% 5.14/5.36 tff(31096,plain,
% 5.14/5.36 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[13303, 178, 27212, 168, 595, 31092])).
% 5.14/5.36 tff(31097,plain,
% 5.14/5.36 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[222, 31096])).
% 5.14/5.36 tff(31098,plain,
% 5.14/5.36 ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[31051, 118, 31097])).
% 5.14/5.36 tff(31099,plain,
% 5.14/5.36 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[31098, 31095])).
% 5.14/5.36 tff(31100,plain,
% 5.14/5.36 (~r(s(s(s(s(z)))), s(elem!1))),
% 5.14/5.36 inference(modus_ponens,[status(thm)],[31099, 19973])).
% 5.14/5.36 tff(31101,plain,
% 5.14/5.36 (b(s(s(s(s(z)))), s(elem!1))),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[2173, 31100, 16183])).
% 5.14/5.36 tff(31102,plain,
% 5.14/5.36 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))),
% 5.14/5.36 inference(modus_ponens,[status(thm)],[31101, 15449])).
% 5.14/5.36 tff(31103,plain,
% 5.14/5.36 ((s(s(z)) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(s(z)) = s(elem!1))),
% 5.14/5.36 inference(monotonicity,[status(thm)],[11730])).
% 5.14/5.36 tff(31104,plain,
% 5.14/5.36 ((s(s(z)) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(elem!1) = s(s(z)))),
% 5.14/5.36 inference(transitivity,[status(thm)],[31103, 1358])).
% 5.14/5.36 tff(31105,plain,
% 5.14/5.36 ((s(elem!1) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(s(s(s(z)))))))))),
% 5.14/5.36 inference(symmetry,[status(thm)],[31104])).
% 5.14/5.36 tff(31106,plain,
% 5.14/5.36 ((~(s(elem!1) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(s(s(s(s(z))))))))))),
% 5.14/5.36 inference(monotonicity,[status(thm)],[31105])).
% 5.14/5.36 tff(31107,plain,
% 5.14/5.36 (~(s(s(z)) = s(s(s(s(s(s(s(s(z)))))))))),
% 5.14/5.36 inference(modus_ponens,[status(thm)],[1056, 31106])).
% 5.14/5.36 tff(31108,plain,
% 5.14/5.36 (~r(s(elem!1), s(s(s(s(z)))))),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[25119, 31094])).
% 5.14/5.36 tff(31109,plain,
% 5.14/5.36 (b(s(elem!1), s(s(s(s(z)))))),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[1084, 31108, 16182])).
% 5.14/5.36 tff(31110,plain,
% 5.14/5.36 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 5.14/5.36 inference(modus_ponens,[status(thm)],[31109, 26257])).
% 5.14/5.36 tff(31111,plain,
% 5.14/5.36 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z))),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[29015, 178, 27212, 168, 31110])).
% 5.14/5.36 tff(31112,plain,
% 5.14/5.36 (~b(s(s(s(s(s(s(s(s(z)))))))), z)),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[31111, 31102])).
% 5.14/5.36 tff(31113,plain,
% 5.14/5.36 (r(s(s(s(s(s(s(s(s(z)))))))), z)),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[16121, 41, 16118, 31112])).
% 5.14/5.36 tff(31114,plain,
% 5.14/5.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))),
% 5.14/5.36 inference(rewrite,[status(thm)],[])).
% 5.14/5.36 tff(31115,plain,
% 5.14/5.36 (((~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))),
% 5.14/5.36 inference(rewrite,[status(thm)],[])).
% 5.14/5.36 tff(31116,plain,
% 5.14/5.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z))))))))))))),
% 5.14/5.36 inference(monotonicity,[status(thm)],[31115])).
% 5.14/5.36 tff(31117,plain,
% 5.14/5.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))),
% 5.14/5.36 inference(transitivity,[status(thm)],[31116, 31114])).
% 5.14/5.36 tff(31118,plain,
% 5.14/5.36 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))),
% 5.14/5.36 inference(quant_inst,[status(thm)],[])).
% 5.14/5.36 tff(31119,plain,
% 5.14/5.36 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z))))))))))),
% 5.14/5.36 inference(modus_ponens,[status(thm)],[31118, 31117])).
% 5.14/5.36 tff(31120,plain,
% 5.14/5.36 (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[31119, 118, 28500, 31113])).
% 5.14/5.36 tff(31121,plain,
% 5.14/5.36 ((s(s(z)) = s(s(s(s(s(s(s(s(z))))))))) | b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[26990, 41, 31120])).
% 5.14/5.36 tff(31122,plain,
% 5.14/5.36 (b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[31121, 31107])).
% 5.14/5.36 tff(31123,plain,
% 5.14/5.36 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 5.14/5.36 inference(modus_ponens,[status(thm)],[1070, 11737])).
% 5.14/5.36 tff(31124,plain,
% 5.14/5.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 5.14/5.36 inference(rewrite,[status(thm)],[])).
% 5.14/5.36 tff(31125,plain,
% 5.14/5.36 (((~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 5.14/5.36 inference(rewrite,[status(thm)],[])).
% 5.14/5.36 tff(31126,plain,
% 5.14/5.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))))),
% 5.14/5.36 inference(monotonicity,[status(thm)],[31125])).
% 5.14/5.36 tff(31127,plain,
% 5.14/5.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 5.14/5.36 inference(transitivity,[status(thm)],[31126, 31124])).
% 5.14/5.36 tff(31128,plain,
% 5.14/5.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 5.14/5.36 inference(quant_inst,[status(thm)],[])).
% 5.14/5.36 tff(31129,plain,
% 5.14/5.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))),
% 5.14/5.36 inference(modus_ponens,[status(thm)],[31128, 31127])).
% 5.14/5.36 tff(31130,plain,
% 5.14/5.36 ($false),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[31129, 178, 202, 31123, 31110, 31122, 31102])).
% 5.14/5.36 tff(31131,plain,((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (s(elem!1) = s(s(z))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (s(s(s(s(z)))) = elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(elem!1), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.36 tff(31132,plain,
% 5.14/5.36 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[31131, 31058, 1056, 202, 28503, 506, 551, 31080, 27396, 28447, 31078])).
% 5.14/5.36 tff(31133,plain,
% 5.14/5.36 (r(z, s(s(s(s(s(s(s(z))))))))),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[271, 31132])).
% 5.14/5.36 tff(31134,plain,
% 5.14/5.36 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[21520, 31133, 28449, 28503, 27212])).
% 5.14/5.36 tff(31135,plain,
% 5.14/5.36 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[20667, 31134])).
% 5.14/5.36 tff(31136,plain,
% 5.14/5.36 (~b(s(s(z)), s(s(s(z))))),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[21439, 31077, 27396, 28447, 31135])).
% 5.14/5.36 tff(31137,plain,
% 5.14/5.36 (r(s(s(z)), s(s(s(z))))),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[5088, 31136])).
% 5.14/5.36 tff(31138,plain,
% 5.14/5.36 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[24478, 31137, 147])).
% 5.14/5.36 tff(31139,plain,
% 5.14/5.36 (b(s(s(s(s(z)))), s(s(s(z))))),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[11185, 31138])).
% 5.14/5.36 tff(31140,plain,
% 5.14/5.36 (~b(z, s(s(s(z))))),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[24318, 31139, 27212, 202, 31077])).
% 5.14/5.36 tff(31141,plain,
% 5.14/5.36 (r(z, s(s(s(z))))),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[4920, 31140])).
% 5.14/5.36 tff(31142,plain,
% 5.14/5.36 ($false),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[29988, 118, 28500, 31137, 31141])).
% 5.14/5.36 tff(31143,plain,((elem!1 = s(s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, z)) | (s(elem!1) = s(s(z))) | (s(s(z)) = elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 5.14/5.36 tff(31144,plain,
% 5.14/5.36 (elem!1 = s(s(s(s(z))))),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[31143, 30924, 10794, 31056, 1056, 12, 30985])).
% 5.14/5.36 tff(31145,plain,
% 5.14/5.36 (s(elem!1) = s(s(s(s(s(z)))))),
% 5.14/5.36 inference(monotonicity,[status(thm)],[31144])).
% 5.14/5.36 tff(31146,plain,
% 5.14/5.36 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 5.14/5.36 inference(monotonicity,[status(thm)],[31145])).
% 5.14/5.36 tff(31147,plain,
% 5.14/5.36 ((~b(s(s(s(z))), s(elem!1))) <=> (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 5.14/5.36 inference(monotonicity,[status(thm)],[31146])).
% 5.14/5.36 tff(31148,plain,
% 5.14/5.36 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(s(s(z)))))),
% 5.14/5.36 inference(monotonicity,[status(thm)],[31144])).
% 5.14/5.36 tff(31149,plain,
% 5.14/5.36 ((s(elem!1) = elem!1) <=> (s(s(s(s(z)))) = s(elem!1))),
% 5.14/5.36 inference(transitivity,[status(thm)],[31148, 2163])).
% 5.14/5.36 tff(31150,plain,
% 5.14/5.36 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(s(s(z)))))),
% 5.14/5.36 inference(transitivity,[status(thm)],[31149, 2164])).
% 5.14/5.36 tff(31151,plain,
% 5.14/5.36 ((~(s(elem!1) = elem!1)) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 5.14/5.36 inference(monotonicity,[status(thm)],[31150])).
% 5.14/5.36 tff(31152,plain,
% 5.14/5.36 (s(s(s(s(z)))) = elem!1),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[325, 31144])).
% 5.14/5.36 tff(31153,plain,
% 5.14/5.36 (~(s(s(elem!1)) = elem!1)),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[338, 31152, 12])).
% 5.14/5.36 tff(31154,plain,
% 5.14/5.36 (~(s(elem!1) = elem!1)),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[672, 31153])).
% 5.14/5.36 tff(31155,plain,
% 5.14/5.36 (~(s(elem!1) = s(s(s(s(z)))))),
% 5.14/5.36 inference(modus_ponens,[status(thm)],[31154, 31151])).
% 5.14/5.36 tff(31156,plain,
% 5.14/5.36 (s(s(s(s(s(z))))) = s(elem!1)),
% 5.14/5.36 inference(symmetry,[status(thm)],[31145])).
% 5.14/5.36 tff(31157,plain,
% 5.14/5.36 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 5.14/5.36 inference(monotonicity,[status(thm)],[31156])).
% 5.14/5.36 tff(31158,plain,
% 5.14/5.36 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 5.14/5.36 inference(monotonicity,[status(thm)],[31145])).
% 5.14/5.36 tff(31159,plain,
% 5.14/5.36 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 5.14/5.36 inference(monotonicity,[status(thm)],[31158])).
% 5.14/5.36 tff(31160,plain,
% 5.14/5.36 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))),
% 5.14/5.36 inference(monotonicity,[status(thm)],[31159, 31145])).
% 5.14/5.36 tff(31161,plain,
% 5.14/5.36 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 5.14/5.36 inference(transitivity,[status(thm)],[31160, 4625])).
% 5.14/5.36 tff(31162,plain,
% 5.14/5.36 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 5.14/5.36 inference(transitivity,[status(thm)],[31161, 31157])).
% 5.14/5.36 tff(31163,plain,
% 5.14/5.36 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 5.14/5.36 inference(monotonicity,[status(thm)],[31162])).
% 5.14/5.36 tff(31164,plain,
% 5.14/5.36 (~(s(s(s(elem!1))) = s(elem!1))),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[348, 31153])).
% 5.14/5.36 tff(31165,plain,
% 5.14/5.36 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 5.14/5.36 inference(modus_ponens,[status(thm)],[31164, 31163])).
% 5.14/5.36 tff(31166,plain,
% 5.14/5.36 (~b(s(s(z)), elem!1)),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[17684, 31144, 105])).
% 5.14/5.36 tff(31167,plain,
% 5.14/5.36 (r(s(s(z)), elem!1)),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[448, 31166, 12])).
% 5.14/5.36 tff(31168,plain,
% 5.14/5.36 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 5.14/5.36 inference(monotonicity,[status(thm)],[31144])).
% 5.14/5.36 tff(31169,plain,
% 5.14/5.36 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), elem!1)),
% 5.14/5.36 inference(symmetry,[status(thm)],[31168])).
% 5.14/5.36 tff(31170,plain,
% 5.14/5.36 (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)))))),
% 5.14/5.36 inference(monotonicity,[status(thm)],[31159])).
% 5.14/5.36 tff(31171,plain,
% 5.14/5.36 (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)))))),
% 5.14/5.36 inference(symmetry,[status(thm)],[31170])).
% 5.14/5.36 tff(31172,plain,
% 5.14/5.36 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), elem!1)),
% 5.14/5.36 inference(transitivity,[status(thm)],[31171, 31169])).
% 5.14/5.36 tff(31173,plain,
% 5.14/5.36 (r(s(s(s(elem!1))), elem!1)),
% 5.14/5.36 inference(modus_ponens,[status(thm)],[24592, 31172])).
% 5.14/5.36 tff(31174,plain,
% 5.14/5.36 (~r(s(elem!1), elem!1)),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[12991, 31173, 10794, 31167, 31164])).
% 5.14/5.36 tff(31175,plain,
% 5.14/5.36 (b(s(elem!1), elem!1)),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[677, 31174, 31154])).
% 5.14/5.36 tff(31176,plain,
% 5.14/5.36 (~(elem!1 = s(elem!1))),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[748, 31154])).
% 5.14/5.36 tff(31177,plain,
% 5.14/5.36 (~r(z, elem!1)),
% 5.14/5.36 inference(unit_resolution,[status(thm)],[8412, 31167, 29994])).
% 5.14/5.37 tff(31178,plain,
% 5.14/5.37 (b(z, elem!1)),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[585, 31177, 30984])).
% 5.14/5.37 tff(31179,plain,
% 5.14/5.37 (~r(s(s(z)), s(elem!1))),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[27961, 31175, 29994, 31056, 31178, 31144, 31176, 10794])).
% 5.14/5.37 tff(31180,plain,
% 5.14/5.37 (b(s(s(z)), s(elem!1))),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[1067, 31179, 2311])).
% 5.14/5.37 tff(31181,plain,
% 5.14/5.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 5.14/5.37 inference(rewrite,[status(thm)],[])).
% 5.14/5.37 tff(31182,plain,
% 5.14/5.37 (((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 5.14/5.37 inference(rewrite,[status(thm)],[])).
% 5.14/5.37 tff(31183,plain,
% 5.14/5.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))))),
% 5.14/5.37 inference(monotonicity,[status(thm)],[31182])).
% 5.14/5.37 tff(31184,plain,
% 5.14/5.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 5.14/5.37 inference(transitivity,[status(thm)],[31183, 31181])).
% 5.14/5.37 tff(31185,plain,
% 5.14/5.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))))),
% 5.14/5.37 inference(quant_inst,[status(thm)],[])).
% 5.14/5.37 tff(31186,plain,
% 5.14/5.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 5.14/5.37 inference(modus_ponens,[status(thm)],[31185, 31184])).
% 5.14/5.37 tff(31187,plain,
% 5.14/5.37 ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[31186, 178, 30978, 30993, 27224, 30122])).
% 5.14/5.37 tff(31188,plain,
% 5.14/5.37 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[31187, 31180, 31175])).
% 5.14/5.37 tff(31189,plain,
% 5.14/5.37 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[395, 31188, 31165])).
% 5.14/5.37 tff(31190,plain,
% 5.14/5.37 (~r(s(elem!1), s(s(s(s(z)))))),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[25119, 31189])).
% 5.14/5.37 tff(31191,plain,
% 5.14/5.37 (b(s(elem!1), s(s(s(s(z)))))),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[1084, 31190, 31155])).
% 5.14/5.37 tff(31192,plain,
% 5.14/5.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))))),
% 5.14/5.37 inference(rewrite,[status(thm)],[])).
% 5.14/5.37 tff(31193,plain,
% 5.14/5.37 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))))),
% 5.14/5.37 inference(rewrite,[status(thm)],[])).
% 5.14/5.37 tff(31194,plain,
% 5.14/5.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1)))))),
% 5.14/5.37 inference(monotonicity,[status(thm)],[31193])).
% 5.14/5.37 tff(31195,plain,
% 5.14/5.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))))),
% 5.14/5.37 inference(transitivity,[status(thm)],[31194, 31192])).
% 5.14/5.37 tff(31196,plain,
% 5.14/5.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))))),
% 5.14/5.37 inference(quant_inst,[status(thm)],[])).
% 5.14/5.37 tff(31197,plain,
% 5.14/5.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1)))),
% 5.14/5.37 inference(modus_ponens,[status(thm)],[31196, 31195])).
% 5.14/5.37 tff(31198,plain,
% 5.14/5.37 ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1)))),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[31197, 178, 30993, 30924, 30124])).
% 5.14/5.37 tff(31199,plain,
% 5.14/5.37 (~b(s(s(s(z))), s(elem!1))),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[31198, 31191])).
% 5.14/5.37 tff(31200,plain,
% 5.14/5.37 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 5.14/5.37 inference(modus_ponens,[status(thm)],[31199, 31147])).
% 5.14/5.37 tff(31201,plain,
% 5.14/5.37 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[9830, 41, 11413, 31200])).
% 5.14/5.37 tff(31202,plain,
% 5.14/5.37 (r(z, s(elem!1)) <=> r(z, s(s(s(s(s(z))))))),
% 5.14/5.37 inference(monotonicity,[status(thm)],[31145])).
% 5.14/5.37 tff(31203,plain,
% 5.14/5.37 ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[14207, 178, 30993, 27212, 30924])).
% 5.14/5.37 tff(31204,plain,
% 5.14/5.37 (~b(z, s(elem!1))),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[31203, 31191])).
% 5.14/5.37 tff(31205,plain,
% 5.14/5.37 (r(z, s(elem!1))),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[2351, 31204])).
% 5.14/5.37 tff(31206,plain,
% 5.14/5.37 (r(z, s(s(s(s(s(z))))))),
% 5.14/5.37 inference(modus_ponens,[status(thm)],[31205, 31202])).
% 5.14/5.37 tff(31207,plain,
% 5.14/5.37 (~r(s(s(s(z))), z)),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[27409, 118, 31206, 31201])).
% 5.14/5.37 tff(31208,plain,
% 5.14/5.37 (b(s(s(s(z))), z)),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[21073, 31207])).
% 5.14/5.37 tff(31209,plain,
% 5.14/5.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 5.14/5.37 inference(rewrite,[status(thm)],[])).
% 5.14/5.37 tff(31210,plain,
% 5.14/5.37 (((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 5.14/5.37 inference(rewrite,[status(thm)],[])).
% 5.14/5.37 tff(31211,plain,
% 5.14/5.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 5.14/5.37 inference(monotonicity,[status(thm)],[31210])).
% 5.14/5.37 tff(31212,plain,
% 5.14/5.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 5.14/5.37 inference(transitivity,[status(thm)],[31211, 31209])).
% 5.14/5.37 tff(31213,plain,
% 5.14/5.37 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))))),
% 5.14/5.37 inference(quant_inst,[status(thm)],[])).
% 5.14/5.37 tff(31214,plain,
% 5.14/5.37 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 5.14/5.37 inference(modus_ponens,[status(thm)],[31213, 31212])).
% 5.14/5.37 tff(31215,plain,
% 5.14/5.37 (~r(z, s(s(s(z))))),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[31214, 118, 31206, 31201])).
% 5.14/5.37 tff(31216,plain,
% 5.14/5.37 (b(z, s(s(s(z))))),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[4920, 31215])).
% 5.14/5.37 tff(31217,plain,
% 5.14/5.37 ($false),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[21518, 178, 27212, 30126, 30124, 31216, 31208])).
% 5.14/5.37 tff(31218,plain,((s(elem!1) = s(s(z))) | (s(s(z)) = elem!1) | b(s(s(z)), s(s(s(s(z))))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.37 tff(31219,plain,
% 5.14/5.37 (s(elem!1) = s(s(z))),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[31218, 12, 105, 28501])).
% 5.14/5.37 tff(31220,plain,
% 5.14/5.37 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 5.14/5.37 inference(monotonicity,[status(thm)],[31219])).
% 5.14/5.37 tff(31221,plain,
% 5.14/5.37 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 5.14/5.37 inference(symmetry,[status(thm)],[31220])).
% 5.14/5.37 tff(31222,plain,
% 5.14/5.37 (s(z) = elem!1),
% 5.14/5.37 inference(transitivity,[status(thm)],[71, 31221, 304])).
% 5.14/5.37 tff(31223,plain,
% 5.14/5.37 (b(s(s(s(s(s(s(s(z))))))), s(z)) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.14/5.37 inference(monotonicity,[status(thm)],[31222])).
% 5.14/5.37 tff(31224,plain,
% 5.14/5.37 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), s(z))),
% 5.14/5.37 inference(symmetry,[status(thm)],[31223])).
% 5.14/5.37 tff(31225,plain,
% 5.14/5.37 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[2832, 31219])).
% 5.14/5.37 tff(31226,plain,
% 5.14/5.37 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[703, 31225])).
% 5.14/5.37 tff(31227,plain,
% 5.14/5.37 (~(elem!1 = s(s(s(s(z)))))),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[11438, 31219])).
% 5.14/5.37 tff(31228,plain,
% 5.14/5.37 (~(z = elem!1)),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[28525, 31219])).
% 5.14/5.37 tff(31229,plain,
% 5.14/5.37 (~(elem!1 = z)),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[2808, 31228])).
% 5.14/5.37 tff(31230,plain,
% 5.14/5.37 (b(s(s(z)), elem!1)),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[23429, 31229, 27212, 28500, 29994, 10794, 12, 31227])).
% 5.14/5.37 tff(31231,plain,
% 5.14/5.37 (~r(elem!1, s(s(s(s(z)))))),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[5670, 450, 147])).
% 5.14/5.37 tff(31232,plain,
% 5.14/5.37 (b(elem!1, s(s(s(s(z)))))),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[483, 31231, 25873])).
% 5.14/5.37 tff(31233,plain,
% 5.14/5.37 (b(s(z), s(s(s(s(z)))))),
% 5.14/5.37 inference(modus_ponens,[status(thm)],[31232, 520])).
% 5.14/5.37 tff(31234,plain,
% 5.14/5.37 (~(z = elem!1)),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[28525, 515])).
% 5.14/5.37 tff(31235,plain,
% 5.14/5.37 (b(z, elem!1)),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[585, 30203, 31234])).
% 5.14/5.37 tff(31236,plain,
% 5.14/5.37 (b(z, s(z))),
% 5.14/5.37 inference(modus_ponens,[status(thm)],[31235, 519])).
% 5.14/5.37 tff(31237,plain,
% 5.14/5.37 (~(elem!1 = z)),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[2808, 31234])).
% 5.14/5.37 tff(31238,plain,
% 5.14/5.37 (b(elem!1, z)),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[498, 30192, 31237])).
% 5.14/5.37 tff(31239,plain,
% 5.14/5.37 (b(s(z), z)),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[593, 31238, 515])).
% 5.14/5.37 tff(31240,plain,
% 5.14/5.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 5.14/5.37 inference(rewrite,[status(thm)],[])).
% 5.14/5.37 tff(31241,plain,
% 5.14/5.37 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z)))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 5.14/5.37 inference(rewrite,[status(thm)],[])).
% 5.14/5.37 tff(31242,plain,
% 5.14/5.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 5.14/5.37 inference(monotonicity,[status(thm)],[31241])).
% 5.14/5.37 tff(31243,plain,
% 5.14/5.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 5.14/5.37 inference(transitivity,[status(thm)],[31242, 31240])).
% 5.14/5.37 tff(31244,plain,
% 5.14/5.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))))),
% 5.14/5.37 inference(quant_inst,[status(thm)],[])).
% 5.14/5.37 tff(31245,plain,
% 5.14/5.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 5.14/5.37 inference(modus_ponens,[status(thm)],[31244, 31243])).
% 5.14/5.37 tff(31246,plain,
% 5.14/5.37 ($false),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[31245, 178, 27212, 28503, 31239, 31236, 31233])).
% 5.14/5.37 tff(31247,plain,((~r(elem!1, s(s(z)))) | (~(s(elem!1) = s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.37 tff(31248,plain,
% 5.14/5.37 (~r(elem!1, s(s(z)))),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[31247, 31219, 10794])).
% 5.14/5.37 tff(31249,plain,
% 5.14/5.37 (b(elem!1, s(s(z)))),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[467, 31248, 312])).
% 5.14/5.37 tff(31250,plain,
% 5.14/5.37 (~r(elem!1, s(s(s(s(z)))))),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[30741, 31249, 10794, 31225, 31230])).
% 5.14/5.37 tff(31251,plain,
% 5.14/5.37 (s(s(elem!1)) = s(s(s(z)))),
% 5.14/5.37 inference(monotonicity,[status(thm)],[31219])).
% 5.14/5.37 tff(31252,plain,
% 5.14/5.37 ((s(s(elem!1)) = elem!1) <=> (s(s(s(z))) = elem!1)),
% 5.14/5.37 inference(monotonicity,[status(thm)],[31251])).
% 5.14/5.37 tff(31253,plain,
% 5.14/5.37 ((s(s(elem!1)) = elem!1) <=> (elem!1 = s(s(s(z))))),
% 5.14/5.37 inference(transitivity,[status(thm)],[31252, 10420])).
% 5.14/5.37 tff(31254,plain,
% 5.14/5.37 ((s(s(elem!1)) = elem!1) <=> (s(s(s(z))) = elem!1)),
% 5.14/5.37 inference(transitivity,[status(thm)],[31253, 10421])).
% 5.14/5.37 tff(31255,plain,
% 5.14/5.37 ((~(s(s(elem!1)) = elem!1)) <=> (~(s(s(s(z))) = elem!1))),
% 5.14/5.37 inference(monotonicity,[status(thm)],[31254])).
% 5.14/5.37 tff(31256,plain,
% 5.14/5.37 (~(elem!1 = s(s(s(s(elem!1)))))),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[1422, 31219])).
% 5.14/5.37 tff(31257,plain,
% 5.14/5.37 (~(s(s(s(elem!1))) = s(elem!1))),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[1509, 31256])).
% 5.14/5.37 tff(31258,plain,
% 5.14/5.37 (~(elem!1 = s(s(elem!1)))),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[1539, 31257])).
% 5.14/5.37 tff(31259,plain,
% 5.14/5.37 (~(s(s(elem!1)) = elem!1)),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[1546, 31258])).
% 5.14/5.37 tff(31260,plain,
% 5.14/5.37 (~(s(s(s(z))) = elem!1)),
% 5.14/5.37 inference(modus_ponens,[status(thm)],[31259, 31255])).
% 5.14/5.37 tff(31261,plain,
% 5.14/5.37 (~b(s(s(s(s(z)))), s(s(z)))),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[31000, 31249, 31225, 31230, 31227, 10794])).
% 5.14/5.37 tff(31262,plain,
% 5.14/5.37 (r(s(s(s(s(z)))), s(s(z)))),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[102, 31261])).
% 5.14/5.37 tff(31263,plain,
% 5.14/5.37 (~r(s(s(s(z))), s(s(z)))),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[30132, 31262, 30126, 30124])).
% 5.14/5.37 tff(31264,plain,
% 5.14/5.37 (b(s(s(s(z))), s(s(z)))),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[4966, 31263])).
% 5.14/5.37 tff(31265,plain,
% 5.14/5.37 (~b(s(s(s(z))), z)),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[30152, 31264, 10794])).
% 5.14/5.37 tff(31266,plain,
% 5.14/5.37 (r(s(s(s(z))), z)),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[21073, 31265])).
% 5.14/5.37 tff(31267,plain,
% 5.14/5.37 (~r(elem!1, z)),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[30868, 31266, 31264, 31230, 31260, 31249])).
% 5.14/5.37 tff(31268,plain,
% 5.14/5.37 (b(elem!1, z)),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[498, 31267, 31229])).
% 5.14/5.37 tff(31269,plain,
% 5.14/5.37 (r(s(s(s(s(z)))), elem!1)),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[28853, 31268, 30126, 31227, 31250])).
% 5.14/5.37 tff(31270,plain,
% 5.14/5.37 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[25879, 31269])).
% 5.14/5.37 tff(31271,plain,
% 5.14/5.37 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[3444, 31270, 31226])).
% 5.14/5.37 tff(31272,plain,
% 5.14/5.37 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 5.14/5.37 inference(modus_ponens,[status(thm)],[31271, 31224])).
% 5.14/5.37 tff(31273,plain,
% 5.14/5.37 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[30886, 31268, 31227, 31225, 31260, 10794, 31230, 31249])).
% 5.14/5.37 tff(31274,plain,
% 5.14/5.37 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.37 inference(unit_resolution,[status(thm)],[20667, 31273])).
% 5.14/5.37 tff(31275,plain,
% 5.14/5.37 (b(s(s(z)), s(z)) <=> b(s(s(z)), elem!1)),
% 5.14/5.37 inference(monotonicity,[status(thm)],[31222])).
% 5.14/5.37 tff(31276,plain,
% 5.14/5.37 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(z))),
% 5.14/5.37 inference(symmetry,[status(thm)],[31275])).
% 5.14/5.37 tff(31277,plain,
% 5.14/5.37 (b(s(s(z)), s(z))),
% 5.14/5.37 inference(modus_ponens,[status(thm)],[31230, 31276])).
% 5.14/5.37 tff(31278,plain,
% 5.14/5.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))))),
% 5.14/5.37 inference(rewrite,[status(thm)],[])).
% 5.14/5.37 tff(31279,plain,
% 5.14/5.37 (((~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(s(s(s(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(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))))),
% 5.14/5.37 inference(rewrite,[status(thm)],[])).
% 5.14/5.37 tff(31280,plain,
% 5.14/5.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(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(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z))))))),
% 5.14/5.37 inference(monotonicity,[status(thm)],[31279])).
% 5.14/5.37 tff(31281,plain,
% 5.14/5.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(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(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))))),
% 5.14/5.37 inference(transitivity,[status(thm)],[31280, 31278])).
% 5.14/5.37 tff(31282,plain,
% 5.14/5.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(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(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 5.14/5.38 inference(quant_inst,[status(thm)],[])).
% 5.14/5.38 tff(31283,plain,
% 5.14/5.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z))))),
% 5.14/5.38 inference(modus_ponens,[status(thm)],[31282, 31281])).
% 5.14/5.38 tff(31284,plain,
% 5.14/5.38 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 5.14/5.38 inference(unit_resolution,[status(thm)],[31283, 178, 31264, 30122, 31277, 31274])).
% 5.14/5.38 tff(31285,plain,
% 5.14/5.38 ($false),
% 5.14/5.38 inference(unit_resolution,[status(thm)],[31284, 31272])).
% 5.14/5.38 tff(31286,plain,((s(s(z)) = elem!1) | b(s(s(z)), s(s(s(s(z))))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.38 tff(31287,plain,
% 5.14/5.38 (s(s(z)) = elem!1),
% 5.14/5.38 inference(unit_resolution,[status(thm)],[31286, 105, 28501])).
% 5.14/5.38 tff(31288,plain,
% 5.14/5.38 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 5.14/5.38 inference(monotonicity,[status(thm)],[31287])).
% 5.14/5.38 tff(31289,plain,
% 5.14/5.38 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 5.14/5.38 inference(transitivity,[status(thm)],[31288, 1526])).
% 5.14/5.38 tff(31290,plain,
% 5.14/5.38 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 5.14/5.38 inference(monotonicity,[status(thm)],[31289])).
% 5.14/5.38 tff(31291,plain,
% 5.14/5.38 (~(s(s(s(elem!1))) = elem!1)),
% 5.14/5.38 inference(modus_ponens,[status(thm)],[1683, 31290])).
% 5.14/5.38 tff(31292,plain,
% 5.14/5.38 (s(s(s(z))) = s(elem!1)),
% 5.14/5.38 inference(monotonicity,[status(thm)],[31287])).
% 5.14/5.38 tff(31293,plain,
% 5.14/5.38 (s(s(s(s(z)))) = s(s(elem!1))),
% 5.14/5.38 inference(monotonicity,[status(thm)],[31292])).
% 5.14/5.38 tff(31294,plain,
% 5.14/5.38 (s(s(elem!1)) = s(s(s(s(z))))),
% 5.14/5.38 inference(symmetry,[status(thm)],[31293])).
% 5.14/5.38 tff(31295,plain,
% 5.14/5.38 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 5.14/5.38 inference(monotonicity,[status(thm)],[31294])).
% 5.14/5.38 tff(31296,plain,
% 5.14/5.38 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), s(s(elem!1)))),
% 5.14/5.38 inference(symmetry,[status(thm)],[31295])).
% 5.14/5.38 tff(31297,plain,
% 5.14/5.38 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 5.14/5.38 inference(monotonicity,[status(thm)],[31292])).
% 5.14/5.38 tff(31298,plain,
% 5.14/5.38 (b(s(elem!1), s(s(s(s(z)))))),
% 5.14/5.38 inference(modus_ponens,[status(thm)],[30124, 31297])).
% 5.14/5.38 tff(31299,plain,
% 5.14/5.38 (b(s(elem!1), s(s(elem!1)))),
% 5.14/5.38 inference(modus_ponens,[status(thm)],[31298, 31296])).
% 5.14/5.38 tff(31300,plain,
% 5.14/5.38 ((s(s(s(s(z)))) = elem!1) <=> (s(s(elem!1)) = elem!1)),
% 5.14/5.38 inference(monotonicity,[status(thm)],[31293])).
% 5.14/5.38 tff(31301,plain,
% 5.14/5.38 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(s(s(elem!1)) = elem!1))),
% 5.14/5.38 inference(monotonicity,[status(thm)],[31300])).
% 5.14/5.38 tff(31302,plain,
% 5.14/5.38 ((s(s(z)) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(z)))))),
% 5.14/5.38 inference(monotonicity,[status(thm)],[31287])).
% 5.14/5.38 tff(31303,plain,
% 5.14/5.38 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 5.14/5.38 inference(transitivity,[status(thm)],[31302, 321])).
% 5.14/5.38 tff(31304,plain,
% 5.14/5.38 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 5.14/5.38 inference(monotonicity,[status(thm)],[31303])).
% 5.14/5.38 tff(31305,plain,
% 5.14/5.38 (~(s(s(s(s(z)))) = elem!1)),
% 5.14/5.38 inference(modus_ponens,[status(thm)],[159, 31304])).
% 5.14/5.38 tff(31306,plain,
% 5.14/5.38 (~(s(s(elem!1)) = elem!1)),
% 5.14/5.38 inference(modus_ponens,[status(thm)],[31305, 31301])).
% 5.14/5.38 tff(31307,plain,
% 5.14/5.38 (r(elem!1, s(s(elem!1)))),
% 5.14/5.38 inference(unit_resolution,[status(thm)],[9352, 31287, 10794])).
% 5.14/5.38 tff(31308,plain,
% 5.14/5.38 (r(s(s(z)), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 5.14/5.38 inference(monotonicity,[status(thm)],[31287])).
% 5.14/5.38 tff(31309,plain,
% 5.14/5.38 (r(elem!1, s(s(s(z)))) <=> r(s(s(z)), s(s(s(z))))),
% 5.14/5.38 inference(symmetry,[status(thm)],[31308])).
% 5.14/5.38 tff(31310,plain,
% 5.14/5.38 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(elem!1))),
% 5.14/5.38 inference(monotonicity,[status(thm)],[31292])).
% 5.14/5.38 tff(31311,plain,
% 5.14/5.38 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(z))))),
% 5.14/5.38 inference(symmetry,[status(thm)],[31310])).
% 5.14/5.38 tff(31312,plain,
% 5.14/5.38 (r(elem!1, s(elem!1)) <=> r(s(s(z)), s(s(s(z))))),
% 5.14/5.38 inference(transitivity,[status(thm)],[31311, 31309])).
% 5.14/5.38 tff(31313,plain,
% 5.14/5.38 ((~r(elem!1, s(elem!1))) <=> (~r(s(s(z)), s(s(s(z)))))),
% 5.14/5.38 inference(monotonicity,[status(thm)],[31312])).
% 5.14/5.38 tff(31314,plain,
% 5.14/5.38 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 5.14/5.38 inference(monotonicity,[status(thm)],[31292])).
% 5.14/5.38 tff(31315,plain,
% 5.14/5.38 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 5.14/5.38 inference(transitivity,[status(thm)],[31314, 2164])).
% 5.14/5.38 tff(31316,plain,
% 5.14/5.38 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 5.14/5.38 inference(monotonicity,[status(thm)],[31315])).
% 5.14/5.38 tff(31317,plain,
% 5.14/5.38 (~(s(elem!1) = s(s(s(s(z)))))),
% 5.14/5.38 inference(modus_ponens,[status(thm)],[4938, 31316])).
% 5.14/5.38 tff(31318,plain,
% 5.14/5.38 (r(elem!1, z)),
% 5.14/5.38 inference(unit_resolution,[status(thm)],[1345, 31287, 28500])).
% 5.14/5.38 tff(31319,plain,
% 5.14/5.38 (r(s(s(z)), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 5.14/5.38 inference(monotonicity,[status(thm)],[31287])).
% 5.14/5.38 tff(31320,plain,
% 5.14/5.38 (r(elem!1, s(s(s(s(z)))))),
% 5.14/5.38 inference(modus_ponens,[status(thm)],[10794, 31319])).
% 5.14/5.38 tff(31321,plain,
% 5.14/5.38 (~r(elem!1, s(elem!1))),
% 5.14/5.38 inference(unit_resolution,[status(thm)],[27585, 31320, 31318, 31317, 30126])).
% 5.14/5.38 tff(31322,plain,
% 5.14/5.38 (~r(s(s(z)), s(s(s(z))))),
% 5.14/5.38 inference(modus_ponens,[status(thm)],[31321, 31313])).
% 5.14/5.38 tff(31323,plain,
% 5.14/5.38 (b(s(s(z)), s(s(s(z))))),
% 5.14/5.38 inference(unit_resolution,[status(thm)],[5088, 31322])).
% 5.14/5.38 tff(31324,plain,
% 5.14/5.38 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), elem!1)),
% 5.14/5.38 inference(monotonicity,[status(thm)],[31287])).
% 5.14/5.38 tff(31325,plain,
% 5.14/5.38 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(z)))),
% 5.14/5.38 inference(symmetry,[status(thm)],[31324])).
% 5.14/5.38 tff(31326,plain,
% 5.14/5.38 (b(s(s(s(z))), elem!1) <=> b(s(elem!1), elem!1)),
% 5.14/5.38 inference(monotonicity,[status(thm)],[31292])).
% 5.14/5.38 tff(31327,plain,
% 5.14/5.38 (b(s(elem!1), elem!1) <=> b(s(s(s(z))), elem!1)),
% 5.14/5.38 inference(symmetry,[status(thm)],[31326])).
% 5.14/5.38 tff(31328,plain,
% 5.14/5.38 (b(s(elem!1), elem!1) <=> b(s(s(s(z))), s(s(z)))),
% 5.14/5.38 inference(transitivity,[status(thm)],[31327, 31325])).
% 5.14/5.38 tff(31329,plain,
% 5.14/5.38 ((elem!1 = s(s(s(z)))) <=> (elem!1 = s(elem!1))),
% 5.14/5.38 inference(monotonicity,[status(thm)],[31292])).
% 5.14/5.38 tff(31330,plain,
% 5.14/5.38 ((elem!1 = s(s(s(z)))) <=> (s(elem!1) = elem!1)),
% 5.14/5.38 inference(transitivity,[status(thm)],[31329, 3190])).
% 5.14/5.38 tff(31331,plain,
% 5.14/5.38 ((~(elem!1 = s(s(s(z))))) <=> (~(s(elem!1) = elem!1))),
% 5.14/5.38 inference(monotonicity,[status(thm)],[31330])).
% 5.14/5.38 tff(31332,plain,
% 5.14/5.38 ((s(s(z)) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 5.14/5.38 inference(monotonicity,[status(thm)],[31287])).
% 5.14/5.38 tff(31333,plain,
% 5.14/5.38 ((~(s(s(z)) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 5.14/5.38 inference(monotonicity,[status(thm)],[31332])).
% 5.14/5.38 tff(31334,plain,
% 5.14/5.38 (~(elem!1 = s(s(s(z))))),
% 5.14/5.38 inference(modus_ponens,[status(thm)],[3205, 31333])).
% 5.14/5.38 tff(31335,plain,
% 5.14/5.38 (~(s(elem!1) = elem!1)),
% 5.14/5.38 inference(modus_ponens,[status(thm)],[31334, 31331])).
% 5.14/5.38 tff(31336,plain,
% 5.14/5.38 (elem!1 = s(s(z))),
% 5.14/5.38 inference(unit_resolution,[status(thm)],[3230, 31287])).
% 5.14/5.38 tff(31337,plain,
% 5.14/5.38 (~b(s(elem!1), z)),
% 5.14/5.38 inference(unit_resolution,[status(thm)],[11775, 363, 27212, 29994, 28503, 1369, 147])).
% 5.14/5.38 tff(31338,plain,
% 5.14/5.38 ($false),
% 5.14/5.38 inference(unit_resolution,[status(thm)],[774, 31337, 28601])).
% 5.14/5.38 tff(31339,plain,((~r(s(elem!1), s(s(z)))) | (s(elem!1) = s(s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.38 tff(31340,plain,
% 5.14/5.38 (~r(s(elem!1), s(s(z)))),
% 5.14/5.38 inference(unit_resolution,[status(thm)],[31339, 31317, 10794])).
% 5.14/5.38 tff(31341,plain,
% 5.14/5.38 (~r(s(elem!1), elem!1)),
% 5.14/5.38 inference(unit_resolution,[status(thm)],[7028, 31340, 31336])).
% 5.14/5.38 tff(31342,plain,
% 5.14/5.38 (b(s(elem!1), elem!1)),
% 5.14/5.38 inference(unit_resolution,[status(thm)],[677, 31341, 31335])).
% 5.14/5.38 tff(31343,plain,
% 5.14/5.38 (b(s(s(s(z))), s(s(z)))),
% 5.14/5.38 inference(modus_ponens,[status(thm)],[31342, 31328])).
% 5.14/5.38 tff(31344,plain,
% 5.14/5.38 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.38 inference(unit_resolution,[status(thm)],[21439, 31343, 27224, 30122, 31323])).
% 5.14/5.38 tff(31345,plain,
% 5.14/5.38 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.38 inference(unit_resolution,[status(thm)],[20667, 31344])).
% 5.14/5.38 tff(31346,plain,
% 5.14/5.38 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 5.14/5.38 inference(unit_resolution,[status(thm)],[21520, 31345, 30124, 30126, 27212])).
% 5.14/5.38 tff(31347,plain,
% 5.14/5.38 (b(z, s(s(s(s(s(s(s(z))))))))),
% 5.14/5.38 inference(unit_resolution,[status(thm)],[271, 31346])).
% 5.14/5.38 tff(31348,plain,
% 5.14/5.38 ((s(elem!1) = s(s(elem!1))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 5.14/5.38 inference(monotonicity,[status(thm)],[31294])).
% 5.14/5.38 tff(31349,plain,
% 5.14/5.38 ((s(elem!1) = s(s(elem!1))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 5.14/5.38 inference(transitivity,[status(thm)],[31348, 2163])).
% 5.14/5.38 tff(31350,plain,
% 5.14/5.38 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(elem!1) = s(s(elem!1)))),
% 5.14/5.38 inference(symmetry,[status(thm)],[31349])).
% 5.14/5.38 tff(31351,plain,
% 5.14/5.38 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(elem!1)) = s(elem!1))),
% 5.14/5.38 inference(transitivity,[status(thm)],[31350, 10922])).
% 5.14/5.38 tff(31352,plain,
% 5.14/5.38 ((~(s(s(s(s(z)))) = s(elem!1))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 5.14/5.38 inference(monotonicity,[status(thm)],[31351])).
% 5.14/5.38 tff(31353,plain,
% 5.14/5.38 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 5.14/5.38 inference(monotonicity,[status(thm)],[31314])).
% 5.14/5.38 tff(31354,plain,
% 5.14/5.38 (~(s(s(s(s(z)))) = s(elem!1))),
% 5.14/5.38 inference(modus_ponens,[status(thm)],[4938, 31353])).
% 5.14/5.38 tff(31355,plain,
% 5.14/5.38 (~(s(s(elem!1)) = s(elem!1))),
% 5.14/5.38 inference(modus_ponens,[status(thm)],[31354, 31352])).
% 5.14/5.38 tff(31356,plain,
% 5.14/5.38 ((s(elem!1) = s(s(z))) <=> (s(elem!1) = elem!1)),
% 5.14/5.38 inference(monotonicity,[status(thm)],[31287])).
% 5.14/5.38 tff(31357,plain,
% 5.14/5.38 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(z)))),
% 5.14/5.38 inference(symmetry,[status(thm)],[31356])).
% 5.14/5.38 tff(31358,plain,
% 5.14/5.38 ((elem!1 = s(s(s(z)))) <=> (s(elem!1) = s(s(z)))),
% 5.14/5.38 inference(transitivity,[status(thm)],[31330, 31357])).
% 5.14/5.38 tff(31359,plain,
% 5.14/5.38 ((~(elem!1 = s(s(s(z))))) <=> (~(s(elem!1) = s(s(z))))),
% 5.14/5.38 inference(monotonicity,[status(thm)],[31358])).
% 5.14/5.38 tff(31360,plain,
% 5.14/5.38 (~(s(elem!1) = s(s(z)))),
% 5.14/5.38 inference(modus_ponens,[status(thm)],[31334, 31359])).
% 5.14/5.38 tff(31361,plain,
% 5.14/5.38 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 5.14/5.38 inference(unit_resolution,[status(thm)],[2840, 31360])).
% 5.14/5.38 tff(31362,plain,
% 5.14/5.38 (~b(s(s(s(z))), z)),
% 5.14/5.38 inference(unit_resolution,[status(thm)],[30152, 31343, 10794])).
% 5.14/5.38 tff(31363,plain,
% 5.14/5.38 (~b(s(elem!1), z)),
% 5.14/5.38 inference(unit_resolution,[status(thm)],[7042, 31362, 31336])).
% 5.14/5.38 tff(31364,plain,
% 5.14/5.38 (r(s(elem!1), z)),
% 5.14/5.38 inference(unit_resolution,[status(thm)],[774, 31363])).
% 5.14/5.38 tff(31365,plain,
% 5.14/5.38 (b(s(s(s(s(z)))), z) <=> b(s(s(elem!1)), z)),
% 5.14/5.38 inference(monotonicity,[status(thm)],[31293])).
% 5.14/5.38 tff(31366,plain,
% 5.14/5.38 (b(s(s(elem!1)), z)),
% 5.14/5.38 inference(modus_ponens,[status(thm)],[30126, 31365])).
% 5.14/5.38 tff(31367,plain,
% 5.14/5.38 ((~(s(s(s(s(z)))) = s(elem!1))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 5.14/5.38 inference(monotonicity,[status(thm)],[31350])).
% 5.14/5.38 tff(31368,plain,
% 5.14/5.38 (~(s(elem!1) = s(s(elem!1)))),
% 5.14/5.38 inference(modus_ponens,[status(thm)],[31354, 31367])).
% 5.14/5.38 tff(31369,plain,
% 5.14/5.38 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 5.14/5.38 inference(unit_resolution,[status(thm)],[3356, 31368])).
% 5.14/5.38 tff(31370,plain,
% 5.14/5.38 (b(z, s(s(s(s(z))))) <=> b(z, s(s(elem!1)))),
% 5.14/5.38 inference(monotonicity,[status(thm)],[31293])).
% 5.14/5.38 tff(31371,plain,
% 5.14/5.38 (b(z, s(s(elem!1)))),
% 5.14/5.38 inference(modus_ponens,[status(thm)],[27212, 31370])).
% 5.14/5.38 tff(31372,plain,
% 5.14/5.38 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 5.14/5.38 inference(transitivity,[status(thm)],[31289, 2486])).
% 5.14/5.38 tff(31373,plain,
% 5.14/5.38 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 5.14/5.38 inference(monotonicity,[status(thm)],[31372])).
% 5.14/5.38 tff(31374,plain,
% 5.14/5.38 (~(elem!1 = s(s(s(elem!1))))),
% 5.14/5.38 inference(modus_ponens,[status(thm)],[1683, 31373])).
% 5.14/5.38 tff(31375,plain,
% 5.14/5.38 ((elem!1 = s(s(s(z)))) <=> (elem!1 = s(elem!1))),
% 5.14/5.38 inference(transitivity,[status(thm)],[31330, 3880])).
% 5.14/5.38 tff(31376,plain,
% 5.14/5.38 ((~(elem!1 = s(s(s(z))))) <=> (~(elem!1 = s(elem!1)))),
% 5.14/5.38 inference(monotonicity,[status(thm)],[31375])).
% 5.14/5.38 tff(31377,plain,
% 5.14/5.38 (~(elem!1 = s(elem!1))),
% 5.14/5.38 inference(modus_ponens,[status(thm)],[31334, 31376])).
% 5.14/5.38 tff(31378,plain,
% 5.14/5.38 (b(elem!1, s(elem!1))),
% 5.14/5.38 inference(unit_resolution,[status(thm)],[756, 31321, 31377])).
% 5.14/5.38 tff(31379,plain,
% 5.14/5.38 (b(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.14/5.38 inference(monotonicity,[status(thm)],[31287])).
% 5.14/5.38 tff(31380,plain,
% 5.14/5.38 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.14/5.38 inference(modus_ponens,[status(thm)],[30122, 31379])).
% 5.14/5.38 tff(31381,plain,
% 5.14/5.38 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.14/5.38 inference(monotonicity,[status(thm)],[31287])).
% 5.14/5.38 tff(31382,plain,
% 5.14/5.38 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.14/5.38 inference(modus_ponens,[status(thm)],[27224, 31381])).
% 5.14/5.38 tff(31383,plain,
% 5.14/5.38 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 5.14/5.38 inference(monotonicity,[status(thm)],[31293])).
% 5.14/5.38 tff(31384,plain,
% 5.14/5.38 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 5.14/5.38 inference(monotonicity,[status(thm)],[31292, 31383])).
% 5.14/5.38 tff(31385,plain,
% 5.14/5.38 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 5.14/5.38 inference(transitivity,[status(thm)],[31384, 3881])).
% 5.14/5.38 tff(31386,plain,
% 5.14/5.38 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 5.14/5.38 inference(monotonicity,[status(thm)],[31385])).
% 5.14/5.38 tff(31387,plain,
% 5.14/5.38 (~(s(s(s(elem!1))) = s(elem!1))),
% 5.14/5.38 inference(modus_ponens,[status(thm)],[11413, 31386])).
% 5.14/5.38 tff(31388,plain,
% 5.14/5.38 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 5.14/5.38 inference(unit_resolution,[status(thm)],[3502, 31305])).
% 5.14/5.38 tff(31389,plain,
% 5.14/5.38 (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 5.14/5.38 inference(unit_resolution,[status(thm)],[8403, 31388])).
% 5.14/5.38 tff(31390,plain,
% 5.14/5.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 5.14/5.38 inference(rewrite,[status(thm)],[])).
% 5.14/5.38 tff(31391,plain,
% 5.14/5.38 (((~b(s(elem!1), 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(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 5.14/5.38 inference(rewrite,[status(thm)],[])).
% 5.14/5.38 tff(31392,plain,
% 5.14/5.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~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(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 5.14/5.38 inference(monotonicity,[status(thm)],[31391])).
% 5.14/5.38 tff(31393,plain,
% 5.14/5.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~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(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 5.14/5.38 inference(transitivity,[status(thm)],[31392, 31390])).
% 5.14/5.38 tff(31394,plain,
% 5.14/5.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~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(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 5.14/5.38 inference(quant_inst,[status(thm)],[])).
% 5.14/5.38 tff(31395,plain,
% 5.14/5.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 5.14/5.38 inference(modus_ponens,[status(thm)],[31394, 31393])).
% 5.14/5.38 tff(31396,plain,
% 5.14/5.38 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 5.14/5.38 inference(unit_resolution,[status(thm)],[31395, 178, 31342, 31378, 31382, 31380])).
% 5.14/5.38 tff(31397,plain,
% 5.14/5.38 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 5.14/5.38 inference(unit_resolution,[status(thm)],[5361, 31287])).
% 5.14/5.38 tff(31398,plain,
% 5.14/5.38 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 5.14/5.38 inference(modus_ponens,[status(thm)],[31397, 2561])).
% 5.14/5.38 tff(31399,plain,
% 5.14/5.38 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 5.14/5.38 inference(unit_resolution,[status(thm)],[806, 41, 31398, 31396])).
% 5.14/5.38 tff(31400,plain,
% 5.14/5.38 (~b(z, s(elem!1))),
% 5.14/5.38 inference(unit_resolution,[status(thm)],[25075, 178, 6604, 6477, 1013, 5391])).
% 5.14/5.38 tff(31401,plain,
% 5.14/5.38 (r(z, s(elem!1))),
% 5.14/5.38 inference(unit_resolution,[status(thm)],[2351, 31400])).
% 5.14/5.38 tff(31402,plain,
% 5.14/5.38 (~r(z, s(s(s(elem!1))))),
% 5.14/5.38 inference(unit_resolution,[status(thm)],[7389, 31401, 683, 356, 1597, 854])).
% 5.14/5.38 tff(31403,plain,
% 5.14/5.38 (b(z, s(s(s(elem!1))))),
% 5.14/5.38 inference(unit_resolution,[status(thm)],[2095, 31402])).
% 5.14/5.38 tff(31404,plain,
% 5.14/5.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~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))))))))))),
% 5.14/5.38 inference(rewrite,[status(thm)],[])).
% 5.14/5.38 tff(31405,plain,
% 5.14/5.38 (((~b(s(s(s(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(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~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))))))))))),
% 5.14/5.38 inference(rewrite,[status(thm)],[])).
% 5.14/5.38 tff(31406,plain,
% 5.14/5.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~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)))))))))))),
% 5.14/5.38 inference(monotonicity,[status(thm)],[31405])).
% 5.14/5.38 tff(31407,plain,
% 5.14/5.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~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))))))))))),
% 5.14/5.38 inference(transitivity,[status(thm)],[31406, 31404])).
% 5.14/5.38 tff(31408,plain,
% 5.14/5.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(elem!1))))))),
% 5.14/5.38 inference(quant_inst,[status(thm)],[])).
% 5.14/5.38 tff(31409,plain,
% 5.14/5.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~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)))))))))),
% 5.14/5.38 inference(modus_ponens,[status(thm)],[31408, 31407])).
% 5.14/5.38 tff(31410,plain,
% 5.14/5.38 ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 5.14/5.38 inference(unit_resolution,[status(thm)],[31409, 178, 1597, 595, 3664])).
% 5.14/5.38 tff(31411,plain,
% 5.14/5.38 (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.38 inference(unit_resolution,[status(thm)],[31410, 31403])).
% 5.14/5.38 tff(31412,plain,
% 5.14/5.38 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.38 inference(unit_resolution,[status(thm)],[3612, 41, 31411, 9361])).
% 5.14/5.38 tff(31413,plain,
% 5.14/5.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 5.14/5.38 inference(rewrite,[status(thm)],[])).
% 5.14/5.38 tff(31414,plain,
% 5.14/5.38 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 5.14/5.38 inference(rewrite,[status(thm)],[])).
% 5.14/5.38 tff(31415,plain,
% 5.14/5.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1))))))),
% 5.14/5.38 inference(monotonicity,[status(thm)],[31414])).
% 5.14/5.38 tff(31416,plain,
% 5.14/5.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 5.14/5.39 inference(transitivity,[status(thm)],[31415, 31413])).
% 5.14/5.39 tff(31417,plain,
% 5.14/5.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 5.14/5.39 inference(quant_inst,[status(thm)],[])).
% 5.14/5.39 tff(31418,plain,
% 5.14/5.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1))))),
% 5.14/5.39 inference(modus_ponens,[status(thm)],[31417, 31416])).
% 5.14/5.39 tff(31419,plain,
% 5.14/5.39 (~b(s(s(elem!1)), elem!1)),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[31418, 178, 683, 854, 1013, 5391])).
% 5.14/5.39 tff(31420,plain,
% 5.14/5.39 (~r(elem!1, s(s(s(elem!1))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[22317, 31403, 5816, 6477, 5222, 6604, 31419, 346])).
% 5.14/5.39 tff(31421,plain,
% 5.14/5.39 (b(elem!1, s(s(s(elem!1))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[2054, 31420, 1586])).
% 5.14/5.39 tff(31422,plain,
% 5.14/5.39 (~b(s(s(s(elem!1))), s(elem!1))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[6420, 31421])).
% 5.14/5.39 tff(31423,plain,
% 5.14/5.39 (r(s(s(s(elem!1))), s(elem!1))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[373, 31422, 356])).
% 5.14/5.39 tff(31424,plain,
% 5.14/5.39 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(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))))))))))),
% 5.14/5.39 inference(rewrite,[status(thm)],[])).
% 5.14/5.39 tff(31425,plain,
% 5.14/5.39 (((~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(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))))))))))),
% 5.14/5.39 inference(rewrite,[status(thm)],[])).
% 5.14/5.39 tff(31426,plain,
% 5.14/5.39 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))))),
% 5.14/5.39 inference(monotonicity,[status(thm)],[31425])).
% 5.14/5.39 tff(31427,plain,
% 5.14/5.39 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 5.14/5.39 inference(transitivity,[status(thm)],[31426, 31424])).
% 5.14/5.39 tff(31428,plain,
% 5.14/5.39 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 5.14/5.39 inference(quant_inst,[status(thm)],[])).
% 5.14/5.39 tff(31429,plain,
% 5.14/5.39 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 5.14/5.39 inference(modus_ponens,[status(thm)],[31428, 31427])).
% 5.14/5.39 tff(31430,plain,
% 5.14/5.39 ($false),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[31429, 118, 31423, 15198, 31412])).
% 5.14/5.39 tff(31431,plain,((~b(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))) | (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(elem!1))) | (elem!1 = s(s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(s(elem!1)), z)) | (s(s(elem!1)) = elem!1) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.39 tff(31432,plain,
% 5.14/5.39 (~b(s(s(elem!1)), s(elem!1))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[31431, 1597, 9361, 356, 683, 15198, 854, 1586, 595, 3664, 5816, 6477, 6444, 6604, 346, 5391])).
% 5.14/5.39 tff(31433,plain,
% 5.14/5.39 (r(s(s(elem!1)), s(elem!1))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[1006, 31432, 1000])).
% 5.14/5.39 tff(31434,plain,
% 5.14/5.39 (~r(elem!1, s(s(s(elem!1))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[23784, 2043, 27212, 168, 437, 2857, 470])).
% 5.14/5.39 tff(31435,plain,
% 5.14/5.39 (b(elem!1, s(s(s(elem!1))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[2054, 31434, 1586])).
% 5.14/5.39 tff(31436,plain,
% 5.14/5.39 (~b(s(s(s(elem!1))), s(elem!1))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[6420, 31435])).
% 5.14/5.39 tff(31437,plain,
% 5.14/5.39 (r(s(s(s(elem!1))), s(elem!1))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[373, 31436, 356])).
% 5.14/5.39 tff(31438,plain,
% 5.14/5.39 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[15350, 31437, 992])).
% 5.14/5.39 tff(31439,plain,
% 5.14/5.39 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[3375, 31438, 1655])).
% 5.14/5.39 tff(31440,plain,
% 5.14/5.39 (~r(s(s(s(elem!1))), z)),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[1557, 31437, 844])).
% 5.14/5.39 tff(31441,plain,
% 5.14/5.39 (b(s(s(s(elem!1))), z)),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[1565, 31440])).
% 5.14/5.39 tff(31442,plain,
% 5.14/5.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 5.14/5.39 inference(rewrite,[status(thm)],[])).
% 5.14/5.39 tff(31443,plain,
% 5.14/5.39 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 5.14/5.39 inference(rewrite,[status(thm)],[])).
% 5.14/5.39 tff(31444,plain,
% 5.14/5.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 5.14/5.39 inference(monotonicity,[status(thm)],[31443])).
% 5.14/5.39 tff(31445,plain,
% 5.14/5.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 5.14/5.39 inference(transitivity,[status(thm)],[31444, 31442])).
% 5.14/5.39 tff(31446,plain,
% 5.14/5.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))),
% 5.14/5.39 inference(quant_inst,[status(thm)],[])).
% 5.14/5.39 tff(31447,plain,
% 5.14/5.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 5.14/5.39 inference(modus_ponens,[status(thm)],[31446, 31445])).
% 5.14/5.39 tff(31448,plain,
% 5.14/5.39 ($false),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[31447, 178, 2043, 31441, 6604, 6477, 31439])).
% 5.14/5.39 tff(31449,plain,((~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (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(elem!1))) | (elem!1 = s(s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.39 tff(31450,plain,
% 5.14/5.39 (~b(z, s(s(s(elem!1))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[31449, 31433, 6477, 1655, 6604, 844, 356, 683, 1597, 854, 1586, 168, 437, 2857, 470])).
% 5.14/5.39 tff(31451,plain,
% 5.14/5.39 (r(z, s(s(s(elem!1))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[2095, 31450])).
% 5.14/5.39 tff(31452,plain,
% 5.14/5.39 (~r(elem!1, s(s(s(elem!1))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[3421, 31451, 437])).
% 5.14/5.39 tff(31453,plain,
% 5.14/5.39 (b(elem!1, s(s(s(elem!1))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[2054, 31452, 1586])).
% 5.14/5.39 tff(31454,plain,
% 5.14/5.39 ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[25419, 178, 1597, 869, 3664])).
% 5.14/5.39 tff(31455,plain,
% 5.14/5.39 (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[31454, 31453])).
% 5.14/5.39 tff(31456,plain,
% 5.14/5.39 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[3612, 41, 31455, 9361])).
% 5.14/5.39 tff(31457,plain,
% 5.14/5.39 (~b(s(s(s(elem!1))), s(elem!1))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[6420, 31453])).
% 5.14/5.39 tff(31458,plain,
% 5.14/5.39 (r(s(s(s(elem!1))), s(elem!1))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[373, 31457, 356])).
% 5.14/5.39 tff(31459,plain,
% 5.14/5.39 ($false),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[31429, 118, 31458, 15198, 31456])).
% 5.14/5.39 tff(31460,plain,((~b(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(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(elem!1, s(elem!1))) | (elem!1 = s(s(s(elem!1)))) | (~r(elem!1, z)) | (~b(z, s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))) | (s(s(elem!1)) = s(elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(elem!1)))) | (s(s(elem!1)) = elem!1) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.39 tff(31461,plain,
% 5.14/5.39 (~b(s(s(s(elem!1))), elem!1)),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[31460, 31399, 31389, 31387, 31382, 31380, 31342, 31378, 31374, 31318, 31371, 31369, 31366, 31364, 30126, 31361, 31320, 31355, 31347, 31307, 31306, 31299])).
% 5.14/5.39 tff(31462,plain,
% 5.14/5.39 (r(s(s(s(elem!1))), elem!1)),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[570, 31461, 31291])).
% 5.14/5.39 tff(31463,plain,
% 5.14/5.39 (r(z, elem!1)),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[7053, 31287, 29994])).
% 5.14/5.39 tff(31464,plain,
% 5.14/5.39 (~r(s(s(s(elem!1))), z)),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[6378, 118, 31463, 31462])).
% 5.14/5.39 tff(31465,plain,
% 5.14/5.39 (~r(z, s(s(s(elem!1))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[565, 31462, 31463])).
% 5.14/5.39 tff(31466,plain,
% 5.14/5.39 (b(z, s(s(s(elem!1))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[2095, 31465])).
% 5.14/5.39 tff(31467,plain,
% 5.14/5.39 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 5.14/5.39 inference(monotonicity,[status(thm)],[31293])).
% 5.14/5.39 tff(31468,plain,
% 5.14/5.39 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 5.14/5.39 inference(symmetry,[status(thm)],[31467])).
% 5.14/5.39 tff(31469,plain,
% 5.14/5.39 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[3404, 31369])).
% 5.14/5.39 tff(31470,plain,
% 5.14/5.39 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[10206, 31462, 31307])).
% 5.14/5.39 tff(31471,plain,
% 5.14/5.39 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[3409, 31470, 31469])).
% 5.14/5.39 tff(31472,plain,
% 5.14/5.39 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 5.14/5.39 inference(modus_ponens,[status(thm)],[31471, 31468])).
% 5.14/5.39 tff(31473,plain,
% 5.14/5.39 (~b(s(s(s(elem!1))), z)),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[22234, 31472, 27212, 30126, 31466])).
% 5.14/5.39 tff(31474,plain,
% 5.14/5.39 ($false),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[1565, 31473, 31464])).
% 5.14/5.39 tff(31475,plain,(b(s(s(z)), s(s(s(s(z))))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.39 tff(31476,plain,
% 5.14/5.39 (b(s(s(z)), s(s(s(s(z)))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[31475, 28501])).
% 5.14/5.39 tff(31477,plain,
% 5.14/5.39 (~r(s(s(s(s(z)))), s(s(z)))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[199, 194, 28500])).
% 5.14/5.39 tff(31478,plain,
% 5.14/5.39 (b(s(s(s(s(z)))), s(s(z)))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[102, 31477])).
% 5.14/5.39 tff(31479,plain,
% 5.14/5.39 (~r(s(s(s(z))), z)),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[28484, 31478, 29994, 194, 167])).
% 5.14/5.39 tff(31480,plain,
% 5.14/5.39 (b(s(s(s(z))), z)),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[21073, 31479])).
% 5.14/5.39 tff(31481,plain,
% 5.14/5.39 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[10454, 4952, 29994, 167, 194, 31478])).
% 5.14/5.39 tff(31482,plain,
% 5.14/5.39 (r(s(s(s(z))), s(s(s(s(z)))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[10755, 31481])).
% 5.14/5.39 tff(31483,plain,
% 5.14/5.39 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[3043, 118, 24592, 31482])).
% 5.14/5.39 tff(31484,plain,
% 5.14/5.39 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 31483])).
% 5.14/5.39 tff(31485,plain,
% 5.14/5.39 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[27236, 118, 24592, 31482])).
% 5.14/5.39 tff(31486,plain,
% 5.14/5.39 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[20667, 31485])).
% 5.14/5.39 tff(31487,plain,
% 5.14/5.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 5.14/5.39 inference(rewrite,[status(thm)],[])).
% 5.14/5.39 tff(31488,plain,
% 5.14/5.39 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), 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(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))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 5.14/5.39 inference(rewrite,[status(thm)],[])).
% 5.14/5.39 tff(31489,plain,
% 5.14/5.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), 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(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 5.14/5.39 inference(monotonicity,[status(thm)],[31488])).
% 5.14/5.39 tff(31490,plain,
% 5.14/5.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), 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(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 5.14/5.39 inference(transitivity,[status(thm)],[31489, 31487])).
% 5.14/5.39 tff(31491,plain,
% 5.14/5.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), 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(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 5.14/5.39 inference(quant_inst,[status(thm)],[])).
% 5.14/5.39 tff(31492,plain,
% 5.14/5.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 5.14/5.39 inference(modus_ponens,[status(thm)],[31491, 31490])).
% 5.14/5.39 tff(31493,plain,
% 5.14/5.39 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[31492, 178, 27531, 24308, 31480])).
% 5.14/5.39 tff(31494,plain,
% 5.14/5.39 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[31493, 31484])).
% 5.14/5.39 tff(31495,plain,
% 5.14/5.39 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[222, 31494])).
% 5.14/5.39 tff(31496,plain,
% 5.14/5.39 ($false),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[21331, 118, 194, 204, 203])).
% 5.14/5.39 tff(31497,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.39 tff(31498,plain,
% 5.14/5.39 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[31497, 31495, 194])).
% 5.14/5.39 tff(31499,plain,
% 5.14/5.39 (b(z, s(s(s(s(s(s(s(z))))))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[271, 31498])).
% 5.14/5.39 tff(31500,plain,
% 5.14/5.39 ($false),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[1207, 178, 31499, 27531, 31480, 31486, 31484])).
% 5.14/5.39 tff(31501,plain,((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.39 tff(31502,plain,
% 5.14/5.39 (~r(z, s(s(s(z))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[31501, 194, 167])).
% 5.14/5.39 tff(31503,plain,
% 5.14/5.39 (b(z, s(s(s(z))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[4920, 31502])).
% 5.14/5.39 tff(31504,plain,
% 5.14/5.39 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[23450, 107, 29994])).
% 5.14/5.39 tff(31505,plain,
% 5.14/5.39 (b(z, s(s(s(s(s(s(s(z))))))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[271, 31504])).
% 5.14/5.39 tff(31506,plain,
% 5.14/5.39 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[23358, 31505, 3008, 146, 1127])).
% 5.14/5.39 tff(31507,plain,
% 5.14/5.39 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 31506])).
% 5.14/5.39 tff(31508,plain,
% 5.14/5.39 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[1319, 178, 31505, 146, 3008, 1127])).
% 5.14/5.39 tff(31509,plain,
% 5.14/5.39 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[20667, 31508])).
% 5.14/5.39 tff(31510,plain,
% 5.14/5.39 (~r(s(s(s(z))), s(s(z)))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[8218, 31509, 107])).
% 5.14/5.39 tff(31511,plain,
% 5.14/5.39 (b(s(s(s(z))), s(s(z)))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[4966, 31510])).
% 5.14/5.39 tff(31512,plain,
% 5.14/5.39 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[24318, 31511, 27212, 202, 3008])).
% 5.14/5.39 tff(31513,plain,
% 5.14/5.39 (r(s(s(s(s(z)))), s(s(s(z))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[11185, 31512])).
% 5.14/5.39 tff(31514,plain,
% 5.14/5.39 ($false),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[25911, 118, 24592, 31513, 31507])).
% 5.14/5.39 tff(31515,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.39 tff(31516,plain,
% 5.14/5.39 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[31515, 31503, 31478, 27531, 31480])).
% 5.14/5.39 tff(31517,plain,
% 5.14/5.39 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[3578, 31516])).
% 5.14/5.39 tff(31518,plain,
% 5.14/5.39 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[31497, 204, 194])).
% 5.14/5.39 tff(31519,plain,
% 5.14/5.39 (b(z, s(s(s(s(s(s(s(z))))))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[271, 31518])).
% 5.14/5.39 tff(31520,plain,
% 5.14/5.39 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[23358, 31519, 3008, 27531, 1127])).
% 5.14/5.39 tff(31521,plain,
% 5.14/5.39 ($false),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[1179, 41, 1104, 27381, 25871])).
% 5.14/5.39 tff(31522,plain,(r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.39 tff(31523,plain,
% 5.14/5.39 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[31522, 31520])).
% 5.14/5.39 tff(31524,plain,
% 5.14/5.39 ($false),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[25911, 118, 24592, 4953, 16063])).
% 5.14/5.39 tff(31525,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.39 tff(31526,plain,
% 5.14/5.39 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[31525, 31523])).
% 5.14/5.39 tff(31527,plain,
% 5.14/5.39 (b(s(s(s(s(z)))), s(s(s(z))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[11185, 31526])).
% 5.14/5.39 tff(31528,plain,
% 5.14/5.39 ($false),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[1245, 178, 146, 3008, 1127, 3002, 21855])).
% 5.14/5.39 tff(31529,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 5.14/5.39 tff(31530,plain,
% 5.14/5.39 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[31529, 3002, 3008, 1127, 27531])).
% 5.14/5.39 tff(31531,plain,
% 5.14/5.39 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.14/5.39 inference(unit_resolution,[status(thm)],[31522, 31530])).
% 5.14/5.39 tff(31532,plain,
% 5.14/5.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 5.14/5.40 inference(rewrite,[status(thm)],[])).
% 5.14/5.40 tff(31533,plain,
% 5.14/5.40 (((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 5.14/5.40 inference(rewrite,[status(thm)],[])).
% 5.14/5.40 tff(31534,plain,
% 5.14/5.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 5.14/5.40 inference(monotonicity,[status(thm)],[31533])).
% 5.14/5.40 tff(31535,plain,
% 5.14/5.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 5.14/5.40 inference(transitivity,[status(thm)],[31534, 31532])).
% 5.14/5.40 tff(31536,plain,
% 5.14/5.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 5.14/5.40 inference(quant_inst,[status(thm)],[])).
% 5.14/5.40 tff(31537,plain,
% 5.14/5.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 5.14/5.40 inference(modus_ponens,[status(thm)],[31536, 31535])).
% 5.14/5.40 tff(31538,plain,
% 5.14/5.40 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 5.14/5.40 inference(unit_resolution,[status(thm)],[31537, 178, 27212, 251, 3008, 3002])).
% 5.14/5.40 tff(31539,plain,
% 5.14/5.40 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 5.14/5.40 inference(unit_resolution,[status(thm)],[31525, 16063])).
% 5.14/5.40 tff(31540,plain,
% 5.14/5.40 ($false),
% 5.14/5.40 inference(unit_resolution,[status(thm)],[11185, 31539, 31538])).
% 5.14/5.40 tff(31541,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.40 tff(31542,plain,
% 5.24/5.40 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[31541, 31531, 3008, 3002])).
% 5.24/5.40 tff(31543,plain,
% 5.24/5.40 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[222, 31542])).
% 5.24/5.40 tff(31544,plain,
% 5.24/5.40 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[31497, 31543, 194])).
% 5.24/5.40 tff(31545,plain,
% 5.24/5.40 (b(z, s(s(s(s(s(s(s(z))))))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[271, 31544])).
% 5.24/5.40 tff(31546,plain,
% 5.24/5.40 ($false),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[1319, 178, 31545, 27531, 3008, 1127, 3002])).
% 5.24/5.40 tff(31547,plain,((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.40 tff(31548,plain,
% 5.24/5.40 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[31547, 3008, 1127, 194])).
% 5.24/5.40 tff(31549,plain,
% 5.24/5.40 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[20667, 31548])).
% 5.24/5.40 tff(31550,plain,
% 5.24/5.40 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[21408, 204, 31549])).
% 5.24/5.40 tff(31551,plain,
% 5.24/5.40 (b(s(s(s(z))), s(s(s(s(z)))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[10755, 31550])).
% 5.24/5.40 tff(31552,plain,
% 5.24/5.40 ($false),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[22536, 178, 27212, 31551, 3008, 31527, 1127])).
% 5.24/5.40 tff(31553,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.40 tff(31554,plain,
% 5.24/5.40 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[31553, 31503, 31480, 194])).
% 5.24/5.40 tff(31555,plain,
% 5.24/5.40 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[222, 31554])).
% 5.24/5.40 tff(31556,plain,
% 5.24/5.40 ($false),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[25920, 178, 166, 167, 251, 202, 1146])).
% 5.24/5.40 tff(31557,plain,((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.40 tff(31558,plain,
% 5.24/5.40 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[31557, 31555, 167, 31478, 31517])).
% 5.24/5.40 tff(31559,plain,
% 5.24/5.40 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[249, 31558])).
% 5.24/5.40 tff(31560,plain,
% 5.24/5.40 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[232, 31559, 28500])).
% 5.24/5.40 tff(31561,plain,
% 5.24/5.40 (b(z, s(s(s(s(s(s(s(z))))))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[271, 31560])).
% 5.24/5.40 tff(31562,plain,
% 5.24/5.40 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[23358, 31561, 31503, 27531, 31480])).
% 5.24/5.40 tff(31563,plain,
% 5.24/5.40 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[31522, 31562])).
% 5.24/5.40 tff(31564,plain,
% 5.24/5.40 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[31547, 31503, 31480, 194])).
% 5.24/5.40 tff(31565,plain,
% 5.24/5.40 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[20667, 31564])).
% 5.24/5.40 tff(31566,plain,
% 5.24/5.40 ($false),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[1269, 118, 224, 1125, 8216])).
% 5.24/5.40 tff(31567,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.40 tff(31568,plain,
% 5.24/5.40 (~r(s(s(s(z))), s(s(z)))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[31567, 31559, 31565])).
% 5.24/5.40 tff(31569,plain,
% 5.24/5.40 (b(s(s(s(z))), s(s(z)))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[4966, 31568])).
% 5.24/5.40 tff(31570,plain,
% 5.24/5.40 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[24318, 31569, 27212, 31478, 31503])).
% 5.24/5.40 tff(31571,plain,
% 5.24/5.40 (r(s(s(s(s(z)))), s(s(s(z))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[11185, 31570])).
% 5.24/5.40 tff(31572,plain,
% 5.24/5.40 ($false),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[31525, 31571, 31563])).
% 5.24/5.40 tff(31573,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.40 tff(31574,plain,
% 5.24/5.40 (~r(s(s(s(s(z)))), z)),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[31573, 31476])).
% 5.24/5.40 tff(31575,plain,
% 5.24/5.40 (b(s(s(s(s(z)))), z)),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[191, 31574])).
% 5.24/5.40 tff(31576,plain,
% 5.24/5.40 (~(s(elem!1) = elem!1)),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[672, 346])).
% 5.24/5.40 tff(31577,plain,
% 5.24/5.40 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[3559, 103, 204])).
% 5.24/5.40 tff(31578,plain,
% 5.24/5.40 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[249, 31577])).
% 5.24/5.40 tff(31579,plain,
% 5.24/5.40 (b(s(s(z)), elem!1)),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[30676, 4235, 28501, 27213, 86])).
% 5.24/5.40 tff(31580,plain,
% 5.24/5.40 (b(elem!1, elem!1) <=> b(s(s(z)), s(s(z)))),
% 5.24/5.40 inference(monotonicity,[status(thm)],[308, 308])).
% 5.24/5.40 tff(31581,plain,
% 5.24/5.40 (b(s(s(z)), s(s(z))) <=> b(elem!1, elem!1)),
% 5.24/5.40 inference(symmetry,[status(thm)],[31580])).
% 5.24/5.40 tff(31582,plain,
% 5.24/5.40 (b(s(s(z)), s(s(z)))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[3238, 308, 817])).
% 5.24/5.40 tff(31583,plain,
% 5.24/5.40 (b(elem!1, elem!1)),
% 5.24/5.40 inference(modus_ponens,[status(thm)],[31582, 31581])).
% 5.24/5.40 tff(31584,plain,
% 5.24/5.40 ($false),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[3220, 31583])).
% 5.24/5.40 tff(31585,plain,((~(elem!1 = s(s(z)))) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.40 tff(31586,plain,
% 5.24/5.40 (~(elem!1 = s(s(z)))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[31585, 31579])).
% 5.24/5.40 tff(31587,plain,
% 5.24/5.40 (b(s(s(z)), elem!1) <=> b(s(s(z)), z)),
% 5.24/5.40 inference(monotonicity,[status(thm)],[928])).
% 5.24/5.40 tff(31588,plain,
% 5.24/5.40 (b(s(s(z)), z) <=> b(s(s(z)), elem!1)),
% 5.24/5.40 inference(symmetry,[status(thm)],[31587])).
% 5.24/5.40 tff(31589,plain,
% 5.24/5.40 ((~b(s(s(z)), z)) <=> (~b(s(s(z)), elem!1))),
% 5.24/5.40 inference(monotonicity,[status(thm)],[31588])).
% 5.24/5.40 tff(31590,plain,
% 5.24/5.40 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[14170, 928, 1146, 166, 1070, 844])).
% 5.24/5.40 tff(31591,plain,
% 5.24/5.40 (b(s(s(s(s(s(s(s(z))))))), z)),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[133, 31590])).
% 5.24/5.40 tff(31592,plain,
% 5.24/5.40 (~b(s(s(z)), z)),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[12409, 31591, 27212, 167, 1146])).
% 5.24/5.40 tff(31593,plain,
% 5.24/5.40 (~b(s(s(z)), elem!1)),
% 5.24/5.40 inference(modus_ponens,[status(thm)],[31592, 31589])).
% 5.24/5.40 tff(31594,plain,
% 5.24/5.40 ($false),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[817, 31593])).
% 5.24/5.40 tff(31595,plain,((~(elem!1 = z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(z)))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.40 tff(31596,plain,
% 5.24/5.40 (~b(s(elem!1), s(s(z)))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[31595, 928, 167, 1146, 166, 817, 844])).
% 5.24/5.40 tff(31597,plain,
% 5.24/5.40 (~(s(elem!1) = s(s(z)))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[28525, 12064])).
% 5.24/5.40 tff(31598,plain,
% 5.24/5.40 ($false),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[421, 31597, 31596, 28539])).
% 5.24/5.40 tff(31599,plain,((~(elem!1 = z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), elem!1)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.40 tff(31600,plain,
% 5.24/5.40 (~(elem!1 = z)),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[31599, 844, 1146, 166, 817, 167])).
% 5.24/5.40 tff(31601,plain,
% 5.24/5.40 (r(elem!1, z)),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[498, 31600, 5723])).
% 5.24/5.40 tff(31602,plain,
% 5.24/5.40 (~r(elem!1, s(elem!1))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[2711, 31601, 844])).
% 5.24/5.40 tff(31603,plain,
% 5.24/5.40 (b(s(elem!1), s(s(z)))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[421, 28539, 1056])).
% 5.24/5.40 tff(31604,plain,
% 5.24/5.40 (~r(s(elem!1), elem!1)),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[13694, 31601, 844])).
% 5.24/5.40 tff(31605,plain,
% 5.24/5.40 (~(elem!1 = s(s(z)))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[31585, 817])).
% 5.24/5.40 tff(31606,plain,
% 5.24/5.40 (~r(elem!1, s(s(z)))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[458, 31601, 28500])).
% 5.24/5.40 tff(31607,plain,
% 5.24/5.40 (b(elem!1, s(s(z)))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[467, 31606, 31605])).
% 5.24/5.40 tff(31608,plain,
% 5.24/5.40 ($false),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[30697, 31607, 31604, 31603, 817, 725, 31602])).
% 5.24/5.40 tff(31609,plain,((~r(s(elem!1), z)) | (~b(s(s(z)), elem!1)) | (s(elem!1) = elem!1) | b(elem!1, z) | (s(elem!1) = s(s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.40 tff(31610,plain,
% 5.24/5.40 (~r(s(elem!1), z)),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[31609, 1056, 725, 5723, 817, 24628, 166, 167])).
% 5.24/5.40 tff(31611,plain,
% 5.24/5.40 (b(s(elem!1), z)),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[774, 31610])).
% 5.24/5.40 tff(31612,plain,
% 5.24/5.40 (~r(s(elem!1), s(s(z)))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[12437, 30961, 29994, 193, 853])).
% 5.24/5.40 tff(31613,plain,
% 5.24/5.40 (b(s(elem!1), s(s(z)))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[421, 31612, 1056])).
% 5.24/5.40 tff(31614,plain,
% 5.24/5.40 ($false),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[5768, 178, 3461, 14162, 1687, 167, 12121])).
% 5.24/5.40 tff(31615,plain,((~(elem!1 = z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.40 tff(31616,plain,
% 5.24/5.40 (~b(s(s(z)), z)),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[31615, 31613, 27212, 167, 853, 928])).
% 5.24/5.40 tff(31617,plain,
% 5.24/5.40 (~b(s(s(z)), elem!1)),
% 5.24/5.40 inference(modus_ponens,[status(thm)],[31616, 31589])).
% 5.24/5.40 tff(31618,plain,
% 5.24/5.40 ($false),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[817, 31617])).
% 5.24/5.40 tff(31619,plain,((~(elem!1 = z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), z)) | (s(elem!1) = s(s(z))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.40 tff(31620,plain,
% 5.24/5.40 (~(elem!1 = z)),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[31619, 31611, 167, 817, 1056, 193])).
% 5.24/5.40 tff(31621,plain,
% 5.24/5.40 (~(z = elem!1)),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[317, 31620])).
% 5.24/5.40 tff(31622,plain,
% 5.24/5.40 (~r(s(s(s(s(z)))), z)),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[31573, 167])).
% 5.24/5.40 tff(31623,plain,
% 5.24/5.40 (b(s(s(s(s(z)))), z)),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[191, 31622])).
% 5.24/5.40 tff(31624,plain,
% 5.24/5.40 (~(elem!1 = s(s(s(s(z)))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[12557, 5723, 31623])).
% 5.24/5.40 tff(31625,plain,
% 5.24/5.40 (r(elem!1, z)),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[498, 31620, 5723])).
% 5.24/5.40 tff(31626,plain,
% 5.24/5.40 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[10809, 31625, 4236])).
% 5.24/5.40 tff(31627,plain,
% 5.24/5.40 (~b(z, elem!1)),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[23466, 31626, 193, 24628, 166, 817, 4235, 28500, 31605, 31624, 31620])).
% 5.24/5.40 tff(31628,plain,
% 5.24/5.40 (r(z, elem!1)),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[585, 31627, 31621])).
% 5.24/5.40 tff(31629,plain,
% 5.24/5.40 (~r(elem!1, s(s(z)))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[458, 31625, 28500])).
% 5.24/5.40 tff(31630,plain,
% 5.24/5.40 (b(elem!1, s(s(z)))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[467, 31629, 31605])).
% 5.24/5.40 tff(31631,plain,
% 5.24/5.40 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[11859, 31630, 166, 24628, 817])).
% 5.24/5.40 tff(31632,plain,
% 5.24/5.40 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[691, 31631, 31626])).
% 5.24/5.40 tff(31633,plain,
% 5.24/5.40 (~(s(elem!1) = s(s(s(s(z)))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[16181, 31632])).
% 5.24/5.40 tff(31634,plain,
% 5.24/5.40 (r(elem!1, s(s(s(s(z)))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[24769, 31632, 3428])).
% 5.24/5.40 tff(31635,plain,
% 5.24/5.40 (~r(elem!1, s(elem!1))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[27585, 31634, 31625, 31633, 31623])).
% 5.24/5.40 tff(31636,plain,
% 5.24/5.40 (~r(s(elem!1), s(s(z)))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[12437, 31633, 29994, 193, 31611])).
% 5.24/5.40 tff(31637,plain,
% 5.24/5.40 (b(s(elem!1), s(s(z)))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[421, 31636, 1056])).
% 5.24/5.40 tff(31638,plain,
% 5.24/5.40 (r(s(elem!1), elem!1)),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[30697, 31637, 31630, 817, 725, 31635])).
% 5.24/5.40 tff(31639,plain,
% 5.24/5.40 (~r(z, s(elem!1))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[7070, 31638, 31628])).
% 5.24/5.40 tff(31640,plain,
% 5.24/5.40 (b(z, s(elem!1))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[2351, 31639])).
% 5.24/5.40 tff(31641,plain,
% 5.24/5.40 (~(s(s(s(s(z)))) = elem!1)),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[504, 31624])).
% 5.24/5.40 tff(31642,plain,
% 5.24/5.40 (~r(z, s(s(s(elem!1))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[30052, 10488, 812, 817, 521, 437, 3261])).
% 5.24/5.40 tff(31643,plain,
% 5.24/5.40 (b(z, s(s(s(elem!1))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[2095, 31642])).
% 5.24/5.40 tff(31644,plain,
% 5.24/5.40 (r(elem!1, s(s(s(s(z)))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[483, 24765, 469])).
% 5.24/5.40 tff(31645,plain,
% 5.24/5.40 (~r(elem!1, s(s(s(elem!1))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[23784, 31643, 10484, 31644, 1687, 168, 437])).
% 5.24/5.40 tff(31646,plain,
% 5.24/5.40 (b(elem!1, s(s(s(elem!1))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[2054, 31645, 10488])).
% 5.24/5.40 tff(31647,plain,
% 5.24/5.40 (~b(s(s(s(elem!1))), elem!1)),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[30085, 10484, 193, 31643, 3771, 1687, 817, 812, 31646])).
% 5.24/5.40 tff(31648,plain,
% 5.24/5.40 (r(s(s(s(elem!1))), elem!1)),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[570, 31647, 10489])).
% 5.24/5.40 tff(31649,plain,
% 5.24/5.40 (~r(s(s(s(elem!1))), z)),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[6378, 118, 521, 31648])).
% 5.24/5.40 tff(31650,plain,
% 5.24/5.40 (b(s(s(s(elem!1))), z)),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[1565, 31649])).
% 5.24/5.40 tff(31651,plain,
% 5.24/5.40 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[22234, 31650, 1687, 168, 31643])).
% 5.24/5.40 tff(31652,plain,
% 5.24/5.40 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[3825, 41, 10484, 31651])).
% 5.24/5.40 tff(31653,plain,
% 5.24/5.40 ($false),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[22214, 118, 31648, 31644, 31652])).
% 5.24/5.40 tff(31654,plain,((~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~r(elem!1, z)) | (~r(z, s(s(z)))) | (elem!1 = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.40 tff(31655,plain,
% 5.24/5.40 (~b(s(s(s(s(z)))), elem!1)),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[31654, 31632, 27212, 29994, 31623, 3428, 193, 31630, 31628, 817, 31624, 31625])).
% 5.24/5.40 tff(31656,plain,
% 5.24/5.40 (r(s(s(s(s(z)))), elem!1)),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[3142, 31655, 31641])).
% 5.24/5.40 tff(31657,plain,
% 5.24/5.40 (~r(s(elem!1), s(s(s(s(z)))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[7010, 31638, 31656])).
% 5.24/5.40 tff(31658,plain,
% 5.24/5.40 (b(s(elem!1), s(s(s(s(z)))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[1084, 31657, 31633])).
% 5.24/5.40 tff(31659,plain,
% 5.24/5.40 ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[11770, 178, 31611, 27212, 31623])).
% 5.24/5.40 tff(31660,plain,
% 5.24/5.40 ($false),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[31659, 31658, 31640])).
% 5.24/5.40 tff(31661,plain,((s(elem!1) = s(s(z))) | (~b(s(s(z)), elem!1)) | (s(elem!1) = elem!1) | (~r(s(s(s(s(z)))), s(s(z)))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | b(z, s(s(s(s(s(s(s(z)))))))) | b(elem!1, z) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.40 tff(31662,plain,
% 5.24/5.40 (s(elem!1) = s(s(z))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[31661, 31579, 725, 103, 27213, 166, 4235, 5723, 31476])).
% 5.24/5.40 tff(31663,plain,
% 5.24/5.40 (r(s(elem!1), z)),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[906, 31662, 28500])).
% 5.24/5.40 tff(31664,plain,
% 5.24/5.40 (~(elem!1 = z)),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[31599, 31663, 27217, 166, 31579, 31476])).
% 5.24/5.40 tff(31665,plain,
% 5.24/5.40 (r(elem!1, z)),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[498, 31664, 5723])).
% 5.24/5.40 tff(31666,plain,
% 5.24/5.40 (~r(elem!1, s(s(z)))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[458, 31665, 28500])).
% 5.24/5.40 tff(31667,plain,
% 5.24/5.40 (b(elem!1, s(s(z)))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[467, 31666, 31586])).
% 5.24/5.40 tff(31668,plain,
% 5.24/5.40 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[2832, 31662])).
% 5.24/5.40 tff(31669,plain,
% 5.24/5.40 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[10809, 31665, 4236])).
% 5.24/5.40 tff(31670,plain,
% 5.24/5.40 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[691, 31669, 31668])).
% 5.24/5.40 tff(31671,plain,
% 5.24/5.40 ($false),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[11859, 31670, 31667, 166, 27217, 31579])).
% 5.24/5.40 tff(31672,plain,(b(z, s(s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | b(elem!1, z) | (s(elem!1) = elem!1) | b(z, s(s(z))) | b(s(s(s(s(z)))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.40 tff(31673,plain,
% 5.24/5.40 (b(z, s(s(s(s(s(s(s(z))))))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[31672, 31576, 5723, 31578, 28501, 86])).
% 5.24/5.40 tff(31674,plain,
% 5.24/5.40 (~(s(s(elem!1)) = s(elem!1))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[986, 3348])).
% 5.24/5.40 tff(31675,plain,
% 5.24/5.40 (~r(elem!1, z)),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[443, 438, 28500])).
% 5.24/5.40 tff(31676,plain,
% 5.24/5.40 (elem!1 = z),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[498, 31675, 5723])).
% 5.24/5.40 tff(31677,plain,
% 5.24/5.40 (s(elem!1) = s(z)),
% 5.24/5.40 inference(monotonicity,[status(thm)],[31676])).
% 5.24/5.40 tff(31678,plain,
% 5.24/5.40 (s(s(elem!1)) = s(s(z))),
% 5.24/5.40 inference(monotonicity,[status(thm)],[31677])).
% 5.24/5.40 tff(31679,plain,
% 5.24/5.40 (s(s(s(elem!1))) = s(s(s(z)))),
% 5.24/5.40 inference(monotonicity,[status(thm)],[31678])).
% 5.24/5.40 tff(31680,plain,
% 5.24/5.40 (s(s(s(z))) = s(s(s(elem!1)))),
% 5.24/5.40 inference(symmetry,[status(thm)],[31679])).
% 5.24/5.40 tff(31681,plain,
% 5.24/5.40 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 5.24/5.40 inference(monotonicity,[status(thm)],[31680])).
% 5.24/5.40 tff(31682,plain,
% 5.24/5.40 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(z))))),
% 5.24/5.40 inference(symmetry,[status(thm)],[31681])).
% 5.24/5.40 tff(31683,plain,
% 5.24/5.40 (r(elem!1, s(s(s(elem!1)))) <=> r(z, s(s(s(elem!1))))),
% 5.24/5.40 inference(monotonicity,[status(thm)],[31676])).
% 5.24/5.40 tff(31684,plain,
% 5.24/5.40 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 5.24/5.40 inference(symmetry,[status(thm)],[31683])).
% 5.24/5.40 tff(31685,plain,
% 5.24/5.40 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(z))))),
% 5.24/5.40 inference(monotonicity,[status(thm)],[31679])).
% 5.24/5.40 tff(31686,plain,
% 5.24/5.40 (r(z, s(s(s(z)))) <=> r(z, s(s(s(elem!1))))),
% 5.24/5.40 inference(symmetry,[status(thm)],[31685])).
% 5.24/5.40 tff(31687,plain,
% 5.24/5.40 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 5.24/5.40 inference(transitivity,[status(thm)],[31686, 31684])).
% 5.24/5.40 tff(31688,plain,
% 5.24/5.40 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 5.24/5.40 inference(monotonicity,[status(thm)],[31679])).
% 5.24/5.40 tff(31689,plain,
% 5.24/5.40 (r(s(s(s(s(elem!1)))), s(s(z))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 5.24/5.40 inference(monotonicity,[status(thm)],[31688])).
% 5.24/5.40 tff(31690,plain,
% 5.24/5.40 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(s(z)))),
% 5.24/5.40 inference(symmetry,[status(thm)],[31689])).
% 5.24/5.40 tff(31691,plain,
% 5.24/5.40 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 5.24/5.40 inference(modus_ponens,[status(thm)],[193, 31690])).
% 5.24/5.40 tff(31692,plain,
% 5.24/5.40 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[3559, 193, 204])).
% 5.24/5.40 tff(31693,plain,
% 5.24/5.40 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[249, 31692])).
% 5.24/5.40 tff(31694,plain,
% 5.24/5.40 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = z)),
% 5.24/5.40 inference(monotonicity,[status(thm)],[31676])).
% 5.24/5.40 tff(31695,plain,
% 5.24/5.40 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 5.24/5.40 inference(symmetry,[status(thm)],[31694])).
% 5.24/5.40 tff(31696,plain,
% 5.24/5.40 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 5.24/5.40 inference(monotonicity,[status(thm)],[31695])).
% 5.24/5.40 tff(31697,plain,
% 5.24/5.40 (~(s(s(s(elem!1))) = elem!1)),
% 5.24/5.40 inference(modus_ponens,[status(thm)],[940, 31696])).
% 5.24/5.40 tff(31698,plain,
% 5.24/5.40 (b(s(elem!1), s(s(z))) <=> b(s(z), s(s(z)))),
% 5.24/5.40 inference(monotonicity,[status(thm)],[31677])).
% 5.24/5.40 tff(31699,plain,
% 5.24/5.40 (~r(s(elem!1), s(s(z)))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[12437, 853, 29994, 193, 30961])).
% 5.24/5.40 tff(31700,plain,
% 5.24/5.40 (b(s(elem!1), s(s(z)))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[421, 31699, 1056])).
% 5.24/5.40 tff(31701,plain,
% 5.24/5.40 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[14677, 31700, 29994, 24628, 595, 166, 2311])).
% 5.24/5.40 tff(31702,plain,
% 5.24/5.40 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[395, 31701, 14147])).
% 5.24/5.40 tff(31703,plain,
% 5.24/5.40 (~r(s(elem!1), s(s(s(s(z)))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[25119, 31702])).
% 5.24/5.40 tff(31704,plain,
% 5.24/5.40 (b(s(elem!1), s(s(s(s(z)))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[1084, 31703, 30961])).
% 5.24/5.40 tff(31705,plain,
% 5.24/5.40 (b(s(z), s(s(s(s(z)))))),
% 5.24/5.40 inference(modus_ponens,[status(thm)],[31704, 14888])).
% 5.24/5.40 tff(31706,plain,
% 5.24/5.40 (~b(z, s(z))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[31245, 178, 27212, 31623, 12121, 31705])).
% 5.24/5.40 tff(31707,plain,
% 5.24/5.40 (~b(elem!1, s(elem!1))),
% 5.24/5.40 inference(modus_ponens,[status(thm)],[31706, 21241])).
% 5.24/5.40 tff(31708,plain,
% 5.24/5.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 5.24/5.40 inference(rewrite,[status(thm)],[])).
% 5.24/5.40 tff(31709,plain,
% 5.24/5.40 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~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(z)), s(z)))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 5.24/5.40 inference(rewrite,[status(thm)],[])).
% 5.24/5.40 tff(31710,plain,
% 5.24/5.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~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(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z))))))))),
% 5.24/5.40 inference(monotonicity,[status(thm)],[31709])).
% 5.24/5.40 tff(31711,plain,
% 5.24/5.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~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(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 5.24/5.40 inference(transitivity,[status(thm)],[31710, 31708])).
% 5.24/5.40 tff(31712,plain,
% 5.24/5.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~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(z)), s(z))))),
% 5.24/5.40 inference(quant_inst,[status(thm)],[])).
% 5.24/5.40 tff(31713,plain,
% 5.24/5.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z))))))),
% 5.24/5.40 inference(modus_ponens,[status(thm)],[31712, 31711])).
% 5.24/5.40 tff(31714,plain,
% 5.24/5.40 (~b(s(s(z)), s(z))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[31713, 178, 31623, 167, 12121, 31705])).
% 5.24/5.40 tff(31715,plain,
% 5.24/5.40 (~b(s(s(elem!1)), s(elem!1))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[1015, 31714, 928])).
% 5.24/5.40 tff(31716,plain,
% 5.24/5.40 (r(s(s(elem!1)), s(elem!1))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[1006, 31715, 1000])).
% 5.24/5.40 tff(31717,plain,
% 5.24/5.40 (~r(z, s(elem!1))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[10967, 31716, 30940])).
% 5.24/5.40 tff(31718,plain,
% 5.24/5.40 (b(z, s(elem!1))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[2351, 31717])).
% 5.24/5.40 tff(31719,plain,
% 5.24/5.40 (b(elem!1, s(elem!1))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[12054, 31718, 928])).
% 5.24/5.40 tff(31720,plain,
% 5.24/5.40 ($false),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[31719, 31707])).
% 5.24/5.40 tff(31721,plain,((~b(s(elem!1), z)) | (~(elem!1 = z)) | (s(s(elem!1)) = s(elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(s(z))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.40 tff(31722,plain,
% 5.24/5.40 (~b(s(elem!1), z)),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[31721, 31676, 1000, 167, 595, 31693, 1056, 193])).
% 5.24/5.40 tff(31723,plain,
% 5.24/5.40 (r(s(elem!1), z)),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[774, 31722])).
% 5.24/5.40 tff(31724,plain,
% 5.24/5.40 (~r(s(elem!1), s(s(z)))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[2258, 31723, 28500])).
% 5.24/5.40 tff(31725,plain,
% 5.24/5.40 (b(s(elem!1), s(s(z)))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[421, 31724, 1056])).
% 5.24/5.40 tff(31726,plain,
% 5.24/5.40 (b(s(z), s(s(z)))),
% 5.24/5.40 inference(modus_ponens,[status(thm)],[31725, 31698])).
% 5.24/5.40 tff(31727,plain,
% 5.24/5.40 (r(s(s(elem!1)), z) <=> r(s(s(z)), z)),
% 5.24/5.40 inference(monotonicity,[status(thm)],[31678])).
% 5.24/5.40 tff(31728,plain,
% 5.24/5.40 (r(s(s(z)), z) <=> r(s(s(elem!1)), z)),
% 5.24/5.40 inference(symmetry,[status(thm)],[31727])).
% 5.24/5.40 tff(31729,plain,
% 5.24/5.40 (r(s(s(elem!1)), z)),
% 5.24/5.40 inference(modus_ponens,[status(thm)],[28500, 31728])).
% 5.24/5.40 tff(31730,plain,
% 5.24/5.40 (~r(s(s(elem!1)), s(elem!1))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[997, 31723, 31729])).
% 5.24/5.40 tff(31731,plain,
% 5.24/5.40 (b(s(s(elem!1)), s(elem!1))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[1006, 31730, 1000])).
% 5.24/5.40 tff(31732,plain,
% 5.24/5.40 (b(s(s(z)), s(z))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[1015, 31731, 31676])).
% 5.24/5.40 tff(31733,plain,
% 5.24/5.40 (r(elem!1, s(s(elem!1))) <=> r(z, s(s(elem!1)))),
% 5.24/5.40 inference(monotonicity,[status(thm)],[31676])).
% 5.24/5.40 tff(31734,plain,
% 5.24/5.40 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 5.24/5.40 inference(symmetry,[status(thm)],[31733])).
% 5.24/5.40 tff(31735,plain,
% 5.24/5.40 (r(z, s(s(elem!1))) <=> r(z, s(s(z)))),
% 5.24/5.40 inference(monotonicity,[status(thm)],[31678])).
% 5.24/5.40 tff(31736,plain,
% 5.24/5.40 (r(z, s(s(z))) <=> r(z, s(s(elem!1)))),
% 5.24/5.40 inference(symmetry,[status(thm)],[31735])).
% 5.24/5.40 tff(31737,plain,
% 5.24/5.40 (r(z, s(s(z))) <=> r(elem!1, s(s(elem!1)))),
% 5.24/5.40 inference(transitivity,[status(thm)],[31736, 31734])).
% 5.24/5.40 tff(31738,plain,
% 5.24/5.40 (r(elem!1, s(s(elem!1)))),
% 5.24/5.40 inference(modus_ponens,[status(thm)],[29994, 31737])).
% 5.24/5.40 tff(31739,plain,
% 5.24/5.40 (b(s(elem!1), elem!1) <=> b(s(elem!1), z)),
% 5.24/5.40 inference(monotonicity,[status(thm)],[31676])).
% 5.24/5.40 tff(31740,plain,
% 5.24/5.40 (b(s(elem!1), z) <=> b(s(elem!1), elem!1)),
% 5.24/5.40 inference(symmetry,[status(thm)],[31739])).
% 5.24/5.40 tff(31741,plain,
% 5.24/5.40 ((~b(s(elem!1), z)) <=> (~b(s(elem!1), elem!1))),
% 5.24/5.40 inference(monotonicity,[status(thm)],[31740])).
% 5.24/5.40 tff(31742,plain,
% 5.24/5.40 (~b(s(elem!1), elem!1)),
% 5.24/5.40 inference(modus_ponens,[status(thm)],[31722, 31741])).
% 5.24/5.40 tff(31743,plain,
% 5.24/5.40 (r(s(elem!1), elem!1)),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[677, 31742, 725])).
% 5.24/5.40 tff(31744,plain,
% 5.24/5.40 (~r(s(s(s(elem!1))), elem!1)),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[12762, 31743, 31738, 31676, 31732, 31726])).
% 5.24/5.40 tff(31745,plain,
% 5.24/5.40 (b(s(s(s(elem!1))), elem!1)),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[570, 31744, 31697])).
% 5.24/5.40 tff(31746,plain,
% 5.24/5.40 ((~b(s(s(s(elem!1))), elem!1)) | (~(elem!1 = z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~r(z, s(s(z))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[30640, 24592])).
% 5.24/5.40 tff(31747,plain,
% 5.24/5.40 (~b(z, s(s(s(z))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[31746, 31745, 29994, 31623, 31693, 27212, 24628, 31676, 31691])).
% 5.24/5.40 tff(31748,plain,
% 5.24/5.40 (r(z, s(s(s(z))))),
% 5.24/5.40 inference(unit_resolution,[status(thm)],[4920, 31747])).
% 5.24/5.40 tff(31749,plain,
% 5.24/5.41 (r(elem!1, s(s(s(elem!1))))),
% 5.24/5.41 inference(modus_ponens,[status(thm)],[31748, 31687])).
% 5.24/5.41 tff(31750,plain,
% 5.24/5.41 (~r(s(s(z)), s(s(s(elem!1))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[7973, 31749, 438])).
% 5.24/5.41 tff(31751,plain,
% 5.24/5.41 (b(s(s(z)), s(s(s(elem!1))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[4223, 31750])).
% 5.24/5.41 tff(31752,plain,
% 5.24/5.41 (b(s(s(z)), s(s(s(z))))),
% 5.24/5.41 inference(modus_ponens,[status(thm)],[31751, 31682])).
% 5.24/5.41 tff(31753,plain,
% 5.24/5.41 (~r(s(s(s(z))), s(s(z)))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[24302, 31748, 29994])).
% 5.24/5.41 tff(31754,plain,
% 5.24/5.41 (b(s(s(s(z))), s(s(z)))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[4966, 31753])).
% 5.24/5.41 tff(31755,plain,
% 5.24/5.41 (b(s(s(s(elem!1))), z) <=> b(s(s(s(z))), z)),
% 5.24/5.41 inference(monotonicity,[status(thm)],[31679])).
% 5.24/5.41 tff(31756,plain,
% 5.24/5.41 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), z)),
% 5.24/5.41 inference(monotonicity,[status(thm)],[31676])).
% 5.24/5.41 tff(31757,plain,
% 5.24/5.41 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), z)),
% 5.24/5.41 inference(transitivity,[status(thm)],[31756, 31755])).
% 5.24/5.41 tff(31758,plain,
% 5.24/5.41 (b(s(s(s(z))), z)),
% 5.24/5.41 inference(modus_ponens,[status(thm)],[31745, 31757])).
% 5.24/5.41 tff(31759,plain,
% 5.24/5.41 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[21413, 31758, 27212, 31623, 204])).
% 5.24/5.41 tff(31760,plain,
% 5.24/5.41 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[20667, 31759])).
% 5.24/5.41 tff(31761,plain,
% 5.24/5.41 (~b(s(s(z)), s(s(s(z))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[21439, 31760, 24628, 31693, 31754])).
% 5.24/5.41 tff(31762,plain,
% 5.24/5.41 ($false),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[31761, 31752])).
% 5.24/5.41 tff(31763,plain,((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = elem!1) | (s(s(elem!1)) = s(elem!1)) | (s(elem!1) = s(s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(z)))) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 5.24/5.41 tff(31764,plain,
% 5.24/5.41 (~r(s(s(z)), elem!1)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[31763, 1056, 725, 1000, 204, 167, 595, 103, 5723])).
% 5.24/5.41 tff(31765,plain,
% 5.24/5.41 (~b(s(s(z)), elem!1)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[31609, 844, 725, 5723, 1056, 27217, 166, 167])).
% 5.24/5.41 tff(31766,plain,
% 5.24/5.41 (s(s(z)) = elem!1),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[448, 31765, 10828])).
% 5.24/5.41 tff(31767,plain,
% 5.24/5.41 (s(s(s(z))) = s(elem!1)),
% 5.24/5.41 inference(monotonicity,[status(thm)],[31766])).
% 5.24/5.41 tff(31768,plain,
% 5.24/5.41 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 5.24/5.41 inference(monotonicity,[status(thm)],[31767])).
% 5.24/5.41 tff(31769,plain,
% 5.24/5.41 (b(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.24/5.41 inference(symmetry,[status(thm)],[31768])).
% 5.24/5.41 tff(31770,plain,
% 5.24/5.41 ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) <=> (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 5.24/5.41 inference(monotonicity,[status(thm)],[31769])).
% 5.24/5.41 tff(31771,plain,
% 5.24/5.41 (b(s(elem!1), elem!1)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[677, 19171, 725])).
% 5.24/5.41 tff(31772,plain,
% 5.24/5.41 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[14677, 31603, 29994, 27217, 595, 166, 2311])).
% 5.24/5.41 tff(31773,plain,
% 5.24/5.41 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[686, 31772, 31771])).
% 5.24/5.41 tff(31774,plain,
% 5.24/5.41 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[703, 31773])).
% 5.24/5.41 tff(31775,plain,
% 5.24/5.41 (~b(s(s(s(s(z)))), elem!1)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[3774, 31766, 86])).
% 5.24/5.41 tff(31776,plain,
% 5.24/5.41 (r(s(s(s(s(z)))), elem!1)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[3142, 31775, 31641])).
% 5.24/5.41 tff(31777,plain,
% 5.24/5.41 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[25879, 31776])).
% 5.24/5.41 tff(31778,plain,
% 5.24/5.41 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[3444, 31777, 31774])).
% 5.24/5.41 tff(31779,plain,
% 5.24/5.41 (s(s(s(s(z)))) = s(s(elem!1))),
% 5.24/5.41 inference(monotonicity,[status(thm)],[31767])).
% 5.24/5.41 tff(31780,plain,
% 5.24/5.41 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(elem!1)))),
% 5.24/5.41 inference(monotonicity,[status(thm)],[31779])).
% 5.24/5.41 tff(31781,plain,
% 5.24/5.41 (b(elem!1, s(s(s(s(z)))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[17989, 31766, 167])).
% 5.24/5.41 tff(31782,plain,
% 5.24/5.41 (b(elem!1, s(s(elem!1)))),
% 5.24/5.41 inference(modus_ponens,[status(thm)],[31781, 31780])).
% 5.24/5.41 tff(31783,plain,
% 5.24/5.41 (s(s(elem!1)) = s(s(s(s(z))))),
% 5.24/5.41 inference(symmetry,[status(thm)],[31779])).
% 5.24/5.41 tff(31784,plain,
% 5.24/5.41 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 5.24/5.41 inference(monotonicity,[status(thm)],[31783])).
% 5.24/5.41 tff(31785,plain,
% 5.24/5.41 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), s(s(elem!1)))),
% 5.24/5.41 inference(symmetry,[status(thm)],[31784])).
% 5.24/5.41 tff(31786,plain,
% 5.24/5.41 (~(s(elem!1) = s(s(s(s(z)))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[12552, 31603, 86])).
% 5.24/5.41 tff(31787,plain,
% 5.24/5.41 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[5361, 31766])).
% 5.24/5.41 tff(31788,plain,
% 5.24/5.41 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[395, 31772, 31787])).
% 5.24/5.41 tff(31789,plain,
% 5.24/5.41 (~r(s(elem!1), s(s(s(s(z)))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[25119, 31788])).
% 5.24/5.41 tff(31790,plain,
% 5.24/5.41 (b(s(elem!1), s(s(s(s(z)))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[1084, 31789, 31786])).
% 5.24/5.41 tff(31791,plain,
% 5.24/5.41 (b(s(elem!1), s(s(elem!1)))),
% 5.24/5.41 inference(modus_ponens,[status(thm)],[31790, 31785])).
% 5.24/5.41 tff(31792,plain,
% 5.24/5.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(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))))),
% 5.24/5.41 inference(rewrite,[status(thm)],[])).
% 5.24/5.41 tff(31793,plain,
% 5.24/5.41 (((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(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(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 5.24/5.41 inference(rewrite,[status(thm)],[])).
% 5.24/5.41 tff(31794,plain,
% 5.24/5.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(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)))))),
% 5.24/5.41 inference(monotonicity,[status(thm)],[31793])).
% 5.24/5.41 tff(31795,plain,
% 5.24/5.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(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))))),
% 5.24/5.41 inference(transitivity,[status(thm)],[31794, 31792])).
% 5.24/5.41 tff(31796,plain,
% 5.24/5.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 5.24/5.41 inference(quant_inst,[status(thm)],[])).
% 5.24/5.41 tff(31797,plain,
% 5.24/5.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 5.24/5.41 inference(modus_ponens,[status(thm)],[31796, 31795])).
% 5.24/5.41 tff(31798,plain,
% 5.24/5.41 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[31797, 178, 31771, 31791, 31782, 31778])).
% 5.24/5.41 tff(31799,plain,
% 5.24/5.41 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.24/5.41 inference(modus_ponens,[status(thm)],[31798, 31770])).
% 5.24/5.41 tff(31800,plain,
% 5.24/5.41 (r(s(s(s(z))), z) <=> r(s(elem!1), z)),
% 5.24/5.41 inference(monotonicity,[status(thm)],[31767])).
% 5.24/5.41 tff(31801,plain,
% 5.24/5.41 (r(s(elem!1), z) <=> r(s(s(s(z))), z)),
% 5.24/5.41 inference(symmetry,[status(thm)],[31800])).
% 5.24/5.41 tff(31802,plain,
% 5.24/5.41 (r(s(s(s(z))), z)),
% 5.24/5.41 inference(modus_ponens,[status(thm)],[844, 31801])).
% 5.24/5.41 tff(31803,plain,
% 5.24/5.41 (~r(s(s(s(z))), s(s(z)))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[24599, 16062, 28500])).
% 5.24/5.41 tff(31804,plain,
% 5.24/5.41 (b(s(s(s(z))), s(s(z)))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[4966, 31803])).
% 5.24/5.41 tff(31805,plain,
% 5.24/5.41 (b(s(s(s(s(z)))), s(s(s(z))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[11185, 31539])).
% 5.24/5.41 tff(31806,plain,
% 5.24/5.41 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[24614, 31805, 167, 16062, 28500, 31804])).
% 5.24/5.41 tff(31807,plain,
% 5.24/5.41 (r(s(s(s(z))), s(s(s(s(z)))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[10755, 31806])).
% 5.24/5.41 tff(31808,plain,
% 5.24/5.41 ($false),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[3043, 118, 24592, 31807, 16063])).
% 5.24/5.41 tff(31809,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.41 tff(31810,plain,
% 5.24/5.41 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[31809, 31802, 167])).
% 5.24/5.41 tff(31811,plain,
% 5.24/5.41 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[31522, 31810])).
% 5.24/5.41 tff(31812,plain,
% 5.24/5.41 ($false),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[31811, 31799])).
% 5.24/5.41 tff(31813,plain,((~r(s(elem!1), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = elem!1) | r(s(s(z)), elem!1) | (s(elem!1) = s(s(z))) | (~r(elem!1, z)) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 5.24/5.41 tff(31814,plain,
% 5.24/5.41 (~r(s(elem!1), z)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[31813, 30257, 86, 595, 166, 725, 10828, 1056, 167, 5723])).
% 5.24/5.41 tff(31815,plain,
% 5.24/5.41 (b(s(elem!1), z)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[774, 31814])).
% 5.24/5.41 tff(31816,plain,
% 5.24/5.41 ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[11770, 178, 853, 27212, 31623])).
% 5.24/5.41 tff(31817,plain,
% 5.24/5.41 (~b(z, s(elem!1))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[31816, 1069])).
% 5.24/5.41 tff(31818,plain,
% 5.24/5.41 (r(z, s(elem!1))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[2351, 31817])).
% 5.24/5.41 tff(31819,plain,
% 5.24/5.41 ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[29218, 178, 853, 31623, 167])).
% 5.24/5.41 tff(31820,plain,
% 5.24/5.41 (~b(s(s(z)), s(elem!1))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[31819, 1069])).
% 5.24/5.41 tff(31821,plain,
% 5.24/5.41 (r(s(s(z)), s(elem!1))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[1067, 31820, 1060])).
% 5.24/5.41 tff(31822,plain,
% 5.24/5.41 ($false),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[2341, 31821, 31818, 28500])).
% 5.24/5.41 tff(31823,plain,((~b(s(elem!1), s(s(s(s(z)))))) | (s(s(z)) = s(elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.41 tff(31824,plain,
% 5.24/5.41 (~b(s(elem!1), s(s(s(s(z)))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[31823, 31815, 2311, 167])).
% 5.24/5.41 tff(31825,plain,
% 5.24/5.41 (r(s(elem!1), s(s(s(s(z)))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[1084, 10925, 5720])).
% 5.24/5.41 tff(31826,plain,
% 5.24/5.41 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[25119, 31825])).
% 5.24/5.41 tff(31827,plain,
% 5.24/5.41 (~r(s(elem!1), s(s(z)))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[12437, 10925, 29994, 193, 853])).
% 5.24/5.41 tff(31828,plain,
% 5.24/5.41 (b(s(elem!1), s(s(z)))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[421, 31827, 1056])).
% 5.24/5.41 tff(31829,plain,
% 5.24/5.41 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[14677, 31828, 29994, 24628, 595, 166, 2311])).
% 5.24/5.41 tff(31830,plain,
% 5.24/5.41 ($false),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[395, 31829, 31826, 8112])).
% 5.24/5.41 tff(31831,plain,((~(s(s(z)) = elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(s(z))) | b(s(elem!1), s(s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(elem!1), z)) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 5.24/5.41 tff(31832,plain,
% 5.24/5.41 (~(s(s(z)) = elem!1)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[31831, 31824, 166, 1056, 595, 103, 31815, 31641])).
% 5.24/5.41 tff(31833,plain,
% 5.24/5.41 (~(elem!1 = s(s(z)))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[311, 31832])).
% 5.24/5.41 tff(31834,plain,
% 5.24/5.41 (~r(elem!1, s(s(z)))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[458, 30257, 28500])).
% 5.24/5.41 tff(31835,plain,
% 5.24/5.41 (b(elem!1, s(s(z)))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[467, 31833, 31834])).
% 5.24/5.41 tff(31836,plain,
% 5.24/5.41 (b(s(s(z)), elem!1)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[448, 31832, 10828])).
% 5.24/5.41 tff(31837,plain,
% 5.24/5.41 (b(elem!1, s(s(z)))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[467, 462, 29536])).
% 5.24/5.41 tff(31838,plain,
% 5.24/5.41 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[11859, 31837, 166, 24628, 817])).
% 5.24/5.41 tff(31839,plain,
% 5.24/5.41 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[16181, 1117])).
% 5.24/5.41 tff(31840,plain,
% 5.24/5.41 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[691, 31839, 31838])).
% 5.24/5.41 tff(31841,plain,
% 5.24/5.41 (~b(elem!1, s(s(s(s(z)))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[30095, 1117, 193, 817, 437, 24628, 168, 2857, 31839, 166, 462])).
% 5.24/5.41 tff(31842,plain,
% 5.24/5.41 (r(elem!1, s(s(s(s(z)))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[483, 31841, 469])).
% 5.24/5.41 tff(31843,plain,
% 5.24/5.41 ($false),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[25883, 31842, 31840])).
% 5.24/5.41 tff(31844,plain,((~(s(elem!1) = s(s(s(s(z)))))) | (elem!1 = s(s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~r(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.41 tff(31845,plain,
% 5.24/5.41 (~(s(elem!1) = s(s(s(s(z)))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[31844, 31836, 103, 31624, 30257, 31623, 13192, 166, 31833])).
% 5.24/5.41 tff(31846,plain,
% 5.24/5.41 (r(s(elem!1), s(s(s(s(z)))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[1084, 31845, 31824])).
% 5.24/5.41 tff(31847,plain,
% 5.24/5.41 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[25119, 31846])).
% 5.24/5.41 tff(31848,plain,
% 5.24/5.41 (~r(s(elem!1), s(s(z)))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[12437, 31845, 29994, 103, 31815])).
% 5.24/5.41 tff(31849,plain,
% 5.24/5.41 (b(s(elem!1), s(s(z)))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[421, 31848, 1056])).
% 5.24/5.41 tff(31850,plain,
% 5.24/5.41 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[14677, 31849, 29994, 27217, 595, 166, 2311])).
% 5.24/5.41 tff(31851,plain,
% 5.24/5.41 (s(elem!1) = s(s(s(s(s(s(s(z)))))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[395, 31850, 31847])).
% 5.24/5.41 tff(31852,plain,
% 5.24/5.41 ((s(elem!1) = elem!1) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 5.24/5.41 inference(monotonicity,[status(thm)],[31851])).
% 5.24/5.41 tff(31853,plain,
% 5.24/5.41 ((s(elem!1) = elem!1) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 5.24/5.41 inference(transitivity,[status(thm)],[31852, 836])).
% 5.24/5.41 tff(31854,plain,
% 5.24/5.41 ((~(s(elem!1) = elem!1)) <=> (~(elem!1 = s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.41 inference(monotonicity,[status(thm)],[31853])).
% 5.24/5.41 tff(31855,plain,
% 5.24/5.41 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 5.24/5.41 inference(modus_ponens,[status(thm)],[725, 31854])).
% 5.24/5.41 tff(31856,plain,
% 5.24/5.41 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[29488, 31855, 167, 27217, 31835, 166, 31624])).
% 5.24/5.41 tff(31857,plain,
% 5.24/5.41 (~r(s(s(s(s(z)))), elem!1)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[25879, 31856])).
% 5.24/5.41 tff(31858,plain,
% 5.24/5.41 (b(s(s(s(s(z)))), elem!1)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[3142, 31857, 31641])).
% 5.24/5.41 tff(31859,plain,
% 5.24/5.41 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[11859, 31835, 166, 27217, 31836])).
% 5.24/5.41 tff(31860,plain,
% 5.24/5.41 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[691, 31855, 31859])).
% 5.24/5.41 tff(31861,plain,
% 5.24/5.41 (~r(elem!1, s(s(s(s(z)))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[25883, 31860])).
% 5.24/5.41 tff(31862,plain,
% 5.24/5.41 (b(elem!1, s(s(s(s(z)))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[483, 31861, 31624])).
% 5.24/5.41 tff(31863,plain,
% 5.24/5.41 ($false),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[16429, 24209, 23454, 168, 3771, 1301])).
% 5.24/5.41 tff(31864,plain,((~r(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (z = elem!1) | (elem!1 = z) | (~r(z, s(s(z)))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.41 tff(31865,plain,
% 5.24/5.41 (~r(elem!1, s(s(z)))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[31864, 3771, 168, 1301, 507, 290, 3261, 106])).
% 5.24/5.41 tff(31866,plain,
% 5.24/5.41 (b(elem!1, s(s(z)))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[467, 31865, 462])).
% 5.24/5.41 tff(31867,plain,
% 5.24/5.41 (~b(s(s(z)), elem!1)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[19781, 31866, 3771, 1301, 167])).
% 5.24/5.41 tff(31868,plain,
% 5.24/5.41 (r(s(s(z)), elem!1)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[448, 31867, 12])).
% 5.24/5.41 tff(31869,plain,
% 5.24/5.41 (~r(elem!1, z)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[443, 31868, 106])).
% 5.24/5.41 tff(31870,plain,
% 5.24/5.41 (b(elem!1, z)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[498, 31869, 290])).
% 5.24/5.41 tff(31871,plain,
% 5.24/5.41 (~r(z, elem!1)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[8412, 31868, 3261])).
% 5.24/5.41 tff(31872,plain,
% 5.24/5.41 (b(z, elem!1)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[585, 31871, 507])).
% 5.24/5.41 tff(31873,plain,
% 5.24/5.41 ($false),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[16429, 31872, 31870, 168, 3771, 1301])).
% 5.24/5.41 tff(31874,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (z = elem!1) | (elem!1 = z) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (s(s(z)) = elem!1) | (~b(s(s(z)), s(s(s(s(z)))))) | (elem!1 = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.41 tff(31875,plain,
% 5.24/5.41 ($false),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[31874, 31862, 31858, 28500, 29994, 167, 31623, 290, 31832, 318, 31833])).
% 5.24/5.41 tff(31876,plain,((elem!1 = z) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = elem!1) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(s(z))) | r(s(s(z)), elem!1) | b(s(s(s(s(z)))), s(s(z))) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 5.24/5.41 tff(31877,plain,
% 5.24/5.41 (elem!1 = z),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[31876, 1056, 31578, 725, 595, 167, 31764, 86, 5723])).
% 5.24/5.41 tff(31878,plain,
% 5.24/5.41 (z = elem!1),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[2808, 31877])).
% 5.24/5.41 tff(31879,plain,
% 5.24/5.41 (b(s(s(s(s(z)))), elem!1)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[20730, 31878, 31623])).
% 5.24/5.41 tff(31880,plain,
% 5.24/5.41 (~(s(s(z)) = elem!1)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[3774, 31879, 86])).
% 5.24/5.41 tff(31881,plain,
% 5.24/5.41 (~b(s(elem!1), z)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[31721, 31877, 1000, 167, 595, 31578, 1056, 103])).
% 5.24/5.41 tff(31882,plain,
% 5.24/5.41 (r(s(elem!1), z)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[774, 31881])).
% 5.24/5.41 tff(31883,plain,
% 5.24/5.41 (~b(s(s(z)), elem!1)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[31609, 31882, 725, 5723, 1056, 27217, 31578, 167])).
% 5.24/5.41 tff(31884,plain,
% 5.24/5.41 ($false),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[448, 31883, 31880, 31764])).
% 5.24/5.41 tff(31885,plain,((s(elem!1) = s(s(z))) | (s(elem!1) = elem!1) | b(elem!1, z) | (~b(s(s(z)), s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(z))) | (s(s(elem!1)) = s(elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.41 tff(31886,plain,
% 5.24/5.41 (s(elem!1) = s(s(z))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[31885, 31576, 5723, 31476, 86, 31674, 31673, 204])).
% 5.24/5.41 tff(31887,plain,
% 5.24/5.41 (r(s(elem!1), z)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[906, 31886, 28500])).
% 5.24/5.41 tff(31888,plain,
% 5.24/5.41 (~(z = elem!1)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[28525, 31886])).
% 5.24/5.41 tff(31889,plain,
% 5.24/5.41 (~(elem!1 = z)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[2808, 31888])).
% 5.24/5.41 tff(31890,plain,
% 5.24/5.41 (r(elem!1, z)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[498, 31889, 5723])).
% 5.24/5.41 tff(31891,plain,
% 5.24/5.41 (~r(s(elem!1), elem!1)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[13694, 31890, 31887])).
% 5.24/5.41 tff(31892,plain,
% 5.24/5.41 (b(s(elem!1), elem!1)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[677, 31891, 31576])).
% 5.24/5.41 tff(31893,plain,
% 5.24/5.41 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 5.24/5.41 inference(monotonicity,[status(thm)],[31886])).
% 5.24/5.41 tff(31894,plain,
% 5.24/5.41 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 5.24/5.41 inference(symmetry,[status(thm)],[31893])).
% 5.24/5.41 tff(31895,plain,
% 5.24/5.41 (s(s(elem!1)) = s(s(s(z)))),
% 5.24/5.41 inference(monotonicity,[status(thm)],[31886])).
% 5.24/5.41 tff(31896,plain,
% 5.24/5.41 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 5.24/5.41 inference(monotonicity,[status(thm)],[31895])).
% 5.24/5.41 tff(31897,plain,
% 5.24/5.41 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 5.24/5.41 inference(monotonicity,[status(thm)],[31896])).
% 5.24/5.41 tff(31898,plain,
% 5.24/5.41 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 5.24/5.41 inference(symmetry,[status(thm)],[31897])).
% 5.24/5.41 tff(31899,plain,
% 5.24/5.41 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 5.24/5.41 inference(transitivity,[status(thm)],[31898, 31894])).
% 5.24/5.41 tff(31900,plain,
% 5.24/5.41 (b(s(elem!1), s(s(s(elem!1))))),
% 5.24/5.41 inference(modus_ponens,[status(thm)],[31476, 31899])).
% 5.24/5.41 tff(31901,plain,
% 5.24/5.41 (~(elem!1 = s(elem!1))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[748, 31576])).
% 5.24/5.41 tff(31902,plain,
% 5.24/5.41 (~r(elem!1, s(elem!1))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[2711, 31890, 31887])).
% 5.24/5.41 tff(31903,plain,
% 5.24/5.41 (b(elem!1, s(elem!1))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[756, 31902, 31901])).
% 5.24/5.41 tff(31904,plain,
% 5.24/5.41 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(s(z)))) = elem!1)),
% 5.24/5.41 inference(monotonicity,[status(thm)],[31896])).
% 5.24/5.41 tff(31905,plain,
% 5.24/5.41 ((s(s(s(s(z)))) = elem!1) <=> (s(s(s(elem!1))) = elem!1)),
% 5.24/5.41 inference(symmetry,[status(thm)],[31904])).
% 5.24/5.41 tff(31906,plain,
% 5.24/5.41 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 5.24/5.41 inference(monotonicity,[status(thm)],[31905])).
% 5.24/5.41 tff(31907,plain,
% 5.24/5.41 (~(elem!1 = s(s(s(s(z)))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[12557, 5723, 31575])).
% 5.24/5.41 tff(31908,plain,
% 5.24/5.41 (~(s(s(s(s(z)))) = elem!1)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[504, 31907])).
% 5.24/5.41 tff(31909,plain,
% 5.24/5.41 (~(s(s(s(elem!1))) = elem!1)),
% 5.24/5.41 inference(modus_ponens,[status(thm)],[31908, 31906])).
% 5.24/5.41 tff(31910,plain,
% 5.24/5.41 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[2832, 31886])).
% 5.24/5.41 tff(31911,plain,
% 5.24/5.41 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(z)))),
% 5.24/5.41 inference(monotonicity,[status(thm)],[31886])).
% 5.24/5.41 tff(31912,plain,
% 5.24/5.41 (b(elem!1, s(s(z)))),
% 5.24/5.41 inference(modus_ponens,[status(thm)],[31903, 31911])).
% 5.24/5.41 tff(31913,plain,
% 5.24/5.41 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[29488, 31912, 31476, 27217, 31910, 31578, 31907])).
% 5.24/5.41 tff(31914,plain,
% 5.24/5.41 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.41 inference(monotonicity,[status(thm)],[31896])).
% 5.24/5.41 tff(31915,plain,
% 5.24/5.41 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.41 inference(symmetry,[status(thm)],[31914])).
% 5.24/5.41 tff(31916,plain,
% 5.24/5.41 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.41 inference(modus_ponens,[status(thm)],[204, 31915])).
% 5.24/5.41 tff(31917,plain,
% 5.24/5.41 (~r(s(s(s(elem!1))), elem!1)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[3682, 31916, 31913])).
% 5.24/5.41 tff(31918,plain,
% 5.24/5.41 (b(s(s(s(elem!1))), elem!1)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[570, 31917, 31909])).
% 5.24/5.41 tff(31919,plain,
% 5.24/5.41 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(s(s(elem!1))))),
% 5.24/5.41 inference(transitivity,[status(thm)],[31905, 2486])).
% 5.24/5.41 tff(31920,plain,
% 5.24/5.41 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 5.24/5.41 inference(monotonicity,[status(thm)],[31919])).
% 5.24/5.41 tff(31921,plain,
% 5.24/5.41 (~(elem!1 = s(s(s(elem!1))))),
% 5.24/5.41 inference(modus_ponens,[status(thm)],[31908, 31920])).
% 5.24/5.41 tff(31922,plain,
% 5.24/5.41 (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(s(z)))))),
% 5.24/5.41 inference(monotonicity,[status(thm)],[31896])).
% 5.24/5.41 tff(31923,plain,
% 5.24/5.41 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 5.24/5.41 inference(symmetry,[status(thm)],[31922])).
% 5.24/5.41 tff(31924,plain,
% 5.24/5.41 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 5.24/5.41 inference(modus_ponens,[status(thm)],[24592, 31923])).
% 5.24/5.41 tff(31925,plain,
% 5.24/5.41 (~r(elem!1, s(s(s(elem!1))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[8969, 31924, 31913])).
% 5.24/5.41 tff(31926,plain,
% 5.24/5.41 (b(elem!1, s(s(s(elem!1))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[2054, 31925, 31921])).
% 5.24/5.41 tff(31927,plain,
% 5.24/5.41 ($false),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[6834, 31926, 31918, 31903, 31900, 31892])).
% 5.24/5.41 tff(31928,plain,((s(s(elem!1)) = elem!1) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | b(elem!1, z) | b(s(s(s(s(z)))), s(s(z))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.41 tff(31929,plain,
% 5.24/5.41 (s(s(elem!1)) = elem!1),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[31928, 5723, 204, 86, 28501])).
% 5.24/5.41 tff(31930,plain,
% 5.24/5.41 (elem!1 = s(s(elem!1))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[1546, 31929])).
% 5.24/5.41 tff(31931,plain,
% 5.24/5.41 (s(s(s(elem!1))) = s(elem!1)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[1539, 31930])).
% 5.24/5.41 tff(31932,plain,
% 5.24/5.41 (elem!1 = s(s(s(s(elem!1))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[1509, 31931])).
% 5.24/5.41 tff(31933,plain,
% 5.24/5.41 (s(s(s(s(elem!1)))) = elem!1),
% 5.24/5.41 inference(symmetry,[status(thm)],[31932])).
% 5.24/5.41 tff(31934,plain,
% 5.24/5.41 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(z)) = elem!1)),
% 5.24/5.41 inference(monotonicity,[status(thm)],[31933])).
% 5.24/5.41 tff(31935,plain,
% 5.24/5.41 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (elem!1 = s(s(z)))),
% 5.24/5.41 inference(transitivity,[status(thm)],[31934, 1666])).
% 5.24/5.41 tff(31936,plain,
% 5.24/5.41 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(elem!1 = s(s(z))))),
% 5.24/5.41 inference(monotonicity,[status(thm)],[31935])).
% 5.24/5.41 tff(31937,plain,
% 5.24/5.41 (~(elem!1 = s(s(z)))),
% 5.24/5.41 inference(modus_ponens,[status(thm)],[2131, 31936])).
% 5.24/5.41 tff(31938,plain,
% 5.24/5.41 ((s(s(elem!1)) = z) <=> (elem!1 = z)),
% 5.24/5.41 inference(monotonicity,[status(thm)],[31929])).
% 5.24/5.41 tff(31939,plain,
% 5.24/5.41 ((s(s(elem!1)) = z) <=> (z = elem!1)),
% 5.24/5.41 inference(transitivity,[status(thm)],[31938, 313])).
% 5.24/5.41 tff(31940,plain,
% 5.24/5.41 ((~(s(s(elem!1)) = z)) <=> (~(z = elem!1))),
% 5.24/5.41 inference(monotonicity,[status(thm)],[31939])).
% 5.24/5.41 tff(31941,plain,
% 5.24/5.41 (~(z = elem!1)),
% 5.24/5.41 inference(modus_ponens,[status(thm)],[970, 31940])).
% 5.24/5.41 tff(31942,plain,
% 5.24/5.41 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(s(s(z)) = elem!1))),
% 5.24/5.41 inference(monotonicity,[status(thm)],[31934])).
% 5.24/5.41 tff(31943,plain,
% 5.24/5.41 (~(s(s(z)) = elem!1)),
% 5.24/5.41 inference(modus_ponens,[status(thm)],[2131, 31942])).
% 5.24/5.41 tff(31944,plain,
% 5.24/5.41 ((s(s(elem!1)) = z) <=> (elem!1 = z)),
% 5.24/5.41 inference(transitivity,[status(thm)],[31939, 314])).
% 5.24/5.41 tff(31945,plain,
% 5.24/5.41 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = z))),
% 5.24/5.41 inference(monotonicity,[status(thm)],[31944])).
% 5.24/5.41 tff(31946,plain,
% 5.24/5.41 (~(elem!1 = z)),
% 5.24/5.41 inference(modus_ponens,[status(thm)],[970, 31945])).
% 5.24/5.41 tff(31947,plain,
% 5.24/5.41 (~(s(elem!1) = s(s(s(s(z)))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[13886, 31931])).
% 5.24/5.41 tff(31948,plain,
% 5.24/5.41 (~(s(s(s(s(z)))) = s(elem!1))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[2168, 31947])).
% 5.24/5.41 tff(31949,plain,
% 5.24/5.41 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[2510, 31948, 31929])).
% 5.24/5.41 tff(31950,plain,
% 5.24/5.41 (r(elem!1, z)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[498, 31946, 5723])).
% 5.24/5.41 tff(31951,plain,
% 5.24/5.41 (~r(elem!1, s(s(z)))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[458, 31950, 28500])).
% 5.24/5.41 tff(31952,plain,
% 5.24/5.41 (b(elem!1, s(s(z)))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[467, 31951, 31937])).
% 5.24/5.41 tff(31953,plain,
% 5.24/5.41 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[29488, 31952, 31476, 27217, 31949, 31578, 31907])).
% 5.24/5.41 tff(31954,plain,
% 5.24/5.41 (~r(s(s(s(s(z)))), elem!1)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[25879, 31953])).
% 5.24/5.41 tff(31955,plain,
% 5.24/5.41 (b(s(s(s(s(z)))), elem!1)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[3142, 31954, 31908])).
% 5.24/5.41 tff(31956,plain,
% 5.24/5.41 (~r(s(s(z)), elem!1)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[443, 31950, 28500])).
% 5.24/5.41 tff(31957,plain,
% 5.24/5.41 (b(s(s(z)), elem!1)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[448, 31956, 31943])).
% 5.24/5.41 tff(31958,plain,
% 5.24/5.41 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[11859, 31952, 31578, 27217, 31957])).
% 5.24/5.41 tff(31959,plain,
% 5.24/5.41 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[691, 31958, 31949])).
% 5.24/5.41 tff(31960,plain,
% 5.24/5.41 (~r(elem!1, s(s(s(s(z)))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[25883, 31959])).
% 5.24/5.41 tff(31961,plain,
% 5.24/5.41 (b(elem!1, s(s(s(s(z)))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[483, 31960, 31907])).
% 5.24/5.41 tff(31962,plain,
% 5.24/5.41 ($false),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[31874, 31961, 31955, 28500, 29994, 31476, 31575, 31946, 31943, 31941, 31937])).
% 5.24/5.41 tff(31963,plain,(b(elem!1, z) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(z)))), s(s(z))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.41 tff(31964,plain,
% 5.24/5.41 (b(elem!1, z)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[31963, 86, 204, 28501])).
% 5.24/5.41 tff(31965,plain,
% 5.24/5.41 (~(s(s(z)) = elem!1)),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[3230, 31605])).
% 5.24/5.41 tff(31966,plain,
% 5.24/5.41 (elem!1 = s(s(s(s(z))))),
% 5.24/5.41 inference(unit_resolution,[status(thm)],[29093, 450, 193, 506])).
% 5.24/5.41 tff(31967,plain,
% 5.24/5.41 (s(elem!1) = s(s(s(s(s(z)))))),
% 5.24/5.41 inference(monotonicity,[status(thm)],[31966])).
% 5.24/5.41 tff(31968,plain,
% 5.24/5.41 (s(s(s(s(s(z))))) = s(elem!1)),
% 5.24/5.41 inference(symmetry,[status(thm)],[31967])).
% 5.24/5.41 tff(31969,plain,
% 5.24/5.41 ((s(s(z)) = s(s(s(s(s(z)))))) <=> (s(s(z)) = s(elem!1))),
% 5.24/5.41 inference(monotonicity,[status(thm)],[31968])).
% 5.24/5.41 tff(31970,plain,
% 5.24/5.41 ((s(s(z)) = s(s(s(s(s(z)))))) <=> (s(elem!1) = s(s(z)))),
% 5.24/5.41 inference(transitivity,[status(thm)],[31969, 1358])).
% 5.24/5.41 tff(31971,plain,
% 5.24/5.41 ((s(elem!1) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(z))))))),
% 5.24/5.41 inference(symmetry,[status(thm)],[31970])).
% 5.24/5.41 tff(31972,plain,
% 5.24/5.41 ((~(s(elem!1) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(s(z)))))))),
% 5.24/5.41 inference(monotonicity,[status(thm)],[31971])).
% 5.24/5.41 tff(31973,plain,
% 5.24/5.41 (~(s(s(z)) = s(s(s(s(s(z))))))),
% 5.24/5.41 inference(modus_ponens,[status(thm)],[1056, 31972])).
% 5.24/5.41 tff(31974,plain,
% 5.24/5.41 (r(s(elem!1), z) <=> r(s(s(s(s(s(z))))), z)),
% 5.24/5.41 inference(monotonicity,[status(thm)],[31967])).
% 5.24/5.41 tff(31975,plain,
% 5.24/5.41 (r(s(s(s(s(s(z))))), z)),
% 5.24/5.41 inference(modus_ponens,[status(thm)],[12569, 31974])).
% 5.24/5.41 tff(31976,plain,
% 5.24/5.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 5.24/5.41 inference(rewrite,[status(thm)],[])).
% 5.24/5.41 tff(31977,plain,
% 5.24/5.41 (((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 5.24/5.41 inference(rewrite,[status(thm)],[])).
% 5.24/5.41 tff(31978,plain,
% 5.24/5.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 5.24/5.42 inference(monotonicity,[status(thm)],[31977])).
% 5.24/5.42 tff(31979,plain,
% 5.24/5.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 5.24/5.42 inference(transitivity,[status(thm)],[31978, 31976])).
% 5.24/5.42 tff(31980,plain,
% 5.24/5.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 5.24/5.42 inference(quant_inst,[status(thm)],[])).
% 5.24/5.42 tff(31981,plain,
% 5.24/5.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 5.24/5.42 inference(modus_ponens,[status(thm)],[31980, 31979])).
% 5.24/5.42 tff(31982,plain,
% 5.24/5.42 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[31981, 118, 28500, 31975])).
% 5.24/5.42 tff(31983,plain,
% 5.24/5.42 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 5.24/5.42 inference(monotonicity,[status(thm)],[31967])).
% 5.24/5.42 tff(31984,plain,
% 5.24/5.42 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 5.24/5.42 inference(monotonicity,[status(thm)],[31983])).
% 5.24/5.42 tff(31985,plain,
% 5.24/5.42 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 5.24/5.42 inference(monotonicity,[status(thm)],[31984, 31967])).
% 5.24/5.42 tff(31986,plain,
% 5.24/5.42 (s(s(s(s(z)))) = elem!1),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[325, 31966])).
% 5.24/5.42 tff(31987,plain,
% 5.24/5.42 (~(s(s(elem!1)) = elem!1)),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[338, 31986, 12])).
% 5.24/5.42 tff(31988,plain,
% 5.24/5.42 (~(s(s(s(elem!1))) = s(elem!1))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[348, 31987])).
% 5.24/5.42 tff(31989,plain,
% 5.24/5.42 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 5.24/5.42 inference(monotonicity,[status(thm)],[31966])).
% 5.24/5.42 tff(31990,plain,
% 5.24/5.42 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 5.24/5.42 inference(symmetry,[status(thm)],[31989])).
% 5.24/5.42 tff(31991,plain,
% 5.24/5.42 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.42 inference(monotonicity,[status(thm)],[31984])).
% 5.24/5.42 tff(31992,plain,
% 5.24/5.42 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 5.24/5.42 inference(symmetry,[status(thm)],[31991])).
% 5.24/5.42 tff(31993,plain,
% 5.24/5.42 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(elem!1))))),
% 5.24/5.42 inference(transitivity,[status(thm)],[31992, 31990])).
% 5.24/5.42 tff(31994,plain,
% 5.24/5.42 (r(elem!1, s(s(s(elem!1))))),
% 5.24/5.42 inference(modus_ponens,[status(thm)],[204, 31993])).
% 5.24/5.42 tff(31995,plain,
% 5.24/5.42 (~(elem!1 = s(elem!1))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[748, 19339])).
% 5.24/5.42 tff(31996,plain,
% 5.24/5.42 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))),
% 5.24/5.42 inference(monotonicity,[status(thm)],[31984, 31967])).
% 5.24/5.42 tff(31997,plain,
% 5.24/5.42 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 5.24/5.42 inference(transitivity,[status(thm)],[31996, 4625])).
% 5.24/5.42 tff(31998,plain,
% 5.24/5.42 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.42 inference(monotonicity,[status(thm)],[31997])).
% 5.24/5.42 tff(31999,plain,
% 5.24/5.42 (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 5.24/5.42 inference(modus_ponens,[status(thm)],[31988, 31998])).
% 5.24/5.42 tff(32000,plain,
% 5.24/5.42 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 5.24/5.42 inference(monotonicity,[status(thm)],[31967])).
% 5.24/5.42 tff(32001,plain,
% 5.24/5.42 (b(s(elem!1), s(s(z)))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[421, 30246, 1056])).
% 5.24/5.42 tff(32002,plain,
% 5.24/5.42 (b(s(s(s(s(s(z))))), s(s(z)))),
% 5.24/5.42 inference(modus_ponens,[status(thm)],[32001, 32000])).
% 5.24/5.42 tff(32003,plain,
% 5.24/5.42 (~r(z, s(elem!1))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[23867, 32002, 29994, 203, 31693, 31986, 31999])).
% 5.24/5.42 tff(32004,plain,
% 5.24/5.42 (b(z, s(elem!1))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[2351, 32003])).
% 5.24/5.42 tff(32005,plain,
% 5.24/5.42 (b(z, elem!1)),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[585, 30203, 6992])).
% 5.24/5.42 tff(32006,plain,
% 5.24/5.42 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 5.24/5.42 inference(monotonicity,[status(thm)],[31966])).
% 5.24/5.42 tff(32007,plain,
% 5.24/5.42 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), elem!1)),
% 5.24/5.42 inference(symmetry,[status(thm)],[32006])).
% 5.24/5.42 tff(32008,plain,
% 5.24/5.42 (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)))))),
% 5.24/5.42 inference(monotonicity,[status(thm)],[31984])).
% 5.24/5.42 tff(32009,plain,
% 5.24/5.42 (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)))))),
% 5.24/5.42 inference(symmetry,[status(thm)],[32008])).
% 5.24/5.42 tff(32010,plain,
% 5.24/5.42 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), elem!1)),
% 5.24/5.42 inference(transitivity,[status(thm)],[32009, 32007])).
% 5.24/5.42 tff(32011,plain,
% 5.24/5.42 (r(s(s(s(elem!1))), elem!1)),
% 5.24/5.42 inference(modus_ponens,[status(thm)],[24592, 32010])).
% 5.24/5.42 tff(32012,plain,
% 5.24/5.42 (b(s(elem!1), elem!1)),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[22822, 32004, 28500, 506, 766, 1056, 32011, 31988])).
% 5.24/5.42 tff(32013,plain,
% 5.24/5.42 (~b(elem!1, s(elem!1))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[1396, 32012, 506, 32005, 32004])).
% 5.24/5.42 tff(32014,plain,
% 5.24/5.42 (r(elem!1, s(elem!1))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[756, 32013, 31995])).
% 5.24/5.42 tff(32015,plain,
% 5.24/5.42 (~r(s(s(s(elem!1))), s(elem!1))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[1591, 32014, 31994])).
% 5.24/5.42 tff(32016,plain,
% 5.24/5.42 (b(s(s(s(elem!1))), s(elem!1))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[373, 32015, 31988])).
% 5.24/5.42 tff(32017,plain,
% 5.24/5.42 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 5.24/5.42 inference(modus_ponens,[status(thm)],[32016, 31985])).
% 5.24/5.42 tff(32018,plain,
% 5.24/5.42 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 5.24/5.42 inference(monotonicity,[status(thm)],[31968])).
% 5.24/5.42 tff(32019,plain,
% 5.24/5.42 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 5.24/5.42 inference(symmetry,[status(thm)],[32018])).
% 5.24/5.42 tff(32020,plain,
% 5.24/5.42 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(s(z)))))),
% 5.24/5.42 inference(monotonicity,[status(thm)],[31966])).
% 5.24/5.42 tff(32021,plain,
% 5.24/5.42 (b(s(elem!1), elem!1) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 5.24/5.42 inference(transitivity,[status(thm)],[32020, 32019])).
% 5.24/5.42 tff(32022,plain,
% 5.24/5.42 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 5.24/5.42 inference(modus_ponens,[status(thm)],[32012, 32021])).
% 5.24/5.42 tff(32023,plain,
% 5.24/5.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 5.24/5.42 inference(rewrite,[status(thm)],[])).
% 5.24/5.42 tff(32024,plain,
% 5.24/5.42 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 5.24/5.42 inference(rewrite,[status(thm)],[])).
% 5.24/5.42 tff(32025,plain,
% 5.24/5.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 5.24/5.42 inference(monotonicity,[status(thm)],[32024])).
% 5.24/5.42 tff(32026,plain,
% 5.24/5.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 5.24/5.42 inference(transitivity,[status(thm)],[32025, 32023])).
% 5.24/5.42 tff(32027,plain,
% 5.24/5.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 5.24/5.42 inference(quant_inst,[status(thm)],[])).
% 5.24/5.42 tff(32028,plain,
% 5.24/5.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 5.24/5.42 inference(modus_ponens,[status(thm)],[32027, 32026])).
% 5.24/5.42 tff(32029,plain,
% 5.24/5.42 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[32028, 178, 167, 32022, 24628, 32017])).
% 5.24/5.42 tff(32030,plain,
% 5.24/5.42 ((s(s(z)) = s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z))))))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[2781, 41, 32029])).
% 5.24/5.42 tff(32031,plain,
% 5.24/5.42 ($false),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[32030, 31982, 31973])).
% 5.24/5.42 tff(32032,plain,((~r(elem!1, s(s(z)))) | (s(elem!1) = s(s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, z)) | b(s(elem!1), z) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (s(s(z)) = elem!1) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.42 tff(32033,plain,
% 5.24/5.42 (~r(elem!1, s(s(z)))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[32032, 766, 167, 506, 1056, 4236, 204, 31965, 103])).
% 5.24/5.42 tff(32034,plain,
% 5.24/5.42 (b(elem!1, s(s(z)))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[467, 32033, 31605])).
% 5.24/5.42 tff(32035,plain,
% 5.24/5.42 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[11859, 32034, 31578, 27217, 817])).
% 5.24/5.42 tff(32036,plain,
% 5.24/5.42 ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(z))))))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[29314, 178, 506, 31623, 167])).
% 5.24/5.42 tff(32037,plain,
% 5.24/5.42 (~b(elem!1, s(s(s(s(z)))))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[32036, 817])).
% 5.24/5.42 tff(32038,plain,
% 5.24/5.42 (~(elem!1 = s(s(s(s(z)))))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[30853, 32034, 86])).
% 5.24/5.42 tff(32039,plain,
% 5.24/5.42 (r(elem!1, s(s(s(s(z)))))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[483, 32038, 32037])).
% 5.24/5.42 tff(32040,plain,
% 5.24/5.42 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[25883, 32039])).
% 5.24/5.42 tff(32041,plain,
% 5.24/5.42 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[691, 32040, 32035])).
% 5.24/5.42 tff(32042,plain,
% 5.24/5.42 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 5.24/5.42 inference(monotonicity,[status(thm)],[32041])).
% 5.24/5.42 tff(32043,plain,
% 5.24/5.42 (b(s(elem!1), z) <=> b(s(s(s(s(s(s(s(s(z)))))))), z)),
% 5.24/5.42 inference(monotonicity,[status(thm)],[32042])).
% 5.24/5.42 tff(32044,plain,
% 5.24/5.42 ((~b(s(elem!1), z)) <=> (~b(s(s(s(s(s(s(s(s(z)))))))), z))),
% 5.24/5.42 inference(monotonicity,[status(thm)],[32043])).
% 5.24/5.42 tff(32045,plain,
% 5.24/5.42 (~b(s(s(s(s(s(s(s(s(z)))))))), z)),
% 5.24/5.42 inference(modus_ponens,[status(thm)],[766, 32044])).
% 5.24/5.42 tff(32046,plain,
% 5.24/5.42 (r(s(s(s(s(s(s(s(s(z)))))))), z)),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[16121, 41, 16118, 32045])).
% 5.24/5.42 tff(32047,plain,
% 5.24/5.42 (r(s(s(z)), s(elem!1)) <=> r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.42 inference(monotonicity,[status(thm)],[32042])).
% 5.24/5.42 tff(32048,plain,
% 5.24/5.42 (~(elem!1 = z)),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[2808, 6992])).
% 5.24/5.42 tff(32049,plain,
% 5.24/5.42 (~b(z, elem!1)),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[23466, 32040, 103, 27217, 31578, 817, 4235, 28500, 31605, 32038, 32048])).
% 5.24/5.42 tff(32050,plain,
% 5.24/5.42 (r(z, elem!1)),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[585, 32049, 6992])).
% 5.24/5.42 tff(32051,plain,
% 5.24/5.42 (b(s(elem!1), elem!1)),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[19342, 32050, 506, 766])).
% 5.24/5.42 tff(32052,plain,
% 5.24/5.42 (~b(s(s(z)), s(elem!1))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[13708, 32051, 32001, 32034, 817])).
% 5.24/5.42 tff(32053,plain,
% 5.24/5.42 (r(s(s(z)), s(elem!1))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[1067, 32052, 2311])).
% 5.24/5.42 tff(32054,plain,
% 5.24/5.42 (r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.42 inference(modus_ponens,[status(thm)],[32053, 32047])).
% 5.24/5.42 tff(32055,plain,
% 5.24/5.42 ($false),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[31119, 118, 28500, 32054, 32046])).
% 5.24/5.42 tff(32056,plain,(b(s(elem!1), z) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | b(z, s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(z)))), s(s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (s(elem!1) = s(s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.42 tff(32057,plain,
% 5.24/5.42 (b(s(elem!1), z)),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[32056, 31579, 31964, 4235, 86, 31476, 1056, 204])).
% 5.24/5.42 tff(32058,plain,
% 5.24/5.42 (~b(s(elem!1), s(s(s(s(z)))))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[31823, 32057, 2311, 31476])).
% 5.24/5.42 tff(32059,plain,
% 5.24/5.42 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[24033, 4236, 31575, 27212, 204])).
% 5.24/5.42 tff(32060,plain,
% 5.24/5.42 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[20667, 32059])).
% 5.24/5.42 tff(32061,plain,
% 5.24/5.42 (~(s(elem!1) = elem!1)),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[2150, 7202])).
% 5.24/5.42 tff(32062,plain,
% 5.24/5.42 (~(elem!1 = s(s(s(s(z)))))),
% 5.24/5.42 inference(modus_ponens,[status(thm)],[32061, 15759])).
% 5.24/5.42 tff(32063,plain,
% 5.24/5.42 (~r(elem!1, s(s(z)))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[29093, 32062, 193, 506])).
% 5.24/5.42 tff(32064,plain,
% 5.24/5.42 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.24/5.42 inference(modus_ponens,[status(thm)],[3002, 15814])).
% 5.24/5.42 tff(32065,plain,
% 5.24/5.42 (~b(elem!1, s(s(z)))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[11859, 32064, 166, 24628, 817])).
% 5.24/5.42 tff(32066,plain,
% 5.24/5.42 ($false),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[467, 32065, 32063, 31605])).
% 5.24/5.42 tff(32067,plain,((~(s(elem!1) = s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.42 tff(32068,plain,
% 5.24/5.42 (~(s(elem!1) = s(s(s(s(z)))))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[32067, 31579, 31578, 103, 31964, 32060])).
% 5.24/5.42 tff(32069,plain,
% 5.24/5.42 (r(s(elem!1), s(s(s(s(z)))))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[1084, 32068, 32058])).
% 5.24/5.42 tff(32070,plain,
% 5.24/5.42 (~r(s(elem!1), s(s(z)))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[12437, 32068, 29994, 103, 32057])).
% 5.24/5.42 tff(32071,plain,
% 5.24/5.42 (b(s(elem!1), s(s(z)))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[421, 32070, 1056])).
% 5.24/5.42 tff(32072,plain,
% 5.24/5.42 (~(s(s(s(s(z)))) = s(elem!1))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[2168, 32068])).
% 5.24/5.42 tff(32073,plain,
% 5.24/5.42 (r(elem!1, s(s(s(s(z)))))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[483, 469, 32037])).
% 5.24/5.42 tff(32074,plain,
% 5.24/5.42 (~r(elem!1, s(elem!1))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[14364, 32073, 908])).
% 5.24/5.42 tff(32075,plain,
% 5.24/5.42 (~r(elem!1, s(s(z)))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[29093, 469, 193, 506])).
% 5.24/5.42 tff(32076,plain,
% 5.24/5.42 (b(elem!1, s(s(z)))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[467, 32075, 31605])).
% 5.24/5.42 tff(32077,plain,
% 5.24/5.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 5.24/5.42 inference(rewrite,[status(thm)],[])).
% 5.24/5.42 tff(32078,plain,
% 5.24/5.42 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 5.24/5.42 inference(rewrite,[status(thm)],[])).
% 5.24/5.42 tff(32079,plain,
% 5.24/5.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))))),
% 5.24/5.42 inference(monotonicity,[status(thm)],[32078])).
% 5.24/5.42 tff(32080,plain,
% 5.24/5.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 5.24/5.42 inference(transitivity,[status(thm)],[32079, 32077])).
% 5.24/5.42 tff(32081,plain,
% 5.24/5.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 5.24/5.42 inference(quant_inst,[status(thm)],[])).
% 5.24/5.42 tff(32082,plain,
% 5.24/5.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))),
% 5.24/5.42 inference(modus_ponens,[status(thm)],[32081, 32080])).
% 5.24/5.42 tff(32083,plain,
% 5.24/5.42 (~b(s(s(s(s(z)))), elem!1)),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[32082, 178, 506, 817, 31623, 167])).
% 5.24/5.42 tff(32084,plain,
% 5.24/5.42 (r(s(s(s(s(z)))), elem!1)),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[3142, 551, 32083])).
% 5.24/5.42 tff(32085,plain,
% 5.24/5.42 (~r(s(elem!1), elem!1)),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[7010, 32084, 908])).
% 5.24/5.42 tff(32086,plain,
% 5.24/5.42 (s(elem!1) = elem!1),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[30697, 32085, 1070, 32076, 32074, 817])).
% 5.24/5.42 tff(32087,plain,
% 5.24/5.42 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[25879, 32084])).
% 5.24/5.42 tff(32088,plain,
% 5.24/5.42 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[29488, 32087, 167, 24628, 32076, 166, 469])).
% 5.24/5.42 tff(32089,plain,
% 5.24/5.42 (~(s(s(elem!1)) = elem!1)),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[2510, 32088, 2508])).
% 5.24/5.42 tff(32090,plain,
% 5.24/5.42 ($false),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[672, 32089, 32086])).
% 5.24/5.42 tff(32091,plain,((elem!1 = s(s(s(s(z))))) | (s(s(s(s(z)))) = s(elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.42 tff(32092,plain,
% 5.24/5.42 (elem!1 = s(s(s(s(z))))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[32091, 32072, 32071, 31579, 31476, 31578, 32069, 103, 31964])).
% 5.24/5.42 tff(32093,plain,
% 5.24/5.42 (s(elem!1) = s(s(s(s(s(z)))))),
% 5.24/5.42 inference(monotonicity,[status(thm)],[32092])).
% 5.24/5.42 tff(32094,plain,
% 5.24/5.42 (s(s(s(s(s(z))))) = s(elem!1)),
% 5.24/5.42 inference(symmetry,[status(thm)],[32093])).
% 5.24/5.42 tff(32095,plain,
% 5.24/5.42 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 5.24/5.42 inference(monotonicity,[status(thm)],[32094])).
% 5.24/5.42 tff(32096,plain,
% 5.24/5.42 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 5.24/5.42 inference(symmetry,[status(thm)],[32095])).
% 5.24/5.42 tff(32097,plain,
% 5.24/5.42 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 5.24/5.42 inference(monotonicity,[status(thm)],[32094])).
% 5.24/5.42 tff(32098,plain,
% 5.24/5.42 ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) <=> (~b(s(s(s(s(z)))), s(elem!1)))),
% 5.24/5.42 inference(monotonicity,[status(thm)],[32097])).
% 5.24/5.42 tff(32099,plain,
% 5.24/5.42 (b(z, s(elem!1)) <=> b(z, s(s(s(s(s(z))))))),
% 5.24/5.42 inference(monotonicity,[status(thm)],[32093])).
% 5.24/5.42 tff(32100,plain,
% 5.24/5.42 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 5.24/5.42 inference(monotonicity,[status(thm)],[32093])).
% 5.24/5.42 tff(32101,plain,
% 5.24/5.42 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 5.24/5.42 inference(monotonicity,[status(thm)],[32100])).
% 5.24/5.42 tff(32102,plain,
% 5.24/5.42 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))),
% 5.24/5.42 inference(monotonicity,[status(thm)],[32101, 32093])).
% 5.24/5.42 tff(32103,plain,
% 5.24/5.42 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 5.24/5.42 inference(transitivity,[status(thm)],[32102, 4625])).
% 5.24/5.42 tff(32104,plain,
% 5.24/5.42 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.42 inference(monotonicity,[status(thm)],[32103])).
% 5.24/5.42 tff(32105,plain,
% 5.24/5.42 (~(s(s(z)) = elem!1)),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[3230, 31586])).
% 5.24/5.42 tff(32106,plain,
% 5.24/5.42 (s(s(s(s(z)))) = elem!1),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[325, 32092])).
% 5.24/5.42 tff(32107,plain,
% 5.24/5.42 (~(s(s(elem!1)) = elem!1)),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[338, 32106, 32105])).
% 5.24/5.42 tff(32108,plain,
% 5.24/5.42 (~(s(s(s(elem!1))) = s(elem!1))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[348, 32107])).
% 5.24/5.42 tff(32109,plain,
% 5.24/5.42 (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 5.24/5.42 inference(modus_ponens,[status(thm)],[32108, 32104])).
% 5.24/5.42 tff(32110,plain,
% 5.24/5.42 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 5.24/5.42 inference(monotonicity,[status(thm)],[32093])).
% 5.24/5.42 tff(32111,plain,
% 5.24/5.42 (b(s(s(s(s(s(z))))), s(s(z)))),
% 5.24/5.42 inference(modus_ponens,[status(thm)],[32071, 32110])).
% 5.24/5.42 tff(32112,plain,
% 5.24/5.42 (~r(z, s(elem!1))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[23867, 32111, 29994, 4236, 31578, 32106, 32109])).
% 5.24/5.42 tff(32113,plain,
% 5.24/5.42 (b(z, s(elem!1))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[2351, 32112])).
% 5.24/5.42 tff(32114,plain,
% 5.24/5.42 (b(z, s(s(s(s(s(z))))))),
% 5.24/5.42 inference(modus_ponens,[status(thm)],[32113, 32099])).
% 5.24/5.42 tff(32115,plain,
% 5.24/5.42 (b(s(elem!1), z) <=> b(s(s(s(s(s(z))))), z)),
% 5.24/5.42 inference(monotonicity,[status(thm)],[32093])).
% 5.24/5.42 tff(32116,plain,
% 5.24/5.42 (b(s(s(s(s(s(z))))), z)),
% 5.24/5.42 inference(modus_ponens,[status(thm)],[32057, 32115])).
% 5.24/5.42 tff(32117,plain,
% 5.24/5.42 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[28077, 178, 27212, 31575, 32116, 32114])).
% 5.24/5.42 tff(32118,plain,
% 5.24/5.42 (~b(s(s(s(s(z)))), s(elem!1))),
% 5.24/5.42 inference(modus_ponens,[status(thm)],[32117, 32098])).
% 5.24/5.42 tff(32119,plain,
% 5.24/5.42 (r(s(s(s(s(z)))), s(elem!1))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[2173, 32118, 32072])).
% 5.24/5.42 tff(32120,plain,
% 5.24/5.42 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 5.24/5.42 inference(modus_ponens,[status(thm)],[32119, 32096])).
% 5.24/5.42 tff(32121,plain,
% 5.24/5.42 ((s(s(z)) = s(s(s(s(s(z)))))) <=> (s(s(z)) = s(elem!1))),
% 5.24/5.42 inference(monotonicity,[status(thm)],[32094])).
% 5.24/5.42 tff(32122,plain,
% 5.24/5.42 ((s(s(z)) = s(s(s(s(s(z)))))) <=> (s(elem!1) = s(s(z)))),
% 5.24/5.42 inference(transitivity,[status(thm)],[32121, 1358])).
% 5.24/5.42 tff(32123,plain,
% 5.24/5.42 ((s(elem!1) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(z))))))),
% 5.24/5.42 inference(symmetry,[status(thm)],[32122])).
% 5.24/5.42 tff(32124,plain,
% 5.24/5.42 ((~(s(elem!1) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(s(z)))))))),
% 5.24/5.42 inference(monotonicity,[status(thm)],[32123])).
% 5.24/5.42 tff(32125,plain,
% 5.24/5.42 (~(s(s(z)) = s(s(s(s(s(z))))))),
% 5.24/5.42 inference(modus_ponens,[status(thm)],[1056, 32124])).
% 5.24/5.42 tff(32126,plain,
% 5.24/5.42 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.42 inference(monotonicity,[status(thm)],[32093])).
% 5.24/5.42 tff(32127,plain,
% 5.24/5.42 ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) <=> (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.42 inference(monotonicity,[status(thm)],[32126])).
% 5.24/5.42 tff(32128,plain,
% 5.24/5.42 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[25119, 32069])).
% 5.24/5.42 tff(32129,plain,
% 5.24/5.42 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.42 inference(modus_ponens,[status(thm)],[32128, 32127])).
% 5.24/5.42 tff(32130,plain,
% 5.24/5.42 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[18760, 41, 32109, 32129])).
% 5.24/5.42 tff(32131,plain,
% 5.24/5.42 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[14448, 32130, 27217, 31578, 32111])).
% 5.24/5.42 tff(32132,plain,
% 5.24/5.42 ((s(s(z)) = s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z))))))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[2781, 41, 32131])).
% 5.24/5.42 tff(32133,plain,
% 5.24/5.42 (r(s(s(z)), s(s(s(s(s(z))))))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[32132, 32125])).
% 5.24/5.42 tff(32134,plain,
% 5.24/5.42 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[14515, 32133, 103])).
% 5.24/5.42 tff(32135,plain,
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% 5.24/5.42 inference(unit_resolution,[status(thm)],[32134, 32120])).
% 5.24/5.42 tff(32136,plain,(b(z, s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.42 tff(32137,plain,
% 5.24/5.42 (b(z, s(s(s(s(s(s(s(z))))))))),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[32136, 1056, 86, 204, 28501])).
% 5.24/5.42 tff(32138,plain,
% 5.24/5.42 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), elem!1)),
% 5.24/5.42 inference(monotonicity,[status(thm)],[331])).
% 5.24/5.42 tff(32139,plain,
% 5.24/5.42 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(s(z)))))),
% 5.24/5.42 inference(symmetry,[status(thm)],[32138])).
% 5.24/5.42 tff(32140,plain,
% 5.24/5.42 ((~b(s(s(z)), elem!1)) <=> (~b(s(s(z)), s(s(s(s(z))))))),
% 5.24/5.42 inference(monotonicity,[status(thm)],[32139])).
% 5.24/5.42 tff(32141,plain,
% 5.24/5.42 (~b(s(s(z)), s(s(s(s(z)))))),
% 5.24/5.42 inference(modus_ponens,[status(thm)],[3241, 32140])).
% 5.24/5.42 tff(32142,plain,
% 5.24/5.42 ($false),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[167, 32141])).
% 5.24/5.42 tff(32143,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,[]))).
% 5.24/5.42 tff(32144,plain,
% 5.24/5.42 (~(s(s(s(s(z)))) = elem!1)),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[32143, 3241, 167])).
% 5.24/5.42 tff(32145,plain,
% 5.24/5.42 (~r(z, elem!1)),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[8412, 438, 29994])).
% 5.24/5.42 tff(32146,plain,
% 5.24/5.42 (b(z, elem!1)),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[585, 32145, 6992])).
% 5.24/5.42 tff(32147,plain,
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% 5.24/5.42 inference(unit_resolution,[status(thm)],[27929, 178, 32146, 506, 12448, 27212, 168])).
% 5.24/5.42 tff(32148,plain,((~r(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (s(s(s(s(z)))) = elem!1) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.42 tff(32149,plain,
% 5.24/5.42 (~r(s(s(z)), elem!1)),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[32148, 32144, 31623, 506, 193])).
% 5.24/5.42 tff(32150,plain,
% 5.24/5.42 (s(s(z)) = elem!1),
% 5.24/5.42 inference(unit_resolution,[status(thm)],[448, 32149, 3241])).
% 5.24/5.43 tff(32151,plain,
% 5.24/5.43 (elem!1 = s(s(z))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[3230, 32150])).
% 5.24/5.43 tff(32152,plain,
% 5.24/5.43 (~(s(elem!1) = s(s(s(s(z)))))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[1353, 32151, 32144])).
% 5.24/5.43 tff(32153,plain,
% 5.24/5.43 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[5361, 32150])).
% 5.24/5.43 tff(32154,plain,
% 5.24/5.43 (b(s(s(z)), z)),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[23817, 32151, 506])).
% 5.24/5.43 tff(32155,plain,
% 5.24/5.43 (~b(s(elem!1), s(s(z)))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[28435, 32154, 167, 166, 24628, 595, 2311, 32153, 32152])).
% 5.24/5.43 tff(32156,plain,
% 5.24/5.43 (r(s(elem!1), s(s(z)))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[421, 32155, 1056])).
% 5.24/5.43 tff(32157,plain,
% 5.24/5.43 (~r(s(elem!1), z)),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[2258, 32156, 28500])).
% 5.24/5.43 tff(32158,plain,
% 5.24/5.43 (~b(s(elem!1), z)),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[12437, 32156, 29994, 193, 32152])).
% 5.24/5.43 tff(32159,plain,
% 5.24/5.43 ($false),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[774, 32158, 32157])).
% 5.24/5.43 tff(32160,plain,(b(s(s(z)), elem!1) | (~r(s(s(s(s(z)))), s(s(z)))) | (s(elem!1) = s(s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.43 tff(32161,plain,
% 5.24/5.43 (b(s(s(z)), elem!1)),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[32160, 1056, 103, 31476, 31578, 32137, 31964])).
% 5.24/5.43 tff(32162,plain,
% 5.24/5.43 (~(elem!1 = s(s(z)))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[31585, 32161])).
% 5.24/5.43 tff(32163,plain,
% 5.24/5.43 (~(s(s(z)) = elem!1)),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[3230, 32162])).
% 5.24/5.43 tff(32164,plain,
% 5.24/5.43 (b(s(s(z)), elem!1)),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[32160, 1056, 193, 167, 31693, 595, 506])).
% 5.24/5.43 tff(32165,plain,
% 5.24/5.43 (~b(s(s(s(s(z)))), elem!1)),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[32082, 178, 506, 32164, 31623, 167])).
% 5.24/5.43 tff(32166,plain,
% 5.24/5.43 (r(s(s(s(s(z)))), elem!1)),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[3142, 323, 32165])).
% 5.24/5.43 tff(32167,plain,
% 5.24/5.43 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[25879, 32166])).
% 5.24/5.43 tff(32168,plain,
% 5.24/5.43 (~(elem!1 = s(s(z)))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[31585, 32164])).
% 5.24/5.43 tff(32169,plain,
% 5.24/5.43 (~r(elem!1, s(s(z)))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[29093, 3130, 193, 506])).
% 5.24/5.43 tff(32170,plain,
% 5.24/5.43 (b(elem!1, s(s(z)))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[467, 32169, 32168])).
% 5.24/5.43 tff(32171,plain,
% 5.24/5.43 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[29488, 32170, 167, 24628, 32167, 31693, 3130])).
% 5.24/5.43 tff(32172,plain,
% 5.24/5.43 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 5.24/5.43 inference(monotonicity,[status(thm)],[32171])).
% 5.24/5.43 tff(32173,plain,
% 5.24/5.43 ((~(s(elem!1) = elem!1)) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.43 inference(monotonicity,[status(thm)],[32172])).
% 5.24/5.43 tff(32174,plain,
% 5.24/5.43 (~(elem!1 = s(s(s(elem!1))))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[2859, 32171, 13192])).
% 5.24/5.43 tff(32175,plain,
% 5.24/5.43 (~(s(s(s(elem!1))) = elem!1)),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[2489, 32174])).
% 5.24/5.43 tff(32176,plain,
% 5.24/5.43 (~(s(elem!1) = elem!1)),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[2150, 32175])).
% 5.24/5.43 tff(32177,plain,
% 5.24/5.43 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 5.24/5.43 inference(modus_ponens,[status(thm)],[32176, 32173])).
% 5.24/5.43 tff(32178,plain,
% 5.24/5.43 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[14677, 1070, 29994, 24628, 595, 31693, 1060])).
% 5.24/5.43 tff(32179,plain,
% 5.24/5.43 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[395, 32178, 2286])).
% 5.24/5.43 tff(32180,plain,
% 5.24/5.43 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.43 inference(modus_ponens,[status(thm)],[32179, 21924])).
% 5.24/5.43 tff(32181,plain,
% 5.24/5.43 ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[31051, 118, 204])).
% 5.24/5.43 tff(32182,plain,
% 5.24/5.43 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[32181, 32180])).
% 5.24/5.43 tff(32183,plain,
% 5.24/5.43 (~r(s(s(s(s(z)))), s(elem!1))),
% 5.24/5.43 inference(modus_ponens,[status(thm)],[32182, 19973])).
% 5.24/5.43 tff(32184,plain,
% 5.24/5.43 (b(s(s(s(s(z)))), s(elem!1))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[2173, 32183, 16183])).
% 5.24/5.43 tff(32185,plain,
% 5.24/5.43 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.43 inference(modus_ponens,[status(thm)],[32184, 15449])).
% 5.24/5.43 tff(32186,plain,
% 5.24/5.43 (~r(s(elem!1), s(s(s(s(z)))))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[32091, 1070, 469, 817, 167, 31693, 16183, 193, 506])).
% 5.24/5.43 tff(32187,plain,
% 5.24/5.43 (b(s(elem!1), s(s(s(s(z)))))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[1084, 32186, 16182])).
% 5.24/5.43 tff(32188,plain,
% 5.24/5.43 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 5.24/5.43 inference(modus_ponens,[status(thm)],[32187, 26257])).
% 5.24/5.43 tff(32189,plain,
% 5.24/5.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 5.24/5.43 inference(rewrite,[status(thm)],[])).
% 5.24/5.43 tff(32190,plain,
% 5.24/5.43 (((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 5.24/5.43 inference(rewrite,[status(thm)],[])).
% 5.24/5.43 tff(32191,plain,
% 5.24/5.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))))),
% 5.24/5.43 inference(monotonicity,[status(thm)],[32190])).
% 5.24/5.43 tff(32192,plain,
% 5.24/5.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 5.24/5.43 inference(transitivity,[status(thm)],[32191, 32189])).
% 5.24/5.43 tff(32193,plain,
% 5.24/5.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), z)))),
% 5.24/5.43 inference(quant_inst,[status(thm)],[])).
% 5.24/5.43 tff(32194,plain,
% 5.24/5.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))),
% 5.24/5.43 inference(modus_ponens,[status(thm)],[32193, 32192])).
% 5.24/5.43 tff(32195,plain,
% 5.24/5.43 (~b(z, s(s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[32194, 178, 27212, 31623, 32188, 32185])).
% 5.24/5.43 tff(32196,plain,
% 5.24/5.43 (~b(z, s(elem!1))),
% 5.24/5.43 inference(modus_ponens,[status(thm)],[32195, 16140])).
% 5.24/5.43 tff(32197,plain,
% 5.24/5.43 (r(z, s(elem!1))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[2351, 32196])).
% 5.24/5.43 tff(32198,plain,
% 5.24/5.43 (~r(s(s(z)), s(elem!1))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[2341, 32197, 28500])).
% 5.24/5.43 tff(32199,plain,
% 5.24/5.43 (b(s(s(z)), s(elem!1))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[1067, 32198, 1060])).
% 5.24/5.43 tff(32200,plain,
% 5.24/5.43 (b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.43 inference(modus_ponens,[status(thm)],[32199, 16232])).
% 5.24/5.43 tff(32201,plain,
% 5.24/5.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 5.24/5.43 inference(rewrite,[status(thm)],[])).
% 5.24/5.43 tff(32202,plain,
% 5.24/5.43 (((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(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(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(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 5.24/5.43 inference(rewrite,[status(thm)],[])).
% 5.24/5.43 tff(32203,plain,
% 5.24/5.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(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(s(s(z)))))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))))),
% 5.24/5.43 inference(monotonicity,[status(thm)],[32202])).
% 5.24/5.43 tff(32204,plain,
% 5.24/5.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(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(s(s(z)))))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 5.24/5.43 inference(transitivity,[status(thm)],[32203, 32201])).
% 5.24/5.43 tff(32205,plain,
% 5.24/5.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(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(s(s(z)))))))), s(s(z)))))),
% 5.24/5.43 inference(quant_inst,[status(thm)],[])).
% 5.24/5.43 tff(32206,plain,
% 5.24/5.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))),
% 5.24/5.43 inference(modus_ponens,[status(thm)],[32205, 32204])).
% 5.24/5.43 tff(32207,plain,
% 5.24/5.43 ($false),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[32206, 178, 167, 31123, 32188, 32185, 32200])).
% 5.24/5.43 tff(32208,plain,((~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (s(s(z)) = s(elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (elem!1 = s(s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.43 tff(32209,plain,
% 5.24/5.43 (~b(s(elem!1), s(s(z)))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[32208, 32171, 167, 2311, 204, 32177, 3130, 32164, 193, 506, 595])).
% 5.24/5.43 tff(32210,plain,
% 5.24/5.43 (r(s(elem!1), s(s(z)))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[421, 32209, 1056])).
% 5.24/5.43 tff(32211,plain,
% 5.24/5.43 (~r(s(elem!1), z)),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[2258, 32210, 28500])).
% 5.24/5.43 tff(32212,plain,
% 5.24/5.43 (~(s(elem!1) = s(s(s(s(z)))))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[16181, 32171])).
% 5.24/5.43 tff(32213,plain,
% 5.24/5.43 (~b(s(elem!1), z)),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[12437, 32210, 29994, 193, 32212])).
% 5.24/5.43 tff(32214,plain,
% 5.24/5.43 ($false),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[774, 32213, 32211])).
% 5.24/5.43 tff(32215,plain,((s(s(s(s(z)))) = elem!1) | (~r(s(s(s(s(z)))), s(s(z)))) | (s(elem!1) = s(s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.43 tff(32216,plain,
% 5.24/5.43 (s(s(s(s(z)))) = elem!1),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[32215, 1056, 103, 31476, 204, 31964, 32137])).
% 5.24/5.43 tff(32217,plain,
% 5.24/5.43 (~(s(s(elem!1)) = elem!1)),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[338, 32216, 32163])).
% 5.24/5.43 tff(32218,plain,
% 5.24/5.43 (~(s(elem!1) = elem!1)),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[672, 32217])).
% 5.24/5.43 tff(32219,plain,
% 5.24/5.43 (elem!1 = s(s(s(s(z))))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[504, 32216])).
% 5.24/5.43 tff(32220,plain,
% 5.24/5.43 (~b(elem!1, s(s(z)))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[30853, 32219, 86])).
% 5.24/5.43 tff(32221,plain,
% 5.24/5.43 (r(elem!1, s(s(z)))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[467, 32220, 32162])).
% 5.24/5.43 tff(32222,plain,
% 5.24/5.43 (~(z = elem!1)),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[6991, 31964])).
% 5.24/5.43 tff(32223,plain,
% 5.24/5.43 (~r(z, elem!1)),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[4862, 32221, 29994])).
% 5.24/5.43 tff(32224,plain,
% 5.24/5.43 (b(z, elem!1)),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[585, 32223, 32222])).
% 5.24/5.43 tff(32225,plain,
% 5.24/5.43 (~r(s(elem!1), s(s(z)))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[17418, 32224, 28500, 31964, 32221, 32218])).
% 5.24/5.43 tff(32226,plain,
% 5.24/5.43 (b(s(elem!1), s(s(z)))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[421, 32225, 1056])).
% 5.24/5.43 tff(32227,plain,
% 5.24/5.43 (~(elem!1 = s(elem!1))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[748, 32218])).
% 5.24/5.43 tff(32228,plain,
% 5.24/5.43 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.24/5.43 inference(monotonicity,[status(thm)],[32216])).
% 5.24/5.43 tff(32229,plain,
% 5.24/5.43 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.24/5.43 inference(modus_ponens,[status(thm)],[204, 32228])).
% 5.24/5.43 tff(32230,plain,
% 5.24/5.43 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[14677, 32226, 29994, 27217, 32137, 31578, 2311])).
% 5.24/5.43 tff(32231,plain,
% 5.24/5.43 (s(s(s(s(s(z))))) = s(elem!1)),
% 5.24/5.43 inference(monotonicity,[status(thm)],[32216])).
% 5.24/5.43 tff(32232,plain,
% 5.24/5.43 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 5.24/5.43 inference(monotonicity,[status(thm)],[32231])).
% 5.24/5.43 tff(32233,plain,
% 5.24/5.43 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 5.24/5.43 inference(monotonicity,[status(thm)],[32232])).
% 5.24/5.43 tff(32234,plain,
% 5.24/5.43 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 5.24/5.43 inference(symmetry,[status(thm)],[32233])).
% 5.24/5.43 tff(32235,plain,
% 5.24/5.43 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 5.24/5.43 inference(monotonicity,[status(thm)],[32234])).
% 5.24/5.43 tff(32236,plain,
% 5.24/5.43 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 5.24/5.43 inference(transitivity,[status(thm)],[32235, 377])).
% 5.24/5.43 tff(32237,plain,
% 5.24/5.43 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.43 inference(monotonicity,[status(thm)],[32236])).
% 5.24/5.43 tff(32238,plain,
% 5.24/5.43 (~(s(s(s(elem!1))) = s(elem!1))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[348, 32217])).
% 5.24/5.43 tff(32239,plain,
% 5.24/5.43 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 5.24/5.43 inference(modus_ponens,[status(thm)],[32238, 32237])).
% 5.24/5.43 tff(32240,plain,
% 5.24/5.43 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[395, 32239, 32230])).
% 5.24/5.43 tff(32241,plain,
% 5.24/5.43 (~r(elem!1, s(elem!1))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[2935, 32240, 32229])).
% 5.24/5.43 tff(32242,plain,
% 5.24/5.43 (b(elem!1, s(elem!1))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[756, 32241, 32227])).
% 5.24/5.43 tff(32243,plain,
% 5.24/5.43 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 5.24/5.43 inference(monotonicity,[status(thm)],[32233])).
% 5.24/5.43 tff(32244,plain,
% 5.24/5.43 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.24/5.43 inference(monotonicity,[status(thm)],[32216])).
% 5.24/5.43 tff(32245,plain,
% 5.24/5.43 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.24/5.43 inference(modus_ponens,[status(thm)],[24592, 32244])).
% 5.24/5.43 tff(32246,plain,
% 5.24/5.43 (r(s(s(s(elem!1))), elem!1)),
% 5.24/5.43 inference(modus_ponens,[status(thm)],[32245, 32243])).
% 5.24/5.43 tff(32247,plain,
% 5.24/5.43 (~(s(elem!1) = s(s(s(elem!1))))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[5395, 32238])).
% 5.24/5.43 tff(32248,plain,
% 5.24/5.43 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.43 inference(monotonicity,[status(thm)],[32234])).
% 5.24/5.43 tff(32249,plain,
% 5.24/5.43 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 5.24/5.43 inference(symmetry,[status(thm)],[32248])).
% 5.24/5.43 tff(32250,plain,
% 5.24/5.43 ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(elem!1), s(s(s(elem!1)))))),
% 5.24/5.43 inference(monotonicity,[status(thm)],[32249])).
% 5.24/5.43 tff(32251,plain,
% 5.24/5.43 (~b(s(elem!1), s(s(s(elem!1))))),
% 5.24/5.43 inference(modus_ponens,[status(thm)],[32230, 32250])).
% 5.24/5.43 tff(32252,plain,
% 5.24/5.43 (r(s(elem!1), s(s(s(elem!1))))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[5432, 32251, 32247])).
% 5.24/5.43 tff(32253,plain,
% 5.24/5.43 (~r(s(elem!1), elem!1)),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[2110, 32252, 32246])).
% 5.24/5.43 tff(32254,plain,
% 5.24/5.43 (b(s(elem!1), elem!1)),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[677, 32253, 32218])).
% 5.24/5.43 tff(32255,plain,
% 5.24/5.43 (~b(z, s(elem!1))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[1396, 32254, 31964, 32224, 32242])).
% 5.24/5.43 tff(32256,plain,
% 5.24/5.43 (r(z, s(elem!1))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[2351, 32255])).
% 5.24/5.43 tff(32257,plain,
% 5.24/5.43 (~r(s(s(z)), s(elem!1))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[2341, 32256, 28500])).
% 5.24/5.43 tff(32258,plain,
% 5.24/5.43 (b(s(s(z)), s(elem!1))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[1067, 32257, 2311])).
% 5.24/5.43 tff(32259,plain,
% 5.24/5.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 5.24/5.43 inference(rewrite,[status(thm)],[])).
% 5.24/5.43 tff(32260,plain,
% 5.24/5.43 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(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)), elem!1)) | (~b(s(elem!1), s(s(z))))) <=> ((~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 5.24/5.43 inference(rewrite,[status(thm)],[])).
% 5.24/5.43 tff(32261,plain,
% 5.24/5.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(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)), elem!1)) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1))))),
% 5.24/5.43 inference(monotonicity,[status(thm)],[32260])).
% 5.24/5.43 tff(32262,plain,
% 5.24/5.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(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)), elem!1)) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 5.24/5.43 inference(transitivity,[status(thm)],[32261, 32259])).
% 5.24/5.43 tff(32263,plain,
% 5.24/5.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(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)), elem!1)) | (~b(s(elem!1), s(s(z)))))),
% 5.24/5.43 inference(quant_inst,[status(thm)],[])).
% 5.24/5.43 tff(32264,plain,
% 5.24/5.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1))),
% 5.24/5.43 inference(modus_ponens,[status(thm)],[32263, 32262])).
% 5.24/5.43 tff(32265,plain,
% 5.24/5.43 ($false),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[32264, 178, 32254, 32161, 32242, 32258, 32226])).
% 5.24/5.43 tff(32266,plain,((s(elem!1) = s(s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(z)))), s(s(z))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.43 tff(32267,plain,
% 5.24/5.43 (s(elem!1) = s(s(z))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[32266, 86, 204, 28501])).
% 5.24/5.43 tff(32268,plain,
% 5.24/5.43 (~(elem!1 = s(s(s(s(z)))))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[11438, 32267])).
% 5.24/5.43 tff(32269,plain,
% 5.24/5.43 (~(s(s(s(s(z)))) = elem!1)),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[504, 32268])).
% 5.24/5.43 tff(32270,plain,
% 5.24/5.43 (~r(s(s(z)), elem!1)),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[32148, 32269, 31575, 31964, 103])).
% 5.24/5.43 tff(32271,plain,
% 5.24/5.43 ((s(elem!1) = elem!1) <=> (s(s(z)) = elem!1)),
% 5.24/5.43 inference(monotonicity,[status(thm)],[32267])).
% 5.24/5.43 tff(32272,plain,
% 5.24/5.43 ((~(s(elem!1) = elem!1)) <=> (~(s(s(z)) = elem!1))),
% 5.24/5.43 inference(monotonicity,[status(thm)],[32271])).
% 5.24/5.43 tff(32273,plain,
% 5.24/5.43 (~(elem!1 = s(s(s(s(elem!1)))))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[1422, 32267])).
% 5.24/5.43 tff(32274,plain,
% 5.24/5.43 (~(s(s(s(elem!1))) = s(elem!1))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[1509, 32273])).
% 5.24/5.43 tff(32275,plain,
% 5.24/5.43 (~(elem!1 = s(s(elem!1)))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[1539, 32274])).
% 5.24/5.43 tff(32276,plain,
% 5.24/5.43 (~(s(s(elem!1)) = elem!1)),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[1546, 32275])).
% 5.24/5.43 tff(32277,plain,
% 5.24/5.43 (~(s(elem!1) = elem!1)),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[672, 32276])).
% 5.24/5.43 tff(32278,plain,
% 5.24/5.43 (~(s(s(z)) = elem!1)),
% 5.24/5.43 inference(modus_ponens,[status(thm)],[32277, 32272])).
% 5.24/5.43 tff(32279,plain,
% 5.24/5.43 (b(s(s(z)), elem!1)),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[448, 32278, 32270])).
% 5.24/5.43 tff(32280,plain,
% 5.24/5.43 ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(z))))))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[29314, 178, 31964, 31575, 31476])).
% 5.24/5.43 tff(32281,plain,
% 5.24/5.43 (~b(elem!1, s(s(s(s(z)))))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[32280, 32279])).
% 5.24/5.43 tff(32282,plain,
% 5.24/5.43 (r(elem!1, s(s(s(s(z)))))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[483, 32281, 32268])).
% 5.24/5.43 tff(32283,plain,
% 5.24/5.43 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[2832, 32267])).
% 5.24/5.43 tff(32284,plain,
% 5.24/5.43 (~r(elem!1, s(s(z)))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[29093, 32268, 103, 31964])).
% 5.24/5.43 tff(32285,plain,
% 5.24/5.43 ((s(elem!1) = elem!1) <=> (elem!1 = s(s(z)))),
% 5.24/5.43 inference(transitivity,[status(thm)],[32271, 1666])).
% 5.24/5.43 tff(32286,plain,
% 5.24/5.43 ((~(s(elem!1) = elem!1)) <=> (~(elem!1 = s(s(z))))),
% 5.24/5.43 inference(monotonicity,[status(thm)],[32285])).
% 5.24/5.43 tff(32287,plain,
% 5.24/5.43 (~(elem!1 = s(s(z)))),
% 5.24/5.43 inference(modus_ponens,[status(thm)],[32277, 32286])).
% 5.24/5.43 tff(32288,plain,
% 5.24/5.43 (b(elem!1, s(s(z)))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[467, 32287, 32284])).
% 5.24/5.43 tff(32289,plain,
% 5.24/5.43 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[11859, 32288, 31578, 27217, 32279])).
% 5.24/5.43 tff(32290,plain,
% 5.24/5.43 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[691, 32289, 32283])).
% 5.24/5.43 tff(32291,plain,
% 5.24/5.43 ($false),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[25883, 32290, 32282])).
% 5.24/5.43 tff(32292,plain,(b(s(s(s(s(z)))), s(s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.43 tff(32293,plain,
% 5.24/5.43 (b(s(s(s(s(z)))), s(s(z)))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[32292, 204, 28501])).
% 5.24/5.43 tff(32294,plain,
% 5.24/5.43 ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z))))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[14239, 178, 27212, 31575, 31476])).
% 5.24/5.43 tff(32295,plain,
% 5.24/5.43 (~b(s(s(z)), z)),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[32294, 32293])).
% 5.24/5.43 tff(32296,plain,
% 5.24/5.43 (~(s(s(s(s(z)))) = elem!1)),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[32143, 3241, 31476])).
% 5.24/5.43 tff(32297,plain,
% 5.24/5.43 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[29042, 108, 31575, 204])).
% 5.24/5.43 tff(32298,plain,
% 5.24/5.43 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[20667, 32297])).
% 5.24/5.43 tff(32299,plain,
% 5.24/5.43 (s(s(z)) = elem!1),
% 5.24/5.43 inference(unit_resolution,[status(thm)],[448, 29538, 3241])).
% 5.24/5.43 tff(32300,plain,
% 5.24/5.43 (s(s(s(z))) = s(elem!1)),
% 5.24/5.43 inference(monotonicity,[status(thm)],[32299])).
% 5.24/5.43 tff(32301,plain,
% 5.24/5.43 (b(z, s(s(s(z)))) <=> b(z, s(elem!1))),
% 5.24/5.43 inference(monotonicity,[status(thm)],[32300])).
% 5.24/5.43 tff(32302,plain,
% 5.24/5.43 (b(z, s(elem!1)) <=> b(z, s(s(s(z))))),
% 5.24/5.43 inference(symmetry,[status(thm)],[32301])).
% 5.24/5.43 tff(32303,plain,
% 5.24/5.43 ((elem!1 = s(s(s(z)))) <=> (elem!1 = s(elem!1))),
% 5.24/5.43 inference(monotonicity,[status(thm)],[32300])).
% 5.24/5.43 tff(32304,plain,
% 5.24/5.43 ((elem!1 = s(s(s(z)))) <=> (s(elem!1) = elem!1)),
% 5.24/5.43 inference(transitivity,[status(thm)],[32303, 3190])).
% 5.24/5.43 tff(32305,plain,
% 5.24/5.43 ((elem!1 = s(s(s(z)))) <=> (elem!1 = s(elem!1))),
% 5.24/5.43 inference(transitivity,[status(thm)],[32304, 3880])).
% 5.24/5.43 tff(32306,plain,
% 5.24/5.43 ((~(elem!1 = s(s(s(z))))) <=> (~(elem!1 = s(elem!1)))),
% 5.24/5.43 inference(monotonicity,[status(thm)],[32305])).
% 5.24/5.43 tff(32307,plain,
% 5.24/5.44 ((s(s(z)) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 5.24/5.44 inference(monotonicity,[status(thm)],[32299])).
% 5.24/5.44 tff(32308,plain,
% 5.24/5.44 ((~(s(s(z)) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 5.24/5.44 inference(monotonicity,[status(thm)],[32307])).
% 5.24/5.44 tff(32309,plain,
% 5.24/5.44 (~(elem!1 = s(s(s(z))))),
% 5.24/5.44 inference(modus_ponens,[status(thm)],[3205, 32308])).
% 5.24/5.44 tff(32310,plain,
% 5.24/5.44 (~(elem!1 = s(elem!1))),
% 5.24/5.44 inference(modus_ponens,[status(thm)],[32309, 32306])).
% 5.24/5.44 tff(32311,plain,
% 5.24/5.44 (elem!1 = s(s(z))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[3230, 32299])).
% 5.24/5.44 tff(32312,plain,
% 5.24/5.44 (~(s(elem!1) = s(s(s(s(z)))))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[1353, 32311, 32144])).
% 5.24/5.44 tff(32313,plain,
% 5.24/5.44 (~(s(s(s(s(z)))) = s(elem!1))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[2168, 32312])).
% 5.24/5.44 tff(32314,plain,
% 5.24/5.44 (b(elem!1, s(s(s(s(z)))))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[17989, 32299, 167])).
% 5.24/5.44 tff(32315,plain,
% 5.24/5.44 (b(s(s(s(s(z)))), elem!1)),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[8526, 32299, 202])).
% 5.24/5.44 tff(32316,plain,
% 5.24/5.44 (b(s(s(s(z))), elem!1) <=> b(s(elem!1), elem!1)),
% 5.24/5.44 inference(monotonicity,[status(thm)],[32300])).
% 5.24/5.44 tff(32317,plain,
% 5.24/5.44 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), elem!1)),
% 5.24/5.44 inference(monotonicity,[status(thm)],[32299])).
% 5.24/5.44 tff(32318,plain,
% 5.24/5.44 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[123, 107, 28500])).
% 5.24/5.44 tff(32319,plain,
% 5.24/5.44 (b(s(s(s(s(s(s(s(z))))))), z)),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[133, 32318])).
% 5.24/5.44 tff(32320,plain,
% 5.24/5.44 (~r(z, s(s(s(z))))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[24302, 1125, 29994])).
% 5.24/5.44 tff(32321,plain,
% 5.24/5.44 (b(z, s(s(s(z))))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[4920, 32320])).
% 5.24/5.44 tff(32322,plain,
% 5.24/5.44 ($false),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[31515, 32321, 30128, 202, 107, 32319])).
% 5.24/5.44 tff(32323,plain,((~r(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.44 tff(32324,plain,
% 5.24/5.44 (~r(s(s(s(z))), s(s(z)))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[32323, 107, 202])).
% 5.24/5.44 tff(32325,plain,
% 5.24/5.44 (b(s(s(s(z))), s(s(z)))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[4966, 32324])).
% 5.24/5.44 tff(32326,plain,
% 5.24/5.44 (b(s(s(s(z))), elem!1)),
% 5.24/5.44 inference(modus_ponens,[status(thm)],[32325, 32317])).
% 5.24/5.44 tff(32327,plain,
% 5.24/5.44 (b(s(elem!1), elem!1)),
% 5.24/5.44 inference(modus_ponens,[status(thm)],[32326, 32316])).
% 5.24/5.44 tff(32328,plain,
% 5.24/5.44 (r(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.24/5.44 inference(monotonicity,[status(thm)],[32299])).
% 5.24/5.44 tff(32329,plain,
% 5.24/5.44 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.24/5.44 inference(modus_ponens,[status(thm)],[107, 32328])).
% 5.24/5.44 tff(32330,plain,
% 5.24/5.44 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[3502, 32144])).
% 5.24/5.44 tff(32331,plain,
% 5.24/5.44 ((s(elem!1) = s(s(z))) <=> (s(elem!1) = elem!1)),
% 5.24/5.44 inference(monotonicity,[status(thm)],[32299])).
% 5.24/5.44 tff(32332,plain,
% 5.24/5.44 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(z)))),
% 5.24/5.44 inference(symmetry,[status(thm)],[32331])).
% 5.24/5.44 tff(32333,plain,
% 5.24/5.44 ((elem!1 = s(s(s(z)))) <=> (s(elem!1) = s(s(z)))),
% 5.24/5.44 inference(transitivity,[status(thm)],[32304, 32332])).
% 5.24/5.44 tff(32334,plain,
% 5.24/5.44 ((~(elem!1 = s(s(s(z))))) <=> (~(s(elem!1) = s(s(z))))),
% 5.24/5.44 inference(monotonicity,[status(thm)],[32333])).
% 5.24/5.44 tff(32335,plain,
% 5.24/5.44 (~(s(elem!1) = s(s(z)))),
% 5.24/5.44 inference(modus_ponens,[status(thm)],[32309, 32334])).
% 5.24/5.44 tff(32336,plain,
% 5.24/5.44 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[2840, 32335])).
% 5.24/5.44 tff(32337,plain,
% 5.24/5.44 (r(z, elem!1)),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[7053, 1324, 29994])).
% 5.24/5.44 tff(32338,plain,
% 5.24/5.44 (~b(z, s(s(s(elem!1))))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[20516, 556, 595, 9361, 521, 2953])).
% 5.24/5.44 tff(32339,plain,
% 5.24/5.44 ($false),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[2095, 32338, 6381])).
% 5.24/5.44 tff(32340,plain,((~r(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.44 tff(32341,plain,
% 5.24/5.44 (~r(s(s(s(elem!1))), elem!1)),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[32340, 32337, 11632, 595, 2953])).
% 5.24/5.44 tff(32342,plain,
% 5.24/5.44 (b(s(s(s(elem!1))), elem!1)),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[570, 32341, 18320])).
% 5.24/5.44 tff(32343,plain,
% 5.24/5.44 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 5.24/5.44 inference(monotonicity,[status(thm)],[3505, 27863])).
% 5.24/5.44 tff(32344,plain,
% 5.24/5.44 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 5.24/5.44 inference(transitivity,[status(thm)],[32343, 3881])).
% 5.24/5.44 tff(32345,plain,
% 5.24/5.44 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 5.24/5.44 inference(monotonicity,[status(thm)],[32344])).
% 5.24/5.44 tff(32346,plain,
% 5.24/5.44 (~(s(s(s(elem!1))) = s(elem!1))),
% 5.24/5.44 inference(modus_ponens,[status(thm)],[11413, 32345])).
% 5.24/5.44 tff(32347,plain,
% 5.24/5.44 ((~b(s(s(elem!1)), s(elem!1))) <=> (~b(s(s(s(s(z)))), s(elem!1)))),
% 5.24/5.44 inference(monotonicity,[status(thm)],[9109])).
% 5.24/5.44 tff(32348,plain,
% 5.24/5.44 (b(elem!1, s(s(elem!1)))),
% 5.24/5.44 inference(modus_ponens,[status(thm)],[1301, 9141])).
% 5.24/5.44 tff(32349,plain,
% 5.24/5.44 (b(s(s(elem!1)), elem!1)),
% 5.24/5.44 inference(modus_ponens,[status(thm)],[3771, 8522])).
% 5.24/5.44 tff(32350,plain,
% 5.24/5.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))))),
% 5.24/5.44 inference(rewrite,[status(thm)],[])).
% 5.24/5.44 tff(32351,plain,
% 5.24/5.44 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))))),
% 5.24/5.44 inference(rewrite,[status(thm)],[])).
% 5.24/5.44 tff(32352,plain,
% 5.24/5.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1))))))),
% 5.24/5.44 inference(monotonicity,[status(thm)],[32351])).
% 5.24/5.44 tff(32353,plain,
% 5.24/5.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))))),
% 5.24/5.44 inference(transitivity,[status(thm)],[32352, 32350])).
% 5.24/5.44 tff(32354,plain,
% 5.24/5.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 5.24/5.44 inference(quant_inst,[status(thm)],[])).
% 5.24/5.44 tff(32355,plain,
% 5.24/5.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1))))),
% 5.24/5.44 inference(modus_ponens,[status(thm)],[32354, 32353])).
% 5.24/5.44 tff(32356,plain,
% 5.24/5.44 (~b(s(s(elem!1)), s(elem!1))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[32355, 178, 683, 854, 32349, 32348])).
% 5.24/5.44 tff(32357,plain,
% 5.24/5.44 (~b(s(s(s(s(z)))), s(elem!1))),
% 5.24/5.44 inference(modus_ponens,[status(thm)],[32356, 32347])).
% 5.24/5.44 tff(32358,plain,
% 5.24/5.44 (r(s(s(s(s(z)))), s(elem!1))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[2173, 32357, 2508])).
% 5.24/5.44 tff(32359,plain,
% 5.24/5.44 (r(elem!1, s(s(s(elem!1))))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[6432, 32358, 2857, 3771, 11627, 32346, 1301, 32341, 683, 854])).
% 5.24/5.44 tff(32360,plain,
% 5.24/5.44 (~r(z, s(s(s(elem!1))))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[3421, 32359, 28704])).
% 5.24/5.44 tff(32361,plain,
% 5.24/5.44 (b(z, s(s(s(elem!1))))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[2095, 32360])).
% 5.24/5.44 tff(32362,plain,
% 5.24/5.44 (r(elem!1, s(s(s(elem!1))))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[6432, 6402, 2857, 3771, 1586, 356, 1301, 854, 683, 6400])).
% 5.24/5.44 tff(32363,plain,
% 5.24/5.44 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[8969, 32362, 2953])).
% 5.24/5.44 tff(32364,plain,
% 5.24/5.44 (b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[5118, 32363, 3521])).
% 5.24/5.44 tff(32365,plain,
% 5.24/5.44 (~r(s(s(s(elem!1))), z)),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[6071, 32362, 437])).
% 5.24/5.44 tff(32366,plain,
% 5.24/5.44 (b(s(s(s(elem!1))), z)),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[1565, 32365])).
% 5.24/5.44 tff(32367,plain,
% 5.24/5.44 (b(s(s(s(elem!1))), elem!1)),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[570, 6402, 949])).
% 5.24/5.44 tff(32368,plain,
% 5.24/5.44 (~r(z, s(s(s(elem!1))))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[7389, 32367, 683, 356, 2333, 854])).
% 5.24/5.44 tff(32369,plain,
% 5.24/5.44 (b(z, s(s(s(elem!1))))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[2095, 32368])).
% 5.24/5.44 tff(32370,plain,
% 5.24/5.44 ($false),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[8059, 178, 32369, 32366, 595, 146, 32364])).
% 5.24/5.44 tff(32371,plain,(r(s(s(s(elem!1))), elem!1) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (elem!1 = s(s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 5.24/5.44 tff(32372,plain,
% 5.24/5.44 (~r(z, s(elem!1))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[32371, 32358, 146, 3521, 28704, 2953, 683, 32346, 595, 32341, 2857, 3771, 11627, 1301, 854, 18320])).
% 5.24/5.44 tff(32373,plain,
% 5.24/5.44 (b(z, s(elem!1))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[2351, 32372])).
% 5.24/5.44 tff(32374,plain,
% 5.24/5.44 (~(s(elem!1) = s(s(elem!1)))),
% 5.24/5.44 inference(modus_ponens,[status(thm)],[2508, 8126])).
% 5.24/5.44 tff(32375,plain,
% 5.24/5.44 ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1))))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[8538, 178, 683, 32349, 32348])).
% 5.24/5.44 tff(32376,plain,
% 5.24/5.44 (~b(s(elem!1), s(s(elem!1)))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[32375, 854])).
% 5.24/5.44 tff(32377,plain,
% 5.24/5.44 (r(s(elem!1), s(s(elem!1)))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[1028, 32376, 32374])).
% 5.24/5.44 tff(32378,plain,
% 5.24/5.44 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 5.24/5.44 inference(monotonicity,[status(thm)],[3506])).
% 5.24/5.44 tff(32379,plain,
% 5.24/5.44 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 5.24/5.44 inference(transitivity,[status(thm)],[32378, 3400])).
% 5.24/5.44 tff(32380,plain,
% 5.24/5.44 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 5.24/5.44 inference(transitivity,[status(thm)],[32379, 12033])).
% 5.24/5.44 tff(32381,plain,
% 5.24/5.44 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 5.24/5.44 inference(monotonicity,[status(thm)],[32380])).
% 5.24/5.44 tff(32382,plain,
% 5.24/5.44 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 5.24/5.44 inference(modus_ponens,[status(thm)],[2857, 32381])).
% 5.24/5.44 tff(32383,plain,
% 5.24/5.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 5.24/5.44 inference(rewrite,[status(thm)],[])).
% 5.24/5.44 tff(32384,plain,
% 5.24/5.44 (((~b(s(s(elem!1)), 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(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 5.24/5.44 inference(rewrite,[status(thm)],[])).
% 5.24/5.44 tff(32385,plain,
% 5.24/5.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(elem!1))), s(s(elem!1)))) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1))))))),
% 5.24/5.44 inference(monotonicity,[status(thm)],[32384])).
% 5.24/5.44 tff(32386,plain,
% 5.24/5.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(elem!1))), s(s(elem!1)))) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 5.24/5.44 inference(transitivity,[status(thm)],[32385, 32383])).
% 5.24/5.44 tff(32387,plain,
% 5.24/5.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 5.24/5.44 inference(quant_inst,[status(thm)],[])).
% 5.24/5.44 tff(32388,plain,
% 5.24/5.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1))))),
% 5.24/5.44 inference(modus_ponens,[status(thm)],[32387, 32386])).
% 5.24/5.44 tff(32389,plain,
% 5.24/5.44 ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[32388, 178, 32342, 32349, 27724])).
% 5.24/5.44 tff(32390,plain,
% 5.24/5.44 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[32389, 32361])).
% 5.24/5.44 tff(32391,plain,
% 5.24/5.44 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[3409, 32390, 32382])).
% 5.24/5.44 tff(32392,plain,
% 5.24/5.44 (~r(s(s(s(elem!1))), s(elem!1))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[5980, 32391, 32377])).
% 5.24/5.44 tff(32393,plain,
% 5.24/5.44 (b(s(s(s(elem!1))), s(elem!1))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[373, 32392, 32346])).
% 5.24/5.44 tff(32394,plain,
% 5.24/5.44 ($false),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[23800, 178, 32393, 32373, 32361, 683, 32342])).
% 5.24/5.44 tff(32395,plain,((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (s(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)))))) | (s(s(s(s(z)))) = s(elem!1)) | (~(s(s(z)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.44 tff(32396,plain,
% 5.24/5.44 (~b(elem!1, s(elem!1))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[32395, 32336, 32319, 32330, 32329, 31505, 32327, 32315, 32314, 32313, 32299])).
% 5.24/5.44 tff(32397,plain,
% 5.24/5.44 (r(elem!1, s(elem!1))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[756, 32396, 32310])).
% 5.24/5.44 tff(32398,plain,
% 5.24/5.44 (~r(z, s(elem!1))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[12189, 32397, 437])).
% 5.24/5.44 tff(32399,plain,
% 5.24/5.44 (b(z, s(elem!1))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[2351, 32398])).
% 5.24/5.44 tff(32400,plain,
% 5.24/5.44 (b(z, s(s(s(z))))),
% 5.24/5.44 inference(modus_ponens,[status(thm)],[32399, 32302])).
% 5.24/5.44 tff(32401,plain,
% 5.24/5.44 (~r(s(elem!1), z)),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[2711, 32397, 437])).
% 5.24/5.44 tff(32402,plain,
% 5.24/5.44 (b(s(elem!1), z)),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[774, 32401])).
% 5.24/5.44 tff(32403,plain,
% 5.24/5.44 (b(s(s(s(z))), z)),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[7042, 32402, 32311])).
% 5.24/5.44 tff(32404,plain,
% 5.24/5.44 (~b(z, s(s(s(z))))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[31515, 32403, 202, 107, 32319])).
% 5.24/5.44 tff(32405,plain,
% 5.24/5.44 ($false),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[32404, 32400])).
% 5.24/5.44 tff(32406,plain,((~r(elem!1, z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 5.24/5.44 tff(32407,plain,
% 5.24/5.44 (~r(elem!1, z)),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[32406, 3241, 15765, 167, 202])).
% 5.24/5.44 tff(32408,plain,
% 5.24/5.44 (~(s(s(z)) = elem!1)),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[1345, 32407, 28500])).
% 5.24/5.44 tff(32409,plain,
% 5.24/5.44 (r(s(s(z)), elem!1)),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[448, 32408, 3241])).
% 5.24/5.44 tff(32410,plain,
% 5.24/5.44 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[17566, 32409, 15765])).
% 5.24/5.44 tff(32411,plain,
% 5.24/5.44 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[123, 15765, 28500])).
% 5.24/5.44 tff(32412,plain,
% 5.24/5.44 (b(s(s(s(s(s(s(s(z))))))), z)),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[133, 32411])).
% 5.24/5.44 tff(32413,plain,
% 5.24/5.44 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[23450, 15765, 29994])).
% 5.24/5.44 tff(32414,plain,
% 5.24/5.44 (b(z, s(s(s(s(s(s(s(z))))))))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[271, 32413])).
% 5.24/5.44 tff(32415,plain,
% 5.24/5.44 (~r(elem!1, z)),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[32406, 3241, 107, 167, 202])).
% 5.24/5.44 tff(32416,plain,
% 5.24/5.44 ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z))))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[14239, 178, 27212, 31623, 167])).
% 5.24/5.44 tff(32417,plain,
% 5.24/5.44 (~b(s(s(z)), z)),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[32416, 202])).
% 5.24/5.44 tff(32418,plain,
% 5.24/5.44 (~r(elem!1, z)),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[443, 4256, 28500])).
% 5.24/5.44 tff(32419,plain,
% 5.24/5.44 (elem!1 = z),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[498, 32418, 5723])).
% 5.24/5.44 tff(32420,plain,
% 5.24/5.44 (s(elem!1) = s(z)),
% 5.24/5.44 inference(monotonicity,[status(thm)],[32419])).
% 5.24/5.44 tff(32421,plain,
% 5.24/5.44 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(z), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.44 inference(monotonicity,[status(thm)],[32420])).
% 5.24/5.44 tff(32422,plain,
% 5.24/5.44 (s(z) = s(elem!1)),
% 5.24/5.44 inference(symmetry,[status(thm)],[32420])).
% 5.24/5.44 tff(32423,plain,
% 5.24/5.44 ((s(s(s(s(s(s(s(z))))))) = s(z)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 5.24/5.44 inference(monotonicity,[status(thm)],[32422])).
% 5.24/5.44 tff(32424,plain,
% 5.24/5.44 ((s(s(s(s(s(s(s(z))))))) = s(z)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 5.24/5.44 inference(transitivity,[status(thm)],[32423, 377])).
% 5.24/5.44 tff(32425,plain,
% 5.24/5.44 ((~(s(s(s(s(s(s(s(z))))))) = s(z))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.44 inference(monotonicity,[status(thm)],[32424])).
% 5.24/5.44 tff(32426,plain,
% 5.24/5.44 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 5.24/5.44 inference(modus_ponens,[status(thm)],[612, 32425])).
% 5.24/5.44 tff(32427,plain,
% 5.24/5.44 (z = elem!1),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[2808, 32419])).
% 5.24/5.44 tff(32428,plain,
% 5.24/5.44 (~(s(elem!1) = s(s(s(s(z)))))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[25360, 32427])).
% 5.24/5.44 tff(32429,plain,
% 5.24/5.44 (~r(s(elem!1), s(s(z)))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[24252, 32426, 29994, 107, 32319, 224, 31505])).
% 5.24/5.44 tff(32430,plain,
% 5.24/5.44 (s(s(elem!1)) = s(s(z))),
% 5.24/5.44 inference(monotonicity,[status(thm)],[32420])).
% 5.24/5.44 tff(32431,plain,
% 5.24/5.44 ((s(elem!1) = s(s(elem!1))) <=> (s(z) = s(s(z)))),
% 5.24/5.44 inference(monotonicity,[status(thm)],[32420, 32430])).
% 5.24/5.44 tff(32432,plain,
% 5.24/5.44 ((s(z) = s(s(z))) <=> (s(elem!1) = s(s(elem!1)))),
% 5.24/5.44 inference(symmetry,[status(thm)],[32431])).
% 5.24/5.44 tff(32433,plain,
% 5.24/5.44 ((s(z) = s(s(z))) <=> (s(s(elem!1)) = s(elem!1))),
% 5.24/5.44 inference(transitivity,[status(thm)],[32432, 10922])).
% 5.24/5.44 tff(32434,plain,
% 5.24/5.44 ((~(s(z) = s(s(z)))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 5.24/5.44 inference(monotonicity,[status(thm)],[32433])).
% 5.24/5.44 tff(32435,plain,
% 5.24/5.44 ((s(z) = s(s(z))) <=> (s(elem!1) = s(s(z)))),
% 5.24/5.44 inference(monotonicity,[status(thm)],[32422])).
% 5.24/5.44 tff(32436,plain,
% 5.24/5.44 ((s(elem!1) = s(s(z))) <=> (s(z) = s(s(z)))),
% 5.24/5.44 inference(symmetry,[status(thm)],[32435])).
% 5.24/5.44 tff(32437,plain,
% 5.24/5.44 ((~(s(elem!1) = s(s(z)))) <=> (~(s(z) = s(s(z))))),
% 5.24/5.44 inference(monotonicity,[status(thm)],[32436])).
% 5.24/5.44 tff(32438,plain,
% 5.24/5.44 (~(s(z) = s(s(z)))),
% 5.24/5.44 inference(modus_ponens,[status(thm)],[1056, 32437])).
% 5.24/5.44 tff(32439,plain,
% 5.24/5.44 (~(s(s(elem!1)) = s(elem!1))),
% 5.24/5.44 inference(modus_ponens,[status(thm)],[32438, 32434])).
% 5.24/5.44 tff(32440,plain,
% 5.24/5.44 (b(s(elem!1), s(s(z))) <=> b(s(z), s(s(z)))),
% 5.24/5.44 inference(monotonicity,[status(thm)],[32420])).
% 5.24/5.44 tff(32441,plain,
% 5.24/5.44 (b(s(elem!1), s(s(z)))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[421, 32429, 1056])).
% 5.24/5.44 tff(32442,plain,
% 5.24/5.44 (b(s(z), s(s(z)))),
% 5.24/5.44 inference(modus_ponens,[status(thm)],[32441, 32440])).
% 5.24/5.44 tff(32443,plain,
% 5.24/5.44 (s(s(s(elem!1))) = s(s(s(z)))),
% 5.24/5.44 inference(monotonicity,[status(thm)],[32430])).
% 5.24/5.44 tff(32444,plain,
% 5.24/5.44 (s(s(s(z))) = s(s(s(elem!1)))),
% 5.24/5.44 inference(symmetry,[status(thm)],[32443])).
% 5.24/5.44 tff(32445,plain,
% 5.24/5.44 ((s(elem!1) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 5.24/5.44 inference(monotonicity,[status(thm)],[32444])).
% 5.24/5.44 tff(32446,plain,
% 5.24/5.44 ((s(elem!1) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 5.24/5.44 inference(transitivity,[status(thm)],[32445, 3881])).
% 5.24/5.44 tff(32447,plain,
% 5.24/5.44 ((s(elem!1) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 5.24/5.44 inference(transitivity,[status(thm)],[32446, 7104])).
% 5.24/5.44 tff(32448,plain,
% 5.24/5.44 ((~(s(elem!1) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 5.24/5.44 inference(monotonicity,[status(thm)],[32447])).
% 5.24/5.44 tff(32449,plain,
% 5.24/5.44 (~(s(elem!1) = s(s(s(elem!1))))),
% 5.24/5.44 inference(modus_ponens,[status(thm)],[23437, 32448])).
% 5.24/5.44 tff(32450,plain,
% 5.24/5.44 (r(s(s(elem!1)), z)),
% 5.24/5.44 inference(modus_ponens,[status(thm)],[28500, 989])).
% 5.24/5.44 tff(32451,plain,
% 5.24/5.44 (~r(s(s(elem!1)), s(elem!1))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[997, 12569, 32450])).
% 5.24/5.44 tff(32452,plain,
% 5.24/5.44 (b(s(s(elem!1)), s(elem!1))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[1006, 32451, 1000])).
% 5.24/5.44 tff(32453,plain,
% 5.24/5.44 (b(s(s(z)), s(z))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[1015, 32452, 928])).
% 5.24/5.44 tff(32454,plain,
% 5.24/5.44 ((~b(s(elem!1), z)) <=> (~b(s(elem!1), elem!1))),
% 5.24/5.44 inference(monotonicity,[status(thm)],[12062])).
% 5.24/5.44 tff(32455,plain,
% 5.24/5.44 (~b(s(elem!1), elem!1)),
% 5.24/5.44 inference(modus_ponens,[status(thm)],[766, 32454])).
% 5.24/5.44 tff(32456,plain,
% 5.24/5.44 (r(s(elem!1), elem!1)),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[677, 32455, 20662])).
% 5.24/5.44 tff(32457,plain,
% 5.24/5.44 (~r(s(s(s(elem!1))), elem!1)),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[12762, 32456, 928, 30943, 32453, 10110])).
% 5.24/5.44 tff(32458,plain,
% 5.24/5.44 (b(s(s(s(elem!1))), elem!1)),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[570, 32457, 941])).
% 5.24/5.44 tff(32459,plain,
% 5.24/5.44 (b(s(s(s(z))), z)),
% 5.24/5.44 inference(modus_ponens,[status(thm)],[32458, 30617])).
% 5.24/5.44 tff(32460,plain,
% 5.24/5.44 (~b(z, s(s(s(z))))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[31515, 32459, 202, 107, 32319])).
% 5.24/5.44 tff(32461,plain,
% 5.24/5.44 (r(z, s(s(s(z))))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[4920, 32460])).
% 5.24/5.44 tff(32462,plain,
% 5.24/5.44 (r(elem!1, s(s(s(elem!1))))),
% 5.24/5.44 inference(modus_ponens,[status(thm)],[32461, 10724])).
% 5.24/5.44 tff(32463,plain,
% 5.24/5.44 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[21413, 32459, 27212, 31623, 204])).
% 5.24/5.44 tff(32464,plain,
% 5.24/5.44 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[20667, 32463])).
% 5.24/5.44 tff(32465,plain,
% 5.24/5.44 (r(s(elem!1), s(s(s(s(z)))))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[1038, 12569, 28500, 167, 202, 928, 927])).
% 5.24/5.44 tff(32466,plain,
% 5.24/5.44 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[25119, 32465])).
% 5.24/5.44 tff(32467,plain,
% 5.24/5.44 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.44 inference(unit_resolution,[status(thm)],[395, 32466, 14147])).
% 5.24/5.44 tff(32468,plain,
% 5.24/5.44 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.44 inference(modus_ponens,[status(thm)],[32467, 20647])).
% 5.24/5.44 tff(32469,plain,
% 5.24/5.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 5.24/5.44 inference(rewrite,[status(thm)],[])).
% 5.24/5.44 tff(32470,plain,
% 5.24/5.44 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 5.24/5.44 inference(rewrite,[status(thm)],[])).
% 5.24/5.44 tff(32471,plain,
% 5.24/5.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 5.24/5.44 inference(monotonicity,[status(thm)],[32470])).
% 5.24/5.44 tff(32472,plain,
% 5.24/5.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 5.24/5.44 inference(transitivity,[status(thm)],[32471, 32469])).
% 5.24/5.44 tff(32473,plain,
% 5.24/5.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))))),
% 5.24/5.45 inference(quant_inst,[status(thm)],[])).
% 5.24/5.45 tff(32474,plain,
% 5.24/5.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 5.24/5.45 inference(modus_ponens,[status(thm)],[32473, 32472])).
% 5.24/5.45 tff(32475,plain,
% 5.24/5.45 ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z)))))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[32474, 178, 32319, 32459, 32468])).
% 5.24/5.45 tff(32476,plain,
% 5.24/5.45 (~b(s(z), s(s(s(z))))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[32475, 32464])).
% 5.24/5.45 tff(32477,plain,
% 5.24/5.45 (~b(s(elem!1), s(s(s(elem!1))))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[25090, 32476, 928])).
% 5.24/5.45 tff(32478,plain,
% 5.24/5.45 (r(s(elem!1), s(s(s(elem!1))))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[5432, 32477, 5425])).
% 5.24/5.45 tff(32479,plain,
% 5.24/5.45 (~r(elem!1, s(s(s(elem!1))))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[9138, 32478, 32456])).
% 5.24/5.45 tff(32480,plain,
% 5.24/5.45 ($false),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[32479, 32462])).
% 5.24/5.45 tff(32481,plain,(b(s(elem!1), z) | (~(elem!1 = z)) | (s(elem!1) = s(s(s(elem!1)))) | (~b(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(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))) | (s(s(elem!1)) = s(elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | r(s(elem!1), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.45 tff(32482,plain,
% 5.24/5.45 (b(s(elem!1), z)),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[32481, 32419, 32449, 202, 107, 204, 32442, 32439, 167, 32429])).
% 5.24/5.45 tff(32483,plain,
% 5.24/5.45 (~b(s(elem!1), s(s(s(s(z)))))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[31823, 32482, 2311, 167])).
% 5.24/5.45 tff(32484,plain,
% 5.24/5.45 (r(s(elem!1), s(s(s(s(z)))))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[1084, 32483, 32428])).
% 5.24/5.45 tff(32485,plain,
% 5.24/5.45 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[25119, 32484])).
% 5.24/5.45 tff(32486,plain,
% 5.24/5.45 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[395, 32485, 32426])).
% 5.24/5.45 tff(32487,plain,
% 5.24/5.45 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.45 inference(modus_ponens,[status(thm)],[32486, 32421])).
% 5.24/5.45 tff(32488,plain,
% 5.24/5.45 (b(s(z), z) <=> b(s(elem!1), z)),
% 5.24/5.45 inference(monotonicity,[status(thm)],[32422])).
% 5.24/5.45 tff(32489,plain,
% 5.24/5.45 (b(s(elem!1), z) <=> b(s(z), z)),
% 5.24/5.45 inference(symmetry,[status(thm)],[32488])).
% 5.24/5.45 tff(32490,plain,
% 5.24/5.45 (b(s(z), z)),
% 5.24/5.45 inference(modus_ponens,[status(thm)],[32482, 32489])).
% 5.24/5.45 tff(32491,plain,
% 5.24/5.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), 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), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), 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), s(s(s(s(s(s(s(z))))))))))),
% 5.24/5.45 inference(rewrite,[status(thm)],[])).
% 5.24/5.45 tff(32492,plain,
% 5.24/5.45 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~b(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), s(s(s(s(s(s(s(z))))))))))),
% 5.24/5.45 inference(rewrite,[status(thm)],[])).
% 5.24/5.45 tff(32493,plain,
% 5.24/5.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(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(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), 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), s(s(s(s(s(s(s(z)))))))))))),
% 5.24/5.45 inference(monotonicity,[status(thm)],[32492])).
% 5.24/5.45 tff(32494,plain,
% 5.24/5.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(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(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), 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), s(s(s(s(s(s(s(z))))))))))),
% 5.24/5.45 inference(transitivity,[status(thm)],[32493, 32491])).
% 5.24/5.45 tff(32495,plain,
% 5.24/5.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(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(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 5.24/5.45 inference(quant_inst,[status(thm)],[])).
% 5.24/5.45 tff(32496,plain,
% 5.24/5.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.45 inference(modus_ponens,[status(thm)],[32495, 32494])).
% 5.24/5.45 tff(32497,plain,
% 5.24/5.45 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[32496, 178, 31505, 32490, 32319, 32487])).
% 5.24/5.45 tff(32498,plain,
% 5.24/5.45 (r(s(z), s(s(s(s(z)))))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[6689, 32484, 32419])).
% 5.24/5.45 tff(32499,plain,
% 5.24/5.45 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[4560, 118, 24592, 32498])).
% 5.24/5.45 tff(32500,plain,
% 5.24/5.45 ($false),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[615, 41, 612, 32499, 32497])).
% 5.24/5.45 tff(32501,plain,((s(s(z)) = elem!1) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(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(s(s(s(s(s(z))))))))) | (s(elem!1) = s(s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | b(elem!1, z) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 5.24/5.45 tff(32502,plain,
% 5.24/5.45 (s(s(z)) = elem!1),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[32501, 1056, 202, 107, 204, 167, 224, 5723, 3241])).
% 5.24/5.45 tff(32503,plain,
% 5.24/5.45 (s(s(s(z))) = s(elem!1)),
% 5.24/5.45 inference(monotonicity,[status(thm)],[32502])).
% 5.24/5.45 tff(32504,plain,
% 5.24/5.45 (b(z, s(s(s(z)))) <=> b(z, s(elem!1))),
% 5.24/5.45 inference(monotonicity,[status(thm)],[32503])).
% 5.24/5.45 tff(32505,plain,
% 5.24/5.45 (b(z, s(elem!1)) <=> b(z, s(s(s(z))))),
% 5.24/5.45 inference(symmetry,[status(thm)],[32504])).
% 5.24/5.45 tff(32506,plain,
% 5.24/5.45 (r(elem!1, z)),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[1345, 32502, 28500])).
% 5.24/5.45 tff(32507,plain,
% 5.24/5.45 ((s(elem!1) = s(s(z))) <=> (s(elem!1) = elem!1)),
% 5.24/5.45 inference(monotonicity,[status(thm)],[32502])).
% 5.24/5.45 tff(32508,plain,
% 5.24/5.45 ((s(elem!1) = s(s(z))) <=> (elem!1 = s(elem!1))),
% 5.24/5.45 inference(transitivity,[status(thm)],[32507, 3880])).
% 5.24/5.45 tff(32509,plain,
% 5.24/5.45 ((~(s(elem!1) = s(s(z)))) <=> (~(elem!1 = s(elem!1)))),
% 5.24/5.45 inference(monotonicity,[status(thm)],[32508])).
% 5.24/5.45 tff(32510,plain,
% 5.24/5.45 (~(elem!1 = s(elem!1))),
% 5.24/5.45 inference(modus_ponens,[status(thm)],[1056, 32509])).
% 5.24/5.45 tff(32511,plain,
% 5.24/5.45 (elem!1 = s(s(z))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[3230, 32502])).
% 5.24/5.45 tff(32512,plain,
% 5.24/5.45 (~(s(elem!1) = s(s(s(s(z)))))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[1353, 32511, 31641])).
% 5.24/5.45 tff(32513,plain,
% 5.24/5.45 (~(s(s(s(s(z)))) = s(elem!1))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[2168, 32512])).
% 5.24/5.45 tff(32514,plain,
% 5.24/5.45 (b(elem!1, s(s(s(s(z)))))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[17989, 32502, 167])).
% 5.24/5.45 tff(32515,plain,
% 5.24/5.45 (b(s(s(s(s(z)))), elem!1)),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[8526, 32502, 202])).
% 5.24/5.45 tff(32516,plain,
% 5.24/5.45 (r(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.24/5.45 inference(monotonicity,[status(thm)],[32502])).
% 5.24/5.45 tff(32517,plain,
% 5.24/5.45 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.24/5.45 inference(modus_ponens,[status(thm)],[107, 32516])).
% 5.24/5.45 tff(32518,plain,
% 5.24/5.45 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[3502, 31641])).
% 5.24/5.45 tff(32519,plain,
% 5.24/5.45 (b(s(elem!1), s(s(z))) <=> b(s(elem!1), elem!1)),
% 5.24/5.45 inference(monotonicity,[status(thm)],[32502])).
% 5.24/5.45 tff(32520,plain,
% 5.24/5.45 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[5361, 32502])).
% 5.24/5.45 tff(32521,plain,
% 5.24/5.45 (~r(s(elem!1), s(s(z)))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[24252, 32520, 29994, 107, 32319, 224, 31505])).
% 5.24/5.45 tff(32522,plain,
% 5.24/5.45 (b(s(elem!1), s(s(z)))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[421, 32521, 1056])).
% 5.24/5.45 tff(32523,plain,
% 5.24/5.45 (b(s(elem!1), elem!1)),
% 5.24/5.45 inference(modus_ponens,[status(thm)],[32522, 32519])).
% 5.24/5.45 tff(32524,plain,
% 5.24/5.45 (~b(elem!1, s(elem!1))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[32395, 32523, 32319, 32518, 32517, 31505, 13192, 32515, 32514, 32513, 32502])).
% 5.24/5.45 tff(32525,plain,
% 5.24/5.45 (r(elem!1, s(elem!1))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[756, 32524, 32510])).
% 5.24/5.45 tff(32526,plain,
% 5.24/5.45 (~r(z, s(elem!1))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[12189, 32525, 32506])).
% 5.24/5.45 tff(32527,plain,
% 5.24/5.45 (b(z, s(elem!1))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[2351, 32526])).
% 5.24/5.45 tff(32528,plain,
% 5.24/5.45 (b(z, s(s(s(z))))),
% 5.24/5.45 inference(modus_ponens,[status(thm)],[32527, 32505])).
% 5.24/5.45 tff(32529,plain,
% 5.24/5.45 (~r(s(elem!1), z)),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[2711, 32525, 32506])).
% 5.24/5.45 tff(32530,plain,
% 5.24/5.45 (b(s(elem!1), z)),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[774, 32529])).
% 5.24/5.45 tff(32531,plain,
% 5.24/5.45 (b(s(s(s(z))), z)),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[7042, 32530, 32511])).
% 5.24/5.45 tff(32532,plain,
% 5.24/5.45 (~b(z, s(s(s(z))))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[31515, 32531, 202, 107, 32319])).
% 5.24/5.45 tff(32533,plain,
% 5.24/5.45 ($false),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[32532, 32528])).
% 5.24/5.45 tff(32534,plain,((s(elem!1) = s(s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | b(elem!1, z) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 5.24/5.45 tff(32535,plain,
% 5.24/5.45 (s(elem!1) = s(s(z))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[32534, 3241, 107, 224, 167, 204, 5723, 202])).
% 5.24/5.45 tff(32536,plain,
% 5.24/5.45 ((s(elem!1) = elem!1) <=> (s(s(z)) = elem!1)),
% 5.24/5.45 inference(monotonicity,[status(thm)],[32535])).
% 5.24/5.45 tff(32537,plain,
% 5.24/5.45 ((s(s(z)) = elem!1) <=> (s(elem!1) = elem!1)),
% 5.24/5.45 inference(symmetry,[status(thm)],[32536])).
% 5.24/5.45 tff(32538,plain,
% 5.24/5.45 (~(z = elem!1)),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[28525, 32535])).
% 5.24/5.45 tff(32539,plain,
% 5.24/5.45 (~(elem!1 = z)),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[2808, 32538])).
% 5.24/5.45 tff(32540,plain,
% 5.24/5.45 (r(elem!1, z)),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[498, 32539, 5723])).
% 5.24/5.45 tff(32541,plain,
% 5.24/5.45 (~r(s(s(z)), elem!1)),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[443, 32540, 28500])).
% 5.24/5.45 tff(32542,plain,
% 5.24/5.45 (s(s(z)) = elem!1),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[448, 32541, 3241])).
% 5.24/5.45 tff(32543,plain,
% 5.24/5.45 (s(elem!1) = elem!1),
% 5.24/5.45 inference(modus_ponens,[status(thm)],[32542, 32537])).
% 5.24/5.45 tff(32544,plain,
% 5.24/5.45 (~(elem!1 = s(s(s(s(elem!1)))))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[1422, 32535])).
% 5.24/5.45 tff(32545,plain,
% 5.24/5.45 (~(s(s(s(elem!1))) = s(elem!1))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[1509, 32544])).
% 5.24/5.45 tff(32546,plain,
% 5.24/5.45 (~(elem!1 = s(s(elem!1)))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[1539, 32545])).
% 5.24/5.45 tff(32547,plain,
% 5.24/5.45 (~(s(s(elem!1)) = elem!1)),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[1546, 32546])).
% 5.24/5.45 tff(32548,plain,
% 5.24/5.45 (~(s(elem!1) = elem!1)),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[672, 32547])).
% 5.24/5.45 tff(32549,plain,
% 5.24/5.45 ($false),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[32548, 32543])).
% 5.24/5.45 tff(32550,plain,(b(s(s(z)), elem!1) | b(elem!1, z) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.45 tff(32551,plain,
% 5.24/5.45 (b(s(s(z)), elem!1)),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[32550, 5723, 107, 287, 167, 204, 202])).
% 5.24/5.45 tff(32552,plain,
% 5.24/5.45 (~b(s(s(z)), elem!1)),
% 5.24/5.45 inference(modus_ponens,[status(thm)],[23814, 31589])).
% 5.24/5.45 tff(32553,plain,
% 5.24/5.45 ($false),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[817, 32552])).
% 5.24/5.45 tff(32554,plain,((~(elem!1 = z)) | (~b(s(s(z)), elem!1)) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 5.24/5.45 tff(32555,plain,
% 5.24/5.45 (~(elem!1 = z)),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[32554, 32551, 32417])).
% 5.24/5.45 tff(32556,plain,
% 5.24/5.45 (r(elem!1, z)),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[498, 32555, 5723])).
% 5.24/5.45 tff(32557,plain,
% 5.24/5.45 (~(z = elem!1)),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[317, 32555])).
% 5.24/5.45 tff(32558,plain,
% 5.24/5.45 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[10835, 32551, 286])).
% 5.24/5.45 tff(32559,plain,
% 5.24/5.45 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[703, 32558])).
% 5.24/5.45 tff(32560,plain,
% 5.24/5.45 (~(elem!1 = s(s(z)))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[31585, 32551])).
% 5.24/5.45 tff(32561,plain,
% 5.24/5.45 (~r(elem!1, s(s(z)))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[458, 32556, 28500])).
% 5.24/5.45 tff(32562,plain,
% 5.24/5.45 (b(elem!1, s(s(z)))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[467, 32561, 32560])).
% 5.24/5.45 tff(32563,plain,
% 5.24/5.45 (~b(elem!1, s(s(s(s(z)))))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[491, 32562, 167, 202, 32551])).
% 5.24/5.45 tff(32564,plain,
% 5.24/5.45 (r(elem!1, s(s(s(s(z)))))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[483, 32563, 31624])).
% 5.24/5.45 tff(32565,plain,
% 5.24/5.45 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[11991, 118, 24592, 32564])).
% 5.24/5.45 tff(32566,plain,
% 5.24/5.45 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[3444, 32565, 32559])).
% 5.24/5.45 tff(32567,plain,
% 5.24/5.45 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[17305, 32551, 167, 204, 202, 31641])).
% 5.24/5.45 tff(32568,plain,
% 5.24/5.45 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[691, 32567, 32558])).
% 5.24/5.45 tff(32569,plain,
% 5.24/5.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 5.24/5.45 inference(rewrite,[status(thm)],[])).
% 5.24/5.45 tff(32570,plain,
% 5.24/5.45 (((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z))) <=> ((~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 5.24/5.45 inference(rewrite,[status(thm)],[])).
% 5.24/5.45 tff(32571,plain,
% 5.24/5.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 5.24/5.45 inference(monotonicity,[status(thm)],[32570])).
% 5.24/5.45 tff(32572,plain,
% 5.24/5.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 5.24/5.45 inference(transitivity,[status(thm)],[32571, 32569])).
% 5.24/5.45 tff(32573,plain,
% 5.24/5.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 5.24/5.45 inference(quant_inst,[status(thm)],[])).
% 5.24/5.45 tff(32574,plain,
% 5.24/5.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 5.24/5.45 inference(modus_ponens,[status(thm)],[32573, 32572])).
% 5.24/5.45 tff(32575,plain,
% 5.24/5.45 (~b(z, elem!1)),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[32574, 178, 32568, 31505, 32319, 32566])).
% 5.24/5.45 tff(32576,plain,
% 5.24/5.45 (r(z, elem!1)),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[585, 32575, 32557])).
% 5.24/5.45 tff(32577,plain,
% 5.24/5.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 5.24/5.45 inference(rewrite,[status(thm)],[])).
% 5.24/5.45 tff(32578,plain,
% 5.24/5.45 (((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 5.24/5.45 inference(rewrite,[status(thm)],[])).
% 5.24/5.45 tff(32579,plain,
% 5.24/5.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(s(z))), s(s(z))))))),
% 5.24/5.45 inference(monotonicity,[status(thm)],[32578])).
% 5.24/5.45 tff(32580,plain,
% 5.24/5.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 5.24/5.45 inference(transitivity,[status(thm)],[32579, 32577])).
% 5.24/5.45 tff(32581,plain,
% 5.24/5.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 5.24/5.45 inference(quant_inst,[status(thm)],[])).
% 5.24/5.45 tff(32582,plain,
% 5.24/5.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(z)))) | (~b(s(s(s(z))), s(s(z))))),
% 5.24/5.45 inference(modus_ponens,[status(thm)],[32581, 32580])).
% 5.24/5.45 tff(32583,plain,
% 5.24/5.45 (~b(s(s(z)), s(s(z)))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[32582, 178, 817, 31804])).
% 5.24/5.45 tff(32584,plain,
% 5.24/5.45 (~(elem!1 = s(s(z)))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[3238, 32583, 817])).
% 5.24/5.45 tff(32585,plain,
% 5.24/5.45 (~b(elem!1, s(s(z)))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[30868, 437, 817, 16062, 4970, 31804])).
% 5.24/5.45 tff(32586,plain,
% 5.24/5.45 ($false),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[467, 32585, 29536, 32584])).
% 5.24/5.45 tff(32587,plain,((~r(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~r(s(s(s(z))), z)) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 5.24/5.45 tff(32588,plain,
% 5.24/5.45 (~r(s(s(s(z))), z)),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[32587, 4970, 817, 437])).
% 5.24/5.45 tff(32589,plain,
% 5.24/5.45 (b(s(s(s(z))), z)),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[21073, 32588])).
% 5.24/5.45 tff(32590,plain,
% 5.24/5.45 (~b(z, s(s(s(z))))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[31515, 32589, 202, 107, 32319])).
% 5.24/5.45 tff(32591,plain,
% 5.24/5.45 (r(z, s(s(s(z))))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[4920, 32590])).
% 5.24/5.45 tff(32592,plain,
% 5.24/5.45 ($false),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[18033, 118, 521, 4952, 18022])).
% 5.24/5.45 tff(32593,plain,((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.45 tff(32594,plain,
% 5.24/5.45 (~r(s(s(s(z))), elem!1)),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[32593, 32591, 521])).
% 5.24/5.45 tff(32595,plain,
% 5.24/5.45 (b(s(s(s(z))), elem!1)),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[4981, 32594, 4970])).
% 5.24/5.45 tff(32596,plain,
% 5.24/5.45 (~r(s(s(s(z))), s(s(z)))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[24302, 32591, 29994])).
% 5.24/5.45 tff(32597,plain,
% 5.24/5.45 (b(s(s(s(z))), s(s(z)))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[4966, 32596])).
% 5.24/5.45 tff(32598,plain,
% 5.24/5.45 (b(elem!1, s(s(z)))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[467, 29536, 31605])).
% 5.24/5.45 tff(32599,plain,
% 5.24/5.45 ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[30865, 178, 817, 32598, 32597])).
% 5.24/5.45 tff(32600,plain,
% 5.24/5.45 (~b(s(s(z)), s(s(s(z))))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[32599, 32595])).
% 5.24/5.45 tff(32601,plain,
% 5.24/5.45 (r(s(s(z)), s(s(s(z))))),
% 5.24/5.45 inference(unit_resolution,[status(thm)],[5088, 32600])).
% 5.24/5.45 tff(32602,plain,
% 5.24/5.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~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))), s(s(z)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~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))), s(s(z)))) | (~b(s(s(s(z))), elem!1)))),
% 5.24/5.46 inference(rewrite,[status(thm)],[])).
% 5.24/5.46 tff(32603,plain,
% 5.24/5.46 (((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~b(elem!1, s(s(z)))) | (~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))), s(s(z)))) | (~b(s(s(s(z))), elem!1)))),
% 5.24/5.46 inference(rewrite,[status(thm)],[])).
% 5.24/5.46 tff(32604,plain,
% 5.24/5.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~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))), s(s(z)))) | (~b(s(s(s(z))), elem!1))))),
% 5.24/5.46 inference(monotonicity,[status(thm)],[32603])).
% 5.24/5.46 tff(32605,plain,
% 5.24/5.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~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))), s(s(z)))) | (~b(s(s(s(z))), elem!1)))),
% 5.24/5.46 inference(transitivity,[status(thm)],[32604, 32602])).
% 5.24/5.46 tff(32606,plain,
% 5.24/5.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 5.24/5.46 inference(quant_inst,[status(thm)],[])).
% 5.24/5.46 tff(32607,plain,
% 5.24/5.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1))),
% 5.24/5.46 inference(modus_ponens,[status(thm)],[32606, 32605])).
% 5.24/5.46 tff(32608,plain,
% 5.24/5.46 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[32607, 178, 32598, 32597, 3664])).
% 5.24/5.46 tff(32609,plain,
% 5.24/5.46 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[32608, 32595])).
% 5.24/5.46 tff(32610,plain,
% 5.24/5.46 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[31522, 32609])).
% 5.24/5.46 tff(32611,plain,
% 5.24/5.46 ($false),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[23362, 32610, 32601, 107])).
% 5.24/5.46 tff(32612,plain,((s(s(s(z))) = elem!1) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.46 tff(32613,plain,
% 5.24/5.46 (s(s(s(z))) = elem!1),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[32612, 32566, 107, 32551, 32576, 202, 32556])).
% 5.24/5.46 tff(32614,plain,
% 5.24/5.46 (s(s(s(s(z)))) = s(elem!1)),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[30856, 32613])).
% 5.24/5.46 tff(32615,plain,
% 5.24/5.46 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(z)) = s(elem!1))),
% 5.24/5.46 inference(monotonicity,[status(thm)],[32614])).
% 5.24/5.46 tff(32616,plain,
% 5.24/5.46 ((s(s(z)) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(z)))),
% 5.24/5.46 inference(transitivity,[status(thm)],[32615, 1358])).
% 5.24/5.46 tff(32617,plain,
% 5.24/5.46 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(z)) = s(elem!1))),
% 5.24/5.46 inference(transitivity,[status(thm)],[32616, 1359])).
% 5.24/5.46 tff(32618,plain,
% 5.24/5.46 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(z)) = s(elem!1)))),
% 5.24/5.46 inference(monotonicity,[status(thm)],[32617])).
% 5.24/5.46 tff(32619,plain,
% 5.24/5.46 (~(s(s(z)) = s(elem!1))),
% 5.24/5.46 inference(modus_ponens,[status(thm)],[159, 32618])).
% 5.24/5.46 tff(32620,plain,
% 5.24/5.46 (~(s(s(elem!1)) = s(s(z)))),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[2386, 32557])).
% 5.24/5.46 tff(32621,plain,
% 5.24/5.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 5.24/5.46 inference(rewrite,[status(thm)],[])).
% 5.24/5.46 tff(32622,plain,
% 5.24/5.46 (((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 5.24/5.46 inference(rewrite,[status(thm)],[])).
% 5.24/5.46 tff(32623,plain,
% 5.24/5.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 5.24/5.46 inference(monotonicity,[status(thm)],[32622])).
% 5.24/5.46 tff(32624,plain,
% 5.24/5.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 5.24/5.46 inference(transitivity,[status(thm)],[32623, 32621])).
% 5.24/5.46 tff(32625,plain,
% 5.24/5.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 5.24/5.46 inference(quant_inst,[status(thm)],[])).
% 5.24/5.46 tff(32626,plain,
% 5.24/5.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z))))),
% 5.24/5.46 inference(modus_ponens,[status(thm)],[32625, 32624])).
% 5.24/5.46 tff(32627,plain,
% 5.24/5.46 (~b(s(s(s(s(z)))), elem!1)),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[32626, 178, 32551, 32562, 167, 202])).
% 5.24/5.46 tff(32628,plain,
% 5.24/5.46 (r(s(s(s(s(z)))), elem!1)),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[3142, 32627, 31641])).
% 5.24/5.46 tff(32629,plain,
% 5.24/5.46 (~(elem!1 = s(s(s(elem!1))))),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[4830, 32613, 32620])).
% 5.24/5.46 tff(32630,plain,
% 5.24/5.46 (~(s(s(s(elem!1))) = elem!1)),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[2489, 32629])).
% 5.24/5.46 tff(32631,plain,
% 5.24/5.46 (~(s(elem!1) = elem!1)),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[2150, 32630])).
% 5.24/5.46 tff(32632,plain,
% 5.24/5.46 (s(elem!1) = s(s(s(s(z))))),
% 5.24/5.46 inference(symmetry,[status(thm)],[32614])).
% 5.24/5.46 tff(32633,plain,
% 5.24/5.46 (b(s(elem!1), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 5.24/5.46 inference(monotonicity,[status(thm)],[32632])).
% 5.24/5.46 tff(32634,plain,
% 5.24/5.46 (b(s(s(s(s(z)))), elem!1) <=> b(s(elem!1), elem!1)),
% 5.24/5.46 inference(symmetry,[status(thm)],[32633])).
% 5.24/5.46 tff(32635,plain,
% 5.24/5.46 ((~b(s(s(s(s(z)))), elem!1)) <=> (~b(s(elem!1), elem!1))),
% 5.24/5.46 inference(monotonicity,[status(thm)],[32634])).
% 5.24/5.46 tff(32636,plain,
% 5.24/5.46 (~b(s(elem!1), elem!1)),
% 5.24/5.46 inference(modus_ponens,[status(thm)],[32627, 32635])).
% 5.24/5.46 tff(32637,plain,
% 5.24/5.46 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 5.24/5.46 inference(monotonicity,[status(thm)],[32614])).
% 5.24/5.46 tff(32638,plain,
% 5.24/5.46 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 5.24/5.46 inference(symmetry,[status(thm)],[32637])).
% 5.24/5.46 tff(32639,plain,
% 5.24/5.46 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(s(s(elem!1))) = s(s(s(s(z))))))),
% 5.24/5.46 inference(monotonicity,[status(thm)],[32638])).
% 5.24/5.46 tff(32640,plain,
% 5.24/5.46 (s(elem!1) = s(s(s(s(z))))),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[2168, 32614])).
% 5.24/5.46 tff(32641,plain,
% 5.24/5.46 (~(s(s(s(elem!1))) = s(elem!1))),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[13886, 32640])).
% 5.24/5.46 tff(32642,plain,
% 5.24/5.46 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 5.24/5.46 inference(modus_ponens,[status(thm)],[32641, 32639])).
% 5.24/5.46 tff(32643,plain,
% 5.24/5.46 (~r(s(elem!1), s(s(s(s(z)))))),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[7010, 28745, 3132])).
% 5.24/5.46 tff(32644,plain,
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% 5.24/5.46 inference(unit_resolution,[status(thm)],[31823, 28748, 1060, 167])).
% 5.24/5.46 tff(32645,plain,
% 5.24/5.46 (s(elem!1) = s(s(s(s(z))))),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[1084, 32644, 32643])).
% 5.24/5.46 tff(32646,plain,
% 5.24/5.46 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 5.24/5.46 inference(monotonicity,[status(thm)],[32645])).
% 5.24/5.46 tff(32647,plain,
% 5.24/5.46 (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))),
% 5.24/5.46 inference(monotonicity,[status(thm)],[32646])).
% 5.24/5.46 tff(32648,plain,
% 5.24/5.46 (s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(z)))))))),
% 5.24/5.46 inference(monotonicity,[status(thm)],[32647])).
% 5.24/5.46 tff(32649,plain,
% 5.24/5.46 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.46 inference(monotonicity,[status(thm)],[32647, 32648])).
% 5.24/5.46 tff(32650,plain,
% 5.24/5.46 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 5.24/5.46 inference(symmetry,[status(thm)],[32649])).
% 5.24/5.46 tff(32651,plain,
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% 5.24/5.46 inference(monotonicity,[status(thm)],[32650])).
% 5.24/5.46 tff(32652,plain,
% 5.24/5.46 (r(s(s(s(s(z)))), s(s(s(z))))),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[7220, 32645, 3132])).
% 5.24/5.46 tff(32653,plain,
% 5.24/5.46 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[31525, 32652])).
% 5.24/5.46 tff(32654,plain,
% 5.24/5.46 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[31522, 32653])).
% 5.24/5.46 tff(32655,plain,
% 5.24/5.46 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 5.24/5.46 inference(monotonicity,[status(thm)],[32645])).
% 5.24/5.46 tff(32656,plain,
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% 5.24/5.46 inference(transitivity,[status(thm)],[517, 32655, 11])).
% 5.24/5.46 tff(32657,plain,
% 5.24/5.46 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.46 inference(monotonicity,[status(thm)],[32656])).
% 5.24/5.46 tff(32658,plain,
% 5.24/5.46 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.46 inference(modus_ponens,[status(thm)],[869, 32657])).
% 5.24/5.46 tff(32659,plain,
% 5.24/5.46 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 5.24/5.46 inference(monotonicity,[status(thm)],[32647, 32656])).
% 5.24/5.46 tff(32660,plain,
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% 5.24/5.46 inference(unit_resolution,[status(thm)],[2498, 32645, 2484])).
% 5.24/5.46 tff(32661,plain,
% 5.24/5.46 (~(s(s(s(elem!1))) = elem!1)),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[2489, 32660])).
% 5.24/5.46 tff(32662,plain,
% 5.24/5.46 (~(s(s(s(elem!1))) = s(elem!1))),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[13886, 32645])).
% 5.24/5.46 tff(32663,plain,
% 5.24/5.46 (~r(z, s(s(s(elem!1))))),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[30052, 32660, 29994, 437, 32598, 521, 817])).
% 5.24/5.46 tff(32664,plain,
% 5.24/5.46 (b(z, s(s(s(elem!1))))),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[2095, 32663])).
% 5.24/5.46 tff(32665,plain,
% 5.24/5.46 (r(s(s(s(elem!1))), elem!1)),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[570, 5308, 949])).
% 5.24/5.46 tff(32666,plain,
% 5.24/5.46 ($false),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[24899, 32665, 5308, 521, 2043, 356, 2141, 725])).
% 5.24/5.46 tff(32667,plain,(b(s(s(s(elem!1))), elem!1) | (~r(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1)) | b(s(elem!1), elem!1) | (s(elem!1) = elem!1) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 5.24/5.46 tff(32668,plain,
% 5.24/5.46 (b(s(s(s(elem!1))), elem!1)),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[32667, 32664, 521, 2141, 32662, 725, 32661])).
% 5.24/5.46 tff(32669,plain,
% 5.24/5.46 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 5.24/5.46 inference(modus_ponens,[status(thm)],[32668, 32659])).
% 5.24/5.46 tff(32670,plain,
% 5.24/5.46 (~r(elem!1, s(s(s(elem!1))))),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[23784, 32664, 27212, 31623, 2857, 437, 470])).
% 5.24/5.46 tff(32671,plain,
% 5.24/5.46 (b(elem!1, s(s(s(elem!1))))),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[2054, 32670, 32660])).
% 5.24/5.46 tff(32672,plain,
% 5.24/5.46 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[6974, 32671, 32645])).
% 5.24/5.46 tff(32673,plain,
% 5.24/5.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 5.24/5.46 inference(rewrite,[status(thm)],[])).
% 5.24/5.46 tff(32674,plain,
% 5.24/5.46 (((~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(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(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(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 5.24/5.46 inference(rewrite,[status(thm)],[])).
% 5.24/5.46 tff(32675,plain,
% 5.24/5.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 5.24/5.46 inference(monotonicity,[status(thm)],[32674])).
% 5.24/5.46 tff(32676,plain,
% 5.24/5.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 5.24/5.46 inference(transitivity,[status(thm)],[32675, 32673])).
% 5.24/5.46 tff(32677,plain,
% 5.24/5.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 5.24/5.46 inference(quant_inst,[status(thm)],[])).
% 5.24/5.46 tff(32678,plain,
% 5.24/5.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 5.24/5.46 inference(modus_ponens,[status(thm)],[32677, 32676])).
% 5.24/5.46 tff(32679,plain,
% 5.24/5.46 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[32678, 178, 32672, 32669, 32658, 32654])).
% 5.24/5.46 tff(32680,plain,
% 5.24/5.46 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 5.24/5.46 inference(modus_ponens,[status(thm)],[32679, 32651])).
% 5.24/5.46 tff(32681,plain,
% 5.24/5.46 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[1649, 32662])).
% 5.24/5.46 tff(32682,plain,
% 5.24/5.46 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[1657, 32681])).
% 5.24/5.46 tff(32683,plain,
% 5.24/5.46 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[1695, 32682])).
% 5.24/5.46 tff(32684,plain,
% 5.24/5.46 (r(s(s(z)), s(s(s(s(elem!1))))) <=> r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.46 inference(monotonicity,[status(thm)],[32648])).
% 5.24/5.46 tff(32685,plain,
% 5.24/5.46 (r(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(z)), s(s(s(s(elem!1)))))),
% 5.24/5.46 inference(symmetry,[status(thm)],[32684])).
% 5.24/5.46 tff(32686,plain,
% 5.24/5.46 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 5.24/5.46 inference(modus_ponens,[status(thm)],[224, 32685])).
% 5.24/5.46 tff(32687,plain,
% 5.24/5.46 (b(elem!1, s(s(z))) <=> b(s(s(s(z))), s(s(z)))),
% 5.24/5.46 inference(monotonicity,[status(thm)],[32656])).
% 5.24/5.46 tff(32688,plain,
% 5.24/5.46 (b(s(s(s(z))), s(s(z)))),
% 5.24/5.46 inference(modus_ponens,[status(thm)],[32598, 32687])).
% 5.24/5.46 tff(32689,plain,
% 5.24/5.46 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(z))))),
% 5.24/5.46 inference(monotonicity,[status(thm)],[32656])).
% 5.24/5.46 tff(32690,plain,
% 5.24/5.46 (b(s(s(z)), s(s(s(z))))),
% 5.24/5.46 inference(modus_ponens,[status(thm)],[817, 32689])).
% 5.24/5.46 tff(32691,plain,
% 5.24/5.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(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(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(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(z))), s(s(z)))))),
% 5.24/5.46 inference(rewrite,[status(thm)],[])).
% 5.24/5.46 tff(32692,plain,
% 5.24/5.46 (((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(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(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(z)))))),
% 5.24/5.46 inference(rewrite,[status(thm)],[])).
% 5.24/5.46 tff(32693,plain,
% 5.24/5.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(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(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(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(z))), s(s(z))))))),
% 5.24/5.46 inference(monotonicity,[status(thm)],[32692])).
% 5.24/5.46 tff(32694,plain,
% 5.24/5.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(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(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(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(z))), s(s(z)))))),
% 5.24/5.46 inference(transitivity,[status(thm)],[32693, 32691])).
% 5.24/5.46 tff(32695,plain,
% 5.24/5.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(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(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(z)))))),
% 5.24/5.46 inference(quant_inst,[status(thm)],[])).
% 5.24/5.46 tff(32696,plain,
% 5.24/5.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(z))))),
% 5.24/5.46 inference(modus_ponens,[status(thm)],[32695, 32694])).
% 5.24/5.46 tff(32697,plain,
% 5.24/5.46 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[32696, 178, 32672, 32690, 32688, 32669])).
% 5.24/5.46 tff(32698,plain,
% 5.24/5.46 (~b(s(s(z)), s(s(s(elem!1))))),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[7268, 32697, 32645])).
% 5.24/5.46 tff(32699,plain,
% 5.24/5.46 (r(s(s(z)), s(s(s(elem!1))))),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[4223, 32698])).
% 5.24/5.46 tff(32700,plain,
% 5.24/5.46 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[4036, 32699, 32686])).
% 5.24/5.46 tff(32701,plain,
% 5.24/5.46 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[1750, 32700, 32683])).
% 5.24/5.46 tff(32702,plain,
% 5.24/5.46 ($false),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[32701, 32680])).
% 5.24/5.46 tff(32703,plain,((s(elem!1) = elem!1) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), elem!1)) | (~r(z, elem!1)) | b(s(elem!1), elem!1) | (s(s(s(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)))), elem!1)) | (s(s(elem!1)) = s(s(z))) | (s(s(z)) = s(elem!1)) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.46 tff(32704,plain,
% 5.24/5.46 ($false),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[32703, 32642, 32636, 32568, 32551, 32576, 287, 32631, 32556, 32564, 32628, 32620, 32619, 167])).
% 5.24/5.46 tff(32705,plain,(b(elem!1, z) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.46 tff(32706,plain,
% 5.24/5.46 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[32705, 5723, 107, 202, 167, 204])).
% 5.24/5.46 tff(32707,plain,
% 5.24/5.46 (elem!1 = z),
% 5.24/5.46 inference(unit_resolution,[status(thm)],[498, 1342, 5723])).
% 5.24/5.46 tff(32708,plain,
% 5.24/5.46 (s(elem!1) = s(z)),
% 5.24/5.46 inference(monotonicity,[status(thm)],[32707])).
% 5.24/5.46 tff(32709,plain,
% 5.24/5.46 (s(s(elem!1)) = s(s(z))),
% 5.24/5.46 inference(monotonicity,[status(thm)],[32708])).
% 5.24/5.46 tff(32710,plain,
% 5.24/5.46 (s(s(s(elem!1))) = s(s(s(z)))),
% 5.24/5.46 inference(monotonicity,[status(thm)],[32709])).
% 5.24/5.46 tff(32711,plain,
% 5.24/5.46 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 5.24/5.46 inference(monotonicity,[status(thm)],[32710])).
% 5.24/5.46 tff(32712,plain,
% 5.24/5.46 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 5.24/5.46 inference(monotonicity,[status(thm)],[32710, 32711])).
% 5.24/5.46 tff(32713,plain,
% 5.24/5.46 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 5.24/5.46 inference(monotonicity,[status(thm)],[32711, 32710])).
% 5.24/5.46 tff(32714,plain,
% 5.24/5.46 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 5.24/5.46 inference(symmetry,[status(thm)],[32713])).
% 5.24/5.46 tff(32715,plain,
% 5.24/5.46 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 5.24/5.46 inference(transitivity,[status(thm)],[32714, 24467])).
% 5.24/5.46 tff(32716,plain,
% 5.24/5.46 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))),
% 5.24/5.46 inference(monotonicity,[status(thm)],[32715])).
% 5.24/5.46 tff(32717,plain,
% 5.24/5.46 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 5.24/5.46 inference(modus_ponens,[status(thm)],[4938, 32716])).
% 5.24/5.46 tff(32718,plain,
% 5.24/5.46 (b(elem!1, s(s(s(s(elem!1))))) <=> b(z, s(s(s(s(elem!1)))))),
% 5.24/5.46 inference(monotonicity,[status(thm)],[32707])).
% 5.24/5.46 tff(32719,plain,
% 5.24/5.46 (b(z, s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 5.24/5.46 inference(symmetry,[status(thm)],[32718])).
% 5.24/5.46 tff(32720,plain,
% 5.24/5.46 (b(z, s(s(s(s(elem!1))))) <=> b(z, s(s(s(s(z)))))),
% 5.24/5.46 inference(monotonicity,[status(thm)],[32711])).
% 5.24/5.46 tff(32721,plain,
% 5.24/5.46 (b(z, s(s(s(s(z))))) <=> b(z, s(s(s(s(elem!1)))))),
% 5.24/5.46 inference(symmetry,[status(thm)],[32720])).
% 5.24/5.46 tff(32722,plain,
% 5.24/5.46 (b(z, s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 5.24/5.46 inference(transitivity,[status(thm)],[32721, 32719])).
% 5.24/5.46 tff(32723,plain,
% 5.24/5.46 (b(elem!1, s(s(s(s(elem!1)))))),
% 5.24/5.46 inference(modus_ponens,[status(thm)],[27212, 32722])).
% 5.24/5.46 tff(32724,plain,
% 5.24/5.46 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(elem!1)))), s(s(z)))),
% 5.24/5.46 inference(monotonicity,[status(thm)],[32709])).
% 5.24/5.46 tff(32725,plain,
% 5.24/5.46 (b(s(s(s(s(elem!1)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 5.24/5.46 inference(symmetry,[status(thm)],[32724])).
% 5.24/5.46 tff(32726,plain,
% 5.24/5.46 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 5.24/5.46 inference(symmetry,[status(thm)],[32711])).
% 5.24/5.46 tff(32727,plain,
% 5.24/5.46 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(z)))),
% 5.24/5.46 inference(monotonicity,[status(thm)],[32726])).
% 5.24/5.46 tff(32728,plain,
% 5.24/5.46 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 5.24/5.46 inference(transitivity,[status(thm)],[32727, 32725])).
% 5.24/5.46 tff(32729,plain,
% 5.24/5.46 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 5.24/5.46 inference(modus_ponens,[status(thm)],[202, 32728])).
% 5.24/5.46 tff(32730,plain,
% 5.24/5.46 (r(elem!1, s(s(elem!1))) <=> r(z, s(s(elem!1)))),
% 5.24/5.46 inference(monotonicity,[status(thm)],[32707])).
% 5.24/5.46 tff(32731,plain,
% 5.24/5.46 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 5.24/5.46 inference(symmetry,[status(thm)],[32730])).
% 5.24/5.46 tff(32732,plain,
% 5.24/5.46 (r(z, s(s(elem!1))) <=> r(z, s(s(z)))),
% 5.24/5.46 inference(monotonicity,[status(thm)],[32709])).
% 5.24/5.46 tff(32733,plain,
% 5.24/5.47 (r(z, s(s(z))) <=> r(z, s(s(elem!1)))),
% 5.24/5.47 inference(symmetry,[status(thm)],[32732])).
% 5.24/5.47 tff(32734,plain,
% 5.24/5.47 (r(z, s(s(z))) <=> r(elem!1, s(s(elem!1)))),
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% 5.24/5.47 tff(32735,plain,
% 5.24/5.47 (r(elem!1, s(s(elem!1)))),
% 5.24/5.47 inference(modus_ponens,[status(thm)],[29994, 32734])).
% 5.24/5.47 tff(32736,plain,
% 5.24/5.47 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(s(elem!1))))),
% 5.24/5.47 inference(monotonicity,[status(thm)],[32709])).
% 5.24/5.47 tff(32737,plain,
% 5.24/5.47 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 5.24/5.47 inference(symmetry,[status(thm)],[32736])).
% 5.24/5.47 tff(32738,plain,
% 5.24/5.47 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 5.24/5.47 inference(monotonicity,[status(thm)],[32737])).
% 5.24/5.47 tff(32739,plain,
% 5.24/5.47 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 5.24/5.47 inference(modus_ponens,[status(thm)],[1683, 32738])).
% 5.24/5.47 tff(32740,plain,
% 5.24/5.47 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = z)),
% 5.24/5.47 inference(monotonicity,[status(thm)],[32707])).
% 5.24/5.47 tff(32741,plain,
% 5.24/5.47 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 5.24/5.47 inference(symmetry,[status(thm)],[32740])).
% 5.24/5.47 tff(32742,plain,
% 5.24/5.47 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
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% 5.24/5.47 tff(32743,plain,
% 5.24/5.47 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 5.24/5.47 inference(monotonicity,[status(thm)],[32742])).
% 5.24/5.47 tff(32744,plain,
% 5.24/5.47 (~(elem!1 = s(s(s(elem!1))))),
% 5.24/5.47 inference(modus_ponens,[status(thm)],[940, 32743])).
% 5.24/5.47 tff(32745,plain,
% 5.24/5.47 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 5.24/5.47 inference(monotonicity,[status(thm)],[32709])).
% 5.24/5.47 tff(32746,plain,
% 5.24/5.47 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
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% 5.24/5.47 tff(32747,plain,
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% 5.24/5.47 tff(32748,plain,
% 5.24/5.47 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 5.24/5.47 inference(monotonicity,[status(thm)],[32747])).
% 5.24/5.47 tff(32749,plain,
% 5.24/5.47 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 5.24/5.47 inference(transitivity,[status(thm)],[32748, 32746])).
% 5.24/5.47 tff(32750,plain,
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% 5.24/5.47 inference(modus_ponens,[status(thm)],[4932, 32749])).
% 5.24/5.47 tff(32751,plain,
% 5.24/5.47 (b(s(s(elem!1)), s(s(s(s(elem!1))))) <=> b(s(s(z)), s(s(s(s(elem!1)))))),
% 5.24/5.47 inference(monotonicity,[status(thm)],[32709])).
% 5.24/5.47 tff(32752,plain,
% 5.24/5.47 (b(s(s(z)), s(s(s(s(elem!1))))) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 5.24/5.47 inference(symmetry,[status(thm)],[32751])).
% 5.24/5.47 tff(32753,plain,
% 5.24/5.47 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(s(elem!1)))))),
% 5.24/5.47 inference(monotonicity,[status(thm)],[32726])).
% 5.24/5.47 tff(32754,plain,
% 5.24/5.47 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
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% 5.24/5.47 inference(modus_ponens,[status(thm)],[167, 32754])).
% 5.24/5.47 tff(32756,plain,
% 5.24/5.47 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[5847, 32755, 32750, 32744, 32739, 32735, 32729, 32723])).
% 5.24/5.47 tff(32757,plain,
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% 5.24/5.47 inference(unit_resolution,[status(thm)],[1750, 32756, 32717])).
% 5.24/5.47 tff(32758,plain,
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% 5.24/5.47 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
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% 5.24/5.47 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
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% 5.24/5.47 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[27236, 118, 24592, 32758])).
% 5.24/5.47 tff(32762,plain,
% 5.24/5.47 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[20667, 32761])).
% 5.24/5.47 tff(32763,plain,
% 5.24/5.47 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 5.24/5.47 inference(monotonicity,[status(thm)],[32747])).
% 5.24/5.47 tff(32764,plain,
% 5.24/5.47 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(z))))),
% 5.24/5.47 inference(symmetry,[status(thm)],[32763])).
% 5.24/5.47 tff(32765,plain,
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% 5.24/5.47 inference(unit_resolution,[status(thm)],[1345, 1342, 28500])).
% 5.24/5.47 tff(32766,plain,
% 5.24/5.47 (r(s(s(z)), elem!1)),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[448, 32765, 3241])).
% 5.24/5.47 tff(32767,plain,
% 5.24/5.47 (r(elem!1, s(s(s(elem!1)))) <=> r(z, s(s(s(elem!1))))),
% 5.24/5.47 inference(monotonicity,[status(thm)],[32707])).
% 5.24/5.47 tff(32768,plain,
% 5.24/5.47 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 5.24/5.47 inference(symmetry,[status(thm)],[32767])).
% 5.24/5.47 tff(32769,plain,
% 5.24/5.47 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(z))))),
% 5.24/5.47 inference(monotonicity,[status(thm)],[32710])).
% 5.24/5.47 tff(32770,plain,
% 5.24/5.47 (r(z, s(s(s(z)))) <=> r(z, s(s(s(elem!1))))),
% 5.24/5.47 inference(symmetry,[status(thm)],[32769])).
% 5.24/5.47 tff(32771,plain,
% 5.24/5.47 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 5.24/5.47 inference(transitivity,[status(thm)],[32770, 32768])).
% 5.24/5.47 tff(32772,plain,
% 5.24/5.47 (~b(z, s(s(s(z))))),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[24674, 178, 595, 146, 32762, 32760])).
% 5.24/5.47 tff(32773,plain,
% 5.24/5.47 (r(z, s(s(s(z))))),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[4920, 32772])).
% 5.24/5.47 tff(32774,plain,
% 5.24/5.47 (r(elem!1, s(s(s(elem!1))))),
% 5.24/5.47 inference(modus_ponens,[status(thm)],[32773, 32771])).
% 5.24/5.47 tff(32775,plain,
% 5.24/5.47 (~r(s(s(z)), s(s(s(elem!1))))),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[7973, 32774, 32766])).
% 5.24/5.47 tff(32776,plain,
% 5.24/5.47 (b(s(s(z)), s(s(s(elem!1))))),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[4223, 32775])).
% 5.24/5.47 tff(32777,plain,
% 5.24/5.47 (b(s(s(z)), s(s(s(z))))),
% 5.24/5.47 inference(modus_ponens,[status(thm)],[32776, 32764])).
% 5.24/5.47 tff(32778,plain,
% 5.24/5.47 ($false),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[22557, 178, 166, 32777, 4932, 32762, 32760])).
% 5.24/5.47 tff(32779,plain,(r(elem!1, z) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | b(s(s(z)), elem!1) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 5.24/5.47 tff(32780,plain,
% 5.24/5.47 ($false),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[32779, 32706, 5723, 32325, 31505, 32319, 202, 167, 3241, 32415])).
% 5.24/5.47 tff(32781,plain,(b(elem!1, z) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | b(s(s(z)), elem!1) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.47 tff(32782,plain,
% 5.24/5.47 (b(elem!1, z)),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[32781, 3241, 167, 202, 15765, 204])).
% 5.24/5.47 tff(32783,plain,
% 5.24/5.47 (~r(z, elem!1)),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[8412, 32409, 29994])).
% 5.24/5.47 tff(32784,plain,
% 5.24/5.47 (~(z = elem!1)),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[6991, 32782])).
% 5.24/5.47 tff(32785,plain,
% 5.24/5.47 (b(z, elem!1)),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[585, 32784, 32783])).
% 5.24/5.47 tff(32786,plain,
% 5.24/5.47 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[3455, 178, 32785, 32782, 32414, 32412])).
% 5.24/5.47 tff(32787,plain,
% 5.24/5.47 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[3444, 32786, 32410])).
% 5.24/5.47 tff(32788,plain,
% 5.24/5.47 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(z)), elem!1)),
% 5.24/5.47 inference(monotonicity,[status(thm)],[32787])).
% 5.24/5.47 tff(32789,plain,
% 5.24/5.47 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.47 inference(symmetry,[status(thm)],[32788])).
% 5.24/5.47 tff(32790,plain,
% 5.24/5.47 ((~b(s(s(z)), elem!1)) <=> (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.47 inference(monotonicity,[status(thm)],[32789])).
% 5.24/5.47 tff(32791,plain,
% 5.24/5.47 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.47 inference(modus_ponens,[status(thm)],[3241, 32790])).
% 5.24/5.47 tff(32792,plain,
% 5.24/5.47 (~(elem!1 = s(s(z)))),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[23817, 506, 32417])).
% 5.24/5.47 tff(32793,plain,
% 5.24/5.47 (~(s(s(z)) = elem!1)),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[3230, 32792])).
% 5.24/5.47 tff(32794,plain,
% 5.24/5.47 (r(s(s(z)), elem!1)),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[448, 3241, 32793])).
% 5.24/5.47 tff(32795,plain,
% 5.24/5.47 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[17566, 32794, 15765])).
% 5.24/5.47 tff(32796,plain,
% 5.24/5.47 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[25652, 32144, 202, 167, 224, 204, 32793])).
% 5.24/5.47 tff(32797,plain,
% 5.24/5.47 (~r(z, elem!1)),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[8412, 32794, 29994])).
% 5.24/5.47 tff(32798,plain,
% 5.24/5.47 (b(z, elem!1)),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[585, 32797, 6992])).
% 5.24/5.47 tff(32799,plain,
% 5.24/5.47 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[18193, 32798, 506, 32414, 32796, 32795])).
% 5.24/5.47 tff(32800,plain,
% 5.24/5.47 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 5.24/5.47 inference(monotonicity,[status(thm)],[32799])).
% 5.24/5.47 tff(32801,plain,
% 5.24/5.47 (s(s(s(s(s(s(s(s(z)))))))) = s(elem!1)),
% 5.24/5.47 inference(symmetry,[status(thm)],[32800])).
% 5.24/5.47 tff(32802,plain,
% 5.24/5.47 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 5.24/5.47 inference(monotonicity,[status(thm)],[32801])).
% 5.24/5.47 tff(32803,plain,
% 5.24/5.47 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 5.24/5.47 inference(transitivity,[status(thm)],[32802, 377])).
% 5.24/5.47 tff(32804,plain,
% 5.24/5.47 ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.47 inference(symmetry,[status(thm)],[32803])).
% 5.24/5.47 tff(32805,plain,
% 5.24/5.47 ((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z))))))))))),
% 5.24/5.47 inference(monotonicity,[status(thm)],[32804])).
% 5.24/5.47 tff(32806,plain,
% 5.24/5.47 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 5.24/5.47 inference(monotonicity,[status(thm)],[32799])).
% 5.24/5.47 tff(32807,plain,
% 5.24/5.47 ((~(s(elem!1) = elem!1)) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.47 inference(monotonicity,[status(thm)],[32806])).
% 5.24/5.47 tff(32808,plain,
% 5.24/5.47 (~(s(elem!1) = s(s(s(s(z)))))),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[16181, 32799])).
% 5.24/5.47 tff(32809,plain,
% 5.24/5.47 (~(s(s(s(s(z)))) = s(elem!1))),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[2168, 32808])).
% 5.24/5.47 tff(32810,plain,
% 5.24/5.47 (~(s(s(elem!1)) = elem!1)),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[2510, 32809, 32799])).
% 5.24/5.47 tff(32811,plain,
% 5.24/5.47 (~(s(elem!1) = elem!1)),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[672, 32810])).
% 5.24/5.47 tff(32812,plain,
% 5.24/5.47 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 5.24/5.47 inference(modus_ponens,[status(thm)],[32811, 32807])).
% 5.24/5.47 tff(32813,plain,
% 5.24/5.47 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.47 inference(modus_ponens,[status(thm)],[32812, 32805])).
% 5.24/5.47 tff(32814,plain,
% 5.24/5.47 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))) <=> r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 5.24/5.47 inference(monotonicity,[status(thm)],[32801])).
% 5.24/5.47 tff(32815,plain,
% 5.24/5.47 (r(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.47 inference(symmetry,[status(thm)],[32814])).
% 5.24/5.47 tff(32816,plain,
% 5.24/5.47 (r(elem!1, s(elem!1)) <=> r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 5.24/5.47 inference(monotonicity,[status(thm)],[32799])).
% 5.24/5.47 tff(32817,plain,
% 5.24/5.47 (r(elem!1, s(elem!1)) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.47 inference(transitivity,[status(thm)],[32816, 32815])).
% 5.24/5.47 tff(32818,plain,
% 5.24/5.47 ((~r(elem!1, s(elem!1))) <=> (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))),
% 5.24/5.47 inference(monotonicity,[status(thm)],[32817])).
% 5.24/5.47 tff(32819,plain,
% 5.24/5.47 (~(elem!1 = s(s(s(s(z)))))),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[325, 32144])).
% 5.24/5.47 tff(32820,plain,
% 5.24/5.47 ((~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z))))))),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[12519, 178, 506, 27212, 31623])).
% 5.24/5.47 tff(32821,plain,
% 5.24/5.47 (~b(elem!1, s(s(s(s(z)))))),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[32820, 32798])).
% 5.24/5.47 tff(32822,plain,
% 5.24/5.47 (r(elem!1, s(s(s(s(z)))))),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[483, 32821, 32819])).
% 5.24/5.47 tff(32823,plain,
% 5.24/5.47 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 5.24/5.47 inference(monotonicity,[status(thm)],[32800])).
% 5.24/5.47 tff(32824,plain,
% 5.24/5.47 (~(s(elem!1) = s(s(z)))),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[2832, 32799])).
% 5.24/5.47 tff(32825,plain,
% 5.24/5.47 (~b(elem!1, s(s(z)))),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[25284, 32799, 3576])).
% 5.24/5.47 tff(32826,plain,
% 5.24/5.47 (r(elem!1, s(s(z)))),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[467, 32825, 32792])).
% 5.24/5.47 tff(32827,plain,
% 5.24/5.47 (~r(s(elem!1), s(s(z)))),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[17418, 32811, 28500, 506, 32798, 32826])).
% 5.24/5.47 tff(32828,plain,
% 5.24/5.47 (b(s(elem!1), s(s(z)))),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[421, 32827, 32824])).
% 5.24/5.47 tff(32829,plain,
% 5.24/5.47 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 5.24/5.47 inference(modus_ponens,[status(thm)],[32828, 32823])).
% 5.24/5.47 tff(32830,plain,
% 5.24/5.47 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 5.24/5.47 inference(modus_ponens,[status(thm)],[1069, 26257])).
% 5.24/5.47 tff(32831,plain,
% 5.24/5.47 (~r(z, s(elem!1))),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[25755, 1069, 29994, 167, 202, 10483, 28500])).
% 5.24/5.47 tff(32832,plain,
% 5.24/5.47 (b(z, s(elem!1))),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[2351, 32831])).
% 5.24/5.47 tff(32833,plain,
% 5.24/5.47 (b(z, s(s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.47 inference(modus_ponens,[status(thm)],[32832, 16109])).
% 5.24/5.47 tff(32834,plain,
% 5.24/5.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 5.24/5.47 inference(rewrite,[status(thm)],[])).
% 5.24/5.47 tff(32835,plain,
% 5.24/5.47 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(s(z))))))))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 5.24/5.47 inference(rewrite,[status(thm)],[])).
% 5.24/5.47 tff(32836,plain,
% 5.24/5.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))))),
% 5.24/5.47 inference(monotonicity,[status(thm)],[32835])).
% 5.24/5.47 tff(32837,plain,
% 5.24/5.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 5.24/5.47 inference(transitivity,[status(thm)],[32836, 32834])).
% 5.24/5.47 tff(32838,plain,
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% 5.24/5.47 inference(quant_inst,[status(thm)],[])).
% 5.24/5.47 tff(32839,plain,
% 5.24/5.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))),
% 5.24/5.47 inference(modus_ponens,[status(thm)],[32838, 32837])).
% 5.24/5.47 tff(32840,plain,
% 5.24/5.47 ((~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[32839, 178, 27212, 202, 16124])).
% 5.24/5.47 tff(32841,plain,
% 5.24/5.47 ($false),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[32840, 32833, 32830])).
% 5.24/5.47 tff(32842,plain,((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.47 tff(32843,plain,
% 5.24/5.47 (~b(s(elem!1), s(s(s(s(z)))))),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[32842, 32829, 202, 32799, 167])).
% 5.24/5.47 tff(32844,plain,
% 5.24/5.47 (r(s(elem!1), s(s(s(s(z)))))),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[1084, 32843, 32808])).
% 5.24/5.47 tff(32845,plain,
% 5.24/5.47 (~r(elem!1, s(elem!1))),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[14364, 32844, 32822])).
% 5.24/5.47 tff(32846,plain,
% 5.24/5.47 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.47 inference(modus_ponens,[status(thm)],[32845, 32818])).
% 5.24/5.47 tff(32847,plain,
% 5.24/5.47 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[16349, 41, 32846])).
% 5.24/5.47 tff(32848,plain,
% 5.24/5.47 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[32847, 32813])).
% 5.24/5.47 tff(32849,plain,
% 5.24/5.47 (~(s(elem!1) = s(s(s(z))))),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[23436, 32793])).
% 5.24/5.47 tff(32850,plain,
% 5.24/5.47 (~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z))))),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[24777, 32799, 32849])).
% 5.24/5.47 tff(32851,plain,
% 5.24/5.47 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z))))))))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 5.24/5.47 inference(monotonicity,[status(thm)],[32801])).
% 5.24/5.47 tff(32852,plain,
% 5.24/5.47 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) <=> (~b(s(s(s(s(z)))), s(elem!1)))),
% 5.24/5.47 inference(monotonicity,[status(thm)],[32851])).
% 5.24/5.47 tff(32853,plain,
% 5.24/5.47 ((s(s(z)) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(s(z)) = s(elem!1))),
% 5.24/5.47 inference(monotonicity,[status(thm)],[32801])).
% 5.24/5.47 tff(32854,plain,
% 5.24/5.47 ((s(s(z)) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(elem!1) = s(s(z)))),
% 5.24/5.47 inference(transitivity,[status(thm)],[32853, 1358])).
% 5.24/5.47 tff(32855,plain,
% 5.24/5.47 ((s(elem!1) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.47 inference(symmetry,[status(thm)],[32854])).
% 5.24/5.47 tff(32856,plain,
% 5.24/5.47 ((~(s(elem!1) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(s(s(s(s(z))))))))))),
% 5.24/5.47 inference(monotonicity,[status(thm)],[32855])).
% 5.24/5.47 tff(32857,plain,
% 5.24/5.47 (~(s(s(z)) = s(s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.47 inference(modus_ponens,[status(thm)],[32824, 32856])).
% 5.24/5.47 tff(32858,plain,
% 5.24/5.47 (b(s(s(s(s(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))))))))),
% 5.24/5.47 inference(monotonicity,[status(thm)],[32801])).
% 5.24/5.47 tff(32859,plain,
% 5.24/5.47 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.47 inference(symmetry,[status(thm)],[32858])).
% 5.24/5.47 tff(32860,plain,
% 5.24/5.47 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[25119, 32844])).
% 5.24/5.47 tff(32861,plain,
% 5.24/5.47 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[395, 32860, 32812])).
% 5.24/5.47 tff(32862,plain,
% 5.24/5.47 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.47 inference(modus_ponens,[status(thm)],[32861, 32859])).
% 5.24/5.47 tff(32863,plain,
% 5.24/5.47 ((~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[22853, 178, 32414, 32412, 32862])).
% 5.24/5.47 tff(32864,plain,
% 5.24/5.47 (~b(s(s(s(s(s(s(s(s(z)))))))), z)),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[32863, 32848])).
% 5.24/5.47 tff(32865,plain,
% 5.24/5.47 (r(s(s(s(s(s(s(s(s(z)))))))), z)),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[16121, 41, 16118, 32864])).
% 5.24/5.47 tff(32866,plain,
% 5.24/5.47 (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[31119, 118, 28500, 32865])).
% 5.24/5.47 tff(32867,plain,
% 5.24/5.47 ((s(s(z)) = s(s(s(s(s(s(s(s(z))))))))) | b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[26990, 41, 32866])).
% 5.24/5.47 tff(32868,plain,
% 5.24/5.47 (b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.47 inference(unit_resolution,[status(thm)],[32867, 32857])).
% 5.24/5.47 tff(32869,plain,
% 5.24/5.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))),
% 5.24/5.47 inference(rewrite,[status(thm)],[])).
% 5.24/5.47 tff(32870,plain,
% 5.24/5.47 (((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))),
% 5.24/5.47 inference(rewrite,[status(thm)],[])).
% 5.24/5.47 tff(32871,plain,
% 5.24/5.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z))))))))))))),
% 5.24/5.47 inference(monotonicity,[status(thm)],[32870])).
% 5.24/5.47 tff(32872,plain,
% 5.24/5.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))),
% 5.24/5.47 inference(transitivity,[status(thm)],[32871, 32869])).
% 5.24/5.47 tff(32873,plain,
% 5.24/5.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 5.24/5.48 inference(quant_inst,[status(thm)],[])).
% 5.24/5.48 tff(32874,plain,
% 5.24/5.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z))))))))))),
% 5.24/5.48 inference(modus_ponens,[status(thm)],[32873, 32872])).
% 5.24/5.48 tff(32875,plain,
% 5.24/5.48 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[32874, 178, 167, 202, 32829, 32868])).
% 5.24/5.48 tff(32876,plain,
% 5.24/5.48 (~b(s(s(s(s(z)))), s(elem!1))),
% 5.24/5.48 inference(modus_ponens,[status(thm)],[32875, 32852])).
% 5.24/5.48 tff(32877,plain,
% 5.24/5.48 (r(s(s(s(s(z)))), s(elem!1))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[2173, 32876, 32809])).
% 5.24/5.48 tff(32878,plain,
% 5.24/5.48 ((s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z))))),
% 5.24/5.48 inference(commutativity,[status(thm)],[])).
% 5.24/5.48 tff(32879,plain,
% 5.24/5.48 ((s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.48 inference(symmetry,[status(thm)],[32878])).
% 5.24/5.48 tff(32880,plain,
% 5.24/5.48 ((~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))))),
% 5.24/5.48 inference(monotonicity,[status(thm)],[32879])).
% 5.24/5.48 tff(32881,plain,
% 5.24/5.48 (~(s(s(s(z))) = s(s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.48 inference(modus_ponens,[status(thm)],[24825, 32880])).
% 5.24/5.48 tff(32882,plain,
% 5.24/5.48 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[31809, 16062, 167])).
% 5.24/5.48 tff(32883,plain,
% 5.24/5.48 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[31522, 32882])).
% 5.24/5.48 tff(32884,plain,
% 5.24/5.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 5.24/5.48 inference(rewrite,[status(thm)],[])).
% 5.24/5.48 tff(32885,plain,
% 5.24/5.48 (((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(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(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(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(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 5.24/5.48 inference(rewrite,[status(thm)],[])).
% 5.24/5.48 tff(32886,plain,
% 5.24/5.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(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(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))))),
% 5.24/5.48 inference(monotonicity,[status(thm)],[32885])).
% 5.24/5.48 tff(32887,plain,
% 5.24/5.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(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(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 5.24/5.48 inference(transitivity,[status(thm)],[32886, 32884])).
% 5.24/5.48 tff(32888,plain,
% 5.24/5.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(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(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 5.24/5.48 inference(quant_inst,[status(thm)],[])).
% 5.24/5.48 tff(32889,plain,
% 5.24/5.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))),
% 5.24/5.48 inference(modus_ponens,[status(thm)],[32888, 32887])).
% 5.24/5.48 tff(32890,plain,
% 5.24/5.48 (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[32889, 178, 31804, 16124, 32883, 27597])).
% 5.24/5.48 tff(32891,plain,
% 5.24/5.48 ((s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[23524, 41, 32890])).
% 5.24/5.48 tff(32892,plain,
% 5.24/5.48 (r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[32891, 32881])).
% 5.24/5.48 tff(32893,plain,
% 5.24/5.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 5.24/5.48 inference(rewrite,[status(thm)],[])).
% 5.24/5.48 tff(32894,plain,
% 5.24/5.48 (((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 5.24/5.48 inference(rewrite,[status(thm)],[])).
% 5.24/5.48 tff(32895,plain,
% 5.24/5.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))))),
% 5.24/5.48 inference(monotonicity,[status(thm)],[32894])).
% 5.24/5.48 tff(32896,plain,
% 5.24/5.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 5.24/5.48 inference(transitivity,[status(thm)],[32895, 32893])).
% 5.24/5.48 tff(32897,plain,
% 5.24/5.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 5.24/5.48 inference(quant_inst,[status(thm)],[])).
% 5.24/5.48 tff(32898,plain,
% 5.24/5.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))),
% 5.24/5.48 inference(modus_ponens,[status(thm)],[32897, 32896])).
% 5.24/5.48 tff(32899,plain,
% 5.24/5.48 ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z))))))))))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[32898, 118, 32892])).
% 5.24/5.48 tff(32900,plain,
% 5.24/5.48 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[32899, 16331])).
% 5.24/5.48 tff(32901,plain,
% 5.24/5.48 (b(s(s(s(z))), s(s(s(s(z)))))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[10755, 32900])).
% 5.24/5.48 tff(32902,plain,
% 5.24/5.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 5.24/5.48 inference(rewrite,[status(thm)],[])).
% 5.24/5.48 tff(32903,plain,
% 5.24/5.48 (((~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 5.24/5.48 inference(rewrite,[status(thm)],[])).
% 5.24/5.48 tff(32904,plain,
% 5.24/5.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))))),
% 5.24/5.48 inference(monotonicity,[status(thm)],[32903])).
% 5.24/5.48 tff(32905,plain,
% 5.24/5.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 5.24/5.48 inference(transitivity,[status(thm)],[32904, 32902])).
% 5.24/5.48 tff(32906,plain,
% 5.24/5.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 5.24/5.48 inference(quant_inst,[status(thm)],[])).
% 5.24/5.48 tff(32907,plain,
% 5.24/5.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))),
% 5.24/5.48 inference(modus_ponens,[status(thm)],[32906, 32905])).
% 5.24/5.48 tff(32908,plain,
% 5.24/5.48 ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z))))))))))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[32907, 118, 32892])).
% 5.24/5.48 tff(32909,plain,
% 5.24/5.48 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[32908, 16331])).
% 5.24/5.48 tff(32910,plain,
% 5.24/5.48 (b(s(s(s(s(z)))), s(s(s(z))))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[11185, 32909])).
% 5.24/5.48 tff(32911,plain,
% 5.24/5.48 ($false),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[24614, 32910, 32901, 167, 16062, 28500, 31804])).
% 5.24/5.48 tff(32912,plain,((~r(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.48 tff(32913,plain,
% 5.24/5.48 (~r(s(s(s(z))), z)),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[32912, 32877, 167, 32799, 32850, 32829, 32848])).
% 5.24/5.48 tff(32914,plain,
% 5.24/5.48 (b(s(s(s(z))), z)),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[21073, 32913])).
% 5.24/5.48 tff(32915,plain,
% 5.24/5.48 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[31073, 32914, 31623, 506, 32799])).
% 5.24/5.48 tff(32916,plain,
% 5.24/5.48 (r(s(s(s(z))), s(s(s(s(z)))))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[10755, 32915])).
% 5.24/5.48 tff(32917,plain,
% 5.24/5.48 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[3043, 118, 24592, 32916])).
% 5.24/5.48 tff(32918,plain,
% 5.24/5.48 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[31522, 32917])).
% 5.24/5.48 tff(32919,plain,
% 5.24/5.48 (~b(z, s(s(s(z))))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[31515, 32914, 202, 15765, 32412])).
% 5.24/5.48 tff(32920,plain,
% 5.24/5.48 (r(z, s(s(s(z))))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[4920, 32919])).
% 5.24/5.48 tff(32921,plain,
% 5.24/5.48 (~r(s(s(s(z))), s(s(z)))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[24302, 32920, 29994])).
% 5.24/5.48 tff(32922,plain,
% 5.24/5.48 (b(s(s(s(z))), s(s(z)))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[4966, 32921])).
% 5.24/5.48 tff(32923,plain,
% 5.24/5.48 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[32889, 178, 32922, 32829, 32848])).
% 5.24/5.48 tff(32924,plain,
% 5.24/5.48 (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[32923, 32918])).
% 5.24/5.48 tff(32925,plain,
% 5.24/5.48 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 5.24/5.48 inference(monotonicity,[status(thm)],[32801])).
% 5.24/5.48 tff(32926,plain,
% 5.24/5.48 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 5.24/5.48 inference(symmetry,[status(thm)],[32925])).
% 5.24/5.48 tff(32927,plain,
% 5.24/5.48 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 5.24/5.48 inference(modus_ponens,[status(thm)],[32844, 32926])).
% 5.24/5.48 tff(32928,plain,
% 5.24/5.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 5.24/5.48 inference(rewrite,[status(thm)],[])).
% 5.24/5.48 tff(32929,plain,
% 5.24/5.48 (((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 5.24/5.48 inference(rewrite,[status(thm)],[])).
% 5.24/5.48 tff(32930,plain,
% 5.24/5.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))))),
% 5.24/5.48 inference(monotonicity,[status(thm)],[32929])).
% 5.24/5.48 tff(32931,plain,
% 5.24/5.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 5.24/5.48 inference(transitivity,[status(thm)],[32930, 32928])).
% 5.24/5.48 tff(32932,plain,
% 5.24/5.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 5.24/5.48 inference(quant_inst,[status(thm)],[])).
% 5.24/5.48 tff(32933,plain,
% 5.24/5.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))),
% 5.24/5.48 inference(modus_ponens,[status(thm)],[32932, 32931])).
% 5.24/5.48 tff(32934,plain,
% 5.24/5.48 (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[32933, 118, 32916, 32927])).
% 5.24/5.48 tff(32935,plain,
% 5.24/5.48 (s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[23524, 41, 32934, 32924])).
% 5.24/5.48 tff(32936,plain,
% 5.24/5.48 (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z)))),
% 5.24/5.48 inference(symmetry,[status(thm)],[32935])).
% 5.24/5.48 tff(32937,plain,
% 5.24/5.48 ($false),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[32850, 32936])).
% 5.24/5.48 tff(32938,plain,(b(s(s(z)), elem!1) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | b(s(s(s(s(s(s(s(z))))))), s(s(z))) | (~r(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)))))))))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.48 tff(32939,plain,
% 5.24/5.48 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[32938, 32782, 202, 167, 3576, 3241, 204])).
% 5.24/5.48 tff(32940,plain,
% 5.24/5.48 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[249, 32939])).
% 5.24/5.48 tff(32941,plain,
% 5.24/5.48 ($false),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[32940, 32791])).
% 5.24/5.48 tff(32942,plain,(b(s(s(z)), elem!1) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | b(s(s(s(s(s(s(s(z))))))), s(s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.48 tff(32943,plain,
% 5.24/5.48 (b(s(s(z)), elem!1)),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[32942, 3576, 167, 202, 204])).
% 5.24/5.48 tff(32944,plain,
% 5.24/5.48 (~(elem!1 = s(s(z)))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[31585, 32943])).
% 5.24/5.48 tff(32945,plain,
% 5.24/5.48 (~(elem!1 = z)),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[32554, 32943, 32417])).
% 5.24/5.48 tff(32946,plain,
% 5.24/5.48 (r(elem!1, z)),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[498, 5723, 32945])).
% 5.24/5.48 tff(32947,plain,
% 5.24/5.48 (~r(elem!1, s(s(z)))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[458, 32946, 28500])).
% 5.24/5.48 tff(32948,plain,
% 5.24/5.48 (b(elem!1, s(s(z)))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[467, 32947, 32944])).
% 5.24/5.48 tff(32949,plain,
% 5.24/5.48 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[25284, 32948, 3576])).
% 5.24/5.48 tff(32950,plain,
% 5.24/5.48 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[703, 32949])).
% 5.24/5.48 tff(32951,plain,
% 5.24/5.48 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[32705, 5723, 15765, 202, 167, 204])).
% 5.24/5.48 tff(32952,plain,
% 5.24/5.48 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[17305, 31641, 167, 204, 202, 32943])).
% 5.24/5.48 tff(32953,plain,
% 5.24/5.48 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[691, 32949, 32952])).
% 5.24/5.48 tff(32954,plain,
% 5.24/5.48 (~b(s(s(s(s(z)))), elem!1)),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[17777, 32953, 202, 32951, 32948])).
% 5.24/5.48 tff(32955,plain,
% 5.24/5.48 (r(s(s(s(s(z)))), elem!1)),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[3142, 32954, 31641])).
% 5.24/5.48 tff(32956,plain,
% 5.24/5.48 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[25879, 32955])).
% 5.24/5.48 tff(32957,plain,
% 5.24/5.48 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[3444, 32956, 32950])).
% 5.24/5.48 tff(32958,plain,
% 5.24/5.48 ($false),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[11910, 178, 32943, 32948, 32951, 32953, 32957])).
% 5.24/5.48 tff(32959,plain,(b(elem!1, z) | (~b(s(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(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.48 tff(32960,plain,
% 5.24/5.48 (b(elem!1, z)),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[32959, 3576, 202, 167, 204])).
% 5.24/5.48 tff(32961,plain,
% 5.24/5.48 (~b(s(s(s(s(z)))), elem!1)),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[32082, 178, 32960, 32943, 31623, 167])).
% 5.24/5.48 tff(32962,plain,
% 5.24/5.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 5.24/5.48 inference(rewrite,[status(thm)],[])).
% 5.24/5.48 tff(32963,plain,
% 5.24/5.48 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 5.24/5.48 inference(rewrite,[status(thm)],[])).
% 5.24/5.48 tff(32964,plain,
% 5.24/5.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 5.24/5.48 inference(monotonicity,[status(thm)],[32963])).
% 5.24/5.48 tff(32965,plain,
% 5.24/5.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 5.24/5.48 inference(transitivity,[status(thm)],[32964, 32962])).
% 5.24/5.48 tff(32966,plain,
% 5.24/5.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), elem!1)))),
% 5.24/5.48 inference(quant_inst,[status(thm)],[])).
% 5.24/5.48 tff(32967,plain,
% 5.24/5.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 5.24/5.48 inference(modus_ponens,[status(thm)],[32966, 32965])).
% 5.24/5.48 tff(32968,plain,
% 5.24/5.48 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[32967, 178, 32960, 32943, 166, 32412])).
% 5.24/5.48 tff(32969,plain,
% 5.24/5.48 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[17305, 323, 167, 204, 202, 32943])).
% 5.24/5.48 tff(32970,plain,
% 5.24/5.48 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[691, 32969, 32968])).
% 5.24/5.48 tff(32971,plain,
% 5.24/5.48 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 5.24/5.48 inference(monotonicity,[status(thm)],[32970])).
% 5.24/5.48 tff(32972,plain,
% 5.24/5.48 (s(s(s(s(s(s(s(s(z)))))))) = s(elem!1)),
% 5.24/5.48 inference(symmetry,[status(thm)],[32971])).
% 5.24/5.48 tff(32973,plain,
% 5.24/5.48 (b(s(s(z)), s(s(s(s(s(s(s(s(z))))))))) <=> b(s(s(z)), s(elem!1))),
% 5.24/5.48 inference(monotonicity,[status(thm)],[32972])).
% 5.24/5.48 tff(32974,plain,
% 5.24/5.48 (b(s(s(z)), s(elem!1)) <=> b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.48 inference(symmetry,[status(thm)],[32973])).
% 5.24/5.48 tff(32975,plain,
% 5.24/5.48 (~(s(elem!1) = s(s(z)))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[2832, 32970])).
% 5.24/5.48 tff(32976,plain,
% 5.24/5.48 (~(s(s(z)) = s(elem!1))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[1058, 32975])).
% 5.24/5.48 tff(32977,plain,
% 5.24/5.48 (~(s(elem!1) = s(s(s(s(z)))))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[16181, 32970])).
% 5.24/5.48 tff(32978,plain,
% 5.24/5.48 (~(s(s(s(s(z)))) = s(elem!1))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[2168, 32977])).
% 5.24/5.48 tff(32979,plain,
% 5.24/5.48 (~(s(s(elem!1)) = elem!1)),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[2510, 32978, 32970])).
% 5.24/5.48 tff(32980,plain,
% 5.24/5.48 (~(s(elem!1) = elem!1)),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[672, 32979])).
% 5.24/5.48 tff(32981,plain,
% 5.24/5.48 (r(s(s(s(s(z)))), elem!1)),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[3142, 323, 32961])).
% 5.24/5.48 tff(32982,plain,
% 5.24/5.48 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 5.24/5.48 inference(monotonicity,[status(thm)],[32971])).
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% 5.24/5.48 inference(unit_resolution,[status(thm)],[467, 32983, 32944])).
% 5.24/5.48 tff(32985,plain,
% 5.24/5.48 (~(z = elem!1)),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[317, 32945])).
% 5.24/5.48 tff(32986,plain,
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% 5.24/5.48 inference(unit_resolution,[status(thm)],[4862, 32984, 29994])).
% 5.24/5.48 tff(32987,plain,
% 5.24/5.48 (b(z, elem!1)),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[585, 32986, 32985])).
% 5.24/5.48 tff(32988,plain,
% 5.24/5.48 (~r(s(elem!1), s(s(z)))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[17418, 32987, 28500, 32960, 32980, 32984])).
% 5.24/5.48 tff(32989,plain,
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% 5.24/5.48 inference(unit_resolution,[status(thm)],[421, 32988, 32975])).
% 5.24/5.48 tff(32990,plain,
% 5.24/5.48 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 5.24/5.48 inference(modus_ponens,[status(thm)],[32989, 32982])).
% 5.24/5.48 tff(32991,plain,
% 5.24/5.48 (~b(s(elem!1), s(s(s(s(z)))))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[32842, 32990, 202, 32970, 167])).
% 5.24/5.48 tff(32992,plain,
% 5.24/5.48 (r(s(elem!1), s(s(s(s(z)))))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[1084, 32991, 32977])).
% 5.24/5.48 tff(32993,plain,
% 5.24/5.48 (~r(s(elem!1), elem!1)),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[7010, 32992, 32981])).
% 5.24/5.48 tff(32994,plain,
% 5.24/5.48 (b(s(elem!1), elem!1)),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[677, 32993, 32980])).
% 5.24/5.48 tff(32995,plain,
% 5.24/5.48 (~(elem!1 = s(elem!1))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[748, 32980])).
% 5.24/5.48 tff(32996,plain,
% 5.24/5.48 (~b(elem!1, s(s(s(s(z)))))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[29314, 178, 32960, 32943, 31623, 167])).
% 5.24/5.48 tff(32997,plain,
% 5.24/5.48 (r(elem!1, s(s(s(s(z)))))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[483, 3130, 32996])).
% 5.24/5.48 tff(32998,plain,
% 5.24/5.48 (~r(elem!1, s(elem!1))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[14364, 32992, 32997])).
% 5.24/5.48 tff(32999,plain,
% 5.24/5.48 (b(elem!1, s(elem!1))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[756, 32998, 32995])).
% 5.24/5.48 tff(33000,plain,
% 5.24/5.48 (~b(z, s(elem!1))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[1396, 32999, 32960, 32987, 32994])).
% 5.24/5.48 tff(33001,plain,
% 5.24/5.48 (r(z, s(elem!1))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[2351, 33000])).
% 5.24/5.48 tff(33002,plain,
% 5.24/5.48 (~r(s(s(z)), s(elem!1))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[2341, 33001, 28500])).
% 5.24/5.48 tff(33003,plain,
% 5.24/5.48 (b(s(s(z)), s(elem!1))),
% 5.24/5.48 inference(unit_resolution,[status(thm)],[1067, 33002, 32976])).
% 5.24/5.48 tff(33004,plain,
% 5.24/5.48 (b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.48 inference(modus_ponens,[status(thm)],[33003, 32974])).
% 5.24/5.48 tff(33005,plain,
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% 5.24/5.48 inference(unit_resolution,[status(thm)],[3230, 32944])).
% 5.24/5.49 tff(33006,plain,
% 5.24/5.49 (~(s(elem!1) = s(s(s(z))))),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[23436, 33005])).
% 5.24/5.49 tff(33007,plain,
% 5.24/5.49 (~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z))))),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[24777, 32970, 33006])).
% 5.24/5.49 tff(33008,plain,
% 5.24/5.49 (r(z, s(s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[24812, 33001, 32970])).
% 5.24/5.49 tff(33009,plain,
% 5.24/5.49 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 5.24/5.49 inference(monotonicity,[status(thm)],[32972])).
% 5.24/5.49 tff(33010,plain,
% 5.24/5.49 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 5.24/5.49 inference(transitivity,[status(thm)],[33009, 377])).
% 5.24/5.49 tff(33011,plain,
% 5.24/5.49 ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.49 inference(symmetry,[status(thm)],[33010])).
% 5.24/5.49 tff(33012,plain,
% 5.24/5.49 ((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z))))))))))),
% 5.24/5.49 inference(monotonicity,[status(thm)],[33011])).
% 5.24/5.49 tff(33013,plain,
% 5.24/5.49 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 5.24/5.49 inference(monotonicity,[status(thm)],[32970])).
% 5.24/5.49 tff(33014,plain,
% 5.24/5.49 ((~(s(elem!1) = elem!1)) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.49 inference(monotonicity,[status(thm)],[33013])).
% 5.24/5.49 tff(33015,plain,
% 5.24/5.49 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 5.24/5.49 inference(modus_ponens,[status(thm)],[32980, 33014])).
% 5.24/5.49 tff(33016,plain,
% 5.24/5.49 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.49 inference(modus_ponens,[status(thm)],[33015, 33012])).
% 5.24/5.49 tff(33017,plain,
% 5.24/5.49 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))) <=> r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 5.24/5.49 inference(monotonicity,[status(thm)],[32972])).
% 5.24/5.49 tff(33018,plain,
% 5.24/5.49 (r(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.49 inference(symmetry,[status(thm)],[33017])).
% 5.24/5.49 tff(33019,plain,
% 5.24/5.49 (r(elem!1, s(elem!1)) <=> r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 5.24/5.49 inference(monotonicity,[status(thm)],[32970])).
% 5.24/5.49 tff(33020,plain,
% 5.24/5.49 (r(elem!1, s(elem!1)) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.49 inference(transitivity,[status(thm)],[33019, 33018])).
% 5.24/5.49 tff(33021,plain,
% 5.24/5.49 ((~r(elem!1, s(elem!1))) <=> (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))),
% 5.24/5.49 inference(monotonicity,[status(thm)],[33020])).
% 5.24/5.49 tff(33022,plain,
% 5.24/5.49 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.49 inference(modus_ponens,[status(thm)],[32998, 33021])).
% 5.24/5.49 tff(33023,plain,
% 5.24/5.49 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[16349, 41, 33022])).
% 5.24/5.49 tff(33024,plain,
% 5.24/5.49 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[33023, 33016])).
% 5.24/5.49 tff(33025,plain,
% 5.24/5.49 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z))))))))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 5.24/5.49 inference(monotonicity,[status(thm)],[32972])).
% 5.24/5.49 tff(33026,plain,
% 5.24/5.49 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) <=> (~b(s(s(s(s(z)))), s(elem!1)))),
% 5.24/5.49 inference(monotonicity,[status(thm)],[33025])).
% 5.24/5.49 tff(33027,plain,
% 5.24/5.49 (b(s(s(s(s(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))))))))),
% 5.24/5.49 inference(monotonicity,[status(thm)],[32972])).
% 5.24/5.49 tff(33028,plain,
% 5.24/5.49 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.49 inference(symmetry,[status(thm)],[33027])).
% 5.24/5.49 tff(33029,plain,
% 5.24/5.49 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[25119, 32992])).
% 5.24/5.49 tff(33030,plain,
% 5.24/5.49 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[395, 33029, 33015])).
% 5.24/5.49 tff(33031,plain,
% 5.24/5.49 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 5.24/5.49 inference(modus_ponens,[status(thm)],[33030, 33028])).
% 5.24/5.49 tff(33032,plain,
% 5.24/5.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 5.24/5.49 inference(rewrite,[status(thm)],[])).
% 5.24/5.49 tff(33033,plain,
% 5.24/5.49 (((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 5.24/5.49 inference(rewrite,[status(thm)],[])).
% 5.24/5.49 tff(33034,plain,
% 5.24/5.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))))),
% 5.24/5.49 inference(monotonicity,[status(thm)],[33033])).
% 5.24/5.49 tff(33035,plain,
% 5.24/5.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 5.24/5.49 inference(transitivity,[status(thm)],[33034, 33032])).
% 5.24/5.49 tff(33036,plain,
% 5.24/5.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))))),
% 5.24/5.49 inference(quant_inst,[status(thm)],[])).
% 5.24/5.49 tff(33037,plain,
% 5.24/5.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.49 inference(modus_ponens,[status(thm)],[33036, 33035])).
% 5.24/5.49 tff(33038,plain,
% 5.24/5.49 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[33037, 178, 166, 202, 32990, 33031])).
% 5.24/5.49 tff(33039,plain,
% 5.24/5.49 (~b(s(s(s(s(z)))), s(elem!1))),
% 5.24/5.49 inference(modus_ponens,[status(thm)],[33038, 33026])).
% 5.24/5.49 tff(33040,plain,
% 5.24/5.49 (r(s(s(s(s(z)))), s(elem!1))),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[2173, 33039, 32978])).
% 5.24/5.49 tff(33041,plain,
% 5.24/5.49 (~r(s(s(s(z))), z)),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[32912, 33040, 167, 32970, 33007, 32990, 33024])).
% 5.24/5.49 tff(33042,plain,
% 5.24/5.49 (b(s(s(s(z))), z)),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[21073, 33041])).
% 5.24/5.49 tff(33043,plain,
% 5.24/5.49 (~b(z, s(s(s(z))))),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[31515, 33042, 202, 15765, 32412])).
% 5.24/5.49 tff(33044,plain,
% 5.24/5.49 (r(z, s(s(s(z))))),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[4920, 33043])).
% 5.24/5.49 tff(33045,plain,
% 5.24/5.49 (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[24823, 33044, 33008])).
% 5.24/5.49 tff(33046,plain,
% 5.24/5.49 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[24832, 33045, 33007])).
% 5.24/5.49 tff(33047,plain,
% 5.24/5.49 (~r(s(s(s(z))), s(s(z)))),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[32323, 15765, 202])).
% 5.24/5.49 tff(33048,plain,
% 5.24/5.49 (b(s(s(s(z))), s(s(z)))),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[4966, 33047])).
% 5.24/5.49 tff(33049,plain,
% 5.24/5.49 ($false),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[29988, 118, 28500, 7670, 4952])).
% 5.24/5.49 tff(33050,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.49 tff(33051,plain,
% 5.24/5.49 (~r(s(s(z)), s(s(s(z))))),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[33050, 33044])).
% 5.24/5.49 tff(33052,plain,
% 5.24/5.49 (b(s(s(z)), s(s(s(z))))),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[5088, 33051])).
% 5.24/5.49 tff(33053,plain,
% 5.24/5.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 5.24/5.49 inference(rewrite,[status(thm)],[])).
% 5.24/5.49 tff(33054,plain,
% 5.24/5.49 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 5.24/5.49 inference(rewrite,[status(thm)],[])).
% 5.24/5.49 tff(33055,plain,
% 5.24/5.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))))),
% 5.24/5.49 inference(monotonicity,[status(thm)],[33054])).
% 5.24/5.49 tff(33056,plain,
% 5.24/5.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 5.24/5.49 inference(transitivity,[status(thm)],[33055, 33053])).
% 5.24/5.49 tff(33057,plain,
% 5.24/5.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))),
% 5.24/5.49 inference(quant_inst,[status(thm)],[])).
% 5.24/5.49 tff(33058,plain,
% 5.24/5.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 5.24/5.49 inference(modus_ponens,[status(thm)],[33057, 33056])).
% 5.24/5.49 tff(33059,plain,
% 5.24/5.49 ($false),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[33058, 178, 33052, 33048, 32990, 33046, 33004])).
% 5.24/5.49 tff(33060,plain,((s(s(s(s(z)))) = elem!1) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(s(s(s(z))))))), s(s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 5.24/5.49 tff(33061,plain,
% 5.24/5.49 (s(s(s(s(z)))) = elem!1),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[33060, 166, 167, 202, 3576, 204])).
% 5.24/5.49 tff(33062,plain,
% 5.24/5.49 (elem!1 = s(s(s(s(z))))),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[504, 33061])).
% 5.24/5.49 tff(33063,plain,
% 5.24/5.49 (~(s(elem!1) = s(s(z)))),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[11438, 33062])).
% 5.24/5.49 tff(33064,plain,
% 5.24/5.49 (~(s(s(z)) = s(elem!1))),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[1058, 33063])).
% 5.24/5.49 tff(33065,plain,
% 5.24/5.49 (b(s(elem!1), s(s(z)))),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[2373, 33062, 28500, 15765, 166, 33005])).
% 5.24/5.49 tff(33066,plain,
% 5.24/5.49 (b(elem!1, s(s(z)))),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[4509, 33061, 202])).
% 5.24/5.49 tff(33067,plain,
% 5.24/5.49 (~(s(s(elem!1)) = elem!1)),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[338, 33061, 33005])).
% 5.24/5.49 tff(33068,plain,
% 5.24/5.49 (~(s(elem!1) = elem!1)),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[672, 33067])).
% 5.24/5.49 tff(33069,plain,
% 5.24/5.49 (s(s(s(s(s(z))))) = s(elem!1)),
% 5.24/5.49 inference(monotonicity,[status(thm)],[33061])).
% 5.24/5.49 tff(33070,plain,
% 5.24/5.49 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 5.24/5.49 inference(monotonicity,[status(thm)],[33069])).
% 5.24/5.49 tff(33071,plain,
% 5.24/5.49 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 5.24/5.49 inference(monotonicity,[status(thm)],[33070])).
% 5.24/5.49 tff(33072,plain,
% 5.24/5.49 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 5.24/5.49 inference(monotonicity,[status(thm)],[33071])).
% 5.24/5.49 tff(33073,plain,
% 5.24/5.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 5.24/5.49 inference(rewrite,[status(thm)],[])).
% 5.24/5.49 tff(33074,plain,
% 5.24/5.49 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 5.24/5.49 inference(rewrite,[status(thm)],[])).
% 5.24/5.49 tff(33075,plain,
% 5.24/5.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 5.24/5.49 inference(monotonicity,[status(thm)],[33074])).
% 5.24/5.49 tff(33076,plain,
% 5.24/5.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 5.24/5.49 inference(transitivity,[status(thm)],[33075, 33073])).
% 5.24/5.49 tff(33077,plain,
% 5.24/5.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 5.24/5.49 inference(quant_inst,[status(thm)],[])).
% 5.24/5.49 tff(33078,plain,
% 5.24/5.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 5.24/5.49 inference(modus_ponens,[status(thm)],[33077, 33076])).
% 5.24/5.49 tff(33079,plain,
% 5.24/5.49 ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[33078, 178, 32960, 32943, 32412])).
% 5.24/5.49 tff(33080,plain,
% 5.24/5.49 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[33079, 166])).
% 5.24/5.49 tff(33081,plain,
% 5.24/5.49 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[25284, 33066, 3576])).
% 5.24/5.49 tff(33082,plain,
% 5.24/5.49 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[703, 33081])).
% 5.24/5.49 tff(33083,plain,
% 5.24/5.49 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[3444, 33082, 33080])).
% 5.24/5.49 tff(33084,plain,
% 5.24/5.49 (r(s(s(s(elem!1))), elem!1)),
% 5.24/5.49 inference(modus_ponens,[status(thm)],[33083, 33072])).
% 5.24/5.49 tff(33085,plain,
% 5.24/5.49 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(elem!1), s(s(z)))),
% 5.24/5.49 inference(monotonicity,[status(thm)],[12866])).
% 5.24/5.49 tff(33086,plain,
% 5.24/5.49 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 5.24/5.49 inference(symmetry,[status(thm)],[33085])).
% 5.24/5.49 tff(33087,plain,
% 5.24/5.49 (b(s(s(s(s(s(z))))), s(s(z)))),
% 5.24/5.49 inference(modus_ponens,[status(thm)],[1070, 33086])).
% 5.24/5.49 tff(33088,plain,
% 5.24/5.49 (~(s(s(elem!1)) = elem!1)),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[338, 331, 31965])).
% 5.24/5.49 tff(33089,plain,
% 5.24/5.49 (~(s(s(s(elem!1))) = s(elem!1))),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[348, 33088])).
% 5.24/5.49 tff(33090,plain,
% 5.24/5.49 (~(s(elem!1) = s(s(s(elem!1))))),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[5395, 33089])).
% 5.24/5.49 tff(33091,plain,
% 5.24/5.49 (b(s(elem!1), s(s(s(elem!1))))),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[5432, 22840, 33090])).
% 5.24/5.49 tff(33092,plain,
% 5.24/5.49 (b(s(s(s(s(s(s(s(z))))))), z) <=> b(s(s(s(elem!1))), z)),
% 5.24/5.49 inference(monotonicity,[status(thm)],[12868])).
% 5.24/5.49 tff(33093,plain,
% 5.24/5.49 (b(s(s(s(elem!1))), z)),
% 5.24/5.49 inference(modus_ponens,[status(thm)],[32319, 33092])).
% 5.24/5.49 tff(33094,plain,
% 5.24/5.49 (b(z, s(s(s(elem!1))))),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[17717, 23848, 31505])).
% 5.24/5.49 tff(33095,plain,
% 5.24/5.49 (b(s(s(s(elem!1))), s(elem!1))),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[373, 21256, 33089])).
% 5.24/5.49 tff(33096,plain,
% 5.24/5.49 (~b(z, s(elem!1))),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[22815, 178, 33095, 33094, 33093, 33091])).
% 5.24/5.49 tff(33097,plain,
% 5.24/5.49 (r(z, s(elem!1))),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[2351, 33096])).
% 5.24/5.49 tff(33098,plain,
% 5.24/5.49 (~r(s(s(z)), s(elem!1))),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[2341, 33097, 28500])).
% 5.24/5.49 tff(33099,plain,
% 5.24/5.49 (b(s(s(z)), s(elem!1))),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[1067, 33098, 23850])).
% 5.24/5.49 tff(33100,plain,
% 5.24/5.49 (b(s(s(z)), s(s(s(s(s(z))))))),
% 5.24/5.49 inference(unit_resolution,[status(thm)],[2330, 33099, 23848])).
% 5.24/5.49 tff(33101,plain,
% 5.24/5.49 (r(s(s(s(s(s(z))))), z) <=> r(s(elem!1), z)),
% 5.24/5.49 inference(monotonicity,[status(thm)],[12866])).
% 5.24/5.49 tff(33102,plain,
% 5.24/5.49 (r(s(elem!1), z) <=> r(s(s(s(s(s(z))))), z)),
% 5.24/5.49 inference(symmetry,[status(thm)],[33101])).
% 5.24/5.49 tff(33103,plain,
% 5.24/5.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 5.24/5.49 inference(rewrite,[status(thm)],[])).
% 5.24/5.49 tff(33104,plain,
% 5.24/5.49 (((~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(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 5.24/5.49 inference(rewrite,[status(thm)],[])).
% 5.24/5.49 tff(33105,plain,
% 5.24/5.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 5.24/5.49 inference(monotonicity,[status(thm)],[33104])).
% 5.24/5.49 tff(33106,plain,
% 5.24/5.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 5.24/5.49 inference(transitivity,[status(thm)],[33105, 33103])).
% 5.24/5.49 tff(33107,plain,
% 5.24/5.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 5.24/5.50 inference(quant_inst,[status(thm)],[])).
% 5.24/5.50 tff(33108,plain,
% 5.24/5.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 5.24/5.50 inference(modus_ponens,[status(thm)],[33107, 33106])).
% 5.24/5.50 tff(33109,plain,
% 5.24/5.50 (~b(s(elem!1), z)),
% 5.24/5.50 inference(unit_resolution,[status(thm)],[33108, 178, 33095, 33094, 33093, 33091])).
% 5.24/5.50 tff(33110,plain,
% 5.24/5.50 (r(s(elem!1), z)),
% 5.24/5.50 inference(unit_resolution,[status(thm)],[774, 33109])).
% 5.24/5.50 tff(33111,plain,
% 5.24/5.50 (r(s(s(s(s(s(z))))), z)),
% 5.24/5.50 inference(modus_ponens,[status(thm)],[33110, 33102])).
% 5.24/5.50 tff(33112,plain,
% 5.24/5.50 (~r(s(s(s(z))), z)),
% 5.24/5.50 inference(unit_resolution,[status(thm)],[30238, 33111, 32325, 33100, 33087])).
% 5.24/5.50 tff(33113,plain,
% 5.24/5.50 (b(s(s(s(z))), z)),
% 5.24/5.50 inference(unit_resolution,[status(thm)],[21073, 33112])).
% 5.24/5.50 tff(33114,plain,
% 5.24/5.50 (~b(z, s(s(s(z))))),
% 5.24/5.50 inference(unit_resolution,[status(thm)],[31515, 33113, 202, 107, 32319])).
% 5.24/5.50 tff(33115,plain,
% 5.24/5.50 (r(z, s(s(s(z))))),
% 5.24/5.50 inference(unit_resolution,[status(thm)],[4920, 33114])).
% 5.24/5.50 tff(33116,plain,
% 5.24/5.50 (~r(s(s(z)), s(s(s(z))))),
% 5.24/5.50 inference(unit_resolution,[status(thm)],[33050, 33115])).
% 5.24/5.50 tff(33117,plain,
% 5.24/5.50 (b(s(s(z)), s(s(s(z))))),
% 5.24/5.50 inference(unit_resolution,[status(thm)],[5088, 33116])).
% 5.24/5.50 tff(33118,plain,
% 5.24/5.50 (~b(s(elem!1), s(s(s(z))))),
% 5.24/5.50 inference(unit_resolution,[status(thm)],[30909, 178, 33099, 1070, 33117, 32325])).
% 5.24/5.50 tff(33119,plain,
% 5.24/5.50 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 5.24/5.50 inference(monotonicity,[status(thm)],[331])).
% 5.24/5.50 tff(33120,plain,
% 5.24/5.50 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 5.24/5.50 inference(transitivity,[status(thm)],[33119, 10421])).
% 5.24/5.50 tff(33121,plain,
% 5.24/5.50 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(z))) = elem!1))),
% 5.24/5.50 inference(monotonicity,[status(thm)],[33120])).
% 5.24/5.50 tff(33122,plain,
% 5.24/5.50 (~(s(s(s(z))) = elem!1)),
% 5.24/5.50 inference(modus_ponens,[status(thm)],[4938, 33121])).
% 5.24/5.50 tff(33123,plain,
% 5.24/5.50 ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 5.24/5.50 inference(unit_resolution,[status(thm)],[30865, 178, 817, 812, 32325])).
% 5.24/5.50 tff(33124,plain,
% 5.24/5.50 (~b(s(s(s(z))), elem!1)),
% 5.24/5.50 inference(unit_resolution,[status(thm)],[33123, 33117])).
% 5.24/5.50 tff(33125,plain,
% 5.24/5.50 (r(s(s(s(z))), elem!1)),
% 5.24/5.50 inference(unit_resolution,[status(thm)],[4981, 33124, 33122])).
% 5.24/5.50 tff(33126,plain,
% 5.24/5.50 (~r(s(elem!1), s(s(s(z))))),
% 5.24/5.50 inference(unit_resolution,[status(thm)],[23906, 33125, 1426])).
% 5.24/5.50 tff(33127,plain,
% 5.24/5.50 (~(s(elem!1) = s(s(s(z))))),
% 5.24/5.50 inference(unit_resolution,[status(thm)],[23436, 31965])).
% 5.24/5.50 tff(33128,plain,
% 5.24/5.50 ($false),
% 5.24/5.50 inference(unit_resolution,[status(thm)],[23881, 41, 33127, 33126, 33118])).
% 5.34/5.50 tff(33129,plain,((~r(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~(s(s(s(s(z)))) = elem!1)) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.50 tff(33130,plain,
% 5.34/5.50 (~r(s(elem!1), elem!1)),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[33129, 33084, 32943, 33065, 202, 15765, 33061, 33066])).
% 5.34/5.50 tff(33131,plain,
% 5.34/5.50 (b(s(elem!1), elem!1)),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[677, 33130, 33068])).
% 5.34/5.50 tff(33132,plain,
% 5.34/5.50 (~b(s(s(z)), s(elem!1))),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[13708, 33131, 33066, 33065, 32943])).
% 5.34/5.50 tff(33133,plain,
% 5.34/5.50 (r(s(s(z)), s(elem!1))),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[1067, 33132, 33064])).
% 5.34/5.50 tff(33134,plain,
% 5.34/5.50 (b(z, s(s(s(s(z))))) <=> b(z, elem!1)),
% 5.34/5.50 inference(monotonicity,[status(thm)],[33061])).
% 5.34/5.50 tff(33135,plain,
% 5.34/5.50 (b(z, elem!1)),
% 5.34/5.50 inference(modus_ponens,[status(thm)],[27212, 33134])).
% 5.34/5.50 tff(33136,plain,
% 5.34/5.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 5.34/5.50 inference(rewrite,[status(thm)],[])).
% 5.34/5.50 tff(33137,plain,
% 5.34/5.50 (((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1)))) <=> ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 5.34/5.50 inference(rewrite,[status(thm)],[])).
% 5.34/5.50 tff(33138,plain,
% 5.34/5.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z))))))),
% 5.34/5.50 inference(monotonicity,[status(thm)],[33137])).
% 5.34/5.50 tff(33139,plain,
% 5.34/5.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 5.34/5.50 inference(transitivity,[status(thm)],[33138, 33136])).
% 5.34/5.50 tff(33140,plain,
% 5.34/5.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))))),
% 5.34/5.50 inference(quant_inst,[status(thm)],[])).
% 5.34/5.50 tff(33141,plain,
% 5.34/5.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z))))),
% 5.34/5.50 inference(modus_ponens,[status(thm)],[33140, 33139])).
% 5.34/5.50 tff(33142,plain,
% 5.34/5.50 ((~b(s(elem!1), elem!1)) | (~b(z, s(elem!1)))),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[33141, 178, 33135, 33066, 33065])).
% 5.34/5.50 tff(33143,plain,
% 5.34/5.50 (~b(z, s(elem!1))),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[33142, 33131])).
% 5.34/5.50 tff(33144,plain,
% 5.34/5.50 (r(z, s(elem!1))),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[2351, 33143])).
% 5.34/5.50 tff(33145,plain,
% 5.34/5.50 ($false),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[12114, 33144, 33133, 29994])).
% 5.34/5.50 tff(33146,plain,((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(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(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.50 tff(33147,plain,
% 5.34/5.50 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[33146, 3576, 202, 167, 204])).
% 5.34/5.50 tff(33148,plain,
% 5.34/5.50 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[10835, 33147, 32943])).
% 5.34/5.50 tff(33149,plain,
% 5.34/5.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 5.34/5.50 inference(rewrite,[status(thm)],[])).
% 5.34/5.50 tff(33150,plain,
% 5.34/5.50 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 5.34/5.50 inference(rewrite,[status(thm)],[])).
% 5.34/5.50 tff(33151,plain,
% 5.34/5.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 5.34/5.50 inference(monotonicity,[status(thm)],[33150])).
% 5.34/5.50 tff(33152,plain,
% 5.34/5.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 5.34/5.50 inference(transitivity,[status(thm)],[33151, 33149])).
% 5.34/5.50 tff(33153,plain,
% 5.34/5.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 5.34/5.50 inference(quant_inst,[status(thm)],[])).
% 5.34/5.50 tff(33154,plain,
% 5.34/5.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 5.34/5.50 inference(modus_ponens,[status(thm)],[33153, 33152])).
% 5.34/5.50 tff(33155,plain,
% 5.34/5.50 ($false),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[33154, 178, 506, 869, 595, 146, 3664])).
% 5.34/5.50 tff(33156,plain,((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(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(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.50 tff(33157,plain,
% 5.34/5.50 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[33156, 3664, 595, 146, 506])).
% 5.34/5.50 tff(33158,plain,
% 5.34/5.50 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[691, 33157, 701])).
% 5.34/5.50 tff(33159,plain,
% 5.34/5.50 (s(s(s(s(z)))) = elem!1),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[17305, 33158, 167, 204, 202, 817])).
% 5.34/5.50 tff(33160,plain,
% 5.34/5.50 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.34/5.50 inference(monotonicity,[status(thm)],[33159])).
% 5.34/5.50 tff(33161,plain,
% 5.34/5.50 (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)))))),
% 5.34/5.50 inference(symmetry,[status(thm)],[33160])).
% 5.34/5.50 tff(33162,plain,
% 5.34/5.50 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 5.34/5.50 inference(modus_ponens,[status(thm)],[3664, 33161])).
% 5.34/5.50 tff(33163,plain,
% 5.34/5.50 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[24071, 595, 31623, 146])).
% 5.34/5.50 tff(33164,plain,
% 5.34/5.50 ($false),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[33163, 33162])).
% 5.34/5.50 tff(33165,plain,((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.50 tff(33166,plain,
% 5.34/5.50 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[33165, 33148, 204, 202, 32943, 167, 32414, 32412, 32960])).
% 5.34/5.50 tff(33167,plain,
% 5.34/5.50 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[703, 33148])).
% 5.34/5.50 tff(33168,plain,
% 5.34/5.50 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[3444, 33167, 33166])).
% 5.34/5.50 tff(33169,plain,
% 5.34/5.50 (~r(s(s(s(s(z)))), elem!1)),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[25879, 33168])).
% 5.34/5.50 tff(33170,plain,
% 5.34/5.50 (s(s(s(s(z)))) = elem!1),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[3142, 33169, 32961])).
% 5.34/5.50 tff(33171,plain,
% 5.34/5.50 (r(s(s(s(s(z)))), z) <=> r(elem!1, z)),
% 5.34/5.50 inference(monotonicity,[status(thm)],[33170])).
% 5.34/5.50 tff(33172,plain,
% 5.34/5.50 (r(elem!1, z) <=> r(s(s(s(s(z)))), z)),
% 5.34/5.50 inference(symmetry,[status(thm)],[33171])).
% 5.34/5.50 tff(33173,plain,
% 5.34/5.50 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[10835, 286, 817])).
% 5.34/5.50 tff(33174,plain,
% 5.34/5.50 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[703, 33173])).
% 5.34/5.50 tff(33175,plain,
% 5.34/5.50 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[33165, 33173, 204, 202, 817, 167, 31505, 32319, 506])).
% 5.34/5.50 tff(33176,plain,
% 5.34/5.50 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[3444, 33175, 33174])).
% 5.34/5.50 tff(33177,plain,
% 5.34/5.50 (~r(s(s(s(s(z)))), elem!1)),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[25879, 33176])).
% 5.34/5.50 tff(33178,plain,
% 5.34/5.50 (s(s(s(s(z)))) = elem!1),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[3142, 33177, 32083])).
% 5.34/5.50 tff(33179,plain,
% 5.34/5.50 (elem!1 = s(s(s(s(z))))),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[504, 33178])).
% 5.34/5.50 tff(33180,plain,
% 5.34/5.50 (~(s(elem!1) = s(s(z)))),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[11438, 33179])).
% 5.34/5.50 tff(33181,plain,
% 5.34/5.50 (~(s(s(z)) = s(elem!1))),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[1058, 33180])).
% 5.34/5.50 tff(33182,plain,
% 5.34/5.50 (b(s(elem!1), s(s(z)))),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[435, 33179, 28500, 107, 287, 31965])).
% 5.34/5.50 tff(33183,plain,
% 5.34/5.50 (~(elem!1 = z)),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[32554, 817, 32417])).
% 5.34/5.50 tff(33184,plain,
% 5.34/5.50 (~(z = elem!1)),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[317, 33183])).
% 5.34/5.50 tff(33185,plain,
% 5.34/5.50 ($false),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[3121, 30203, 450, 28500, 286, 817, 507, 595, 1342])).
% 5.34/5.50 tff(33186,plain,((~r(elem!1, s(s(z)))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), elem!1)) | (z = elem!1) | (~b(z, s(s(s(s(s(s(s(z))))))))) | r(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 5.34/5.50 tff(33187,plain,
% 5.34/5.50 (~r(elem!1, s(s(z)))),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[33186, 286, 817, 33184, 31505, 1342])).
% 5.34/5.50 tff(33188,plain,
% 5.34/5.50 (b(elem!1, s(s(z)))),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[467, 33187, 31605])).
% 5.34/5.50 tff(33189,plain,
% 5.34/5.50 (~(s(s(elem!1)) = elem!1)),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[338, 33178, 31965])).
% 5.34/5.50 tff(33190,plain,
% 5.34/5.50 (~(s(elem!1) = elem!1)),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[672, 33189])).
% 5.34/5.50 tff(33191,plain,
% 5.34/5.50 (s(s(s(s(s(z))))) = s(elem!1)),
% 5.34/5.50 inference(monotonicity,[status(thm)],[33178])).
% 5.34/5.50 tff(33192,plain,
% 5.34/5.50 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 5.34/5.50 inference(monotonicity,[status(thm)],[33191])).
% 5.34/5.50 tff(33193,plain,
% 5.34/5.50 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 5.34/5.50 inference(monotonicity,[status(thm)],[33192])).
% 5.34/5.50 tff(33194,plain,
% 5.34/5.50 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 5.34/5.50 inference(monotonicity,[status(thm)],[33193])).
% 5.34/5.50 tff(33195,plain,
% 5.34/5.50 (r(s(s(s(elem!1))), elem!1)),
% 5.34/5.50 inference(modus_ponens,[status(thm)],[33176, 33194])).
% 5.34/5.50 tff(33196,plain,
% 5.34/5.50 (~r(s(elem!1), elem!1)),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[33129, 33182, 817, 33188, 202, 107, 33178, 33195])).
% 5.34/5.50 tff(33197,plain,
% 5.34/5.50 (b(s(elem!1), elem!1)),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[677, 33196, 33190])).
% 5.34/5.50 tff(33198,plain,
% 5.34/5.50 (~b(s(s(z)), s(elem!1))),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[13708, 33197, 33188, 33182, 817])).
% 5.34/5.50 tff(33199,plain,
% 5.34/5.50 (r(s(s(z)), s(elem!1))),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[1067, 33198, 33181])).
% 5.34/5.50 tff(33200,plain,
% 5.34/5.50 (b(z, s(s(s(s(z))))) <=> b(z, elem!1)),
% 5.34/5.50 inference(monotonicity,[status(thm)],[33178])).
% 5.34/5.50 tff(33201,plain,
% 5.34/5.50 (b(z, elem!1)),
% 5.34/5.50 inference(modus_ponens,[status(thm)],[27212, 33200])).
% 5.34/5.50 tff(33202,plain,
% 5.34/5.50 ((~b(s(elem!1), elem!1)) | (~b(z, s(elem!1)))),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[33141, 178, 33201, 33188, 33182])).
% 5.34/5.50 tff(33203,plain,
% 5.34/5.50 (~b(z, s(elem!1))),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[33202, 33197])).
% 5.34/5.50 tff(33204,plain,
% 5.34/5.50 (r(z, s(elem!1))),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[2351, 33203])).
% 5.34/5.50 tff(33205,plain,
% 5.34/5.50 ($false),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[12114, 33204, 33199, 29994])).
% 5.34/5.50 tff(33206,plain,(b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, z)) | r(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 5.34/5.50 tff(33207,plain,
% 5.34/5.50 (r(elem!1, z)),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[33206, 33147, 202, 15765, 204, 167, 32960, 32943])).
% 5.34/5.50 tff(33208,plain,
% 5.34/5.50 (r(s(s(s(s(z)))), z)),
% 5.34/5.50 inference(modus_ponens,[status(thm)],[33207, 33172])).
% 5.34/5.50 tff(33209,plain,
% 5.34/5.50 ($false),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[31622, 33208])).
% 5.34/5.50 tff(33210,plain,(b(s(s(s(s(s(s(s(z))))))), s(s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.50 tff(33211,plain,
% 5.34/5.50 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[33210, 204, 32293, 31476])).
% 5.34/5.50 tff(33212,plain,
% 5.34/5.50 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[3102, 108, 28500])).
% 5.34/5.50 tff(33213,plain,
% 5.34/5.50 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[249, 33212])).
% 5.34/5.50 tff(33214,plain,
% 5.34/5.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))))),
% 5.34/5.50 inference(rewrite,[status(thm)],[])).
% 5.34/5.50 tff(33215,plain,
% 5.34/5.50 (((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))))),
% 5.34/5.50 inference(rewrite,[status(thm)],[])).
% 5.34/5.50 tff(33216,plain,
% 5.34/5.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z))))))),
% 5.34/5.50 inference(monotonicity,[status(thm)],[33215])).
% 5.34/5.50 tff(33217,plain,
% 5.34/5.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))))),
% 5.34/5.50 inference(transitivity,[status(thm)],[33216, 33214])).
% 5.34/5.50 tff(33218,plain,
% 5.34/5.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 5.34/5.50 inference(quant_inst,[status(thm)],[])).
% 5.34/5.50 tff(33219,plain,
% 5.34/5.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(z))))),
% 5.34/5.50 inference(modus_ponens,[status(thm)],[33218, 33217])).
% 5.34/5.50 tff(33220,plain,
% 5.34/5.50 ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[33219, 178, 166, 202, 3002])).
% 5.34/5.50 tff(33221,plain,
% 5.34/5.50 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[33220, 4932])).
% 5.34/5.50 tff(33222,plain,
% 5.34/5.50 (r(s(s(s(s(z)))), s(s(s(z))))),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[11185, 33221])).
% 5.34/5.50 tff(33223,plain,
% 5.34/5.50 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[27268, 178, 166, 1146, 3002])).
% 5.34/5.50 tff(33224,plain,
% 5.34/5.50 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[33223, 4932])).
% 5.34/5.50 tff(33225,plain,
% 5.34/5.50 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[31522, 33224])).
% 5.34/5.50 tff(33226,plain,
% 5.34/5.50 ($false),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[31525, 33225, 33222])).
% 5.34/5.50 tff(33227,plain,((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.50 tff(33228,plain,
% 5.34/5.50 (~b(s(s(s(z))), s(s(z)))),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[33227, 33213, 33211, 32298, 32293])).
% 5.34/5.50 tff(33229,plain,
% 5.34/5.50 (r(s(s(s(z))), s(s(z)))),
% 5.34/5.50 inference(unit_resolution,[status(thm)],[4966, 33228])).
% 5.34/5.51 tff(33230,plain,
% 5.34/5.51 (~r(s(s(s(z))), z)),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[24599, 33229, 28500])).
% 5.34/5.51 tff(33231,plain,
% 5.34/5.51 (b(s(s(s(z))), z)),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[21073, 33230])).
% 5.34/5.51 tff(33232,plain,
% 5.34/5.51 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), z)),
% 5.34/5.51 inference(monotonicity,[status(thm)],[32707])).
% 5.34/5.51 tff(33233,plain,
% 5.34/5.51 (r(s(s(s(s(s(s(s(z))))))), z) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.34/5.51 inference(symmetry,[status(thm)],[33232])).
% 5.34/5.51 tff(33234,plain,
% 5.34/5.51 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.34/5.51 inference(modus_ponens,[status(thm)],[108, 33233])).
% 5.34/5.51 tff(33235,plain,
% 5.34/5.51 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[3502, 32296])).
% 5.34/5.51 tff(33236,plain,
% 5.34/5.51 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 5.34/5.51 inference(monotonicity,[status(thm)],[32741])).
% 5.34/5.51 tff(33237,plain,
% 5.34/5.51 (~(s(s(s(elem!1))) = elem!1)),
% 5.34/5.51 inference(modus_ponens,[status(thm)],[940, 33236])).
% 5.34/5.51 tff(33238,plain,
% 5.34/5.51 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(elem!1)))), z)),
% 5.34/5.51 inference(monotonicity,[status(thm)],[32707])).
% 5.34/5.51 tff(33239,plain,
% 5.34/5.51 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 5.34/5.51 inference(symmetry,[status(thm)],[33238])).
% 5.34/5.51 tff(33240,plain,
% 5.34/5.51 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(z)))), z)),
% 5.34/5.51 inference(monotonicity,[status(thm)],[32711])).
% 5.34/5.51 tff(33241,plain,
% 5.34/5.51 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(elem!1)))), z)),
% 5.34/5.51 inference(symmetry,[status(thm)],[33240])).
% 5.34/5.51 tff(33242,plain,
% 5.34/5.51 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 5.34/5.51 inference(transitivity,[status(thm)],[33241, 33239])).
% 5.34/5.51 tff(33243,plain,
% 5.34/5.51 (b(s(s(s(s(elem!1)))), elem!1)),
% 5.34/5.51 inference(modus_ponens,[status(thm)],[31575, 33242])).
% 5.34/5.51 tff(33244,plain,
% 5.34/5.51 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(elem!1)))))),
% 5.34/5.51 inference(monotonicity,[status(thm)],[32714])).
% 5.34/5.51 tff(33245,plain,
% 5.34/5.51 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 5.34/5.51 inference(modus_ponens,[status(thm)],[4938, 33244])).
% 5.34/5.51 tff(33246,plain,
% 5.34/5.51 ((s(elem!1) = s(s(s(s(elem!1))))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 5.34/5.51 inference(monotonicity,[status(thm)],[32711])).
% 5.34/5.51 tff(33247,plain,
% 5.34/5.51 ((s(elem!1) = s(s(s(s(elem!1))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 5.34/5.51 inference(transitivity,[status(thm)],[33246, 2163])).
% 5.34/5.51 tff(33248,plain,
% 5.34/5.51 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 5.34/5.51 inference(symmetry,[status(thm)],[33247])).
% 5.34/5.51 tff(33249,plain,
% 5.34/5.51 ((~(s(s(s(s(z)))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(elem!1))))))),
% 5.34/5.51 inference(monotonicity,[status(thm)],[33248])).
% 5.34/5.51 tff(33250,plain,
% 5.34/5.51 (z = elem!1),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[2808, 32707])).
% 5.34/5.51 tff(33251,plain,
% 5.34/5.51 (~(s(elem!1) = s(s(s(s(z)))))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[25360, 33250])).
% 5.34/5.51 tff(33252,plain,
% 5.34/5.51 (~(s(s(s(s(z)))) = s(elem!1))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[2168, 33251])).
% 5.34/5.51 tff(33253,plain,
% 5.34/5.51 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 5.34/5.51 inference(modus_ponens,[status(thm)],[33252, 33249])).
% 5.34/5.51 tff(33254,plain,
% 5.34/5.51 (b(elem!1, s(s(s(elem!1)))) <=> b(z, s(s(s(elem!1))))),
% 5.34/5.51 inference(monotonicity,[status(thm)],[32707])).
% 5.34/5.51 tff(33255,plain,
% 5.34/5.51 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 5.34/5.51 inference(symmetry,[status(thm)],[33254])).
% 5.34/5.51 tff(33256,plain,
% 5.34/5.51 (~b(elem!1, s(s(z)))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[30983, 33250, 28501])).
% 5.34/5.51 tff(33257,plain,
% 5.34/5.51 (~r(z, s(s(s(elem!1))))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[30606, 33256, 203, 1146, 32707])).
% 5.34/5.51 tff(33258,plain,
% 5.34/5.51 (b(z, s(s(s(elem!1))))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[2095, 33257])).
% 5.34/5.51 tff(33259,plain,
% 5.34/5.51 (b(elem!1, s(s(s(elem!1))))),
% 5.34/5.51 inference(modus_ponens,[status(thm)],[33258, 33255])).
% 5.34/5.51 tff(33260,plain,
% 5.34/5.51 (b(s(elem!1), elem!1) <=> b(s(elem!1), z)),
% 5.34/5.51 inference(monotonicity,[status(thm)],[32707])).
% 5.34/5.51 tff(33261,plain,
% 5.34/5.51 (b(s(elem!1), z) <=> b(s(elem!1), elem!1)),
% 5.34/5.51 inference(symmetry,[status(thm)],[33260])).
% 5.34/5.51 tff(33262,plain,
% 5.34/5.51 (~(s(elem!1) = s(s(z)))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[28525, 33250])).
% 5.34/5.51 tff(33263,plain,
% 5.34/5.51 (~r(s(elem!1), z)),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[28541, 33262, 1146, 108, 33213, 32707])).
% 5.34/5.51 tff(33264,plain,
% 5.34/5.51 (b(s(elem!1), z)),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[774, 33263])).
% 5.34/5.51 tff(33265,plain,
% 5.34/5.51 (b(s(elem!1), elem!1)),
% 5.34/5.51 inference(modus_ponens,[status(thm)],[33264, 33261])).
% 5.34/5.51 tff(33266,plain,
% 5.34/5.51 ((s(s(s(z))) = s(elem!1)) <=> (s(elem!1) = s(s(s(z))))),
% 5.34/5.51 inference(commutativity,[status(thm)],[])).
% 5.34/5.51 tff(33267,plain,
% 5.34/5.51 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(z))) = s(elem!1))),
% 5.34/5.51 inference(monotonicity,[status(thm)],[32710])).
% 5.34/5.51 tff(33268,plain,
% 5.34/5.51 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(z))))),
% 5.34/5.51 inference(transitivity,[status(thm)],[33267, 33266])).
% 5.34/5.51 tff(33269,plain,
% 5.34/5.51 ((s(elem!1) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 5.34/5.51 inference(symmetry,[status(thm)],[33268])).
% 5.34/5.51 tff(33270,plain,
% 5.34/5.51 ((s(elem!1) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 5.34/5.51 inference(transitivity,[status(thm)],[33269, 7104])).
% 5.34/5.51 tff(33271,plain,
% 5.34/5.51 ((~(s(elem!1) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 5.34/5.51 inference(monotonicity,[status(thm)],[33270])).
% 5.34/5.51 tff(33272,plain,
% 5.34/5.51 (~(s(elem!1) = s(s(s(z))))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[23436, 32765])).
% 5.34/5.51 tff(33273,plain,
% 5.34/5.51 (~(s(elem!1) = s(s(s(elem!1))))),
% 5.34/5.51 inference(modus_ponens,[status(thm)],[33272, 33271])).
% 5.34/5.51 tff(33274,plain,
% 5.34/5.51 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(z, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.51 inference(monotonicity,[status(thm)],[32707])).
% 5.34/5.51 tff(33275,plain,
% 5.34/5.51 (r(z, s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.51 inference(symmetry,[status(thm)],[33274])).
% 5.34/5.51 tff(33276,plain,
% 5.34/5.51 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.51 inference(modus_ponens,[status(thm)],[203, 33275])).
% 5.34/5.51 tff(33277,plain,
% 5.34/5.51 (~r(z, s(elem!1))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[23953, 33234, 29994, 32707, 32766, 33262, 33276])).
% 5.34/5.51 tff(33278,plain,
% 5.34/5.51 (b(z, s(elem!1))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[2351, 33277])).
% 5.34/5.51 tff(33279,plain,
% 5.34/5.51 (b(elem!1, s(elem!1))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[12054, 33278, 32707])).
% 5.34/5.51 tff(33280,plain,
% 5.34/5.51 (~b(s(s(s(elem!1))), elem!1)),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[24015, 33279, 33273, 33265, 33259, 33253, 33245, 32723, 33243])).
% 5.34/5.51 tff(33281,plain,
% 5.34/5.51 (r(s(s(s(elem!1))), elem!1)),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[570, 33280, 33237])).
% 5.34/5.51 tff(33282,plain,
% 5.34/5.51 (~(elem!1 = s(s(z)))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[311, 32765])).
% 5.34/5.51 tff(33283,plain,
% 5.34/5.51 (r(elem!1, s(s(z)))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[467, 33256, 33282])).
% 5.34/5.51 tff(33284,plain,
% 5.34/5.51 (~r(s(s(s(elem!1))), s(s(z)))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[4205, 33281, 33283])).
% 5.34/5.51 tff(33285,plain,
% 5.34/5.51 ($false),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[26027, 33284, 33281, 33235, 33213, 33234, 1146])).
% 5.34/5.51 tff(33286,plain,(r(elem!1, z) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | b(z, s(s(z))) | b(s(s(z)), elem!1) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 5.34/5.51 tff(33287,plain,
% 5.34/5.51 (r(elem!1, z)),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[33286, 203, 108, 1146, 28501, 3241, 5723])).
% 5.34/5.51 tff(33288,plain,
% 5.34/5.51 (~r(s(s(z)), elem!1)),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[443, 33287, 28500])).
% 5.34/5.51 tff(33289,plain,
% 5.34/5.51 (s(s(z)) = elem!1),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[448, 33288, 3241])).
% 5.34/5.51 tff(33290,plain,
% 5.34/5.51 (s(s(s(z))) = s(elem!1)),
% 5.34/5.51 inference(monotonicity,[status(thm)],[33289])).
% 5.34/5.51 tff(33291,plain,
% 5.34/5.51 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 5.34/5.51 inference(monotonicity,[status(thm)],[33290])).
% 5.34/5.51 tff(33292,plain,
% 5.34/5.51 (b(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.34/5.51 inference(symmetry,[status(thm)],[33291])).
% 5.34/5.51 tff(33293,plain,
% 5.34/5.51 ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) <=> (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 5.34/5.51 inference(monotonicity,[status(thm)],[33292])).
% 5.34/5.51 tff(33294,plain,
% 5.34/5.51 (b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.51 inference(monotonicity,[status(thm)],[33290])).
% 5.34/5.51 tff(33295,plain,
% 5.34/5.51 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.51 inference(modus_ponens,[status(thm)],[3002, 33294])).
% 5.34/5.51 tff(33296,plain,
% 5.34/5.51 (r(z, elem!1)),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[7053, 33289, 29994])).
% 5.34/5.51 tff(33297,plain,
% 5.34/5.51 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[11027, 33296, 108])).
% 5.34/5.51 tff(33298,plain,
% 5.34/5.51 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[23292, 33213, 31476, 202, 1146])).
% 5.34/5.51 tff(33299,plain,
% 5.34/5.51 (b(elem!1, s(s(s(s(z)))))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[17989, 33289, 31476])).
% 5.34/5.51 tff(33300,plain,
% 5.34/5.51 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[3434, 33299, 33298])).
% 5.34/5.51 tff(33301,plain,
% 5.34/5.51 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[703, 33300])).
% 5.34/5.51 tff(33302,plain,
% 5.34/5.51 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[3444, 33301, 33297])).
% 5.34/5.51 tff(33303,plain,
% 5.34/5.51 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[10809, 33287, 203])).
% 5.34/5.51 tff(33304,plain,
% 5.34/5.51 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[691, 33300, 33303])).
% 5.34/5.51 tff(33305,plain,
% 5.34/5.51 (elem!1 = s(s(z))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[3230, 33289])).
% 5.34/5.51 tff(33306,plain,
% 5.34/5.51 (~(s(elem!1) = s(s(s(s(z)))))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[1353, 33305, 32296])).
% 5.34/5.51 tff(33307,plain,
% 5.34/5.51 (s(s(s(s(z)))) = s(s(elem!1))),
% 5.34/5.51 inference(monotonicity,[status(thm)],[33290])).
% 5.34/5.51 tff(33308,plain,
% 5.34/5.51 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 5.34/5.51 inference(monotonicity,[status(thm)],[33307])).
% 5.34/5.51 tff(33309,plain,
% 5.34/5.51 (b(s(s(s(s(z)))), elem!1)),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[8526, 33289, 202])).
% 5.34/5.51 tff(33310,plain,
% 5.34/5.51 (b(s(s(elem!1)), elem!1)),
% 5.34/5.51 inference(modus_ponens,[status(thm)],[33309, 33308])).
% 5.34/5.51 tff(33311,plain,
% 5.34/5.51 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 5.34/5.51 inference(monotonicity,[status(thm)],[33289])).
% 5.34/5.51 tff(33312,plain,
% 5.34/5.51 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 5.34/5.51 inference(transitivity,[status(thm)],[33311, 1526])).
% 5.34/5.51 tff(33313,plain,
% 5.34/5.51 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 5.34/5.51 inference(transitivity,[status(thm)],[33312, 2486])).
% 5.34/5.51 tff(33314,plain,
% 5.34/5.51 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 5.34/5.51 inference(monotonicity,[status(thm)],[33313])).
% 5.34/5.51 tff(33315,plain,
% 5.34/5.51 (~(elem!1 = s(s(s(elem!1))))),
% 5.34/5.51 inference(modus_ponens,[status(thm)],[1683, 33314])).
% 5.34/5.51 tff(33316,plain,
% 5.34/5.51 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 5.34/5.51 inference(monotonicity,[status(thm)],[33312])).
% 5.34/5.51 tff(33317,plain,
% 5.34/5.51 (~(s(s(s(elem!1))) = elem!1)),
% 5.34/5.51 inference(modus_ponens,[status(thm)],[1683, 33316])).
% 5.34/5.51 tff(33318,plain,
% 5.34/5.51 (~r(z, s(s(s(elem!1))))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[17868, 33317, 108, 33296, 33301, 33235, 33304, 33315])).
% 5.34/5.51 tff(33319,plain,
% 5.34/5.51 (b(z, s(s(s(elem!1))))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[2095, 33318])).
% 5.34/5.51 tff(33320,plain,
% 5.34/5.51 (r(s(elem!1), elem!1)),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[677, 2141, 10915])).
% 5.34/5.51 tff(33321,plain,
% 5.34/5.51 (~r(z, s(elem!1))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[7070, 33320, 32337])).
% 5.34/5.51 tff(33322,plain,
% 5.34/5.51 (b(z, s(elem!1))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[2351, 33321])).
% 5.34/5.51 tff(33323,plain,
% 5.34/5.51 (~r(s(elem!1), z)),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[13694, 33320, 437])).
% 5.34/5.51 tff(33324,plain,
% 5.34/5.51 (b(s(elem!1), z)),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[774, 33323])).
% 5.34/5.51 tff(33325,plain,
% 5.34/5.51 ((elem!1 = s(s(s(z)))) <=> (s(s(z)) = s(elem!1))),
% 5.34/5.51 inference(transitivity,[status(thm)],[10907, 10973, 1359])).
% 5.34/5.51 tff(33326,plain,
% 5.34/5.51 ((~(elem!1 = s(s(s(z))))) <=> (~(s(s(z)) = s(elem!1)))),
% 5.34/5.51 inference(monotonicity,[status(thm)],[33325])).
% 5.34/5.51 tff(33327,plain,
% 5.34/5.51 (~(s(s(z)) = s(elem!1))),
% 5.34/5.51 inference(modus_ponens,[status(thm)],[10912, 33326])).
% 5.34/5.51 tff(33328,plain,
% 5.34/5.51 (~b(s(elem!1), s(s(s(s(z)))))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[31823, 33324, 33327, 167])).
% 5.34/5.51 tff(33329,plain,
% 5.34/5.51 (r(s(elem!1), s(s(s(s(z)))))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[1084, 33328, 1369])).
% 5.34/5.51 tff(33330,plain,
% 5.34/5.51 (r(s(elem!1), s(s(elem!1)))),
% 5.34/5.51 inference(modus_ponens,[status(thm)],[33329, 16783])).
% 5.34/5.51 tff(33331,plain,
% 5.34/5.51 (~(s(elem!1) = s(s(elem!1)))),
% 5.34/5.51 inference(modus_ponens,[status(thm)],[2169, 8126])).
% 5.34/5.51 tff(33332,plain,
% 5.34/5.51 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[3356, 33331])).
% 5.34/5.51 tff(33333,plain,
% 5.34/5.51 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[3404, 33332])).
% 5.34/5.51 tff(33334,plain,
% 5.34/5.51 (b(s(s(s(elem!1))), elem!1)),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[32667, 2141, 32337, 2043, 32346, 10915, 18320])).
% 5.34/5.51 tff(33335,plain,
% 5.34/5.51 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[32388, 178, 2043, 33334, 5434, 27724])).
% 5.34/5.51 tff(33336,plain,
% 5.34/5.51 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[3409, 33335, 33333])).
% 5.34/5.51 tff(33337,plain,
% 5.34/5.51 (~r(s(s(s(elem!1))), s(elem!1))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[5980, 33336, 33330])).
% 5.34/5.51 tff(33338,plain,
% 5.34/5.51 (b(s(s(s(elem!1))), s(elem!1))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[373, 33337, 32346])).
% 5.34/5.51 tff(33339,plain,
% 5.34/5.51 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 5.34/5.51 inference(transitivity,[status(thm)],[32344, 7104])).
% 5.34/5.51 tff(33340,plain,
% 5.34/5.51 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 5.34/5.51 inference(monotonicity,[status(thm)],[33339])).
% 5.34/5.51 tff(33341,plain,
% 5.34/5.51 (~(s(elem!1) = s(s(s(elem!1))))),
% 5.34/5.51 inference(modus_ponens,[status(thm)],[11413, 33340])).
% 5.34/5.51 tff(33342,plain,
% 5.34/5.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 5.34/5.51 inference(rewrite,[status(thm)],[])).
% 5.34/5.51 tff(33343,plain,
% 5.34/5.51 (((~b(s(s(s(elem!1))), 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(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 5.34/5.51 inference(rewrite,[status(thm)],[])).
% 5.34/5.51 tff(33344,plain,
% 5.34/5.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 5.34/5.51 inference(monotonicity,[status(thm)],[33343])).
% 5.34/5.51 tff(33345,plain,
% 5.34/5.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 5.34/5.51 inference(transitivity,[status(thm)],[33344, 33342])).
% 5.34/5.51 tff(33346,plain,
% 5.34/5.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))),
% 5.34/5.51 inference(quant_inst,[status(thm)],[])).
% 5.34/5.51 tff(33347,plain,
% 5.34/5.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 5.34/5.51 inference(modus_ponens,[status(thm)],[33346, 33345])).
% 5.34/5.51 tff(33348,plain,
% 5.34/5.51 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[33347, 178, 2043, 33334, 5434, 27724])).
% 5.34/5.51 tff(33349,plain,
% 5.34/5.51 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[3375, 33348, 33332])).
% 5.34/5.51 tff(33350,plain,
% 5.34/5.51 (~r(s(elem!1), s(s(s(elem!1))))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[5994, 33349, 33330])).
% 5.34/5.51 tff(33351,plain,
% 5.34/5.51 (b(s(elem!1), s(s(s(elem!1))))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[5432, 33350, 33341])).
% 5.34/5.51 tff(33352,plain,
% 5.34/5.51 ($false),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[6736, 33351, 33338, 33324, 33322, 2043])).
% 5.34/5.51 tff(33353,plain,(b(s(elem!1), elem!1) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~(s(s(z)) = elem!1)) | (s(elem!1) = s(s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.51 tff(33354,plain,
% 5.34/5.51 (b(s(elem!1), elem!1)),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[33353, 33319, 33310, 33289, 33306, 31476, 33287])).
% 5.34/5.51 tff(33355,plain,
% 5.34/5.51 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[29941, 33354, 33304, 33302, 33295])).
% 5.34/5.51 tff(33356,plain,
% 5.34/5.51 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.34/5.51 inference(modus_ponens,[status(thm)],[33355, 33293])).
% 5.34/5.51 tff(33357,plain,
% 5.34/5.51 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[31522, 33356])).
% 5.34/5.51 tff(33358,plain,
% 5.34/5.51 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 5.34/5.51 inference(monotonicity,[status(thm)],[33290])).
% 5.34/5.51 tff(33359,plain,
% 5.34/5.51 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 5.34/5.51 inference(symmetry,[status(thm)],[33358])).
% 5.34/5.51 tff(33360,plain,
% 5.34/5.51 (s(s(elem!1)) = s(s(s(s(z))))),
% 5.34/5.51 inference(symmetry,[status(thm)],[33307])).
% 5.34/5.51 tff(33361,plain,
% 5.34/5.51 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 5.34/5.51 inference(monotonicity,[status(thm)],[33360])).
% 5.34/5.51 tff(33362,plain,
% 5.34/5.51 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 5.34/5.51 inference(transitivity,[status(thm)],[33361, 33359])).
% 5.34/5.51 tff(33363,plain,
% 5.34/5.51 ((~b(s(s(elem!1)), s(elem!1))) <=> (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 5.34/5.51 inference(monotonicity,[status(thm)],[33362])).
% 5.34/5.51 tff(33364,plain,
% 5.34/5.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 5.34/5.51 inference(rewrite,[status(thm)],[])).
% 5.34/5.51 tff(33365,plain,
% 5.34/5.51 (((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), 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(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 5.34/5.51 inference(rewrite,[status(thm)],[])).
% 5.34/5.51 tff(33366,plain,
% 5.34/5.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 5.34/5.51 inference(monotonicity,[status(thm)],[33365])).
% 5.34/5.51 tff(33367,plain,
% 5.34/5.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 5.34/5.51 inference(transitivity,[status(thm)],[33366, 33364])).
% 5.34/5.51 tff(33368,plain,
% 5.34/5.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 5.34/5.51 inference(quant_inst,[status(thm)],[])).
% 5.34/5.51 tff(33369,plain,
% 5.34/5.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 5.34/5.51 inference(modus_ponens,[status(thm)],[33368, 33367])).
% 5.34/5.51 tff(33370,plain,
% 5.34/5.51 ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[33369, 178, 33310, 33304, 33295])).
% 5.34/5.51 tff(33371,plain,
% 5.34/5.51 (~b(s(s(elem!1)), s(elem!1))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[33370, 33354])).
% 5.34/5.51 tff(33372,plain,
% 5.34/5.51 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 5.34/5.51 inference(modus_ponens,[status(thm)],[33371, 33363])).
% 5.34/5.51 tff(33373,plain,
% 5.34/5.51 (r(s(s(s(s(z)))), s(s(s(z))))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[11185, 33372])).
% 5.34/5.51 tff(33374,plain,
% 5.34/5.51 ($false),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[31525, 33373, 33357])).
% 5.34/5.51 tff(33375,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | b(s(s(z)), elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | b(z, s(s(z))) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 5.34/5.51 tff(33376,plain,
% 5.34/5.51 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[33375, 108, 32298, 32293, 3241, 33211, 28501, 5723])).
% 5.34/5.51 tff(33377,plain,
% 5.34/5.51 (b(z, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[271, 33376])).
% 5.34/5.51 tff(33378,plain,
% 5.34/5.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)))),
% 5.34/5.51 inference(rewrite,[status(thm)],[])).
% 5.34/5.51 tff(33379,plain,
% 5.34/5.51 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)))),
% 5.34/5.51 inference(rewrite,[status(thm)],[])).
% 5.34/5.51 tff(33380,plain,
% 5.34/5.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z))))),
% 5.34/5.51 inference(monotonicity,[status(thm)],[33379])).
% 5.34/5.51 tff(33381,plain,
% 5.34/5.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)))),
% 5.34/5.51 inference(transitivity,[status(thm)],[33380, 33378])).
% 5.34/5.51 tff(33382,plain,
% 5.34/5.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 5.34/5.51 inference(quant_inst,[status(thm)],[])).
% 5.34/5.51 tff(33383,plain,
% 5.34/5.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), z))),
% 5.34/5.51 inference(modus_ponens,[status(thm)],[33382, 33381])).
% 5.34/5.51 tff(33384,plain,
% 5.34/5.51 ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[33383, 178, 31575, 33377, 32298])).
% 5.34/5.51 tff(33385,plain,
% 5.34/5.51 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[33384, 33231])).
% 5.34/5.51 tff(33386,plain,
% 5.34/5.51 (r(s(s(s(s(z)))), s(s(s(z))))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[11185, 33385])).
% 5.34/5.51 tff(33387,plain,
% 5.34/5.51 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[31525, 33386])).
% 5.34/5.51 tff(33388,plain,
% 5.34/5.51 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.34/5.51 inference(unit_resolution,[status(thm)],[31522, 33387])).
% 5.34/5.51 tff(33389,plain,
% 5.34/5.51 (~r(z, s(s(s(z))))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[24302, 33229, 29994])).
% 5.34/5.52 tff(33390,plain,
% 5.34/5.52 (b(z, s(s(s(z))))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[4920, 33389])).
% 5.34/5.52 tff(33391,plain,
% 5.34/5.52 ($false),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[20712, 178, 33377, 33390, 33231, 32298, 33388])).
% 5.34/5.52 tff(33392,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | b(s(s(z)), elem!1) | b(z, s(s(z))) | b(elem!1, z) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.52 tff(33393,plain,
% 5.34/5.52 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[33392, 5723, 28501, 3241, 204])).
% 5.34/5.52 tff(33394,plain,
% 5.34/5.52 (b(s(s(s(s(s(s(s(z))))))), z)),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[133, 33393])).
% 5.34/5.52 tff(33395,plain,
% 5.34/5.52 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(z), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.52 inference(monotonicity,[status(thm)],[32708])).
% 5.34/5.52 tff(33396,plain,
% 5.34/5.52 (s(z) = s(elem!1)),
% 5.34/5.52 inference(symmetry,[status(thm)],[32708])).
% 5.34/5.52 tff(33397,plain,
% 5.34/5.52 ((s(s(s(s(s(s(s(z))))))) = s(z)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 5.34/5.52 inference(monotonicity,[status(thm)],[33396])).
% 5.34/5.52 tff(33398,plain,
% 5.34/5.52 ((s(s(s(s(s(s(s(z))))))) = s(z)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 5.34/5.52 inference(transitivity,[status(thm)],[33397, 377])).
% 5.34/5.52 tff(33399,plain,
% 5.34/5.52 ((~(s(s(s(s(s(s(s(z))))))) = s(z))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 5.34/5.52 inference(monotonicity,[status(thm)],[33398])).
% 5.34/5.52 tff(33400,plain,
% 5.34/5.52 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 5.34/5.52 inference(modus_ponens,[status(thm)],[612, 33399])).
% 5.34/5.52 tff(33401,plain,
% 5.34/5.52 (~(s(s(z)) = s(elem!1))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[1058, 33262])).
% 5.34/5.52 tff(33402,plain,
% 5.34/5.52 ((s(elem!1) = elem!1) <=> (s(elem!1) = z)),
% 5.34/5.52 inference(monotonicity,[status(thm)],[32707])).
% 5.34/5.52 tff(33403,plain,
% 5.34/5.52 ((s(elem!1) = z) <=> (s(elem!1) = elem!1)),
% 5.34/5.52 inference(symmetry,[status(thm)],[33402])).
% 5.34/5.52 tff(33404,plain,
% 5.34/5.52 ((~(s(elem!1) = z)) <=> (~(s(elem!1) = elem!1))),
% 5.34/5.52 inference(monotonicity,[status(thm)],[33403])).
% 5.34/5.52 tff(33405,plain,
% 5.34/5.52 (~(s(elem!1) = elem!1)),
% 5.34/5.52 inference(modus_ponens,[status(thm)],[769, 33404])).
% 5.34/5.52 tff(33406,plain,
% 5.34/5.52 ((s(elem!1) = s(s(elem!1))) <=> (s(z) = s(s(z)))),
% 5.34/5.52 inference(monotonicity,[status(thm)],[929, 930])).
% 5.34/5.52 tff(33407,plain,
% 5.34/5.52 ((s(z) = s(s(z))) <=> (s(elem!1) = s(s(elem!1)))),
% 5.34/5.52 inference(symmetry,[status(thm)],[33406])).
% 5.34/5.52 tff(33408,plain,
% 5.34/5.52 ((s(z) = s(s(z))) <=> (s(s(elem!1)) = s(elem!1))),
% 5.34/5.52 inference(transitivity,[status(thm)],[33407, 10922])).
% 5.34/5.52 tff(33409,plain,
% 5.34/5.52 ((~(s(z) = s(s(z)))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 5.34/5.52 inference(monotonicity,[status(thm)],[33408])).
% 5.34/5.52 tff(33410,plain,
% 5.34/5.52 ((s(z) = s(s(z))) <=> (s(elem!1) = s(s(z)))),
% 5.34/5.52 inference(monotonicity,[status(thm)],[6683])).
% 5.34/5.52 tff(33411,plain,
% 5.34/5.52 ((s(elem!1) = s(s(z))) <=> (s(z) = s(s(z)))),
% 5.34/5.52 inference(symmetry,[status(thm)],[33410])).
% 5.34/5.52 tff(33412,plain,
% 5.34/5.52 ((~(s(elem!1) = s(s(z)))) <=> (~(s(z) = s(s(z))))),
% 5.34/5.52 inference(monotonicity,[status(thm)],[33411])).
% 5.34/5.52 tff(33413,plain,
% 5.34/5.52 (~(s(z) = s(s(z)))),
% 5.34/5.52 inference(modus_ponens,[status(thm)],[31597, 33412])).
% 5.34/5.52 tff(33414,plain,
% 5.34/5.52 (~(s(s(elem!1)) = s(elem!1))),
% 5.34/5.52 inference(modus_ponens,[status(thm)],[33413, 33409])).
% 5.34/5.52 tff(33415,plain,
% 5.34/5.52 (r(s(elem!1), z)),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[28387, 1426, 12064])).
% 5.34/5.52 tff(33416,plain,
% 5.34/5.52 (~r(s(s(elem!1)), s(elem!1))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[997, 33415, 32450])).
% 5.34/5.52 tff(33417,plain,
% 5.34/5.52 (b(s(s(elem!1)), s(elem!1))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[1006, 33416, 33414])).
% 5.34/5.52 tff(33418,plain,
% 5.34/5.52 (b(s(s(z)), s(z))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[1015, 33417, 928])).
% 5.34/5.52 tff(33419,plain,
% 5.34/5.52 (b(s(elem!1), s(s(z)))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[421, 21856, 31597])).
% 5.34/5.52 tff(33420,plain,
% 5.34/5.52 (b(s(z), s(s(z)))),
% 5.34/5.52 inference(modus_ponens,[status(thm)],[33419, 14161])).
% 5.34/5.52 tff(33421,plain,
% 5.34/5.52 (~r(s(s(s(elem!1))), elem!1)),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[12762, 33420, 928, 30943, 1426, 33418])).
% 5.34/5.52 tff(33422,plain,
% 5.34/5.52 (b(s(s(s(elem!1))), elem!1)),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[570, 33421, 941])).
% 5.34/5.52 tff(33423,plain,
% 5.34/5.52 (b(s(s(s(z))), z)),
% 5.34/5.52 inference(modus_ponens,[status(thm)],[33422, 30617])).
% 5.34/5.52 tff(33424,plain,
% 5.34/5.52 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[21413, 33423, 27212, 31623, 204])).
% 5.34/5.52 tff(33425,plain,
% 5.34/5.52 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[20667, 33424])).
% 5.34/5.52 tff(33426,plain,
% 5.34/5.52 ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[1319, 178, 595, 146, 33423])).
% 5.34/5.52 tff(33427,plain,
% 5.34/5.52 (~b(z, s(s(s(z))))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[33426, 33425])).
% 5.34/5.52 tff(33428,plain,
% 5.34/5.52 (r(z, s(s(s(z))))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[4920, 33427])).
% 5.34/5.52 tff(33429,plain,
% 5.34/5.52 (r(elem!1, s(s(s(elem!1))))),
% 5.34/5.52 inference(modus_ponens,[status(thm)],[33428, 10724])).
% 5.34/5.52 tff(33430,plain,
% 5.34/5.52 (r(s(elem!1), s(s(s(s(z)))))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[1038, 33415, 28500, 167, 202, 928, 21856])).
% 5.34/5.52 tff(33431,plain,
% 5.34/5.52 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[25119, 33430])).
% 5.34/5.52 tff(33432,plain,
% 5.34/5.52 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[395, 33431, 14147])).
% 5.34/5.52 tff(33433,plain,
% 5.34/5.52 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.52 inference(modus_ponens,[status(thm)],[33432, 20647])).
% 5.34/5.52 tff(33434,plain,
% 5.34/5.52 ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z)))))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[32474, 178, 146, 33423, 33433])).
% 5.34/5.52 tff(33435,plain,
% 5.34/5.52 (~b(s(z), s(s(s(z))))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[33434, 33425])).
% 5.34/5.52 tff(33436,plain,
% 5.34/5.52 (~b(s(elem!1), s(s(s(elem!1))))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[25090, 33435, 928])).
% 5.34/5.52 tff(33437,plain,
% 5.34/5.52 (r(s(elem!1), s(s(s(elem!1))))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[5432, 33436, 5425])).
% 5.34/5.52 tff(33438,plain,
% 5.34/5.52 (~r(elem!1, s(s(s(elem!1))))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[9138, 33437, 1426])).
% 5.34/5.52 tff(33439,plain,
% 5.34/5.52 ($false),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[33438, 33429])).
% 5.34/5.52 tff(33440,plain,((~r(s(elem!1), elem!1)) | (~(elem!1 = z)) | (s(elem!1) = s(s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.52 tff(33441,plain,
% 5.34/5.52 (~r(s(elem!1), elem!1)),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[33440, 32707, 33273, 146, 595, 204, 167, 202, 32766])).
% 5.34/5.52 tff(33442,plain,
% 5.34/5.52 (b(s(elem!1), elem!1)),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[677, 33441, 33405])).
% 5.34/5.52 tff(33443,plain,
% 5.34/5.52 (b(s(elem!1), z)),
% 5.34/5.52 inference(modus_ponens,[status(thm)],[33442, 33260])).
% 5.34/5.52 tff(33444,plain,
% 5.34/5.52 (~b(s(elem!1), s(s(s(s(z)))))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[31823, 33443, 33401, 167])).
% 5.34/5.52 tff(33445,plain,
% 5.34/5.52 (r(s(elem!1), s(s(s(s(z)))))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[1084, 33444, 33251])).
% 5.34/5.52 tff(33446,plain,
% 5.34/5.52 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[25119, 33445])).
% 5.34/5.52 tff(33447,plain,
% 5.34/5.52 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[395, 33446, 33400])).
% 5.34/5.52 tff(33448,plain,
% 5.34/5.52 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.52 inference(modus_ponens,[status(thm)],[33447, 33395])).
% 5.34/5.52 tff(33449,plain,
% 5.34/5.52 (b(s(z), z) <=> b(s(elem!1), z)),
% 5.34/5.52 inference(monotonicity,[status(thm)],[33396])).
% 5.34/5.52 tff(33450,plain,
% 5.34/5.52 (b(s(elem!1), z) <=> b(s(z), z)),
% 5.34/5.52 inference(symmetry,[status(thm)],[33449])).
% 5.34/5.52 tff(33451,plain,
% 5.34/5.52 (b(s(elem!1), elem!1) <=> b(s(z), z)),
% 5.34/5.52 inference(transitivity,[status(thm)],[33260, 33450])).
% 5.34/5.52 tff(33452,plain,
% 5.34/5.52 (b(s(z), z)),
% 5.34/5.52 inference(modus_ponens,[status(thm)],[33442, 33451])).
% 5.34/5.52 tff(33453,plain,
% 5.34/5.52 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[32496, 178, 595, 33452, 146, 33448])).
% 5.34/5.52 tff(33454,plain,
% 5.34/5.52 (r(s(z), s(s(s(s(z)))))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[6689, 33445, 32707])).
% 5.34/5.52 tff(33455,plain,
% 5.34/5.52 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[4560, 118, 24592, 33454])).
% 5.34/5.52 tff(33456,plain,
% 5.34/5.52 ($false),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[615, 41, 612, 33455, 33453])).
% 5.34/5.52 tff(33457,plain,(r(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(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | b(s(s(z)), elem!1) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 5.34/5.52 tff(33458,plain,
% 5.34/5.52 (r(elem!1, z)),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[33457, 29578, 146, 167, 204, 202, 3241, 5723])).
% 5.34/5.52 tff(33459,plain,
% 5.34/5.52 (~r(s(s(z)), elem!1)),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[443, 33458, 28500])).
% 5.34/5.52 tff(33460,plain,
% 5.34/5.52 (s(s(z)) = elem!1),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[448, 33459, 3241])).
% 5.34/5.52 tff(33461,plain,
% 5.34/5.52 (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(s(z)))))),
% 5.34/5.52 inference(monotonicity,[status(thm)],[3507])).
% 5.34/5.52 tff(33462,plain,
% 5.34/5.52 (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(elem!1)))),
% 5.34/5.52 inference(symmetry,[status(thm)],[33461])).
% 5.34/5.52 tff(33463,plain,
% 5.34/5.52 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 5.34/5.52 inference(modus_ponens,[status(thm)],[24592, 33462])).
% 5.34/5.52 tff(33464,assumption,(~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))), introduced(assumption)).
% 5.34/5.52 tff(33465,plain,
% 5.34/5.52 ($false),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[33464, 33463])).
% 5.34/5.52 tff(33466,plain,(r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) | (~(s(s(z)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.52 tff(33467,plain,
% 5.34/5.52 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[33466, 33460])).
% 5.34/5.52 tff(33468,plain,
% 5.34/5.52 (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[8403, 32330])).
% 5.34/5.52 tff(33469,plain,
% 5.34/5.52 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 5.34/5.52 inference(monotonicity,[status(thm)],[33460])).
% 5.34/5.52 tff(33470,plain,
% 5.34/5.52 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 5.34/5.52 inference(transitivity,[status(thm)],[33469, 1526])).
% 5.34/5.52 tff(33471,plain,
% 5.34/5.52 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 5.34/5.52 inference(monotonicity,[status(thm)],[33470])).
% 5.34/5.52 tff(33472,plain,
% 5.34/5.52 (~(s(s(s(elem!1))) = elem!1)),
% 5.34/5.52 inference(modus_ponens,[status(thm)],[1683, 33471])).
% 5.34/5.52 tff(33473,plain,
% 5.34/5.52 (elem!1 = s(s(z))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[3230, 33460])).
% 5.34/5.52 tff(33474,plain,
% 5.34/5.52 (~(s(elem!1) = s(s(s(s(z)))))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[1353, 33473, 32144])).
% 5.34/5.52 tff(33475,plain,
% 5.34/5.52 (~(s(s(s(s(z)))) = s(elem!1))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[2168, 33474])).
% 5.34/5.52 tff(33476,plain,
% 5.34/5.52 (s(s(s(z))) = s(elem!1)),
% 5.34/5.52 inference(monotonicity,[status(thm)],[33460])).
% 5.34/5.52 tff(33477,plain,
% 5.34/5.52 (s(s(s(s(z)))) = s(s(elem!1))),
% 5.34/5.52 inference(monotonicity,[status(thm)],[33476])).
% 5.34/5.52 tff(33478,plain,
% 5.34/5.52 (s(s(elem!1)) = s(s(s(s(z))))),
% 5.34/5.52 inference(symmetry,[status(thm)],[33477])).
% 5.34/5.52 tff(33479,plain,
% 5.34/5.52 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 5.34/5.52 inference(monotonicity,[status(thm)],[33478])).
% 5.34/5.52 tff(33480,plain,
% 5.34/5.52 ((~b(s(s(elem!1)), s(elem!1))) <=> (~b(s(s(s(s(z)))), s(elem!1)))),
% 5.34/5.52 inference(monotonicity,[status(thm)],[33479])).
% 5.34/5.52 tff(33481,plain,
% 5.34/5.52 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(elem!1)))),
% 5.34/5.52 inference(monotonicity,[status(thm)],[33477])).
% 5.34/5.52 tff(33482,plain,
% 5.34/5.52 (b(elem!1, s(s(s(s(z)))))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[17989, 33460, 167])).
% 5.34/5.52 tff(33483,plain,
% 5.34/5.52 (b(elem!1, s(s(elem!1)))),
% 5.34/5.52 inference(modus_ponens,[status(thm)],[33482, 33481])).
% 5.34/5.52 tff(33484,plain,
% 5.34/5.52 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 5.34/5.52 inference(monotonicity,[status(thm)],[33477])).
% 5.34/5.52 tff(33485,plain,
% 5.34/5.52 (b(s(s(s(s(z)))), elem!1)),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[8526, 33460, 202])).
% 5.34/5.52 tff(33486,plain,
% 5.34/5.52 (b(s(s(elem!1)), elem!1)),
% 5.34/5.52 inference(modus_ponens,[status(thm)],[33485, 33484])).
% 5.34/5.52 tff(33487,plain,
% 5.34/5.52 ((elem!1 = s(s(s(z)))) <=> (elem!1 = s(elem!1))),
% 5.34/5.52 inference(monotonicity,[status(thm)],[33476])).
% 5.34/5.52 tff(33488,plain,
% 5.34/5.52 ((elem!1 = s(s(s(z)))) <=> (s(elem!1) = elem!1)),
% 5.34/5.52 inference(transitivity,[status(thm)],[33487, 3190])).
% 5.34/5.52 tff(33489,plain,
% 5.34/5.52 ((elem!1 = s(s(s(z)))) <=> (elem!1 = s(elem!1))),
% 5.34/5.52 inference(transitivity,[status(thm)],[33488, 3880])).
% 5.34/5.52 tff(33490,plain,
% 5.34/5.52 ((~(elem!1 = s(s(s(z))))) <=> (~(elem!1 = s(elem!1)))),
% 5.34/5.52 inference(monotonicity,[status(thm)],[33489])).
% 5.34/5.52 tff(33491,plain,
% 5.34/5.52 ((s(s(z)) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 5.34/5.52 inference(monotonicity,[status(thm)],[33460])).
% 5.34/5.52 tff(33492,plain,
% 5.34/5.52 ((~(s(s(z)) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 5.34/5.52 inference(monotonicity,[status(thm)],[33491])).
% 5.34/5.52 tff(33493,plain,
% 5.34/5.52 (~(elem!1 = s(s(s(z))))),
% 5.34/5.52 inference(modus_ponens,[status(thm)],[3205, 33492])).
% 5.34/5.52 tff(33494,plain,
% 5.34/5.52 (~(elem!1 = s(elem!1))),
% 5.34/5.52 inference(modus_ponens,[status(thm)],[33493, 33490])).
% 5.34/5.52 tff(33495,plain,
% 5.34/5.52 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[5361, 33460])).
% 5.34/5.52 tff(33496,plain,
% 5.34/5.52 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[11305, 33460, 224])).
% 5.34/5.52 tff(33497,plain,
% 5.34/5.52 (b(s(elem!1), s(s(z))) <=> b(s(elem!1), elem!1)),
% 5.34/5.52 inference(monotonicity,[status(thm)],[33460])).
% 5.34/5.52 tff(33498,plain,
% 5.34/5.52 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(z)))),
% 5.34/5.52 inference(symmetry,[status(thm)],[33497])).
% 5.34/5.52 tff(33499,plain,
% 5.34/5.52 ((~(elem!1 = s(s(s(z))))) <=> (~(s(elem!1) = elem!1))),
% 5.34/5.52 inference(monotonicity,[status(thm)],[33488])).
% 5.34/5.52 tff(33500,plain,
% 5.34/5.52 (~(s(elem!1) = elem!1)),
% 5.34/5.52 inference(modus_ponens,[status(thm)],[33493, 33499])).
% 5.34/5.52 tff(33501,plain,
% 5.34/5.52 (b(s(s(s(s(z)))), z) <=> b(s(s(elem!1)), z)),
% 5.34/5.52 inference(monotonicity,[status(thm)],[33477])).
% 5.34/5.52 tff(33502,plain,
% 5.34/5.52 (b(s(s(elem!1)), z)),
% 5.34/5.52 inference(modus_ponens,[status(thm)],[31623, 33501])).
% 5.34/5.52 tff(33503,plain,
% 5.34/5.52 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 5.34/5.52 inference(symmetry,[status(thm)],[9111])).
% 5.34/5.52 tff(33504,plain,
% 5.34/5.52 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 5.34/5.52 inference(transitivity,[status(thm)],[9109, 33503])).
% 5.34/5.52 tff(33505,plain,
% 5.34/5.52 ((~b(s(s(elem!1)), s(elem!1))) <=> (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 5.34/5.52 inference(monotonicity,[status(thm)],[33504])).
% 5.34/5.52 tff(33506,plain,
% 5.34/5.52 (r(s(elem!1), s(s(z)))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[7028, 1426, 10916])).
% 5.34/5.52 tff(33507,plain,
% 5.34/5.52 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[390, 33506, 224])).
% 5.34/5.52 tff(33508,plain,
% 5.34/5.52 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[395, 33507, 8112])).
% 5.34/5.52 tff(33509,plain,
% 5.34/5.52 (~r(s(elem!1), z)),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[13694, 1426, 437])).
% 5.34/5.52 tff(33510,plain,
% 5.34/5.52 (b(s(elem!1), z)),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[774, 33509])).
% 5.34/5.52 tff(33511,plain,
% 5.34/5.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(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))))))))))),
% 5.34/5.52 inference(rewrite,[status(thm)],[])).
% 5.34/5.52 tff(33512,plain,
% 5.34/5.52 (((~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(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(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))))))))))),
% 5.34/5.52 inference(rewrite,[status(thm)],[])).
% 5.34/5.52 tff(33513,plain,
% 5.34/5.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(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)))))))))))),
% 5.34/5.52 inference(monotonicity,[status(thm)],[33512])).
% 5.34/5.52 tff(33514,plain,
% 5.34/5.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(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))))))))))),
% 5.34/5.52 inference(transitivity,[status(thm)],[33513, 33511])).
% 5.34/5.52 tff(33515,plain,
% 5.34/5.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 5.34/5.52 inference(quant_inst,[status(thm)],[])).
% 5.34/5.52 tff(33516,plain,
% 5.34/5.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 5.34/5.52 inference(modus_ponens,[status(thm)],[33515, 33514])).
% 5.34/5.52 tff(33517,plain,
% 5.34/5.52 (~b(s(s(elem!1)), s(elem!1))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[33516, 178, 33510, 6604, 33508, 29578])).
% 5.34/5.52 tff(33518,plain,
% 5.34/5.52 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 5.34/5.52 inference(modus_ponens,[status(thm)],[33517, 33505])).
% 5.34/5.52 tff(33519,plain,
% 5.34/5.52 (b(s(s(s(z))), z)),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[7042, 33510, 10916])).
% 5.34/5.52 tff(33520,plain,
% 5.34/5.52 (b(z, s(elem!1)) <=> b(z, s(s(s(z))))),
% 5.34/5.52 inference(symmetry,[status(thm)],[8572])).
% 5.34/5.52 tff(33521,plain,
% 5.34/5.52 (~r(z, s(elem!1))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[7070, 1426, 32337])).
% 5.34/5.52 tff(33522,plain,
% 5.34/5.52 (b(z, s(elem!1))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[2351, 33521])).
% 5.34/5.52 tff(33523,plain,
% 5.34/5.52 (b(z, s(s(s(z))))),
% 5.34/5.52 inference(modus_ponens,[status(thm)],[33522, 33520])).
% 5.34/5.52 tff(33524,plain,
% 5.34/5.52 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[23358, 33523, 146, 29578, 33519])).
% 5.34/5.52 tff(33525,plain,
% 5.34/5.52 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[31522, 33524])).
% 5.34/5.52 tff(33526,plain,
% 5.34/5.52 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[31525, 33525])).
% 5.34/5.52 tff(33527,plain,
% 5.34/5.52 (b(s(s(s(s(z)))), s(s(s(z))))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[11185, 33526])).
% 5.34/5.52 tff(33528,plain,
% 5.34/5.52 ($false),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[33527, 33518])).
% 5.34/5.52 tff(33529,plain,((~r(s(elem!1), elem!1)) | (~(s(s(z)) = elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.52 tff(33530,plain,
% 5.34/5.52 (~r(s(elem!1), elem!1)),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[33529, 33460, 146, 33502, 224, 33458])).
% 5.34/5.52 tff(33531,plain,
% 5.34/5.52 (b(s(elem!1), elem!1)),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[677, 33530, 33500])).
% 5.34/5.52 tff(33532,plain,
% 5.34/5.52 (b(s(elem!1), s(s(z)))),
% 5.34/5.52 inference(modus_ponens,[status(thm)],[33531, 33498])).
% 5.34/5.52 tff(33533,plain,
% 5.34/5.52 (b(s(elem!1), s(s(s(s(z)))))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[1084, 26122, 1369])).
% 5.34/5.52 tff(33534,plain,
% 5.34/5.52 (b(s(s(z)), s(elem!1))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[1337, 10934, 1324, 10915])).
% 5.34/5.52 tff(33535,plain,
% 5.34/5.52 ($false),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[1079, 33534, 33533, 167, 202, 1070])).
% 5.34/5.52 tff(33536,plain,((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~(s(s(z)) = elem!1)) | (s(elem!1) = s(s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.52 tff(33537,plain,
% 5.34/5.52 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[33536, 33532, 202, 167, 33460, 33474, 33496])).
% 5.34/5.52 tff(33538,plain,
% 5.34/5.52 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[395, 33537, 33495])).
% 5.34/5.52 tff(33539,plain,
% 5.34/5.52 (b(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.34/5.52 inference(monotonicity,[status(thm)],[33460])).
% 5.34/5.52 tff(33540,plain,
% 5.34/5.52 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[33210, 204, 202, 167])).
% 5.34/5.52 tff(33541,plain,
% 5.34/5.52 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.34/5.52 inference(modus_ponens,[status(thm)],[33540, 33539])).
% 5.34/5.52 tff(33542,plain,
% 5.34/5.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 5.34/5.52 inference(rewrite,[status(thm)],[])).
% 5.34/5.52 tff(33543,plain,
% 5.34/5.52 (((~b(s(s(s(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(s(elem!1), 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(z, s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 5.34/5.52 inference(rewrite,[status(thm)],[])).
% 5.34/5.52 tff(33544,plain,
% 5.34/5.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(s(elem!1), 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(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 5.34/5.52 inference(monotonicity,[status(thm)],[33543])).
% 5.34/5.52 tff(33545,plain,
% 5.34/5.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(s(elem!1), 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(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 5.34/5.52 inference(transitivity,[status(thm)],[33544, 33542])).
% 5.34/5.52 tff(33546,plain,
% 5.34/5.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(s(elem!1), 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(z, s(elem!1))))),
% 5.34/5.52 inference(quant_inst,[status(thm)],[])).
% 5.34/5.52 tff(33547,plain,
% 5.34/5.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 5.34/5.52 inference(modus_ponens,[status(thm)],[33546, 33545])).
% 5.34/5.52 tff(33548,plain,
% 5.34/5.52 ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[33547, 178, 33531, 29578, 33541])).
% 5.34/5.52 tff(33549,plain,
% 5.34/5.52 (~b(z, s(elem!1))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[33548, 33538])).
% 5.34/5.52 tff(33550,plain,
% 5.34/5.52 (r(z, s(elem!1))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[2351, 33549])).
% 5.34/5.52 tff(33551,plain,
% 5.34/5.52 (~r(elem!1, s(elem!1))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[12189, 33550, 33458])).
% 5.34/5.52 tff(33552,plain,
% 5.34/5.52 (b(elem!1, s(elem!1))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[756, 33551, 33494])).
% 5.34/5.52 tff(33553,plain,
% 5.34/5.52 (~b(s(s(elem!1)), s(elem!1))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[32355, 178, 33531, 33552, 33486, 33483])).
% 5.34/5.52 tff(33554,plain,
% 5.34/5.52 (~b(s(s(s(s(z)))), s(elem!1))),
% 5.34/5.52 inference(modus_ponens,[status(thm)],[33553, 33480])).
% 5.34/5.52 tff(33555,plain,
% 5.34/5.52 (r(s(s(s(s(z)))), s(elem!1))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[2173, 33554, 33475])).
% 5.34/5.52 tff(33556,plain,
% 5.34/5.52 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 5.34/5.52 inference(transitivity,[status(thm)],[33470, 2486])).
% 5.34/5.52 tff(33557,plain,
% 5.34/5.52 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 5.34/5.52 inference(monotonicity,[status(thm)],[33556])).
% 5.34/5.52 tff(33558,plain,
% 5.34/5.52 (~(elem!1 = s(s(s(elem!1))))),
% 5.34/5.52 inference(modus_ponens,[status(thm)],[1683, 33557])).
% 5.34/5.52 tff(33559,plain,
% 5.34/5.52 ((s(elem!1) = s(s(z))) <=> (s(elem!1) = elem!1)),
% 5.34/5.52 inference(monotonicity,[status(thm)],[33460])).
% 5.34/5.52 tff(33560,plain,
% 5.34/5.52 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(z)))),
% 5.34/5.52 inference(symmetry,[status(thm)],[33559])).
% 5.34/5.52 tff(33561,plain,
% 5.34/5.52 ((elem!1 = s(s(s(z)))) <=> (s(elem!1) = s(s(z)))),
% 5.34/5.52 inference(transitivity,[status(thm)],[33488, 33560])).
% 5.34/5.52 tff(33562,plain,
% 5.34/5.52 ((~(elem!1 = s(s(s(z))))) <=> (~(s(elem!1) = s(s(z))))),
% 5.34/5.52 inference(monotonicity,[status(thm)],[33561])).
% 5.34/5.52 tff(33563,plain,
% 5.34/5.52 (~(s(elem!1) = s(s(z)))),
% 5.34/5.52 inference(modus_ponens,[status(thm)],[33493, 33562])).
% 5.34/5.52 tff(33564,plain,
% 5.34/5.52 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[2840, 33563])).
% 5.34/5.52 tff(33565,plain,
% 5.34/5.52 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 5.34/5.52 inference(monotonicity,[status(thm)],[33477])).
% 5.34/5.52 tff(33566,plain,
% 5.34/5.52 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 5.34/5.52 inference(monotonicity,[status(thm)],[33476, 33565])).
% 5.34/5.52 tff(33567,plain,
% 5.34/5.52 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 5.34/5.52 inference(transitivity,[status(thm)],[33566, 3881])).
% 5.34/5.52 tff(33568,plain,
% 5.34/5.52 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 5.34/5.52 inference(monotonicity,[status(thm)],[33567])).
% 5.34/5.52 tff(33569,plain,
% 5.34/5.52 (~(s(s(s(elem!1))) = s(elem!1))),
% 5.34/5.52 inference(modus_ponens,[status(thm)],[11413, 33568])).
% 5.34/5.52 tff(33570,plain,
% 5.34/5.52 (r(elem!1, s(s(s(elem!1))))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[6432, 6402, 2857, 3771, 1586, 356, 1301, 683, 6400, 854])).
% 5.34/5.52 tff(33571,plain,
% 5.34/5.52 (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[3623, 33570, 1265])).
% 5.34/5.52 tff(33572,plain,
% 5.34/5.52 (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.52 inference(unit_resolution,[status(thm)],[31409, 178, 32369, 32367, 595, 3664])).
% 5.34/5.52 tff(33573,plain,
% 5.34/5.53 ($false),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[3612, 41, 33572, 33571, 9361])).
% 5.34/5.53 tff(33574,plain,(r(s(s(s(elem!1))), elem!1) | (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (elem!1 = s(s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 5.34/5.53 tff(33575,plain,
% 5.34/5.53 (r(s(s(s(elem!1))), elem!1)),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[33574, 29578, 33468, 33541, 33496, 33531, 33569, 33550, 33552, 33564, 33485, 33558, 33482, 33555, 33472])).
% 5.34/5.53 tff(33576,plain,
% 5.34/5.53 (r(z, elem!1)),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[7053, 33460, 29994])).
% 5.34/5.53 tff(33577,plain,
% 5.34/5.53 (~r(s(s(s(elem!1))), z)),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[6378, 118, 33576, 33575])).
% 5.34/5.53 tff(33578,plain,
% 5.34/5.53 (b(s(s(s(elem!1))), z)),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[1565, 33577])).
% 5.34/5.53 tff(33579,plain,
% 5.34/5.53 (~r(z, s(s(s(elem!1))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[565, 33575, 33576])).
% 5.34/5.53 tff(33580,plain,
% 5.34/5.53 (b(z, s(s(s(elem!1))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[2095, 33579])).
% 5.34/5.53 tff(33581,plain,
% 5.34/5.53 (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[20514, 178, 33580, 33578, 29578, 146])).
% 5.34/5.53 tff(33582,plain,
% 5.34/5.53 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[3612, 41, 33581, 33468])).
% 5.34/5.53 tff(33583,plain,
% 5.34/5.53 ((s(elem!1) = s(s(elem!1))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 5.34/5.53 inference(monotonicity,[status(thm)],[33478])).
% 5.34/5.53 tff(33584,plain,
% 5.34/5.53 ((s(elem!1) = s(s(elem!1))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 5.34/5.53 inference(transitivity,[status(thm)],[33583, 2163])).
% 5.34/5.53 tff(33585,plain,
% 5.34/5.53 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(elem!1) = s(s(elem!1)))),
% 5.34/5.53 inference(symmetry,[status(thm)],[33584])).
% 5.34/5.53 tff(33586,plain,
% 5.34/5.53 ((~(s(s(s(s(z)))) = s(elem!1))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 5.34/5.53 inference(monotonicity,[status(thm)],[33585])).
% 5.34/5.53 tff(33587,plain,
% 5.34/5.53 (~(s(elem!1) = s(s(elem!1)))),
% 5.34/5.53 inference(modus_ponens,[status(thm)],[33475, 33586])).
% 5.34/5.53 tff(33588,plain,
% 5.34/5.53 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[3356, 33587])).
% 5.34/5.53 tff(33589,plain,
% 5.34/5.53 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[3404, 33588])).
% 5.34/5.53 tff(33590,plain,
% 5.34/5.53 (b(z, s(s(s(s(z))))) <=> b(z, s(s(elem!1)))),
% 5.34/5.53 inference(monotonicity,[status(thm)],[33477])).
% 5.34/5.53 tff(33591,plain,
% 5.34/5.53 (b(z, s(s(elem!1)))),
% 5.34/5.53 inference(modus_ponens,[status(thm)],[27212, 33590])).
% 5.34/5.53 tff(33592,plain,
% 5.34/5.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 5.34/5.53 inference(rewrite,[status(thm)],[])).
% 5.34/5.53 tff(33593,plain,
% 5.34/5.53 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(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(s(elem!1))), z)) | (~b(z, s(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)))))),
% 5.34/5.53 inference(rewrite,[status(thm)],[])).
% 5.34/5.53 tff(33594,plain,
% 5.34/5.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1))))))),
% 5.34/5.53 inference(monotonicity,[status(thm)],[33593])).
% 5.34/5.53 tff(33595,plain,
% 5.34/5.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 5.34/5.53 inference(transitivity,[status(thm)],[33594, 33592])).
% 5.34/5.53 tff(33596,plain,
% 5.34/5.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 5.34/5.53 inference(quant_inst,[status(thm)],[])).
% 5.34/5.53 tff(33597,plain,
% 5.34/5.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1))))),
% 5.34/5.53 inference(modus_ponens,[status(thm)],[33596, 33595])).
% 5.34/5.53 tff(33598,plain,
% 5.34/5.53 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[33597, 178, 33580, 33578, 33502, 33591])).
% 5.34/5.53 tff(33599,plain,
% 5.34/5.53 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[3409, 33598, 33589])).
% 5.34/5.53 tff(33600,plain,
% 5.34/5.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~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(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~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(elem!1)))))),
% 5.34/5.53 inference(rewrite,[status(thm)],[])).
% 5.34/5.53 tff(33601,plain,
% 5.34/5.53 (((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~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(elem!1)))))),
% 5.34/5.53 inference(rewrite,[status(thm)],[])).
% 5.34/5.53 tff(33602,plain,
% 5.34/5.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~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(elem!1))))))),
% 5.34/5.53 inference(monotonicity,[status(thm)],[33601])).
% 5.34/5.53 tff(33603,plain,
% 5.34/5.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~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(elem!1)))))),
% 5.34/5.53 inference(transitivity,[status(thm)],[33602, 33600])).
% 5.34/5.53 tff(33604,plain,
% 5.34/5.53 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 5.34/5.53 inference(quant_inst,[status(thm)],[])).
% 5.34/5.53 tff(33605,plain,
% 5.34/5.53 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 5.34/5.53 inference(modus_ponens,[status(thm)],[33604, 33603])).
% 5.34/5.53 tff(33606,plain,
% 5.34/5.53 ($false),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[33605, 118, 33599, 33582, 33467])).
% 5.34/5.53 tff(33607,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | b(s(s(z)), elem!1) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 5.34/5.53 tff(33608,plain,
% 5.34/5.53 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[33607, 33394, 32293, 31476, 3241, 204, 5723])).
% 5.34/5.53 tff(33609,plain,
% 5.34/5.53 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[249, 33608])).
% 5.34/5.53 tff(33610,plain,
% 5.34/5.53 (~b(s(s(s(z))), s(s(z)))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[33227, 3002, 1146, 166, 202])).
% 5.34/5.53 tff(33611,plain,
% 5.34/5.53 (r(s(s(s(z))), s(s(z)))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[4966, 33610])).
% 5.34/5.53 tff(33612,plain,
% 5.34/5.53 (~r(s(s(s(z))), z)),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[24599, 33611, 28500])).
% 5.34/5.53 tff(33613,plain,
% 5.34/5.53 (b(s(s(s(z))), z)),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[21073, 33612])).
% 5.34/5.53 tff(33614,plain,
% 5.34/5.53 (~r(z, s(s(s(z))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[24302, 33611, 29994])).
% 5.34/5.53 tff(33615,plain,
% 5.34/5.53 (b(z, s(s(s(z))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[4920, 33614])).
% 5.34/5.53 tff(33616,plain,
% 5.34/5.53 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[31529, 33615, 146, 33613, 3002])).
% 5.34/5.53 tff(33617,plain,
% 5.34/5.53 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[31522, 33616])).
% 5.34/5.53 tff(33618,plain,
% 5.34/5.53 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[31525, 33617])).
% 5.34/5.53 tff(33619,plain,
% 5.34/5.53 (b(s(s(s(s(z)))), s(s(s(z))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[11185, 33618])).
% 5.34/5.53 tff(33620,plain,
% 5.34/5.53 ($false),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[23651, 178, 27212, 168, 33615, 33619, 33613])).
% 5.34/5.53 tff(33621,plain,((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.53 tff(33622,plain,
% 5.34/5.53 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[33621, 33394, 31575, 33211, 33609, 32293])).
% 5.34/5.53 tff(33623,plain,
% 5.34/5.53 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[20667, 33622])).
% 5.34/5.53 tff(33624,plain,
% 5.34/5.53 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[24033, 33623, 31575, 27212, 204])).
% 5.34/5.53 tff(33625,plain,
% 5.34/5.53 (b(z, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[271, 33624])).
% 5.34/5.53 tff(33626,plain,
% 5.34/5.53 (r(elem!1, z)),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[33457, 33625, 33394, 31476, 204, 32293, 3241, 5723])).
% 5.34/5.53 tff(33627,plain,
% 5.34/5.53 (~r(s(s(z)), elem!1)),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[443, 33626, 28500])).
% 5.34/5.53 tff(33628,plain,
% 5.34/5.53 (s(s(z)) = elem!1),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[448, 33627, 3241])).
% 5.34/5.53 tff(33629,plain,
% 5.34/5.53 (s(s(s(z))) = s(elem!1)),
% 5.34/5.53 inference(monotonicity,[status(thm)],[33628])).
% 5.34/5.53 tff(33630,plain,
% 5.34/5.53 (s(s(s(s(z)))) = s(s(elem!1))),
% 5.34/5.53 inference(monotonicity,[status(thm)],[33629])).
% 5.34/5.53 tff(33631,plain,
% 5.34/5.53 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(elem!1)))),
% 5.34/5.53 inference(monotonicity,[status(thm)],[33630])).
% 5.34/5.53 tff(33632,plain,
% 5.34/5.53 (b(elem!1, s(s(s(s(z)))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[17989, 33628, 31476])).
% 5.34/5.53 tff(33633,plain,
% 5.34/5.53 (b(elem!1, s(s(elem!1)))),
% 5.34/5.53 inference(modus_ponens,[status(thm)],[33632, 33631])).
% 5.34/5.53 tff(33634,plain,
% 5.34/5.53 (s(s(elem!1)) = s(s(s(s(z))))),
% 5.34/5.53 inference(symmetry,[status(thm)],[33630])).
% 5.34/5.53 tff(33635,plain,
% 5.34/5.53 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 5.34/5.53 inference(monotonicity,[status(thm)],[33634])).
% 5.34/5.53 tff(33636,plain,
% 5.34/5.53 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), s(s(elem!1)))),
% 5.34/5.53 inference(symmetry,[status(thm)],[33635])).
% 5.34/5.53 tff(33637,plain,
% 5.34/5.53 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 5.34/5.53 inference(monotonicity,[status(thm)],[33629])).
% 5.34/5.53 tff(33638,plain,
% 5.34/5.53 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[21408, 33623, 204])).
% 5.34/5.53 tff(33639,plain,
% 5.34/5.53 (b(s(s(s(z))), s(s(s(s(z)))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[10755, 33638])).
% 5.34/5.53 tff(33640,plain,
% 5.34/5.53 (b(s(elem!1), s(s(s(s(z)))))),
% 5.34/5.53 inference(modus_ponens,[status(thm)],[33639, 33637])).
% 5.34/5.53 tff(33641,plain,
% 5.34/5.53 (b(s(elem!1), s(s(elem!1)))),
% 5.34/5.53 inference(modus_ponens,[status(thm)],[33640, 33636])).
% 5.34/5.53 tff(33642,plain,
% 5.34/5.53 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 5.34/5.53 inference(monotonicity,[status(thm)],[33630])).
% 5.34/5.53 tff(33643,plain,
% 5.34/5.53 (b(s(s(s(s(z)))), elem!1)),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[8526, 33628, 32293])).
% 5.34/5.53 tff(33644,plain,
% 5.34/5.53 (b(s(s(elem!1)), elem!1)),
% 5.34/5.53 inference(modus_ponens,[status(thm)],[33643, 33642])).
% 5.34/5.53 tff(33645,plain,
% 5.34/5.53 (~b(s(s(s(z))), z)),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[21413, 33623, 27212, 31575, 204])).
% 5.34/5.53 tff(33646,plain,
% 5.34/5.53 (elem!1 = s(s(z))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[3230, 33628])).
% 5.34/5.53 tff(33647,plain,
% 5.34/5.53 (~b(s(elem!1), z)),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[7042, 33646, 33645])).
% 5.34/5.53 tff(33648,plain,
% 5.34/5.53 (r(s(elem!1), z)),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[774, 33647])).
% 5.34/5.53 tff(33649,plain,
% 5.34/5.53 (~r(elem!1, s(elem!1))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[2711, 33648, 33626])).
% 5.34/5.53 tff(33650,plain,
% 5.34/5.53 (~r(s(elem!1), s(s(z)))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[2258, 33648, 28500])).
% 5.34/5.53 tff(33651,plain,
% 5.34/5.53 (~(elem!1 = s(s(s(elem!1))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[17414, 33650, 29994, 31476, 204, 32293, 33609, 33625, 33211])).
% 5.34/5.53 tff(33652,plain,
% 5.34/5.53 (~(s(s(s(elem!1))) = elem!1)),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[2489, 33651])).
% 5.34/5.53 tff(33653,plain,
% 5.34/5.53 (~(s(elem!1) = elem!1)),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[2150, 33652])).
% 5.34/5.53 tff(33654,plain,
% 5.34/5.53 (~(elem!1 = s(elem!1))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[748, 33653])).
% 5.34/5.53 tff(33655,plain,
% 5.34/5.53 (b(elem!1, s(elem!1))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[756, 33654, 33649])).
% 5.34/5.53 tff(33656,plain,
% 5.34/5.53 (~r(s(elem!1), elem!1)),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[13694, 33648, 33626])).
% 5.34/5.53 tff(33657,plain,
% 5.34/5.53 (b(s(elem!1), elem!1)),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[677, 33653, 33656])).
% 5.34/5.53 tff(33658,plain,
% 5.34/5.53 ($false),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[8538, 178, 33657, 33655, 33644, 33641, 33633])).
% 5.34/5.53 tff(33659,plain,(b(elem!1, z) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | b(s(s(z)), elem!1) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.53 tff(33660,plain,
% 5.34/5.53 (b(elem!1, z)),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[33659, 3241, 204, 28501])).
% 5.34/5.53 tff(33661,plain,
% 5.34/5.53 (~(z = elem!1)),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[6991, 33660])).
% 5.34/5.53 tff(33662,plain,
% 5.34/5.53 (~(elem!1 = s(s(z)))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[23817, 33660, 32295])).
% 5.34/5.53 tff(33663,plain,
% 5.34/5.53 (~(s(s(z)) = elem!1)),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[3230, 33662])).
% 5.34/5.53 tff(33664,plain,
% 5.34/5.53 (r(s(s(z)), elem!1)),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[448, 33663, 3241])).
% 5.34/5.53 tff(33665,plain,
% 5.34/5.53 (~r(z, elem!1)),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[8412, 33664, 29994])).
% 5.34/5.53 tff(33666,plain,
% 5.34/5.53 (b(z, elem!1)),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[585, 33665, 33661])).
% 5.34/5.53 tff(33667,plain,
% 5.34/5.53 (~b(s(s(s(s(z)))), elem!1)),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[27929, 178, 33666, 33660, 27212, 31575])).
% 5.34/5.53 tff(33668,plain,
% 5.34/5.53 (r(s(s(s(s(z)))), elem!1)),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[3142, 33667, 32296])).
% 5.34/5.53 tff(33669,plain,
% 5.34/5.53 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[25879, 33668])).
% 5.34/5.53 tff(33670,plain,
% 5.34/5.53 (~(elem!1 = s(s(s(s(z)))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[325, 32296])).
% 5.34/5.53 tff(33671,plain,
% 5.34/5.53 (~b(elem!1, s(s(s(s(z)))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[12519, 178, 33666, 33660, 27212, 31575])).
% 5.34/5.53 tff(33672,plain,
% 5.34/5.53 (r(elem!1, s(s(s(s(z)))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[483, 33671, 33670])).
% 5.34/5.53 tff(33673,plain,
% 5.34/5.53 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[25883, 33672])).
% 5.34/5.53 tff(33674,plain,
% 5.34/5.53 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[3102, 24392, 28500])).
% 5.34/5.53 tff(33675,plain,
% 5.34/5.53 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[249, 33674])).
% 5.34/5.53 tff(33676,plain,
% 5.34/5.53 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[29042, 24392, 168, 204])).
% 5.34/5.53 tff(33677,plain,
% 5.34/5.53 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[20667, 33676])).
% 5.34/5.53 tff(33678,plain,
% 5.34/5.53 (~b(s(s(s(z))), s(s(z)))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[33227, 33677, 1146, 33675, 202])).
% 5.34/5.53 tff(33679,plain,
% 5.34/5.53 (r(s(s(s(z))), s(s(z)))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[4966, 33678])).
% 5.34/5.53 tff(33680,plain,
% 5.34/5.53 (~r(s(s(s(z))), elem!1)),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[25248, 33679, 438])).
% 5.34/5.53 tff(33681,plain,
% 5.34/5.53 (~r(s(s(s(z))), z)),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[24599, 33679, 28500])).
% 5.34/5.53 tff(33682,plain,
% 5.34/5.53 (b(s(s(s(z))), z)),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[21073, 33681])).
% 5.34/5.53 tff(33683,plain,
% 5.34/5.53 (~r(z, s(s(s(z))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[24302, 33679, 29994])).
% 5.34/5.53 tff(33684,plain,
% 5.34/5.53 (b(z, s(s(s(z))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[4920, 33683])).
% 5.34/5.53 tff(33685,plain,
% 5.34/5.53 (~b(s(s(s(z))), elem!1)),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[23556, 178, 32146, 506, 33684, 33682])).
% 5.34/5.53 tff(33686,plain,
% 5.34/5.53 (s(s(s(z))) = elem!1),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[4981, 33685, 33680])).
% 5.34/5.53 tff(33687,plain,
% 5.34/5.53 (s(s(s(s(z)))) = s(elem!1)),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[30856, 33686])).
% 5.34/5.53 tff(33688,plain,
% 5.34/5.53 (s(elem!1) = s(s(s(s(z))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[2168, 33687])).
% 5.34/5.53 tff(33689,plain,
% 5.34/5.53 (~(s(s(s(elem!1))) = s(elem!1))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[13886, 33688])).
% 5.34/5.53 tff(33690,plain,
% 5.34/5.53 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 5.34/5.53 inference(monotonicity,[status(thm)],[33687])).
% 5.34/5.53 tff(33691,plain,
% 5.34/5.53 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 5.34/5.53 inference(monotonicity,[status(thm)],[33690])).
% 5.34/5.53 tff(33692,plain,
% 5.34/5.53 (s(s(s(s(s(s(s(z))))))) = s(s(s(s(elem!1))))),
% 5.34/5.53 inference(monotonicity,[status(thm)],[33691])).
% 5.34/5.53 tff(33693,plain,
% 5.34/5.53 (b(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(z)))),
% 5.34/5.53 inference(monotonicity,[status(thm)],[33692])).
% 5.34/5.53 tff(33694,plain,
% 5.34/5.53 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 5.34/5.53 inference(modus_ponens,[status(thm)],[1146, 33693])).
% 5.34/5.53 tff(33695,plain,
% 5.34/5.53 (~(elem!1 = s(s(s(elem!1))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[4830, 33686, 7200])).
% 5.34/5.53 tff(33696,plain,
% 5.34/5.53 (~(s(s(s(elem!1))) = elem!1)),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[2489, 33695])).
% 5.34/5.53 tff(33697,plain,
% 5.34/5.53 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[951, 33696])).
% 5.34/5.53 tff(33698,plain,
% 5.34/5.53 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[4343, 33697])).
% 5.34/5.53 tff(33699,plain,
% 5.34/5.53 (s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(z)))))))),
% 5.34/5.53 inference(symmetry,[status(thm)],[33692])).
% 5.34/5.53 tff(33700,plain,
% 5.34/5.53 (r(s(elem!1), s(s(s(s(elem!1))))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.53 inference(monotonicity,[status(thm)],[33699])).
% 5.34/5.53 tff(33701,plain,
% 5.34/5.53 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(s(s(elem!1)))))),
% 5.34/5.53 inference(symmetry,[status(thm)],[33700])).
% 5.34/5.53 tff(33702,plain,
% 5.34/5.53 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.53 inference(monotonicity,[status(thm)],[33687])).
% 5.34/5.53 tff(33703,plain,
% 5.34/5.53 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.53 inference(modus_ponens,[status(thm)],[204, 33702])).
% 5.34/5.53 tff(33704,plain,
% 5.34/5.53 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 5.34/5.53 inference(modus_ponens,[status(thm)],[33703, 33701])).
% 5.34/5.53 tff(33705,plain,
% 5.34/5.53 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[25879, 3132])).
% 5.34/5.53 tff(33706,plain,
% 5.34/5.53 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[28842, 125, 506])).
% 5.34/5.53 tff(33707,plain,
% 5.34/5.53 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[18193, 33706, 506, 32146, 644, 33705])).
% 5.34/5.53 tff(33708,plain,
% 5.34/5.53 (r(z, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[271, 33707])).
% 5.34/5.53 tff(33709,plain,
% 5.34/5.53 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 5.34/5.53 inference(monotonicity,[status(thm)],[2165])).
% 5.34/5.53 tff(33710,plain,
% 5.34/5.53 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 5.34/5.53 inference(monotonicity,[status(thm)],[33709])).
% 5.34/5.53 tff(33711,plain,
% 5.34/5.53 (s(s(s(s(s(s(s(z))))))) = s(s(s(s(elem!1))))),
% 5.34/5.53 inference(monotonicity,[status(thm)],[33710])).
% 5.34/5.53 tff(33712,plain,
% 5.34/5.53 (s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(z)))))))),
% 5.34/5.53 inference(symmetry,[status(thm)],[33711])).
% 5.34/5.53 tff(33713,plain,
% 5.34/5.53 (r(z, s(s(s(s(elem!1))))) <=> r(z, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.53 inference(monotonicity,[status(thm)],[33712])).
% 5.34/5.53 tff(33714,plain,
% 5.34/5.53 (r(z, s(s(s(s(s(s(s(z)))))))) <=> r(z, s(s(s(s(elem!1)))))),
% 5.34/5.53 inference(symmetry,[status(thm)],[33713])).
% 5.34/5.53 tff(33715,plain,
% 5.34/5.53 (r(z, s(s(s(s(elem!1)))))),
% 5.34/5.53 inference(modus_ponens,[status(thm)],[203, 33714])).
% 5.34/5.53 tff(33716,assumption,(~r(z, s(s(s(s(elem!1)))))), introduced(assumption)).
% 5.34/5.53 tff(33717,plain,
% 5.34/5.53 ($false),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[33716, 33715])).
% 5.34/5.53 tff(33718,plain,(r(z, s(s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~(s(s(s(s(z)))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.53 tff(33719,plain,
% 5.34/5.53 (r(z, s(s(s(s(elem!1)))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[33718, 33708, 33687])).
% 5.34/5.53 tff(33720,plain,
% 5.34/5.53 (b(s(s(s(s(z)))), z) <=> b(s(elem!1), z)),
% 5.34/5.53 inference(monotonicity,[status(thm)],[33687])).
% 5.34/5.53 tff(33721,plain,
% 5.34/5.53 (b(s(elem!1), z)),
% 5.34/5.53 inference(modus_ponens,[status(thm)],[168, 33720])).
% 5.34/5.53 tff(33722,plain,
% 5.34/5.53 (b(z, s(s(s(s(z))))) <=> b(z, s(elem!1))),
% 5.34/5.53 inference(monotonicity,[status(thm)],[33687])).
% 5.34/5.53 tff(33723,plain,
% 5.34/5.53 (b(z, s(elem!1))),
% 5.34/5.53 inference(modus_ponens,[status(thm)],[27212, 33722])).
% 5.34/5.53 tff(33724,plain,
% 5.34/5.53 (~r(s(elem!1), s(s(s(elem!1))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[5858, 118, 1876, 1451])).
% 5.34/5.53 tff(33725,plain,
% 5.34/5.53 (b(s(elem!1), s(s(s(elem!1))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[5432, 33724, 5396])).
% 5.34/5.53 tff(33726,plain,
% 5.34/5.53 (~r(s(s(s(elem!1))), s(elem!1))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[5885, 118, 1876, 1451])).
% 5.34/5.53 tff(33727,plain,
% 5.34/5.53 (b(s(s(s(elem!1))), s(elem!1))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[373, 33726, 356])).
% 5.34/5.53 tff(33728,assumption,(r(z, s(s(s(s(elem!1)))))), introduced(assumption)).
% 5.34/5.53 tff(33729,plain,
% 5.34/5.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))))),
% 5.34/5.53 inference(rewrite,[status(thm)],[])).
% 5.34/5.53 tff(33730,plain,
% 5.34/5.53 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))))),
% 5.34/5.53 inference(rewrite,[status(thm)],[])).
% 5.34/5.53 tff(33731,plain,
% 5.34/5.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1)))))))),
% 5.34/5.53 inference(monotonicity,[status(thm)],[33730])).
% 5.34/5.53 tff(33732,plain,
% 5.34/5.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))))),
% 5.34/5.53 inference(transitivity,[status(thm)],[33731, 33729])).
% 5.34/5.53 tff(33733,plain,
% 5.34/5.53 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))))),
% 5.34/5.53 inference(quant_inst,[status(thm)],[])).
% 5.34/5.53 tff(33734,plain,
% 5.34/5.53 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1)))))),
% 5.34/5.53 inference(modus_ponens,[status(thm)],[33733, 33732])).
% 5.34/5.53 tff(33735,plain,
% 5.34/5.53 (~r(z, s(s(s(elem!1))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[33734, 118, 1876, 33728])).
% 5.34/5.53 tff(33736,plain,
% 5.34/5.53 (b(z, s(s(s(elem!1))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[2095, 33735])).
% 5.34/5.53 tff(33737,plain,
% 5.34/5.53 ($false),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[6736, 33736, 33727, 855, 853, 33725])).
% 5.34/5.53 tff(33738,plain,((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.53 tff(33739,plain,
% 5.34/5.53 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[33738, 33723, 33721, 33689, 33719, 33704])).
% 5.34/5.53 tff(33740,plain,
% 5.34/5.53 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[1750, 33739, 33698])).
% 5.34/5.53 tff(33741,plain,
% 5.34/5.53 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 5.34/5.53 inference(monotonicity,[status(thm)],[33711])).
% 5.34/5.53 tff(33742,plain,
% 5.34/5.53 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 5.34/5.53 inference(symmetry,[status(thm)],[33741])).
% 5.34/5.53 tff(33743,plain,
% 5.34/5.53 (s(elem!1) = s(s(s(s(z))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[2168, 2165])).
% 5.34/5.53 tff(33744,plain,
% 5.34/5.53 (~(s(s(s(elem!1))) = s(elem!1))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[13886, 33743])).
% 5.34/5.53 tff(33745,plain,
% 5.34/5.53 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[1649, 33744])).
% 5.34/5.53 tff(33746,plain,
% 5.34/5.53 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[1657, 33745])).
% 5.34/5.53 tff(33747,plain,
% 5.34/5.53 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(z)), s(s(s(s(elem!1)))))),
% 5.34/5.53 inference(monotonicity,[status(thm)],[33711])).
% 5.34/5.53 tff(33748,plain,
% 5.34/5.53 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 5.34/5.53 inference(modus_ponens,[status(thm)],[33213, 33747])).
% 5.34/5.53 tff(33749,plain,
% 5.34/5.53 (~r(s(s(z)), s(s(s(elem!1))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[1831, 557, 28500])).
% 5.34/5.53 tff(33750,plain,
% 5.34/5.53 (b(s(s(z)), s(s(s(elem!1))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[4223, 33749])).
% 5.34/5.53 tff(33751,plain,
% 5.34/5.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 5.34/5.53 inference(rewrite,[status(thm)],[])).
% 5.34/5.53 tff(33752,plain,
% 5.34/5.53 (((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 5.34/5.53 inference(rewrite,[status(thm)],[])).
% 5.34/5.53 tff(33753,plain,
% 5.34/5.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1))))))))),
% 5.34/5.53 inference(monotonicity,[status(thm)],[33752])).
% 5.34/5.53 tff(33754,plain,
% 5.34/5.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 5.34/5.53 inference(transitivity,[status(thm)],[33753, 33751])).
% 5.34/5.53 tff(33755,plain,
% 5.34/5.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 5.34/5.53 inference(quant_inst,[status(thm)],[])).
% 5.34/5.53 tff(33756,plain,
% 5.34/5.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1))))))),
% 5.34/5.53 inference(modus_ponens,[status(thm)],[33755, 33754])).
% 5.34/5.53 tff(33757,plain,
% 5.34/5.53 ($false),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[33756, 178, 1518, 3898, 4291, 4401, 3709])).
% 5.34/5.53 tff(33758,plain,((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.53 tff(33759,plain,
% 5.34/5.53 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[33758, 33750, 4401, 33748, 3898])).
% 5.34/5.53 tff(33760,plain,
% 5.34/5.53 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[1988, 33759, 33746])).
% 5.34/5.53 tff(33761,plain,
% 5.34/5.53 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 5.34/5.53 inference(modus_ponens,[status(thm)],[33760, 33742])).
% 5.34/5.53 tff(33762,plain,
% 5.34/5.53 ($false),
% 5.34/5.53 inference(unit_resolution,[status(thm)],[17854, 33761])).
% 5.34/5.53 tff(33763,plain,((~r(z, s(s(s(elem!1))))) | (~(s(s(s(s(z)))) = s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.54 tff(33764,plain,
% 5.34/5.54 (~r(z, s(s(s(elem!1))))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[33763, 33687, 33740, 33694, 24392])).
% 5.34/5.54 tff(33765,plain,
% 5.34/5.54 (b(z, s(s(s(elem!1))))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[2095, 33764])).
% 5.34/5.54 tff(33766,plain,
% 5.34/5.54 (b(elem!1, s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.54 inference(monotonicity,[status(thm)],[33699])).
% 5.34/5.54 tff(33767,plain,
% 5.34/5.54 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 5.34/5.54 inference(symmetry,[status(thm)],[33766])).
% 5.34/5.54 tff(33768,plain,
% 5.34/5.54 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[691, 33706, 644])).
% 5.34/5.54 tff(33769,plain,
% 5.34/5.54 (b(elem!1, s(s(s(s(elem!1)))))),
% 5.34/5.54 inference(modus_ponens,[status(thm)],[33768, 33767])).
% 5.34/5.54 tff(33770,plain,
% 5.34/5.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 5.34/5.54 inference(rewrite,[status(thm)],[])).
% 5.34/5.54 tff(33771,plain,
% 5.34/5.54 (((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 5.34/5.54 inference(rewrite,[status(thm)],[])).
% 5.34/5.54 tff(33772,plain,
% 5.34/5.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 5.34/5.54 inference(monotonicity,[status(thm)],[33771])).
% 5.34/5.54 tff(33773,plain,
% 5.34/5.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 5.34/5.54 inference(transitivity,[status(thm)],[33772, 33770])).
% 5.34/5.54 tff(33774,plain,
% 5.34/5.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 5.34/5.54 inference(quant_inst,[status(thm)],[])).
% 5.34/5.54 tff(33775,plain,
% 5.34/5.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 5.34/5.54 inference(modus_ponens,[status(thm)],[33774, 33773])).
% 5.34/5.54 tff(33776,plain,
% 5.34/5.54 ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[33775, 178, 32146, 33769, 33740])).
% 5.34/5.54 tff(33777,plain,
% 5.34/5.54 (~b(s(s(s(elem!1))), elem!1)),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[33776, 33765])).
% 5.34/5.54 tff(33778,plain,
% 5.34/5.54 (s(elem!1) = s(s(s(s(z))))),
% 5.34/5.54 inference(symmetry,[status(thm)],[33687])).
% 5.34/5.54 tff(33779,plain,
% 5.34/5.54 (b(s(elem!1), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 5.34/5.54 inference(monotonicity,[status(thm)],[33778])).
% 5.34/5.54 tff(33780,plain,
% 5.34/5.54 (b(s(s(s(s(z)))), elem!1) <=> b(s(elem!1), elem!1)),
% 5.34/5.54 inference(symmetry,[status(thm)],[33779])).
% 5.34/5.54 tff(33781,plain,
% 5.34/5.54 ((~b(s(s(s(s(z)))), elem!1)) <=> (~b(s(elem!1), elem!1))),
% 5.34/5.54 inference(monotonicity,[status(thm)],[33780])).
% 5.34/5.54 tff(33782,plain,
% 5.34/5.54 (~b(s(s(s(s(z)))), elem!1)),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[27929, 178, 32146, 506, 27212, 168])).
% 5.34/5.54 tff(33783,plain,
% 5.34/5.54 (~b(s(elem!1), elem!1)),
% 5.34/5.54 inference(modus_ponens,[status(thm)],[33782, 33781])).
% 5.34/5.54 tff(33784,plain,
% 5.34/5.54 (r(s(s(s(elem!1))), elem!1)),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[570, 33777, 33696])).
% 5.34/5.54 tff(33785,plain,
% 5.34/5.54 (~b(s(s(s(elem!1))), s(elem!1))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[7117, 33784, 33783, 33723, 33721, 33765, 33689, 33777])).
% 5.34/5.54 tff(33786,plain,
% 5.34/5.54 (r(s(s(s(s(z)))), elem!1) <=> r(s(elem!1), elem!1)),
% 5.34/5.54 inference(monotonicity,[status(thm)],[33687])).
% 5.34/5.54 tff(33787,plain,
% 5.34/5.54 (r(s(elem!1), elem!1)),
% 5.34/5.54 inference(modus_ponens,[status(thm)],[3132, 33786])).
% 5.34/5.54 tff(33788,plain,
% 5.34/5.54 (~r(s(s(s(elem!1))), s(elem!1))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[1576, 33784, 33787])).
% 5.34/5.54 tff(33789,plain,
% 5.34/5.54 ($false),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[373, 33788, 33785, 33689])).
% 5.34/5.54 tff(33790,plain,(b(s(s(s(s(s(s(s(z))))))), z) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~b(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | r(elem!1, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.54 tff(33791,plain,
% 5.34/5.54 (b(s(s(s(s(s(s(s(z))))))), z)),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[33790, 33668, 204, 31575, 33211, 33660, 33664, 32293, 33673])).
% 5.34/5.54 tff(33792,plain,
% 5.34/5.54 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[4690, 203, 29994])).
% 5.34/5.54 tff(33793,plain,
% 5.34/5.54 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[249, 33792])).
% 5.34/5.54 tff(33794,plain,
% 5.34/5.54 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[24033, 203, 168, 27212, 204])).
% 5.34/5.54 tff(33795,plain,
% 5.34/5.54 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[20667, 33794])).
% 5.34/5.54 tff(33796,plain,
% 5.34/5.54 ($false),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[33621, 33795, 33793, 168, 1146, 146, 202])).
% 5.34/5.54 tff(33797,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), 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(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.54 tff(33798,plain,
% 5.34/5.54 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[33797, 33791, 33211, 31575, 32293, 204])).
% 5.34/5.54 tff(33799,plain,
% 5.34/5.54 (b(z, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[271, 33798])).
% 5.34/5.54 tff(33800,plain,
% 5.34/5.54 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[18193, 33799, 33660, 33666, 33673, 33669])).
% 5.34/5.54 tff(33801,plain,
% 5.34/5.54 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 5.34/5.54 inference(monotonicity,[status(thm)],[33800])).
% 5.34/5.54 tff(33802,plain,
% 5.34/5.54 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 5.34/5.54 inference(monotonicity,[status(thm)],[33801])).
% 5.34/5.54 tff(33803,plain,
% 5.34/5.54 (~(s(elem!1) = s(s(z)))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[2832, 33800])).
% 5.34/5.54 tff(33804,plain,
% 5.34/5.54 (s(s(s(s(s(s(s(s(z)))))))) = s(elem!1)),
% 5.34/5.54 inference(symmetry,[status(thm)],[33801])).
% 5.34/5.54 tff(33805,plain,
% 5.34/5.54 (b(s(s(s(s(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))))))))),
% 5.34/5.54 inference(monotonicity,[status(thm)],[33804])).
% 5.34/5.54 tff(33806,plain,
% 5.34/5.54 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.54 inference(symmetry,[status(thm)],[33805])).
% 5.34/5.54 tff(33807,plain,
% 5.34/5.54 (~(s(elem!1) = s(s(s(s(z)))))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[16181, 33800])).
% 5.34/5.54 tff(33808,plain,
% 5.34/5.54 (~(s(s(s(s(z)))) = s(elem!1))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[2168, 33807])).
% 5.34/5.54 tff(33809,plain,
% 5.34/5.54 (~(s(s(elem!1)) = elem!1)),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[2510, 33808, 33800])).
% 5.34/5.54 tff(33810,plain,
% 5.34/5.54 (~(s(elem!1) = elem!1)),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[672, 33809])).
% 5.34/5.54 tff(33811,plain,
% 5.34/5.54 (b(s(elem!1), s(s(z)))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[421, 21856, 10483])).
% 5.34/5.54 tff(33812,plain,
% 5.34/5.54 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 5.34/5.54 inference(modus_ponens,[status(thm)],[33811, 11737])).
% 5.34/5.54 tff(33813,plain,
% 5.34/5.54 (b(s(elem!1), s(s(s(s(z)))))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[1084, 22629, 16182])).
% 5.34/5.54 tff(33814,plain,
% 5.34/5.54 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[32842, 33813, 202, 679, 167])).
% 5.34/5.54 tff(33815,plain,
% 5.34/5.54 ($false),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[33814, 33812])).
% 5.34/5.54 tff(33816,plain,((~r(s(elem!1), elem!1)) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.54 tff(33817,plain,
% 5.34/5.54 (~r(s(elem!1), elem!1)),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[33816, 33800, 32293, 31476, 33664, 33668])).
% 5.34/5.54 tff(33818,plain,
% 5.34/5.54 (b(s(elem!1), elem!1)),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[677, 33817, 33810])).
% 5.34/5.54 tff(33819,plain,
% 5.34/5.54 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[686, 33818, 33800])).
% 5.34/5.54 tff(33820,plain,
% 5.34/5.54 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.54 inference(modus_ponens,[status(thm)],[33819, 33806])).
% 5.34/5.54 tff(33821,plain,
% 5.34/5.54 (b(s(s(z)), s(elem!1))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[1067, 28890, 16233])).
% 5.34/5.54 tff(33822,plain,
% 5.34/5.54 (b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 5.34/5.54 inference(modus_ponens,[status(thm)],[33821, 16232])).
% 5.34/5.54 tff(33823,plain,
% 5.34/5.54 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z)))))))))),
% 5.34/5.54 inference(modus_ponens,[status(thm)],[25678, 19271])).
% 5.34/5.54 tff(33824,plain,
% 5.34/5.54 (r(elem!1, s(elem!1)) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 5.34/5.54 inference(transitivity,[status(thm)],[19264, 19262])).
% 5.34/5.54 tff(33825,plain,
% 5.34/5.54 ((~r(elem!1, s(elem!1))) <=> (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))),
% 5.34/5.54 inference(monotonicity,[status(thm)],[33824])).
% 5.34/5.54 tff(33826,plain,
% 5.34/5.54 (~b(s(elem!1), s(s(s(s(z)))))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[25755, 2333, 29994, 167, 202, 10483, 28500])).
% 5.34/5.54 tff(33827,plain,
% 5.34/5.54 (r(s(elem!1), s(s(s(s(z)))))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[1084, 33826, 16182])).
% 5.34/5.54 tff(33828,plain,
% 5.34/5.54 (~r(elem!1, s(elem!1))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[14364, 33827, 470])).
% 5.34/5.54 tff(33829,plain,
% 5.34/5.54 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 5.34/5.54 inference(modus_ponens,[status(thm)],[33828, 33825])).
% 5.34/5.54 tff(33830,plain,
% 5.34/5.54 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[16349, 41, 33829])).
% 5.34/5.54 tff(33831,plain,
% 5.34/5.54 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[33830, 33823])).
% 5.34/5.54 tff(33832,plain,
% 5.34/5.54 (~r(s(elem!1), s(s(z)))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[11762, 2333, 29994])).
% 5.34/5.54 tff(33833,plain,
% 5.34/5.54 (b(s(elem!1), s(s(z)))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[421, 33832, 10483])).
% 5.34/5.54 tff(33834,plain,
% 5.34/5.54 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 5.34/5.54 inference(modus_ponens,[status(thm)],[33833, 11737])).
% 5.34/5.54 tff(33835,plain,
% 5.34/5.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 5.34/5.54 inference(rewrite,[status(thm)],[])).
% 5.34/5.54 tff(33836,plain,
% 5.34/5.54 (((~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(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(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(s(z)))))))), 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(s(z)))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 5.34/5.54 inference(rewrite,[status(thm)],[])).
% 5.34/5.54 tff(33837,plain,
% 5.34/5.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(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(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(s(z)))))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))))),
% 5.34/5.54 inference(monotonicity,[status(thm)],[33836])).
% 5.34/5.54 tff(33838,plain,
% 5.34/5.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(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(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(s(z)))))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 5.34/5.54 inference(transitivity,[status(thm)],[33837, 33835])).
% 5.34/5.54 tff(33839,plain,
% 5.34/5.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(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(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(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 5.34/5.54 inference(quant_inst,[status(thm)],[])).
% 5.34/5.54 tff(33840,plain,
% 5.34/5.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))),
% 5.34/5.54 inference(modus_ponens,[status(thm)],[33839, 33838])).
% 5.34/5.54 tff(33841,plain,
% 5.34/5.54 ($false),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[33840, 178, 1146, 33834, 33831, 16237, 33822])).
% 5.34/5.54 tff(33842,plain,((~r(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.54 tff(33843,plain,
% 5.34/5.54 (~r(z, s(elem!1))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[33842, 33820, 33211, 33800, 33672, 31476, 32293])).
% 5.34/5.54 tff(33844,plain,
% 5.34/5.54 (b(z, s(elem!1))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[2351, 33843])).
% 5.34/5.54 tff(33845,plain,
% 5.34/5.54 (~b(s(elem!1), z)),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[26790, 33844, 31575, 33660, 33666, 33672, 33800])).
% 5.34/5.54 tff(33846,plain,
% 5.34/5.54 (r(s(elem!1), z)),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[774, 33845])).
% 5.34/5.54 tff(33847,plain,
% 5.34/5.54 (~r(s(elem!1), s(s(z)))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[2258, 33846, 28500])).
% 5.34/5.54 tff(33848,plain,
% 5.34/5.54 (b(s(elem!1), s(s(z)))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[421, 33847, 33803])).
% 5.34/5.54 tff(33849,plain,
% 5.34/5.54 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 5.34/5.54 inference(modus_ponens,[status(thm)],[33848, 33802])).
% 5.34/5.54 tff(33850,plain,
% 5.34/5.54 (~(elem!1 = s(elem!1))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[748, 33810])).
% 5.34/5.54 tff(33851,plain,
% 5.34/5.54 (~b(elem!1, s(elem!1))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[1396, 33844, 33660, 33666, 33818])).
% 5.34/5.54 tff(33852,plain,
% 5.34/5.54 (r(elem!1, s(elem!1))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[756, 33851, 33850])).
% 5.34/5.54 tff(33853,plain,
% 5.34/5.54 (~r(s(elem!1), s(s(s(s(z)))))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[14364, 33852, 33672])).
% 5.34/5.54 tff(33854,plain,
% 5.34/5.54 (b(s(elem!1), s(s(s(s(z)))))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[1084, 33853, 33807])).
% 5.34/5.54 tff(33855,plain,
% 5.34/5.54 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[32842, 33854, 32293, 33800, 31476])).
% 5.34/5.54 tff(33856,plain,
% 5.34/5.54 ($false),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[33855, 33849])).
% 5.34/5.54 tff(33857,plain,(b(s(s(z)), elem!1) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.54 tff(33858,plain,
% 5.34/5.54 (b(s(s(z)), elem!1)),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[33857, 204, 28501])).
% 5.34/5.54 tff(33859,plain,
% 5.34/5.54 (~(elem!1 = z)),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[32554, 33858, 32295])).
% 5.34/5.54 tff(33860,plain,
% 5.34/5.54 (b(s(z), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.54 inference(symmetry,[status(thm)],[17783])).
% 5.34/5.54 tff(33861,plain,
% 5.34/5.54 ((~b(s(z), s(s(s(s(s(s(s(z))))))))) <=> (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 5.34/5.54 inference(monotonicity,[status(thm)],[33860])).
% 5.34/5.54 tff(33862,plain,
% 5.34/5.54 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[29042, 24392, 31623, 204])).
% 5.34/5.54 tff(33863,plain,
% 5.34/5.54 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[20667, 33862])).
% 5.34/5.54 tff(33864,plain,
% 5.34/5.54 (~b(s(s(s(z))), s(s(z)))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[33227, 33863, 33540, 33675, 202])).
% 5.34/5.54 tff(33865,plain,
% 5.34/5.54 (r(s(s(s(z))), s(s(z)))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[4966, 33864])).
% 5.34/5.54 tff(33866,plain,
% 5.34/5.54 (r(elem!1, z)),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[498, 5723, 33183])).
% 5.34/5.54 tff(33867,plain,
% 5.34/5.54 (~r(elem!1, s(s(z)))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[458, 33866, 28500])).
% 5.34/5.54 tff(33868,plain,
% 5.34/5.54 (b(elem!1, s(s(z)))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[467, 33867, 31605])).
% 5.34/5.54 tff(33869,plain,
% 5.34/5.54 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[29488, 701, 167, 1146, 812, 166, 469])).
% 5.34/5.54 tff(33870,plain,
% 5.34/5.54 (~r(s(s(s(s(z)))), elem!1)),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[25879, 33869])).
% 5.34/5.54 tff(33871,plain,
% 5.34/5.54 (b(s(s(s(s(z)))), elem!1)),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[3142, 33870, 551])).
% 5.34/5.54 tff(33872,plain,
% 5.34/5.54 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[17777, 33871, 812, 166, 202])).
% 5.34/5.54 tff(33873,plain,
% 5.34/5.54 (r(elem!1, s(s(s(s(z)))))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[24866, 33870, 167, 202, 551, 812])).
% 5.34/5.54 tff(33874,plain,
% 5.34/5.54 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[25883, 33873])).
% 5.34/5.54 tff(33875,plain,
% 5.34/5.54 ($false),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[691, 33874, 33872, 701])).
% 5.34/5.54 tff(33876,plain,((elem!1 = s(s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (elem!1 = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.54 tff(33877,plain,
% 5.34/5.54 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[33876, 33868, 202, 1146, 167, 166, 31624])).
% 5.34/5.54 tff(33878,plain,
% 5.34/5.54 (~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z))))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[24777, 33877, 33127])).
% 5.34/5.54 tff(33879,plain,
% 5.34/5.54 (~(s(elem!1) = s(s(z)))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[2832, 33877])).
% 5.34/5.54 tff(33880,plain,
% 5.34/5.54 (~(s(elem!1) = s(s(s(s(z)))))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[16181, 33877])).
% 5.34/5.54 tff(33881,plain,
% 5.34/5.54 (~(s(s(s(s(z)))) = s(elem!1))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[2168, 33880])).
% 5.34/5.54 tff(33882,plain,
% 5.34/5.54 (~(s(s(elem!1)) = elem!1)),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[2510, 33881, 33877])).
% 5.34/5.54 tff(33883,plain,
% 5.34/5.54 (~(s(elem!1) = elem!1)),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[672, 33882])).
% 5.34/5.54 tff(33884,plain,
% 5.34/5.54 (~r(s(elem!1), z)),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[31609, 33883, 1146, 817, 5723, 33879, 166, 167])).
% 5.34/5.54 tff(33885,plain,
% 5.34/5.54 (b(s(elem!1), z)),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[774, 33884])).
% 5.34/5.54 tff(33886,plain,
% 5.34/5.54 (b(s(s(s(s(s(s(s(s(z)))))))), z)),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[24205, 33885, 33877])).
% 5.34/5.54 tff(33887,plain,
% 5.34/5.54 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 5.34/5.54 inference(monotonicity,[status(thm)],[33877])).
% 5.34/5.54 tff(33888,plain,
% 5.34/5.54 (s(s(s(s(s(s(s(s(z)))))))) = s(elem!1)),
% 5.34/5.54 inference(symmetry,[status(thm)],[33887])).
% 5.34/5.54 tff(33889,plain,
% 5.34/5.54 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 5.34/5.54 inference(monotonicity,[status(thm)],[33888])).
% 5.34/5.54 tff(33890,plain,
% 5.34/5.54 (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(s(s(s(s(z)))))))))),
% 5.34/5.54 inference(symmetry,[status(thm)],[33889])).
% 5.34/5.54 tff(33891,plain,
% 5.34/5.54 (b(elem!1, s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 5.34/5.54 inference(monotonicity,[status(thm)],[33877])).
% 5.34/5.54 tff(33892,plain,
% 5.34/5.54 (~b(elem!1, s(s(s(s(z)))))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[491, 33868, 167, 202, 817])).
% 5.34/5.54 tff(33893,plain,
% 5.34/5.54 (r(elem!1, s(s(s(s(z)))))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[483, 33892, 31624])).
% 5.34/5.54 tff(33894,plain,
% 5.34/5.54 (~r(elem!1, s(elem!1))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[27585, 33893, 33866, 33880, 31623])).
% 5.34/5.54 tff(33895,plain,
% 5.34/5.54 (~(elem!1 = s(elem!1))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[748, 33883])).
% 5.34/5.54 tff(33896,plain,
% 5.34/5.54 (b(elem!1, s(elem!1))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[756, 33895, 33894])).
% 5.34/5.54 tff(33897,plain,
% 5.34/5.54 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 5.34/5.54 inference(modus_ponens,[status(thm)],[33896, 33891])).
% 5.34/5.54 tff(33898,plain,
% 5.34/5.54 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 5.34/5.54 inference(modus_ponens,[status(thm)],[33897, 33890])).
% 5.34/5.54 tff(33899,plain,
% 5.34/5.54 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[23651, 178, 27212, 31623, 32321, 30128])).
% 5.34/5.54 tff(33900,plain,
% 5.34/5.54 (r(s(s(s(s(z)))), s(s(s(z))))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[11185, 33899])).
% 5.34/5.54 tff(33901,plain,
% 5.34/5.54 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[31525, 33900])).
% 5.34/5.54 tff(33902,plain,
% 5.34/5.54 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.34/5.54 inference(unit_resolution,[status(thm)],[31522, 33901])).
% 5.34/5.54 tff(33903,plain,
% 5.34/5.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 5.34/5.54 inference(rewrite,[status(thm)],[])).
% 5.34/5.54 tff(33904,plain,
% 5.34/5.54 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(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))))) | (~b(s(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(s(s(s(s(z))))))))))) <=> ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 5.34/5.54 inference(rewrite,[status(thm)],[])).
% 5.34/5.54 tff(33905,plain,
% 5.34/5.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(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))))) | (~b(s(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(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))))),
% 5.34/5.54 inference(monotonicity,[status(thm)],[33904])).
% 5.34/5.54 tff(33906,plain,
% 5.34/5.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(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))))) | (~b(s(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(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 5.34/5.54 inference(transitivity,[status(thm)],[33905, 33903])).
% 5.34/5.54 tff(33907,plain,
% 5.34/5.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(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))))) | (~b(s(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(s(s(s(s(z)))))))))))),
% 5.34/5.54 inference(quant_inst,[status(thm)],[])).
% 5.34/5.54 tff(33908,plain,
% 5.34/5.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 5.34/5.55 inference(modus_ponens,[status(thm)],[33907, 33906])).
% 5.34/5.55 tff(33909,plain,
% 5.34/5.55 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[33908, 178, 30128, 33902, 33898, 33886])).
% 5.34/5.55 tff(33910,plain,
% 5.34/5.55 (r(s(elem!1), s(s(z))) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 5.34/5.55 inference(monotonicity,[status(thm)],[33887])).
% 5.34/5.55 tff(33911,plain,
% 5.34/5.55 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.55 inference(monotonicity,[status(thm)],[33877])).
% 5.34/5.55 tff(33912,plain,
% 5.34/5.55 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), elem!1)),
% 5.34/5.55 inference(symmetry,[status(thm)],[33911])).
% 5.34/5.55 tff(33913,plain,
% 5.34/5.55 ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) <=> (~r(s(elem!1), elem!1))),
% 5.34/5.55 inference(monotonicity,[status(thm)],[33912])).
% 5.34/5.55 tff(33914,plain,
% 5.34/5.55 (~(s(s(z)) = s(elem!1))),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[1058, 33879])).
% 5.34/5.55 tff(33915,plain,
% 5.34/5.55 (~b(s(elem!1), s(s(s(s(z)))))),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[31823, 33885, 33914, 167])).
% 5.34/5.55 tff(33916,plain,
% 5.34/5.55 (r(s(elem!1), s(s(s(s(z)))))),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[1084, 33915, 33880])).
% 5.34/5.55 tff(33917,plain,
% 5.34/5.55 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[25119, 33916])).
% 5.34/5.55 tff(33918,plain,
% 5.34/5.55 (~r(s(elem!1), elem!1)),
% 5.34/5.55 inference(modus_ponens,[status(thm)],[33917, 33913])).
% 5.34/5.55 tff(33919,plain,
% 5.34/5.55 (~b(s(elem!1), s(s(z)))),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[30697, 33918, 817, 33868, 33894, 33883])).
% 5.34/5.55 tff(33920,plain,
% 5.34/5.55 (r(s(elem!1), s(s(z)))),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[421, 33919, 33879])).
% 5.34/5.55 tff(33921,plain,
% 5.34/5.55 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 5.34/5.55 inference(modus_ponens,[status(thm)],[33920, 33910])).
% 5.34/5.55 tff(33922,plain,
% 5.34/5.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 5.34/5.55 inference(rewrite,[status(thm)],[])).
% 5.34/5.55 tff(33923,plain,
% 5.34/5.55 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 5.34/5.55 inference(quant_inst,[status(thm)],[])).
% 5.34/5.55 tff(33924,plain,
% 5.34/5.55 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 5.34/5.55 inference(modus_ponens,[status(thm)],[33923, 33922])).
% 5.34/5.55 tff(33925,plain,
% 5.34/5.55 (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[33924, 118, 1125, 33921])).
% 5.34/5.55 tff(33926,plain,
% 5.34/5.55 ($false),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[24832, 33925, 33909, 33878])).
% 5.34/5.55 tff(33927,plain,(b(elem!1, z) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.55 tff(33928,plain,
% 5.34/5.55 (b(elem!1, z)),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[33927, 33865, 817, 167, 33540, 33675, 202])).
% 5.34/5.55 tff(33929,plain,
% 5.34/5.55 (~b(s(s(s(s(z)))), elem!1)),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[32082, 178, 33928, 817, 31623, 167])).
% 5.34/5.55 tff(33930,plain,
% 5.34/5.55 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[123, 24392, 28500])).
% 5.34/5.55 tff(33931,plain,
% 5.34/5.55 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[28842, 33928, 125])).
% 5.34/5.55 tff(33932,plain,
% 5.34/5.55 (~b(s(s(s(z))), s(s(z)))),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[33227, 3002, 33540, 166, 202])).
% 5.34/5.55 tff(33933,plain,
% 5.34/5.55 (r(s(s(s(z))), s(s(z)))),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[4966, 33932])).
% 5.34/5.55 tff(33934,plain,
% 5.34/5.55 (b(elem!1, z)),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[33927, 33933, 817, 167, 33540, 166, 202])).
% 5.34/5.55 tff(33935,assumption,(s(s(s(z))) = s(elem!1)), introduced(assumption)).
% 5.34/5.55 tff(33936,plain,
% 5.34/5.55 (s(elem!1) = s(s(s(z)))),
% 5.34/5.55 inference(symmetry,[status(thm)],[33935])).
% 5.34/5.55 tff(33937,plain,
% 5.34/5.55 ($false),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[23528, 33936])).
% 5.34/5.55 tff(33938,plain,((~(s(s(s(z))) = s(elem!1))) | (s(elem!1) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.55 tff(33939,plain,
% 5.34/5.55 (~(s(s(s(z))) = s(elem!1))),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[33938, 33127])).
% 5.34/5.55 tff(33940,plain,
% 5.34/5.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(elem!1))))),
% 5.34/5.55 inference(rewrite,[status(thm)],[])).
% 5.34/5.55 tff(33941,plain,
% 5.34/5.55 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(elem!1))))),
% 5.34/5.55 inference(quant_inst,[status(thm)],[])).
% 5.34/5.55 tff(33942,plain,
% 5.34/5.55 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(elem!1)))),
% 5.34/5.55 inference(modus_ponens,[status(thm)],[33941, 33940])).
% 5.34/5.55 tff(33943,plain,
% 5.34/5.55 (~r(s(s(s(z))), s(elem!1))),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[33942, 118, 363, 1125])).
% 5.34/5.55 tff(33944,assumption,(~(s(s(s(z))) = s(elem!1))), introduced(assumption)).
% 5.34/5.55 tff(33945,plain,
% 5.34/5.55 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[15275, 363, 3575])).
% 5.34/5.55 tff(33946,plain,
% 5.34/5.55 (~b(s(elem!1), s(s(s(s(z)))))),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[31823, 28602, 1060, 167])).
% 5.34/5.55 tff(33947,plain,
% 5.34/5.55 (r(s(elem!1), s(s(s(s(z)))))),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[1084, 33946, 1369])).
% 5.34/5.55 tff(33948,plain,
% 5.34/5.55 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[25119, 33947])).
% 5.34/5.55 tff(33949,plain,
% 5.34/5.55 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[395, 33948, 33945])).
% 5.34/5.55 tff(33950,plain,
% 5.34/5.55 (~r(z, s(elem!1))),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[11762, 363, 29994])).
% 5.34/5.55 tff(33951,plain,
% 5.34/5.55 (b(z, s(elem!1))),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[2351, 33950])).
% 5.34/5.55 tff(33952,plain,
% 5.34/5.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(elem!1))))),
% 5.34/5.55 inference(rewrite,[status(thm)],[])).
% 5.34/5.55 tff(33953,plain,
% 5.34/5.55 (((~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(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(elem!1))))),
% 5.34/5.55 inference(rewrite,[status(thm)],[])).
% 5.34/5.55 tff(33954,plain,
% 5.34/5.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(elem!1)))))),
% 5.34/5.55 inference(monotonicity,[status(thm)],[33953])).
% 5.34/5.55 tff(33955,plain,
% 5.34/5.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(elem!1))))),
% 5.34/5.55 inference(transitivity,[status(thm)],[33954, 33952])).
% 5.34/5.55 tff(33956,plain,
% 5.34/5.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))))),
% 5.34/5.55 inference(quant_inst,[status(thm)],[])).
% 5.34/5.55 tff(33957,plain,
% 5.34/5.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(elem!1)))),
% 5.34/5.55 inference(modus_ponens,[status(thm)],[33956, 33955])).
% 5.34/5.55 tff(33958,plain,
% 5.34/5.55 (~b(s(s(s(z))), s(elem!1))),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[33957, 178, 33951, 33949, 32321, 3002])).
% 5.34/5.55 tff(33959,plain,
% 5.34/5.55 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1)) | r(s(s(s(z))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1)) | r(s(s(s(z))), s(elem!1)))),
% 5.34/5.55 inference(rewrite,[status(thm)],[])).
% 5.34/5.55 tff(33960,plain,
% 5.34/5.55 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1)) | r(s(s(s(z))), s(elem!1)))),
% 5.34/5.55 inference(quant_inst,[status(thm)],[])).
% 5.34/5.55 tff(33961,plain,
% 5.34/5.55 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1)) | r(s(s(s(z))), s(elem!1))),
% 5.34/5.55 inference(modus_ponens,[status(thm)],[33960, 33959])).
% 5.34/5.55 tff(33962,plain,
% 5.34/5.55 ($false),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[33961, 41, 33958, 33944, 33943])).
% 5.34/5.55 tff(33963,plain,((~r(s(elem!1), s(s(z)))) | (s(s(s(z))) = s(elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(z)))) | (s(elem!1) = s(s(s(s(z))))) | (s(s(z)) = s(elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | r(s(s(s(s(s(s(s(z))))))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.55 tff(33964,plain,
% 5.34/5.55 (~r(s(elem!1), s(s(z)))),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[33963, 2311, 3002, 33933, 1369, 33939, 167, 3575])).
% 5.34/5.55 tff(33965,plain,
% 5.34/5.55 (b(s(elem!1), s(s(z)))),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[421, 33964, 1056])).
% 5.34/5.55 tff(33966,plain,
% 5.34/5.55 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(z)), s(elem!1))),
% 5.34/5.55 inference(monotonicity,[status(thm)],[657])).
% 5.34/5.55 tff(33967,plain,
% 5.34/5.55 (b(s(s(z)), s(elem!1))),
% 5.34/5.55 inference(modus_ponens,[status(thm)],[166, 33966])).
% 5.34/5.55 tff(33968,plain,
% 5.34/5.55 (s(elem!1) = s(s(s(s(s(s(s(z)))))))),
% 5.34/5.55 inference(modus_ponens,[status(thm)],[657, 377])).
% 5.34/5.55 tff(33969,plain,
% 5.34/5.55 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(z)))) = elem!1)),
% 5.34/5.55 inference(monotonicity,[status(thm)],[15082])).
% 5.34/5.55 tff(33970,plain,
% 5.34/5.55 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 5.34/5.55 inference(monotonicity,[status(thm)],[33969])).
% 5.34/5.55 tff(33971,plain,
% 5.34/5.55 (~(s(s(s(s(z)))) = elem!1)),
% 5.34/5.55 inference(modus_ponens,[status(thm)],[3698, 33970])).
% 5.34/5.55 tff(33972,plain,
% 5.34/5.55 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[17305, 33971, 167, 204, 202, 817])).
% 5.34/5.55 tff(33973,plain,
% 5.34/5.55 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[691, 33972, 701])).
% 5.34/5.55 tff(33974,plain,
% 5.34/5.55 (b(elem!1, s(elem!1))),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[871, 33973, 33968])).
% 5.34/5.55 tff(33975,plain,
% 5.34/5.55 ($false),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[32264, 178, 683, 817, 33974, 33967, 1070])).
% 5.34/5.55 tff(33976,plain,((~(s(s(s(s(s(s(s(z))))))) = s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.55 tff(33977,plain,
% 5.34/5.55 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[33976, 683, 817, 1070, 701, 167, 204, 202, 166])).
% 5.34/5.55 tff(33978,plain,
% 5.34/5.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 5.34/5.55 inference(rewrite,[status(thm)],[])).
% 5.34/5.55 tff(33979,plain,
% 5.34/5.55 (((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 5.34/5.55 inference(rewrite,[status(thm)],[])).
% 5.34/5.55 tff(33980,plain,
% 5.34/5.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(elem!1), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 5.34/5.55 inference(monotonicity,[status(thm)],[33979])).
% 5.34/5.55 tff(33981,plain,
% 5.34/5.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(elem!1), 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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 5.34/5.55 inference(transitivity,[status(thm)],[33980, 33978])).
% 5.34/5.55 tff(33982,plain,
% 5.34/5.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 5.34/5.55 inference(quant_inst,[status(thm)],[])).
% 5.34/5.55 tff(33983,plain,
% 5.34/5.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 5.34/5.55 inference(modus_ponens,[status(thm)],[33982, 33981])).
% 5.34/5.55 tff(33984,plain,
% 5.34/5.55 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[33983, 178, 683, 817, 1070, 33540])).
% 5.34/5.55 tff(33985,plain,
% 5.34/5.55 ((s(s(s(s(s(s(s(z))))))) = s(elem!1)) | r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[806, 41, 33984])).
% 5.34/5.55 tff(33986,plain,
% 5.34/5.55 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[33985, 33977])).
% 5.34/5.55 tff(33987,plain,
% 5.34/5.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 5.34/5.55 inference(rewrite,[status(thm)],[])).
% 5.34/5.55 tff(33988,plain,
% 5.34/5.55 (((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 5.34/5.55 inference(rewrite,[status(thm)],[])).
% 5.34/5.55 tff(33989,plain,
% 5.34/5.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 5.34/5.55 inference(monotonicity,[status(thm)],[33988])).
% 5.34/5.55 tff(33990,plain,
% 5.34/5.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 5.34/5.55 inference(transitivity,[status(thm)],[33989, 33987])).
% 5.34/5.55 tff(33991,plain,
% 5.34/5.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 5.34/5.55 inference(quant_inst,[status(thm)],[])).
% 5.34/5.55 tff(33992,plain,
% 5.34/5.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 5.34/5.55 inference(modus_ponens,[status(thm)],[33991, 33990])).
% 5.34/5.55 tff(33993,plain,
% 5.34/5.55 (~b(s(s(s(s(z)))), s(elem!1))),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[33992, 178, 683, 817, 1070, 202])).
% 5.34/5.55 tff(33994,plain,
% 5.34/5.55 (r(s(s(s(s(z)))), s(elem!1))),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[2173, 33993, 2508])).
% 5.34/5.55 tff(33995,plain,
% 5.34/5.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(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(s(z)))))))),
% 5.34/5.55 inference(rewrite,[status(thm)],[])).
% 5.34/5.55 tff(33996,plain,
% 5.34/5.55 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 5.34/5.55 inference(quant_inst,[status(thm)],[])).
% 5.34/5.55 tff(33997,plain,
% 5.34/5.55 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 5.34/5.55 inference(modus_ponens,[status(thm)],[33996, 33995])).
% 5.34/5.55 tff(33998,plain,
% 5.34/5.55 ($false),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[33997, 118, 24592, 33994, 33986])).
% 5.34/5.55 tff(33999,plain,((~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(z)))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.55 tff(34000,plain,
% 5.34/5.55 (~b(s(elem!1), elem!1)),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[33999, 33965, 817, 701, 167, 204, 202, 166, 2169])).
% 5.34/5.55 tff(34001,plain,
% 5.34/5.55 (s(elem!1) = elem!1),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[677, 34000, 724])).
% 5.34/5.55 tff(34002,plain,
% 5.34/5.55 (s(s(s(elem!1))) = elem!1),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[2150, 34001])).
% 5.34/5.55 tff(34003,plain,
% 5.34/5.55 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[3907, 34002, 33964])).
% 5.34/5.55 tff(34004,plain,
% 5.34/5.55 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[1170, 34003])).
% 5.34/5.55 tff(34005,plain,
% 5.34/5.55 (s(s(elem!1)) = elem!1),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[672, 34001])).
% 5.34/5.55 tff(34006,plain,
% 5.34/5.55 (elem!1 = s(s(elem!1))),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[1546, 34005])).
% 5.34/5.55 tff(34007,plain,
% 5.34/5.55 (s(s(s(elem!1))) = s(elem!1)),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[1539, 34006])).
% 5.34/5.55 tff(34008,plain,
% 5.34/5.55 (elem!1 = s(s(s(s(elem!1))))),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[1509, 34007])).
% 5.34/5.55 tff(34009,plain,
% 5.34/5.55 (~(s(s(s(s(z)))) = elem!1)),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[338, 34005, 31965])).
% 5.34/5.55 tff(34010,plain,
% 5.34/5.55 (~(elem!1 = s(s(s(s(z)))))),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[325, 34009])).
% 5.34/5.55 tff(34011,plain,
% 5.34/5.55 (~b(elem!1, s(s(z)))),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[33876, 34010, 202, 33540, 167, 166, 701])).
% 5.34/5.55 tff(34012,plain,
% 5.34/5.55 ($false),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[3901, 34011, 34008, 34004])).
% 5.34/5.55 tff(34013,plain,((s(elem!1) = s(s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | r(s(elem!1), elem!1) | (~b(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(s(s(s(z))))) | r(s(s(s(s(s(s(s(z))))))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.55 tff(34014,plain,
% 5.34/5.55 (s(elem!1) = s(s(z))),
% 5.34/5.55 inference(unit_resolution,[status(thm)],[34013, 724, 167, 166, 701, 202, 817, 204, 3002, 1369, 3575])).
% 5.34/5.56 tff(34015,plain,
% 5.34/5.56 (b(s(elem!1), z) <=> b(s(s(z)), z)),
% 5.34/5.56 inference(monotonicity,[status(thm)],[515])).
% 5.34/5.56 tff(34016,plain,
% 5.34/5.56 (b(s(s(z)), z) <=> b(s(elem!1), z)),
% 5.34/5.56 inference(symmetry,[status(thm)],[34015])).
% 5.34/5.56 tff(34017,plain,
% 5.34/5.56 ((~b(s(s(z)), z)) <=> (~b(s(elem!1), z))),
% 5.34/5.56 inference(monotonicity,[status(thm)],[34016])).
% 5.34/5.56 tff(34018,plain,
% 5.34/5.56 (~b(s(elem!1), z)),
% 5.34/5.56 inference(modus_ponens,[status(thm)],[23814, 34017])).
% 5.34/5.56 tff(34019,plain,
% 5.34/5.56 ($false),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[853, 34018])).
% 5.34/5.56 tff(34020,plain,((~(s(elem!1) = s(s(z)))) | (~b(s(elem!1), z)) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 5.34/5.56 tff(34021,plain,
% 5.34/5.56 (~b(s(elem!1), z)),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[34020, 34014, 32417])).
% 5.34/5.56 tff(34022,plain,
% 5.34/5.56 (~(s(elem!1) = elem!1)),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[790, 34021, 33934])).
% 5.34/5.56 tff(34023,plain,
% 5.34/5.56 (b(s(elem!1), elem!1)),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[677, 34022, 724])).
% 5.34/5.56 tff(34024,plain,
% 5.34/5.56 (~b(s(s(s(s(z)))), elem!1)),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[32082, 178, 33934, 817, 31623, 167])).
% 5.34/5.56 tff(34025,plain,
% 5.34/5.56 (~(elem!1 = s(s(s(s(z)))))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[11438, 34014])).
% 5.34/5.56 tff(34026,plain,
% 5.34/5.56 (~(s(s(s(s(z)))) = elem!1)),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[504, 34025])).
% 5.34/5.56 tff(34027,plain,
% 5.34/5.56 (r(s(s(s(s(z)))), elem!1)),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[3142, 34026, 34024])).
% 5.34/5.56 tff(34028,plain,
% 5.34/5.56 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[25879, 34027])).
% 5.34/5.56 tff(34029,plain,
% 5.34/5.56 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[3444, 34028, 4245])).
% 5.34/5.56 tff(34030,plain,
% 5.34/5.56 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[17305, 34026, 167, 204, 202, 817])).
% 5.34/5.56 tff(34031,plain,
% 5.34/5.56 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[691, 34030, 701])).
% 5.34/5.56 tff(34032,plain,
% 5.34/5.56 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.56 inference(monotonicity,[status(thm)],[34014])).
% 5.34/5.56 tff(34033,plain,
% 5.34/5.56 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.56 inference(symmetry,[status(thm)],[34032])).
% 5.34/5.56 tff(34034,plain,
% 5.34/5.56 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.56 inference(modus_ponens,[status(thm)],[166, 34033])).
% 5.34/5.56 tff(34035,plain,
% 5.34/5.56 (b(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 5.34/5.56 inference(monotonicity,[status(thm)],[34014])).
% 5.34/5.56 tff(34036,plain,
% 5.34/5.56 (b(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 5.34/5.56 inference(symmetry,[status(thm)],[34035])).
% 5.34/5.56 tff(34037,plain,
% 5.34/5.56 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 5.34/5.56 inference(modus_ponens,[status(thm)],[33540, 34036])).
% 5.34/5.56 tff(34038,plain,
% 5.34/5.56 ($false),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[29941, 34037, 34034, 34031, 34029, 34023])).
% 5.34/5.56 tff(34039,plain,(r(s(elem!1), elem!1) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(s(s(s(z))))) | r(s(s(s(s(s(s(s(z))))))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.56 tff(34040,plain,
% 5.34/5.56 (r(s(elem!1), elem!1)),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[34039, 1369, 33931, 167, 204, 202, 817, 33863, 33675, 33930])).
% 5.34/5.56 tff(34041,plain,
% 5.34/5.56 (r(s(s(z)), elem!1) <=> r(s(elem!1), elem!1)),
% 5.34/5.56 inference(symmetry,[status(thm)],[1425])).
% 5.34/5.56 tff(34042,plain,
% 5.34/5.56 ((~r(s(s(z)), elem!1)) <=> (~r(s(elem!1), elem!1))),
% 5.34/5.56 inference(monotonicity,[status(thm)],[34041])).
% 5.34/5.56 tff(34043,plain,
% 5.34/5.56 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[17305, 25875, 167, 204, 202, 817])).
% 5.34/5.56 tff(34044,plain,
% 5.34/5.56 (r(s(s(s(s(z)))), elem!1)),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[3142, 25875, 33929])).
% 5.34/5.56 tff(34045,plain,
% 5.34/5.56 (~r(s(s(z)), elem!1)),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[33790, 34044, 204, 31623, 33540, 125, 33928, 202, 34043])).
% 5.34/5.56 tff(34046,plain,
% 5.34/5.56 (~r(s(elem!1), elem!1)),
% 5.34/5.56 inference(modus_ponens,[status(thm)],[34045, 34042])).
% 5.34/5.56 tff(34047,plain,
% 5.34/5.56 ($false),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[1426, 34046])).
% 5.34/5.56 tff(34048,plain,((~(s(elem!1) = s(s(z)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(s(s(s(z))))))), z) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.56 tff(34049,plain,
% 5.34/5.56 (~(s(elem!1) = s(s(z)))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[34048, 34040, 204, 125, 202, 167, 817])).
% 5.34/5.56 tff(34050,plain,
% 5.34/5.56 ($false),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[33963, 2278, 2311, 3002, 1125, 1369, 33944, 167, 3575])).
% 5.34/5.56 tff(34051,plain,((s(elem!1) = s(s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(z)))) | (s(elem!1) = s(s(s(s(z))))) | (s(s(s(z))) = s(elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | r(s(s(s(s(s(s(s(z))))))), s(s(z))) | b(s(elem!1), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.56 tff(34052,plain,
% 5.34/5.56 (b(s(elem!1), s(s(z)))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[34051, 34049, 33865, 1369, 33939, 167, 33930, 33863])).
% 5.34/5.56 tff(34053,plain,
% 5.34/5.56 (~r(z, s(elem!1))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[25755, 1069, 29994, 167, 202, 1056, 28500])).
% 5.34/5.56 tff(34054,plain,
% 5.34/5.56 ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[14207, 178, 1070, 27212, 202])).
% 5.34/5.56 tff(34055,plain,
% 5.34/5.56 (~b(z, s(elem!1))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[34054, 1069])).
% 5.34/5.56 tff(34056,plain,
% 5.34/5.56 ($false),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[2351, 34055, 34053])).
% 5.34/5.56 tff(34057,plain,((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (s(elem!1) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.56 tff(34058,plain,
% 5.34/5.56 (~b(s(elem!1), s(s(s(s(z)))))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[34057, 34052, 202, 167, 34049])).
% 5.34/5.56 tff(34059,plain,
% 5.34/5.56 (r(s(elem!1), s(s(s(s(z)))))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[1084, 34058, 1369])).
% 5.34/5.56 tff(34060,plain,
% 5.34/5.56 (~r(s(s(s(s(z)))), elem!1)),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[7010, 34059, 34040])).
% 5.34/5.56 tff(34061,plain,
% 5.34/5.56 (s(s(s(s(z)))) = elem!1),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[3142, 34060, 33929])).
% 5.34/5.56 tff(34062,plain,
% 5.34/5.56 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(z))), elem!1)),
% 5.34/5.56 inference(monotonicity,[status(thm)],[34061])).
% 5.34/5.56 tff(34063,plain,
% 5.34/5.56 (~r(s(s(s(z))), z)),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[24599, 33865, 28500])).
% 5.34/5.56 tff(34064,plain,
% 5.34/5.56 (b(s(s(s(z))), z)),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[21073, 34063])).
% 5.34/5.56 tff(34065,plain,
% 5.34/5.56 (~r(z, s(s(s(z))))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[24302, 33865, 29994])).
% 5.34/5.56 tff(34066,plain,
% 5.34/5.56 (b(z, s(s(s(z))))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[4920, 34065])).
% 5.34/5.56 tff(34067,plain,
% 5.34/5.56 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[21518, 178, 27212, 31623, 34066, 34064])).
% 5.34/5.56 tff(34068,plain,
% 5.34/5.56 (r(s(s(s(z))), s(s(s(s(z)))))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[10755, 34067])).
% 5.34/5.56 tff(34069,plain,
% 5.34/5.56 (r(s(s(s(z))), elem!1)),
% 5.34/5.56 inference(modus_ponens,[status(thm)],[34068, 34062])).
% 5.34/5.56 tff(34070,plain,
% 5.34/5.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))),
% 5.34/5.56 inference(rewrite,[status(thm)],[])).
% 5.34/5.56 tff(34071,plain,
% 5.34/5.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))),
% 5.34/5.56 inference(quant_inst,[status(thm)],[])).
% 5.34/5.56 tff(34072,plain,
% 5.34/5.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1)))),
% 5.34/5.56 inference(modus_ponens,[status(thm)],[34071, 34070])).
% 5.34/5.56 tff(34073,plain,
% 5.34/5.56 (~r(s(s(s(z))), s(elem!1))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[34072, 118, 34040, 34069])).
% 5.34/5.56 tff(34074,plain,
% 5.34/5.56 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[25119, 34059])).
% 5.34/5.56 tff(34075,plain,
% 5.34/5.56 (s(s(s(s(s(z))))) = s(elem!1)),
% 5.34/5.56 inference(monotonicity,[status(thm)],[34061])).
% 5.34/5.56 tff(34076,plain,
% 5.34/5.56 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 5.34/5.56 inference(monotonicity,[status(thm)],[34075])).
% 5.34/5.56 tff(34077,plain,
% 5.34/5.56 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 5.34/5.56 inference(monotonicity,[status(thm)],[34076])).
% 5.34/5.56 tff(34078,plain,
% 5.34/5.56 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 5.34/5.56 inference(symmetry,[status(thm)],[34077])).
% 5.34/5.56 tff(34079,plain,
% 5.34/5.56 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 5.34/5.56 inference(monotonicity,[status(thm)],[34078])).
% 5.34/5.56 tff(34080,plain,
% 5.34/5.56 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 5.34/5.56 inference(transitivity,[status(thm)],[34079, 377])).
% 5.34/5.56 tff(34081,plain,
% 5.34/5.56 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 5.34/5.56 inference(monotonicity,[status(thm)],[34080])).
% 5.34/5.56 tff(34082,plain,
% 5.34/5.56 (~(s(s(elem!1)) = elem!1)),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[338, 34061, 31965])).
% 5.34/5.56 tff(34083,plain,
% 5.34/5.56 (~(s(s(s(elem!1))) = s(elem!1))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[348, 34082])).
% 5.34/5.56 tff(34084,plain,
% 5.34/5.56 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 5.34/5.56 inference(modus_ponens,[status(thm)],[34083, 34081])).
% 5.34/5.56 tff(34085,plain,
% 5.34/5.56 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[395, 34084, 34074])).
% 5.34/5.56 tff(34086,plain,
% 5.34/5.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), 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(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), 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(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(elem!1))))),
% 5.34/5.56 inference(rewrite,[status(thm)],[])).
% 5.34/5.56 tff(34087,plain,
% 5.34/5.56 (((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(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(z))), s(elem!1)))) <=> ((~b(s(elem!1), 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(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(elem!1))))),
% 5.34/5.56 inference(rewrite,[status(thm)],[])).
% 5.34/5.56 tff(34088,plain,
% 5.34/5.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(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(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), 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(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(elem!1)))))),
% 5.34/5.56 inference(monotonicity,[status(thm)],[34087])).
% 5.34/5.56 tff(34089,plain,
% 5.34/5.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(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(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), 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(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(elem!1))))),
% 5.34/5.56 inference(transitivity,[status(thm)],[34088, 34086])).
% 5.34/5.56 tff(34090,plain,
% 5.34/5.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(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(z))), s(elem!1))))),
% 5.34/5.56 inference(quant_inst,[status(thm)],[])).
% 5.34/5.56 tff(34091,plain,
% 5.34/5.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(elem!1)))),
% 5.34/5.56 inference(modus_ponens,[status(thm)],[34090, 34089])).
% 5.34/5.56 tff(34092,plain,
% 5.34/5.56 ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(elem!1)))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[34091, 178, 34052, 33540, 33863])).
% 5.34/5.56 tff(34093,plain,
% 5.34/5.56 (~b(s(s(s(z))), s(elem!1))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[34092, 34085])).
% 5.34/5.56 tff(34094,plain,
% 5.34/5.56 ($false),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[33961, 41, 34093, 33939, 34073])).
% 5.34/5.56 tff(34095,plain,((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(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(s(s(s(z))))))), z) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.56 tff(34096,plain,
% 5.34/5.56 (s(elem!1) = s(s(s(s(z))))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[34095, 125, 167, 204, 202, 817])).
% 5.34/5.56 tff(34097,plain,
% 5.34/5.56 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 5.34/5.56 inference(monotonicity,[status(thm)],[34096])).
% 5.34/5.56 tff(34098,plain,
% 5.34/5.56 (elem!1 = s(s(s(z)))),
% 5.34/5.56 inference(transitivity,[status(thm)],[517, 34097, 11])).
% 5.34/5.56 tff(34099,plain,
% 5.34/5.56 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(z))))),
% 5.34/5.56 inference(monotonicity,[status(thm)],[34098])).
% 5.34/5.56 tff(34100,plain,
% 5.34/5.56 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), elem!1)),
% 5.34/5.56 inference(symmetry,[status(thm)],[34099])).
% 5.34/5.56 tff(34101,plain,
% 5.34/5.56 ((~b(s(s(z)), s(s(s(z))))) <=> (~b(s(s(z)), elem!1))),
% 5.34/5.56 inference(monotonicity,[status(thm)],[34100])).
% 5.34/5.56 tff(34102,plain,
% 5.34/5.56 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[23651, 178, 27212, 31623, 34066, 34064])).
% 5.34/5.56 tff(34103,plain,
% 5.34/5.56 (r(s(s(s(s(z)))), s(s(s(z))))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[11185, 34102])).
% 5.34/5.56 tff(34104,plain,
% 5.34/5.56 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[31525, 34103])).
% 5.34/5.56 tff(34105,plain,
% 5.34/5.56 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[31522, 34104])).
% 5.34/5.56 tff(34106,plain,
% 5.34/5.56 (~b(s(s(z)), s(s(s(z))))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[27335, 34105, 33540, 33675, 33863])).
% 5.34/5.56 tff(34107,plain,
% 5.34/5.56 (~b(s(s(z)), elem!1)),
% 5.34/5.56 inference(modus_ponens,[status(thm)],[34106, 34101])).
% 5.34/5.56 tff(34108,plain,
% 5.34/5.56 ($false),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[817, 34107])).
% 5.34/5.56 tff(34109,plain,(b(s(s(s(s(s(s(s(z))))))), z) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.56 tff(34110,plain,
% 5.34/5.56 (b(s(s(s(s(s(s(s(z))))))), z)),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[34109, 817, 167, 204, 202])).
% 5.34/5.56 tff(34111,plain,
% 5.34/5.56 (~b(s(s(s(z))), z)),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[21413, 8216, 27212, 31623, 204])).
% 5.34/5.56 tff(34112,plain,
% 5.34/5.56 (r(s(s(s(z))), z)),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[21073, 34111])).
% 5.34/5.56 tff(34113,plain,
% 5.34/5.56 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[31809, 34112, 167])).
% 5.34/5.56 tff(34114,plain,
% 5.34/5.56 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[31522, 34113])).
% 5.34/5.56 tff(34115,plain,
% 5.34/5.56 (~r(s(s(s(z))), s(s(z)))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[24599, 34112, 28500])).
% 5.34/5.56 tff(34116,plain,
% 5.34/5.56 (b(s(s(s(z))), s(s(z)))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[4966, 34115])).
% 5.34/5.56 tff(34117,plain,
% 5.34/5.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), 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(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), 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(z))), s(s(z)))))),
% 5.34/5.56 inference(rewrite,[status(thm)],[])).
% 5.34/5.56 tff(34118,plain,
% 5.34/5.56 (((~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(z))), s(s(z)))) | (~b(s(s(s(s(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(s(z)))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), 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(z))), s(s(z)))))),
% 5.34/5.56 inference(rewrite,[status(thm)],[])).
% 5.34/5.56 tff(34119,plain,
% 5.34/5.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(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(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), 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(z))), s(s(z))))))),
% 5.34/5.56 inference(monotonicity,[status(thm)],[34118])).
% 5.34/5.56 tff(34120,plain,
% 5.34/5.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(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(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), 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(z))), s(s(z)))))),
% 5.34/5.56 inference(transitivity,[status(thm)],[34119, 34117])).
% 5.34/5.56 tff(34121,plain,
% 5.34/5.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(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(s(z))))))),
% 5.34/5.56 inference(quant_inst,[status(thm)],[])).
% 5.34/5.56 tff(34122,plain,
% 5.34/5.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 5.34/5.56 inference(modus_ponens,[status(thm)],[34121, 34120])).
% 5.34/5.56 tff(34123,plain,
% 5.34/5.56 ($false),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[34122, 178, 167, 21410, 34116, 1146, 34114])).
% 5.34/5.56 tff(34124,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.56 tff(34125,plain,
% 5.34/5.56 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[34124, 33540, 167, 204])).
% 5.34/5.56 tff(34126,plain,
% 5.34/5.56 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[20667, 34125])).
% 5.34/5.56 tff(34127,plain,
% 5.34/5.56 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[33621, 34126, 31623, 33540, 34110, 202])).
% 5.34/5.56 tff(34128,plain,
% 5.34/5.56 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[10835, 34127, 817])).
% 5.34/5.56 tff(34129,plain,
% 5.34/5.56 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[703, 34128])).
% 5.34/5.56 tff(34130,plain,
% 5.34/5.56 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[33797, 34110, 33540, 31623, 202, 204])).
% 5.34/5.56 tff(34131,plain,
% 5.34/5.56 (b(z, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[271, 34130])).
% 5.34/5.56 tff(34132,plain,
% 5.34/5.56 ($false),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[3121, 30203, 450, 28500, 817, 286, 507, 595, 30192])).
% 5.34/5.56 tff(34133,plain,((~r(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | (z = elem!1) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.56 tff(34134,plain,
% 5.34/5.56 (~r(elem!1, s(s(z)))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[34133, 817, 34127, 33184, 34131])).
% 5.34/5.56 tff(34135,plain,
% 5.34/5.56 (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(s(z)))))),
% 5.34/5.56 inference(monotonicity,[status(thm)],[546])).
% 5.34/5.56 tff(34136,plain,
% 5.34/5.56 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 5.34/5.56 inference(symmetry,[status(thm)],[34135])).
% 5.34/5.56 tff(34137,plain,
% 5.34/5.56 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 5.34/5.56 inference(modus_ponens,[status(thm)],[24592, 34136])).
% 5.34/5.56 tff(34138,plain,
% 5.34/5.56 (r(elem!1, s(s(s(elem!1)))) <=> r(s(z), s(s(s(s(z)))))),
% 5.34/5.56 inference(monotonicity,[status(thm)],[518, 546])).
% 5.34/5.56 tff(34139,plain,
% 5.34/5.56 (r(s(z), s(s(s(s(z))))) <=> r(elem!1, s(s(s(elem!1))))),
% 5.34/5.56 inference(symmetry,[status(thm)],[34138])).
% 5.34/5.56 tff(34140,plain,
% 5.34/5.56 (r(elem!1, s(s(s(s(z))))) <=> r(s(z), s(s(s(s(z)))))),
% 5.34/5.56 inference(monotonicity,[status(thm)],[518])).
% 5.34/5.56 tff(34141,plain,
% 5.34/5.56 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(s(s(elem!1))))),
% 5.34/5.56 inference(transitivity,[status(thm)],[34140, 34139])).
% 5.34/5.56 tff(34142,plain,
% 5.34/5.56 (b(elem!1, s(s(z)))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[467, 460, 31605])).
% 5.34/5.56 tff(34143,plain,
% 5.34/5.56 (~b(elem!1, s(s(s(s(z)))))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[491, 34142, 167, 202, 817])).
% 5.34/5.56 tff(34144,plain,
% 5.34/5.56 (r(elem!1, s(s(s(s(z)))))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[483, 34143, 25873])).
% 5.34/5.56 tff(34145,plain,
% 5.34/5.56 (r(elem!1, s(s(s(elem!1))))),
% 5.34/5.56 inference(modus_ponens,[status(thm)],[34144, 34141])).
% 5.34/5.56 tff(34146,plain,
% 5.34/5.56 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[8969, 34145, 34137])).
% 5.34/5.56 tff(34147,plain,
% 5.34/5.56 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[3444, 34146, 3914])).
% 5.34/5.56 tff(34148,plain,
% 5.34/5.56 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 5.34/5.56 inference(modus_ponens,[status(thm)],[34147, 17826])).
% 5.34/5.56 tff(34149,plain,
% 5.34/5.56 (~(s(z) = s(s(z)))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[2610, 515, 31965])).
% 5.34/5.56 tff(34150,plain,
% 5.34/5.56 (~r(s(z), s(s(z)))),
% 5.34/5.56 inference(modus_ponens,[status(thm)],[460, 1583])).
% 5.34/5.56 tff(34151,plain,
% 5.34/5.56 (b(s(z), s(s(z)))),
% 5.34/5.56 inference(unit_resolution,[status(thm)],[1619, 41, 34150, 34149])).
% 5.34/5.56 tff(34152,plain,
% 5.34/5.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 5.34/5.56 inference(rewrite,[status(thm)],[])).
% 5.34/5.56 tff(34153,plain,
% 5.34/5.56 (((~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(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(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(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 5.34/5.56 inference(rewrite,[status(thm)],[])).
% 5.34/5.56 tff(34154,plain,
% 5.34/5.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 5.34/5.56 inference(monotonicity,[status(thm)],[34153])).
% 5.34/5.56 tff(34155,plain,
% 5.34/5.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 5.34/5.56 inference(transitivity,[status(thm)],[34154, 34152])).
% 5.34/5.56 tff(34156,plain,
% 5.34/5.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 5.34/5.56 inference(quant_inst,[status(thm)],[])).
% 5.34/5.56 tff(34157,plain,
% 5.34/5.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 5.34/5.57 inference(modus_ponens,[status(thm)],[34156, 34155])).
% 5.34/5.57 tff(34158,plain,
% 5.34/5.57 ($false),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[34157, 178, 34151, 1146, 19557, 4669, 34148])).
% 5.34/5.57 tff(34159,plain,(r(elem!1, s(s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~(s(elem!1) = s(s(z)))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.57 tff(34160,plain,
% 5.34/5.57 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[34159, 515, 33540, 34134, 34129, 167, 202, 817])).
% 5.34/5.57 tff(34161,plain,
% 5.34/5.57 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.57 inference(modus_ponens,[status(thm)],[34160, 33861])).
% 5.34/5.57 tff(34162,plain,
% 5.34/5.57 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[691, 34043, 34128])).
% 5.34/5.57 tff(34163,plain,
% 5.34/5.57 ($false),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[34162, 34161])).
% 5.34/5.57 tff(34164,plain,((~(s(elem!1) = s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.57 tff(34165,plain,
% 5.34/5.57 (~(s(elem!1) = s(s(z)))),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[34164, 204, 31476, 32293, 33858])).
% 5.34/5.57 tff(34166,plain,
% 5.34/5.57 (~(s(s(z)) = s(elem!1))),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[1058, 34165])).
% 5.34/5.57 tff(34167,plain,
% 5.34/5.57 (~(z = elem!1)),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[317, 33859])).
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% 5.34/5.57 inference(monotonicity,[status(thm)],[34180])).
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% 5.34/5.57 tff(34183,plain,
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% 5.34/5.57 tff(34186,plain,
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% 5.34/5.57 inference(monotonicity,[status(thm)],[34190])).
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% 5.34/5.57 inference(unit_resolution,[status(thm)],[666, 34192, 31641])).
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% 5.34/5.57 inference(unit_resolution,[status(thm)],[5558, 118, 24592, 908])).
% 5.34/5.57 tff(34195,plain,
% 5.34/5.57 ((s(s(s(s(s(s(s(z))))))) = s(elem!1)) | b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[806, 41, 34194])).
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% 5.34/5.57 inference(unit_resolution,[status(thm)],[34195, 34193])).
% 5.34/5.57 tff(34197,plain,
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% 5.34/5.57 inference(modus_ponens,[status(thm)],[34196, 34191])).
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% 5.34/5.57 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
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% 5.34/5.57 tff(34199,plain,
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% 5.34/5.57 inference(unit_resolution,[status(thm)],[691, 34198, 701])).
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% 5.34/5.57 tff(34202,plain,
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% 5.34/5.57 inference(unit_resolution,[status(thm)],[32082, 178, 34202, 817, 31623, 167])).
% 5.34/5.57 tff(34207,plain,
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% 5.34/5.57 inference(unit_resolution,[status(thm)],[3142, 34206, 34205])).
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% 5.34/5.57 inference(monotonicity,[status(thm)],[34207])).
% 5.34/5.57 tff(34209,plain,
% 5.34/5.57 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(s(z)))))),
% 5.34/5.57 inference(symmetry,[status(thm)],[34208])).
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% 5.34/5.57 inference(unit_resolution,[status(thm)],[338, 34207, 31965])).
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% 5.34/5.57 (~(s(elem!1) = elem!1)),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[672, 34210])).
% 5.34/5.57 tff(34212,plain,
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% 5.34/5.57 inference(unit_resolution,[status(thm)],[677, 34211, 724])).
% 5.34/5.57 tff(34213,plain,
% 5.34/5.57 (b(s(elem!1), s(s(s(s(z)))))),
% 5.34/5.57 inference(modus_ponens,[status(thm)],[34212, 34209])).
% 5.34/5.57 tff(34214,plain,
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% 5.34/5.57 inference(unit_resolution,[status(thm)],[5720, 34213])).
% 5.34/5.57 tff(34215,plain,(r(s(elem!1), elem!1) | b(s(elem!1), s(s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.57 tff(34216,plain,
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% 5.34/5.57 tff(34218,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,[]))).
% 5.34/5.57 tff(34219,plain,
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% 5.34/5.57 tff(34221,plain,
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% 5.34/5.57 tff(34223,plain,((elem!1 = s(s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (elem!1 = z) | (elem!1 = s(s(z))) | r(s(s(s(s(z)))), elem!1) | r(elem!1, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.57 tff(34224,plain,
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% 5.34/5.57 tff(34225,plain,
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% 5.34/5.57 inference(monotonicity,[status(thm)],[34224])).
% 5.34/5.57 tff(34226,plain,
% 5.34/5.57 (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(s(z))))))),
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% 5.34/5.57 tff(34227,plain,
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% 5.34/5.57 inference(symmetry,[status(thm)],[34225])).
% 5.34/5.57 tff(34228,plain,
% 5.34/5.57 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 5.34/5.57 inference(monotonicity,[status(thm)],[34227])).
% 5.34/5.57 tff(34229,plain,
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% 5.34/5.57 inference(monotonicity,[status(thm)],[34225])).
% 5.34/5.57 tff(34230,plain,
% 5.34/5.57 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 5.34/5.57 inference(monotonicity,[status(thm)],[34229])).
% 5.34/5.57 tff(34231,plain,
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% 5.34/5.57 inference(modus_ponens,[status(thm)],[34237, 34234])).
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% 5.34/5.57 (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
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% 5.34/5.57 inference(unit_resolution,[status(thm)],[2341, 34256, 28500])).
% 5.34/5.57 tff(34258,plain,
% 5.34/5.57 (b(s(s(z)), s(elem!1))),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[1067, 34257, 2311])).
% 5.34/5.57 tff(34259,plain,
% 5.34/5.57 (b(s(s(z)), s(s(s(s(s(z))))))),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[2330, 34258, 34224])).
% 5.34/5.57 tff(34260,plain,
% 5.34/5.57 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 5.34/5.57 inference(monotonicity,[status(thm)],[34225])).
% 5.34/5.57 tff(34261,plain,
% 5.34/5.57 (b(s(s(s(s(s(z))))), s(s(z)))),
% 5.34/5.57 inference(modus_ponens,[status(thm)],[34186, 34260])).
% 5.34/5.57 tff(34262,plain,
% 5.34/5.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 5.34/5.57 inference(rewrite,[status(thm)],[])).
% 5.34/5.57 tff(34263,plain,
% 5.34/5.57 (((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(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(z))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 5.34/5.57 inference(rewrite,[status(thm)],[])).
% 5.34/5.57 tff(34264,plain,
% 5.34/5.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(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(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 5.34/5.57 inference(monotonicity,[status(thm)],[34263])).
% 5.34/5.57 tff(34265,plain,
% 5.34/5.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(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(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 5.34/5.57 inference(transitivity,[status(thm)],[34264, 34262])).
% 5.34/5.57 tff(34266,plain,
% 5.34/5.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(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(z))))), s(s(s(s(s(s(s(z))))))))))),
% 5.34/5.57 inference(quant_inst,[status(thm)],[])).
% 5.34/5.57 tff(34267,plain,
% 5.34/5.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 5.34/5.57 inference(modus_ponens,[status(thm)],[34266, 34265])).
% 5.34/5.57 tff(34268,plain,
% 5.34/5.57 ($false),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[34267, 178, 34261, 34259, 33540, 34249, 34242])).
% 5.34/5.57 tff(34269,plain,(b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (s(elem!1) = s(s(s(s(z))))) | (s(elem!1) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.57 tff(34270,plain,
% 5.34/5.57 (s(elem!1) = s(s(s(s(z))))),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[34269, 34165, 33858, 204, 32293, 34175, 31476])).
% 5.34/5.57 tff(34271,plain,
% 5.34/5.57 ((s(elem!1) = elem!1) <=> (s(s(s(s(z)))) = elem!1)),
% 5.34/5.57 inference(monotonicity,[status(thm)],[34270])).
% 5.34/5.57 tff(34272,plain,
% 5.34/5.57 ((~(s(elem!1) = elem!1)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 5.34/5.57 inference(monotonicity,[status(thm)],[34271])).
% 5.34/5.57 tff(34273,plain,
% 5.34/5.57 (~(elem!1 = s(s(s(elem!1))))),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[2498, 34270, 34168])).
% 5.34/5.57 tff(34274,plain,
% 5.34/5.57 (~(s(s(s(elem!1))) = elem!1)),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[2489, 34273])).
% 5.34/5.57 tff(34275,plain,
% 5.34/5.57 (~(s(elem!1) = elem!1)),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[2150, 34274])).
% 5.34/5.57 tff(34276,plain,
% 5.34/5.57 (~(s(s(s(s(z)))) = elem!1)),
% 5.34/5.57 inference(modus_ponens,[status(thm)],[34275, 34272])).
% 5.34/5.57 tff(34277,plain,
% 5.34/5.57 (r(s(s(s(s(z)))), elem!1)),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[3142, 34276, 34178])).
% 5.34/5.57 tff(34278,plain,
% 5.34/5.57 (~b(elem!1, s(s(s(s(z)))))),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[491, 34177, 31476, 32293, 33858])).
% 5.34/5.57 tff(34279,plain,
% 5.34/5.57 ((s(elem!1) = elem!1) <=> (elem!1 = s(s(s(s(z)))))),
% 5.34/5.57 inference(transitivity,[status(thm)],[34271, 501])).
% 5.34/5.57 tff(34280,plain,
% 5.34/5.57 ((~(s(elem!1) = elem!1)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 5.34/5.57 inference(monotonicity,[status(thm)],[34279])).
% 5.34/5.57 tff(34281,plain,
% 5.34/5.57 (~(elem!1 = s(s(s(s(z)))))),
% 5.34/5.57 inference(modus_ponens,[status(thm)],[34275, 34280])).
% 5.34/5.57 tff(34282,plain,
% 5.34/5.57 (r(elem!1, s(s(s(s(z)))))),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[483, 34281, 34278])).
% 5.34/5.57 tff(34283,plain,
% 5.34/5.57 (b(s(elem!1), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 5.34/5.57 inference(monotonicity,[status(thm)],[34270])).
% 5.34/5.57 tff(34284,plain,
% 5.34/5.57 (b(s(s(s(s(z)))), elem!1) <=> b(s(elem!1), elem!1)),
% 5.34/5.57 inference(symmetry,[status(thm)],[34283])).
% 5.34/5.57 tff(34285,plain,
% 5.34/5.57 ((~b(s(s(s(s(z)))), elem!1)) <=> (~b(s(elem!1), elem!1))),
% 5.34/5.57 inference(monotonicity,[status(thm)],[34284])).
% 5.34/5.57 tff(34286,plain,
% 5.34/5.57 (~b(s(elem!1), elem!1)),
% 5.34/5.57 inference(modus_ponens,[status(thm)],[34178, 34285])).
% 5.34/5.57 tff(34287,plain,
% 5.34/5.57 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 5.34/5.57 inference(monotonicity,[status(thm)],[34270])).
% 5.34/5.57 tff(34288,plain,
% 5.34/5.57 (elem!1 = s(s(s(z)))),
% 5.34/5.57 inference(transitivity,[status(thm)],[517, 34287, 11])).
% 5.34/5.57 tff(34289,plain,
% 5.34/5.57 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.57 inference(monotonicity,[status(thm)],[34288])).
% 5.34/5.57 tff(34290,plain,
% 5.34/5.57 (b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.57 inference(symmetry,[status(thm)],[34289])).
% 5.34/5.57 tff(34291,plain,
% 5.34/5.57 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.57 inference(modus_ponens,[status(thm)],[34174, 34290])).
% 5.34/5.57 tff(34292,plain,
% 5.34/5.57 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[249, 34175])).
% 5.34/5.57 tff(34293,plain,
% 5.34/5.57 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[2840, 34165])).
% 5.34/5.57 tff(34294,plain,
% 5.34/5.57 ((~b(z, elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[26070, 178, 34177, 34172, 33211])).
% 5.34/5.57 tff(34295,plain,
% 5.34/5.57 (~b(z, elem!1)),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[34294, 34291])).
% 5.34/5.57 tff(34296,plain,
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% 5.34/5.57 inference(unit_resolution,[status(thm)],[585, 34295, 34167])).
% 5.34/5.57 tff(34297,plain,
% 5.34/5.57 (~r(elem!1, z)),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[32703, 34296, 33858, 34293, 34292, 34291, 34275, 34286, 34282, 34277, 34168, 34166, 31476])).
% 5.34/5.57 tff(34298,plain,
% 5.34/5.57 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[10835, 34175, 33858])).
% 5.34/5.57 tff(34299,plain,
% 5.34/5.57 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[703, 34298])).
% 5.34/5.57 tff(34300,plain,
% 5.34/5.57 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[25879, 34277])).
% 5.34/5.57 tff(34301,plain,
% 5.34/5.57 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[3444, 34300, 34299])).
% 5.34/5.57 tff(34302,plain,
% 5.34/5.57 (~b(elem!1, z)),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[33165, 34301, 204, 32293, 33858, 31476, 34172, 34170, 34298])).
% 5.34/5.57 tff(34303,plain,
% 5.34/5.57 ($false),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[498, 34302, 34297, 33859])).
% 5.34/5.57 tff(34304,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.57 tff(34305,plain,
% 5.34/5.57 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[34304, 28501])).
% 5.34/5.57 tff(34306,plain,
% 5.34/5.57 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[222, 34305])).
% 5.34/5.57 tff(34307,plain,
% 5.34/5.57 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[3102, 224, 28500])).
% 5.34/5.57 tff(34308,plain,
% 5.34/5.57 (b(s(s(s(s(s(s(s(z))))))), z)),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[133, 34307])).
% 5.34/5.57 tff(34309,plain,
% 5.34/5.57 ($false),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[13303, 178, 27212, 168, 251, 595, 146])).
% 5.34/5.57 tff(34310,plain,((~b(s(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(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.57 tff(34311,plain,
% 5.34/5.57 ($false),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[34310, 34308, 29578, 251, 168])).
% 5.34/5.57 tff(34312,plain,((~r(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))))))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.57 tff(34313,plain,
% 5.34/5.57 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[34312, 34306, 31575])).
% 5.34/5.57 tff(34314,plain,
% 5.34/5.57 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[249, 34313])).
% 5.34/5.57 tff(34315,plain,
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% 5.34/5.57 inference(unit_resolution,[status(thm)],[34310, 31505, 32319, 251, 168])).
% 5.34/5.57 tff(34316,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.57 tff(34317,plain,
% 5.34/5.57 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[34316, 34306, 31575])).
% 5.34/5.57 tff(34318,plain,
% 5.34/5.57 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[3578, 34317])).
% 5.34/5.57 tff(34319,plain,
% 5.34/5.57 (~b(s(s(s(s(z)))), s(s(z)))),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[31557, 34318, 31476, 34306, 34314])).
% 5.34/5.57 tff(34320,plain,
% 5.34/5.57 (b(z, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[30676, 3241, 28501, 86, 27213])).
% 5.34/5.57 tff(34321,plain,
% 5.34/5.57 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[34310, 34320, 34306, 31575])).
% 5.34/5.57 tff(34322,plain,
% 5.34/5.57 (r(s(s(s(s(s(s(s(z))))))), z)),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[133, 34321])).
% 5.34/5.57 tff(34323,plain,
% 5.34/5.57 (~b(elem!1, z)),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[32160, 1056, 193, 167, 3241, 595, 166])).
% 5.34/5.57 tff(34324,plain,
% 5.34/5.57 (s(elem!1) = s(s(s(s(z))))),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[12437, 28602, 29994, 193, 363])).
% 5.34/5.57 tff(34325,plain,
% 5.34/5.57 (~(z = elem!1)),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[25360, 34324])).
% 5.34/5.57 tff(34326,plain,
% 5.34/5.57 (~(elem!1 = z)),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[2808, 34325])).
% 5.34/5.57 tff(34327,plain,
% 5.34/5.57 (~b(s(elem!1), s(s(s(s(z)))))),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[31823, 28602, 2311, 167])).
% 5.34/5.57 tff(34328,plain,
% 5.34/5.57 (~(s(s(z)) = elem!1)),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[31831, 28602, 193, 595, 166, 1056, 34327, 32144])).
% 5.34/5.57 tff(34329,plain,
% 5.34/5.57 (r(s(s(z)), elem!1)),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[448, 34328, 3241])).
% 5.34/5.57 tff(34330,plain,
% 5.34/5.57 (~r(elem!1, z)),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[443, 34329, 28500])).
% 5.34/5.57 tff(34331,plain,
% 5.34/5.57 ($false),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[498, 34330, 34326, 34323])).
% 5.34/5.57 tff(34332,plain,((~r(s(elem!1), s(s(z)))) | b(s(s(z)), elem!1) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(s(z))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.57 tff(34333,plain,
% 5.34/5.57 (~r(s(elem!1), s(s(z)))),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[34332, 1056, 103, 595, 33213, 3241, 167])).
% 5.34/5.57 tff(34334,plain,
% 5.34/5.57 (b(s(elem!1), s(s(z)))),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[421, 34333, 1056])).
% 5.34/5.57 tff(34335,plain,
% 5.34/5.57 (~(s(elem!1) = s(s(s(s(z)))))),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[12552, 34334, 86])).
% 5.34/5.57 tff(34336,plain,
% 5.34/5.57 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[14677, 34334, 29994, 27217, 595, 33213, 2311])).
% 5.34/5.57 tff(34337,plain,
% 5.34/5.57 (~r(s(elem!1), z)),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[28541, 928, 24628, 108, 33213, 1056])).
% 5.34/5.57 tff(34338,plain,
% 5.34/5.57 (b(s(elem!1), z)),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[774, 34337])).
% 5.34/5.57 tff(34339,plain,
% 5.34/5.57 (~b(s(elem!1), s(s(s(s(z)))))),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[31823, 34338, 2311, 167])).
% 5.34/5.57 tff(34340,plain,
% 5.34/5.57 (r(s(elem!1), s(s(s(s(z)))))),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[1084, 34339, 1369])).
% 5.34/5.57 tff(34341,plain,
% 5.34/5.57 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[25119, 34340])).
% 5.34/5.57 tff(34342,plain,
% 5.34/5.57 (s(elem!1) = s(s(s(s(s(s(s(z)))))))),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[395, 34341, 643])).
% 5.34/5.57 tff(34343,plain,
% 5.34/5.57 (s(s(elem!1)) = s(elem!1)),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[31721, 34338, 193, 167, 595, 33213, 1056, 928])).
% 5.34/5.57 tff(34344,plain,
% 5.34/5.57 (s(elem!1) = s(s(elem!1))),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[986, 34343])).
% 5.34/5.57 tff(34345,plain,
% 5.34/5.57 (s(s(elem!1)) = elem!1),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[979, 34344])).
% 5.34/5.57 tff(34346,plain,
% 5.34/5.57 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[666, 34345, 323])).
% 5.34/5.57 tff(34347,plain,
% 5.34/5.57 ($false),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[4019, 34346, 34342])).
% 5.34/5.57 tff(34348,plain,((~(elem!1 = z)) | (s(s(s(s(z)))) = elem!1) | b(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.57 tff(34349,plain,
% 5.34/5.57 (~(elem!1 = z)),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[34348, 34336, 32144, 34335, 103, 167, 595, 1056, 108])).
% 5.34/5.57 tff(34350,plain,
% 5.34/5.57 (~b(elem!1, z)),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[32160, 1056, 103, 167, 3241, 595, 33213])).
% 5.34/5.57 tff(34351,plain,
% 5.34/5.57 (r(elem!1, z)),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[498, 34349, 34350])).
% 5.34/5.57 tff(34352,plain,
% 5.34/5.57 (~r(s(s(z)), elem!1)),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[443, 34351, 28500])).
% 5.34/5.57 tff(34353,plain,
% 5.34/5.57 (s(elem!1) = elem!1),
% 5.34/5.57 inference(unit_resolution,[status(thm)],[31876, 34352, 86, 33213, 1056, 167, 595, 34350, 34349])).
% 5.34/5.58 tff(34354,plain,
% 5.34/5.58 (s(s(elem!1)) = elem!1),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[672, 34353])).
% 5.34/5.58 tff(34355,plain,
% 5.34/5.58 (elem!1 = s(s(elem!1))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[1546, 34354])).
% 5.34/5.58 tff(34356,plain,
% 5.34/5.58 (s(s(s(elem!1))) = s(elem!1)),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[1539, 34355])).
% 5.34/5.58 tff(34357,plain,
% 5.34/5.58 (s(s(z)) = elem!1),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[448, 34352, 3241])).
% 5.34/5.58 tff(34358,plain,
% 5.34/5.58 (~b(elem!1, s(s(z)))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[3223, 34357])).
% 5.34/5.58 tff(34359,plain,
% 5.34/5.58 (s(s(s(elem!1))) = elem!1),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[2150, 34353])).
% 5.34/5.58 tff(34360,plain,
% 5.34/5.58 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[3907, 34359, 34333])).
% 5.34/5.58 tff(34361,plain,
% 5.34/5.58 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[1170, 34360])).
% 5.34/5.58 tff(34362,plain,
% 5.34/5.58 (~(elem!1 = s(s(s(s(elem!1)))))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[3901, 34361, 34358])).
% 5.34/5.58 tff(34363,plain,
% 5.34/5.58 ($false),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[1509, 34362, 34356])).
% 5.34/5.58 tff(34364,plain,((s(elem!1) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | b(s(s(z)), elem!1) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.58 tff(34365,plain,
% 5.34/5.58 (s(elem!1) = s(s(z))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[34364, 34320, 31476, 86, 3241, 34322])).
% 5.34/5.58 tff(34366,plain,
% 5.34/5.58 (~(z = elem!1)),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[28525, 34365])).
% 5.34/5.58 tff(34367,plain,
% 5.34/5.58 (~(elem!1 = z)),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[2808, 34366])).
% 5.34/5.58 tff(34368,plain,
% 5.34/5.58 ((s(elem!1) = elem!1) <=> (s(s(z)) = elem!1)),
% 5.34/5.58 inference(monotonicity,[status(thm)],[34365])).
% 5.34/5.58 tff(34369,plain,
% 5.34/5.58 ((~(s(elem!1) = elem!1)) <=> (~(s(s(z)) = elem!1))),
% 5.34/5.58 inference(monotonicity,[status(thm)],[34368])).
% 5.34/5.58 tff(34370,plain,
% 5.34/5.58 (~(elem!1 = s(s(s(s(elem!1)))))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[1422, 34365])).
% 5.34/5.58 tff(34371,plain,
% 5.34/5.58 (~(s(s(s(elem!1))) = s(elem!1))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[1509, 34370])).
% 5.34/5.58 tff(34372,plain,
% 5.34/5.58 (~(elem!1 = s(s(elem!1)))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[1539, 34371])).
% 5.34/5.58 tff(34373,plain,
% 5.34/5.58 (~(s(s(elem!1)) = elem!1)),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[1546, 34372])).
% 5.34/5.58 tff(34374,plain,
% 5.34/5.58 (~(s(elem!1) = elem!1)),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[672, 34373])).
% 5.34/5.58 tff(34375,plain,
% 5.34/5.58 (~(s(s(z)) = elem!1)),
% 5.34/5.58 inference(modus_ponens,[status(thm)],[34374, 34369])).
% 5.34/5.58 tff(34376,plain,
% 5.34/5.58 (r(s(s(z)), elem!1)),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[448, 34375, 3241])).
% 5.34/5.58 tff(34377,plain,
% 5.34/5.58 (~r(elem!1, z)),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[443, 34376, 28500])).
% 5.34/5.58 tff(34378,plain,
% 5.34/5.58 (~b(elem!1, z)),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[32148, 34376, 31575, 103, 32296])).
% 5.34/5.58 tff(34379,plain,
% 5.34/5.58 ($false),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[498, 34378, 34377, 34367])).
% 5.34/5.58 tff(34380,plain,(b(s(s(z)), elem!1) | b(s(s(s(s(z)))), s(s(z))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.58 tff(34381,plain,
% 5.34/5.58 (b(s(s(z)), elem!1)),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[34380, 34319, 28501])).
% 5.34/5.58 tff(34382,plain,
% 5.34/5.58 (r(s(s(s(s(z)))), s(s(z)))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[102, 34319])).
% 5.34/5.58 tff(34383,plain,
% 5.34/5.58 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[4690, 4236, 29994])).
% 5.34/5.58 tff(34384,plain,
% 5.34/5.58 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[249, 34383])).
% 5.34/5.58 tff(34385,plain,
% 5.34/5.58 (~r(elem!1, s(s(z)))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[29093, 506, 193, 469])).
% 5.34/5.58 tff(34386,plain,
% 5.34/5.58 (b(elem!1, s(s(z)))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[467, 34385, 31605])).
% 5.34/5.58 tff(34387,plain,
% 5.34/5.58 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[11859, 34386, 24628, 817, 166])).
% 5.34/5.58 tff(34388,plain,
% 5.34/5.58 (~b(elem!1, s(s(s(s(z)))))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[29314, 178, 506, 817, 31623, 167])).
% 5.34/5.58 tff(34389,plain,
% 5.34/5.58 (r(elem!1, s(s(s(s(z)))))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[483, 34388, 469])).
% 5.34/5.58 tff(34390,plain,
% 5.34/5.58 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[25883, 34389])).
% 5.34/5.58 tff(34391,plain,
% 5.34/5.58 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[691, 34390, 34387])).
% 5.34/5.58 tff(34392,plain,
% 5.34/5.58 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.58 inference(monotonicity,[status(thm)],[34391])).
% 5.34/5.58 tff(34393,plain,
% 5.34/5.58 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(z)))), elem!1)),
% 5.34/5.58 inference(symmetry,[status(thm)],[34392])).
% 5.34/5.58 tff(34394,plain,
% 5.34/5.58 (b(s(s(s(s(z)))), elem!1)),
% 5.34/5.58 inference(modus_ponens,[status(thm)],[251, 34393])).
% 5.34/5.58 tff(34395,plain,
% 5.34/5.58 ($false),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[32083, 34394])).
% 5.34/5.58 tff(34396,plain,((~b(elem!1, z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (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(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.58 tff(34397,plain,
% 5.34/5.58 (~b(elem!1, z)),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[34396, 34384, 469, 817, 167, 251, 193])).
% 5.34/5.58 tff(34398,plain,
% 5.34/5.58 (s(elem!1) = elem!1),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[31661, 34397, 193, 817, 3428, 34384, 1056, 4235, 167])).
% 5.34/5.58 tff(34399,plain,
% 5.34/5.58 (s(s(elem!1)) = elem!1),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[672, 34398])).
% 5.34/5.58 tff(34400,plain,
% 5.34/5.58 (elem!1 = s(s(elem!1))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[1546, 34399])).
% 5.34/5.58 tff(34401,plain,
% 5.34/5.58 (s(s(s(elem!1))) = s(elem!1)),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[1539, 34400])).
% 5.34/5.58 tff(34402,plain,
% 5.34/5.58 (~(s(elem!1) = s(s(s(s(z)))))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[13886, 34401])).
% 5.34/5.58 tff(34403,plain,
% 5.34/5.58 (~(s(s(s(s(z)))) = s(elem!1))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[2168, 34402])).
% 5.34/5.58 tff(34404,plain,
% 5.34/5.58 (~r(elem!1, s(s(z)))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[458, 10801, 28500])).
% 5.34/5.58 tff(34405,plain,
% 5.34/5.58 (b(elem!1, s(s(z)))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[467, 34404, 31605])).
% 5.34/5.58 tff(34406,plain,
% 5.34/5.58 (s(elem!1) = elem!1),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[31661, 5723, 193, 817, 3428, 34384, 1056, 4235, 167])).
% 5.34/5.58 tff(34407,plain,
% 5.34/5.58 (s(s(elem!1)) = elem!1),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[672, 34406])).
% 5.34/5.58 tff(34408,plain,
% 5.34/5.58 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[2510, 34407, 2508])).
% 5.34/5.58 tff(34409,plain,
% 5.34/5.58 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[691, 10810, 34408])).
% 5.34/5.58 tff(34410,plain,
% 5.34/5.58 ($false),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[11859, 34409, 34405, 24628, 817, 34384])).
% 5.34/5.58 tff(34411,plain,(b(elem!1, z) | (~b(s(s(z)), elem!1)) | (s(s(s(s(z)))) = s(elem!1)) | (elem!1 = z) | (~r(s(s(s(s(z)))), s(s(z)))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | (s(elem!1) = s(s(z))) | b(z, s(s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.58 tff(34412,plain,
% 5.34/5.58 (elem!1 = z),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[34411, 34403, 817, 34397, 193, 3428, 1056, 4235, 167])).
% 5.34/5.58 tff(34413,plain,
% 5.34/5.58 (s(s(s(elem!1))) = elem!1),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[2150, 34398])).
% 5.34/5.58 tff(34414,plain,
% 5.34/5.58 (elem!1 = s(s(s(elem!1)))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[2489, 34413])).
% 5.34/5.58 tff(34415,plain,
% 5.34/5.58 (elem!1 = s(elem!1)),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[19381, 34401, 34414])).
% 5.34/5.58 tff(34416,plain,
% 5.34/5.58 (~b(s(elem!1), z)),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[12026, 34415, 34397])).
% 5.34/5.58 tff(34417,plain,
% 5.34/5.58 (r(s(elem!1), z)),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[774, 34416])).
% 5.34/5.58 tff(34418,plain,
% 5.34/5.58 ($false),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[31599, 34417, 34412, 24628, 817, 34384, 167])).
% 5.34/5.58 tff(34419,plain,(b(z, s(s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | (s(elem!1) = s(s(z))) | (elem!1 = s(s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.58 tff(34420,plain,
% 5.34/5.58 (b(z, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[34419, 469, 167, 103, 27213, 1056, 817, 251])).
% 5.34/5.58 tff(34421,plain,
% 5.34/5.58 (~b(s(s(z)), z)),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[14395, 178, 27212, 167, 251, 34420])).
% 5.34/5.58 tff(34422,plain,
% 5.34/5.58 (~(elem!1 = z)),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[32554, 34421, 817])).
% 5.34/5.58 tff(34423,plain,
% 5.34/5.58 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[34310, 34420, 251, 31623])).
% 5.34/5.58 tff(34424,plain,
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% 5.34/5.58 inference(unit_resolution,[status(thm)],[133, 34423])).
% 5.34/5.58 tff(34425,plain,
% 5.34/5.58 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[3102, 34424, 28500])).
% 5.34/5.58 tff(34426,plain,
% 5.34/5.58 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[249, 34425])).
% 5.34/5.58 tff(34427,plain,
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% 5.34/5.58 inference(unit_resolution,[status(thm)],[34396, 34426, 469, 817, 167, 251, 103])).
% 5.34/5.58 tff(34428,plain,
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% 5.34/5.58 inference(unit_resolution,[status(thm)],[498, 34422, 34427])).
% 5.34/5.58 tff(34429,plain,
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% 5.34/5.58 inference(unit_resolution,[status(thm)],[443, 34428, 28500])).
% 5.34/5.58 tff(34430,plain,
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% 5.34/5.58 inference(unit_resolution,[status(thm)],[31876, 34429, 86, 1056, 34420, 167, 34426, 34427, 34422])).
% 5.34/5.58 tff(34431,plain,
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% 5.34/5.58 inference(unit_resolution,[status(thm)],[672, 34430])).
% 5.34/5.58 tff(34432,plain,
% 5.34/5.58 (~(s(elem!1) = s(s(s(s(z)))))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[31844, 34428, 103, 817, 469, 31623, 13192, 34426, 31605])).
% 5.34/5.58 tff(34433,plain,
% 5.34/5.58 (~(s(s(s(s(z)))) = s(elem!1))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[2168, 34432])).
% 5.34/5.58 tff(34434,plain,
% 5.34/5.58 (~r(elem!1, s(s(z)))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[458, 34428, 28500])).
% 5.34/5.58 tff(34435,plain,
% 5.34/5.58 (b(elem!1, s(s(z)))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[467, 34434, 31605])).
% 5.34/5.58 tff(34436,plain,
% 5.34/5.58 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[11831, 34435, 29994, 34424, 34428, 817])).
% 5.34/5.58 tff(34437,plain,
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% 5.34/5.58 inference(unit_resolution,[status(thm)],[2510, 34436, 34433, 34431])).
% 5.34/5.58 tff(34438,plain,((elem!1 = s(s(s(s(z))))) | (~b(s(s(z)), elem!1)) | b(s(s(s(s(z)))), s(s(z))) | (s(elem!1) = s(s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.58 tff(34439,plain,
% 5.34/5.58 (elem!1 = s(s(s(s(z))))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[34438, 1056, 86, 817, 167, 251])).
% 5.34/5.58 tff(34440,plain,
% 5.34/5.58 (s(elem!1) = s(s(s(s(s(z)))))),
% 5.34/5.58 inference(monotonicity,[status(thm)],[34439])).
% 5.34/5.58 tff(34441,plain,
% 5.34/5.58 (s(s(s(s(s(z))))) = s(elem!1)),
% 5.34/5.58 inference(symmetry,[status(thm)],[34440])).
% 5.34/5.58 tff(34442,plain,
% 5.34/5.58 ((s(s(z)) = s(s(s(s(s(z)))))) <=> (s(s(z)) = s(elem!1))),
% 5.34/5.58 inference(monotonicity,[status(thm)],[34441])).
% 5.34/5.58 tff(34443,plain,
% 5.34/5.58 ((s(s(z)) = s(s(s(s(s(z)))))) <=> (s(elem!1) = s(s(z)))),
% 5.34/5.58 inference(transitivity,[status(thm)],[34442, 1358])).
% 5.34/5.58 tff(34444,plain,
% 5.34/5.58 ((s(elem!1) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(z))))))),
% 5.34/5.58 inference(symmetry,[status(thm)],[34443])).
% 5.34/5.58 tff(34445,plain,
% 5.34/5.58 ((~(s(elem!1) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(s(z)))))))),
% 5.34/5.58 inference(monotonicity,[status(thm)],[34444])).
% 5.34/5.58 tff(34446,plain,
% 5.34/5.58 (~(s(s(z)) = s(s(s(s(s(z))))))),
% 5.34/5.58 inference(modus_ponens,[status(thm)],[1056, 34445])).
% 5.34/5.58 tff(34447,plain,
% 5.34/5.58 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 5.34/5.58 inference(monotonicity,[status(thm)],[34441])).
% 5.34/5.58 tff(34448,plain,
% 5.34/5.58 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 5.34/5.58 inference(symmetry,[status(thm)],[34447])).
% 5.34/5.58 tff(34449,plain,
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% 5.34/5.58 inference(unit_resolution,[status(thm)],[30853, 34439, 86])).
% 5.34/5.58 tff(34450,plain,
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% 5.34/5.58 inference(unit_resolution,[status(thm)],[467, 34449, 31605])).
% 5.34/5.58 tff(34451,plain,
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% 5.34/5.58 inference(unit_resolution,[status(thm)],[12557, 34439, 31623])).
% 5.34/5.58 tff(34452,plain,
% 5.34/5.58 (s(s(s(s(z)))) = elem!1),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[325, 34439])).
% 5.34/5.58 tff(34453,plain,
% 5.34/5.58 (~(s(s(elem!1)) = elem!1)),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[338, 34452, 31965])).
% 5.34/5.58 tff(34454,plain,
% 5.34/5.58 (~(s(elem!1) = elem!1)),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[672, 34453])).
% 5.34/5.58 tff(34455,plain,
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% 5.34/5.58 inference(unit_resolution,[status(thm)],[6991, 34451])).
% 5.34/5.58 tff(34456,plain,
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% 5.34/5.58 inference(unit_resolution,[status(thm)],[4862, 34450, 29994])).
% 5.34/5.58 tff(34457,plain,
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% 5.34/5.58 inference(unit_resolution,[status(thm)],[585, 34456, 34455])).
% 5.34/5.58 tff(34458,plain,
% 5.34/5.58 (~r(s(elem!1), s(s(z)))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[17418, 34457, 28500, 34454, 34451, 34450])).
% 5.34/5.58 tff(34459,plain,
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% 5.34/5.58 inference(unit_resolution,[status(thm)],[421, 34458, 1056])).
% 5.34/5.58 tff(34460,plain,
% 5.34/5.58 (~(s(elem!1) = s(s(s(s(z)))))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[12552, 34459, 86])).
% 5.34/5.58 tff(34461,plain,
% 5.34/5.58 (~(s(s(s(s(z)))) = s(elem!1))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[2168, 34460])).
% 5.34/5.58 tff(34462,plain,
% 5.34/5.58 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 5.34/5.58 inference(monotonicity,[status(thm)],[34441])).
% 5.34/5.58 tff(34463,plain,
% 5.34/5.58 ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) <=> (~b(s(s(s(s(z)))), s(elem!1)))),
% 5.34/5.58 inference(monotonicity,[status(thm)],[34462])).
% 5.34/5.58 tff(34464,plain,
% 5.34/5.58 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.58 inference(monotonicity,[status(thm)],[34440])).
% 5.34/5.58 tff(34465,plain,
% 5.34/5.58 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 5.34/5.58 inference(monotonicity,[status(thm)],[34441])).
% 5.34/5.58 tff(34466,plain,
% 5.34/5.58 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 5.34/5.58 inference(monotonicity,[status(thm)],[34440])).
% 5.34/5.58 tff(34467,plain,
% 5.34/5.58 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 5.34/5.58 inference(monotonicity,[status(thm)],[34466])).
% 5.34/5.58 tff(34468,plain,
% 5.34/5.58 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))),
% 5.34/5.58 inference(monotonicity,[status(thm)],[34467, 34440])).
% 5.34/5.58 tff(34469,plain,
% 5.34/5.58 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 5.34/5.58 inference(transitivity,[status(thm)],[34468, 4625])).
% 5.34/5.58 tff(34470,plain,
% 5.34/5.58 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 5.34/5.58 inference(transitivity,[status(thm)],[34469, 34465])).
% 5.34/5.58 tff(34471,plain,
% 5.34/5.58 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 5.34/5.58 inference(monotonicity,[status(thm)],[34470])).
% 5.34/5.58 tff(34472,plain,
% 5.34/5.58 (~(s(s(s(elem!1))) = s(elem!1))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[348, 34453])).
% 5.34/5.58 tff(34473,plain,
% 5.34/5.58 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 5.34/5.58 inference(modus_ponens,[status(thm)],[34472, 34471])).
% 5.34/5.58 tff(34474,plain,
% 5.34/5.58 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 5.34/5.58 inference(monotonicity,[status(thm)],[34441])).
% 5.34/5.58 tff(34475,plain,
% 5.34/5.58 ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) <=> (~b(s(elem!1), s(s(s(s(z))))))),
% 5.34/5.58 inference(monotonicity,[status(thm)],[34474])).
% 5.34/5.58 tff(34476,plain,
% 5.34/5.58 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 5.34/5.58 inference(monotonicity,[status(thm)],[34440])).
% 5.34/5.58 tff(34477,plain,
% 5.34/5.58 (b(s(s(s(s(s(z))))), s(s(z)))),
% 5.34/5.58 inference(modus_ponens,[status(thm)],[34459, 34476])).
% 5.34/5.58 tff(34478,plain,
% 5.34/5.58 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[34133, 286, 817, 507, 450])).
% 5.34/5.58 tff(34479,plain,
% 5.34/5.58 ($false),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[271, 29652, 34478])).
% 5.34/5.58 tff(34480,plain,(b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), elem!1)) | (z = elem!1) | (~r(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.58 tff(34481,plain,
% 5.34/5.58 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[34480, 34455, 817, 34450])).
% 5.34/5.58 tff(34482,plain,
% 5.34/5.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(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))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(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))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 5.34/5.58 inference(rewrite,[status(thm)],[])).
% 5.34/5.58 tff(34483,plain,
% 5.34/5.58 (((~b(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))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(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))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 5.34/5.58 inference(rewrite,[status(thm)],[])).
% 5.34/5.58 tff(34484,plain,
% 5.34/5.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(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))))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 5.34/5.58 inference(monotonicity,[status(thm)],[34483])).
% 5.34/5.58 tff(34485,plain,
% 5.34/5.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(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))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 5.34/5.58 inference(transitivity,[status(thm)],[34484, 34482])).
% 5.34/5.58 tff(34486,plain,
% 5.34/5.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 5.34/5.58 inference(quant_inst,[status(thm)],[])).
% 5.34/5.58 tff(34487,plain,
% 5.34/5.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 5.34/5.58 inference(modus_ponens,[status(thm)],[34486, 34485])).
% 5.34/5.58 tff(34488,plain,
% 5.34/5.58 ($false),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[34487, 178, 166, 167, 251, 1851, 1664])).
% 5.34/5.58 tff(34489,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(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(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.58 tff(34490,plain,
% 5.34/5.58 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[34489, 34481, 167, 251, 34477])).
% 5.34/5.58 tff(34491,plain,
% 5.34/5.58 (~b(s(elem!1), s(s(s(s(z)))))),
% 5.34/5.58 inference(modus_ponens,[status(thm)],[34490, 34475])).
% 5.34/5.58 tff(34492,plain,
% 5.34/5.58 (r(s(elem!1), s(s(s(s(z)))))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[1084, 34491, 34460])).
% 5.34/5.58 tff(34493,plain,
% 5.34/5.58 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[25119, 34492])).
% 5.34/5.58 tff(34494,plain,
% 5.34/5.58 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[395, 34493, 34473])).
% 5.34/5.58 tff(34495,plain,
% 5.34/5.58 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 5.34/5.58 inference(modus_ponens,[status(thm)],[34494, 34464])).
% 5.34/5.58 tff(34496,plain,
% 5.34/5.58 (b(z, s(elem!1)) <=> b(z, s(s(s(s(s(z))))))),
% 5.34/5.58 inference(monotonicity,[status(thm)],[34440])).
% 5.34/5.58 tff(34497,plain,
% 5.34/5.58 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))))),
% 5.34/5.58 inference(monotonicity,[status(thm)],[34469])).
% 5.34/5.58 tff(34498,plain,
% 5.34/5.58 (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 5.34/5.58 inference(modus_ponens,[status(thm)],[34472, 34497])).
% 5.34/5.58 tff(34499,plain,
% 5.34/5.58 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[14677, 34494, 29994, 27217, 34459, 34481, 2311])).
% 5.34/5.58 tff(34500,plain,
% 5.34/5.58 (r(z, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[271, 34499])).
% 5.34/5.58 tff(34501,plain,
% 5.34/5.58 (~r(z, s(elem!1))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[28897, 34500, 34439, 34481, 34498, 27217, 34477])).
% 5.34/5.58 tff(34502,plain,
% 5.34/5.58 (b(z, s(elem!1))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[2351, 34501])).
% 5.34/5.58 tff(34503,plain,
% 5.34/5.58 (b(z, s(s(s(s(s(z))))))),
% 5.34/5.58 inference(modus_ponens,[status(thm)],[34502, 34496])).
% 5.34/5.58 tff(34504,plain,
% 5.34/5.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))))),
% 5.34/5.58 inference(rewrite,[status(thm)],[])).
% 5.34/5.58 tff(34505,plain,
% 5.34/5.58 (((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(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(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))))),
% 5.34/5.58 inference(rewrite,[status(thm)],[])).
% 5.34/5.58 tff(34506,plain,
% 5.34/5.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(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(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z))))))))),
% 5.34/5.58 inference(monotonicity,[status(thm)],[34505])).
% 5.34/5.58 tff(34507,plain,
% 5.34/5.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(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(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z)))))))),
% 5.34/5.58 inference(transitivity,[status(thm)],[34506, 34504])).
% 5.34/5.58 tff(34508,plain,
% 5.34/5.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(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(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))),
% 5.34/5.58 inference(quant_inst,[status(thm)],[])).
% 5.34/5.58 tff(34509,plain,
% 5.34/5.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(z))))))),
% 5.34/5.58 inference(modus_ponens,[status(thm)],[34508, 34507])).
% 5.34/5.58 tff(34510,plain,
% 5.34/5.58 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[34509, 178, 27212, 251, 34503, 34495])).
% 5.34/5.58 tff(34511,plain,
% 5.34/5.58 (~b(s(s(s(s(z)))), s(elem!1))),
% 5.34/5.58 inference(modus_ponens,[status(thm)],[34510, 34463])).
% 5.34/5.58 tff(34512,plain,
% 5.34/5.58 (r(s(s(s(s(z)))), s(elem!1))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[2173, 34511, 34461])).
% 5.34/5.58 tff(34513,plain,
% 5.34/5.58 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 5.34/5.58 inference(modus_ponens,[status(thm)],[34512, 34448])).
% 5.34/5.58 tff(34514,plain,
% 5.34/5.58 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[14515, 34513, 103])).
% 5.34/5.58 tff(34515,plain,
% 5.34/5.58 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 5.34/5.58 inference(monotonicity,[status(thm)],[34467, 34440])).
% 5.34/5.58 tff(34516,plain,
% 5.34/5.58 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 5.34/5.58 inference(monotonicity,[status(thm)],[34439])).
% 5.34/5.58 tff(34517,plain,
% 5.34/5.58 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), elem!1)),
% 5.34/5.58 inference(symmetry,[status(thm)],[34516])).
% 5.34/5.58 tff(34518,plain,
% 5.34/5.58 (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)))))),
% 5.34/5.58 inference(monotonicity,[status(thm)],[34467])).
% 5.34/5.58 tff(34519,plain,
% 5.34/5.58 (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)))))),
% 5.34/5.58 inference(symmetry,[status(thm)],[34518])).
% 5.34/5.58 tff(34520,plain,
% 5.34/5.58 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), elem!1)),
% 5.34/5.58 inference(transitivity,[status(thm)],[34519, 34517])).
% 5.34/5.58 tff(34521,plain,
% 5.34/5.58 (r(s(s(s(elem!1))), elem!1)),
% 5.34/5.58 inference(modus_ponens,[status(thm)],[24592, 34520])).
% 5.34/5.58 tff(34522,plain,
% 5.34/5.58 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(s(z)))))),
% 5.34/5.58 inference(monotonicity,[status(thm)],[34439])).
% 5.34/5.58 tff(34523,plain,
% 5.34/5.58 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), elem!1)),
% 5.34/5.58 inference(symmetry,[status(thm)],[34522])).
% 5.34/5.58 tff(34524,plain,
% 5.34/5.58 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(elem!1), elem!1)),
% 5.34/5.58 inference(transitivity,[status(thm)],[34474, 34523])).
% 5.34/5.58 tff(34525,plain,
% 5.34/5.58 ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) <=> (~b(s(elem!1), elem!1))),
% 5.34/5.58 inference(monotonicity,[status(thm)],[34524])).
% 5.34/5.58 tff(34526,plain,
% 5.34/5.58 (~b(s(elem!1), elem!1)),
% 5.34/5.58 inference(modus_ponens,[status(thm)],[34490, 34525])).
% 5.34/5.58 tff(34527,plain,
% 5.34/5.58 (r(s(elem!1), elem!1)),
% 5.34/5.58 inference(unit_resolution,[status(thm)],[677, 34526, 34454])).
% 5.34/5.58 tff(34528,plain,
% 5.34/5.58 (~r(s(s(s(elem!1))), s(elem!1))),
% 5.34/5.59 inference(unit_resolution,[status(thm)],[1576, 34527, 34521])).
% 5.34/5.59 tff(34529,plain,
% 5.34/5.59 (b(s(s(s(elem!1))), s(elem!1))),
% 5.34/5.59 inference(unit_resolution,[status(thm)],[373, 34528, 34472])).
% 5.34/5.59 tff(34530,plain,
% 5.34/5.59 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 5.34/5.59 inference(modus_ponens,[status(thm)],[34529, 34515])).
% 5.34/5.59 tff(34531,plain,
% 5.34/5.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), 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(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), 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(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 5.34/5.59 inference(rewrite,[status(thm)],[])).
% 5.34/5.59 tff(34532,plain,
% 5.34/5.59 (((~b(s(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))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), 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))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), 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(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 5.34/5.59 inference(rewrite,[status(thm)],[])).
% 5.34/5.59 tff(34533,plain,
% 5.34/5.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), 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(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 5.34/5.59 inference(monotonicity,[status(thm)],[34532])).
% 5.34/5.59 tff(34534,plain,
% 5.34/5.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(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(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), 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(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 5.34/5.59 inference(transitivity,[status(thm)],[34533, 34531])).
% 5.34/5.59 tff(34535,plain,
% 5.34/5.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 5.34/5.59 inference(quant_inst,[status(thm)],[])).
% 5.34/5.59 tff(34536,plain,
% 5.34/5.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 5.34/5.59 inference(modus_ponens,[status(thm)],[34535, 34534])).
% 5.34/5.59 tff(34537,plain,
% 5.34/5.59 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 5.34/5.59 inference(unit_resolution,[status(thm)],[34536, 178, 34481, 167, 251, 27217, 34495, 34530])).
% 5.34/5.59 tff(34538,plain,
% 5.34/5.59 ((s(s(z)) = s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z))))))),
% 5.34/5.59 inference(unit_resolution,[status(thm)],[2781, 41, 34537])).
% 5.34/5.59 tff(34539,plain,
% 5.34/5.59 ($false),
% 5.34/5.59 inference(unit_resolution,[status(thm)],[34538, 34514, 34446])).
% 5.34/5.59 tff(34540,plain,((s(elem!1) = s(s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | b(s(s(s(s(z)))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.59 tff(34541,plain,
% 5.34/5.59 (s(elem!1) = s(s(z))),
% 5.34/5.59 inference(unit_resolution,[status(thm)],[34540, 34381, 31476, 34306, 34319])).
% 5.34/5.59 tff(34542,plain,
% 5.34/5.59 (~(elem!1 = s(s(s(s(z)))))),
% 5.34/5.59 inference(unit_resolution,[status(thm)],[11438, 34541])).
% 5.34/5.59 tff(34543,plain,
% 5.34/5.59 (~b(elem!1, z)),
% 5.34/5.59 inference(unit_resolution,[status(thm)],[34396, 34542, 34314, 34381, 31476, 34306, 34382])).
% 5.34/5.59 tff(34544,plain,
% 5.34/5.59 (r(s(elem!1), z)),
% 5.34/5.59 inference(unit_resolution,[status(thm)],[906, 34541, 28500])).
% 5.34/5.59 tff(34545,plain,
% 5.34/5.59 (~(elem!1 = z)),
% 5.34/5.59 inference(unit_resolution,[status(thm)],[31599, 34544, 34314, 34318, 34381, 31476])).
% 5.34/5.59 tff(34546,plain,
% 5.34/5.59 (r(elem!1, z)),
% 5.34/5.59 inference(unit_resolution,[status(thm)],[498, 34545, 34543])).
% 5.34/5.59 tff(34547,plain,
% 5.34/5.59 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 5.34/5.59 inference(unit_resolution,[status(thm)],[2832, 34541])).
% 5.34/5.59 tff(34548,plain,
% 5.34/5.59 (~(elem!1 = s(s(z)))),
% 5.34/5.59 inference(unit_resolution,[status(thm)],[31585, 34381])).
% 5.34/5.59 tff(34549,plain,
% 5.34/5.59 (~r(elem!1, s(s(z)))),
% 5.34/5.59 inference(unit_resolution,[status(thm)],[458, 34546, 28500])).
% 5.34/5.59 tff(34550,plain,
% 5.34/5.59 (b(elem!1, s(s(z)))),
% 5.34/5.59 inference(unit_resolution,[status(thm)],[467, 34549, 34548])).
% 5.34/5.59 tff(34551,plain,
% 5.34/5.59 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 5.34/5.59 inference(unit_resolution,[status(thm)],[11831, 34550, 29994, 34547, 34546, 34381])).
% 5.34/5.59 tff(34552,plain,
% 5.34/5.59 (~(elem!1 = s(s(s(s(elem!1)))))),
% 5.34/5.59 inference(unit_resolution,[status(thm)],[1422, 34541])).
% 5.34/5.59 tff(34553,plain,
% 5.34/5.59 (~(s(s(s(elem!1))) = s(elem!1))),
% 5.34/5.59 inference(unit_resolution,[status(thm)],[1509, 34552])).
% 5.34/5.59 tff(34554,plain,
% 5.34/5.59 (~(elem!1 = s(s(elem!1)))),
% 5.34/5.59 inference(unit_resolution,[status(thm)],[1539, 34553])).
% 5.34/5.59 tff(34555,plain,
% 5.34/5.59 (~(s(s(elem!1)) = elem!1)),
% 5.34/5.59 inference(unit_resolution,[status(thm)],[1546, 34554])).
% 5.34/5.59 tff(34556,plain,
% 5.34/5.59 (~(s(elem!1) = elem!1)),
% 5.34/5.59 inference(unit_resolution,[status(thm)],[672, 34555])).
% 5.34/5.59 tff(34557,plain,
% 5.34/5.59 (b(z, s(s(s(s(s(s(s(z))))))))),
% 5.34/5.59 inference(unit_resolution,[status(thm)],[31672, 34556, 34319, 34543, 28501, 34314])).
% 5.34/5.59 tff(34558,plain,
% 5.34/5.59 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 5.34/5.59 inference(unit_resolution,[status(thm)],[34310, 34557, 34306, 31575])).
% 5.34/5.59 tff(34559,plain,
% 5.34/5.59 ($false),
% 5.34/5.59 inference(unit_resolution,[status(thm)],[133, 34558, 34551])).
% 5.34/5.59 tff(34560,plain,(b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.34/5.59 tff(34561,plain,
% 5.34/5.59 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 5.34/5.59 inference(unit_resolution,[status(thm)],[21544, 34560, 28500, 27212])).
% 5.34/5.59 tff(34562,plain,
% 5.34/5.59 (b(s(s(s(s(z)))), s(s(z)))),
% 5.34/5.59 inference(unit_resolution,[status(thm)],[29527, 34560, 34561])).
% 5.34/5.59 tff(34563,plain,
% 5.34/5.59 ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z))))))),
% 5.34/5.59 inference(unit_resolution,[status(thm)],[21308, 28500])).
% 5.44/5.60 tff(34564,plain,
% 5.44/5.60 (~r(s(s(s(s(z)))), z)),
% 5.44/5.60 inference(unit_resolution,[status(thm)],[34563, 147])).
% 5.44/5.60 tff(34565,plain,
% 5.44/5.60 ((~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 5.44/5.60 inference(unit_resolution,[status(thm)],[29990, 34560, 34562])).
% 5.44/5.60 tff(34566,plain,
% 5.44/5.60 (~b(s(s(s(s(z)))), z)),
% 5.44/5.60 inference(unit_resolution,[status(thm)],[34565, 147])).
% 5.44/5.60 tff(34567,plain,
% 5.44/5.60 ($false),
% 5.44/5.60 inference(unit_resolution,[status(thm)],[191, 34566, 34564])).
% 5.44/5.60 tff(34568,plain,(~r(s(s(z)), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 5.44/5.60 tff(34569,plain,
% 5.44/5.60 (b(s(s(z)), s(s(s(s(z)))))),
% 5.44/5.60 inference(unit_resolution,[status(thm)],[164, 34568])).
% 5.44/5.60 tff(34570,plain,
% 5.44/5.60 (~r(s(s(s(s(z)))), z)),
% 5.44/5.60 inference(unit_resolution,[status(thm)],[31573, 34569])).
% 5.44/5.60 tff(34571,plain,
% 5.44/5.60 (b(s(s(s(s(z)))), z)),
% 5.44/5.60 inference(unit_resolution,[status(thm)],[191, 34570])).
% 5.44/5.60 tff(34572,plain,
% 5.44/5.60 ($false),
% 5.44/5.60 inference(unit_resolution,[status(thm)],[1736, 178, 34560, 27212, 34571, 34569, 34562])).
% 5.44/5.60 % SZS output end Proof
% 5.44/5.60 % E exiting
%------------------------------------------------------------------------------